# Can you imagine geometry without matter and light?

1. Oct 15, 2013

### marcus

I recently received a private communication that raised this question? I find that I personally cannot imagine the universe having geometry without also having some kind of matter. I mean matter in a general sense, including light, dynamical fields of any sort. No "test particles", no vibrating atoms to serve as a clock. Indeed no clock of any sort. Nothing to measure distance with either.

I think of the universe's geometry as a bunch of relations between stuff, or between material events. Distances, angles, change... Without stuff, geometry seems meaningless. I'd like to know what other people here think about this. Do you agree? Or can you imagine and talk sensibly about geometry in the total absence of stuff?

==quote==
Hello,
It is regarding your old post of accelerating universe
in which you said space is not independent of matter.(https://www.physicsforums.com/showthread.php?p=2594462)
Then if we pull out all matter from universe(somehow it disappear) then there is no concept like expansion of space?? ...
==endquote==

2. Oct 15, 2013

### Staff: Mentor

I feel its meaningless.

3. Oct 15, 2013

### UltrafastPED

Any empty universe lacks dynamics; so what is left would be something like Euclidean geometry in 3D, but empty.

So imagine an empty graph.

4. Oct 15, 2013

### martinbn

It depends what you mean by empty. General relativity allows dynamic empty space solutions.

5. Oct 15, 2013

### WannabeNewton

Marcus what you're speaking of looks to me like topological field theory.

6. Oct 15, 2013

### UltrafastPED

What would the interactions be? I suppose space could be expanding ...

7. Oct 15, 2013

### Staff: Mentor

Am I correct when I say that geometry is a mathematical way of describing the real world? If so, it seems meaningless to try associate any results you get from the math with a universe that doesn't exist.

Let's look at the scaling factor or whatever it is in GR that says the universe expands. Without any real objects to measure distances between, does it make any sense to say the universe is expanding? I'm sure you could put points down in the math and make calculations, but does that have any meaning outside of your model?

8. Oct 15, 2013

### WannabeNewton

The Milne universe is an example.

9. Oct 15, 2013

### Chronos

I'm sympathetic to Dr. Sten Odenwald's argument that there is no space without matter [re:http://einstein.stanford.edu/content/relativity/a11332.html} [Broken]

Last edited by a moderator: May 6, 2017
10. Oct 15, 2013

### us40

Last edited by a moderator: May 6, 2017
11. Oct 16, 2013

### Chalnoth

De Sitter space, anti-De Sitter space, and the Schwarschild metric (as well as all other black hole solutions) are all solutions to the vacuum Einstein field equations.

12. Oct 16, 2013

### mathman

Given the title, it is important to define what you mean by "geometry". From a a mathematical point of view, it does not depend on any notion of physical reality.

13. Oct 16, 2013

### Mandelbroth

Can I imagine geometry without matter and light? No, I need both for my brain to function. :tongue:

That being said, geometry itself has nothing to do with matter or light mathematically. A lot of people like to think that all math applies to reality. In truth, most of it is really just abstract.

14. Oct 16, 2013

### Chalnoth

To expand a bit on my above statement: empty space-time metrics are pretty common in General Relativity, and they are quite non-trivial. In particular, most non-trivial metrics exhibit thermal behavior. This is, I think, a massive clue as to the nature of space-time. Thermal behavior elsewhere in physics is a result of the collective behavior of large numbers of microscopic objects (usually atoms and molecules, but potentially other things as well such as photons).

This indicates, to me, that space-time itself can probably be described as a collection of particles or particle-like objects whose collective behavior produces what we experience as curvature/gravity.

15. Oct 16, 2013

### us40

If in de sitter space and anti de sitter space spacetime has curvature without the need of matter and energy and empty space itself has its own energy then we can say that space itself is independent of matter and can we consider itself as absolute as newton think??

16. Oct 16, 2013

### dkotschessaa

Indeed, there are lots of geometries (I'm thinking weird metric spaces) that I can't picture in any physical way.

-Dave K

17. Oct 16, 2013

### WannabeNewton

There are still sources that generate the curvature even if the curvature is of a vacuum type. The Schwarzschild metric is the space-time geometry due to some localized spherically symmetric static source so it is not independent of matter.

