Fredrik said:
Pete, thinking about it that way only made sense before GR was discovered.
I disagree of course. The assertion "only made sense" implies that the argument for it can be proven to be wrong and I certainly don't believe that is true. In fact I know of no valid argument which could possibly prove it wrong. Especially since it makes perfect sense. And just because that reasoning is what led to GR it does't mean that it can or should be dismissed after its discovery. Each of us is different and as such we all think differently. We all arrive at ideas along different paths. To say that one way of thinking is right and another, equally valid line of thinking, is wrong is a very wrong statement. In fact it is for that reason that both Feynman and Einstein presented those arguements.
Let me ask you this: If it indeed makes no sense then why do you think Einstein and Feynman explained the defection of light using the mass-energy equivalence arguement? Let me quote them
The Evolution of Physics - from Early Concepts to Relativity and Quanta, Albert Einstein and Leopold Infeld, Simone & Schuster (1938), page 221 - Einstein commented on an observation made by an observer inside an accelerating elevator that light is ‘weightless’ Einstein wrote
But there is, fortunately, a grave fault in the reasoning of the inside observer, which saves our previous conclusion. He said: “A beam of light is weightless and, therefore, it will not be affected by the gravitational field.” This cannot be right! A beam of light carries energy and energy has mass.
This same sentiment was expressed by Feynman in Feynman Lectures Vol - I, page 7-11. Section entitled Gravitation and Relativity
One feature of this new law is quite easy to understand is this: In Einstein relativity theory, anything which has energy has mass -- mass in the sense that it is attracted gravitationaly. Even light, which has energy, has a "mass". When a light beam, which has energy in it, comes past the sun there is attraction on it by the sun.
The reasoning would have to go something like this:
1. We can prove that a massive particle at rest has an energy mc2.
2. We can define a velocity-dependent "relativistic mass" such that the energy of a massive particle is always mc2.
3. This suggests that maybe it's E/c2 that should go into Newton's law of gravity, not the rest mass.
4. A photon must have some energy, so if we were right in step 3, then light should be affected by Newtonian gravity too.
This doesn't really have anything to do with GR.
Of course it does. What possible reason could you have for saying otherwise?
By the way, Einstein never proved that a body at rest has energy. When Einstein first derived the expression E = mc
2 he started the derivation with the
assumption that a body which was at rest had energy. As such the body was able to emit radiation and this requires that the body had energy, E, to begin with. What Einstein showed was, not that a body at rest has energy, but that the energy of a body at rest is related to its proper mass, m, by E = mc
2.
Saying that the world line of a ray of light is a null geodesic is definitely a much better "explanation" of why the path of light is bent by a heavy object than the idea that it's the energy/c2 that should go into Newton's law of gravity instead of the mass.
Why do you consider that a "better" explanation??
In any case it can't be taken as an explanation since it is a description of the phenomena and not an explanation. Its quite wrong to consider things like this as "explanations" since laws of physics are formulated, not to explain the phenomena in nature that we observe, but to
describe the phenomena. This is a fundamental fact of all the sciences. Unfortunately many people miss this
very important fact. If you ever have the chance I highly recommend reading the first chapter of Fritz Rohrlich's book "Classical Charged Particles" The author is very good and very well known physicist. He's top notch as a matter of fact, a first rate physicist. He certainly knows what he's talking about and that chapter does an excellant job at explaining the philosophy of physics. You'd do yourself a great service by studying that chapter and knowing the material by heart. I know it did me a world of good .. although I knew the material anyway. The author just does a wonderful job at it.
I'm also surprised that you're characterizing the GR explanation as a "description" and the SR+Newton explanation as the "reason" why gravity bends light.
Me? I wish I could take the credit but this is due to Einstein and not myself. Eddington himself explained that GR is not an explanation of gravity but a description of it. This must be kept in mind so that one has a good understanding of the relationship between mass and gravity in both its active and passive aspects.
If the relativistic mass of a photon is the reason why it's affected by gravity (as defined by GR), then its world line would be a time-like geodesic, not a null geodesic.
Because timelike geodesics are for particles which have a non-zero
proper mass (aka rest mass).
I hope you're not confusing the notion of rest mass with the gravitational mass of light?
By the way. The
definition of relativist mass is as follows: If "m" is the inertial mass (aka relativistic mass) of a body,
v its velocity and
p its momentum then
p = m
v. In otherwords inertial mass m is defined as the m such that the quantity m
v is conserved in elastic collisions. This quantity is then given the name (i.e. defined) as the relativistic momentum of the object.
Best wishes
Pete
ps - By the way. One can go on and on about this and never get past semantics and opinions. If this thread gets to that point then I'll bow out.