The Elegant Universe by Brian Greene - drneutron tutoring bell7

Bear with me, as this is the first time I'm a participant rather than a lurker in a tutored read.

I'm setting this up a little earlier than planned because I forgot to bring a book to read on my break at work and about the only one I could find at the library that I was either in the midst of reading or planning on reading soon was this one. :)

I'll be starting The Elegant Universe over the long weekend, and have a rough plan to read about a chapter every two days - about 30 days of reading - with the caveat that I may slow down (or, I suppose, speed up) as needed. I don't have a background in science and never took high school physics, but I enjoy reading popular science books, and have read A Short History of Nearly Everything and A Brief History of Time in recent years. (And in case you're wondering, yes, I was lost for most of the second half of the latter, and I started reading only 5 pages at a time because that was all my brain could take.)

So... I should be back with questions from Chapter 1 on Monday, but here's a few I have to start with:

In his introduction, Greene writes, "And now...physicists believe they have finally found a framework for stitching these insights together into a seamless whole -- a single theory that, in principle, is capable of describing all physical phenomena" (ix-x).

Do most/all physicists accept superstring theory as THE unified theory?
If not, what are some other possibilities?

Are there phenomena which do not fit into the "seamless whole" of superstring theory?

What happens to the unified theories out there if particles can travel faster than the speed of light? (This last one has nothing to do with the book, but it's just something I wondered after reading an article about some experiments with particles that appeared to travel faster than the speed of light.)

UPDATE: Now that I'm home, I see my particular edition is c2003, 1999, with a new preface, so the pages for the quote are actually xi to xii in my edition. As far as I can tell, nothing else was changed.

Lurking?

(and side comment if I'm allowed--if you're talking about the OPERA experiments in which they reported that neutrinos beamed to them from CERN moved faster than the speed of light, they recently had to recall that claim. It was due to small errors in calculations and equipment. This recall was probably very bad for many careers.)

>2 The_Hibernator: Yay, someone's lurking! ;)

That may have been it - I don't really remember the details, so thanks for the comment; I hadn't heard about the recall, only the possibility (last I knew, more experiments had to be done). It must be frustrating to go through all that work and find out the calculations were wrong.

I just picked up my copy of The Elegant Universe yesterday, and am looking forward to working through it with you. I'm a physicist by education, engineer in the subject of radiation detection and measurement. I still try to keep up with the field, but haven't read Greene's books. So it'll be an interesting read!

You've picked a very interesting time to look at superstring theory. Recent results from high energy proton collisions at CERN have most likely uncovered a particle called the Higgs boson with a particular mass predicted by the Standard Model (*not* a string theory). String theories were invented to explain why the Standard Model works the way it does (for instance, why the known particles have the masses they do, how to unify gravity with the other forces, etc). But the data for the Higgs the scientists are seeing seems to call into question many varieties of string theory, and maybe all. So the answer to your first question is that up until now, string theory was the leading candidate for a unified theory, but nobody really knows where the experiments will lead!

There are other theories out there. String theory describes in mathematics particles as tiny strings - open strings in some versions, closed in others. Other theories use different descriptions. I'll see if I can come up with a good summary.

As particles traveling faster than the speed of light, there's nothing about string theory that prevents some particles from doing that. In fact, in some versions of the theory, there have to be partners to ordinary matter that are supraluminal. What's forbidden is for ordinary particles like protons or neutrinos to travel faster than light. The OPERA experiment detected neutrinos at supposedly faster than light speeds. Now, neutrinos have a very small mass, so this should be impossible. And when folks tried to understand these results, problems with the experiment were found, and the results were tainted. A classic case of the scientific method!

I'll be lurking, too, but my book has not yet arrived.

Lurking as well, but I'm not sure I'll understand very much at all as I don't have time to read the book.

Hey, any knowledge I get out of this thread will be more than I have now! :)

So, maybe I should back up a bit.

I remember from my earlier reading that relativity and quantum mechanics can't both be right - one successfully predicts large-scale and the other small-scale, but not both. (Do I have that right so far, or is that an oversimplification?) Is that the Standard Model? So how would the Standard Model and string theory be different in their predictions of the mass of particles?

up until now, string theory was the leading candidate for a unified theory, but nobody really knows where the experiments will lead!

That's one of the reasons I find physics books so fascinating and wish I understood more of it. So I'm looking forward to this tutored read and picking your brain more. :)

>5 streamsong: I hope you can get the book soon and read along! I'll be going pretty slowly, I think, if Chapter 1 is anything to go by.

>6 SqueakyChu: Madeleine, I feel exactly the same way, and I'm the one reading the book! :)

Unfortunately, I spent the evening watching A Prairie Home Companion at Wolftrap, so haven't had a chance to put together a decent description of the Standard Model and such. I'll post in the morning... :)

No worries, I didn't have as much time spent reading this weekend as I thought I would, so while I plan on posting my first batch of questions tomorrow, I probably won't have finished Chapter 1 yet.

CHAPTER 1 - Questions mainly pertaining to particles, and with a question repeated just to make it more easily found.

(Here is where I prove I've never taken physics before.)

1. What is the Standard Model, and how does it differ from string theory?

2. So on page 5 and 6, both special relativity and general relativity are described. Are they both in play, or mutually exclusive? How does general relativity give space a "gently curving geometrical shape" (6). (Side question: Is geometry used in physics? A friend of mine told me that it's usually calculus and algebra can be used to approximate things for students like me who never took calculus either...)

3. Also mentioned on page 6 is the fact that string theory claims that our universe has many more dimensions than the three spatial ones we are familiar with. How many dimensions could there be? What would they be, and how would/could they be measured?

4. Do particles have an intrinsic electromagnetic charge? (asked primarily because of the description of protons and neutrons as made up of quarks - I'm trying to figure out how protons, neutrons, and electrons could have the charges I'm familiar with while being made up of these particles)

5. "Everything you see in the terrestrial world and the heavens above appears to be made from combinations of electrons, up-quarks, and down-quarks" (7). So where are all these other particles found? What do they do? Has the mystery of why a top quark weighs so much more than the rest been solved since the writing of this book (the author asks it himself)?

6. What's the difference between these particles and particles of forces? (Is one set matter and the other energy?)

7. Would the Higgs boson fit into the "Family" categorization of Table 1.1, or does it make things appear more random? Would its existence indicate another "family" of particles?

8. How can a particle have 0 mass (referring to particles of force, Table 1.2)?

9. In his description of string theory, Greene talks about the vibration of strings, and says that, in theory, each type of particle would be the manifestation of a different oscillatory pattern. How many patterns could their be (I mean, I know in theory "as many patterns as there are particles," but I guess what I'm getting at is, how could it be measured, or what would it look like? Would it be like different notes on a musical instrument, where some are repeated but at different intervals? Is there a limit to how many variations there can be?)

10. So far he's done a great job of not making it math-heavy, but Greene definitely acknowledges the difficulty of the math involved: "the mathematics of string theory is so complicated that, to date, no one knows the exact equations of the theory. Instead, physicists know only approximations to these equations and even the approximate equations are so complicated that they as yet have been only partially solved" (19). So this being the case, how are the approximate equations developed? And how has the approximate math affected the development of the theory? (What kind of math is involved? Calculus?)

Aaaaaand...with that, I wrap up chapter 1!

*double post deleted*

1. What is the Standard Model, and how does it differ from string theory?

Let me give you a short answer here, and if you need more, I'll develop a longer answer. First, physics is primarily interested in matter and how it moves and how bits of matter interact. For instance, an early problem was to understand how a rock thrown into the air travels - can we predict its path if we know its mass and how hard it's thrown? Another example is the path of billiard balls as they bounce around on a table. We'd like to be able to predict where the balls will go. To do this, we develop equations of motion, equations involving calculus that when solved give us the position of the object at any time covered by the problem.

The same thing is true for subatomic particles. From experiments, we know what types of particles exist and the possible forces between them. These are listed in Greene's tables. We'd also like to be able to predict their motion and interaction once we set up an experiment, just like for billiard balls. Again, we're looking for equations of motion. Except now that we're dealing with the subatomic world, quantum mechanics applies, and the equations are a lot harder to solve. The Standard Model is the name given for the set of particles and forces, plus the equations of motion where the math describes these particles as "waves in a field", quantum field theory. These equations are successful at predicting the results of all known particle physics experiments so far.

But as Greene mentions, there are some things about the Standard Model equations we don't like. First, we can only approximate a solution by applying some mathematical tricks. The approximation is very good, but it bothers physicists that the theory is so complicated and that approximate solutions are needed. Also, the inputs to the theory - the types and masses of particles, their characteristics like electric charge - are put into the theory by hand. There's no explanation for why the particles are what they are, and the general feeling is that a complete theory should do a better job of explaining why the universe is the way it is. And worst of all, there seems to be no way to integrate gravity into the Standard Model equations in a way that makes mathematical sense. All these things lead us to believe that a broader, more general theory may exist.

String theory is one possible, more general theory that attempts to explain things. It's been the leading candidate for many years. In this case, we picture particles as tiny strings that can vibrate. Different particles are different modes of vibrations - similar to harmonics on a piano or guitar string. (I believe that Greene will go into this a bit more in the upcoming chapters.) There are different types of string theory (open strings vs string loops, etc.) and a lot of the work done over the years has been to sort through all these types of string theories to find which ones may be candidates for the theory everyone's been looking for. The way we do this is to use a particular version of the string theory equations to make predictions and then compare to experiment to see if the predictions come true. One of the difficulties of string theory is that it's a very general theory, so it's notoriously hard to make predictions, and this has fueled research on both theory and experiment for quite some time. Because of this, some in the field are working on alternatives to string theory as our more general theory - something called "loop quantum gravity", for instance. None of these alternatives to string theory have been developed far enough along to even begin to predict experimental results, so string theory is important as the leading candidate for the unified theory we want.

Um, ok, so my definition of a short answer needs work... :)

2. So on page 5 and 6, both special relativity and general relativity are described. Are they both in play, or mutually exclusive? How does general relativity give space a "gently curving geometrical shape" (6). (Side question: Is geometry used in physics? A friend of mine told me that it's usually calculus and algebra can be used to approximate things for students like me who never took calculus either...)

Back in Newton's day, Isaac developed an equation of motion for objects. It's still studied today in basic physics class to describe everyday things moving at relatively slow speeds. As work progressed, folks realized that as things move faster or become really massive, the Newtonian equations don't do such a good job anymore. (Astronomy is great for testing these conditions!) Einstein came up with relativity theory as a more general theory to make up for these deficiencies. General relativity (GR) is the overarching theory that includes gravity. Special relativity is a special case for when gravity can be ignored, so it's a simplification of GR. Newtonian theory is a special case of special relativity where objects are moving slowly compared to the speed of light.

One of the key aspects of GR is that gravity is explained not as a force between objects, but as a bending of space around objects. Picture a a stretched rubber sheet. Now throw some balls on that sheet. These will form pockets in the sheet - it's no longer straight. If I roll a small ball in the area around one of these bigger balls, its path will bend toward the bigger ball. In the old view, this was described as a gravitational force. In the GR view, there is no specific force, just a warping of the area around stuff. In fact, that's the best non-technical summary of GR: mass bends space, and bent space affects the path of moving mass. Because of this, GR (and really nearly all of physics) is fundamentally about geometry, specifically a blend of geometry and calculus called "differential geometry".

3. Also mentioned on page 6 is the fact that string theory claims that our universe has many more dimensions than the three spatial ones we are familiar with. How many dimensions could there be? What would they be, and how would/could they be measured?

So as I said, string theory involves trying to solve specific equations of motion to make predictions about particles. General relativity uses 3 spatial dimension plus time, for a 4-dimensional space-time, and experiments indicate that this is right so far. Unfortunately, string theory equations can't be solved in 4-D spacetime. Instead, extra dimensions are needed to cancel out parts of the equation that become infinite so that they can be solved. In one particular form of the theory, 10 dimensions are needed; in other forms, 26 dimensions are needed. As you might imagine, this has caused some consternation. The string theorists try to get around this problem by reducing those extra dimensions to something that isn't observed, to match experiments. One way they do this is by considering those extra dimensions to be really small, so small we can't see them. There's no good answer to this problem yet. Greene's in the camp that believes these dimensions exist, and his discussions later will describe some of the effects we would expect to see if they are.

4. Do particles have an intrinsic electromagnetic charge? (asked primarily because of the description of protons and neutrons as made up of quarks - I'm trying to figure out how protons, neutrons, and electrons could have the charges I'm familiar with while being made up of these particles)

Particles do have intrinsic electric charge. We call electrons negatively charged. Protons have the opposite, or positive, charge. Neutrons are neutral; they have no charge and are not affected by electric fields for the most part. Electrons are "fundamental", meaning we haven't been able to break them up into smaller pieces and don't believe we can. Protons and neutrons are not. In fact, the point of big accelerators like the one at CERN in Switzerland is to smash protons together to break them up. By doing this we've figured out that protons and neutrons are made of quarks - which we believe are fundamental. An "up" quark has an electric charge of +2/3 that of the electron; a "down" quark has charge -1/3 that of an electron. (Note: there's not a significant meaning to the names up and down, mostly just physicists being puckish). If I combine two ups and a down, I get a charge of 2/3 + 2/3 - 1/3 = 1, the same as the electron, only positive instead of negative. This is a proton! If I combine one up and two downs, I get 2/3 - 1/3 - 1/3 = 0, a neutral particle that's the neutron.

5. "Everything you see in the terrestrial world and the heavens above appears to be made from combinations of electrons, up-quarks, and down-quarks" (7). So where are all these other particles found? What do they do? Has the mystery of why a top quark weighs so much more than the rest been solved since the writing of this book (the author asks it himself)?

What he means here is that atoms are made of electrons flying around protons and neutrons. Since protons and neutrons are made of up and down quarks bound together, he says that everything seems to be made of combinations of these three things. This is mostly true. Atoms are stable - they don't spontaneously break down into other things - and are made of electrons, ups and downs.

But you can find these other particles in nature. Muons, for example, are similar electrons, except heavier. When an energetic proton from space hits our atmosphere, it loses energy by creating a shower of particles, some of which are muons. While muons are unstable, and transform into electrons rather quickly, they do make it to the ground in one of these showers, and can detected. In fact, this happens so often that we are constantly surrounded by a muon sea when we're walking around outside. Fortunately, these have little effect on us! We can also make these particles in laboratories for study - this happens all the time.

We still haven't solved the question of the top quark mass - it's one of the motivators for looking for a more general theory than the Standard Model.

