# In which areas of physics is relativistic mass used?

1. Mar 18, 2009

### Staff: Mentor

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.

2. Mar 18, 2009

### ZapperZ

Staff Emeritus
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.

Last edited by a moderator: Apr 24, 2017
3. Mar 18, 2009

### Staff: Mentor

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.

4. Mar 18, 2009

### robphy

5. Mar 18, 2009

### 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 text book 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.

6. Mar 18, 2009

### atyy

7. Mar 18, 2009

### 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].

8. Mar 18, 2009

### atyy

Last edited by a moderator: May 4, 2017
9. Mar 18, 2009

### 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?

10. Mar 19, 2009

### 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/ [Broken]

"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 [Broken]

Last edited by a moderator: May 4, 2017
11. Mar 19, 2009

### Staff: Mentor

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.

12. Mar 19, 2009

### robphy

13. Mar 19, 2009

### atyy

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).

Last edited: Mar 19, 2009
14. Mar 19, 2009

### 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.

15. Mar 19, 2009

### ZapperZ

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

Zz.

16. Mar 20, 2009

### DrGreg

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".

17. Mar 21, 2009

### bernhard.rothenstein

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.