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SamRoss
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Is relativistic mass not an appropriate concept?
Meir Achuz said:It is unfortunate that some physicists still use it.
It goes against the grain of SR, by almost denying that
m^2 is an invariant.
lugita15 said:Personally, I like the concept of relativistic mass, which actually arose before Einstein came up with Special Relativity.
A bit of history: In the late nineteenth century, physicists realized that charged particles would more difficult to accelerate than uncharged particles, since accelerating charges emit energy in the form of electromagnetic radiation. Thus, in addition to ordinary "mechanical" inertia there would have to be an electromagnetic contribution to the mass. Using Maxwell's equations alone, Abraham found that the electromagnetic mass varies as [tex]\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/tex]. Lorentz believed that all forces were electromagnetic in origin, so he assumed that all mass would vary in this way. He interpreted this result as saying that the mass of an object depends on its motion with respect to the aether. Then Einstein came along and showed that the aether was unnecessary, but the formula for how mass changes with velocity remained.
My point is that you shouldn't be so quick to dismiss a notion that occurred naturally in the development of relativity. I don't see why rest mass is so overwhelmingly preferred in textbooks. Just as we talk about how length and time change in different inertial frames, why can't we also mention that mass changes? Rest mass shouldn't be taught exclusively, just as proper time and proper length shouldn't be taught exclusively.
SamRoss said:Is relativistic mass not an appropriate concept?
I don't know about you, but I see mass as the measure of resistance to acceleration. Thus mass should be the ratio of (longitudinal) force to acceleration, or equivalently the ratio of momentum to velocity. And this naturally leads to relativistic mass.SamRoss said:(1) I would not look to nineteenth century physicists for confirmation regarding twentieth century physics.
(2) Einstein was not a proponent of relativistic mass. In a 1948 letter to Lincoln Barnett, Einstein wrote:
"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass 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." I found this quote at http://www.weburbia.com/physics/mass.html It may also be found in The Concept of Mass (Mass, Energy, Relativity) by Lev Okun.
lugita15 said:I don't know about you, but I see mass as the measure of resistance to acceleration. Thus mass should be the ratio of (longitudinal) force to acceleration, or equivalently the ratio of momentum to velocity. And this naturally leads to relativistic mass.
But my basic point remains. I don't know anyone who would only teach proper time and not time dilation. So why only teach rest mass and not mass increase? They're exactly analogous.
Actually, you can do the derivation the other way around; you can start with just the relativistic mass formula, and then derive all of special relativity including the Lorentz transformations. See http://www.mathpages.com/home/kmath635/kmath635.htm" .jason12345 said:Relativistic mass can give the appearance to beginners that it's an add-on to SR, rather than the LTs of the equation of motion of a particle in its proper frame giving rise to a gamma factor in another frame.
SamRoss said:Right, and in that derivation he is using the fact that the force on the electron alters relativistically, not the mass
Dickfore said:of course. Come to think of it, if there is "relativistic mass", then shouldn't there be "relativistic charge" as well?
lugita15 said:Actually, you can do the derivation the other way around; you can start with just the relativistic mass formula, and then derive all of special relativity including the Lorentz transformations. See http://www.mathpages.com/home/kmath635/kmath635.htm" .
jason12345 said:Relativistic mass can give the appearance to beginners that it's an add-on to SR, rather than the LTs of the equation of motion of a particle in its proper frame giving rise to a gamma factor in another frame.
SamRoss said:For those keeping track, of the four Science Advisors who have taken part in this discussion, not one has been a cheerleader for relativistic mass. I am satisfied that my original question has been answered in the negative. Thanks to all.
atyy said:Relativistic mass is "inertial mass" in the special relativistic generalization of Newton's second law.
By the principle of equivalence, it is "gravitational mass".
By the equivalence of relativistic mass and energy, this implies that energy should be "gravitational mass".
Searching for generally covariant equations for a relativistic theory of gravity, this suggests that a tensor whose components include the relativistic mass should be "gravitational mass".
The stress-energy tensor is such a tensor.
Once you get there, you can discard mass.
Even the invariant mass of particles, since there are no particles in general relativity.
As I said before, relativistic mass has a perfectly sound basis in experiment, and the concept was invented before relativity itself.SamRoss said:lugita 15,
It would be beneficial to read past the first paragraph of stuff you find on a webpage. Here are the first few paragraphs of the link that you just posted...
"Does Relativistic Mass Imply Special Relativity?
