# How did gravity exist before mass?

I'm brushing up on my Big Bang, and I noticed that, apparently, although gravity is the first force to split from the original "superforce", mass does not appear on the scene until after the second force (strong interaction) has split form the superforce. I understand that there are some things that need to exist before mass can show up, but how does one understand or even scientifically predict the existence of gravity without the existence of mass, in those early fractions of a second in the universe's life?

• You have to look at the total mass-energy content. There was plenty of energy. Apr 22 '16 at 13:23
• But how does gravity affect energy, when there is no mass involved? Relativity states that gravity acts through the distortions in spacetime made by massive objects; no mass, no distortions, right? Or....? Apr 22 '16 at 13:51

In general relativity, the field equation relates the metric (through the associated curvature tensor) to the stress energy tensor $T^{\mu\nu}$. This can be interpreted as a flux of energy and momentum in spacetime (i.e. integrating $T^{\mu\nu}$ over a spacetime hypersurface, like a three dimensional hypersurface of constant time, tells you the rate at which energy and momentum [i.e. 4-momentum] flows through that surface). $T^{\mu\nu}$ is a sort of generalized mass.

Even before particles acquire mass through the Higgs mechanism, some effective stress energy tensor associated with the gauge and matter fields of the standard model provides the source to a quantum mechanical version of Einstein's field equations. Finding the physically meaningful effective stress energy tensor for quantum fields is subtle (it's a basic problem in quantum gravity).

• So there truly was no "mass", but there is "something else" that makes the raw primal energy respond to gravity as if it were mass caught in a gravity well (which I assume was an immense well at that point)? Do we have any idea what that "something else" is? Does it have a name? Apr 22 '16 at 14:26
• The einstein equations. The connect mass and energy through the stress energy tenson Apr 22 '16 at 14:37
• anna v answered your question, but I'll elaborate since it can be subtle. First, a non-interacting relativistic fluid evolves (according to 'classical' GR) along geodesics of the spacetime. The stress energy tensor is then determined from the state of the fluid according to some physically motivated equation of state. With nice initial conditions, this gives a well-posed PDE with a unique solution (up to behavior hidden by event horizons). If you add interactions, then you just 'perturb' the non-interacting solutions locally. With defects/gravitational radiation, well-posedness is trickier.
– TLDR
Apr 22 '16 at 14:55
• Quite clearly, I am a person who needs that elaboration, and I am more than thankful for it. On that note, I get that GR is general relativity, but what does PDE stand for? I am not quite sharp on my QM abbrieviations, yet... Apr 22 '16 at 15:24
• Actually, PDE stands for "Partial Differential Equation", and can be viewed as a general mathematical framework to describe both gravity and quantum mechanics. Mathematically (and abstractly), you can think of quantum mechanics as the practice of approximating a non-linear PDE with a very high dimensional linear PDE (i.e. a Schroedinger equation). Of course, some technical conditions apply (i.e. both evolution rules should be deterministic, but mostly for theoretical reasons).
– TLDR
Apr 22 '16 at 15:29