Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Pmb on 30/07/2013 02:58:58
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I just came across the following article Einstein Never Approved of Relativistic Mass by Eugene Hecht, The Physics Teacher, 47, Sep. (2009)
http://link.aip.org/link/phteah/v47/i6/p336/s1
Abstract - During much of the 20th century it was widely believed that one of the significant insights of special relativity was “relativistic mass.” Today there are two schools on that issue: the traditional view that embraces speed-dependent “relativistic mass,” and the more modern position that rejects it, maintaining that there is only one mass and it's speed-independent. This paper explores the history of “relativistic mass,” emphasizing Einstein's public role and private thoughts. We show how the concept of speed-dependent mass mistakenly evolved out of a tangle of ideas despite Einstein's prescient reluctance. Along the way there will be previously unrevealed surprises (e.g., Einstein never derived the expression for “relativistic mass,” and privately disapproved of it).
I’m curious about something. Does anyone here believe articles and assertions like this?
I find this article to be very irritating. Not only does the author claim
Today there are two schools of on that issue: the traditional view that embraces speed-dependant “relativistic mass,” and the more modern position that rejects it, maintaining that there is only one mass and it’s speed-independent.
I find it irritating when people claim that the view they don’t like is the “modern” one which implies that the view they don’t like is “old fashioned.” It’s extremely misleading and altogether wrong in fact. If you try to define momentum as p = gamma * m*v then it only holds in special circumstances. Everyone who takes the mass = rest mass approach fails to recognize and thus understand this very basic fact.
In reality Einstein really did use relativistic mass. Contrary to what this author thinks relativistic mass is not defined as gamma * m, its defined as m = p/v. This later relationship always holds true while the other doesn’t. Einstein used relativistic mass in his textbook The Meaning of Relativity.
To see how he used it see Eq. (12) and Eq. (14) in
http://home.comcast.net/~peter.m.brown/gr/force_falling_particle.htm
and let v << c. Einstein called that value the “inert mass.”
Einstein also derived an expression for the mass density of radiation in his article The Principle of Conservation of the Center of Gravity and the Inertia of Energy[/b], Albert Einstein, Annalen der Physik, 20 (1906): 626-633.
This is another example of relativistic mass since when you assign mass density to radiation as Einstein did in that paper it’s called relativistic mass. So the author made many errors in his paper. I e-mailed him and explained all this but never got a response. I explained all of the above in my paper on mass.
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Pete,
I'm not disagreeing with you, just bringing this to your notice, although you have probably seen this letter before.
Letter from Albert Einstein to Lincoln Barnett, 19 june 1948. ‘’ it is not good to introduce the concept of the mass M =m/( gamma)^0.5 of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ‘rest mass’ m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.’’
From this pdf. Page 2. http://www.physics.uoguelph.ca/~des/Phys2320/concept%20of%20mass.pdf (http://www.physics.uoguelph.ca/~des/Phys2320/concept%20of%20mass.pdf)
Have I copied the equation right?
Is that saying not to use relativistic mass?
Here's Matt Strassler's take on the subject.
http://profmattstrassler.com/2013/07/11/mass-ive-source-of-confusion/ (http://profmattstrassler.com/2013/07/11/mass-ive-source-of-confusion/)
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Is that saying not to use relativistic mass?
No! It doesn't say that. In fact that’s my entire point. It's only saying that one shouldn't use a velocity dependant mass. Notice that ratio p/v = p/c (since v = c for a photon) is not a function of speed. p/c for a photon is, by definition, the relativistic mass of the photon noting that for radiation E = pc we get m = p/c = E/c2.
Also, as I explained in the OP the value ratio gamma*m0 = m0dt/d(tau) when evaluated for v=0 in a gravitational field where the gravitational potential is function of position does not have the value of m0. However m0dt/d(tau) is the relativistic mass of a particle.
Here's Matt Strassler's take on the subject.
http://profmattstrassler.com/2013/07/11/mass-ive-source-of-confusion/ (http://profmattstrassler.com/2013/07/11/mass-ive-source-of-confusion/)
Thanks. I'm (overly) aware of that position. He makes the same mistakes that Lev Okun makes in all of his articles. This is a very ignorant comment for a physicist to make. It’s blatantly false. He’s a particle physicist and they have no other use or application for anything other than proper mass so many of them have incorrectly assumed that since they don’t use it tat nobody else does either. A friend of mine, Alan Guth, uses relativistic mass in his thinking and in his teaching and he’s one of the most well-known particle physicists/cosmologists around!
He also makes the common mistake of confusing relativistic mass with energy. Consider the energy of a charged particle moving through a static electric field. The relativistic mass-energy is not the total energy that is conserved but only part of that energy, i.e. the kinetic energy + rest energy. It doesn’t include potential energy. If the frame of reference is not an inertial one but the components of the metric are time-independent. Then the frame has a gravitational field in it. Now consider a free particle (only inertial forces are acting). The time component of 4-momentum is what particle physicists call “energy” but that is not true for a particle moving in the gravitational field. The energy is the time component of the 1-form associated with 4-momentum and has gravitational potential energy in it. So his claim that mass and energy are the same is invalid in general.
Everything he’s saying there applies only to particle physics and to nothing else. Beware of such people when they make such statements. They tend to think that they know what every single particle physicist in the world thinks. And that’s just silly.
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I'm curious, Pete: can you formulate general relativity without recourse to mass, purely in terms of energy and momentum? If that's the case, then it seems to me that there's a strong argument to be made that mass isn't a fundamental concept, but rather is a quantity derived from energy and momentum. It's particularly useful (and unambiguous) in the Newtonian limit and there are multiple generalizations beyond the Newtonian limit.