“One aspect of quantum mechanics that is difficult for budding young scientists to accept is that the equation proposed by Schrödinger predicts that under certain conditions matter can pass through what should be an impenetrable barrier. In this way quantum mechanics informs us that electrons are a lot like Kitty Pryde of the X-Men, who possesses the mutant ability to walk through solid walls (as shown in fig. 32), or the Flash, who is able to “vibrate” through barriers. (illustrated in fig. 33). This very strange prediction is no less weird for being true. Schrödinger’s equation enables one to calculate the probability of the electron moving from one region of space to another even if common sense tells you that the electron should never be able to make this transition. Imagine that you are on an open-air handball court with a chain-link fence on three sides of the court and a concrete wall along the fourth side. On the other side of the concrete wall is another identical open-air court, also surrounded by a fence on three sides and sharing the concrete wall with the first court. You are free to wander anywhere you’d like within the first court, but lacking superpowers you cannot leap over the concrete wall to go to the second court. If one solves the Schrödinger equation for this situation, one finds something rather surprising: The calculation finds that you have a very high probability of being in the first open-air court (no surprise there) and a small but nonzero probability of winding up on the other side of the wall in the second openair court (Huh?). Ordinarily the probability of passing through a barrier is very small, but only situations for which the probability is exactly zero can be called impossible. Everything else is just unlikely. This is an intrinsically quantum mechanical phenomenon, in that classically there is no possible way to ever find yourself in the second court. This quantum process is called “tunneling,” which is a misnomer, as you do not create a tunnel as you go through the wall. There is no hole left behind, nor have you gone under the wall or over it. If you were to now run at the wall in the other direction it would be as formidable a barrier as when you were in the first open-air court, and you would now have the same very small probability of returning to the first court. But “tunneling” is the term that physicists use to describe this phenomenon. The faster you run at the wall, the larger the probability you will wind up on the other side, though you are not moving so quickly that you leap over the wall. This is no doubt how the Flash, both the Golden and Silver Age versions, is able to use his great speed to pass through solid objects, as shown in fig. 33. He is able to increase his kinetic energy to the point where the probability, from the Schrödinger equation, of passing through the wall becomes nearly certain.”

In “The Physics of Superheroes” by James Kakalios

One problem with travelling faster than light is that there is no requirement that this only happens in a time like dimension. What if Superman is passing through every point of a particular inertial frame within the lower bound for the smallest possible electro-chemical event? In that case, Superman can be decisive over every action within a particular light cone as it propagates (except that we don't know what impact the interface between the quantum world and the classical world has, and at what point the laws switch over. Schrödinger's cat magnifies the quantum up to the large classical, but at the chemical-electrical level that you mention Superman could become subject to quantum fluctuations which would not be good for his health, never mind the control of subsequent ramifications of events in the light cone.) I believe your reliance is perfectly justified. Both Marvel and DC have embraced a form of the Many Worlds hypothesis of Hugh Everett. DC's "Crisis On Infinite Earths" story-line is based precisely on this notion. I guess I am relying on a 'many worlds' interpretation and always choosing the one where Supers prevails. From the way I understand quantum tunneling, and I do know a thing or two about quantum physics, the matter tunneling through would simply teleport onto the other side of said wall or bad guy as opposed to moving at a constant speed through the space between the two. Along with the fact that quantum physics typically only applies to members of the quantum realm (rip Mrs. Pym)

I can however pose a different theory. The amount of space both between atoms in molecular structures, as well as within atoms themselves, is massive. There is more empty space in an atom than actual atom parts. The reason that atoms can't move between these spaces, and why we can't walk through walls (I know Heinlein wrote a novel called “A Cat Who Walks Through Walls”…), is the negative change in electrons; and yes, I do know Kakalios touched upon this. The negative charges, while very weak, are like two magnets aimed negative sides at each other. It's hard to touch the two together. However... if you disabled the negative charge, there would be no problem at all moving through a solid object. But wait! The negative charges are actually what keep atoms together... and they bond molecules... so... if you disable the charges then the entire structure would basically atomize into nothingness... not fun unless you're a villain from James Bond. So here is the possibility. What if instead of fully cutting off the charge, they just have the ability to reduce it? Lower the electron charge constant within themselves to a perfect balance... right between weak enough to phase through, and strong enough to still hold the molecules together? Finding this balance would allow the physics of phase shifting to work perfectly. Actually, I think the Pauli Exclusion Principle plays a much larger role in preventing atoms from passing through each other. Even without the charge of the electron getting in the way, an atom trying to pass through the electron cloud of another atom would run into the issues of degeneracy pressure: electrons, protons and neutrons are fermions and cannot occupy the same quantum state as another fermion at the same time. Electrons are not merely particles, they exist in a superposition of their possible states in any particular orbital around the nucleus, so if the electron cloud of one atom passed through that of another, it would require those electrons to occupy the same state, because their superpositions would overlap. Quantum tunneling on the other hand, would still make some sense. As I said above, it occurs instantly, but that doesn't mean the superhero would have to phase through the wall instantly; it would make much more sense for their individual particles to tunnel simultaneously and rapidly through each atom in the material they were passing through, giving it the appearance of a continuous motion-- assuming theirs had the ability to control the quantum mechanical action of all of their atoms.

