E=mc2 : a biography of the world's most famous equation

by David Bodanis

Hardcover, 2000




New York : Walker, 2000


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.

User reviews

LibraryThing member timjones
I don't usually enjoy science books which are focused more on the biographies of the scientists than on the science itself, but perhaps because Bodanis is a historian, he carries of this mix of biography and science very well. A strong secondary theme is the waste of scientific talent caused by the
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sexism that has historically held back female scientists, several of whom are included in this tale.
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LibraryThing member careburpee
Quick Version:

This book is a well laid out explanation of each part of the equation, its history, and its role in our universe.

Long Version:

The genesis of David Bodanis’ book was an interview he read in which actress Cameron Diaz expressed the desire-serious or in jest-to know what E=mc² really
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meant. Bodanis realized that the truth is that very few people have even a rudimentary knowledge of the usefulness of the world’s most famous equation; this book is his attempt to rectify that.

The format chosen is an interesting one. Those who are true novices to physics-or lack interest in pursuing the equation beyond the basics-can read the front half of the book and walk away far more knowledgeable than they were when they picked it up. After a brief introduction to the time and place in which Einstein generated the paper which introduce the theory to the scientific world, Bodanis goes on to break down the equation and discuss each of its parts separately. What do they mean, and how do they interact with each other? The reader is then led on a quick trip through history with regards to how the scientific community used the theory-the race to be the first to build “The Bomb” during World War II. Finally, the author discusses the theory in our universe. Those not interested in a brain drain of a read would still likely read the Epilogue, which discusses what else Einstein did, and the interesting appendix, which gives closure regarding the other key participants.

Of particular interest with regards to the structure of the book are the notes. If you would like to know more details (and are not afraid of either the odd equation or in depth descriptions), Bodanis suggests that you read the notes, where he has taken things a bit further. It is here that I have a bone to pick. The format that was chosen was that of endnotes, as opposed to footnotes. When endnotes are used, there is absolutely no indication within the text that there is a back of the book furtherance of the topic-two members of our book club did not even realize they were there and thus missed the opportunity to add to their reading experience. For those readers that do choose to read the endnotes concurrent with the front half of the book, you are left constantly flipping between the text and the notes to see if you have reached the next note (they are listed by page number). This is extremely disruptive to the flow of a book which requires some level of concentration to read and annoyed me to no end. Footnotes within the text would have been grand. As a side note, a member of our group tried to read the e-reader version. Footnotes would have enabled her to flip from text to notes with ease. As it was, she quickly gave up on trying to maneuver between the two.

The final section, a guide to further reading, is one of the finest source guides I have ever seen. Books are divided into categories and are each given a paragraph of explanation designed to help the reader ascertain if they are a good fit for their reading list.

Bodanis tops off his two leveled read with one final feat-he has a website to which he directs the serious student for further, more in depth, study. Whether you are interested in a basic explanation of a complicated theory, have a fascination with physics and would like to know more, or would like to go beyond your high school physics knowledge, this book is likely to fit your need.
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LibraryThing member John
I have always had an interest in the theories of relativity and the life of Einstein; I remember enjoying Clark's biography of Einstein many years ago, and at one stage, in my twenties, I read several books that gave layman's explanations of the meaning and impact of Einstein's theories.

Bodnis has
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taken a different, and interesting approach. He provides, as he says, a biography of this most famous equation, by going back to describe the early practitioners and discoveries of science and physics that Einstein built upon to come to his startling insight that energy and matter are interchangeable and that the conversion of even a tiny bit of matter leads to an enormous output of energy given that the coefficient is the speed of light, squared. The story also describes the race between the Germans and the Allies to build the first atomic bomb, and the critical role played by the destruction by commandos of heavy water shipments out of Norway.

I learned a few interesting things. For instance, why is the speed of light designated a "c"? Because "c" is from the Latin "celeritas" which means swiftness. The speed is 670 million mph. And why does it have to be squared? Because the geometry of our world often produces squared numbers. For instance, when you move twice as close to a reading lamp, the light doesn't get twice as strong, its intensity increases four times. Almost anything that steadily accumulates will turn out to grow in terms of simple squared numbers. Thus, if you accelerate on a road from 20 to 80mph, your speed has gone up four times, but your accumulated energy will have increased by the square of four, i.e 16 times and that's how much longer your skid will be. The square of the speed of light is 448,900,000,000,000,000...small wonder that converting even a tiny bit of matter will create an incredible release of energy. In fact, a major contributor to the discovery of the meaning mv2 was Emile du Chatlet who lived in the 1700s, was a lover of Voltaire, and an exceptionally bright and intelligent woman in a time when women were expected to be neither. She was an active lover, with many partners, and she died in childbirth at the age of 40. Sad to read that she fully expected to die, given the abysmal record of women surviving childbirth especially those of her age. She was also one of a number of women who made tremendous contributions, either in providing building blocks for Einstein's work, or in proving it afterwards, who were thwarted, discriminated against, and given no due for their work. Another example was Lisa Meitner whose work was practically stolen from her by a former colleague and someone she thought was a friend and who won the Nobel for physics for a lot of the work that Meitner did. And Ceclia Payne who fought against considerable adversity to prove that she was right in determining that the sun is primarily composed of hydrogen, not iron. A distressing litany. I also learned that Heisenberg was a not very sympathetic character: more than willing to serve the Nazis in the race for the bomb, and with no compunction about using the products of slave-labour to do so. There is also a milisecond my milisecond description of what was happening in the bomb that drifted down in the skies above Hiroshima before it unleashed its awful power.

