# When and why did the concept of relativistic mass become outdated?

While browsing on Physics Stack Exchange, I discovered numerous posts (these two are examples) which assert that relativistic mass is an outdated concept used in older textbooks. Looking through my own physics textbooks, I noticed the same dichotomy, of relativistic mass being treated in older texts. I then searched up this concept in Wikipedia wherein it outlined both approaches. It includes a quote from Arnold B Arons:

"For many years it was conventional to enter the discussion of dynamics through derivation of the relativistic mass, that is the mass–velocity relation, and this is probably still the dominant mode in textbooks. More recently, however, it has been increasingly recognized that relativistic mass is a troublesome and dubious concept"

which seems to corroborate the idea that relativistic mass is outdated.

Based on these points, I have the following questions: What are the origins of this movement which question the concept of relativistic mass? When did textbooks begin to abandon the old approach and adopt the new approach? What are the reasons for the abandoning of relativistic mass, beyond those outlined by Arnold B. Arons and Taylor and Wheeler (which are provided in wikipedia, whose explanation I still don't completely understand)?

• – Ben Crowell Jun 25 '15 at 20:26
• Is the question about when and why relativists stopped using it, or when and why textbooks stopped using it? Relativists stopped using it around 1950, but it took another 50 years after that for the change to filter down into textbooks of various levels. – Ben Crowell Jun 28 '15 at 12:11
• @BenCrowell I was not aware of the discrepancy. It appears that Conifold has detailed the change for textbooks, but not for relativists. I would very much like to know why relativists stopped using relativistic mass in the 1950s -- can you perhaps provide an answer? Thanks for the information. – Cicero Jun 28 '15 at 18:56
• There was a point at which relativists realized the advantages of expressing relativity in terms of objects that transformed as tensors, rather than having lots of different objects each with its own idiosyncratic transformation law. You can see this presented systematically starting ca. 1923 with Eddington's book, archive.org/details/mathematicaltheo00eddiuoft , and also in Schouten's 1954 book Ricci-Calculus. As this caught on with theorists, they abandoned the non-tensorial relativistic mass for the tensorial (scalar) invariant mass. – Ben Crowell Jun 22 '17 at 20:40

The "movement" against relativistic mass was started by Adler in 1987 with Does Mass Really Depend on Velocity, Dad? (his answer, "actually no, but don't tell your teacher"). It got a boost from Okun's two 1989 papers. In 1990 American Journal of Physics solicited Okun's contribution on the relativistic mass to be published alongside Sandin's, who defended it. Okun declined because he was helping Taylor and Wheeler write a dialog on the subject in the second addition of their book, and published a book of his own that addresses it.

Two decades later in The mass versus relativistic and rest masses Okun did not sound as optimistic as Physics SE:"The article “In defense of relativistic mass” by Sandin was published in 1991 and propagated the concept of relativistic mass for almost 20 years. In August 2008 I read a recent Wikipedia article “Mass in special relativity” which confronts the arguments of Adler and myself with arguments of Sandin. The unknown author in Wikipedia seems to share the views that relativistic mass and rest mass are ‘pedagogically useful’. The idea that according to the theory of relativity the mass of a body increases with its velocity is spread almost as widely as twenty years ago. It is promoted by the very popular books by Hawking and Jammer".

Here is the gist of Adler-Okun's argument as expressed by Okun in 2008:"The concept of relativistic mass, which increases with velocity, appears only in the framework of a language which is not compatible with the standard language of relativity theory and therefore impedes the understanding and learning the theory by beginners... The four equations... defining relativistic and rest masses completely ignore the space-time relativistic symmetry. Relativistic mass $m$ in these equations is a kind of a stub of a four-vector.These equations are based on a naive but unfounded requirement that masses in relativity must have the property of additivity. They are based on the purely non-relativistic concept of mass as the measure of inertia. It is well known that in relativity this role is played not by mass but by energy".

He then traces the root of the problem to Einstein's famous equation:"Sandin keeps stressing that relativistic mass is the best concept for introducing relativity to ‘introductory students’. He thinks so because all of them know ‘the famous equation $E=mc^2$. This equation... is indeed deeply ingrained in the mass culture and widely believed to represent relativity theory. But unfortunately it misrepresents the standard theory of relativity as known to a majority of relativity experts. One consequence of the equation is the mass increasing with velocity. Though in his popular writings Einstein sometimes resorted to this equation, he carefully explained that ‘it is not good’ to introduce velocity dependent mass. He kept insisting that mass increases with energy but not with velocity and that this is expressed by the formula $E_0=mc^2$, where $E_0$ is the rest energy of a body".

• It has come to my attention, by Ben Crowley (see comments on question) that relativists stopped using relativistic mass in the 1950s. Is this true, and why the lag between this event and the papers of Adler and Okun? – Cicero Jun 29 '15 at 14:13
• @Cicero Ben can answer more authoritatively, but the reasons are the same as Okun's, the concept does not fit with relativistic symmetry, and is based on pre-relativistic ideas about inertia. The lag is probably due to Sandin's rationale, it is easier to teach with it, especially when pressed on time. – Conifold Jul 3 '15 at 0:27
• Another useful source of information is Oas, "On the Abuse and Use of Relativistic Mass," 2005, arxiv.org/abs/physics/0504110 – Ben Crowell Jun 20 '17 at 16:06

Relativistic mass is not outdated. "Roche states that about 60% of modern authors just use rest mass and avoid relativistic mass." Who is Roche? "Roche suggests that relativistic mass is only an artifact." That should say enough. https://en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass

When a photon of relativistic mass m is absorbed, then the mass of the absorber increases by m, although the rest mass of the photon is zero. That should say all.

• This isn't really an answer, and it doesn't provide any historical evidence. – Ben Crowell Jun 20 '17 at 16:08
• If the question "When happened X" is answered by "X never happened" then this is an answer. If a proponent of a minority-opinion estimates that 60 % share his view, then this is irrelevant. – Otto Jun 20 '17 at 16:18

Interestingly, the shift in physics appears to have occured late in the 20th c. while philosophers were already discussing it as an exemple. Max Jammer's book Concepts of Mass remains an invaluable source here.

In philosophy it is well known one word used by two authors may be taken either to mean the same thing ('stuff') or the same role ('function'), (e.g. 'soul' used by Christian authors and Greek thinkers). That is what happened with the term mass and in order to sort out the confusion one has to distinguish: 'classical' mass(1) in Newton and 'rest'(2) or 'relativistic'(3) mass after Einstein. It appears that (1) and (2) are the same thing while (1) and (3) play the same role. Philosophical debates about paradigm shifts after Kuhn's book hinge on such issues.

A paper from 1976 (Eriksen and Voyenli, “The Classical and Relativistic Concepts of Mass,” Found. Phys. 6, 115–24 (Feb.1976)) pointed that there is an invariant mass in the old and new theories but only in the old theory a sum is conserved. In Relativistic physics it is the sum of relativistic masses that is conserved and this is the new role.

In language use sometimes a shift in semantics is prefered to a neologism. In the 70s a computer was a device filling half of your basement but later appeared personal computers; today an unqualified computer is a PC while descriptions are supplied for the other kind. Inversely relativistic mass did not become so widespread as to became simply mass and contemporary writers obviously prefer to preserve the semantics and to use the new desription when it is needed.

• relativistic mass did not become so widespread as to became simply mass Do you really mean relativistic mass here, or did you mean invariant mass? Or did you mean that relativistic mass became mass-energy?? – Ben Crowell Jun 23 '17 at 19:37