6. What's the difference between these particles and particles of forces? (Is one set matter and the other energy?)

Particles of force only exist as a means of exchanging energy between matter. For instance, light is made up of many photons. These are emitted by your computer screen and travel to your eye, where they are absorbed. So energy has been transferred from the screen to your eye, which is detected, allowing you to see. Unfortunately, some force particles have mass, so aren't pure energy in the way photons are, but are still only around to transfer energy from one matter particle to another. This is again one of the things not explained by the Standard Model, motivating a more general theory.

7. Would the Higgs boson fit into the "Family" categorization of Table 1.1, or does it make things appear more random? Would its existence indicate another "family" of particles?

The Higgs boson doesn't fit into the families, and there doesn't seem to be a Higgs family. When you write down the equations of motion in the Standard Model describing real particles with mass, this extra term is needed to make the math work right. That term looks like it describes a particle separate from the rest. There are two possible ways to interpret this: (i) it's not a real particle and represents a problem with the theory, or (ii) it's a real particle that was predicted out of the blue by the theory. One of the things string theory is supposed to help with is understanding this extra term. It turns out that we have almost certainly found the signature of the Higgs boson in experiments at CERN at a particular mass. If it's true, this is strong support for the Standard Model as the correct theory and can be used to eliminate some versions of string theory as incorrect, as they either predicted no Higgs or predicted the wrong mass.

8. How can a particle have 0 mass (referring to particles of force, Table 1.2)?

Some particles do have zero mass. That means they're pure energy. Relativity tells us, though, that mass and energy are in some sense we don't fully understand, the same thing. All particles that have zero mass always move at the speed of light. Particles with mass always move at less than the speed of light. Photons are bundles of light, and are the most prevalent example.

Certain theories have solutions to equations of motion that have mass and yet always move faster than the speed of light. These are called tachyons, and if they don't exist, would indicate that these equations of motion are wrong and don't describe our universe.

9. In his description of string theory, Greene talks about the vibration of strings, and says that, in theory, each type of particle would be the manifestation of a different oscillatory pattern. How many patterns could their be (I mean, I know in theory "as many patterns as there are particles," but I guess what I'm getting at is, how could it be measured, or what would it look like? Would it be like different notes on a musical instrument, where some are repeated but at different intervals? Is there a limit to how many variations there can be?)

Theoretically, there could be an infinite number of oscillatory patterns. Picture a stretched rubber band. if you pull it to the side and let is go, it vibrates. SInce it's held in place at each end, the vibration happens so that a single wave fits between the ends. It's also possible that the vibration could happen so that *two* waves fit between the end. Or *three* waves. Or any integer number of waves. These waves are indeed called harmonics and are like different notes.

10. So far he's done a great job of not making it math-heavy, but Greene definitely acknowledges the difficulty of the math involved: "the mathematics of string theory is so complicated that, to date, no one knows the exact equations of the theory. Instead, physicists know only approximations to these equations and even the approximate equations are so complicated that they as yet have been only partially solved" (19). So this being the case, how are the approximate equations developed? And how has the approximate math affected the development of the theory? (What kind of math is involved? Calculus?)

The way they do this is to write down a differential equation in some geometry they pick. This is an equation involving heavy duty multi-dimensional calculus. Then because they can't solve it, they make some simplifying assumptions. Usually by assuming that some term in the equation is small so that it doesn't affect the results and can be discarded. This is called perturbation theory (theory here in the sense of a mathematical technique rather than a theory that describes the universe). This has indeed affected the development of the theory, mainly by offering many different versions of string theory that need to be sorted out. SInce they are all approximations, none are absolutely correct solutions. Much of the work in string theory is to understand how the approximations affect the answers we get, and how these should be interpreted physically. Note, approximations aren't bad, per se. Newton's gravitational law is an approximation that works quite well in everyday life.

Aaaaaand...with that, I wrap up chapter 1!
Excellent! Hope this helps clear some things up.

Thanks, that was both very informative & helpful and rather awe-inspiring about how much is still unknown (though, as you say, approximations can work well in everyday life). :)

I'll be diving into chapter 2 today, but looking at my schedule, I'd say the soonest I'd post questions would be tomorrow evening.

Sounds good. I'll read it tonight as well.

I'm lurking here, too. (And providing comic relief)

I'm completely in awe of Jim right now. I feel like there are going to be some fabulous conversations going on 10 days from now.

*snerk*

LOL @ Nora - I like your comic relief. :)

CHAPTER 2 - Special Relativity

OK, so I took some notes, but I actually feel like I understood most of that pretty well. The constancy of the speed of light leads to some interesting effects in his examples, though it seems that the effect is often so small we can't detect it. Is there any instance in everyday life that we can detect it?

Here's something that was a new concept for me: "Einstein proclaimed that all objects in the universe are always traveling through spacetime at once fixed speed - that of light....We are presently talking about an object's combined speed through all four dimensions - three space and one time - and it is the object's speed in this generalized sense that is equal to that of light" (50, emphasis in original text).

So - I'm sitting down typing, moving through space along with the earth, and through time - at light speed, combined? I'm rather floored by that thought and don't know how to frame a question around it, so I'll just ask... could you expand on that? :)

Delurking at the speed of light, almost.
I've ordered the book and will copy the conversation to keep on hand when I get the chance to read it. Thanks Jim and Mary

I'm waiting to get on an airplane in Orlando, so I'll try to get this in quick...

First, I can't think of any everyday examples where relativistic effects are seen, but there *are* so me more rare occasions. I'm building a spacecraft that will travel within the Sun's atmosphere. While we're close to the Sun, we'll notice time dilation in our onboard precision clock but not enough to need to correct.

Second, we normally think of velocity as distance divided by time (for instance, miles per hour). In relativity, "distance" includes the time dimension, so we treat time like space. This distance is called a "four-vector" since it's now four dimensional. In relativity, we also use a time-like parameter called "proper time" to calculate velocities by dividing the four-dimensional distance by the proper time. When you do this, you see that this "four-velocity" equals the speed of light. This recognizes that even when we're sitting still in space, we're moving through time.

Frankly, it is a freaky thought. To expand a little: you know how the shortest distance between two points is a straight line between the points? In essence, what this "velocity" means is that except for when acted upon by a force, objects travel through space-time along paths that are the shortest paths between two points, or geodesics. The essence of general relativity is to calculate what these geodesics are when matter is present to bend space-time.

>23 Carmenere: *waving* to Lynda - hope you enjoy it when you get to it and that all my questions help answer yours! :)

>24 drneutron: While we're close to the Sun, we'll notice time dilation in our onboard precision clock but not enough to need to correct. How cool!

Frankly, it is a freaky thought. Sometimes just knowing that scientists/engineers think so too is helpful. ;) Actually, the explanations - yours and Greene's - make sense, and it helps me understand why spacetime is, well, spacetime instead of separated, which hadn't quite clicked before. It's a little mind-boggling though.

Alright, so I'll probably start Chapter 3 tonight and work on it a bit tomorrow. I'll try to get my questions in tomorrow night, but it'll probably be late as before if not Saturday. It kind of depends on how much much I'll want to read about the general theory of relativity after fighting with my computer all day. Things at work have been kind of crazy - we're switching over our integrated library system (catalog, check out, cataloging, the whole works), and we're still learning the system and dealing with glitches. (The good news is, it gets better every day as we learn it...)

Just an update to say I am indeed behind. I'm reading Chapter 3 right now, and will try to post questions tomorrow night.

But...because I'm behind, I'll take a page from Madeline's book and open it the floor for any lurkers with questions - let's say tonight and tomorrow before 7PM EDT. Anyone?

Ha! I've already fallen so far behind you that I've given up...I'll have to read at my own pace....so no questions! :( But I've enjoyed the discussion so far!

I only have a year of college physics, and no quantum background at all. As far as I'm concerned, physics stopped making sense after Newton! ;)

>27 The_Hibernator: As far as I'm concerned, physics stopped making sense after Newton! ;) :) Don't give up - I'd only not want questions to be about parts of the book I haven't read yet, because then I'd get really confused! Besides, I'm working really slowly through Chapter 3.

Chapter 3 - General Relativity

Part 1 - I've got got 20+ pages left, but I have a few questions

I don't quite get the relationship between accelerated motion and gravity. They are virtually indistinguishable? So if the earth went off its orbit, what would we feel? The effects of a changed motion?

I did get the part on the warping of space and time, actually. The Tornado example mostly made sense to me.

One of the footnotes mentioned that there were different interpretations (or something like that) of the example. What are the others?

I stopped at page 67, partly because it's getting late to be reading about this and comprehending and partly because I got to a stopping point where I had to ponder Einstein's conclusion: "Gravity, according to Einstein, is the warping of space and time" (67).

Granted, Greene may go into this more in the next part of the chapter, but I'm still trying to get my head wrapped around that one. Does that mean that the rotation of the planets around the sun is caused by a warping of space and time? What would "unwarped" space and time look like? (or is that even possible?)

I hope you don't mind my slowing down the pace a bit. Sometimes when I really get into a groove and feel like I'm understanding it, I can really move, but other times if I'm tired or there's too much going on, it's tough to read and feel like I'm truly comprehending it.

I don't mind you taking whatever pace you need! This has been fun. :)

I've been out all day and haven't had a chance to read Chapter 3 yet. Will post responses to your latest questions in the morning.

don't quite get the relationship between accelerated motion and gravity. They are virtually indistinguishable? So if the earth went off its orbit, what would we feel? The effects of a changed motion?

Yes, they're indistinguishable. If you were in a sealed capsule with thrusters pushing against your feet, you wouldn't be able to tell whether what you feel is gravity or rockets (aside from vibration from the rockets, etc). Greene makes the point that we can use a spinning capsule to simulate gravity (you may have seen this in sci-fi movies; it really works). The only way the Earth can go off orbit is if it's pushed by a force, and so accelerated. If this happened, we'd feel it in proportion to the size of the force, and we'd only know it's an external force rather than gravity since it's different from what we felt the day before.

I did get the part on the warping of space and time, actually. The Tornado example mostly made sense to me.

I liked this example too. It was new to me, but worked well.

Granted, Greene may go into this more in the next part of the chapter, but I'm still trying to get my head wrapped around that one. Does that mean that the rotation of the planets around the sun is caused by a warping of space and time? What would "unwarped" space and time look like? (or is that even possible?)

That's exactly what we mean. A little later in the chapter, he goes into the rubber sheet example I mentioned above. It'll show what this looks like and talk about how the planets move in the context of spacetime warping.

Just discovered this thread. Lurking at the periphery...

>32 qebo: *waving* Welcome!

REMAINDER OF CHAPTER 3 - General Relativity

So, it took me a bit, but I think I get the gravity/acceleration . It made more sense by the end, anyway. If I understand it correctly, then, "unwarped" space is flat, and it's the presence of mass that warps/curves it.
Is this the "gentle curve" of space that he mentions in chapter 1?

If gravity is a warping of spacetime, then what is a (theorized) graviton, and what does it do?

He mentions the "age of the presently observed universe, about 15 billion years" (82). I'm mostly asking because it seems to me this figure has changed in my lifetime - how do we measure/figure the age of the known universe?

On to Chapter 4!

So, it took me a bit, but I think I get the gravity/acceleration . It made more sense by the end, anyway. If I understand it correctly, then, "unwarped" space is flat, and it's the presence of mass that warps/curves it.
Is this the "gentle curve" of space that he mentions in chapter 1?

You've got it exactly right.

If gravity is a warping of spacetime, then what is a (theorized) graviton, and what does it do?

Ok, so remember earlier when I talked about the Standard Model? One of the things that bothers physicists about the SM is that gravity is different in the equations of motion from all the other forces. The others act at a quantum level through the exchange of particles - photons for the electromagnetic force, etc - while gravity shows up in a mathematically different way. We think that this means we don't fully understand either quantum mechanics or general relativity, that there's a more general theory out there that incorporates both. The quantum version of general relativity includes a force particle similar to the photon that we've named the graviton. So far, this is only a theory - no evidence has been seen for this particle. If it works out, this quantum theory for gravity would work out a lot like electromagnetic theory. At the macroscopic level, we have electric and magnetic fields that we can describe on the quantum level as big groups of photons.

Just as a kicker, the idea that there should be a quantum theory of gravity may not be right! :)

He mentions the "age of the presently observed universe, about 15 billion years" (82). I'm mostly asking because it seems to me this figure has changed in my lifetime - how do we measure/figure the age of the known universe?

You're right, the number has changed over the years as the theories of the early universe have changed. These days, the simple Big Bang theory is known not to work so well for very early times. So the cosmologists have added "inflation" to the Big Band, and have proposed "dark matter" and "dark energy" to make the theories work. The estimated age of the universe has changed as these ideas have been proposed and people have made more astrophysical observations on the edges of the Universe we can see. There are experiments in the works to try to detect dark matter and dark energy to compare to these theories. Oh, and it's not clear what these things are and how they would fit into the particle physics scheme of things.

On to Chapter 4!

Excellent!

One of the things that bothers physicists about the SM is that gravity is different in the equations of motion from all the other forces. The others act at a quantum level through the exchange of particles - photons for the electromagnetic force, etc - while gravity shows up in a mathematically different way.

OK, so the warping of spacetime is part of general relativity and a particle/graviton would be part of quantum mechanics - so this would be one of the instances where the theories don't mesh, right?

The estimated age of the universe has changed as these ideas have been proposed and people have made more astrophysical observations on the edges of the Universe we can see. There are experiments in the works to try to detect dark matter and dark energy to compare to these theories.

So we could be off with our estimate and find it changing again as more experiments make things more clear?

Yep and yep.

>37 drneutron: Cool. It's very nice, by the way, to be able to confirm with someone that some of the connections I'm making are actually right, and I'm starting to understand some of this stuff. :)

Just an update to say I haven't forgotten. I'm planning on starting Chapter 4 tonight and hope to have some questions up on Friday, whether or not I manage to finish the chapter.

joining this discussion too-- will try to catch up with bell7 this weekend on my reading (and reading drneutron's posts (and the other participants) on this topic) so that I can follow along with you all.

>40 ThePrib: Great! I'm reading through very slowly, and the only thing I'll ask since we've set this up as "tutoring" me through the book is that you don't ask anything from parts of the book I haven't read yet - wouldn't want spoilers. ;) Hope you don't mind - I'm happy to have folks follow along!

no problem; i'm on page 35 right now taking notes... no rush-- I'm not going to pass you up on the reading or understanding-- I'm here to share and learn too!

