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E=mc2: A Biography of the World's Most Famous Equation (2000)

by David Bodanis

Other authors: See the other authors section.

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Examines the science and scientists who provided the backdrop to Einstein's influential 1905 discovery and offers an explanation of the equation from mathematical, historical, and scientific perspectives.
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English (27)  Swedish (2)  Dutch (1)  Finnish (1)  Danish (1)  All languages (32)
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Había oído hablar bastantes veces de este libro, y finalmente lo encontré barato. Y no saben cuánto me alegro. David Bodanis [DB] justifica en el prólogo el porqué de un libro como éste: En una reunión de amigos, todos ellos “de letras”, surgió el tema de conversación de E=mc2, y DB, curioso, preguntó si todos conocían esta ecuación. ¡Por supuesto que sí! ¡Es una ecuación famosísima de Einstein! ¿Y sabéis qué significa? Ah, ni idea. DB utilizó esta excusa para profundizar en todo lo relacionado con esta ecuación, y le salió este estupendo libro.
El libro no comienza con Einstein, que tarda un rato en aparecer. Comienza estudiando qué es la energía y cómo llegó el ser humano a comprender este concepto, nos habla de la velocidad de la luz, del origen del signo “=” y de por qué debe ser un cuadrado y no un cubo.
Pasamos en estos primeros capítulos por las biografías de multitud de científicos y personajes importantes en el desarrollo de la Ciencia. Entre ellos está Voltaire, quien fue amante de Emilie du Châtelet, una señora con una mente prodigiosa que ayudó no sólo a propagar las ideas de Newton traduciéndolo al francés, sino que fue determinante en el establecimiento del concepto de “energía”, entre otras cosas.
Luego aparece Einstein en escena, su trabajo como inspector de tercera en la oficina de patentes de Berna y su gran hallazgo, seguido diez años después por un hallazgo aún mayor, la Relatividad General, que incluye a la especial. Tras conocer a Einstein, su vida privada, sus éxitos y sus fracasos, la ecuación adquiere vida propia y nos vamos a la II Guerra Mundial a ver cómo alemanes y Aliados lucharon por obtener energía a partir de los materiales radiactivos. Aprendemos que los americanos tuvieron antes la bomba en parte gracias a las acciones de sabotaje que sufrieron los alemanes en sus fábricas de agua pesada.
Finalmente salimos de nuestro planeta y viajamos por el Universo, y aprendemos que gracias a la transformación de masa en energía existe la Tierra tal y como la conocemos, con sus elementos más pesados que el hierro, que sólo pudieron formarse en el núcleo a millones de grados de las estrellas viejas.
El libro repasa las vidas de decenas de científicos de primera fila, nos llena de datos interesantísimos, nos muestra cómo hay tantas cosas interdependientes que en realidad el avance de la ciencia es siempre un esfuerzo conjunto, en definitiva, nos da una visión a vista de pájaro del funcionamiento del mundo a base de pequeños vuelos sobre todo lo relacionado con una única ecuación.
El libro incluye un apéndice fantástico: “¿Qué fue de…”? Como en algunas películas, que al acabar nos muestran a los protagonistas unos años después: “Johhn MCCullough siguió en el negocio del caucho. Compró un concesionario en Idaho y vive felizmente casado criando avestruces y caracoles”. Pues lo mismo. ¿Qué fue de James Chadwick, que descubrió el neutrón en 1932, abriendo la puerta al conocimiento del átomo? Pues se fue a vivir a Inglaterra, y se convirtió en administrador del proyecto Manhattan junto a Oppenheimer. Tras el bombardeo de Hiroshima y Nagasaki no pudo volver a dormir sin la ayuda de píldoras en los 28 años de vida que siguieron. Emilio Segrè, colaborador de Fermi, descubrió el Tecnecio. En la tumba de su madre esparció un poco de polvo de este material. “Es muy poco radiactivo y su vida media es de miles de años. Pensándolo bien, no puedo traerle nada a mi madre que vaya a ser más perdurable que esto”. Y así decenas y decenas, estimados lectores.
Por si fuera poco, el libro incluye un montón de notas al final, que no sólo indican la fuente bibliográfica de donde se cita, sino que incluyen un montón de historias que no se encuentran en el texto principal. Aprendemos en las notas, entre otras muchas cosas, sobre los barcos alemanes que llegaron a la Luna, una historia increíble.
Ya en un tono más desenfadado, al ver la contraportada me sorprendí. ¡Ostrás, Joaquín Cortés ha escrito un libro de física! Luego resultó que no, que sólo se parecen un poco
DB menciona en el libro una viñeta cómica en la que Einstein aparece delante de una pizarra cavilando. En la pizarra puede verse E=mc1

E=mc2

E=mc3
Buscando por curiosidad ese chiste no lo encontré (se agradecerá ayuda), pero encontré otro que se le parece mucho:

La gracia del chiste no le hace justicia, sin embargo, a Einstein, quien no llegó por prueba y error a la fórmula famosa, sino tras una deducción matemática basada en la conservación del momento relativista que había propuesto en su artículo de 1905.


