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Natural Science Forum / Physics / Research / July 2008Who coined the term "relativistic mass"?
[Moderator's note: Lines reformatted to make them shorter. Although 80 is a maximum to enable nice display on almost all terminals, it's better to keep your own, original, unquoted text in posts at 72 characters per line or less, to enable it to be quoted a couple of times and still keep things at less than 80 characters per line total. Also, don't use more than 2 characters (including space) for a quote symbol. -P.H.] I asked this question before and never got an answer. I'm hoping that new people are on here who might just know the answer to the question: Who coined the term "relativistic mass" and where, i.e. I need a reference so I can read the source of the terms original usage. Thanks in advance. Pete [Moderator's note: Too much quoted text trimmed. -P.H.] > I asked this question before and never got an answer. I'm hoping that > new people are on here who might just know the answer to the question: > Who coined the term "relativistic mass" and where, i.e. I need a > reference so I can read the source of the terms original usage. Thanks > in advance. Wikipedia says that Richard Tolman did it, in 1912, by defining relativistic momentum (as defined by Planck) as relativistic mass times velocity. (thereby getting rid of the miseries of transverse and longitudinal 'masses', and freeing the concept from attemps to formulate quasi-Newtonian 'force laws') This seems to be common knowledge. You have a reason for doubting this? Jan > [Moderator's note: Too much quoted text trimmed. -P.H.] > [quoted text clipped - 7 lines] > relativistic momentum (as defined by Planck) as relativistic mass times > velocity. He defined the concept of a velocity dependant mass. However he didn't use the term "relativistic mass" in that paper. > (thereby getting rid of the miseries of transverse and > longitudinal 'masses', and freeing the concept from attemps to formulate > quasi-Newtonian 'force laws') > > This seems to be common knowledge. You have a reason for doubting this? I don't doubt that Tolman defined mass as the m in p = mv. What I'm looking for is the first usage of the term "relativistic mass." I had stated this above. I had hoped I was being clear. Perhaps not? Thanks for your response. Always appreciated. Pete > > [Moderator's note: Too much quoted text trimmed. -P.H.] > > [quoted text clipped - 9 lines] > > He defined the concept of a velocity dependant mass. That's most certainly wrong. The velocity dependent mass (Lorentz, electromagnetic mass) predated relativity by about 10 years. > However he didn't use the term "relativistic mass" in that paper. Wiki says explicitly 'coined the expression' that he did === > The velocity dependent mass of Lorentz and Abraham were replaced by the > concept of relativistic mass, an expression which was coined by Richard C. > Tolman in 1912, who stated: "the expression m0(1 - v2/c2)-1/2 is best > suited for THE mass of a moving body."[13] === If you know better you should perhaps correct this wiki entry. Do you have a copy of of their ref [13] R. Tolman, Philosophical Magazine 23, 375 (1912). at hand? > > (thereby getting rid of the miseries of transverse and > > longitudinal 'masses', and freeing the concept from attemps to formulate [quoted text clipped - 6 lines] > above. I had hoped I was being clear. Perhaps not? Thanks for your response. > Always appreciated. You are not clear about having seen ref. [13] yourself. (I'll try to have a look later) Did you? Jan >> > [Moderator's note: Too much quoted text trimmed. -P.H.] >> > [quoted text clipped - 28 lines] > R. Tolman, Philosophical Magazine 23, 375 (1912). > at hand? Yes. >> > (thereby getting rid of the miseries of transverse and >> > longitudinal 'masses', and freeing the concept from attemps to [quoted text clipped - 13 lines] > (I'll try to have a look later) > Did you? Yes. I thought I made this clear since I stated explicitly above "However he didn't use the term "relativistic mass" in that paper." Didn't that tell you that I read the paper? If not then I apologize for the confusion. I'll write to wiki. Thanks. Pete >>> > [Moderator's note: Too much quoted text trimmed. -P.H.] >>> > [quoted text clipped - 14 lines] >> >> That's most certainly wrong. Correction. He originated the concept of relativistic mass. However the notion was there before him. This is evident when (if I recall correctly that is) Planck expressed the Lorentz force as d(gamma*m*v)/dt = q[E + vxB] Did Planck ever hint at "gamma*m*v" being considered some sort of mass? Pete > >>> > [Moderator's note: Too much quoted text trimmed. -P.H.] > [quoted text clipped - 24 lines] > > Pete One of the problems with "Planck's Proposal" for his relativistic re- definition of momentum in 1906/7 (the actual basis of today's 'derivation' of E = Mc2) is that the final form of the formula (P = L m v) is ambiguous, as different textbook authors illustrate. Some choose the 'relativistic mass' M = L m while others allocate the 'Lorentz' (gamma) factor L to the velocity, generating the spatial part of a relativistic '4-velocity' V = L v. > One of the problems with "Planck's Proposal" for his relativistic re- > definition of momentum in 1906/7 (the actual basis of today's [quoted text clipped - 3 lines] > 'Lorentz' (gamma) factor L to the velocity, generating the spatial > part of a relativistic '4-velocity' V = L v. IMHO is the least doubtful way to figure out, what the expressions for basic quantities, energy, momentum, and angular momentum, are