How much gossip is
required before science becomes interesting?
A review of David
Bodanis’ book e=mc2
By Hans O. Melberg
E=mc2
A biography of the
world’s most famous equation
David Bodanis
Gyldendal,
First published by
Walker Publishing Company,
320 pages, ISBN: 82-05-29980-3
E = m c2
Energy = Mass * Speed of light2
Introduction
David Bodanis’ book e=mc2 is a good read. It is entertaining because of its anecdotes about the people involved and it is understandable for non-scientists because of its use of analogies and examples. Although good, the book is not perfect. Occasionally I found myself suspecting that the pictures painted of several individuals were overly black and white. Also some of the analogies (inevitably) left some details quite hazy and sometimes they may make the reader feel that she understands more than she really does. Moreover, I sometimes found myself strongly doubting his more speculative arguments about why people came up with certain ideas. These weaknesses, however, are relatively minor and my main message is that this is a very readable and useful book.
Before
Einstein
Before Einstein published his article with the famous equation in 1905, the scientific community used to think, according to Bodanis, that energy and mass were two separate domains. Within these separate fields great progress had been made before Einstein connected the two. For instance, in 1820 the Danish scientist H.C. Řrsted discovered that a magnetic needle was affected by a voltaic current. This showed that that different forces previously believed to be unrelated – like magnetism and electricity – were in fact related. Building on this idea Michael Faraday in 1821 developed an experiment in which he demonstrated the basic principle behind the electro motor (by showing how a magnet could make a wire go round and round like a small boat in a whirlpool when he used electricity to fuel it). The significance of this experiment was not only in showing that electricity and magnetism was related, but it showed that force was not just linear – pulling one thing from or towards another - but that it could be circular (a field). It also opened up the possibility for measurement and further experimentation. Since in all experiments the energy lost by one source was found to be equal the energy gained by another, these experiments led the scientific community to what was believed to be a great law of nature: Energy can be transformed from one form to another (e.g. electrical energy gets converted to mechanical energy), but the total amount of energy in the universe is constant.
When asked why Faraday was central in these discoveries, Bodanis points to Faraday’s religious beliefs. He belonged to a Christian sect which, amongst other things, strongly believed in circles of reciprocity (the Sandemanians). In short, if I help my neighbour, he will be nice to someone else and this someone else might, in turn, be kind to me. Given his religiously inspired belief in circles and his lack of formal scientific training, Bodanis argues it was natural for Faraday to seek circular patterns, as opposed to the already mentioned more conventional view that force was linear (like when similarly charged electrons repel each other). There might, of course, be something to this, but the story is too thin to be convincing. To be fair, Bodanis notes in the appendix that the connection between Faraday’s religious beliefs and the scientific discovery is his own subjective interpretation based on ideas from cognitive social anthropology about the relationship between ideologies and social behaviour.
The second term of the equation – mass –
was also the result of steady scientific progress starting with
Lavoisier and Faraday are “heroes” in the
book. Hence, Lavoisier’s marriage to a 13 year old
girl is interpreted as a sign of his romantic nature and as an unselfish rescue
operation to prevent the girl from ending up with an even older and uglier man.
Also, there is no mention of what other’s believe was Lavoisier’s
tendency to sometimes report results as his own when they were in fact
developed by others (see http://scienceworld.wolfram.com/biography/Lavoisier.html).
Faraday who was accused of the same, is completely
vindicated by Bodanis (probably correctly) and his mentor Humphry
Davy (largely a villain in the book) is given short shrift for trying to claim
credit for Faraday’s work.
