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Objections to Relativistic mass

  1. Nov 22, 2005 #1
    Hi folks. I need your help. I'm starting to rewrite my paper on the concept of mass in relativity and I'm trying to compile a list of objections to the concept of relativistic mass. I've managed to compress tghe objections to a list of about 17 items long. If you have any objections you believe should be added to the list please let me know. If you believe that there is an item on the list which doesn't deserve/merit being there then please let me know your thoughts on that as well. I really appreciate your input to this. Thank you very much in advance.

    The list is at


  2. jcsd
  3. Nov 22, 2005 #2

    Most of these do not seem like good objections (although a few do).

    1. This one I agree with (sort of). Not that it obscures the physics, but that using [tex]m = \gamma m_0[/tex] creates inconsistency.

    2. Huh? Mass can be converted into that energy, that's the point. Fusion reactions convert mass to energy (in the case of hydrogen fusion, 7% of the involved mass is converted into energy). What do you mean m is the total energy? I really don't see what you're trying to say with this one.

    3. This is very true.

    4. I'm not sure what that one is supposed to say, but it looks like [tex]m^Q \frac{E}{c^2}[/tex]?

    5. Ok, but regardless of the term what quantity are they using? Words used are irrelevant, so long as you are consistent.

    6. Confuses students at least, but its not a hard concept to get a grip on and keep track of.

    7. How so? And what does that have to do with using relativistic mass?

    8. Huh? Why? This looks like inconsitency in terms to me, not an actual problem.

    9. The newtonian relation is not [tex]\vec{F}=m \vec{a}[/tex], though it is usually taught that way. It is actually [tex]\vec{F} = \frac{d\vec{p}}{dt}[/tex] and you can use that with relativistic mass.

    10. Not the gravitational mass? So what you're saying is the proton mass of [tex]1.673 \times 10^-27 kg[/tex] is the gravitational mass but the mass of [tex] 938.3 \frac{MeV}{c^2}[/tex] is not? If so, that doesn't make any sense. Its irrelevant how gravity works in GR, the two numbers for mass are equivalent. Besides, [tex]E=mc^2[/tex] gives the REST energy of a particle, when [tex]\vec{v} = 0 [/tex], so relativistic mass has nothing to do with that.

    edit: This is an example of why using two definitions of mass is bad. I just realised the problem with my statement, which suffers from inconsistent use of the word mass. See, I tend to use the formula [tex]E^2 = (pc)^2+(mc^2)^2[/tex] in relativity, so in my mind [tex]mc^2[/tex] is for no motion. But if you use relativistic mass, then [tex]E=\gamma m_0c^2[/tex] is [tex]E=mc^2[/tex]. This inconsistency creates confusion, which causes problems.

    11. Arguments from authority have no merit. Now, if you give his reasons for saying that, then this may be a valid point.

    12. How so?

    13. Bad ones are yes. But this is a reflection on textbook writers not on the usefulness of a concept.

    14. Again, arguments from authority have no merit. But if you go into why they don't use it, then this may be a valid point.

    15. So is Newton's theory of gravity, but we still used it to put men on the moon.

    16. How so? Why? This doesn't give a reason.

    17. This is a good reason. This reason makes sense, and is by far the best one in the list. Tying it in to the context of theory, and why a convention like that does not fit in the conventions of the theory is good.

    While I find the use of relativistic mass superfluous, I don't see how its a flawed concept in anyway. Unnecessary, yes. Inconsistent? At times. Worthless? Not really.

    Hope this helps.
    Last edited: Nov 22, 2005
  4. Nov 23, 2005 #3
    Thank you for your input franznietzsche. The questions you're asking are really questions of the people who make those claims. I don't make those claims myself. I'm trying to summarize them and then I'll address then in the paper I'll write (or rewrite actually). In fact the purpose of this thread is to get input regarding how accurate that list is in summarizing the objections listed in the following articles

    The Advantage of Teaching Relativity with Four-Vectors, Robert W. Brehme, Am. J. Phys., 36(10), October 1968

    The Concept of Mass, Lev Okun, Physics Today, June 1989

    Putting to Rest Mass Misconceptions, Physics Today, May 1990

    If you'd like to read them then they are in PDF format towards the bottom of this web page -


    Once I get an accurate summation of what the objections are as given by those authors then I can correctly site them in the paper I will write. Its a lofty task but if the objections sound like objections you've heard before then I'll accept that as an "objection" I'll state in the paper to be written. If you object to an "objection" then I can reference the particular paper and show you where the objection/comment was made.

    Okun made the comment "Rest energy was one of Einstein’s great discoveries..” in his paper "The Concept of Mass" listed in the link above. Einstein did not make this discovery. In Einstein's first derivation of E = mc2 he assumed that the body had energy which could be released in the form of electromagnetic energy.

    Items 1-3 are from Brehme's article. Items 4-11 are from Okun's article. Item 12 is a letter to editor of Physics today from a "Poovan Murugesan." Item 13 is from a student who was studying relativity whose name is "Catherine Sauter." I forget where Items 14 to 17 came from but they're somewhere in the articles listed above. Item 18 is from a letter to the editor of "Physics Education."


    ps - A previous version of my paper is at

    Its far too long and pretty messy at places. That's the problem with having dyslexia! :)
    Last edited: Nov 23, 2005
  5. Nov 23, 2005 #4


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    While I know you are trying to shoot all the objections down, it's not fair having all the objections be expressed in sentence fragments & poor grammar. You have to "spiff them up" so that they appear readable and at least form complete sentences.
  6. Nov 23, 2005 #5


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    Concerning 17
    "Special relativity is a theory about geometry and from the modern, geometric viewpoint, the mass is invariant, not velocity dependant",

    It's not so much that "mass is invariant", where the mass is taken to already mean the invariant quantity.
    Instead, it's that it is often best to work with invariant quantities (e.g., the rest mass) rather than observer-dependent quantities (e.g. the relativistic mass). In an analogous way, in Euclidean geometry, it's often best to work with magnitudes and direction rather than with x-components and y-components. As you know, magnitude and direction describes a vector (with a Euclidean metric) independent of a set of axes, whereas a description with x- and y-components requires additional information about the choice of axes used.

