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Those who use relativistic mass and why

  1. Jul 25, 2004 #1
    I'm starting this thread since my response to Tom was too long for one post.

    That's why I said is was misleading and not incorrect. You're giving the impression that there is an overwhelming number of physicists who use the concept you suggest.

    Let me clarify by example: Suppose it were true that 60% of all relativistist use relativistic mass and 40% who didn’t. Then I'd say that a claim that the "majority of physicists don't use it" is incorrect. If the stats where 1% who use it and 99% who don't then I'd say that your statement was very accurate. If the stats were 40% who use it and 60% who don't then a statement that the majority do use it is misleading. It gives the wrong impression as far as how much its accepted. "The majority ..." makes one think that all but 10 or 20, who teach in community colleges, use it.

    However I don't have the stats and I doubt that anyone does so its impossible to tell. One would actually have to poll all physicists who use relativity and ask them if they ever use it either in papers or in their thinking/motivation etc. That too is impossible.
    If its not too much trouble, can you please list the relevant texts of which you speak?

    Here is a list of the texts/books I'm speaking of --

    Gravity from the ground up, Bernard F. Schutz, Cambridge Press, (2003)

    Relativity: Special, General and Cosmological, Wolfgang Rindler, Oxford Univ., Press, (2001)

    Cosmological Principles, John A. Peacock, Cambridge University Press, (1999)

    Understanding Relativity: A Simplified Approach to Einstein's Theories, Leo Sartori, University of California Press, (1996)

    Basic Relativity, Richard A. Mould, Springer Verlag, (1994)

    Introducing Einstein's Relativity, Ray D'Inverno, Oxford Univ. Press, (1992)

    Gravitation, Misner, Thorne and Wheeler (MTW)

    Concepts of Mass in Contemporary Physics and Philosophy, Mass Jammer, Princeton University Press, (2000)

    Classical Electromagnetic Theory, Vanderlinde, John Wiley & Sons, (1993)

    A First Course in General Relativity, Schutz, Cambridge Univ. Press, (1990)

    A Short Course in General Relativity, Foster & Nightingale, Springer Verlag, (1994)

    Quantum Mechanics, Cohen-Tannoudji et al

    The Cosmic Perspective, Bennet, Donahue, Schneider, Voit, Addison Wesley, (2001)

    (dw uses a few of those, e.g. MTW and Rindler)

    There are tricky little instances too. One such tricky thing can be found in Classical Electrodynamics - 2nd Ed., J.D. Jackson, page 617, [And, as I recall, there is something similar in Classical Mechanics 3rd Ed., Goldstein, Safko and Poole (2001)] problem 12.16. The student is supposed to find a a general relationship for the center of mass of an electromagnetic field. Now, as that term is used, in that problem, it can only be meaningful if the "mass" is relativistic mass. I worked out the solution here

    arxiv --


    You didn't ask about physics journal articles on this subject. For a list please see -- http://www.geocities.com/physics_world/mass_articles.htm as well as the other link and articles from AJP

    There should be one more in the future when mine is proof read and all the typos and grammatical errors are out.

    I have Alan Guth's lecture notes from his Early Universe course. He says in one place in his notes that he doesn't use it, yet in another place he actually uses it. I asked him about that and he said he didn't realize he was doing it.

    Note: I don't hold that all relativists that use relativistic mass use it in all places at all times. That'd be silly for anyone to do. They use it where it is appropriate or useful to to use it.

    See -- http://www.geocities.com/physics_world/relativistic_mass.htm

    There are online class notes from universitys that use the concept as well as from particle accelerator labs such as CERN.

    Thanks for the very direct response. It is greatly appreciated. Especially since you explained in a very professional tone. Thanks! :approve:

    Question: Why do you refer to the magnitude of the 4-momentum as mass and not rest energy?
    I used Cohen-Tannoudji in grad school and they used the velocity dependance of mass.
    As in particle physics these folks work with matter on a microscopic scale and they study the structure of matter. They don't really study the dynamics of matter. Consider this - Does the lifetime of a particle depend on the speed of the particle? Relativity says it does. Call the lifetime as measured in the particle's rest frame the proper lifetime. The proper lifetime is an inherent property of the particle and is one of the things particle physicists study. Do you think that when a particle physicist says "the lifetime of a free neutron is 15 minutes" that he didn't know that the lifetime depends on the speed of the particle? Do you think that particle physicist doesn't know that the particle's lifetime is different than the particle's lifetime? Sometimes people use the letter tau to represent proper lifetime and some use T. Quantites which appear in 4tensor equations are proper quantities, e.g. proper mass, proper time, proper distance, etc. Time does not appear in such equationsm, proper time does. Relativists know the difference right? The relativistic Lagrangian contains the proper mass of a particle, not the mass.