I'm on the sidelines, observing, but not measuring time dilation or Lorentzian contractions. Yet. :)

>42 ThePrib: Sounds good. :)

Alright, here's Chapter 4, a combination of summary and questions, especially as later parts of the chapter started answering some of my earlier questions:

I liked that he started out with quotes from scientists admitting that this was difficult to understand. It helped me feel like I'm not unintelligent if I don't get it right away. At the same time, it's a little scary.

On "lumps" of energy: "Planck boldly guessed that the energy carried by an electromagnetic wave in the oven...comes in lumps. The energy can be one times some fundamental 'energy denomination,' or two times it, or three time it, and so forth -- but that's it...no fractions are allowed" (92).

QUESTION 1: I get it in theory, but where are the "lumps"? Is he talking about a physical characteristic, or saying that the measure of energy in a wavelength is a "lump sum"?

QUESTION 2: How to the higher-frequency waves not contribute to the energy/heat in an oven?

h-bar was defined as "the proportionality factor between the frequency of a wave and the minimal lump of energy it can have" (93) or 1.05 x 10 to the negative 27th power grams-centimeters squared per second.

QUESTION 3: What does that mean?

QUESTION 4: If "quanta" are "bundles" (97), does that mean that quantum mechanics are "bundle mechanics"?

QUESTION 5: The parenthetical note about noise-cancelling headphones intrigued me - Do headphones measure and produce waves? How does that work?

"By increasing the number of individual photons that hit the photographic place you have decreased the brightness in certain areas. Somehow, temporally separated, individual particulate photons are able to cancel each other out" (102).

The rest of the chapter answered this for me, but I'm still floored by the idea... we can individually shoot photons or electrons or what have you, and they can cancel each other out?
QUESTION 6: How was Einstein able to prove it?

QUESTION 7: Can we see the wavelength of matter under a microscope? (referring to p. 105)

So... another question I was going to have had to do with probability and the wavelength of an electron. What are waves? Is probability as precise as it gets, or will technology eventually answer more precisely?

But if I understand the remainder of the chapter, this is something that - at least at the writing of this book - couldn't really be answered, and there are multiple theories trying to explain the possibilities.

QUESTION 8: Greene refers a few times to the magnitude of a wave - what does he mean? Why/how do we use its square in determining probability?

I was also going to ask that, given the probability of where an electron is, how does that coincide with other reading I'd done that indicated you could either measure where an electron was or how fast it was going, but not both. From the end of the chapter, a more correct way of understanding is that, no matter what, we're talking about probability - just that either its position or velocity is going to be more precise. Am I understanding this right so far?

QUESTION 9: (I'm pretty sure I know the answer to this one too) In the double-slit experiment, do all particles behave the same way (ie., creating interference patterns)?

It was a stretch for my mind to finish this chapter this morning, so I mostly likely won't be starting Chapter 5 'til tomorrow or maybe later (how's that for probability? Hm...).

Good questions! I'll work on 'em this evening.

Sounds good! I have a pretty busy day today, and I'll wait for the answers before starting on Chapter 5 (I'm planning on Monday at this point).

Cool-- the tachyons live on, at least theoretically. I remember reading about them 30+ years ago in an introductory physics book and they blew my mind. Move faster than the speed of light-- so does that mean they travel backwards through time?

QUESTION 1: I get it in theory, but where are the "lumps"? Is he talking about a physical characteristic, or saying that the measure of energy in a wavelength is a "lump sum"?

Here we mean lumps as in can't make the amount of energy carried by a photon any smaller. Coins are a good way to think of it. Photons are like pennies. There's a fixed value to a penny. I can carry around a bag full of pennies to buy very expensive things with, but the fundamental unit is the penny. If I buy something worth a dollar, I have to spend 100 pennies.

Now, photons are the particles by which electrical energy is exchanged from one electron to another. When two electrons interact, one loses energy while the other gains energy. This can only happen in integer numbers of photons (1, 2, 3…) just like I can only spend my money in integer numbers of pennies.

QUESTION 2: How to the higher-frequency waves not contribute to the energy/heat in an oven?

It's really an issue of having enough energy around to put into those higher frequency waves. The higher the frequency, the more energy must be put into making the wave. In reality, there's only so much energy available, so only the lower wavelengths really occur. Think of a guitar string again: the higher the note, the smaller the wavelength and the more energy is needed to pluck the string. If you can't hit the string hard enough, it won't vibrate.

In a theory, we write down a set of equations that we think describe reality. In the case of the old theory prior to Einstein and company, the model of reality didn't include everything we know now, so was wrong. Once folks worked out the math, they knew it was wrong. But nobody had a better idea until the idea of discrete energy packets in photons came along.

h-bar was defined as "the proportionality factor between the frequency of a wave and the minimal lump of energy it can have" (93) or 1.05 x 10 to the negative 27th power grams-centimeters squared per second.

QUESTION 3: What does that mean?

As we said above, the higher the frequency of the wave, the more energy it has. In fact, this is a linear relationship. In equation terms, E = h-bar times frequency. H-bar is just a number, and in the units above, the value happens to be 1.05 x 10 to the -27 power. In other words, really, really small and so the energy bits are really, really small. Which means it takes a huge number of photons to exchange real-world amounts of energy.

As another example, you can calculate the distance you can go on a tank of gas by miles = mpg times gallons. I get 22 miles per gallon in my truck, and so for a 15 gallon tank, I can go 22 times 15, or 330 miles. I could do the same calculation in km per liter (which they use in Europe). The equation is the same, but the value of the proportionality factor (i.e., mpg ) changes. In the case given here, the units are grams-cm squared per second, but there are other systems of units that could be used (this is a unit of momentum times distance or energy times time).

QUESTION 4: If "quanta" are "bundles" (97), does that mean that quantum mechanics are "bundle mechanics"?

Essentially, yes. Quantum field theory, which he gets to later in the chapter is essentially the theory of little bundles of matter and energy and how they interact.

QUESTION 5: The parenthetical note about noise-cancelling headphones intrigued me - Do headphones measure and produce waves? How does that work?

Yep. There's a microphone in the headset that measures sound levels and nearly instantaneously the circuit calculates the sound wave that's needed to cancel the detected sound. The headphones have speakers that emit this canceling sound wave and the result is nearly zero sound at your ears. By the way, these are better at canceling repetitive noise. Noise spikes are harder to cancel in real time since they happen too fast. Engine noise on an airplane is much easier to cancel in real time than a sneeze in a concert hall.

"By increasing the number of individual photons that hit the photographic place you have decreased the brightness in certain areas. Somehow, temporally separated, individual particulate photons are able to cancel each other out" (102).

The rest of the chapter answered this for me, but I'm still floored by the idea... we can individually shoot photons or electrons or what have you, and they can cancel each other out?

Yup. Lasers are pretty good at doing this for photons. Electron tubes do the same for electrons (cathode ray tubes like in old tvs!) And yep, it's one of the trippier concepts in QM.

QUESTION 6: How was Einstein able to prove it?

Well, Einstein was a theorist and didn't do much experimental work. But others have been able to build and run experiments on equipment doing exactly this. As I mentioned, lasers can be used for photons along with the proper optical equipment, or electron tubes can use magnetic fields to steer electrons in the same way. One can also use particular kinds of crystals to make interference patterns with neutrons as well.

QUESTION 7: Can we see the wavelength of matter under a microscope? (referring to p. 105)

Nope, too small. We're just getting to the point where we can use high tech electron microscopes to see individual molecules and atoms, which are much bigger than individual electrons. Photons can't be seen as such, since seeing involves absorbing the photon itself.

So... another question I was going to have had to do with probability and the wavelength of an electron. What are waves? Is probability as precise as it gets, or will technology eventually answer more precisely?

But if I understand the remainder of the chapter, this is something that - at least at the writing of this book - couldn't really be answered, and there are multiple theories trying to explain the possibilities.

You've hit it exactly right. We don't know what an electron really is. We have a mathematical theory that describes the behavior of an electron, but doesn't address the question of what an electron is really made of. That's one of the questions that pushes scientists to look for deeper theories. String theory is one attempt to try to get a grip on that problem.

QUESTION 8: Greene refers a few times to the magnitude of a wave - what does he mean? Why/how do we use its square in determining probability?

I'm going to throw in some technical jargon, so feel free to ask more questions if it's not clear. The fundamental equation of regular QM, which is what he's describing here, is the Schroedinger equation. It's the equation of motion in this theory like we discussed in the last set of questions. This equation describes how something called the "wave function" varies in space and time. It turns out that the square of the wave function is a measure of the likelihood that the particle we're describing is at a particular place at a particular time, or probability of it's location and time history. Now, this should bother you - it bothers us as well. But it works very well, to the point of accurately predicting how electrons move in atoms, for example, matching experiments very precisely. The Schroedinger equation doesn't work well when we have to also account for special relativity - say, for very energetic particles. But the more general theory, quantum field theory, works and encompasses basic QM using those very same wave functions.

I was also going to ask that, given the probability of where an electron is, how does that coincide with other reading I'd done that indicated you could either measure where an electron was or how fast it was going, but not both. From the end of the chapter, a more correct way of understanding is that, no matter what, we're talking about probability - just that either its position or velocity is going to be more precise. Am I understanding this right so far?

Yup. Exactly right.

QUESTION 9: (I'm pretty sure I know the answer to this one too) In the double-slit experiment, do all particles behave the same way (ie., creating interference patterns)?

Yep.

It was a stretch for my mind to finish this chapter this morning, so I mostly likely won't be starting Chapter 5 'til tomorrow or maybe later (how's that for probability? Hm…).

:)

#46 - thePrib

Not necessarily. Tachyons are a mathematical artifact of certain flavors of theories that unify gravity and quantum mechanics. Just how they're supposed to behave depends on the specifics of the proposed theory. It's not at all clear that these theories are right and that tachyons exist. And even if they do exist, most theories predict that they don't interact with ordinary matter anyway.

But at least they made Star Trek fun! :)

I read the questions over for the first time while I was still at work, and I had to share with a co-worker how noise-cancelling headphones work. That's really fascinating!

And thanks, those answers (even the technical ones!) do help my understanding - and confidence - in reading.

I'm curious: What do you think is the most likely explanation for the electron probability problem?

Starting Chapter 5 tonight, and since it's only 15 pages I think it's likely I'll have questions up by tomorrow.

CHAPTER 5: "The Need for a New Theory" - Questions and One Random Thought

Question 1: So he mentions Schrodinger's equation, one that incorporates special relativity (the Klein-Gordon equation) and one that doesn't. I'm sure I don't know enough math to actually understand the equations themselves, but what are they used for? When would one be used and not the other?

Question 2: Greene's discussion here made it obvious to me that the uncertainly principle means much more than the fact that if we have a better estimate of where an electron is, we have a worse estimate for how fast it was moving (and vice versa). What are the implications of the uncertainly principle (probably especially as it pertains to quantum mechanics vs. general relativity, as that's his focus here, but... well, anything, really)?

I would have had questions on quantum chromodynamics and quantum electroweak theory, but it sounds like he's going to get into that more later, so I'll hold off for now.

Question 3: I'm not sure I get gauge symmetries and why they're important (beyond the fact that all of the forces keep observations "the same" in the same way that gravity does). Is there more to it than that?

"Calculations that merge the equations of general relativity and those of quantum mechanics typically yield one and the same ridiculous answer: infinity" (129).

Couldn't help but note that this was the same "answer" that once existed for how much energy is in an oven.

Question 4: If we can get a more precise answer to where a particle is or how fast it is moving, does that change the uncertainly principle and the geometric shape of space? Does "quantum foam" exist no matter what?

Question 5: (This and the next question refer to the Notes for the chapter on pages 396 and 397.) What is renormalization and how did it "fix" the results for the quantum theories for strong and weak forces?

Question 6: At the time of Greene's writing, he mentions two other theories being pursued - twistor theory and new variables method. What are these theories? Are they still considered viable?

Looks like Chapter 6 is plunging into superstring theory. Considering my schedule for the next few days, I'm not sure when I'll have the chapter finished, but I'll post again when I have a better idea.

Wow! This is my first time on this site. You have all been busy.

I wound up making a flying trip to Louisiana to visit my dad as he has surgery tomorrow, so I'll tackle your questions on Chapter 5 in the morning while I'm sitting with him. In the meantime - I honestly have no idea what an electron really is. The best I can come up with is some sort of coalesced energy. But really, I'm not sure I understand what that means. We could be at an interesting boundary of what science can tell us. It's interesting, for sure!

Hope everything goes well with your father's surgery. No rush on the answers - I think I'm OK starting Chapter 6 without them because Greene's changing gears, and I don't think I'll be finishing it 'til Saturday at this point.

yes, drneutron, i too hope all goes well for your father. i don't have any questions above and beyond what bell7 has asked you about and appreciate your answers. in fact, i need to go back over the questions and answers to make sure i'm up to speed.

hi fuzzyphil!

Question 1: So he mentions Schrodinger's equation, one that incorporates special relativity (the Klein-Gordon equation) and one that doesn't. I'm sure I don't know enough math to actually understand the equations themselves, but what are they used for? When would one be used and not the other?

Both equations are equations of motion liked we talked about before, so are used to predict the behavior of particles. The Schroedinger equation is the standard non-relativistic, non-field theory equation that assumes particles are of low enough energy that special relativity can be ignored. The K-G equation is an attempt to incorporate special relativity into QM.

So what's the difference between them? Remember in an earlier chapter we talked about uniting space and time into a 4-dimensional space-time? Well, that's the difference. The Schroedinger equation defines a "wave function" (when squared, this is a probability) that depends on time and space separately, where time is a parameter and space is what's called an "operator". There are two approaches to bringing in special relativity: make time an operator too, or make space a set of parameters along with time. It turns out only one makes sense mathematically - treat time and space as a set of parameters in the wave function. When you do this, you get the Klein-Gordon equation as the equation of motion.

It turns out that the the K-G equation works, but the wave functions are very complicated. Feynman's "path integral" approach that Greene discusses is an equivalent approach, but with easier math, so that's what mostly gets used today in working with the Standard Model.

Question 2: Greene's discussion here made it obvious to me that the uncertainly principle means much more than the fact that if we have a better estimate of where an electron is, we have a worse estimate for how fast it was moving (and vice versa). What are the implications of the uncertainly principle (probably especially as it pertains to quantum mechanics vs. general relativity, as that's his focus here, but... well, anything, really)?