Einstein’s
idea
As mentioned Bodanis claims that before Einstain mass and energy were believed to be separate domains. In the equation e=mc2 Einstein unites these two domains by claiming that if we could transform mass into energy, we could get mc2 units of energy out it the process. This is a startling claim because it implies that within 1 kg of mass lies hidden about 25 billion kilowatt units of energy (if we somehow could convert the mass into energy). The reason such small amount of materials contains so much energy is because of the large value of c – the speed of light. Light travels 300 000 km in one second (a fact first discovered by the Danish scientist Ole Rřmer in 1676). Einstein says that to find the energy of mass it should be multiplied by this large number no only once, but twice. That is, to find the energy of some material we multiply its mass first by 300 000 and then we multiply this again by 300 000. No wonder we get such a large number in the end even with a small starting point! In effect, then, the equation says that mass is the purest form of concentrated energy and it raises the possibility that mass can be transformed to energy and vice versa.
How did Einstein get this idea? Even before Einstein it was known that energy was most conveniently measured by the its mass times the square of its velocity. Bodanis presents this, as always, in a fascinating story where the hero is a rich, beautiful and very intelligent woman named Emilie du Chătelet (a modern day equivalent, Bodanis says, is Geena Davies!). The background was as follows. Newton had suggested that energy should be measured by the mass of something times it velocity. The problem with this was that it opened up the possibility for energy to disappear, as when two objects collide and come to rest. The energy from one seems to cancel the other and the result is a loss of energy. And, if collisions caused a loss of energy, the word should gradually come to a standstill since all objects occasionally collide and loose energy.
For
du Chătelet herself did not conduct such an experiment, but she knew about an experiment conducted by Williem s’Gravesande. He had discovered that if you double the speed of a bullet it will not go twice as far into a layer of mud or clay, but four times as far. Triple its speed and it goes nine times as deep. It is the same with cars, double the speed of a car and the distance it takes to stop becomes four times as long (2 squared). The same phenomenon is observed in many other processes and one may speculate that it expresses some kind of fundamental law derived from a deeper mathematical symmetry or unity in nature. In any case, the point is that even before Einstein it was established that energy should be measured as mass times velocity squared.
I fount the story above very fascinating,
if nothing else because it reveals what today must seem like quite quaint
arguments about the existence of God was used to support or reject a theory
about how to measure energy. I was, however, also slightly confused. First,
measuring energy in terms of the square of the velocity does not seem to
prevent energy from being lost. If both objects reduce their velocity to zero
after the collision, the energy is lost even if it measured by velocity squared
since zero times something else is zero. Also the story seems to contradict the
argument that Einstein was the first to connect energy and mass together. That
had been done by
To explain this Bodanis adapts an analogy
used by Einstein himself. Imagine you are flying a very fast space-ship and
that you try to go faster than the speed of light (300 000 km/s). What
happens when you are flying at 299 999 km/s and tries to go even faster?
The answer, according to Einstein, is that the space shuttle will not go
faster, but the energy used in trying to go faster will result in larger mass:
the space-ship will become larger and heavier! Today we can prove this
experimentally. Using the particle accelerators outside
The analogy, however, does not explain exactly why nothing can go faster than light, or, indeed, why the phenomenon is gradual and not discrete. To take the latter first: You do not need to approach the speed of light to before the energy is increasing the mass. The analogy may make people believe that only the “extra” energy that is used trying to go beyond the speed of light will be used to increase in mass, but in fact the phenomenon can be observed at all speeds – although the effect is much larger when the speed is high.
Second, why is the speed of light an absolute “speed-limit” in the universe? Bodanis has a go at this question. He first introduces us to absolute limits in nature. For instance, nothing can become colder than -274 degrees Celsius because at that point the atoms stop vibrating. It is impossible to vibrate less than “no vibration” and since “no vibration” occurs at -274 degrees then this is the “absolute zero” – nothing can be colder by vibrating less! This shows that “absolute” limits exist in nature, but it does not show why nothing can go faster than the speed of light.
