What all factors must be included to determine the gravitational field a body will create? Now what I have in mind is a compound object (i.e., more than just a single particle). A compound object can be any object that you can think of that is composed of 2 or more particles. I would like every aspect of the compound object to be analyzed and if you say a certain aspect contributes to it's gravitational field (such as thermal energy for instance) then it should be backed up with references that explain why that is so - at least that is what I am interested in, the explanations.
Well, I was refering to relativistic, but if you want to consider some other theory instead, that is just as fine. Just be sure to state what theory you are talking about first.
Internal energy, for sure, because the kinetic energy of each particle brings up a relativistic mass, and this changes the total mass of the body. Then there's the translational and rotational velocities of the body, which also change the mass.
Please come back when you understand modern relativity and not outdated early 1900's relativity. Relativistic mass has no part in modern relativity. In fact, it isn't even taught in the most basic physics classes at a lot of universities and certainly not in any advanced physics courses.
Relativistic mass and momentum are inherent in four-vectors, and hence in Minkowskian space, and therefore in General Relativity. You might not be using it explicitly in your math, but it is implicit. Maybe you should learn some "outdated early 1900's relativty", and try to understand the relation between this and modern physics.
You are refereing to the 4 vector: [γmc<sup>2</sup>, p<sub>x</sub>c, p<sub>y</sub>c, p<sub>z</sub>c]. Nothing special here, the first quantity, γmc<sup>2</sup> is total energy, including kinetic energy, and the other 3 terms are the 3 momentum vectors. THERE IS NO RELATIVISTIC MASS IN MODERN RELATIVITY. PERIOD. γm has as much use as the ass from which it squirted.
What the heck are you talking about? Are you saying that the relativistic four vector is an absolutely outdated concept? Then what do you mean by relativity at all?
I believe all Aer means is that the words "relativistic mass" are not often used in modern discussions of relativity. Historically, the factor of gamma was first associated by Einstein with the rest mass, a combination he called relativistic mass since it varied with velocity. Today, however, the factor gamma is usually taught as arising from the definition of the four velocity. The energy momentum four vector that is being discussed here has then a spacelike part, "the momentum", which is the product of rest mass, gamma, and ordinary three velocity (usual classical mechanics velocity) and a timelike part, "the energy" which is the product of rest mass, gamma, and the speed of light. What we call energy today is just what einstein called relativistic mass (up to a constant c^2), but we no longer attach such a mystical notion to "relativistic mass". On to the topic at hand, part of the reason Einstein originally called gamma times rest mass the relativistic mass was because he found that gamma times rest mass, and not just rest mass, contributed to the gravitational field. The notion that all kinds of energy, not just rest mass energy, could contribute to the gravitational field was not really a part of Newtonian gravity. In general relatvity, the total energy density contributes to the gravitional field (though this is not the only contribution). This includes the energy of particles, which may be thermal energy if the system is statistical (remember thermal energy is just the average kinetic energy of particles, nothing mysterious), the energy of electromagnetic fields, the energy of other fundamental fields like the strong or weak nuclear force, the energy of the gravitional field itself (and this list is not exhaustive). The fact that gravitational energy contributes back to the gravitational field means that gravity in general relativity is nonlinear and self-interacting, this also true of the strong nuclear force for instance, or for electromagnetic fields at very high intensities. If you would like some references please let me know your technical level and I would be happy to recommend some excellent resources.
Glad to have you here. I've already pointed out to Aer that relativistic mass is now implicit in the use of four vectors, and he chooses not to understand that. And what you say supports my original post. Nice explanation. Maybe Aer can learn something from this.
Where did you get the idea that the 4 vector is outdated? I just gave it to you above and explained what it means. I never said it was outdated.
This is not general accepted in modern terms. A hydrogren atom could have a relativistic mass of a black hole! It does not create the gravitation of a black hole.. You need to check your facts. Within the energy-momentum tensor exists non-gravitation energies per Wikipedia, but they don't state what these energies are that are non-gravitational. You need not worry about the technical level of any references, I can handle them. The more technical the better, in fact i do not want reference that are just statements, I want the technical information. If you want to take that as a challenge to find the most technical reference you can - then go right ahead (that was my intention Please Register or Log in to view the hidden image!)
Rosnet, on the concept of relativistic mass, I am not sure how highly you regard Harvard, but here is what David Morin, professor at Harvard says:
I find your question ill-formed. You should ask two questions. Is mass independent of velocity? Is energy independent of velocity? I would say yes to the first and no to the second.
OK - perhaps it was a misinterpretation on my part Please Register or Log in to view the hidden image!
Thanks for the interesting reply, Aer. Let me address you points: 1. Actually, if we could accelerate a hydrogen atom to the point where it has energy close to that of a black hole, it would in fact resemble a black hole from a gravitational point of view. In simple terms, the hydrogen atom would create the gravitational field of a black hole. There are some subtleties here since it is really energy density that couples directly to the gravitational field, but the basic idea is right. The reason why we have not observed black hole like hydrogen atoms is simply that we can't move them fast enough! The best we can do right now is obtain energies for protons of the order of TeV which amounts to a paltry 10^(-24) kilograms, hardly enough for a black hole or even the sun or even the Earth! Because gravity is so exceptionally weak, we have not yet reached the point we can generate sufficient energy to seriously affect the gravitational field. 2. I'm sorry but I don't think I understand your objection here. Just after the part of my post you qoute, I list a number of different non-gravitational sources of energy. I will list them again here: electromagnetic energy, strong and weak nuclear energy, particle energy. Each of these sources of energy contribute to the gravitational field and are a part of the 00 component of the stress-energy tensor. You might also have more exotic kinds of matter or fields contributing such as dark matter or dark energy, but this is speculative at the moment. I fear I may be missing the mark on your comment so please help me to understand what you are confused about if this doesn't satisfy you. 3. I'm pleased to see you so interested. I shall indeed try to find the most obscure and incomprehensible resources to direct you too Please Register or Log in to view the hidden image! . But seriously, I will dig up some good reviews and post them here. Thanks to Rosnet for the welcome.
No, this is wrong. All I can do to express this is defer to authority: link I cannot accept your claim to the contrary unless you provide an adequate source.