The biggest implication is that there really is this sea of virtual particles around us all the time. These are the very short-lived particle-antiparticle pairs that he mentions. When you solve the equations of motion, for instance in Feynman's path integral approach, you have to account for the energy associated with these pairs to get answers that match reality.

I would have had questions on quantum chromodynamics and quantum electroweak theory, but it sounds like he's going to get into that more later, so I'll hold off for now.

That's cool. If he doesn't, we can revisit these topics later.

Question 3: I'm not sure I get gauge symmetries and why they're important (beyond the fact that all of the forces keep observations "the same" in the same way that gravity does). Is there more to it than that?

The idea with gauge symmetries is that there are certain things that shouldn't affect physics. For instance, if I throw a baseball to the right fielder from home plate, the path of the ball (neglecting air currents, etc) is an arc depending on how I initially throw it, and gravity. Now, if I rotate to throw the ball to the left fielder, the path of the ball should still only depend on the initial conditions and gravity. So the equation of motion for the ball doesn't depend on which way I'm standing when I throw the ball. This "rotational symmetry" is a gauge symmetry. It's not a deep or particularly interesting one, but all gauge symmetries are the same basic idea.

The neat thing is, for every gauge symmetry in the equation of motion, we get a conservation law that helps us solve the equations of motion. For instance, If I do an experiment in Baltimore, I get a result. If I do the same exact experiment in Cleveland, I will get the same result (assuming that I've conducted the experiment in exactly the same way). This is called "translational symmetry" and means that the equations of motion don't depend on where in space the experiment is done. The consequence of this symmetry is that momentum is conserved, a very useful result.

"Calculations that merge the equations of general relativity and those of quantum mechanics typically yield one and the same ridiculous answer: infinity" (129).

Couldn't help but note that this was the same "answer" that once existed for how much energy is in an oven.

Yup. When we get infinity as the answer in physics, it usually means something's wrong with the theory. There are some exceptions to this. When he gets to "renormalization", we'll see infinities that can be worked around. They are still an indication that the theory has something askew, though, which is one of the motivators for looking at more general theories.

Question 4: If we can get a more precise answer to where a particle is or how fast it is moving, does that change the uncertainly principle and the geometric shape of space? Does "quantum foam" exist no matter what?

Quantum foam exists no matter what. The uncertainty principle doesn't change no matter how the particle is moving or how precisely we measure one aspect or the other.

By the way, if you're a Star Trek fan, you may have heard mention of Heisenberg Compensators. The transporter they made up basically measures the position and velocity of every particle making up the thing you want to transport and copies them at some other location. This clearly violates the Heisenberg principle. So they invented this gadget that "supresses" the Heisenberg uncertainty principle to make the transporter sound reasonable! Nothing like that exists, or is suspected to be possible.

Question 5: (This and the next question refer to the Notes for the chapter on pages 396 and 397.) What is renormalization and how did it "fix" the results for the quantum theories for strong and weak forces?

OK, so I didn't look at this note when I read the chapter, but here goes anyway! Remember I said infinities are bad? Well, when we solve the equations of motion in quantum mechanics, we're often trying to calculate some property of an interaction, such as the likelihood a particular interaction occurs or the energies of the outgoing particles. Since the equations are so complicated, they generally can't be solved exactly, so we make approximations to the equations that can be solved. We do this in a relatively straight-forward, well understood mathematical technique called a Taylor series expansion (named for the person who invented the method). When we do this, certain terms in the expansion are each infinite - which as I said, means the theory isn't working right. So we get answers that almost make sense but not quite. It turns out, though, that there's a way to make the infinite terms cancel each other out to get sensible answers. And believe it or not, the theory works very well. All of the equations of motion for the Standard Model are solved using renormalization, yet we get very precisely correct answers!

It's a bit like sweeping the dirt under the rug, though, and so is another motivator for looking for either a way to solve the original equations or a more general theory that doesn't require expansion and renormalization.

Question 6: At the time of Greene's writing, he mentions two other theories being pursued - twistor theory and new variables method. What are these theories? Are they still considered viable?

Yes. Papers still are published on both. There's also a way to incorporate gravity into QM called loop quantum gravity that "competes" with string theory. Here, the idea is to try to quantize the geometric structure of space-time. It's related to hidden variables or new variables methodology.

By the way, my dad came through his surgery with flying colors!

Good for him!

very good for your dad (and a relief for you, i'm sure)!

Glad to hear your dad's surgery went well!

I've started Chapter 6, and might post questions today or tomorrow whether I actually finish it or not (though when I've done that so far, I've found some of my questions were covered later in the chapter... oh well).

Out of curiosity, what's the gist of the competing theories? (I know these probably have long answers, I'm sorry...)

All theories about how particles behave are models. The Standard Model pictures particles as 0-dimensional objects that interact by exchanging force particles. Quantum field theory pictures particles as clumps of energy in a field that extends throughout space (think of those weird spots on the highway where traffic slows down or stops for no good reason. String theory pictures them as little bands that vibrate and interact by merging and separating.

So every theory is a description written in mathematical language. Most of the theories we've seen picture what we see as particles as one type or another of geometrical object. For instance, a closed string is a loop. A twistor is a geometrical object that includes rotational motion in various forms. Loop quantum gravity pictures space-time as a fine fabric of quantized loops of excited gravitational fields called spin networks - called "spin foam", not to be confused with the quantum foam we've seen with the discussion of the Heisenberg uncertainty principle. This is the main contender of those "hidden variables" or "new variables" models that Greene mentions.

From that description, I think I can kind of see why Greene says that twistor and new variables can be considered sort of variations on string theory.

Sorry to be AWOL for a couple of days. I have been reading Chapter 6 (I've even been bringing the book & my notebook to read and take notes for my breaks at work), and have about 15 pages to go. I don't mind posting questions mid-chapter, except that I often find that some of my questions from earlier in the chapter are addressed later, and I'd rather wait to have the whole picture before asking for more clarification, if that makes sense.

I won't promise anything, since I've got a meeting tomorrow night, but Friday is a possibility to have the questions up for Chapter 6 - I have about 15 pages left to go.

No prob. We're doing this at your pace! :)

Yeah, I just feel like a slacker. Generally three weeks in one book is a long time for me, so for this to take longer... :)

BUT I'm learning a lot, and taking notes and being able to ask questions will, I think, help me retain a lot more too.

Humor break:

http://www.smbc-comics.com/index.php?db=comics&id=2657#comic

*snerk*

>64 norabelle414: The sad thing is, I just got the first joke you shared...

CHAPTER 6: "The Essentials of Superstring Theory"

1. A note for the chapter mentions that this is perturbative string theory. What does that mean, and what's the other one all about?

2. Greene says that point particles are zero dimensions and strings are one dimensional. Is that like a point and a line in math?

3. I suppose the book may go into more detail on this later, but since strings are so incredibly small, what methods are or can be used more indirectly to determine if string theory explains the universe better than the standard model?

4. What is the Euler Beta-function? ("seemed to describe numerous properties of strongly interacting particles in one fell swoop" p. 137) More details, please! What's he referring to?

5. Greene mentions that there are "subtle conflicts" between string theory and quantum mechanics, but that they were largely resolved in 1984. What are the conflicts, and what was the resolution?

6. By the way, you mentioned that the discovery of the Higgs boson is more in line with the standard model. How does it conflict with string theory?

7. There was a lot of summary of things in this chapter, and here's one case where I wasn't sure if I was supposed to already know or if it was just too detailed that he didn't want to go into it here: "the 19 numbers summarizing the elementary particle masses, their force charges, and the relative strength of the forces, numbers that are known from experiment but are not understood theoretically" (139). What are these numbers? (I mean, I get mass and charge and such, but that seems like more than was summarized in the early chapters) How are they "known" but "not understood theoretically"?

8. "String theorists, as of this writing, are working vigorously to sharpen a set of new methods that promise to overcome the theoretical obstacles previously encountered" (140). What are they doing, and what are the methods? Can computers be used for the complicated math?

9. "To date there are intriguing hints in theoretical studies that strings may have further substructure" (142). I find this interesting, because he talks later of how string theory "smears out" the quantum foam, that it's too small to affect the string and therefore doesn't exist on some level. If strings have further substructure, does this change? What are some of the theoretical studies, and have they turned up anything intriguing in the time since the book has been written (I'm assuming he'll cover anything pre-2003)?

10. Since the vibrations/resonances of the string would be theoretically infinite, how is this an improvement over what he terms the flexibility of the standard model? (I see how he's talking about cause and effect - that the standard model doesn't explain the why of mass and other numbers, which addresses what I ask in question 7 as well - I guess what I don't get is, it seems that you're exchanging one infinity for another - if there's an infinite number of particles possible, why do only some exist?)

**Chapter note number 7 on page 398 made me cross my eyes, I didn't understand a word of it**

11. On page 148, Greene details how they figured out the tension needed for the graviton. Does this work with the other particles and forces as well, to figure out their tensions and have the numbers come out right?

12. "In effect, through the weirdness of quantum mechanics, the energy associated with the quantum jitters of a string is negative, and this reduces the overall energy content of a vibrating string by an amount that is roughly equal to Planck energy" (150) and then on the next page, "energy cancellations certainly can occur, but for reasons that will become increasingly clear in subsequent chapters, verifying the cancellations to such a high level of precision is generally beyond our theoretical ken at present" (151). Two part questions: 1. what? and 2. do the cancellations happen or not?

13. Does a no-mass particle mean it's pure energy? (I may have already asked this, if so, sorry to repeat!)

14. If electrons and so on are not really "particles" as such but made up of string, (for some reason that reminds me of "brown paper packages tied up with string"... ahem, back to the question) does this affect the results of probes and the renditions we've created from them? If so, how?

15. "Smearing" he refers to on and around page 156 - this made up a good deal of my confusion, actually. What I really don't get, I think, is - if we're "smearing" it, what are we saying - that quantum foam doesn't exist, or that it's too small to affect anything? Does this affect the uncertainty principle? (On a related note, my understanding was there was quantum foam because of the uncertainty principle, but am I conflating two different things?) On another page, he seemed to be saying that it might be nonexistent and really just a side effect of the incompatibility of quantum mechanics and relativity, so I'm really confused on this point.

So that wraps up Chapter 7. What with a weekend and holidays coming up, I'm hoping to progress on the next couple of chapters faster than the last. I'm hoping Monday for a set of Chapter 7 questions.

Have a good weekend!

Excellent questions! I'm spending the day recovering from the big storm Friday evening. We lost power and just got it back at midnight last night. Plus we had 50 people over for our birthday party - even with no power - and today's cleanup. So I'll get something out tomorrow.

>68 drneutron: Glad to hear you have power again! My sister was without power yesterday, too, and I hope she gets it back as fast. Hope your 100th birthday party was fun, even with no power. :)

CHAPTER 6: "The Essentials of Superstring Theory"

1. A note for the chapter mentions that this is perturbative string theory. What does that mean, and what's the other one all about?

Perturbative means this is an approximate theory. The full equations are too difficult to solve, so physicists make simplifying assumptions. To do this, though, they need to show that the simplification doesn't change the equations enough to give bad answers.

In this case, it's kind of like approximating a circle with a polygon. The more sides to the polygon, the more like a circle it is. Eventually, you get to the point where your eye can't distinguish between the polygon and the circle, but the shape is still different.

2. Greene says that point particles are zero dimensions and strings are one dimensional. Is that like a point and a line in math?

Yup, exactly. In the case of strings, there are two types: open and closed. Closed strings are loops. Open strings are lines of some length.

3. I suppose the book may go into more detail on this later, but since strings are so incredibly small, what methods are or can be used more indirectly to determine if string theory explains the universe better than the standard model?

So when we smash energetic protons together, for instance, many different kinds of reactions can happen. Some are more likely than others. We do this many, many times and measure the reaction products for each collision. Then we can form statistics for the reaction rates, types of particles that are formed, etc. The Standard Model can be used to predict these data, and if the prediction doesn't match the data, something's wrong about the theory. Now, to date, no inconsistencies with the Standard Model predictions have been found to very high precision (except, see below about the Higgs findings).

String theorists do the same thing. They predict reaction rates and end particle production based on their theory. If the results of that prediction are the same as for the Standard Model, there's no way to tell which is the correct theory. However, if the two theories predict different behavior, we can do an experiment to see what matches. reality. This is exactly what's going on with the Higgs Boson right now. The experiments at CERN have measured production rates for the Higgs in various types of reactions. We're now sorting through the theories to see which match and which don't.

Yesterday, the folks at CERN announced the discovery of the Higgs boson. This means that they've looked at the statistics for the reactions the Standard Model and they see evidence for these reactions above background at a statistically significant level. This is interesting news in that it confirms the mechanism predicted by the current Standard Model. Now, the data are roughly the values predicted by the SM, but not exactly. This means that there may be room for a different, or at least more generalized theory. As a reminder, it was small discrepancies from the predictions of classical gravity that led to general relativity.

By the way, one of the issues with string theory as it's understood right now is that it's very difficult to make testable predictions. Especially ones that differ from the Standard Model. If that continues to be the case, it's hard to see how accepting string theory makes any difference.

4. What is the Euler Beta-function? ("seemed to describe numerous properties of strongly interacting particles in one fell swoop" p. 137) More details, please! What's he referring to?

As I mentioned above, one of the things we care about is the distribution of rates for the various reactions particles can undergo in collisions. The technical term for this is a "scattering amplitude". Like the wave functions in the Schroedinger equation, it's a sort of square root of the probability that the reaction will take place, and depends on things like incoming particle mass and energy, spin state, etc. When we look at the data, the scattering amplitude for a particular particle as a function of its energy has a bunch of peaks and valleys with a characteristic shape.

The Euler beta function is a curve that matches that shape well. It's a mathematical function like the sine wave is a mathematical function. When we do the math to calculate scattering amplitudes, these all take the shape of an Euler beta function with parameters that depend on energy,etc. More on the Euler beta function at http://en.wikipedia.org/wiki/Euler_beta_function

5. Greene mentions that there are "subtle conflicts" between string theory and quantum mechanics, but that they were largely resolved in 1984. What are the conflicts, and what was the resolution?

Honestly, I wasn't quite sure that he meant by this. I think he's talking about the efforts to use string theory to predict reaction rates and particle production that didn't work out to match reality. This was tackled by introducing supersymmetry into string theory. He talks about this in Chapter 7. If I remember right, that was the right timeframe for when I saw all the flood of papers on supersymmetry. :)

6. By the way, you mentioned that the discovery of the Higgs boson is more in line with the standard model. How does it conflict with string theory?