    In relativity, the above preference suggests that one should work with the "electromagnetic field tensor" rather than its components (the "electric and magnetic fields").
  7. Nov 23, 2005 #6


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    All 17 objections, after some corrections and/or modifications, boil down to one and only one objection;
    the concept of frame-dependant mass is misleading. only the scalar invariant concept of mass (p^2=m^2) is useful.


  8. Nov 24, 2005 #7
    I'll bite.

    So are you saying that energy has the same units as mass? Please, explain this point of view more thoroughly. Do you have any real reason to refute decades of experimental work pointing to the contrary?

    Photons are massless, but they have energy. The two are not exactly the same, just look at all the ways energy can be stored in a system: thermal, kinetic, potential, electro-magnetic. Mass can only be stored one way, as mass.

    The way you talk, throwing out hand-waving arguments, without citing any relevant supporting data certainly makes it appear that way. Though I'm really trying to give you a fair chance, you're just not helping yourself out much.
  9. Nov 24, 2005 #8
    The purpose of this thread is to make a good attempt at summarizing the objections in the most complete and precise/concise form while not taking up too much space. For each objection I must have a reference from the physics literature so I took these from the main literature concerning this debate [the grammar will be corrected, of course, when I write the paper]. What is fair is giving the reader the reference to where she can read the entire arguement. But the more room I give to the objection the less room I give to the response. The room for the objection is in the published articles.

    This is my first cut at a precise statement. I hope to get the spirit of the objection into a one-line statement. A correct way to state an objection is to write a paper. But that's been done.

    So please recommend how you'd spiff them up and make them a much better statement. Thanks.

    Note - My purpose is to illuminate the errors in the arguements presented to date. It is not to suggest that proper mass has no place in relativity. That'd be just plain dumb and I don't believe it anyway.

    Sam - That arguement would never fly in a physics journal. One must back such claims up if the topic of the paper is the claim itself.

    Last edited: Nov 24, 2005
  10. Nov 24, 2005 #9
    The main reason I don't like relativistic mass (and yes it's a personal flavour if you like the term or not) is that nature is coordinate independent. So a physicist has to explain nature in a coordinate independent way and try to avoid coordinate dependent properties.

    A good text about the equivalence between mass and energie (E=mc²) can you find here: http://www.mathpages.com/rr/s2-03/2-03.htm
  11. Nov 24, 2005 #10
    I don't see why that's a problem because when physicists actually make a measurement in a laboratory they're measuring a component of a geometric quantity such as a vector or tensor. Relativistic mass is an observer dependant quantity and since the observer can be defined in terms of a 4-velocity then the relativistic mass can be described in purely geometric terms. I.e. if P is the 4 -momentum of a particle and Uobs is the 4-velocity of an observer then P*Uobs/c2 is the relativistic mass of the particle as measured by that observer. Anytime you speak about things like time dilation, Lorentz contraction, total inertial energy, kinetic energy, potential energy etc. then you're speaking about observer dependant quantities.

    Anytime you have a conserved quantity in physics then its an important quantity. The conservation of relativistic mass is a theorem that can be derived without involking the principle of conservation of energy. For proof see


    Last edited: Nov 24, 2005
  12. Nov 24, 2005 #11


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    That's the point! When you discuss your measurement of the component P*Uobs/c2, you also have to specify information about the measurer U. In other words, your component describes the particle of interest and its relationship to the measurer.
    Then, to extract and isolate the coordinate-independent physics (and factor out the measurer), you show that the components are those of a tensor by showing that they form "a set of components that transform... ".
    In the end, you'll find that the coordinate-independent quantity is P*P.
  13. Nov 24, 2005 #12
    What's the point??
    And you see a problem with that? The observer is just as much a geometric object as is P. Anytime one wishes to speak about non-intrinsic properties of an object one is speaking about an observer. E.g. if someone asks what the lifetime of a particle is one must specify an observer Uobs, unlike the situation when one asks what the proper lifetime of a particle is. These aren't "problems." They are simply observer dependant quantities. I see no reason to refer to an observer dependant quantity as being a "problem."
    There's a difference between being observer dependant/independant and being a problem/non-problem. Observer dependant quantities are not problematic, they are simply aspects of SR to be considered.

    Anyway, this has gotten off topic. The topic here is to determine an actual set of objections which are in the physics literature for which I can give a specific reference. This has not been very easy and I was simply looking for help in compiling such a list in a short amout of space.

    Thanks for your response though. Always appreciated Rob! :smile:

  14. Nov 25, 2005 #13


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    I'd say that #3, #6, and #13 are essentially the same;
    unless you more clearly distinguish them from each other,
    you should probably treat them as the same.

    #12 and #16 might also be different vague wordings of:
    "mass is intended as an intrinsic property of an object,
    so it is contradictory to refer to [tex]\gamma m_0[/tex] as a mass".
    Perhaps #1 is another of the same genre.

    I'm not sure how you're intending to treat #9, but it seems to me
    that the main reason folks introduce [tex]m = \gamma m_0[/tex]
    is so they can use it in F = ma ... .
    Whether THAT is a good idea is a different issue.
    Last edited: Nov 25, 2005
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