In a collection of essays on the subject of special relativity (“Six Not-So-Easy Pieces”), Richard Feynman presents the formula for relativistic mass
M=m(1-v^2/c^2)^-1/2
and then remarks that
For those who want to learn just enough about it so they can solve problems, that is all there is to the [special] theory of relativity – it just changes Newton’s laws by introducing a correction factor to the mass.
Unfortunately he gives no explicit explanation of this assertion. Later he discusses how the relativistic mass formula can be derived from the Lorentz transformation, but that’s the reverse of what’s needed to support the above claim, i.e., he needs to show that the Lorentz transformation follows from the relativistic mass formula. Incidentally, Feynman was well aware of the questionable nature of such claims. For example, in Vol II of his Lectures on Physics (section 26) he wrote
Whenever you see a sweeping statement that a tremendous amount can come from a small number of assumptions, you always find that it is false. There are usually a large number of implied assumptions that are far from obvious if you think about them sufficiently carefully. "
In any event, even if you did start from relativistic mass and derive the Lorentz equations mathematically, your result would be dubious because your original postulate of relativistic mass would not be based on empirical evidence. Contrary to this, the postulate of the constancy of the velocity of light is well founded in the Michelson-Morley experiment as well as being contained within Maxwell's equations. In addition, the assertion of the relativity postulate is demonstrated with the equivalent phenomena found by passing a magnet through a coil, first considering the magnet to be moving, then the coil. These two postulates lead directly to the Lorentz equations.
A better generalization is in terms of the four-momentum. The four-vector approach extends to GR much better, and it makes the geometry much clearer.atyy said:Relativistic mass is "inertial mass" in the special relativistic generalization of Newton's second law.
No, (as you mention below) in GR the source of gravity is a tensor, not a scalar. The equivalence principle does not imply otherwise.atyy said:By the principle of equivalence, it is "gravitational mass".
By the equivalence of relativistic mass and energy, this implies that energy should be "gravitational mass".
Yes.atyy said:Searching for generally covariant equations for a relativistic theory of gravity, this suggests that a tensor whose components include the relativistic mass should be "gravitational mass".
The stress-energy tensor is such a tensor.
Sure there are particles, just classical particles and not quantum particles.atyy said:Once you get there, you can discard mass.
Even the invariant mass of particles, since there are no particles in general relativity.
pervect said:Only sometimes. Sometimes you need "longitudinal mass". Always using relativistic mass as a substitute for Newtonian mass will NOT consistently give you the right answer in dynamics problems in relativity.
Komar mass, which is defined differently than relativistic mass because it includes pressure, is a much better substitue for gravitational mass than relativistic mass IF you have a static system. Though Komar mass doesn't work quantitatively for the common question about the gravitational effects of a relativistic fly-by any more than relativistic mass does because that's not a static system.
That's pretty much the modern view, though GR doesn't really throw out mass totally. Sometimes one is interested in the mass of a large system in GR. This gives rise to the ADM, Bondi, and Komar masses, each of which is subtly different, and none of which is the relativistic mass.
And - we don't really need two different words for energy (energy and relativistic mass). Especially not with three other sorts of "mass" waiting in the wings.
DaleSpam said:A better generalization is in terms of the four-momentum. The four-vector approach extends to GR much better, and it makes the geometry much clearer.
No, (as you mention below) in GR the source of gravity is a tensor, not a scalar. The equivalence principle does not imply otherwise.
Yes.
Sure there are particles, just classical particles and not quantum particles.
AFAIK there is no generalization of Newtonian gravity which is consistent with SR. I always make the point that the source of gravity in GR is the stress-energy tensor precisely to encourage the understanding that GR is not merely an extension of Newtonian gravity.atyy said:how do you motivate that the stress-energy tensor is the generalization of "gravitational mass" when searching for a generalization of Newton's gravity consistent with special relativity?
Relativistic mass is a concept in physics that describes the mass of an object as it approaches the speed of light. It takes into account the increase in an object's energy as it accelerates, resulting in an apparent increase in its mass.
Relativistic mass is not an appropriate concept because it is a result of the outdated theory of special relativity. According to the modern theory of relativity, mass is a constant property of an object and does not change with velocity.
The concept of relativistic mass takes into account the object's velocity, while rest mass is the mass of an object at rest. As an object's velocity increases, its relativistic mass increases while its rest mass remains constant.
Using relativistic mass in calculations can lead to errors and inconsistencies. It also complicates equations and makes them less intuitive. Therefore, the concept of relativistic mass is not widely used in modern physics.
Yes, the concept of rest mass is more appropriate for describing the mass of objects at high velocities. It is a constant property of an object and does not change with velocity, making it a more reliable and accurate concept in modern physics.