See answer to 3. The main things about the Higgs boson predicted by theories is its mass and rate at which it's produced in various types of proton-proton collisions. The SM predicts 125 GeV, plus or minus. String theory, since it's an approximate theory, will predict different masses depending on how the approximations are done. So if a particular flavor of string theory predicts a very different mass from the SM, we see now that that theory is unlikely to be supported by the data.

7. There was a lot of summary of things in this chapter, and here's one case where I wasn't sure if I was supposed to already know or if it was just too detailed that he didn't want to go into it here: "the 19 numbers summarizing the elementary particle masses, their force charges, and the relative strength of the forces, numbers that are known from experiment but are not understood theoretically" (139). What are these numbers? (I mean, I get mass and charge and such, but that seems like more than was summarized in the early chapters) How are they "known" but "not understood theoretically"?

The 19 numbers we're talking about are the masses and charges of the fundamental particles from that table in Chapter 1 along with the relative strengths of the four forces (gravity, electromagnetism, weak nuclear force, strong nuclear force). These are measured by experiments and are "free parameters" in the Standard Model. This means we plug the values directly in the equations. "Known but not understood theoretically" just means that we have measured the values and can make predictions, but we have no idea why the numbers take the values they do. Part of what the theorists are trying to accomplish with string theory is to develop a deeper theory that predicts these values.

8. "String theorists, as of this writing, are working vigorously to sharpen a set of new methods that promise to overcome the theoretical obstacles previously encountered" (140). What are they doing, and what are the methods? Can computers be used for the complicated math?

The main areas of research for the string theorists are developing new mathematics to be able to solve the full string theory equations rather than just the simplified ones. Most of these are developed by applying geometric techniques - differential geometry, topology, category theory, braids, etc - from the front lines of mathematical research.

9. "To date there are intriguing hints in theoretical studies that strings may have further substructure" (142). I find this interesting, because he talks later of how string theory "smears out" the quantum foam, that it's too small to affect the string and therefore doesn't exist on some level. If strings have further substructure, does this change? What are some of the theoretical studies, and have they turned up anything intriguing in the time since the book has been written (I'm assuming he'll cover anything pre-2003)?

I haven't heard of anything like this, so I suspect it's something that didn't pan out. There have been lots of efforts to extend string theory. So if the SM is about 0-dimensional point particles, and string theory is about 1-dimensional objects, why not look at 2-dimensional objects or 3-dimensional objects? In fact, the 2-D version of string theory is called M-theory, for membrane theory. It treats particles as what look like drumheads that can vibrate. This is in the early stages, yet. We haven't yet begun looking at something similar in 3-D.

10. Since the vibrations/resonances of the string would be theoretically infinite, how is this an improvement over what he terms the flexibility of the standard model? (I see how he's talking about cause and effect - that the standard model doesn't explain the why of mass and other numbers, which addresses what I ask in question 7 as well - I guess what I don't get is, it seems that you're exchanging one infinity for another - if there's an infinite number of particles possible, why do only some exist?)

You're right and this picks up on one of the criticisms of string theory.

**Chapter note number 7 on page 398 made me cross my eyes, I didn't understand a word of it**

I'll have to go back and look.

11. On page 148, Greene details how they figured out the tension needed for the graviton. Does this work with the other particles and forces as well, to figure out their tensions and have the numbers come out right?

Yes, but since these are simplified models, how the simplifications are applied make a difference. It's not fair to tweak a model just to make the numbers come out right. One needs to have strong physics motivation for the assumptions that are made. Otherwise, the theory is no better than adding in the SM free parameters by hand.

12. "In effect, through the weirdness of quantum mechanics, the energy associated with the quantum jitters of a string is negative, and this reduces the overall energy content of a vibrating string by an amount that is roughly equal to Planck energy" (150) and then on the next page, "energy cancellations certainly can occur, but for reasons that will become increasingly clear in subsequent chapters, verifying the cancellations to such a high level of precision is generally beyond our theoretical ken at present" (151). Two part questions: 1. what? and 2. do the cancellations happen or not?

This is one of the magic things about string theory that's a bit bothersome. It's a mathematical/theoretical result, and Greene is presenting it as best he can from a non-technical aspect. The theory predicts that they occur, but we don't know yet whether this is a picture of reality, or just a trick that keeps the math working.

13. Does a no-mass particle mean it's pure energy? (I may have already asked this, if so, sorry to repeat!)

Yup.

14. If electrons and so on are not really "particles" as such but made up of string, (for some reason that reminds me of "brown paper packages tied up with string"... ahem, back to the question) does this affect the results of probes and the renditions we've created from them? If so, how?

These are a few of my favorite things! We're hoping that string theory predicts results that are different from the SM theory. If it doesn't, we're beyond physics and into philosophy! The only way to tell which theory is better at representing reality is to compare with data. As mentioned above, it's reaction rates and particles that are produced in the various reactions we study that matter.

15. "Smearing" he refers to on and around page 156 - this made up a good deal of my confusion, actually. What I really don't get, I think, is - if we're "smearing" it, what are we saying - that quantum foam doesn't exist, or that it's too small to affect anything? Does this affect the uncertainty principle? (On a related note, my understanding was there was quantum foam because of the uncertainty principle, but am I conflating two different things?) On another page, he seemed to be saying that it might be nonexistent and really just a side effect of the incompatibility of quantum mechanics and relativity, so I'm really confused on this point.

Well, I think he's confusing in this discussion, so you're not alone. The Heisenberg uncertainty principle isn't in question. It's been verified over and over, so is well established by experiment. His picture of quantum foam at the smallest chunks of space-time is an imperfect attempt to picture what's happening there. The idea that he's trying to convey is that this foam-y nature of space-time may not matter if we use the string picture to "smear" or average over a slightly bigger chunk of space-time. For instance, when you look very closely at whipped cream, it's a foam, but when you back up just a bit, it looks smoother, and if you back up a bit more it looks like a surface. String theory is a mathematical analog to backing up a bit.

So that wraps up Chapter 7. What with a weekend and holidays coming up, I'm hoping to progress on the next couple of chapters faster than the last. I'm hoping Monday for a set of Chapter 7 questions.

Cool! I need to get my copy of the book back to the library in the next week or so, so I'm going to finish up. That shouldn't be a problem for answering questions, though.

On page 148, Greene details how they figured out the tension needed for the graviton. Does this work with the other particles and forces as well, to figure out their tensions and have the numbers come out right?

Yes, but since these are simplified models, how the simplifications are applied make a difference. It's not fair to tweak a model just to make the numbers come out right. One needs to have strong physics motivation for the assumptions that are made. Otherwise, the theory is no better than adding in the SM free parameters by hand.

What I was really having more trouble with was (but didn't want to sound too negative), it sounds a little difficult to (partly) base a theory on the numbers working for only the theoretical particle. I was trying to get a sense of whether or not it "works" for the known particles as well.

This is one of the magic things about string theory that's a bit bothersome.
OK, good. I was afraid I was missing something in not quite following his argument.

If it doesn't, we're beyond physics and into philosophy!
It seems to me there's a fine line sometimes. :)

Well, I think he's confusing in this discussion, so you're not alone. The Heisenberg uncertainty principle isn't in question. It's been verified over and over, so is well established by experiment. His picture of quantum foam at the smallest chunks of space-time is an imperfect attempt to picture what's happening there.

Good again. I won't worry so much about understanding his discussion of it, then. String theory is a mathematical analog to backing up a bit. OK - This one sentence makes much more sense to me than Greene's paragraphs on "smearing."

I need to get my copy of the book back to the library in the next week or so, so I'm going to finish up.

This is exactly why I bought the book (used) - I knew it would take me too long to read it as a library book. :)

I did start on Chapter 7 but my weekend and holiday turned out to be busier than I expected. So far I don't have any questions on the chapter, but I'll work on it more today and try to get back to you soon.

Sounds good!

On the subject of tensions and how that flows into predicted particle properties: it's possible at this point to write down a string theory that predicts almost any set of particle masses. In some sense we've exchanged the SM with some numbers that are measured and inserted by hand with a hand-picked theory to get correct values. When we do this, we also get a particle in the new theory that looks like it might be the exchange particle for gravity. So that's a plus. On the minus side (and he covers this later), we have to incorporate extra space-time dimensions and something called supersymmetry, for which there's no experimental evidence yet. This is why many theorists think that string theory is also a simplification of some bigger theory. He covers this later in the book as well.

You've now reached the cutting edge of theoretical physics! :)

it's possible at this point to write down a string theory that predicts almost any set of particle masses.

Ah. So we really haven't improved upon not knowing the whys behind the numbers for particles, then, have we?

You've now reached the cutting edge of theoretical physics!

Sweet! :)

Oh, and I spoke waaaaay too soon about having no questions for Chapter 7. HA. I am going to be reading some this evening though, so hopefully I will post the next set of questions soon.

For once, I'm not eating my own words on how long it might take me to post questions. Here's what I've got for Chapter 7 - I apologize in advance for what I anticipate will be a lack of organization. I started the chapter a few days ago, got confused and started over tonight, so my notes are not in order and I've managed to answer some of the questions by rereading or reading further.

CHAPTER 7 - Supersymmetry

1. First of all, what is supersymmetry, and how is it sensitive to spin? I'm finding myself getting frustrated with the in-between of a simple explanation and the details of the mathematical equation. I know I can't get it if he gives me the math, but it's annoying to be given an approximate explanation and then be told that he's using quotes to show how approximate his explanation is. (That's actually one reason I'm liking the tutored read, is that I can get both less technical and more technical explanations as needed...)

2. Going back a little bit to spin, he was a little vague on what that meant too. What does he mean by "spin that is somewhat akin to the usual image but inherently quantum mechanical in nature" (171)?

3. There's a note on page 399-400 that refers to the Higgs boson as a "mass-giving particle" and that its mass must be within certain parameters. Did its mass and such match up to what was expected?

4. If I understand him correctly, all particles with spin-1 are bosons, and all those with spin-1/2 are fermions, including the particles from Tables 1.1 and 1.2?

5. I was a little confused by the statement "strings necessarily have a vibrational pattern in their repertoire that is massless and has spin-2 - the hallmark features of the graviton" (172). I thought that there were infinite possible vibrational patterns. If so, what makes this one "necessary"?

For the record, I love the word squarks. Wino makes me laugh, but "squark" is just fun to say.

A couple of the questions I'm now discarding had to do with why supersymmetry is such a good thing. The first was the mathematical "neatness" of it, and the second was the precision necessary in the numerical parameters of the standard model. He addresses this at the end of the chapter, admitting that neither really prove supersymmetry. The argument that worked a little better for me was how the forces "met" - they almost-but-don't quite meet unless supersymmetry is incorporated. Still not a perfect argument, but definitely a nice and neat result. Could gravity ever be incorporated somehow?

6. At the end of the chapter, Greene discusses the fact that supersymmetry can be incorporated into string theory in five different ways, with five different resulting theories - have any been ruled out at this time?

So I'm planning on reading about multiple dimensions while at the laundromat tomorrow. I sometimes wonder to myself what kind of profile of me the regulars there could put together based on the books I've brought in to read while doing my laundry... (Also, I know for a fact I'm the only one who doesn't hate being there, merely because I have two hours of guilt-free reading time.)

CHAPTER 8 - Multiple Dimensions

Clearly I need to either do more laundry or simply neglect to promise being done a chapter by a certain day.

Just a couple of questions on this one:

1. What is chirality?

2. It sounds like if there aren't these nine (or ten) dimensions that superstring theory falls apart. Is this the case?

3. What if there are more dimensions even than that?

And with that, I've passed the halfway point in both chapters and pages!

CHAPTER 7 - Supersymmetry

As a preparatory note, I need to mention the state of physics these days. Greene is a believer in string theory, and much of his writing in the rest of the book comes from the point of view that superstrings exist and all the implication of the theory for extra dimensions and such are true. In fact, we don't know this. I like the theory. I think it's elegant. But there's no data yet that indicates the theory matches reality Having said that, it's worth reading about because it likely is true, or at least resembles what is true. Just take the next batch of chapters with a grain of salt! :)

1. First of all, what is supersymmetry, and how is it sensitive to spin? I'm finding myself getting frustrated with the in-between of a simple explanation and the details of the mathematical equation. I know I can't get it if he gives me the math, but it's annoying to be given an approximate explanation and then be told that he's using quotes to show how approximate his explanation is. (That's actually one reason I'm liking the tutored read, is that I can get both less technical and more technical explanations as needed…)

All particles have this intrinsic property called "spin" (technically, spin angular momentum). This is similar to mass in that all particles have it, but we don't worry too much about how to define it. (Technically, even massless particles have a property called "mass", it's just that the value of the mass is zero. Same thing for spin: all particles have the property, but the value can be zero.)

So the Standard Model breaks the fundamental particles into two kinds: bosons are those with integer spin (i.e., the value of the spin this property has for these particles is 0,1, 2, ...) and fermions are those with half-integer spin (i.e., 1/2, 3/2, 5/2…). Bosons are the force-transmitting particles like photons. Fermions are the other particles like electrons, proton (technically quarks, but anything made of fermions is also a fermion) or neutrons. Bosons and fermions behave differently, specifically when it comes to quantum states. Many bosons can be in the same quantum state (i.e., have the same energy and spin, etc). For fermions, only one particle can be in a given state at a time, which has important consequences for how electrons move around in atoms, for instance.

Supersymmetry is the idea that for every fermion we know about, there's a boson partner. And for every boson we know about, there's a fermion partner. We haven't detected these yet, since the mass of these partner particles is well beyond what we can produce in our labs. Doing this makes the math easier as Greene talks about. However, no evidence of supersymmetry has been seen yet. The CERN folks may get close if they can get the intensity and energy of their beams up in the big collider, LHC.

2. Going back a little bit to spin, he was a little vague on what that meant too. What does he mean by "spin that is somewhat akin to the usual image but inherently quantum mechanical in nature" (171)?

I'm going to punt here a bit, just like every other physicist. Spin is defined as an intrinsic property of the particles at hand that has a particular mathematical form. However, we can't really define it any better than that. THe Harlem Globetrotters are good at spinning basketballs. You can see the ball rotate as it spins, so it's easy to figure out what "spin" means. With zero-dimensional point particles, we have a harder time. You can't see the particle spin, but that spin affects the behavior of the particle as it moves. We have to include spin in the equations of motion to make our predictions come out right, but it's strictly a quantum mechanical property.This is what he means: the math is the same as for a spinning object, but you can't really define what spin means for a point particle. Now, if strings are real, the problem goes away, because strings have a finite size, so we can define what a spinning string is.