    A particle physicist, nor a solid state physicist, will never ask himself what the mass of a charged capacitor is or how to compute it. Its not as simple as it is for a particle. See

    Nor will they compute the inertial mass of a gas. But it can be done and it has nothing to do with a magnitude of a 4-vector.

    This stuff can be so confusing at times that even the best relativists can make serious mistakes when they don't fully think about what "mass" means. Even Schutz made a serious error in his new text and got a calculation wrong. But that's a topic for another thread. :smile:

    As Scotty said How many times do I have to tell ye? The proper tool for the proper job! :biggrin:

    Last edited: Jul 25, 2004
  2. jcsd
  3. Jul 26, 2004 #2


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    Mass is to be measured and not just defined
  4. Jul 26, 2004 #3
    I agree. In fact I don't recall ever saying otherwise. However its impossible to measure something unless you first define what it is you're measuring.

  5. Jul 26, 2004 #4
    When they've found a Higgs particle I'll believe that physicists
    understand what mass is.Until then...
  6. Jul 26, 2004 #5
    There are many mechanisms to inertia. One is the internal energy of a body. Another is the base rest mass (the mass a body has when it gives up all the energy it can besides the energy from the individual rest masses of the individual particles). Time dilation - that is the mechanism behind relativistic mass/inertial mass. It is why a moving body is harder to accelerate than the same body which is moving slower. The Higgs thingy is the mechanism behind the bare mass of a fundamental particle.

  7. Jul 26, 2004 #6

    Tom Mattson

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    I suppose everyone is free to interpret the word "majority" as they will. But the fact of the matter is that even if "only" 51% of physicists use the invariant mass convention, then it is neither misleading nor incorrect nor inaccurate to say that that is a majority. Your quibble is not with me, but with the dictionary.

    It's probably impossible to get an exact count of research papers that use it vs those that don't, but it doesn't seem that it would be that difficult to get a picture of how much research activity is being done in HEP vs. GR/QC. But I don't care enough about this to find out, so I'll concede the point.

    I'll do it when I get home from work.

    Were any of those eventually publised anywhere?

    That's because I wanted to take a quick look, and the arxiv is easiest to access. I figure I can use the list of references to follow the paper trail into the journals.

    OK, but AJP is a research journal of physics education. Does this concept appear in PRL or Phys Rev D? That's where working relativists (and not just teachers of relativity) publish.


    Don't get me wrong: I did use the "noninvariant mass" concept as an undergrad in nuclear engineering. We used it to calculate the yield from fission reactions, and it works just fine. I was saying that my coursework led me to the conclusion that the noninvariant mass concept is not widely used in physics, not that it is wrong.

    Because in natural units (hbar=c=1), the mass and the rest energy are identical. Being a particle physicist, I use natural units (as Feynman said, "Only stupid people carry c's and hbar's around" :tongue2: ).

    The QM book? I took QM I out of volume I, and there is no relativity in it at all. Is there in volume II?

    That's not true, QFT with interacting fields is our bread and butter, and it is the dynamic theory of matter par excellence.

    I've snipped off the rest of the exposition on this and will just say, Yes, the particle physicist does understand that all mean lifetimes are proper lifetimes. I'll just note that when it comes to lifetimes (or lengths for that matter) we have no choice but to use speed-dependent lifetimes (and lengths) because, as DW correctly points out in the thread "Einstein's inconsistency", the Lorentz factor γ enters at the level of spatiotemporal intervals. But we do have a choice of convention when it comes to mass.

    It seems that you're making the same mistake as DW here, but in the opposite direction. The relativistic Lagrangian does indeed contain the mass of a particle if I adopt the convention that the norm of the 4-momentum is the mass. If one convention cannot be said to be wrong, then neither can the other.
  8. Jul 26, 2004 #7
    dw got carried away. But since I don't know you all that well yet I wanted to get to understand what you mean a bit more.
    Perhaps it was a poor choice of wording on my part.

    re - "Were any of those eventually publised anywhere?"

    This one was -- http://xxx.lanl.gov/abs/physics/0103051
    It was publsihed in Physics - Uspekhi, 43 (12), 1267 (2000). The one I wrote was reviewed by AJP. They said that while it was new and it was correct, it wasn't spectacular enough for them to print. Ah well!
    I'm sorry Tom but I don't see how that makes the physics any less meaningful or valid. Working relativists publish papers there and not soley for pedagogical reasons per se. Articles which appear there are often of theoretical interest in relativity.
    That is where physicists who use relativity publish articles whose subject fit under the general title of Particles, Fields, Gravitation and Cosmology. Its not where theoretical relativity is published.
    Yes. If you ever pick up Vol. II then turn to page 1214 and read section b. Interpretation of the various terms of the fine structure Hamiltonian Subsection alpha Variation of the mass with the velocity (Wsub]mv[/sub] term). The authors write
    I can scan and e-mail you that section if you'd like. But its also online at
    That's quantum dynamics, not classical dynamics. In QFT velocity does not have a meaning outside of a statistical sense.

