ZapperZ said:
Darwin123: your explanation adds a lot of confusing contradiction here. "Relativistic mass" in SR is simply defined as
m = gamma m_0
But yet, for a photon, the rest mass m_0 is zero. So already this "relativistic mass" being non-zero is inconsistent.
A photon has momentum. That should be sufficient to show why it can interact. The next logical step is to show why something with zero mass can have a momentum. This is gives us the opportunity to introduce a more general idea of what a "momentum" is.
Please note that there are plenty of supporting arguments on why the concept of "relativistic mass" should not be used, both in the teaching of SR, and also when we deal with general question such as this. I had already outlined this (with references) in another thread.
https://www.physicsforums.com/showthread.php?t=642188
Zz.
My main defense is that Einstein used the concept of relativistic mass. However, I acknowledge that the idea has a few problems with it. I find the relativistic mass concept useful as a heuristic model.
Physicists often get around the concept of relativistic mass. I know that this concept runs into problems in the limit of the speed of light. However, I think the problem is more mathematical than physical. The ambiguity has to do with the mathematical definition of limit rather than the physical definition of mass.
Note that relativistic mass works fine with particles that are moving just below the speed of light. I have seen explanations of cyclotrons that use the concept of "relativistic mass". Engineers working with particle accelerators seem to use the idea of relativistic mass with respect to charge particles. So dismissing the idea as nonsense seems a little premature. Maybe the concept should be introduced with appropriate caveats.
Another reason that I like the relativistic mass idea is that it leads naturally (for me) to the idea that photons never change. Photons can only be created or destroyed near an electric charge or electric current. So one can "semi-intuitively" get to the idea of Feynman diagrams. I am not pushing the idea of solving all relativistic problems with "relativistic mass". However, I was trying to answer the OP in a very rough but useful way.
When one tries to analyze the photon in terms of mass, one look at fractions where the limits as velocity goes to the speed of light of nominator and denominator are both zero. Of course, zero divided by zero is undeterminable. However, there are "intuitive" ways to handle such a limit. If one thinks of a photon with a rest mass about 10^-40 times the rest mass of an electron, then one can sort of see why it acts the way it does.
I will stop answering this way if one of the moderators tells me that "relativistic mass" is against forum rules. However, I see no rule saying "never use relativistic mass". If engineers use it, then the idea should be considered main stream. Apparently, I have difficulty knowing distinguishing "main stream" from "nonsense".
I was told that I should always present at least some links if someone disagrees with me. Here are a few.
Read the following link on mass in special relativity. Note that “some authors” present relativistic mass as a fundamental concept. "It has been argued" otherwise. I am arguing that relativistic mass still has uses as a phenomenological concept. In any case, I don’t know how SR was presented to the OP. Maybe he already has been exposed to “relativistic mass”.
http://en.wikipedia.org/wiki/Mass_in_special_relativity
The term relativistic mass is also sometimes used. This is the sum total quantity of energy in a body or system (divided by c2). As seen from the center of momentum frame, the relativistic mass is also the invariant mass, as discussed above (just as the relativistic energy of a single particle is the same as its rest energy, when seen from its rest frame). For other frames, the relativistic mass (of a body or system of bodies) includes a contribution from the "net" kinetic energy of the body (the kinetic energy of the center of mass of the body), and is larger the faster the body moves. Thus, unlike the invariant mass, the relativistic mass depends on the observer's frame of reference. However, for given single frames of reference and for isolated systems, the relativistic mass is also a conserved quantity.
Although some authors present relativistic mass as a fundamental concept of the theory, it has been argued that this is wrong as the fundamentals of the theory relate to space-time. There is disagreement over whether the concept is pedagogically useful.[1][2][3] The notion of mass as a property of an object from Newtonian mechanics does not bear a precise relationship to the concept in relativity.[4]
I am a big H.A. Lorentz fan. I really like the way Lorentz approached electromagnetic theory. I realize that the approach has limitations. However, it is useful.
Read the following link on Lorentz.
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
The idea of relativistic mass actually dates back to Lorentz's work. His 1904 paper Electromagnetic Phenomena in a System Moving With Any Velocity Less Than That of Light introduced the "longitudinal" and "transverse" electromagnetic masses of the electron. With these he could write the equations of motion for an electron in an electromagnetic field in the Newtonian form, provided the electron's mass increased with its speed. Between 1905 and 1909, the relativistic theory of force, momentum, and energy was developed by Planck, Lewis, and Tolman. A single mass dependence could be used for any acceleration—thus enabling mass to be now defined independently of direction—if F = d(mv)/dt (where m is relativistic mass) were to replace F = ma. It seems to have been Lewis who introduced the appropriate speed dependence of mass in 1908, but the term "relativistic mass" appeared later. (Gilbert Lewis was a chemist whose other claim to fame in physics was naming the photon in 1926.) Relativistic mass came into common usage in the relativity textbooks of the early 1920s written by Pauli, Eddington, and Born. What does the OP think about "relativistic mass"? Is it confusing or clarifying?