To go further Bodanis tries to explain how light moves. The starting point of the story is James Clark Maxwell’s discovery that light is a physical process involving “jumps” and squeezes. Light is, briefly, a jump made by an electric field from a magnetic field. Out of this magnetic field jumps an electric field and so the process goes on. This is only make things slightly more understandable. The explanation in terms of “jumps” is very general and it does not add much to my knowledge except, maybe, to make me believe that light is a physical process and as such it has an inherent “speed” by which it can move. It does not, however, say exactly why this is the speed limit for all kinds of movement.
A third step in the argument tries to make this last argument more explicit, but I am unsure about how convincing it is. In brief, the argument is that since light IS movement, then there will be no light if you go faster than light itself. This I understand, but I still do not know why things cannot move faster than light (even if they then will be “in the dark” or only seeing/catching up “old light”). This is not to say that I believe things can go faster than light, only to say that I do not fully understand why. I basically accept the velocity of light as an empirically established “speed limit” in nature, although I do have some problems even with this based on experiments from quantum physics where things seem to “communicate” or “react” faster than can be explained by the speed of light (but my competence here is far to thin to be convincing). In short, Bodanis’ arguments, analogies, and examples did bring me closer to an understanding, but I did not reach the point where I felt “everything” fell into place.
How did Einstein arrive at his revolutionary equation? Bodanis suggest that it was a combination of several factors. First of all Einstein disliked authority, so he was always eager to challenge the established physical laws. Hence, the “old” laws that total mass is constant and total energy is constant were not – for Einstein – unquestionable truths and in fact, his equation implies that the laws are wrong. Since energy can be transformed into mass and mass into energy then sum of each is not constant, but it is the sum of energy and mass together that is constant. Why was Einstein so critical of authority? Building on an argument from Thorstein Veblen, Bodanis suggests that religion played a role here. The argument is that if you as a child is taught to believe in a religious world view, you might later develop a deep suspicion of authority when you discover that some of these teachings seems to be wrong. Second, Bodanis suggests that not having a job in research was important since such a job could have promoted a tendency to superficial research. Third – and slightly in conflict with the first argument, there was the importance of being supported and encouraged by his family to challenge established truths even from childhood. There are also several other arguments and although some of them are plausible, I think it is a field ill suited for generalization. All kinds of people with all kinds of different backgrounds seem to make important discoveries and although there might be some common tendencies in their background, I am not sure what they are.
The
bomb
Einstein himself did not “invent” the nuclear bomb, but the equation e=mc2 was certainly a vital step in the process since it implied that a small amount mass in principle could be converted to a large amount of energy. To create a bomb, however, you had to know how to convert mass into energy.
Nature and previous research had given some hints. For instance, prior to Einstein’s work Marie Curie had studied the phenomenon of radioactivity, that is the energy (radiation) omitted by certain rocks. Although she did not know it, this was an example of Einstein’s equation. The radiation was in fact fuelled by the material in the rock itself, its mass was slowly – very slowly – being transformed into energy. How is this possible?
The short answer is that the atom nucleus in certain metals – like uranium – is stuffed with so many neutrons and protons that when the nucleus is hit by new neutrons it may break. It so happens that the added mass of the two separate units is smaller than the mass of the original. Hence, some mass is lost in the process and this is transformed into energy, just as Einstein’s equation predicts. Although one is talking about very small amounts of mass (atoms are very small!), we known that even very small amounts of mass can create quite a lot of energy since it is twice multiplied by a very large number: 300 000 km/s. Moreover, the splitting of an atom can cause a chain-reaction since when it splits it sends out new neutrons which may hit some of the remaining uranium, thus splitting these apart – causing both emission of more energy and even more neutrons that can split more uranium and so on.
Potentially, then we see how we could create a nuclear bomb. First of all we need a material that is “fragile” in the sense that the nucleus of its atoms are so full of protons and neutrons that it can easily fall apart (Or at least that the force holding the nucleus together is fragile for some other reason. The protons in the nucleus do not like each other, but they are kept together by a force. The point is that this force is easier to break in some metals than others). Uranium fits the bill; lead – for instance - does not since its core is very stable. Second, we need to organize the material such that it causes a chain reaction. Third, this chain-reaction must be slow enough to allow many steps before it blows up (create a big bang), but fast enough to avoid just a fizzle (like the rocks studied by Curie).