Ok. “Tunneling” is one thing. What about the rest of the Superheroes stuff? Nerd train incoming...

The problem with Superman goes a lot deeper than the points Kakalios touched on. It seems that the creators back in 1933 had a different concept for the character. As I understand it, Superman could not fly when he debuted in Action Comics #1. He could only leap over things that were beyond the range of a normal man. He had quick speed and had great strength. Not sure if he had x-ray and heat vision, or if he blew with the force of a hurricane and froze objects with his breath. Clearly he was not the god he has become. The character changed from a man that could do superhuman things, to a man who is virtually indestructible and has the power to move the planet earth when America got into World War II. The country needed a hero that the Nazis could not stop. In fiction, Superman became that hero because as you pointed out, the limits of what he could do had not been defined.

By the time the war was over, Superman and his god like powers where here to stay and with each new story, it was revealed he could do whatever the plot called for to save the day. A cap on his powers was never imposed because the writers of Superman stories for comic books, television and the silver screen knew they could bring the world to the brink of destruction and no matter how great the challenge, they could tweak Superman's powers, thus allowing him to save the day. However, I agree that a character that cannot be harmed or killed poses a problem for storytelling. As a writer, I created my own superheros and wrote stories. What I found was you had to cheat for the villains to give them an upper hand. Usually this is accomplished by:

[A] The villain gets a hold of a weapon that has the power to kill the hero;

[B] The villain creates a being with equal or slightly stronger powers;

[C] You create a weakness in the hero's armor and allow the villain to exploit it.

This is why Kryptonite was wrote into the story. The only substance that can harm Superman comes from his own planet. When Krypton exploded, rocks from the debris were thrown out into space. Some of them entered the earth's atmosphere becoming meteorites. Harmless to mortals, these glowing green meteors are highly toxic to Superman. First of all it makes no sense that something from the characters home world would have a negative effect on him/her. It has been established that the closer Superman gets to the red Krypton sun, the more his powers fade. So in theory, Kryptonite would have to be remains from the red sun in order to have a negative effect. Rocks from the planet would simply absorb our sun's rays and give off energy that Superman could use. The fact that Kryptonite is green reveals that its inventors did not intend for it to come from the red Krypton sun.

The destruction of Krypton in “Superman The Movie” (1978) was the result of the sun becoming a red giant and dying. “In Man Of Steel” (2013) careless mining of Krypton's core leads to the planet exploding. However the established conclusion is Kryptonite comes from the planet and not the sun. That's one reason why this is not a good weakness for Superman.

The problem I have with Superman is that the whole franchise is taken too seriously when in essence it's an OP dude who will always have enough power to defeat his opponent. The guy can literally fly into the sun for a recharge. Aside from his super strength he has super speed, super hard impenetrable skin, super senses, and super X-ray vision. He's practically impossible to defeat - neither by a direct assault, nor by subterfuge. And since Shad mentioned that at some point Superman gained the power of telepathy - it's impossible to plot anything against him in secret. And the kryptonite - no one can even get close to Superman with that thing since - as I've mentioned above - he has all the super senses: he can see, hear and - I'd argue - feel where the kryptonite is approaching from: he can simply use a pole or his super breath to swat it away. And yet the authors are trying to convince us that he is constantly in some sort of danger - he is not. That's why I prefer Saitame the One Punch Man - the author is aware that the hero is overpowered, and that's why the whole manga is taken light-heartedly - the hero is never in any sort of danger, he destroys all his opponents with a single punch, and he is not feeling any pride in his victories over foes that could destroy the whole planet. Instead he's bored. This type of story is a lot easier to understand, and it does not require the fans to think for the lazy authors and come up with Deus Ex Machinas to cover all the plot holes.

In a nutshell, the problem with Superman is that his powers are too great.

In the first Superman movie he turns back the clock. It may look like what he is doing is 'reversing the polarity of the Earth’s spin (he increases his relativistic mass by 13.7m times by travelling close to the speed of light' but that is just half of the story. The other is that the whole arrow of time reverses because he is flying faster than light. Since Superman has super intelligence, what he ought to do, in order to minimize crime, is to go back to whatever day his decision to fight crime became operational and micro-manage things till the best possible state of society and situation for each individual is achieved. So no more biffing super-villains, just lots of little nudges- e.g. making sure baby Lex Luthor got a nice Teddy from Santa instead of a Ray Gun.

