The Increasing Mass of Lincoln Barnett

In the April, May, and June issues of Harper’s magazine in 1948 there appeared a series of articles on modern physics by the well-known science writer Lincoln Barnett.  In these articles Barnett gave an account of Einstein’s theory of relativity, placing special emphasis on the concept of relativistic mass. He said

The most important practical results of relativity have arisen from this principle – the relativity of mass…  As used by the physicist, “mass” denotes resistance to a change of motion… relativity asserts that the mass of a moving body is by no means constant, but increases with its velocity relative to the observer. Einstein’s equation giving the increase of mass with velocity is similar in form to the other equations of relativity but vastly more important in its consequences

Here m stands for the mass of a body moving with velocity v, m₀ for its mass when at rest, and c for the velocity of light… Of all aspects of relativity, the principle of increase of mass has been most often verified and most fruitfully applied by experimental physicists… By further deduction from his principle of relativity of mass, Einstein arrived at… the most famous equation in history: E = mc².

Barnett was not alone in thinking that the concept of relativistic mass was the most important principle of special relativity, from which everything else follows. For example, in Feynman’s famous lectures in the 1960s the subject of relativity is introduced by stating that “the mass of a body increases with velocity”, quoting the same formula as above, and going on to say that

For those who want to learn just enough about it to solve problems, that is all there is to the theory of relativity – it just changes Newton’s law by introducing a correction factor to the mass.

Interestingly, whenever the subject of “relativistic mass” comes up in conversation today, someone mentions a letter that Einstein evidently wrote to Barnett on June 19, 1948 after seeing Barnett’s articles. In this letter (now in the possession of the Hebrew University of Jerusalem), Einstein wrote (in German)

…it is not proper to speak of the mass M = m(1 – v²/c²)^–1/2 of a moving body, because no clear definition can be given for M. It is better to restrict oneself to the ‘rest mass’, m. Besides, one may of course use the expressions for momentum and energy when referring to the inertial behavior of rapidly moving bodies.

This is cited in support of the idea that one should never refer to the noted quantity as “mass” (or relativistic mass, or inertial mass), although the stated reason is not particularly compelling. Immediately after giving a clear definition of M, Einstein says no clear definition of it can be given. Indeed Barnett describes it as “resistance to a change of motion”, which can be made precise in terms of changes in relativistic momentum (F = dp/dt). Many people have explained why they believe the concept of relativistic mass is unhelpful or even misleading, but to say that no clear definition of it can be given is simply false.

Ultimately this is a Humpty-Dumpty battle over semantics (“the question is, who is to be master?”), with workers in different sub-fields of physics tending to have different preferences. The belief in some primitive concept of “rest mass” as distinct from relativistic mass is (or at least was) popular among particle physicists, although now that the Higgs mechanism has been confirmed, showing that even the rest mass of elementary quarks and Leptons is actually relativistic mass bound by its interactions with the Higgs field, even the particle physicists may need to re-examine their preferences. In any case, we certainly can refer to relativistic mass as being proportional to the total energy, and recognizing the inertia of energy is still valuable.

Setting aside the merits of this semantic squabble, it’s interesting that, despite Einstein’s scolding letter, when Barnett published his articles in the form of a book, entitled “The Universe and Dr. Einstein”, it still contained the full emphasis on the importance of the concept of relativistic mass, still touting it as the central idea – the very essence – of special relativity. Even more interesting is the fact that a Forward to the book was contributed by none other than Einstein himself, in which he praises the exposition

Lincoln Barnett’s book represents a valuable contribution to popular scientific writing. The main ideas of the theory of relativity are extremely well presented. Moreover, the present state of our knowledge in physics is aptly characterized.

The Forward is dated September 10, 1948, nearly three months after Einstein sent the famous letter to Barnett, telling him not to talk about relativistic mass, and yet the published book retains the discussion of relativistic mass as the whole basis and foundation of special relativity… and Einstein praises the book by saying the main ideas of the theory of relativity are extremely well presented.

What are we to make of this?  Was there, between June 19 and September 10, some further communication between Barnett and Einstein, in which they came to agreement on the suitability of the presentation?  Einstein’s Forward begins with a somewhat disconnected commentary on popular science writing, noting that most books either present vague and superficial descriptions that give the reader only a deceptive illusion of comprehension, or else they provide an expert account that the untrained reader is unable to follow. He doesn’t actually say that Barnett’s book avoids both of these problems, but he does say that the book is “a valuable contribution to popular scientific writing”.  Perhaps Einstein’s aversion to the use of the term “relativistic mass” has been exaggerated, and he was persuaded that the book’s presentation was, after all, a workable way of giving the readers a reasonably accurate understanding.

It would be interesting to know what Einstein would have thought about Feynman’s lectures on special relativity. The two of them met in 1940 when the young Feynman was giving his first seminar on what came to be called the Wheeler-Feynman absorber theory. Feynman tells us that, aside from commenting that the absorber theory would be difficult to reconcile with general relativity, the only thing Einstein said to him was when he arrived and said “Hello, I’m coming to your seminar, but first, where is the tea?”

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