When and why did the concept of relativistic mass become outdated?

Question

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Physics Stack Exchange, I discovered numerous posts (these two are examples) which assert that relativistic mass is an outdated concept used in older textbooks.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which seems to corroborate the idea that relativistic mass is outdated.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)?

Answer 1

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".

Answer 2

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.

Answer 3

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.

Answer 4

There are researchers both for and against the concept of relativistic mass even to this day. In fact, Lorentz was the first to propose the idea of relativistic mass in the form of mgamma=m/Sqrt(1-v^2/c^2) back in 1899. Later, in his 1905 paper, Einstein suggested two forms of relativistic mass, mgamma^2 and mgamma^3, but neither of these formulas are used today. Despite this, some researchers still use the Lorentz relativistic mass. However, Einstein himself eventually abandoned the concept altogether, which is one reason why the general relativity community has been largely negative towards it.

Although some prominent physicists, such as Wolfgang Rindler, have been positive towards relativistic mass, neither the proponents nor the opponents have investigated the implications of Lorentz relativistic mass.

Personally, I believe it was a mistake to abandon the concept of Lorentz relativistic mass without fully investigating it. Taking it into account may eliminate the mathematical possibility of wormholes and provide a theoretical explanation for Supernova type Ia without relying on the hypothesis of dark energy. There are papers available online discussing this. Ignoring the concept of Lorentz relativistic mass could lead to missed opportunities for scientific advancement. Therefore, discussions surrounding relativistic mass are ongoing, and this question is far from settled. There have been a series of recently published papers discussing relativistic mass.

The paper by T. R. Sandin "In defense of relativistic mass" American Journal of Physics 59, 1032 (1991); https://doi.org/10.1119/1.16642

is discussing the arguments against relativistic mass, it becomes apparent that they are generally weak. In his latest book on mass, Jammer dedicates an entire chapter to examining the pros and cons of these arguments that have been presented in the literature.

One can have different views here, but the debate for or against relativistic mass is clearly not over.