# Can you imagine geometry without matter and light?

• marcus

#### marcus

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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==

I feel its meaningless.

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

So imagine an empty graph.

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

So imagine an empty graph.

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

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

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

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

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?

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

The Milne universe is an example.

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]

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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}[/QUOTE] [Broken]

I have read the page you have quoted but in it author writes "General relativity tells us that what we call space is just another feature of the gravitational field of the universe, so space and space-time can and do not exist apart from the matter and energy that creates the gravitational field." So does it mean that matter which creates gravitational field has a property say it can not reach speed of light but matter which has a feature that is space can reach speed greater than speed of light??

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

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.

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==
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.

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.

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

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.

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

-Dave K

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??

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.

... No "test particles", no vibrating atoms to serve as a clock. Indeed no clock of any sort. Nothing to measure distance with either...

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.

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??

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 weren't 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.

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.

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 weren't 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.

First of all thanks for your reply and to put my question as thread.

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.)

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Here's from post #1, where the thread question was posed.
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?...

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.

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:

I feel its meaningless.

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

Isn't the question

marcus said:
Can you imagine geometry without matter and light?

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:

I mean matter in a general sense, including light, dynamical fields of any sort.

Or?

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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.

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

Like vectors without covectors :p

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??
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.

I guess the relationship between marcus's and WannabeNewton's points are that pure GR in the absence of matter has no local observables, just like a topological field theory?

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.

But what exactly is the matter in the case of a Schwarzschild black hole?

But what exactly is the matter in the case of a Schwarzschild black hole?

I suppose that the use of the term matter is not accurate; I meant that there is a source with compact support having some mass parameter ##M## that is responsible for the external vacuum Schwarzschild geometry.

I suppose that the use of the term matter is not accurate; I meant that there is a source with compact support having some mass parameter ##M## that is responsible for the external vacuum Schwarzschild geometry.
There actually isn't any source in the manifold. The problem is that the singularity has to be excluded from the manifold in order for the solution to be well-defined.

Of course, you might argue that the Schwarzschild geometry is an approximation to a real black hole which actually does contain matter. But that still leaves the De Sitter and anti-De Sitter space-times which don't include any matter sources, but nevertheless have a temperature.

Sure ##T_{ab} = 0## in the exterior vacuum region but that doesn't mean there is no source (in this case with compact support) associated with the Schwarzschild space-time geometry; when solving for the Schwarzschild metric we fix the boundary conditions at infinity in such a way that the metric corresponds to the space-time geometry exterior to some static spherically symmetric source of mass ##M##. It's the exact same situation as in Laplace's equation ##\nabla^2 \varphi = 0## for the electrostatic potential ##\varphi##: we are solving for the potential is a charge-free region but there is some charge source somewhere in space with compact support that is associated with the potential in the charge-free region of interest.

It is not exactly the same situation as with the electrostatic potential. Here we know what all of space and time is and can tell whether there is more space other than the region with no charge.

First of all thanks for your reply and to put my question as thread.

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.)