# How does empty space curve?

1. Apr 7, 2009

### only_theory

I've thought about this one a few times in the past and can't wrap my head around it, how can space or rather nothing actually curve to cause the effect of gravity?

Is it possible that it just looks like space curves and it's actually caused by something similar to magnetism?

Think about it, if something like magnetism worked similar to the effect of gravity, would it look any different to space curving? im sure they would look the same but one is reality and one is theory!

Interesting thought to consider, note im not suggesting anything is wrong with current theory etc im just curious, thanks.

2. Apr 7, 2009

### A.T.

Curved space-time is just a mathematical model used to quantify the observed effects of gravitation. Humans invented it just like numbers and forces to describe what they observe.

3. Apr 7, 2009

### Dmitry67

As well as flat spacetime...

4. Apr 7, 2009

### Staff: Mentor

I think the premise is a little off. Empty spacetime does not curve. Spacetime is only curved in the presence of some stress-energy.

5. Apr 7, 2009

6. Apr 7, 2009

7. Apr 7, 2009

### dx

Space never looks curved, no matter what. Our brains will always interpret anything that we see in a flat euclidean space framework.

8. Apr 7, 2009

### Staff: Mentor

Yeah, but the Schwarzschild solution requires some energy at the center and gravitational waves require some quadrupole (whatever that means) mass. Similarly with other vacuum solutions. So unless I am missing some subtelty here spacetime still doesn't curve except in the presence of some stress-energy.

9. Apr 7, 2009

### robphy

Given a spacetime (M,g),
one can excise portions of it and end up with a spacetime (M',g').

Here are discussions of this idea [in the context of causal structure and singularities]:

"The Space-time M is Minkowski space with one point removed. "

"..but such points can be excised from the manifold, leaving a spacetime... "

So, if there is a source somewhere... and one cuts out a portion of the curved but matter-free [i.e. zero-ricci but nonzero weyl] section. That section, together with its metric, is itself a curved vacuum spacetime.

10. Apr 7, 2009

### samalkhaiat

Like Maxwell's, Einstein's equations have non-trivial solutions (waves) in the absence of matter! Indeed, Einstein's equations can be written in the equivalent (Maxwell-Like) form

$$(-g)[ T^{ab} + t^{ab}] = \partial_{c}h^{abc}$$

where t is the energy-momentum pseudotensor of the gravitational field, and $h^{abc} = -h^{acb}$ is the spin pseudotensor. The vacuum solutions (i.e., when T = 0)of this equation describe the so-called gravitational waves.

regards

sam

11. Apr 7, 2009

### Staff: Mentor

Is there any reason to believe that the resulting boundary conditions would represent any "massless" physical situation? In other words, is there any reason to believe that you could physically have a Schwarzschild spacetime without the presence of a mass?

12. Apr 7, 2009

### StatusX

Einstein's equation in vacuum is $R_{\mu \nu} = R^\rho_{\mu \rho \nu} = 0$, while the condition for zero curvature is $R^\mu_{\nu \rho \sigma} = 0$, which is strictly stronger, so it's possible for there to be curvature in a vacuum. Whether there's matter far away does not pertain to the original question, but in principle it is possible to have curvature in an empty ($R_{\mu \nu} = 0$ everywhere) universe. Whether such a universe is physically reasonable depends on what you mean: in a certain sense, any universe without matter is unphysical.

13. Apr 7, 2009

### robphy

I'm not qualified to fully address that question.
However, one thing I learned in this line of thinking is
that such a question relies on formulating mathematical statements
that try to "capture the physics", then prove theorems based on what was formulated.

This might be worth browsing over to get a sense of this line of thinking,
http://philsci-archive.pitt.edu/archive/00004506/01/PhysReas.pdf ,
which quotes a paper by Geroch [which I can't find online]

"The space-times obtained by cutting and patching are not normally
considered as serious models of our universe. However, the
mere existence of a space-time having certain global features suggests
that there are many models--some perhaps quite reasonable physically--with similar properties."

14. Apr 8, 2009

### only_theory

Ah i see, so If space itself doesn't curve what does or just gives the appearance of it?

15. Apr 8, 2009

### Niles

The way I have understood it (someone please correct me if I am wrong), space-time does curve, but what we are "seeing" is just the projection of the curved space-time onto a 3D space.

16. Apr 8, 2009

### A.T.

If you assume a flat space-time around a mass like Newton did, then the path of a falling object in space-time (its worldline) is curved. So the object is accelerated (by Newtons force of gravity). But you could just as well assume (like GR does) that space-time is curved in such a way, that the worldline of the free faller is straight. So it is not accelerated anymore by any force.

17. Apr 8, 2009

### Staff: Mentor

That's OK, I am probably not qualified to fully understand the answer anyway

18. Apr 8, 2009

### only_theory

When talking about space what are most peoples definitions of it? To me space means just an area of nothing that can contain stuff, if this is correct how can nothing curve?

On the other hand if you're to say that something occupying space causes gravity that would make more sense to me.

19. Apr 8, 2009

### A.T.

How can nothing be flat?

20. Apr 8, 2009

### Naty1

Some even perhaps many here will answer that space is just a mathematical model... I say it IS something...it just doesn't seem "empty" to me.....you can use Penrose twister theory, geodesics, quantum spinfoam and/or branes as representations...all are related views.....whether any of those ARE "something" is an open issue.

Space seems like one form of a once unified entity that spawned the universe...mass,time,energy,etc are other vestiges of that very high energy and unstable but unified initial condition....

Whatever space(time) really might be, mass,energy and pressure cause our mathematical models of it to deform...to curve....keep in mind these entities curve time as well...Einstein viewed "empty" spacetime, meaning spacetime without these three entities, as flat..no curvature...

I don't know what "occupying space" means...mass would "occupy" space in laymens terms, likely pressure and energy would not....but Nobody knows precisely how mass relates to space since nobody knows precisely what either is!!!!!!

Last edited: Apr 8, 2009