Aer, I'm sorry but I didn't realize that you were going to arbitrarily determine what statements were to be accepted from physicists. You deny the right of gravitational physicists to speak about kinetic energy contributing, but you support the "accepted fact" (a fact told to you by these same gravitational physicists) that extra kinetic energy a body may have because we do not examine it in its rest frame does not contribute. Let us be clear. The stress energy tensor of a single particle is proportional to m u * u where * denotes tensor product, m is the mass, and u is the four velocity. In the rest frame we find that every component is zero except T_00 which is proportional to m. If I calculate the stress energy tensor in a different coordinate system I will get different components, but the tensor is the same. The geometry it creates is the same. Now, in a different system of coordinates the energy (T_00) can look larger than m (simple special relativity), so we might be in trouble except that other components of T are now nonzero. If we are in a frame where the particle is moving at some velocity, then there is suddenly a momentum flux as well as an energy density. The key is that whether I am in a frame where the particle is docile looking and at rest with no momentum flux or I am in a frame where the incredibly energetic particle is zipping along and there is a huge momentum flux, the geometry is the same. In the frame with the particle moving, the kinetic energy of the particle does technically contribute in the sense that it enters Einstein's equations as written in this frame, but we musn't forget that the huge momentum flux also 'contributes' in this frame. We plug through the math and obtain the components of the metric in whatever frame. The components of the metric may look different in the frame with the particle moving as compared to the frame with the particle at rest. The key, as I have said, is that the geometry can be the same even if the metric components look different in different frames. Now GR has been tested experimentally with amazing precision and has never been found to fail a single experiment. If you begin removing energies that you don't like from "contributing" to gravity when GR says they do, well then you're disrupting the internal structure of an amazingly predictive theory. The comparison, and good agreement, between GR cosmological models based on ideal gases and the observable universe is your evidence that kinetic energy contributes since this contribution is necessary and explicitly assumed in these models.
Define "extra kinetic energy". In reading all of this, I came to a very profound realization. Wipe that big grin off your face! The realization was not that I am wrong Please Register or Log in to view the hidden image! but rather you are misinterpreting the stress-energy tensor and it's place in General Relativity. Now let me be specific. You appear to be claiming that the gravitation that an object will create is proportional to the stress-energy tensor when in fact that is not true. The reaction between two objects is proportional, but that is because an object moving with great velocity through a gravitational potential will behave differently (think orbits) than an object moving with relatively little velocity through a gravitational field (i.e. orbit velocity taken to zero will make a satellite fall towards the object). Anyway, I am just throwing this out there in the hopes that you will clarify exactly what you mean and the physicists you quote mean with this in mind.
Let me be even more particular. On pp. 708-713 of Gravitation the authors discuss the present cosmological situation. I quote from p. 713, "The density rho is made up material mass density (rest mass plus negligible kinetic energy of galaxies; rest mass plus kinetic energy of cosmic rays; rest mass plus thermal energy of intergalactic gas -- all 'smeared out' over a unit volume), and also of radiation energy density (electromagnetic radiation, neutrino radiation, gravitational radiation)." Now I know this is just another claim by physicists, but let's follow along. The total mass-energy density determines the Hubble constant. The Hubble constant is only reproduced correctly if kinetic energy and thermal energy are included. This is your experimental evidence and it is all outlined in the reference I indicate. I suppose of course that the famous authors of this famous book could be lying to us all, but that would pretty much require a global conspiracy of physicists to suppress the truth which I hope we can all agree is nonsense.
Physics Monkey, the only problem I have is the fact that the mass is measured such that everything works out. There is no other way to verify the mass by observation, is there? So the actual rest-mass could be assumed less than it actually is - I don't have the book in front of me so I cannot comment on the context in which any of this has been brought up.
I'm sorry for the confusion, Aer. I hope I never claimed that the gravity (I assume you mean metric) is proportional to the stress-energy tensor. Let me elaborate: when I said "we plug through the math" I meant we solve the horribly nonlinear partial differential equations that are the Einstein field equations. The resulting metric will certainly not be proportional to the stress energy tensor in general.
You said paraphrase: "kinetic energy contributes to the gravitational potential". Then you talk about the stress-energy tensor as if that is proof. Then you say "I never claimed that the gravity is proportional to the stress-energy tensor". Now come on.. perhaps we are not talking about the same thing, but the only thing I am discussing in this thread is the gravity an object will create and that is it.
Aer, it is possible to distinguish between rest mass and kinetic energy contributions to total mass-energy, just not with gravity alone since gravity responds only the total mass-energy. Astronomical observations of doppler and red shifts etc can be used to determine speeds of rotation etc for galaxies. For instance, we know from obervations that the kinetic energy of a galaxy in the galaxy's rest frame is usually much less than it's rest mass energy. I believe the factor is 10^-6 on average.
The kinetic energy of a galaxy in the galaxies own rest frame is 0. Now are you talking about the kinetic energy of stars within? If so, be specific. And exactly how is the rest mass of a galaxy exactly known? Your argument is very much leading to circularity (just an FYI - a circular proof is not a proof).
I think I see the conclusion, 'contributes' does not mean 'is proportional to'. I think you have in mind that I want to say the gravitational potential produced by a body is - G / r (rest mass + kinetic energy + thermal energy + etc). I do not mean this in general since this Newtonian form is only appropriate if the field is weak and not time dependent.
That would be linear proportionality and is not what I meant. Proportional does in fact just mean contributes.
Ah, this is not true because the different parts (stars, etc) of the galaxy are still moving. Rememebr that there is no frame where the every part of galaxy is at rest. The phrase "galaxy's rest frame" means the frame where the center of mass of the galaxy is at rest.
See, I told you that you were refering to the stars. I know that the stars are not "at rest" in the galaxy's rest frame. You are just assuming that this kinetic energy contributes to the gravity the entire galaxy will produce and in turn calculate the "rest mass", etc.
To determine rest mass of a galaxy we determine average mass of stars in a galaxy and multiply by number of stars. How do we determine the mass of star? If the star is a binary then we simply look at the stars orbit. Otherwise, I think we rely in general on stellar models in conjuction with obersavations of luminosity, spectra, etc to find the mass of stars.
And this was done individually for each star in a single galaxy? Come on.. Please Register or Log in to view the hidden image!
I'm not assuming the kinetic energy of stars in galaxy contributes, this is an experimental fact. If we do not include the kinetic energy of stars, cosmic rays, etc in our value for the total mass-energy density then we find we are missing energy. We get the Hubble constant wrong.
Obviously we don't measure every star, but I'm sure you knew that. We can however draw average conclusions based on some observations and our knowledge of galactic structure.