to use Noether's theorem. By definition these quantities are the generators for time translation, spatial translations, and rotations. Further, if in this connection one looks at the representation theory of the Poincare group, there is no doubt that mass in SRT should better be used only in the sense of "invariant mass", i.e., as one of the Casimir operators of the Poincare group. This concept has the advantage that then by definition "mass" is a scalar quantity. Energy should be called energy and not "relativistic masss". It's the time component of the energy-momentum four vector: E=m/sqrt(1-v^2) \vec{p}=m \vec{v}/sqrt(1-v^2), where I've set c=1 (natural units) to keep the expressions simple. -- Hendrik van Hees Institut für Theoretische Physik Phone: +49 641 99-33342 Justus-Liebig-Universität Gießen Fax: +49 641 99-33309 D-35392 Gießen http://theory.gsi.de/~vanhees/faq/ > IMHO is the least doubtful way to figure out, what the expressions for > basic quantities, energy, momentum, and angular momentum, are to use [quoted text clipped - 12 lines] > > where I've set c=1 (natural units) to keep the expressions simple. If my understanding of your reply is correct than what you write is almost identical with the document by Lev B. Okun at: http://www.physicstoday.org/vol-42/iss-6/vol42no6p31_36.pdf Specific See page 32. Both of you consider m to be a scalar (constant) and as such m does not change with speed. The subject energy-momemtum four-vector is also discussed at: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/vec4.html Here we read: "The invariance of the energy-momentum four-vector is associated with the fact that the rest mass of a particle is invariant under coordinate transformations." My impression is that Mr Okun will not agree with this. What is your opinion ? At page 47 of the book by Ray d'Inverno "Introducing Einstein's Relativity" we see a curve going upwards starting from m0 at v=0 to m(u)=infinity for v=c with the text: Fig 4.4 Relativistic mass as a function of velocity. Should not this be: Fig 4.4 Energy as a function of velocity ? Nicolaas Vroom http://users.pandora.be/nicvroom/ >> One of the problems with "Planck's Proposal" for his relativistic re- >> definition of momentum in 1906/7 (the actual basis of today's [quoted text clipped - 13 lines] > operators of the Poincare group. This concept has the advantage that > then by definition "mass" is a scalar quantity. That's a bit besides the topic, but it raises an interesting point: according to some dictionaries and uses, a scalar simply has no direction while a vector does have direction - http://en.wiktionary.org/wiki/scalar Anyway, would you also call energy "not a scalar quantity"? If so, do you deem that to be a disadvantage of the use of "energy"? > Energy should be called energy and not "relativistic masss". Indeed, energy is physically not the same as mass and in general it's not the same numerically either (see http://groups.google.com/group/sci.physics.research/msg/dcd13814f4019d50). [...] Thanks, Harald Thus spake harry <harald.vanlintelButNotThis@epfl.ch> >Anyway, would you also call energy >"not a scalar quantity"? If so, do you deem that to be a disadvantage of >the use of "energy"? Energy is the time component of a vector quantity. >> Energy should be called energy and not "relativistic masss". > >Indeed, energy is physically not the same as mass and in general it's >not the same numerically either (see >http://groups.google.com/group/sci.physics.research/msg/dcd13814f4019d50). Bear in mind that the author of that post was discussing mass in the Newtonian correspondence, in which there is also a gravitational potential energy. Strictly, from a gr perspective, both the flat background required of Newtonian gravity, and this potential, are somewhat artificial concepts. Regards  SignatureCharles Francis moderator sci.physics.foundations. charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and braces) http://www.teleconnection.info/rqg/MainIndex > Thus spake harry <harald.vanlintelButNotT...@epfl.ch> > [quoted text clipped - 13 lines] > Newtonian correspondence, in which there is also a gravitational > potential energy. I don't really see what all the fuss is about here. The most famous relativistic equation (in the population at large) is E = Mc^2. Clearly this has to be modified for masses with K.E.too, relative to the observer. Gravitational potential energy would seem to be an arbitrary additional red herring in this respect. Potential energy relative to what? The Earth? The Sun? The galactic nucleus? A given celestial body's surface, or its core? >> >>> > [Moderator's note: Too much quoted text trimmed. -P.H.] >> [quoted text clipped - 33 lines] > 'Lorentz' (gamma) factor L to the velocity, generating the spatial > part of a relativistic '4-velocity' V = L v. This is not relevant to my question. I've been trying to avoid these kinds of issues in this thread. Especially since its being discussed in other threads. Pete > >>> > [Moderator's note: Too much quoted text trimmed. -P.H.] > [quoted text clipped - 24 lines] > > Pete No, he didn't. As opposed to your rather silly carrying on with "relativistic mass", Planck did the obvious thing and he continued by writing: m (v*d\gamma/dt+\gamma*dv/dt)=q(E+vxB) where \gamma=1/sqrt(1-(v/c)^2) Then, he proceeded to solve the above differential equation. You solved it (albeit incorrectly) on your webpage for the trivial case E=0. Can you solve it for the general case E=! 0 ? I'll give you a hint, you can't use "relativisic mass" :-) |
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