Ahora el escritorio tiene mucha mejor pinta. Ha quedado todo bien “cuadrado”.

Sí señor, todo ha quedado bien cuadraaaaaaaado


Para obtener la ecuación E=mc2, se parte del supuesto de un cuerpo que emite dos fotones de la misma energía, uno hacia delante y otro hacia atrás. Al tener los dos fotones el mismo momento lineal (m·v, o más bien hν/c en el caso de un fotón), el cuerpo deberá seguir moviéndose a la misma velocidad que antes. Sin embargo, ha emitido energía, por lo que la energía total del cuerpo debe haber disminuido un poco. Estudiando exactamente cuánto ha disminuido esa energía se llega a la fórmula. Los curiosos avezados en física pueden ver aquí una reconstrucción breve del razonamiento de Einstein: De dónde surge E=mc2

Mi nota para este libro: Muy bueno y muy completo. ( )
  Remocpi | Apr 22, 2020 |
This is not really a book about E=mc² equation per se, i.e., it's not a physics book. It's more a book about the atomic bomb which was something I was not expecting. For those of you expecting something more Physics-oriented, here's a quick rundown of the equation.

There's a lot of confusion surrounding this equation caused by oversimplification. As it stands, the equation gives the energy equivalence of the mass of an object, and as this post goes on to say, there's a more complicated expression connecting energy and momentum in a reference frame in which the momentum is non-zero: E^2 = p^2c^2+m^2c^4. So yes, mc^2 gives the total energy only in the rest frame. Einstein did initially introduce two sorts of mass, the "rest mass" and the "relativistic mass", and if you interpret m as the relativistic mass then E=mc² is valid in all inertial frames. But Einstein distanced himself from the concept of relativistic mass late in life, and it is no longer taught in physics courses and not used by physicists, at least not by particle physicists. But its legacy lingers on, unfortunately, particularly in popular science.

One of the sillier uses of the equation I've ever read some years back when someone tried to argue that if you load files into an electronic device such as a Kindle, it gains energy, and therefore gets heavier. A slightly less daft version is actually taught in some SR courses, namely that objects get heavier if you heat them up - despite the fact that Einstein's "rigid bodies" lack any sort of internal structure, and hence are physically incapable of heating up!

People also confuse E=mc² with F=ma. The latter (Newton's second law) relates force to acceleration. When the car is cruising its engine is exerting just enough force on the wheels to overcome friction (including air resistance), so there is no net force on the car and the speed stays constant. It accelerates when there is a net forward force, although the backward force you feel inside the car as a result is sometimes called a "fictitious force" which arises because Newton's laws don't hold in an accelerating reference frame.

Special relativity is quite distinct from all this. The rather surprising relationship between energy, mass and the speed of light arises from deductions made from the two basic postulates of the theory - the principle of special relativity, and the principle of the constancy of the speed of light. But you have to be travelling at speeds close to c to notice any effect.

Although no one did it at the time, if you plug the numbers into Maxwell's equations, they work fine for moving charges up to a speed of c, then they generate an inconsistency for faster speeds. So you could say that they indicate that c is the greatest speed at which charged particles can move. This might have led someone to wonder why it was impossible for charges to move faster than c - if someone had done so, the idea that the speed of light was some kind of universal constant could have been discovered earlier. But no one did this until after Einstein had put forward his ideas - perhaps because Maxwell's equations are hard to get your heads round, so few people would have understood them well enough to really grasp the inconsistency.

The nitty-gritty of the equation is as follows. In the derivation of relativistic kinetic energy:

KE = mc^2/(1-v^2/c^2)^(1/2) - mc^2 where m is the rest mass of the object.

OK, so an object is moving at v relative to me and this is its KE. This is an exact equation.

At low v the first RHS expression expands to [an approx. -(*)]:

mc^2(1+(1/2)v^2/c^2)

After multiplying through by mc^2 and subtracting mc^2 gets (1/2)mv^2, the classical kinetic energy. So the origin of the classical KE is in the bottom 1-v^2/c^2 term x. Of course classical KE can be simply found by calculation. the energy needed to get a mass "m" to a velocity "v", but it's so satisfying to see it nicely pop out of the relativistic mass equation (as it should!)

It's interesting to think like this too...when an object (relativity) is coming towards me I see its length contract (space-time is different), so in a way, an object that has just been sitting there (doing nothing) and then gets imparted an energy from a force, is suddenly behaving according to relativity (which has at its base the in-variance of laws at different speeds). So one would kind of expect, intuitively, to see its mass/energy vary with speed (and I guess one could do some hand-waving arguments to show this must increase) - just as it's clock sitting on it slows down (from my perspective).