I just wish Kakalios hadn’t limited the book just to high school algebra. Some topics required higher math to be properly addressed.

NB: Don't forget, Deadpool killed the marvel universe. Since he is totally aware that he is a fictional character, he could easily read the DC comics and movies too and kill all of them as well. Did they discover that-far from gaining superpowers from their doses of radiation, The Hulk and Spiderman would actually be bald and sterile and not long for this world? Batman has been shown escaping Darkseid's Omega beams through agility alone. Flash barely escapes those beams and Superman, himself, gets hit by them while actively trying to escape them. Batman must, on the other hand, therefore, have superpowers in terms of strength and agility. More to the point, surely Batman's cape is nowhere near big enough to enable him to glide in the first place. A real-life hang-glider would be far too big and cumbersome to allow flight between the towers of Gotham City. I suspect that a real-life Batman would have to live on Mars to be able to do what he does.

I didn't also see anything about lightsabres in Kakalios’ book...Here’s my suggestion physics-wise:

A replica handle containing a ring of lasers and reflectors and a retractable radio aerial style fencing foil/blade, extremely strong and rigid so it doesn't bend when swiped or on contact with solid objects (similar to an extendable baton). Attached to the end of the foil/blade is a small reflector disk, facing back towards the handle. When activated the foil/blade smoothly extends to its full one metre length in approx 0.25 seconds. Simultaneously a series of lasers are emitted from the handle towards the reflector disk on the end of the foil blade creating loops of lasers and the appearance of a solid, rounded blade. The rapid extension of the light blade as it is switched on would be visible to the naked eye as it would be a mechanical process rather than the instant switching on of a laser. The reflector disk on the tip of the blade would be externally illuminated to the same colour and intensity as the laser blade to disguise it. The inner foil blade would be largely protected from damage in combat by the laser blade surrounding it, which would do the cutting. Authentic sound effects would be motion or contact activated. All you need to do now is sort out how to power it, wireless is not possible but add a long cable hidden up your shirtsleeve/down your trouser leg and a power source and you could probably make one good enough to pop balloons now. I think I need a lie down. Suspend the reflector in a magnetic field, a metre away from the handle - no need to have an extending baton. Switching the device off causes the field to shrink, returning the reflector to its housing at the end of the handle. The laser would cut anything they came into contact with, but the magnetic field would repel the field of another sabre, thus appearing solid when striking the beam of another sabre. That's how it worked in my back-of-an-exercise-book doodles in the late '80s. Unfortunately, blasters and lightsabres have a bigger problem than accuracy, and that's the fact that they vary so much in how much damage they do, without ever being adequately defined. Sometimes (when it's a main character) blaster bolts can just give a nasty burn, other times they're insta-kill. Don't even get me onto the purpose of armour in star wars, when shots to armour are from what I've seen, far MORE deadly than shots to unarmoured characters.. ( )

This is a fun book that teaches some physics such as electromagnetism and quantum phenomena. Features qualitative descriptions with minimal mathematics. ( )

Un buon libro di divulgazione fisica; fornisce alcuni spunti e idee interessanti su come spiegare i principi della fisica con immagini semplici e comprensibili. ( )

It is about the physics of superheroes. It explains the real science behind the people, powers, etc. It explains how the hulk is able to transform, and his shorts don't fall of. It even explains if Vibrainium (Captain America's shield) can block Adimantium (Wolverine's claws. Vibrainium wins, because it absorbs the sound, of the claws, meaning there is no damage. The reason why hulk's pants stay on is because of the CCA (Comic Code Authority), it wouldn't exactly be appropriate for children. This is all accurate because the author is a professor of the School of Physics and Astronomy, in the University of Minnesota. Oh, and he loves superheroes.
It is an amazing book, because it shows the science in a fun way. I completely adore superheroes, as does many people in the world. Knowing that this book exists, is awesome. It teaches science in the most fun way possible. However, some of the parts are confusing, but that is expected. It is also cool to know that the professor claims he knows the science, because he learned it from comic books. He discusses about all the best and most respected superheroes (OK, not all, but a lot). He uses the superheroes, to teach science in he most fun way possible, which is the coolest thing ever. ( )

A fun read by an educator who clearly loves and appreciates comics. Although the science is rather basic for anyone who majored in the field, the exploration of how super-powers might actually work was informative for those of us who lack such a background. And it probably kept a few students more awake in his classes. ( )