The story about the discoveries that
eventually led to the bomb is fascinating reading. It involves deep personal
betrayal, gross incompetence, brilliant minds and ultimately, noting less than
competition for world domination. For instance, Bodanis claims that the person
most responsible for realizing how fission (the splitting of atoms) could
create energy, was Lisa Meitner (together with Robert
Frisch). She is one of Bodanis’ heroes, while her fellow researcher Otto Hahn
is viewed as a less intelligent, cowardly and insincere person who tries to
claim credit for Meitner’s work. I have no grounds for saying that this is a
wrong picture – sometimes the world really is black and white – except to note
that it relies quite heavily on one source (a fellow researcher called Strassman). The gross incompetence is exemplified by the
initial American reaction to Einstein and other’s concerns about the German
effort to build a bomb and the initial lack of American interest in this line
of research. When the Americans eventually came around, however, they did so
with an enormous effort. The
Although fascinating, I did not always understand Bodanis’ explanations. For instance, exactly why is it that splitting a nucleus results in something with less mass than the original? If you split a regular rock this is not the case: Its separate parts has mass equal to the original rock (or is this just an “almost” equality too?).
Another question is how a neutron can split the nucleus of an atom. In 1932 James Chadwick had discovered that the neutron could be used to get “into” the nucleus of an atom. Because it is not positively or negatively charged it was not repelled either by the layer of negative electrons around the nucleus or the positive protons inside it. Enrico Fermi then discovered that the best way to make the neutrons hit or get inside the nucleus, was to slow them down. Herein lies the importance of heavy water since this was very efficient in slowing down the neutrons. To explain how a neutron could split the nucleus, Bodanis uses the analogy of a balloon that once hit, may start to wobble and eventually burst. Although suggestive, the analogy did not quite work for me since I do not understand why atoms should react like balloons.
Finally, Bodanis explains how implosion was used to solve the problem of making the process slow enough to generate a big build up before the “bang.” The problem was to make enough of the plutonium (purified or “converted” uranium) stay together to allow a build up of chain reactions (atoms splitting causing new atoms to split). An early “bang” would make the material spread, thus ending the chain reaction too early compared to what you need for a big bang! The solution was implosion and at this point Bodanis is (deliberately?) somewhat imprecise because he does not go into detail about the process. In general implosion uses a ball shaped core with low density plutonium surrounded by explosives. When these explosives go off they force the plutonium together, the chain reaction of splitting atoms starts (each releasing some energy as predicted by e=mc2) and it has enough time to work before the bang that it creates an enormous amount of energy. Bodanis, however, does not go into much detail about how this process really works – how the explosives are arranged to create the almost impossibly precise folding of the plutonium ball and so on. Maybe this is only technical details, and maybe there is a limit to how far one should go in providing a recipe for how to create a nuclear bomb.
After
the war
Einstein’s equation was not only useful to provide theoretical inspiration about how to create a nuclear bomb. It could also be used to explain how the sun manages to create so much energy, the life history of stars and our own planet, and event the possibility of black holes.
Every second the sun converts four million tons of mass (hydrogen) into energy. Initially scientists did not understand this because spectral analysis of the sun seemed to indicate that the sun was made up largely of iron. This was a problem because, as mentioned previously, iron is very stable and it was not the kind of fuel needed to explain how the sun could use e=mc2 to produce energy. The paradox was solved by Cecilia Payne who showed that one could just as easily get the answer “hydrogen” from the spectral analysis if one were willing to look at the patterns from spectral analysis with less preconceived opinions (people had had a tendency to look for iron once they believed that iron was the answer). Once again the story is fascinating in that the discovery was first suppressed and the “discoveree” was made an outcast in the academic community. Once again the story is very black and white, but there is no reason to doubt that both discrimination and prestige invested in old ideas were widespread in the scientific community at that time (as well as today?).