Fundamentals to do with the object change, so I guess even here in special relativity, there's the hint that mass is linked into space-time etc. etc. and a clue to general relativity - where mass/energy actually distorts space time. I think it's really good to think of fundamentals like this because you can just gently see where all these things came from.

If it's a Newtonian object its rest mass is zero and mass is undefined if it's just sitting there in space staring at me, being only defined as m = F/a. When I kick it, it magically "appears"! Alternatively if it's going past me at v, m = 2(kinetic energy)/v^2, so now “m” is defined, but this has relied on the object being given a force anyway. However I can make “m” go away by moving at the speed of the object - I measure a KE of zero. Such is the appearance/disappearance of inertial mass, only existing in relation to forces.

A completely different mass is Newtonian gravitational mass from:

F = GmM/r^2.

Here, F is only defined when “m” and M exist in space. Only one, force is undefined. But if F is undefined mass is undefined...same issue above...mass/forces defined together.

If we put ma = F = GmM/r^2 then:

a = GM/r^2 but we are doing something naughty here. Mixing inertial mass into the gravitational mass eqn. What results is an object M in space, just sitting there, but it is producing an instant effect over space (not limited by c speeds), and “a” is the gravitational field strength.

But from Einstein, an object sitting in space does have “m” defined! m = E/c^2. And you cannot magic it away like above by going to another reference frame. So where does this m come from? Space itself? Marilyn Monroe? For Newton, “m” means something when changing motion happens or, for a different phenomenon, its gravity. With Einstein, you just require the laws of physics to look the same in all reference frames, this implies c is constant...then m = E/c^2. So mass and energy intimately tied to space-time, clues for general relativity, quantum theory. Newton collapses under conceptual contradictions, Einstein opens up much more stuff.

There are people writing here who think that such equations are examples of "mathematical idealism" and also seem to think that they have never been empirically corroborated. The same people seem to think that philosophy stopped with Hegel in the same way that some Catholics think that it ended with Aquinas. And in the same way that such Catholics interpret everything in terms of Aquinas those who follow Hegel insist on everything being interpreted in terms of his ideology. As a friend of mine likes say to debunk Einstein every chance he gets, the real equation is: E = MC^2 + 0.5 and it's been covered up by the New World Order Tiberians. I always tell him I don't care about stuff like that. What I really want to know is whether he or did not shag Marilyn Monroe.

Never mind all this scientific mumbo-jumbo.

That’s what Bodanis should have written (I know I sound smug but I hate books that don’t address what’s in the title ffs!!! If I had wanted a book on the atomic book I’d have bought one!).

NB: (*)

KE = mc^2/(1-v^2/c^2)^(1/2) - mc^2 (m here is the rest mass) - which is really what we are dealing with.

or KE = m(r)c^2 - mc^2 where m(r) is the relativistic mass.

When v ( )
  antao | Aug 3, 2019 |
Very interesting pop-science book that shows the history of ideas, culminating in the famous Einstein equation and following with the practical usage of it. A definite plus is noting not only well-known male scientists, but also quite a few women, who are usually not mentioned is ‘classical’ history o science. ( )
  Oleksandr_Zholud | Jan 9, 2019 |
I loved this book, it was insightful, funny at times and packed full of interesting information. For someone who has a basic understanding of physics this is a wonderful read. It is easy to understand and I really enjoyed the historical approach to this magnificent equation that many people know but are at a loss to explain. ( )
  KatiaMDavis | Dec 19, 2017 |
A discussion of the impact and nature of Einstein's work structured like a biography of the equation, E = mc^2. A lively narrative, not terribly technical. The book covers Einstein's original addendum to a paper (the birth), and each element in the equation, its origin, and its meaning at the time Einstein took it up.
Each part has a bit of a biography associated with it, as, E (Michael Farraday), m (Antoine Lavoisier), c (Ole Roemer), ^2 (Emilie du Chatelet). The equation is first ignored, eventually seized upon, and finally used in many ways. An epilogue on general relativity, the descendants.

Besides those mentioned above, many people trip through these pages. Werner Heisenberg (working on a bomb for Germany), Cecilia Payne (conjecturing that the sun is not so much made of iron as of hydrogen), Arthur Eddington (observing the bending of starlight instead of being incarcerated as a conscientous objector), Enrico Fermi, Lise Meitner (envisaging nuclear fission), James Chadwick (discovering the neutron), Ernest Rutherford (many things), Fred Hoyle, Subramanyan Chandraseckhar (his limit).

Succint and lively, but occasionally a bit sloppy. I listened to this on audio, but would probably be prepared to read the book. ( )
  themulhern | Jul 5, 2015 |
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Bodanis, Davidprimary authorall editionsconfirmed
Lindgren, NilleTranslatorsecondary authorsome editionsconfirmed
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A while ago I was reading an interview with the actress Cameron Diaz in a movie magazine.
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13 April 1901
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Examines the science and scientists who provided the backdrop to Einstein's influential 1905 discovery and offers an explanation of the equation from mathematical, historical, and scientific perspectives.

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