In which areas of physics is relativistic mass used?

[jtbell]

When I was a graduate student in experimental high-energy particle physics c. 1980, none of the people I worked with (fellow experimentalists and theorists alike, in that field) used relativistic mass

$$m = \frac {m_0} {\sqrt {1 - v^2 / c^2}}$$

in their work, to the best of my memory. The only place I remember seeing relativistic mass used was in a textbook about particle-accelerator design, written in the 1950s and hence already rather old.

I recognize that my experience is limited to HEP. Therefore, I am genuinely curious, in light of the arguments that sometimes break out here about relativistic mass:

In which areas of physics nowadays do physicists use relativistic mass in their work? I'd like some references to examples of professional research publications (journal articles, monographs, etc.) that use relativistic mass, as opposed to writings for laymen, or treatments in introductory school or university textbooks, or polemics for or against the use of relativistic mass. They should be fairly recent, ideally from this century, but at least since about 1980 or so.

 

[ZapperZ]

In Accelerator Physics, we do still use relativistic effects, such as "relativistic mass" when we model the particle beam dynamics and when we design accelerator components in the lab frame. If not, the particles will be moving way to fast in the simulation when compared to experiment.

These are described in standard accelerator physics texts. I know you don't want "university textbooks", but these are books that professionals in this field still use. I would recommend, for example, the "standard" text in accelerator design by Tom Wangler (RF Linear Accelerator), or check out Stan Humphries free online text http://www.fieldp.com/cpa.html".

Zz.

 

[jtbell]

Thanks! To clarify about textbooks, specialized or upper-level textbooks like the ones you mention are fine. I just want to exclude things like freshman-level "general physics" textbooks or intermediate-level "intro modern physics" textbooks which are usually not written by specialists, and certainly not for specialists.

 

[robphy]

You might hunt around at http://scholar.google.com/scholar?q="relativistic mass"

 

[DrGreg]

For what it's worth:

Rindler, W. (2006 2nd ed), Relativity: Special, General and Cosmological, Oxford University Press, Oxford, ISBN 978-0-19-856732-5.

I was rather surprised to find Rindler (yes, the Rindler whose name is attached to Rindler coordinates) using relativistic mass throughout this undergraduate-level specialist textbook and calling it just "mass". (Although to be fair he does comment on differing usages when he introduces the topic.)

This might, however, fall into the category of books you want to exclude.

 

[atyy]

http://books.google.com/books?id=P_T0xxhDcsIC&printsec=frontcover#PPA190,M1

http://www.quotationspage.com/quote/26933.html

 

[robphy]

Rindler's 1977 Essential Relativity: Special, General, and Cosmological, Springer-Verlag has a similar viewpoint.

This preprint http://arxiv.org/abs/physics/0504111 might be a useful starting point.

Of course, all of this doesn't really matter...
as long as one knows what one is doing [...for the author and (hopefully) the reader].

 

[atyy]

http://books.google.com/books?id=DGSpO1yBPgIC&printsec=frontcover#PPA23,M1

 

[bernhard.rothenstein]

Consider that physicists repeat with high accuracy the experiments performed in 1900 in order to determine the speed dependence of mass (in a modern language the relationship between rest mass and relativistic mass of an electron). Consider that the equation m=gm(0) best fits the experimental results. Multiplying both its sides with c^2 we obtain, taking into account the physical dimensions of the product massx(speed)^2
E=gE(0).
Is there more to say?

 

[atyy]

"Now the inertial mass of a typical laboratory body is made up of several types of mass-energy: rest energy, electromagnetic energy, weak-interaction energy, and so on." http://relativity.livingreviews.org/Articles/lrr-2006-3/

"How is it possible that massive protons and neutrons can be built up out of strictly massless quarks and gluons? The key is m = E/c2. There is energy stored in the motion of the quarks, and energy in the color gluon fields that connect them. This bundling of energy makes the proton’s mass." http://www.aip.org/pt/nov99/wilczek.html

 

[jtbell]

You might hunt around at http://scholar.google.com/scholar?q="relativistic mass"

Thanks for that tip. I'd forgotten about Google Scholar. When I get some time, I'll try to classify and tabulate the first few pages of hits.

