# Mechanism by which mass curves space

1. Nov 1, 2013

### taicleis

Hi everybody. This will be my first post here on PF. :)

I'm wondering about the mechanism by which mass causes space to warp and curve within General Relativity.

I did a cursory search on the subject and did come across some brief discussion here from a few years ago. At the time, the question was posed as "why does mass curve space," and so most responses were explaining that science is not about "why." So to be clear, I'm wondering HOW mass affects space-time - that is to say, the mechanism by which the presence of mass alters the geometry of space-time.

Is there any information or thinking on this subject you could share?

2. Nov 1, 2013

### WannabeNewton

You're asking the exact same "why" question. GR doesn't provide a mechanism; GR claims that energy-density and pressure result in space-time curvature, a claim which is supported through various experimental tests of GR. The answer to the "how" question is simply given by the Einstein field equation $R_{ab} - \frac{1}{2}g_{ab}R = 8\pi T_{ab}$.

3. Nov 1, 2013

### taicleis

Right; I wouldn't expect GR to provide a mechanism. That would be opening one can of worms with another.

The answer as to "how," in the sense that you answered it, I am aware of. That's why I was careful to specify that I was wondering about the mechanism behind the relationship that the EFE describe, as opposed to wondering about the relationship itself. In other words, not "how" as in "in what way," but "how" as in "caused by what."

I'm aware that there is probably no generally accepted answer to the question. What I'm wondering is if there are any interesting, testable or plausible ideas as to some underlying mechanism.

In much the same way that we described the "in what way" before "caused by" for gravity itself (Newtonian motion described it pretty well but gave no mechanism by which the 'force' of gravity is caused, until GR gave an actual mechanism), I am wondering if there are any decent ideas floating around as to a mechanism THROUGH WHICH mass has an effect on space.

I realize that doesn't really fall within the purview of relativity any more than GR falls within the purview of Newton's laws, so if this is the wrong forum for the question I apologize. But I think it's at the least an interesting question that someone might have some ideas about.

4. Nov 2, 2013

### dextercioby

There is no cause of anything. You must understand that what theoretical/mathematical physicists do is search/find/provide (more or less mathematica) models. Some of them follow Hilbert's ideas and are structured nicely: axioms = > theorems. That's also the case for QM or GR. You have to start somewhere (put in some unchallangeble facts/statements we choose to call axioms). The results/theorems are then candidates to answer some deep question: how is that the spin is quantized ? how is that the Sodium atom has the quadruplet of spectral lines in the visble side of the spectrum ? how is that Mercury has an anomaly ?

5. Nov 2, 2013

### Staff: Mentor

The EFE is how mass curves spacetime. Anything with mass has a lot of energy and according to the EFE energy, momentum, pressure, and stress all curve spacetime.

http://en.wikipedia.org/wiki/Einstein_field_equations

6. Nov 2, 2013

### Staff: Mentor

However, it sounds like what you really want is another theory which explains GR in some limit. We do not have such a theory, and even if we did then you could ask the same question about that theory. There will always be a fundamental theory whose postulates we simply accept because they fit the data.

7. Nov 2, 2013

### Bill_K

Massless spin-2 particle in Minkowski space. Consistency requires gauge invariance, which in turn requires a conserved source, namely Tμν, which leads to General Relativity.

8. Nov 6, 2013

9. Nov 7, 2013

### haael

It can also be retrieved from variating the Ricci curvature scalar with respect to the metric tensor.

I find this approach especially well suited for various philosophical interpretations.

10. Nov 8, 2013

### K^2

(Via Noether's theorem with the local symmetry group being the Poincare group. Might be worth looking up for the OP.)