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I've always seen older books talking about relativistic mass all over their special relativity introduction $m=\gamma m_0$. But I can't stand it. It makes no sense to define this quantity at all.

To explain myself, mass can't be measured for a moving object, so why even bother bringing this concept up in the first place. Also, it is not needed in any way to derive any other formula from special relativity.

I just think it's pointless to even point out that mass could change for a moving particle when no one could ever measure it.

Maybe I'm wrong in all my explanation, if so, is there any meaningful use of this relativistic mass?

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  • $\begingroup$ "Mass can't be measured for a moving object..." can you say more about this? $\endgroup$
    – M. Enns
    Mar 4, 2019 at 22:57
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    $\begingroup$ how else to measure mass? I thought you should move it.... $\endgroup$
    – Žarko Tomičić
    Mar 4, 2019 at 22:58
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    $\begingroup$ Einstein never derived an equation for "relativistic mass", and in later years he expressed his dislike of the idea:[23] "It is not good to introduce the concept of the mass $\displaystyle M=m/{\sqrt {1-v^{2}/c^{2}}}$ $M = m/\sqrt{1 - v^2/c^2}$ of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion." en.wikipedia.org/wiki/Mass_in_special_relativity $\endgroup$
    – Gert
    Mar 5, 2019 at 0:13
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    $\begingroup$ From the same link: "The concept of "relativistic mass" is subject to misunderstanding. That's why we don't use it. First, it applies the name mass – belonging to the magnitude of a 4-vector – to a very different concept, the time component of a 4-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of spacetime itself."[7] $\endgroup$
    – Gert
    Mar 5, 2019 at 0:25
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    $\begingroup$ "mass can't be measured for a moving object" Yes it can. Including the invariant kind, the so-called "transverse mass" $\gamma m$, and the "longitudinal mass" $\gamma^3 m$. I invite you to consider—for instance—the operation of a mass spectrometer. Questions for the student: which quantity (or quantities) can be found from the results? Why do you say that? $\endgroup$
    – dmckee --- ex-moderator kitten
    Mar 5, 2019 at 3:45

2 Answers 2

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It is now common to assert that mass is invariant, and what changes as an object is accelerated to near the speed of light is not its mass but instead the relationship between that object's mass and its momentum- and this is how the topic is currently taught.

This does not mean, however, that the results of earlier analyses which were based on the concept of relativistic mass were numerically incorrect or "wrong". The claim is that the current formalism for special relativity leads more naturally to an understanding of general relativity, which is why it is taught today instead of (as you point out) the earlier concept of "relativistic mass".

I invite the specialists here to check this for correctness and to add their perspectives.

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  • $\begingroup$ I thank @johnrennie for originally explaining this to me. -NN $\endgroup$
    – niels nielsen
    Mar 5, 2019 at 18:03
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It's a matter of definition. Everybody (I hope.) agrees that E=m\gamma (with c absent). The argument is over what to do with \gamma. Unfortunately some (even serious) people put the \gamma into the mass, thus calling relativistic mass M=E. This has lead to confusion and arguments over language (although some call it philosophy). The whole issue is further confounded by Einstein's famous E=mc^2, which is usually misinterpreted. My understanding is that Einstein, who argued each way, ultimately concluded with a statement against relativistic mass.

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