3. There's a note on page 399-400 that refers to the Higgs boson as a "mass-giving particle" and that its mass must be within certain parameters. Did its mass and such match up to what was expected?

Yes, very well. The big announcement on July 4th gave a mass right where it was expected to be per the Standard Model, but did mention that one of the reaction rates was a bit higher than predicted by the SM. THis might be a statistical artifact of the data, or it might be an indicator that the Standard Model isn't quite right. Time will tell!

4. If I understand him correctly, all particles with spin-1 are bosons, and all those with spin-1/2 are fermions, including the particles from Tables 1.1 and 1.2?

Yup, see above question 1.

5. I was a little confused by the statement "strings necessarily have a vibrational pattern in their repertoire that is massless and has spin-2 - the hallmark features of the graviton" (172). I thought that there were infinite possible vibrational patterns. If so, what makes this one "necessary"?

Every string theory we can come up with has this one particular vibrational pattern as well as an infinite number of other vibrational patterns. When you get to a later chapter he'll discuss the 5 types of string theories. The spin-2 particle is a feature of all of them. This comes out of the math. Essentially, the curvature of space has to be included in the theory no matter what type of string theory we use. The spin-2 particle comes from including the curvature in the equations as what's called a "metric", basically a way to calculate distance between two points in curved space.

For the record, I love the word squarks. Wino makes me laugh, but "squark" is just fun to say.

We physicists are a crazy bunch! :)

A couple of the questions I'm now discarding had to do with why supersymmetry is such a good thing. The first was the mathematical "neatness" of it, and the second was the precision necessary in the numerical parameters of the standard model. He addresses this at the end of the chapter, admitting that neither really prove supersymmetry. The argument that worked a little better for me was how the forces "met" - they almost-but-don't quite meet unless supersymmetry is incorporated. Still not a perfect argument, but definitely a nice and neat result. Could gravity ever be incorporated somehow?

The string theory people certainly think so! Remember that his discussion of supersymmetry is bigger than strain theory, though. On the one hand it's needed in string theory to make the theory work right. But it's also used in other types of theories as a way to unify forces.

6. At the end of the chapter, Greene discusses the fact that supersymmetry can be incorporated into string theory in five different ways, with five different resulting theories - have any been ruled out at this time?

Yes. Bosonic string theory doesn't really match reality at all. Heterotic string theories are probably the closest to actually being able to make real predictions that can be tested.

So I'm planning on reading about multiple dimensions while at the laundromat tomorrow. I sometimes wonder to myself what kind of profile of me the regulars there could put together based on the books I've brought in to read while doing my laundry... (Also, I know for a fact I'm the only one who doesn't hate being there, merely because I have two hours of guilt-free reading time.)

I'm with you there! I have a reputation for reading all kinds of weird things at lunchtime at the various restaurants close to work. The people I work with are used to seeing me with an odd book in my hands at the next-door Chick-Fil-A or Subway. :)

CHAPTER 8 - Multiple Dimensions

Clearly I need to either do more laundry or simply neglect to promise being done a chapter by a certain day.

Just a couple of questions on this one:

1. What is chirality?

Things that spin can spin either clockwise or counter-clockwise. Chirality is the property that tells us which way a given particle is spinning.

2. It sounds like if there aren't these nine (or ten) dimensions that superstring theory falls apart. Is this the case?

Yup. If we can't figure out what happened to the dimensions in reality or if we can't figure out a way to reduce string theory to a 4-D theory, it's wrong.

3. What if there are more dimensions even than that?

Same thing. More dimensions than those predicted by the theory is just as bad as fewer than predicted.

And with that, I've passed the halfway point in both chapters and pages!

Excellent!

Bosonic string theory doesn't really match reality at all.

Which one(s) was bosonic?

I have a reputation for reading all kinds of weird things at lunchtime at the various restaurants close to work. The people I work with are used to seeing me with an odd book in my hands at the next-door Chick-Fil-A or Subway. :)

My co-workers are used to my eclectic reading habits, too. When I was reading Crime and Punishment, I did bring it once but felt kind of funny bringing it in and purposely brought a different book the next time. (Also, if it's busy, I can't concentrate on something too in-depth with all the noise of the washers and dryers and people.)

Just so you know, I will not be posting in the next week and a half or so. I'm going away and will be really busy (aside from the travel time itself). Also, while I may get some reading done, I won't have access to a computer to post.

Bosonic string theory is also called Type 1 string theory. I forget which chapter it is, but he breaks down the five types and then discusses how some physicists think they're all different flavors of some larger theory.

My oddest read - I Am Not A Serial Killer on a plane. I'm pretty sure the person sitting next to me was glad to get off that flight! :)

Ah, thanks, he listed the five types but didn't go into detail yet. LOL on your oddest read - I could imagine that creeping out a seatmate! Probably the oddest response of my own in my reading was choosing to read Reading Matters (for fun) instead of V for Vendetta (for school) because so many people came up to me when I was reading the graphic novel to ask me if I'd seen the movie (I haven't). I got so sick of it, I stopped reading V in public.

CHAPTER 9 - Experimental Signatures - in which I learn that string theory, if it is to be proven, must be so indirectly because we don't have an accelerator the size of the galaxy (or possibly the universe)

I was a little interested by Greene's reference to the debate about the theory including the philosophy of "how things should be done" - experiment or theory first. Does this debate still go on? (I suppose any profession would have some sort of debate/balancing act, I was just kind of curious how it plays out for physicists.) :)

What is a multidimensional "hole" (p. 216 when discussing Calabi-Yau shapes and particle families)

On page 216, Greene writes, "If the curled-up Calabi-Yau has three holes, then we will find three families of elementary particles" (216).
Are there actually 3 holes in this shape - he answers this later, that there are many possible shapes right now
What about the other particles required for supersymmetry? Do there need to be more "holes"?
(Sorry to keep coming back to this one, but it seems important and it's not something Greene can address) Since the Higgs boson doesn't fit into the families, does that mean that for string theory to be accurate, the Calabi-Yau shape would have to have a different number of "holes"?

The Large Hadron Collider is mentioned on page 222 - seems to me, I've heard something about it, so I'm curious about anything that's turned up (whether related to string theory or not, it's just interesting...)

Finally, when Greene is listing the experimental signature "long shots," he mentions the cosmological constant. I was a little bit confused about this, since I know that Einstein took it out of his equation, yet here it sounds theoretically possible and measurable? How does the existence of a cosmological contact affect relativity?

Like I mentioned before, I'll be leaving tomorrow for a short trip (should be back on the 22nd, though I still haven't decided whether or not to bring this book). I didn't want you to be surprised if I didn't post for awhile and now you've got plenty of time before I really start looking for the answers. :)

Have a good weekend!

Lurker checking in.

I've had a year of college general physics, no quantum physics or relativity. My dd-in-college who has taken only the most general science classes has had more exposure and has more understanding of this than I do.

I've just started reading and I'm in chapter three. This is fascinating stuff! But I do feel a bit like I've fallen down the rabbit hole .......

>81 streamsong: Welcome! I hope you enjoy it. I'm going slower than I'd hoped, but I've enjoyed taking my time and getting to ask about anything that's confusing me.

UPDATE: I'm back from vacation, but haven't read a lick of Chapter 10. I hope to do so soon, now that I've finished the book for the library book discussion tomorrow.

Welcome back!

Thanks!

*bump* on the questions for Chapter 9. I know you're in the midst of another tutored read, and I'm in the midst of Chapter 10 so no rush really, just didn't want to be forgotten. :)

I tried to read it some tonight, but I am brain dead and can't take it. I will try again tomorrow after work, as I have the evening off.

Oh my. I thought I had answered these! Sorry about that! I'll put something together in the morning when I'm more coherent.

Not a problem - like I said, I'll be reading more of Chapter 10 when I'm coherent too, so I probably couldn't comprehend the answers tonight either. :)

CHAPTER 9 - Experimental Signatures - in which I learn that string theory, if it is to be proven, must be so indirectly because we don't have an accelerator the size of the galaxy (or possibly the universe)

I was a little interested by Greene's reference to the debate about the theory including the philosophy of "how things should be done" - experiment or theory first. Does this debate still go on? (I suppose any profession would have some sort of debate/balancing act, I was just kind of curious how it plays out for physicists.) :)

Oh, yes, the debate goes on. And on. :) Ideally, we'd like to develop a theory, make some predictions, then carry out experiments to verify the predictions. This gets us away from the issue of tailoring (or more unkindly, fudging!) the theory to meet some experimental result we already know.

The reality is that this never happens. Science is an iterative process, and sometimes we do experiments to see what happens. Now, this is rare when the experiment involves building a particle accelerator costing billions of dollars, but still, many physicists are tinkerers at heart! Also, we sometimes do experiments and get unexpected results we don't understand. Plus, there's always some back-and-forth between theory and experiment as we improve our understanding of each.

But the golden standard is make a prediction, then verify it.

What is a multidimensional "hole" (p. 216 when discussing Calabi-Yau shapes and particle families)

Think of a bubble in a glass of beer. (For discussion's sake, let's assume that the bubble doesn't rise to the top and doesn't pop.) That bubble is in the shape of a sphere. There's no liquid inside the bubble, so you can think of it as a hole in the liquid - any motion of the fluid doesn't go through it, instead it goes around. This a three-dimensional hole. Now imagine space is the fluid. The bubbles are the holes in the Calabi-Yau manifold. Except that instead of three-dimensional holes, they are some higher number of dimension that I can't picture in my head! :)

On page 216, Greene writes, "If the curled-up Calabi-Yau has three holes, then we will find three families of elementary particles" (216).
Are there actually 3 holes in this shape - he answers this later, that there are many possible shapes right now
What about the other particles required for supersymmetry? Do there need to be more "holes"?
(Sorry to keep coming back to this one, but it seems important and it's not something Greene can address) Since the Higgs boson doesn't fit into the families, does that mean that for string theory to be accurate, the Calabi-Yau shape would have to have a different number of "holes"?

So as you noticed, there are an infinite number of shapes that this manifold can take. This is the source of previous comments on string theory's inability to make specific predictions. We can find a a shape that predicts nearly any set of particle properties. And that's the issue that some physicists have - if the theory can't make a specific prediction without tailoring by hand, how is this better than the Standard Model? The thing that would clarify the situation is if there were some experimental results that differed from the predictions of the Standard Model to use as a test case to sort out these theories. So far, though, no luck with that...

The Large Hadron Collider is mentioned on page 222 - seems to me, I've heard something about it, so I'm curious about anything that's turned up (whether related to string theory or not, it's just interesting...)

The Large Hadron Collider is the big proton ring at CERN, the leading particle physics laboratory on the Swiss/French border near Geneva. It's a big circular pipe about 16 miles around buried in a tunnel underground. Protons are injected into the ring, and as they travel around it, magnets are used to accelerate the protons to very high energy. In fact, there are two such beams, one traveling clockwise, the other counterclockwise. At specific spots, the beams are allowed to cross (any Ghostbusters fans out there? :) and at the intersection points, these energetic protons undergo reactions, producing various clouds of secondary particles in big (warehouse-sized!) detector systems. These are the reactions that we compare with theory. The experiments that finally uncovered the Higgs bosons were exactly this - reactions in the LHC detector systems.

Finally, when Greene is listing the experimental signature "long shots," he mentions the cosmological constant. I was a little bit confused about this, since I know that Einstein took it out of his equation, yet here it sounds theoretically possible and measurable? How does the existence of a cosmological contact affect relativity?

Einstein recognized that the general relativity equations can include a constant energy term without changing the fundamental nature of the equations. His original version included it, but he felt this was a mistake, and eventually took it out of later papers. There was no experimental evidence for or against such a term, it's just that he thought the term spoiled the beauty of the theory and made things unnecessarily messy. Ever since then, some physicists have been studying the theory with and without the cosmological constant and working on experiments to determine whether such a term is supported by reality.

The term itself doesn't affect the formulation of the theory of general relativity. The case without the constant is just the more general equation where the value of the cosmological constant is zero. If we solve the equations for the universe as a whole with a zero cosmological constant, we get a predicted evolution for the universe. If we change the value of the constant, the predicted expansion/contraction of the universe and the rate at which it occurs changes. We believe that the term is small, if it is in fact non-zero, based on experiments, and so any impact on calculations only occurs over the longest timescales and the biggest distance, at least in classical general relativity. So one of the interesting things about quantum gravity is whether a non-zero cosmological constant will have implication at the quantum level that we might actually be able to observe.

We can find a a shape that predicts nearly any set of particle properties. And that's the issue that some physicists have - if the theory can't make a specific prediction without tailoring by hand, how is this better than the Standard Model?

Yeah, and that's not really something Greene ever addresses, at least not so far.
Actually, it's been helpful to be able to ask you when something is part of string theory and when it is not. He's writing about string theory as if it's fact at this point, and I'm having a hard time distinguishing when something has already been proven and is just used (perhaps differently) in the theory, or when it's part of the theory and contingent upon it being proven.

So my brain was functioning MUCH better this evening and I finished Chapter 10!

CHAPTER 10: Quantum Geometry - distances in string theory

My first thought starting the chapter was "uh oh... I was always stronger in algebra than geometry." But it wasn't so bad. Here are my questions:

1. Space is curved according to our current understanding of general relativity and geometry (pp. 231-232), but, Greene writes, "string theory asserts this is true only if we examine the fabric of the universe on large enough scales" (232). What shape would it be if we examined it on other scales? And while I'm thinking of it, the name quantum geometry kind of confuses me - is it a portion of quantum mechanics, string theory, or both?

2. Greene briefly mentions dark matter on page 235, referring to evidence that it permeates the universe. What is the evidence, and what is its significance? What could dark matter be (I know we don't know what it is), and how much might it affect the density of the universe?

3. Again related to my confusion between what part of this is referring to quantum mechanics and string theory - Greene says that quantum mechanics invalidates equations of general relativity when we're discussing Planck length. Is this a feature of quantum mechanics alone, or the different geometry he's using in string theory? (I didn't quote enough of the book to remember exactly what the discussion was, other than the discussion was about the expansion of the universe.)

4. "This leads us to a key fact: For any large circular radius of the Garden-hose universe, there is a corresponding small circular radius for which the winding energies of strings in the former universe equal the vibration energies of strings in the latter, and vibration energies of strings in the former equal winding energies of strings in the latter" (240) - First of all, this is a terribly long sentence and by the time I got to the end, I had no idea what it was saying. Could be break this down a bit.