18. Oct 16, 2013

### marcus

Everybody knows there are solutions to GR equation which do not involve matter!
Without any test particles, light rays, clocks those solutions are merely "on paper". Nothing physical is experiencing their distances, their curvature, their geometry.

Good question. I'd say the answer is no. Real physical geometry only exists in interaction among things. A real triangle (as Nugatory has observed) with real angles between lightrays or between stretched string. Angles you can measure and add up to see if they add up to more or less than 180.

I'm not talking about a purely abstract unphysical geometry with distances that are never measured, angles that have no physical meaning.

BTW Newton had a lot of good ideas (though absolute space and time werent so great). One of his ideas was the "action-reaction" one. Nothing acts without itself being reciprocally acted upon. It's interesting (maybe you find it interesting too, Route 40 :^) that the GR equation hints at that kind of reciprocity between geometry and matter. Geometry guides matter and matter reciprocally bends geometry.

19. Oct 16, 2013

### WannabeNewton

The behavior of clocks and light rays determines the metric tensor up to a conformal factor. If you don't have clocks and rulers etc. then you're working with topological field theory.

20. Oct 16, 2013

### us40

What I am try to say about is we are approaching de sitter phase and universe was also in de sitter phase when inflation epoch started.(http://en.wikipedia.org/wiki/De_Sitter_universe).So [Broken] all matter and energy will be diluted so nothing left but ever expanding space with cosmological constant.So doesn't it mean that space was there before big bang when all matter and radiation created and after there when all will be diluted so space is not property of big bang but only time is.Means time is created with big bang and it may be the reason time has property like arrow but space does not because entities that perceive time creates with big bang.While space doesn't need it.(Here I think an analogy,if you drink coffee you need mug first,and after you drink coffee mug is still there.But when coffee was there it increase temperature the surface of mug,like when universe was in matter dominated era expansion of universe is slower,but after you consume your coffee,mug retain its temperature and like that space retain its energy dominated properties again.)

Last edited by a moderator: May 6, 2017
21. Oct 16, 2013

### marcus

Here's from post #1, where the thread question was posed.
I get what you are trying to say and I think you understand what I am driving at, Wannabe. Different people will take different views of this and say it in different words. I'm not talking about abstract unreal geometry and for me real physical geometry exists in how it interacts with other dynamical fields: essentially light and material stuff. Without that, it's meaningless.
Drakkith put it succinctly in post #2:

22. Oct 16, 2013

### DennisN

I hesitated to participate in this thread, but I could not resist since I saw nobody has mentioned it ;

Isn't the question

also dependent on whether an (imagined) universe without matter and light still would contain quantum fields? I'm sorry if I suddenly made the thread more problematic, but I could not resist bringing it up...

EDIT: sorry, I think marcus already took quantum fields into consideration:

Or?

Last edited: Oct 16, 2013
23. Oct 16, 2013

### WannabeNewton

Yes I agree that without measuring rods, clocks, and light rays there is no physically meaningful (i.e. operational) way to determine the metric tensor. But my point, which isn't contradictory to your statements as noted, is that there is still meaningful physics without the notion of a metric tensor. An action term of the form $S = \int _{\mathcal{M}}\epsilon^{\mu_1...\mu_n}\alpha_{\mu_1...\mu_n}d^nx$, where $\epsilon^{\mu_1...\mu_n}$ is the Levi-Civita symbol and $\alpha_{\mu_1...\mu_n}$ is some n-form, is a purely topological term in the sense that it does not depend at all on the metric tensor.

24. Oct 16, 2013

### atyy

I think it is like an EM field without charge - it exists but is meaningless.

Like vectors without covectors :p

25. Oct 16, 2013

### Chalnoth

No, that doesn't follow. Space-time is its own thing with its own behavior. It interacts with matter, and matter reacts to the curvature of space-time.

In the Newtonian framework, the key point is that space-time is fixed, independent of matter. This absolutely isn't the case. While space-time can exhibit non-trivial features without matter, it still interacts with and responds to matter.