Cosmoclast versus Iconoclast

Some of the scientists who participated in developing the atomic bomb at Los Alamos downplayed the relevance of the theory of relativity to the development of nuclear power.  For example, one of Oppenhiemer’s assistants, Robert Serber, wrote technical notes that were used as introductory material for people joining the effort at Los Alamos during the war, and in a memoir on this pamphlet in 1992 (“The Los Alamos Primer”) Serber wrote

Somehow the popular notion took hold long ago that Einstein’s theory of relativity, in particular his famous equation  E=mc², plays some essential role in the theory of fission.  Albert Einstein had a part in alerting the United States government to the possibility of building an atomic bomb, but his theory of relativity is not required in discussing fission.  The theory of fission is what physicists call a nonrelativistic theory, meaning that relativistic effects are too small to affect the dynamics of the fission process significantly.

Another notable participant in the Manhattan Project, Richard Feynman, explained that in fact the liberation of energy in an atomic bomb is in accord with the relativistic relation, but suggested that this was of little practical significance:

Suppose that we have an object whose mass M  is measured, and suppose something happens so that it flies into two equal pieces moving with speed w, so that they each have a [relativistic] mass m_w. Now suppose that these pieces encounter enough material to slow them up until they stop; then they will have [rest] mass m₀. How much energy will they have given to the material when they have stopped?   The liberated energy is E = (M − 2m₀)c². This equation was used to estimate how much energy would be liberated under fission in the atomic bomb.. [and] for this reason poor old Einstein was called the “father” of the atomic bomb in all the newspapers. …as soon as the energy was in fact liberated, someone measured it directly (and if Einstein’s formula had not worked, they would have measured it anyway), and the moment they measured it they no longer needed the formula. Of course, we should not belittle Einstein, but rather should criticize the newspapers…

To say that a formula becomes redundant once it has been confirmed experimentally is not a very robust criticism, nor does it seem plausible that “if Einstein’s formula had not worked” it would have been inconsequential. Surely Feynman did not intend to argue that if special relativity was wrong it would be inconsequential for physical phenomena – especially since his own later work on quantum electrodynamics was based so heavily on special relativity.

In any case, it’s undeniable that the theory of relativity, and in particular the equation E=mc², has long been associated with the idea that it might be possible to release vast amounts of energy from a small amount of matter, even as early as the 1920s, long before anyone had a clear idea of how this release might be accomplished. A biography of Einstein published in 1921 (based on interviews conducted around 1916-1918) explained that the public fascination with the equation E=mc² was largely due to the perceived promise of a vast amount of untapped energy. Einstein himself was skeptical that anyone would succeed in “disintegrating the atom”, and worried about the consequences if they did. (He commented that if scientists developed this capability, soon any untrained person would have the means to blow up a whole town.) However, after Rutherford succeeded in splitting the atom, Einstein acknowledged that the release of at least some of the energy of an atomic nucleus may be possible.

Just 25 years later the atomic bombs were dropped in Japan, a country Einstein had visited in the 1920s. Less than 11 months after the bombings, the 1 July 1946 cover of Time magazine showed a painting of Albert Einstein (in a suit and tie) beside an atomic mushroom cloud, on which the famous equation E=mc² was superimposed. The headline read

Cosmoclast Einstein

All matter is speed and flame.

It would be interesting to know the origin of that motto, and in general how this magazine cover came about, especially considering that Einstein had no involvement in the Manhattan Project, may even have been considered a security risk for his leftist sympathies, and as a lifelong pacifist (notwithstanding his signing of the Szilard letters to Roosevelt) would presumably have been horrified to be associated with the mass murder of Japanese civilians – not to mention that he hardly ever wore a suit and tie. The magazine cover must also have been a surprise to individuals like Serber who believed the atomic bomb was “nonrelativistic” and that fission had nothing to do with E=mc². The Time article justified the connection by saying

Albert Einstein did not work directly on the atomic bomb, but Einstein was the father of the bomb in two important ways:  1) it was his [sic] initiative which started U.S. bomb research; 2) it was his equation (E=mc²) which made the atomic bomb theoretically possible.

Likewise many popular science texts associate relativity with atomic bombs and nuclear power, explaining that the energy released is equal to c² times the reduction in rest mass of the constituent particles before and after the reaction. One could also mention that the foundational study of atomic and sub-atomic particles in high-speed accelerators made essential use of relativistic dynamics – a fact that Serber neglected to mention. Furthermore, Serber’s claim that the dynamics of fission are non-relativistic is misleading, because (roughly speaking) the relativistic masses of all the constituents are conserved when an atom is split, but the rest masses are reduced and the excess is due to the relativistic inertial mass associated with the kinetic energies of the parts. After that kinetic energy is conveyed to the surroundings by slowing down the parts, what remains is the reduced rest masses. Now, it’s true that we can compute the speeds of the parts from knowledge of the binding forces, without recourse to an explicitly relativistic calculation, but the process undeniably relies on relativistic dynamics.