When converting hydrogen to energy, the sun creates helium as a waste product. Incidentally, the sun does not use fission, but fusion to create the energy. That is, it “unites” four hydrogen units to create one helium unit, but the mass of the helium unit is less than the mass of the four separate hydrogen units and the missing mass is converted to energy. What happens, then, when the sun runs out of hydrogen? Bodanis tells the story of another original researcher – Fred Hoyle – who pursued this thought. As the sun becomes older there is less and less hydrogen and more and more helium. Eventually, when there is not enough hydrogen, the sun will collapse – or to be more precise: it will implode. As with plutonium in the nuclear bomb, this implosion will create forces that make the helium burn. Burning helium will create carbon and when there is not enough helium, the sun will implode, thus causing the carbon to burn and so on. In short, as Bodanis writes, the combination of e=mc2 and implosion shows how the stars can make the elements of life: the various materials that go into creating life can start with one material (say hydrogen) and from this a chain reaction can start that will create all the elements we see around us. Fred Hoyle, of course, was not the only person to make this discovery, but he was central. Moreover, he is an interesting person in himself, aversive to authorities (like Einstein), largely self-educated in his youth and a very good writer (Bodanis claims).
What would happen in the end if we follow Fred Hoyles’s chain of though? The Indian scientist Subrahmanyan Chandrasekhar, was one of those who pursued the idea to its logical end. As explained by Bodanis, Chandrasekhar, realized that Einstein’s equation implied not only that mass could be converted to energy and vice versa. In fact, mass is energy. As mentioned, we could view mass is the purest, most concentrated for of energy that exists. Building on this Chandrasekhar wondered about what would happen “in the end,” that is, after all things that can be burn has been burnt. The “last” implosion will then crush some of the material in the star. This will cause the star to become even denser. One might imagine that the increased density will crush the star even more, the result is an even denser star, but then it may crush even tougher material and so on until you have something very, very small that is very, very dense (with a huge gravity because of its density). It would be so dense that even light could not escape because of the gravitational force. In other words, we have a black hole! Initially it was considered to be an absurd idea, but one has later found a star that seems to circle around “nothing” i.e. probably around a black hole (which is different from nothing since it is very, very much, only very, very dense and not emitting any light).
Einstein’s
theory of relativity
The title of Bodanis’ book is e=mc2, not the theory of relativity. This is probably a good thing since the term “relativity” is often misunderstood to mean “everything is possible” or “nothing is true” or “no precise results are possible.” In fact, as Bodanis explains very well, the special theory of relativity is best understood by Einstein’s equation combined with an assumption that the speed of light is 50 km/hour. This would imply that a car would change its mass as it went faster. Things would appear different depending from where I was watching the cars. If I were sitting in a car going at a certain speed things would appear to be different than if I were standing still, or going slightly faster. Mass and so on would be relative and since no position can be defined as the “true” perspective, things could be called relative (although Einstein himself did not like the expression). The general theory of relativity, takes this a bit further and tries to unite not only mass and energy, but time and space as well as mass and energy, but this is the topic of a whole new subject and Bodanis ends his story of e=mc2 before going into the general theory of relativity.
Conclusion
Would the book about e=mc2 be equally readable if there were fewer anecdotes about the people and more emphasis on the concepts? I do not know. Also I do not mean to suggest that the anecdotes are just unnecessary ornaments. They paint a picture of how science really works – with all its prejudices and biases – and this is interesting in its own right. Maybe the anecdotes are slightly too politically correct and somewhat black and white, but they certainly make the story interesting and my wish for “more science” and less gossip might have resulted in worse book with far fewer readers. In fact, one of the things I learned was that we should probably have more gossip in science both to make it interesting but also because it is a constant reminder of how good ideas were suppressed because of prejudice and personal rivalry.