    I wasn't going in that direction. I was saying that since the Lagrangian is an explicity function of m0 and not m(v) (call them what you will, I was just making this point).

    Thanks Tom

    Last edited by a moderator: Aug 9, 2004
  9. Jul 26, 2004 #8

    Tom Mattson

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    AJP articles aren't any less meaningful or valid. It's just that they aren't at the forefront of research in either gravitation or cosmology.

    Plenty of theoretical and experimental relativity is published there. The "Gravitation and Cosmology" part includes classical GR, and a quick perusal of the table of contents in recent issues reveals current research in gravitational waves.

    No need, I know people who have a copy of volume II.

    Quantum Dynamics: Is there any other kind? :biggrin:
  10. Jul 26, 2004 #9
    How did "forefront of research" get into this conversation?
    You're saying that some of it contains physics which is not related to Particles, Fields, Gravitation and Cosmology?
    Ask the string people that, not me. :confused:

  11. Jul 26, 2004 #10
    I don't agree. People have a tendancy to think that things like cosmology are just more "sexy" than things like a homopolar generator etc. There are papers in it which report experimental results. For example

    Measurement of the relativistic potential difference across a rotating magnetic dielectric cylinder, J. B. Hertzberg, S. R. Bickman, M. T. Hummon, D. Krause, Jr., S. K. Peck, and L. R. Hunter, Am. J. Phys. 69, 648 (2001)
    Personally I find things like the homopolar generator more sexy that black holes and dark energy etc.

  12. Jul 26, 2004 #11

    Tom Mattson

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    It got there by me inquiring about it.

    No. "Gravitation and Cosmology" includes GR, and research in that field is published there.

    What I mean is this:

    When you raise the objection, "But that's quantum dynamics...", my response is, "That's the only kind of dynamics that takes place in reality."
  13. Jul 26, 2004 #12
    You inquired about the forefront of research? Sorry. I didn't see that inquiry.

    I had a feeling you were going to say that. But since this thread is on a classical concept based on a classical thing like velocity. There are many relativistic topics which are meaningless in QFT but are quite meaningful otherwise. Relativistic mass is one such quantity. To this end I'm refering to the notion that QFT people don't use relativsitc mass as if that's something meaningful. They don't seek of things like velocity in relativistic quantum mechanics but that doesn't mean that people who do that work never use the notion of velocity.

  14. Jul 26, 2004 #13
    My burning question is whether one can get by with a fundamentally given relativistic concept of 3-momentum (mvγ) and just avoid the mass issue by always talking in momentum terms in any high speed mass scenario. I am not particularly happy about elementary derivations of this 3-momentum usually offered, but that might just be on account of my prejudices.

    In short, what is the sense in which speed-dependent mass is an essential rather than a derived (specified) concept?

    Thank you,
  15. Jul 26, 2004 #14

    Tom Mattson

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    I inquired about it by asking about articles from PRL and Phys Rev D.
  16. Jul 26, 2004 #15


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    Sorry I blinked and the thread shot off way ahead of me!

    The measurement problem has two components: what is to be used as a standard unit, and how is that standard to be transported around the universe for the comparison to be made?
    In GR, based on the EEP, energy-momentum is conserved therefore, in that theory, the standard is an atom, and because mass is defined to be invariant by the EEP it is assumed that masses, lengths and times on the far side of the universe can be measured by that standard.
    In the Jordan frame of the conformal gravity theory of self-creation it is energy and not energy-momentum that is conserved. (Incidentally this allows a form of continuous creation.) The standard becomes a “standard photon”, carefully defined – cosmologically it is a photon sampled at the peak intensity of the CMB – its energy, which is invariant in this frame, yields a measure of mass, its frequency time and hence length. (c is constant in the theory)
  17. Jul 26, 2004 #16
    Depends on what you want to know.
    I'm sorry but I don't know what that means or what you're asking. E.g. Regarless of what anyone defines things the physics is the same and the equations as as well. The only thing that changes is the symbols and the names.

    It should be stated at this point that, unless the subject matter contains potential energy, or the subject matter is energy, the concept of energy in SR is not required. I don't think its required in GR either. One can replace energy by mass in all such cases.

  18. Jul 27, 2004 #17


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    Back to the original question. "Those who use relativistic mass and why"

    One reason for the use of relativistic mass is simply "the faster it gets the harder it is to push".