Nevertheless, in opposition to the popular association, there is a contrary “iconoclastic” tradition, arguing that relativity theory should not be considered to have any unique relevance to nuclear energy. The iconoclastic thesis is that “popular science texts get it wrong” by saying that an atomic bomb involves “transformation of matter and energy”.  In defense of this denial, the iconoclast points out that ordinary chemical reactions also involve a conversion of rest mass into kinetic energy, again in accord with E=mc², so “the difference between chemical reactions and nuclear reactions must be due to something other than E=mc²”.  Well, of course it is. The difference between chemical and nuclear reactions is that the amount of energy is so much larger in nuclear reactions that the change in rest mass is appreciable.  This is actually the opposite of the iconoclast’s thesis, which is to relegate E=mc² to a secondary role in nuclear reactions, whereas in fact it elevates E=mc² to a primary role in all reactions. 

The iconoclast’s underlying idea seems to be that if we are merely converting one kind of energy into another (as we are doing in both chemical and nuclear reactions), we are not invoking the relation E=mc², but that is incorrect, because all mass consists of bound energy. (“All matter is speed and flame”.)  One might think the portion of an object’s rest mass that is contributed by binding energy, internal kinetic energy, etc., is not “real mass”, and therefore (the iconoclast thinks) when any such bound energy is released as unbound energy the relation E=mc² is not involved, because there is no “m”…  but that’s wrong on several levels. 

In chemical reactions and in nuclear reactions, the large amount of energy released corresponds to a given reduction in rest mass, in accord with the large conversion factor c². In other words, the ratio of 'energy released' to 'rest mass reduction' is the same. However, for chemical reactions, the reduction in rest mass (for a given release of energy) is so small that it is imperceptible, which is why Lavoisier concluded that the mass of the parts before and after combustion was the same, leading to the principle of conservation of mass. Prior to E=mc², energy and mass were thought to be subject to independent conservation laws, and there was no question of a conversion factor, nor of relating 'energy released' to 'mass reduced'. With the discovery of E=mc² it was realized that every quantity of mass actually represents a huge amount of energy, in proportion to c², and that the energy we had been getting from chemical reactions was extremely tiny – almost insignificant – compared with how much energy is actually represented by each gram of mass. The potential implications of this were grasped historically right from the start.

Now, the technical details of how one might go about releasing some or all of that huge amount of energy in every gram of rest mass – going beyond chemical reactions – can be considered. The whole point of Einstein’s September 1905 paper was to answer the question “Does the Inertia of a Body Depend on its Energy Content?”  After deducing E=mc² relating the reduction in rest mass m to the emission of energy E, and extrapolating this to a general proportionality – all mass is a measure of energy content – he concludes the paper by saying

It is not impossible that with bodies whose energy content is variable to a high degree (e.g., with radium salts) the theory may be successfully put to the test.

Thus his very first paper on this equation refers to the change in rest mass of a body after nuclear radioactive decay. So, this kind of reaction is clearly an example of the applicability of the proportionality between inertia and energy. The reason we look to nuclear reactions for evidence of this effect, rather than chemical reactions, is simply because the effect is much larger.  It’s the same reason we look at high speed clocks for evidence of time dilation, rather than low speed clocks.  It’s true that time dilation strictly applies to low speed clocks like our wrist watch as we walk down the street, but this doesn’t imply that relativity tells us nothing new about how high speed clocks will behave. 

Going further, we could try inducing fusion of light atoms, or fission of heavy atoms, or even smashing electrons and positrons together. Even the so-called "elementary" particles consist entirely of bound energy... the mass of two up quarks and one down quark combined is only 1% of the rest mass of a proton. The remainder comes from binding and kinetic energy of the quarks... and we now know that even the mass of quarks and electrons is due to the internal degrees of freedom via interaction with the Higgs field, without which they too would be massless energy. So the distinction between "matter" and things like kinetic energy and binding energy (speed and flame) is illusory.

It's certainly true that a nuclear bomb could be constructed without understanding E=mc², just as it's possible to start a fire without understanding E=mc². It's also possible that some people have the misconception that a nuclear bomb converts some amount of uranium totally into pure energy, but even most popular expositions are careful to note that the released energy just corresponds to the reduction in rest masses of the constituents before and after fission. This process, along with fusion in hydrogen bombs, just happens to be the "best" that could be done (so far) to unleash as much as possible of the vast amount of energy that resides in every gram of mass, which we are led to expect by knowledge of E=mc². This, I think, is what the popular expositions are trying to convey when they connect nuclear power with relativity and the relation E=mc².

Having said all this, and recognizing the vital importance of the inertia of energy in all physical processes, including nuclear reactions, there is an undeniable irony in associating Einstein with the creation of the atomic bomb, both because of his (lapsed) pacifism and because of how the technology of nuclear devices developed along a path that was largely independent of the theoretical foundations. From a purely technical standpoint of proprietary development, the former patent examiner actually has much more claim to being the inventor of television (photo-electric effect) and the laser (stimulated emission).

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