On a related subject which pops up here frequently, I tried searching Google Scholar for "photon relativistic mass" and "relativistic mass of photon" and didn't see any indication at first glance that anyone actually uses the m that you get from equating $E_{photon} = mc^2$, as a photon mass. The only hit that looks relevant is a polemical article about relativistic mass in general, by Sandin. Searching simply for "photon mass" gives me lots of tests and upper limits on the invariant mass.

 

[robphy]

It might be interesting to search by year:
scholar.google.com/scholar?&as_epq=relativistic+mass+&as_ylo=2001&as_yhi=2001
(Note this is different from an imperfect search with additional keyword 2001 [since entries with page number 2001 might show up].)

Maybe there is a way to restrict to a certain set of journals (say, Physical Review).

 

[atyy]

"photon mass"

If the deflection (12) truly reflects the “weight of kinetic energy,” a light beam with energy U should contribute an amount 2U to the gravitational mass of the box. ... For our “box of light,” 2T + U therefore vanishes, and 3T + 2U = T + U = E. The apparent violation of the equivalence principle has thus rather mysteriously disappeared." http://arxiv.org/abs/gr-qc/9909014

Edit: I think relativistic mass is most useful as a heuristic. If I understand correctly, there is strictly speaking no relativistic mass, and no gravitational mass in GR. However, there is gravitational mass and inertial mass in Newtonian gravity, and inertial mass in classical special relativity. GR reduces to the former at low speeds, and the latter in the absence of gravity, and it is interesting to see how the various masses emerge from certain limits of GR. Perhaps a related sort of question is whether invariant mass in quantum field theory (where everything is a wave and massiveness or masslessness are just a dispersion relations) is the same as rest mass of classical special relativity (where there are classical particles except for light, which is a wave).

 

[Bob S]

When the energy of an accelerator is mentioned in newsmedia, the value is usually the relativistic energy. The Fermilab Tevatron, for example was designed to go to 1 TeV (1 trillion electron volts or 1000 Gillion (billion in U.S.) electron volts). Right now (10 minutes ago) it was running at 980 GeV or 0.98 TeV. In any case, the proton rest mass is about 938 MeV (million electron volts) so most of the proton's energy in the Tevatron is due to relativistic mass gain.

 

[ZapperZ]

When the energy of an accelerator is mentioned in newsmedia, the value is usually the relativistic energy. The Fermilab Tevatron, for example was designed to go to 1 TeV (1 trillion electron volts or 1000 Gillion (billion in U.S.) electron volts). Right now (10 minutes ago) it was running at 980 GeV or 0.98 TeV. In any case, the proton rest mass is about 938 MeV (million electron volts) so most of the proton's energy in the Tevatron is due to relativistic mass gain.

For electron accelerators, it doesn't even have to be that high. For all our simulations, anything above 1 MeV is already relativistic.

Zz.

 

[DrGreg]

You might hunt around at http://scholar.google.com/scholar?q="relativistic mass"

A caveat. I suspect few practitioners actually use the phrase "relativistic mass", except to discuss the pros & cons of the concept.

Probably most pro-relativistic mass users call relativistic mass just "mass".

Probably most anti-relativistic mass users call relativistic mass "energy", and rest mass just "mass".

 

[bernhard.rothenstein]

A caveat. I suspect few practitioners actually use the phrase "relativistic mass", except to discuss the pros & cons of the concept.

Probably most pro-relativistic mass users call relativistic mass just "mass".

Probably most anti-relativistic mass users call relativistic mass "energy", and rest mass just "mass".

Please let me know how would describe physicists, who avoid the use of the concept of relativistic mass, the experiments performed by Bucherer, Kaufmann and Guye and Lavanchy [1] in order to confirm m=gm(0)? What would be the corresponding terminology?
[1] A.P. French, Special Relativity (Nelson, 1968) pp. 20-24

I think that most pro-relativistic mass users make a net distinction between the concepts "rest mass" and "relativistic (inertial) mass.