Gravity, Mass, Dark Matter & Energy - Exploring Relationships

[professor]

in energy directly related to gravity as mass is, it seems that it should be according to relativity, but this leads me to the question of why dark matter need be proposed to explain the differences in gravity and mass proportionality of galaxy clusters and such. Is this difference not as simply related to the energies of momentum in relation to each other, or perhaps a sum of many weak forces on each of the particles/bodies in this system. In an atom the graviton seems to come up in similar questions, or is that allready explained by other attractions without the addition of a graviton?

hopefully someone can work out what i am trying to ask, if it is too much of a jumble let me know and i will attempt at a revision, i wanted to get the questions down whilst i had them fresh in my mind.

 

[coalquay404]

In a word, yes, energy and gravity are directly linked. Schoen and Yau proved, for example, that the total mass/energy of a spacetime is non-negative, with the mass/energy equal to zero only in the case of Minkowski space. This duality between mass/energy and gravity effectively means that Minkowski space is regarded as a stable ground state of the gravitational field, and that a spacetime cannot decay (by some bizarre quantum tunnelling effect or otherwise) into a state of lower energy. Witten's spinorial proof of the positive energy theorem is particularly enlightening in this respect.

I'm afraid that I can't quite work out what you're trying to say in the rest of your post, particularly the comments about gravitons, which are completely unneccessary in general relativity. Gravitons appear principally in string theory as massless spin-2 states of the string configuration, but have no role in the classical theory.