An interesting book and well worth reading.
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LibraryThing member eduscapes
I love biographies, but I wasn't sure what to think about the biography of a formula. As I read the book, I began to understand why they gave the book this title. Many people contributed to this formula over many years. One of the best parts was the large amount of content focusing on dispelling
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misunderstandings and giving credit to some of the lesser known contributors.
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LibraryThing member stevenschmitt
I'm no Einstein, but I do know a good book when I read one, and this one qualifies. Bodanis uses the famous equation to share biographical sketches of fascinating scientists working toward the discovery and application of the 20th century's great scientific breakthrough. With any popular science
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writing success can be measured by how well the author can take the obscure and esoteric come alive and show science to be what it ultimately is, a compelling human story. Without question the author succeeds.
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LibraryThing member sorryforthemess
This one cracks me up! It's a biography of an EQUATION, but the bulk of the story is apparently about the scandalous (and/or not so scandalous) lives of the scientists involved.
LibraryThing member Janzz
This book explained to me what no teacher ever did about relativity etc and why it is so important in modern life.
LibraryThing member willyt
I've read this book several years ago, so I will not provide a detailed review of this particular book. This is first book by David Bodanis that I read. I have immensely enjoyed all of the David Bodanis books that I have read. I am a working scientist, and I believe that Mr. Bodanis does an
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excellent job of writing popular science. In this particular book I thought his approach on showing the antecedents of aspects of this equation was excellent, and I learned quite a bit. His books always provide me with ideas or concepts that I will study in more detail.
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LibraryThing member helices
This book is not only about the equation. It is also about how to apply it in reality. And how that has been done. Interesting and well written. Not least the part describing the Norwegians’ struggle during the blow-up of the factory producing deuterium during World War II.
Denna bok handlar
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inte bara om ekvationen. Den handlar också om hur man kan applicera den i verkligheten. Och hur det har gjorts. Intressant och välskrivet. Inte minst avdelningen som beskriver norrmännens vedermödor under sprängningen av fabriken som tillverkade tungt vatten under andra världskriget.
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LibraryThing member siafl
This is an exciting book to read. Very gripping through the middle, especially the part where America raced Germany for being first to make an atomic bomb. I find the idea of the book very smart. On one hand it's an account of Albert Einstein, on the other it's the impact of one of his most
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important realizations on the rest of mankind.

The part about what each of E, =, m, c, 2 means is a bit excessive I think, and the stuff that comes after Hiroshima drags on a bit, but I had a great time reading it nonetheless. It took only two days to finish.
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LibraryThing member paulrach
An easy to understand guide to Einstein's famous equation. Starting with Einstein, and his discovery, the book goes onto explain the history of the terms of the equation, looking how the ideas and terms have developed over the centuries.

Bodanis then examines the development of the atomic bomb and
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how E=mc2 is at the heart of the process.

An excellent well written book. Certainly worth a read.
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LibraryThing member Sandydog1
Excellent. The first chapters actually pertain to the equation components E, "equals sign", m, C and yes, "squared". The remainder is comprised of the history of relativity and atomic theory, with plenty of real lives drama among the various scientists (Einstein's life comprises only s small
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portion of this). The description of the Hiroshima bomb and the eventual demise of the sun, are awe-inspiring. I still don't know what the darn equation means but it was a heck of an entertaining book.
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LibraryThing member carterchristian1
If science is not your thing but biography is this is the book for you.
LibraryThing member ogroft
Many of my students will have heard about this small equation, but I'm not sure if they will understand its gravity. I hope to expound their knowledge on the importance of these five symbols in a line.
LibraryThing member themulhern
Quite an interesting book. I started to lose track around Enrico Fermi, but I'ld be happy to give it another go
LibraryThing member antao
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
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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. -(*)]:


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
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Independent Publisher Book Awards (Finalist — Science — 2001)
LA Times Book Prize (Finalist — Science & Technology — 2000)



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