Talk:Mass in special relativity

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Invariant mass section

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This section could be removed as it adds nothing new to the sections above. I edited it to correct/remove equations which were wrong. It had said that the invariant mass was the ratio of momentum to speed (beta). That is wrong and contradicts text above it and contradicts the reference cited. The confusion may have originated from the reference's use of U which is defined as \gamma \beta. It shows that p = m U which may have been misinterpreted as p = m \beta but should, instead be written as p = m \gamma \beta = m_\text{rel} \beta. — Preceding unsigned comment added by 2601:547:CD81:D870:DCFF:B198:A56A:A59F (talk) 07:42, 12 August 2025 (UTC)[reply]

Mass density of a field

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This article seems to focus on a very limited concept of mass, namely the mass of an object. If we extend the concepts to fields, a very different picture seems to emerge. In particular, there is no obvious way to attribute a velocity to a field (a charge distribution, say, or a classical electromagnetic field, both at a given point in the field). One can determine a well-defined local charge–current density (the four-current or the current 3-form) and an electromagnetic energy–momentum density (the electromagnetic stress–energy tensor). One could artificially try to tease out a velocity (e.g. by dividing the current density by the charge density), but the electromagnetic case is more problematic, being a degree-2 tensor. The energy density, and hence "relativistic mass density" is well-defined, being T00. An invariant mass density of sorts, namely gijTij, might make sense of sorts, but does not correspond to the total energy density of a body at rest under pressure or tension, and suggests that the concept of invariant mass is flawed in the context of special relativity: it makes the implicit assumption that there are no external forces on a body (e.g. a stationary conductive rod in and aligned with a static electric field is internally under mechanical tension).

My questions is: Is anyone aware of published work that considers the invariant/relativistic mass question for fields? I think this would be an enlightening and welcome addition to the article. —Quondum 22:43, 28 July 2020 (UTC)[reply]

The photon and graviton are considered massless because the force fields decay proportionate to R−2. For a massive particle, there would be an exponential decay with −R/m in the exponent. More generally, if a field satisfies the Klein–Gordon equation with mass m, then that m is considered the invariant mass of the quanta of the field. JRSpriggs (talk) 14:57, 29 July 2020 (UTC)[reply]
You are introducing the concept of a parameter in a quantum-mechanical field equation as the invariant mass of a particle associated with a field. Such a definition of an invariant "quantum mass" is not problematic, but it does not correspond to the concept of "invariant mass" in special relativity (except perhaps in extremely limited conditions, and even then are their sizes even the same, considering the "dressed" and "undressed" differences?). Further, this is a classical context, where all arguments should be complete without appealing to quantum mechanics. As such, this observation does not really help in this context. —Quondum 15:55, 29 July 2020 (UTC)[reply]

This whole article needs to be rewritten

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I just fixed an equation that was plain wrong. But this is a mess. I think everyone that wants to edit should read this paper first: On the Abuse and Use of Relativistic Mass by Gary Oas. Basically, he affirms the whole "relativistic mass" thing is wrong (and yes, he affirms that if a body has energy E and mass m (invariant mass, rest mass, the only mass there should be), then the equation E = mc² is just wrong). And he shows that there are almost no textbooks (not even introductory ones) today that use that concept. Edelacroixx (talk) 05:57, 11 July 2022 (UTC)[reply]

The equation E = mc² is perfectly correct and backed by the literature, provided it its clear from the context that this is a stuation where v = 0, which clearly is the case here. This is not mathematics, but physics, where the meanings of the variables are described in the text that accompanies the equations. - DVdm (talk) 08:57, 11 July 2022 (UTC)[reply]

First of all, and to be clear, I don't think that the article as it is has a fundamental error, now that we fixed that it said E_0 instead of E in that (poorly written) section.

Now, when I said "the equation E = mc² is just wrong", I was referring to the general case for any value of speed. When v = 0, we have E = E_0, which is in fact equal to mc². In that case we just write E_0 = mc² (I say "we" because I teach the subject at uni...). (I realize that this may sound contradictory to my edit; that's because it is poorly to begin with, and I can't rewrite the whole thing right now).

My point (Oas' point, the point of Minutephysics' two minute video on the subject) is that old books made people think that the famous equation E = mc² is not only valid at any speed, but is also a fundamental equation in special relativity. Both are wrong, that's what Oas' article is about. And it's not a matter of nomenclature, we're talking about a completely different approach on the introductory level of special relativity, that can create misconception amongst students. Today, you will find no textbook using E = mc². And IMHO I think all of this must be addressed on the article (I will give it a go on the future) to help students understand better both the "old" and the "new" nomenclature for mass. (It really isn't new: as it is shown on the article, Einstein at the end didn't like to talk about relativistic mass, this means he didn't like E = mc²; he liked E² = (pc)² + E_0² and E_0 = mc².) Edelacroixx (talk) 03:14, 12 July 2022 (UTC)[reply]