Secondly, he does on: "As physical properties are sensitive to the total energy of a string configuration - and not how the energy is divided between vibration and winding contributions - there is no physical distinction between these geometrically distinct forms for the Garden-hose universe" (240-241).

He addresses some of this later, but here's the questions I had about this as I read:
Is there's no physical difference, how do you tell the difference? Are there essentially "two answers" for a radius like those equations where "x" could have multiple numbers? How is it useful to have two answers?
Is the universe expanding either way?
NOTE - I think I kind of get what he's saying when he starts explaining the inverse and "bouncing" universe that results in simply measuring things differently. But seems to me not to be a very clear theory if there are two opposite ways to explain the same thing.

5. On page 254, Greene briefly mentioned that we don't exactly know the implications if dimensions are not circular. Does this mean that what he's discussed about distance is NOT essential to string theory? Or would the discovery of dimensions in a different shape affect part or all of the theory?

6. Finally, is it not so much that there are two answers as it is one can be used instead of the other to simplify the math (mirror symmetry)? (Dare I ask this when I know it's already complicated math...) What gets simplified?

I think that's it. I will be reading some fluffy fiction now to rest up my brain for Chapter 11. :)

*bump* on questions for Chapter 10.

Tonight's my book discussion and tomorrow I have jury duty, but I'm hoping to get to Chapter 11 over the weekend so no rush. Just didn't want it getting lost in the many threads. :)

Arghhh! Completely missed them!

Probably doesn't help that I'm reading it so slowly that now you're now tutoring two people. (Sorry about that!) :)

Like I said, I won't even start the next chapter 'til at least tomorrow (it's not going to be my read of choice while waiting for jury duty), and probably won't have it finished 'til the weekend, so no hurry at all.

1. Space is curved according to our current understanding of general relativity and geometry (pp. 231-232), but, Greene writes, "string theory asserts this is true only if we examine the fabric of the universe on large enough scales" (232). What shape would it be if we examined it on other scales? And while I'm thinking of it, the name quantum geometry kind of confuses me - is it a portion of quantum mechanics, string theory, or both?

He's referring back to the idea of a quantum foam at very small scales. One of the ideas that seems to fall out of the desire to unite QM and general relativity/gravity is that space-time itself is quantized - it comes in discrete chunks. So there's no smooth curvature to space at the smallest scales (remember the Planck length?). Quantum geometry is what folks call this effort to understand geometry when it's made discrete. Different theories use the term differently. Since Greene is a string theorist, he's referring to things that matter to strings. Mostly this means how you describe the curvature of space mathematically when there are discontinuities and distance between two points when space isn't smooth. Other theorists studying loop quantum gravity use the term to refer to how geometry is expressed through the mathematical language of quantum mechanics. It's bleeding edge stuff!

2. Greene briefly mentions dark matter on page 235, referring to evidence that it permeates the universe. What is the evidence, and what is its significance? What could dark matter be (I know we don't know what it is), and how much might it affect the density of the universe?

The evidence for dark matter is all indirect. The first signs that something is up came from folks studying how galaxies move and how big masses affect things like gravitation lensing of light (lift is bent as it travels near big things, and this can be directly observed). Basically, the math only matches reality if the universe is some 8 times more massive than we think it is based on astronomical observations. That means there's a bunch of stuff out there we can't see. The big question is what that stuff is. Leading candidates: ordinary matter that doesn't produce light and so can't be observed, or some new subatomic particle that's heavy and only interacts with other particles by gravity (perhaps the weak nuclear force). The leading candidate for the latter is a Weakly Interacting Massive Particle, or WIMP. No direct evidence has been found for any dark matter yet!

3. Again related to my confusion between what part of this is referring to quantum mechanics and string theory - Greene says that quantum mechanics invalidates equations of general relativity when we're discussing Planck length. Is this a feature of quantum mechanics alone, or the different geometry he's using in string theory? (I didn't quote enough of the book to remember exactly what the discussion was, other than the discussion was about the expansion of the universe.)

We have a perfectly good classical theory of electromagnetism, at least for everyday applications. We use Maxwell's equations all the time to engineer telecommunications, electronics, etc. These are equations that describe electric and magnetic fields.Yet, when we look at the quantum level, those equations don't apply. We find that electromagnetic forces are really an exchange of photons between two charged particles, which mathematically isn't anything like a classical field equation. So in that sense, quantum mechanics invalidates the Maxwell equations. But really, we also require that quantum mechanics reproduce the results of classical theory when the appropriate conditions are included (i.e., we're describing something big). This is called a classical approximation, or sometimes semi-classical theory. And in fact, QM produces the Maxwell equations in the case where we're describing lots of photons over macroscopic distances.

He means the same thing for string theory and general relativity.Frankly, it's a bit of a cheat since as with electromagnetic theory, we require that QM is consistent with general relativity when the appropriate conditions are applied. Otherwise we can't call it a unified theory.

4. "This leads us to a key fact: For any large circular radius of the Garden-hose universe, there is a corresponding small circular radius for which the winding energies of strings in the former universe equal the vibration energies of strings in the latter, and vibration energies of strings in the former equal winding energies of strings in the latter" (240) - First of all, this is a terribly long sentence and by the time I got to the end, I had no idea what it was saying. Could be break this down a bit.

Secondly, he does on: "As physical properties are sensitive to the total energy of a string configuration - and not how the energy is divided between vibration and winding contributions - there is no physical distinction between these geometrically distinct forms for the Garden-hose universe" (240-241).

He addresses some of this later, but here's the questions I had about this as I read:
Is there's no physical difference, how do you tell the difference? Are there essentially "two answers" for a radius like those equations where "x" could have multiple numbers? How is it useful to have two answers?
Is the universe expanding either way?
NOTE - I think I kind of get what he's saying when he starts explaining the inverse and "bouncing" universe that results in simply measuring things differently. But seems to me not to be a very clear theory if there are two opposite ways to explain the same thing.

Ok, so we talk about tiny strings that vibrate as a description of subatomic particles. There's a mathematical transformation that can be applied to the string theory equations that describes the universe in a different way. When we do this there's a one-to-one correspondence between the description of particles as vibrations on a string and as a string wound multiple times around a cylinder. One-to-one equivalences are neat in math, since that means we can take equations that are really hard to solve and turn them into something easier and be assured that the answers we get still apply and are correct for the original problem. That's what's being done here.

In the case of string theory, we get solutions to the equation that have different combinations of winding and vibrating modes, but have the same total energy. It's kind like making change. There are multiple ways of combining coins to get a dollar, but each combination still equals a dollar. In QM, this is called degeneracy, when you get multiple solutions to an equation that are equal, in the math, the level of degeneracy needs to be accounted for.

The question of whether the universe is expanding is still an open one, and Greene's being a little presumptuous in his description here. I'd say he's described an interesting theory, but lots of work still needs to be done to sort out how well this describes reality.

5. On page 254, Greene briefly mentioned that we don't exactly know the implications if dimensions are not circular. Does this mean that what he's discussed about distance is NOT essential to string theory? Or would the discovery of dimensions in a different shape affect part or all of the theory?

I think he just means that the math has only been worked out for circular windings. He seems to be speculating that there might be some physical effect associated with non-circular wings, but I'm having trouble figuring out what that shape would be that would allow windings and not be topologically equivalent to a circle. So I'm stumped!

6. Finally, is it not so much that there are two answers as it is one can be used instead of the other to simplify the math (mirror symmetry)? (Dare I ask this when I know it's already complicated math...) What gets simplified?

Yeah, it's not that there are two answers, it's that the string problem can be translated into a different problem that gives an equivalent answer. This is a common approach to solving equations in physics. For instance, we can write down equations of motion for a pendulum swinging, and can do some fairly sophisticated calculus to solve for position of the pendulum as a function of time. Or we can do a mathematical transformation called a Fourier transformation that changes the equation of motion over to calculate frequency of the pendulum. This becomes an algebra problem instead of a calculus problem. We then do the inverse transformation on the answer and get the solution to the original equation back.

It's going to be tough to go into what exactly gets simplified without a long discussion on string equations of motion and how to solve them as best we can. In this case, the T-duality transformation (the technical name for the transformation used) turns the set of linked nonlinear differential equations into a set of unlinked linear ones that can be solved independently. If you really want to know more, I can send you some papers on the subject… :)

I think that's it. I will be reading some fluffy fiction now to rest up my brain for Chapter 11. :)

Well. I'm deep into Truman for the US Presidents challenge, so no physics involved until we get to the development of the atomic bomb! :)

Sorry for being gone so long! I've had a couple of books to read for work for the book discussion I facilitate, and while it does barely cut into my total reading time, it has affected the amount of time I feel like I can devote to a difficult book.

Here are my questions for Chapter 11:

1. In the beginning of his discussion about the tearing of space, Green illustrates what happens to a Cailibi-Yau shape if the sphere in the middle changes - it gets pinched and could, theoretically, tear. Is there a sphere like this in all the proposed Calibi-Yau shapes? If there are a finite number of Calibi-Yau shapes possible in a given theory, can the shape only change from one to another, even if the fabric of space tears?

2. What does a "tear" in the fabric of space actually mean?

3. Greene mentions something about a string sort of wrapping around the tear, canceling out any negative effects. What does that mean? What could it look like?

4. Just because it can mathematically be possible for the fabric of space to tear, does that really give us any indication that it does? How would we prove it?

1. In the beginning of his discussion about the tearing of space, Green illustrates what happens to a Cailibi-Yau shape if the sphere in the middle changes - it gets pinched and could, theoretically, tear. Is there a sphere like this in all the proposed Calibi-Yau shapes? If there are a finite number of Calibi-Yau shapes possible in a given theory, can the shape only change from one to another, even if the fabric of space tears?

Yes, this is a possible C-Y manifold in a higher-dimensional form and it could theoretically tear. The changes to the manifold he uses as a demonstration is an example of a smooth deformation in topology and differential geometry. There's a way to describe this mathematically. Jumps from one type of manifold to another or introducing discontinuities like tears are much more difficult to deal with mathematically, and tend to force us to special cases like the sample he shows.

2. What does a "tear" in the fabric of space actually mean?

Beats the heck out of me. :) we think of spacetime as smooth and continuous. Technically, this means we think of spacetime as an infinitely differentiable manifold - no matter how many times I differentiate a function on the manifold, I can always do it again. If there's a tear in spacetime, it's possible that, for instance, a billiard ball can have a position and velocity on one side of the tear and a different one on the other side without an interaction in between. This has some weird implications for conservation of energy and momentum that fly in the face of our understanding of physics.

3. Greene mentions something about a string sort of wrapping around the tear, canceling out any negative effects. What does that mean? What could it look like?

Since there are bad implications for energy conservation, folks speculate that if such a thing were to occur, it must somehow Be shielded from he rest of the universe. Greene's suggesting that cosmic strings could do this by covering the tear completely like a ball of yarn can be wrapped around a stone. Physically, I think that this would look like a very massive particle - remember that more windings of a string looks like higher modes of vibrations, which represents more massive particles.

4. Just because it can mathematically be possible for the fabric of space to tear, does that really give us any indication that it does? How would we prove it?

My guess is we'd need to work out a theory that predicts a particle spectrum, then look for them, probably as remnants of the Big Bang or some other cosmic event. My guess is they'd be really rare, so hard to find.

</i>
I started Chapter 12 this morning. This is a loooong chapter, but I'll try not to take three weeks to post again. :)

Woohoo, another chapter read!

Here are my CHAPTER 12 questions (with a few observations thrown in):

M-Theory - the unification of five-six theories.

1. What happens to M-theory if one or more "parts" (the five or six "arms" of the starfish, as Greene puts it) turn out not to be correct? Does it work in a modified way, or fall apart completely?

Come to think of it, that was a question I had at the beginning of the chapter, but I think he kind of answers it in the end. The separate theories are less parts of a unified whole than they are a map of all possible outcomes, so if one outcome is ruled out, it just makes a rather loose theory more precise.

I was also going to ask how a tenth space dimension unifies the five theories, but Greene answers that in his discussion of duality.

2. Why are there membranes and blobs in M-theory? What are they?

His explanation of perturbation helped me understand the emphasis on the approximate nature of the equations used in string theory.

3. Does the duality of the various theories mean that no matter whether the coupling constant is less than or greater than 1, our equations are still close? Or could we still be way off if the coupling constant turns out to be an unexpected value?

4. "Physicists use the term duality to describe theoretical models that appear to be different but nevertheless can be shown to describe exactly the same physics" (298). Does this mean that one mathematical equation is insufficient to describe the universe, or just that the theory is incomplete if we use multiple equations to describe a significant duality?

5. BPS states - the idea of "charges in a box" seemed a little manufactured to me. Can you explain it a little bit more, and give me an example of a way it's used (either in theory or in the real world)?

If the coupling constant in Heterotic-E theory is larger than 1, an eleventh dimension comes into play as the string itself becomes cylindrical (309). Since this dimension isn't one in which the string can vibrate, most of our approximations assuming a ten-dimensional universe still work out.

6. So it sounds like M-theory is almost unknown. Do we have enough information to even say that it pulls together all five string theories? Have there been any developments on the theory since the writing of this book?

If I understand him correctly, the six theories (counting eleventh dimensional supergravity) are basically a map of a range of possibilities, and the actual theory can be refined as some aspects of these are ruled out.

7. On page 316, Greene listed a whole bunch of multidimensional possibilities beyond one-dimensional strings. Is this where the possibility of 26 dimensions come in? What are earth ARE these multidimensional things?

8. Super-massive objects - if they exist, why haven't we observed them? Wouldn't they be hard to miss?

That's all for now. I make no promises about when I'll finish the next chapter, but I'm feeling pretty good about my reading now. At the moment, having only a few chapters left is rather motivating to keep on with it, and since I had book discussion last night, I've got a whole month before I run into an actual deadline for finishing a book. :)

1. What happens to M-theory if one or more "parts" (the five or six "arms" of the starfish, as Greene puts it) turn out not to be correct? Does it work in a modified way, or fall apart completely?

Come to think of it, that was a question I had at the beginning of the chapter, but I think he kind of answers it in the end. The separate theories are less parts of a unified whole than they are a map of all possible outcomes, so if one outcome is ruled out, it just makes a rather loose theory more precise.

Yep, that's right. M-theory is a more global theory that encompasses string theory. Any parts that don't match our universe just make the broader theory more specific.

I was also going to ask how a tenth space dimension unifies the five theories, but Greene answers that in his discussion of duality.