    Of course this experimental fact can be interpreted in two ways.
    1. The first is to say the mass of a body moving relative to an observer increases when measured by the observer - relativistic mass.
    2. The second is to say that Newton's law of inertia, F = ma, has to be modified by the relativistic gamma factor and the mass of the body does not change.

    Both are equally correct, one is equivalent to the other, it is simply a matter of convention as to which is the more convenient. As we have seen above this is a matter of opinion, however, the No. 2 formulation is generally adopted because it is also consistent with Einstein's Equivalence Principle (the EEP). Mass is invariant, and the word refers to what otherwise might be called "rest mass", that is the mass as measured by a co-moving observer in whose frame of reference the body is at rest and equal to the body's four-momentum.

    However to the simple mind the idea of relativistic mass may be more in keeping with E = mc^2, that is to say energy can actually turn into mass (and vice versa) and not just have a mass equivalent value.

    In the No. 2, standard convention you are stuck with the mass in those particles that you have, apart from particle/antiparticle creation/annihilation, all the energy released in an nuclear reaction for example, is that "system energy" formely bound with the nuclear particles. Particle mass has not been converted into pure energy at all, as is popularly thought. Furthermore, if the mass of a particle actually does change, due to absorption of energy,
    this convention would be incapable of recognising the fact, it is tautological in definition and blind to any variation that might be taking place.

    Yet at a fundamental level a particle is not some indestructible mass but seems to be 'just' energy, in the form of energetic vibrating strings, or whatever, which has acquired inertia; so although the No. 2 convention is adopted because it is convenient for a lot of applications it may be the No.1 convention that is more fundamentally 'true' and favoured by the 'String people'.
    Our experiments may yield the data about the universe out there, but we have to interpret that data and that requires an act of faith, in which we choose one particular interpretation over another. The choice is yours!
    Last edited: Jul 27, 2004
  19. Jul 27, 2004 #18
    Granted the SR ordinary momentum defined by mvγ, I can readily derive the energy-momentum-restmass relationship. If I opt for a relativistic mass M defined by mγ, then the momentum is a cinch: it is just Mv, just as Newton said "quantity of motion" should be quantified. But the energy-first school thinks that is improper, reifying something as substantial without warrant. So can I render the relativistic 3-D momentum as a primary dynamic quantity and avoid the conflict? If so, M would just be a convenient calculus substitution variable, enough to pull out the derivation.
  20. Jul 27, 2004 #19


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    We have already been through all this here already. The law of motion for special and general relativity is the four-vector law:
    [tex]F^{\lambda } = mA^{\lambda }[/tex].
    The mass m in that equation does NOT change with speed! How many times do I have to say that here? I really wish those who are still using the mistake called "relativistic mass" would actually read this:

    You are wanting to replace the m in that form of Newton's second law with Planck's variable mass concept, but in doing so would wind up with an equation of motion that is just plain wrong according to relativity, even accoding to Planck, Tolman, and Lewis version of special relativistic dynamics.
  21. Jul 27, 2004 #20
    I agree that this is why many people think in terms of relativistic mass.

    [tex]\bold a_{\|}[/tex] = Component of acceleration parallel to the particle's velocity

    [tex]\bold a_{\bot}[/tex] = Component of acceleration perpendicular to the particle's velocity

    The force, F, on a particle whose proper mass is m0 is related to those components of acceleration through the relation

    [tex] \bold F = m_{\|}\bold a_{\|} + m_{\bit}\bold a_{\bot} [/tex]


    [tex] m_{\|} = \gamma m[/tex] = Longitudinal mass

    [tex] m{\bot} = \gamma^3 m [/tex] = Transverse mass

    For proof please see - http://www.geocities.com/physics_world/sr/long_trans_mass.htm

    The relationship F = ma not valid. It is only valid when the mass, m, is not a function of time. In SR, when a particle is accelerating the mass is a function of time. The correct relation between mass and force is F = dp/dt where p = mv.

    To measure the mass of a charged particle one can place the particle in a uniform magnetic field and observer the particle's trajectory, measure its velocity and then, once you've made the appropriate calculations, you can be said to have "measured" its mass. E.g. let the charge be q. Let the magnetic field be parallel to the z-axis and have a magnitude B. Let the velocity vector be parallel to the xy-plane. The trajectory will be a cirlce (for the most part). Measure the radiius of that circle and call it r. Then the mass is found to be

    [tex]m = \frac{qBr}{v}[/tex]

    For a derivation of this please see

    Do you think that the qualifier proper should be left off of the term proper time and simply call d(tau) "time"? If not please explain why.

    So long as one does not confuse simplicity with stupidity. :wink:

    I disagree. The proper mass of a particle can change. You can still legitimately call that "invariant mass" since the term "invariant", as aplied to mass means "unchanged by a change in coordinates." It does not mean "unchanged with time."

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