2. Why are there membranes and blobs in M-theory? What are they?

His explanation of perturbation helped me understand the emphasis on the approximate nature of the equations used in string theory.

So, originally we thought of fundamental particles as point particles - no size or shape at all. Then folks began to think about particles as 1-dimensional object - strings in string theory where the strings have length but no diameter. The next logical step is to think of particles as a 2-dimensional object - think of a drum head that has no thickness that can now vibrate in 2 dimensions; this is a membrane. A blob is the next step - an extended object that can vibrate in three dimensions.

Why do this? In string theory, we identify particles with particular vibrations of the string. Unfortunately this identification doesn't work so well. It's not specific enough, it doesn't match experimental results, etc. The thought is that if we now allow vibration in more dimensions, the math might work out better - the resulting spectrum may be more like the real universe.

The motivation, I think, is in looking around us. Macroscopic objects aren't limited to one spatial dimension, or two. They exist as three-spatiall dimension objects. We naively expect that the same should be true of microscopic objects. This is very active research, though, so the picture isn't at all clear, nor is there solid support for particles as extended objects. In fact, experiments with electrons, to very good accuracy, match the point particle theory, strongly suggesting that the point particle idea is right. Or at least that the size of the electron is so small we can't distinguish between a point particle and an extended object.

3. Does the duality of the various theories mean that no matter whether the coupling constant is less than or greater than 1, our equations are still close? Or could we still be way off if the coupling constant turns out to be an unexpected value?

The general form of the equations should be valid for any coupling constant, but since this describes the strength of interactions, if the value is too weird, the universe described isn't possible - the description of the beginning of the universe doesn't allow for a stable expansion, for instance. So there are, I think, some limitations on how far off the nominal the coupling constant can be.

4. "Physicists use the term duality to describe theoretical models that appear to be different but nevertheless can be shown to describe exactly the same physics" (298). Does this mean that one mathematical equation is insufficient to describe the universe, or just that the theory is incomplete if we use multiple equations to describe a significant duality?

Mmmm, neither. One equation (or at least, one theory contained in a set of equations) probably is sufficient to describe the universe. Duality is really just a way to transform an equation into a different but equivalent one. As a simple example, we can measure the intensity of an electric field as a function of time and use Maxwell's equations to describe that field. Generally on a graph, this will look like a squiggly line that bounces around all over the place. Or we can use a particular mathematical technique called the Fourier transform to describe that same field as a function of time. The field is the same, but now we can see that the field is oscillating at a particular set of frequencies. This description is tons easier to deal with, but describes the same thing. In fact, this wi what your car radio does when you tune it to a particular station. It only looks at one particular frequency in the frequency space.

There are many dualities like this in physics. The point is always to develop an equivalent but easier description of the problem. And by equivalent we mean "predicts the same result". Dualities are always some sort of mathematical transformation that can be applied. Fourier transforms are one, there are a bunch more. In the case of string theory, the transformation comes from geometry and topology, but the intent is the same.

5. BPS states - the idea of "charges in a box" seemed a little manufactured to me. Can you explain it a little bit more, and give me an example of a way it's used (either in theory or in the real world)?

If the coupling constant in Heterotic-E theory is larger than 1, an eleventh dimension comes into play as the string itself becomes cylindrical (309). Since this dimension isn't one in which the string can vibrate, most of our approximations assuming a ten-dimensional universe still work out.

"Charges in a box" is code for a standard way physicists limit the scope of certain problems. For instance, we can picture living on Earth as being inside a gravity well where we have to climb "uphill" to get out of Earth's influence, meaning we're stuck here unless we apply energy to go away from the Earth. This is the kind of box he's discussing. Particles in atoms are another example. Electrons don't leave an atom unless given enough energy to get away. Within the confines of the atomic "box", they're free to move pretty much anywhere, but are confined to within some distance of the nucleus.

What he's really talking about is what we call boundary conditions for the differential equations that describe the motion of the charges in that particular configuration. "Charge in a box" is the particular condition where we force the probability of the particle being outside the box to zero.

6. So it sounds like M-theory is almost unknown. Do we have enough information to even say that it pulls together all five string theories? Have there been any developments on the theory since the writing of this book?

Well, originally the "M" stood for membrane. Many say, though, that it really stands for "mysterious" or "magic", which tells you something about our understanding of the theory. :)

This is another very active area of research. And frankly, only minor progress has been made since the book was written. The field is a bit chaotic.

If I understand him correctly, the six theories (counting eleventh dimensional supergravity) are basically a map of a range of possibilities, and the actual theory can be refined as some aspects of these are ruled out.

Yes. That's the idea. Although some physicists think that we may not have enough info to ever narrow it down. Others think it's all off-base, and so won't pan out.

7. On page 316, Greene listed a whole bunch of multidimensional possibilities beyond one-dimensional strings. Is this where the possibility of 26 dimensions come in? What are earth ARE these multidimensional things?

Frankly, this is all pretty speculative stuff. The physicists have found some cool mathematical toys and are rooting through the toolbox! :)

On of the problems is that the idea of dimension is getting thrown around a lot. First there's the dimensionality of space-time. The experimental evidence so far says space-time has four dimensions, one time and three space. String theory predicts that there are more spatial dimensions - 9, 10, 11, 26, etc, depending on which theory we like. There are tricks like compactification with Calibi-Yau manifolds to make these higher dimensional space-times look like 4-D space-time.

There's also the dimension of the objects that live in space-time. As crude example, think of an inflated balloon. If the thickness of the balloon is very thin, that balloon is essentially a two-dimensional thing (the surface of the balloon) that lives in three space dimensions. Now, a balloon or a particle can't have more dimensions than space-time, but there's nothing that forbids it from having less. So a particle could be a point, a 1-D string, a 2-D membrane, a 3-D blob, or an 8 dimensional thing in a 9 dimensional space-time. As to what a multidimensional object really *is*? Beats the heck out of me. :)

8. Super-massive objects - if they exist, why haven't we observed them? Wouldn't they be hard to miss?
This is also an area of basic research. supermassive black holes may have been seen in some pretty far away places. But more observations are needed and the next decade should be pretty telling.

I stumbled across this thread when my copy of the book arrived, and have been reading the posts as I read the chapters. My thanks to you both! The Q&A has greatly enhanced my understanding of the subject. Most helpful, I think, have been your comments, DrNeutron, about when Greene is branching out into speculation. Without your help, I probably would have read the whole thing as factual. I'm looking forward to lurking around? through? the topic for the next book. :)

>100 JudiY: Hi Judy! Glad you were able to get something out of the tutored read. I think I myself will be taking a break from physics for a few months, but you may get a kick out of this tutored read too: http://www.librarything.com/topic/140388 (on The Fabric of the Cosmos).

Alright, here we go with Chapter 13! Black holes have absolutely fascinated me since I was a kid, so I really enjoyed this chapter. I don't have as many specific questions (though I'd be happy to read more if you have any thoughts, explanations or corrections you think I should know).

Here's a couple though - he mentions the possibility of black holes being gigantic elementary particles, as well as them being related to a multiple brane wrapping a tear in multidimensional space. Is he saying that there are multiple possibilities for what a black hole is?

He says later in the chapter that if a tear were to happen in a Calabi-Yau shape that it would reshape itself, but with one more hole - and thus, another possible particle. How many C-Y shapes are even possible in a given theory? Is it theoretically possible for certain strings to only exist when a C-Y shape is the right one for it, and ultimately only in certain places?

Have black holes been observed "evaporating," or is that merely theoretical?

Umm.... I think that's all I had. He throws out some intriguing possibilities, but in this chapter it's a little more clear than in the others that he's talking primarily in hypotheticals. I'd be interested in knowing if anything has been ruled out or discovered since his writing though.

Yeah, I'm a big fan of black holes. :) Seriously, they're the classic General Relativity application I read about when I can.

1. He's saying there are different things that look like what we think of as a black hole - a singularity in spacetime behind an event horizon. The things he describes are mathematical objects that could be interpreted this way.

2. Hmmm. I'm not an expert here, so take my opinion with a grain of salt on CY-tears and such. But yeah, if I understand the theory right, a new hole in the manifold would mean a new type of particle is possible. I think things would remain the same otherwise, though. Other than that, he's way beyond my understanding at this point... :)

3. Evaporating black holes haven't been directly observed yet, nor has Hawking radiation, the primary mechanism for evaporation. However, back in 2010, some researchers set up lab conditions that are supposed to simulate a black hole event horizon and claim to have observed Hawking radiation. THe jury's still out on whether they truly did simulate a black hole. Also, the GLAST spacecraft is working to observe the gamma ray emission of primordial black hole evaporation as they disappear from evaporation. No results yet as far as I know. And the CERN folks could theoretically observe the evaporation of microscopic black holes in their proton beam experiments. Again, nothing yet. But interesting work's being done!

4. As we've talked about before, the biggest conflict between the book and recent work is that the CERN Higgs experiments matched up so well with the Standard Model, throwing the need for string theory into question. The problem all along with string theory and it's meta-theories like M-theory is that (i) predictions are all over the ma and the theories aren't readily testable, and (ii) recent experiments don't show any real discrepancies with the Standard Model. At least so far, anyway. Of course, there's still the desire to find a way to unify gravity with the other forces and understand what happens on the very smallest spatial scales and at the beginning of the universe. So we'll see folks keep working, I'm sure!

W00t! I finished! I don't really have a ton of questions on Chapters 14 and 15, as they were largely summary and "looking forward" chapters. Made me wonder why it took me staying home with a cold before I could manage to finish the book... but hey, six months later I'm done. ;)

Here are my last set of questions on the final chapters -

Chapter 14: Reflections on Cosmology

1. "In the beginning, all of the spatial elements of string theory are tightly curled up to their smallest possible extent, which is roughly Planck length" (358) - and then wrapped strings and their antistring partners collide and annihilate each other, allowing 3 of the dimension of a C-Y shape to expand.

I'm having a tough time framing this question, but at its heart, I think what I'm wondering is why would this happen, and is this explanation possible? What are the implications if the alternate theory he describes of a cold universe that started expanding and warming up? Or are both of these just possibilities of how the universe began if string theory (or M-theory) turns out to be right?

Chapter 15: Prospects

2. I was a little confused about his description of zero-brane membranes. Can you explain about that in more detail?

And finally, any last thoughts as we wrap up our tutored read?

Thanks very much for doing this, and for your patience when it turned out I couldn't quite read it as fast as I'd hoped. It was a huge help to me to feel assured when I did understand things, and to help me gain a greater understanding of what I was reading.

Yay! I hope you enjoyed dipping into the weird world of particle physics. :) On to the questions!

1. Ok, so if the universe is expanding, one can "run the clock backward" to the very early universe. This is a single small spacetime about the size of the Planck length (because QM seems to indicate that nothing can be smaller than that). In the string theory picture, this space contains strings and anti-strings that collide. Now, this is an 11- or 26-dimensional space, right, and at the beginning of the universe, all these dimensions apparently look alike. Mathematically, these collisions bring about the collapse of the higher dimensional spacetime into a space with 3 flat space dimensions, one flat time dimension, and the remaining dimensions curled up into a particular "compactified" C-Y manifold. Keep in mind that this all happens in the first 10^-43 second of the universe, so it's as instantaneous as we know how to describe. This process, by the way, is called symmetry breaking. There's nothing special about which dimensions got picked to be flat and which got curled up; the specific ones are randomly selected by the dynamics of the initial interactions. Once that symmetry breaking occurs, our universe is essentially set. The rest of the time it's been around has been in responding to the overall expansion as a result of that first explosion and local structure like galaxies and stars that formed ultimately from quantum fluctuations in the matter-energy field of the universe.

Now, this is the stringy picture of how the universe started. If you as a loop quantum gravity person, all this nonsense about colliding strings and compactification becomes moot. Their description of the process looks more like what's called cyclic cosmology - the universe has always existed as a sequence of expansions and contractions. What we call the Big Bang is really the collapse of the previous universe and rapid expansion of the current one. There's speculation about whether a universe can change properties - things like the relative strengths of the fundamental forces - that might cause a very different universe this time compared to last time. All of this is very speculative!

The lack of support for superstring theory and higher dimensional objects by the recent CERN experiments really calls into question this whole idea of compactification and symmetry breaking as it's applied to cosmology. Stay tuned to see what happens!

2. We use differential equations to describe the motion of strings. Differential equations have solutions that are not unique. For instance, I can add two solutions of a differential equation and that sum is also a solution to the DE. Multiplying a solution by a constant results in another solution to the DE. So we have to impose some boundary conditions on the overall solution to derive the unique solution for a particular problem.

The boundary of an open string is the set of two points at each end of the string. That's the physical limit of the object. There are in general, two types of boundary conditions we can impose to narrow the general solution to our particular solution. One of these types is called the Dirichlet condition, and just means that we require the ends of the string to be confined in some way. In a guitar string, the ends of the string are fixed and can't move. This is the primary example students use to learn about this stuff.

It's possible to confine the ends of strings to more extended objects. For instance, they could be confined to a line, or a surface. Or even unconfined, which means confined to an object with the same number of dimensions as the universe. Confining an object to movement in some number of dimensions is called confining the ends of the string to a manifold (which is a fancy technical term for a surface of some dimension), or membrane, or brane. Confining the ends to a line means confining the ends to a D1-brane. When the ends are confined to a point, that means they're confined to a D0-brane. So, long answer to your short question, a zero-brane is a point, and a string confined to D0-branes on the ends looks like a guitar string.

So I hope your reading has given you a sense that the physics world is in the midst of a real shake-up. There's been a generation of physicists working on string theory. Have these people been off on a wrong tangent? Is there some room for the recent experimental results to support string theory ideas? It'll be interesting to see where we are in ten years!

I hope you enjoyed dipping into the weird world of particle physics. :)

Very much so! Thanks for all your helping me understand and expanding, explaining, or correcting as needed! (And if nothing else, reading this makes me get some of the nerdier jokes in The Big Bang Theory...not all, but some of them. (: )

So I hope your reading has given you a sense that the physics world is in the midst of a real shake-up. There's been a generation of physicists working on string theory. Have these people been off on a wrong tangent? Is there some room for the recent experimental results to support string theory ideas? It'll be interesting to see where we are in ten years!

I'll be looking forward to seeing what happens in the next decade or so; I think it's going to be quite interesting.

Brian Greene was on The Colbert Report last night! It was hilarious, of course:

http://www.hulu.com/watch/598660

That was great! "Don't patronize me Mr. String Theory, I know the sun is hot!" Thanks, Nora.

Bump