Is spacetime really curved? Embedded somewhere?

[Duda Jarek]

When light goes through different materials, it chooses path to locally minimalize distance - it's trajectory is geodesic of some metric (usually diagonal - isotropic) . It is the result of that microscopic structure of the material can reduce wave propagation speed.

 

Microscopic models of physics usually assume that we have some field everywhere and it's fluctuations transfer interactions/energy/momentum.

So maybe these microscopic structure can reduce waves propagation speeds?

Reciprocals of these velocities creates (anisotropic) metric tensor (g) and so for example particles travel through geodesics like in general relativity theory.

 

Standard interpretation of general relativity says that particles goes through geodesics because of space time internal curvature: theory, experiments suggest some equations, which looks like being a result of internal curvature of spacetime.

But if we live on some curved manifold, it intuitively should be embedded somewhere(?) (and for example black holes are some spikes)

So why our energy/matter is imprisoned on something infinitely flat?

Why we doesn't interact with the rest of this something?

What happen if our manifold will intersect with itself? (optimists say that it would allow for time travel/hyperspace jumps?...)

And less philosophical, but most fundamental (to connect GR and QM) question is: how energy/momentum density can create curvature?

 

Maybe it's not the only possible interpretation.

Maybe we live in flat R^4 and GR is only the result of reducing the speed of wave propagation by microscopic structure of some field, which somehow is ruled by similar equations to Einstein-Hilbert.

This interpretation doesn't allow for instant time/space travel, but it get rid of some inconvenient questions ... and creates a chance to answer to the last one.

 

So how should look such connection of QM(QFT?) and GR?

What are particles? From spacetime point of view, they are some localized in some three dimensions and relatively long in the last one, solutions of let say some field to some equations. These solutions want to be more or less straight in four dimensions (constant velocities), but they turn accordingly to interactions transferred by the field.

Many of them were created in big bang (boundary conditions), so their long dimension is similarly directed - creating local time arrow (GR).

Bolzman distribution among such trajectories, can purely classically create QM like statistical behavior ( http://www.scienceforums.net/forum/showthread.php?t=36034 ).

 

Are there any arguments for spacetime internal curvature other than that the equations looks like being be a result of it?

What do you think about these interpretations?

If the curvature is the only option, is spacetime embedded somewhere... ?

[ajb]

You do not need to embed a manifold into another (including [math]\mathbb{R}^{n}[/math] for some n) in order to describe it. This extends to manifold with structure like a metric. (Isotropic embeddings of Riemannian manifolds is an interesting topic.)

 

General relativity does not require any embedding, but it also does not rule it out.

[Duda Jarek]

So maybe it only looks like it was a result of a curvature?

Einstein - Hilbert equations connects internal curvature with energy/momentum, but how physically is made this connection? Until we understand it, these equations aren't argument for internal curvature.

 

Especially that it can be an analogous effect to minimal optical path principle: because of interference with responses of local atoms, light travels along geodesic of metric tensor being 'refractive index'*'identity matrix'.

In GR, such refractive index has to be four-dimensional and usually anisotropic (different wave speeds for different directions). It could be created for example by that interactions are transferred by some waves of field, so they creates some local structure of the field - small differences between being in different phase could cause that large interactions make interference needed to change propagation speed/direction of other waves.

 

If GR is really the result of internal curvature and spacetime is not embedded anywhere, what would happen if it looks like it should intersect with itself?

[ajb]

Embeddings don't have self-intersections.

 

Immersions may do.

[Duda Jarek]

Ok, You are right ... let's call it immersion ...

So what do You think about the possibility of instant time/space travels?

[ajb]

Instant does not really fit well into general relativity. Let me have a think about it.

 

It may be possible to have "virtual instantaneous" motion in classical GR. Viz wormholes maybe.

Edited December 11, 2008 by ajb

[Duda Jarek]

Two dimensional manifold with positive constant internal curvature should create a sphere... (somewhere...)

If spacetime is really immersed somewhere, when it should intersect with itself, it probably could change topology instead (like going through a critical point in the Morse theory). I think it's the concept for time travels/wormholes(?).

[ajb]

Again, you don't need it to be immersed to have wormholes. They are however topological features.

[Duda Jarek]

I was recently told ( http://groups.google.pl/group/sci.physics.foundations/browse_thread/thread/e6e26b84d19a17ff# ) that there is quite new Relativistic Theory of Gravity (RTG) by Russian physicist Logunov, which explains GR without internal curvature.

It uses speeds of clocks. But any clock (mechanical, atomic,biological...) bases on some chain of reason-result relations. These relations are made by some interactions - transferred by some waves ... So speed of clock can be translated into wave propagation speed.

 

I have a question: does strong (electro)magnetic field bend the light?

In field theories like QED we add some nonlinear terms (like phi^4) to introduce interactions between different frequencies... From the second side electromagnetic interactions has some similarities to gravity interaction...

Have You heard about such experiments, calculations? Dedicated experiment should find it, and so using different EM fields we could tell a lot about fundamental details of QED... (and maybe GR...)

Edited December 14, 2008 by Duda Jarek

[ajb]

You do have photon-photon scattering in QED, it is of course not at tree level and so has no classical counterpart.

[Duda Jarek]

Cannot GR be viewed as such graviton-graviton scatterings?

[ajb]

In the (not very well founded) perturbative limit, yes.

[Duda Jarek]

So we don't need any mystical internal curvature...

 

SRT can be derived from the assumption that light travels with given constant speed. Gravity waves has the same.

From the point of view of spacetime, it says the angle (45 deg) of solutions for waves which carries (probably?) all interactions.

The only difference in GRT is that these solutions: interaction/light cones has changed their directions.

[ajb]

Gravitons are really inherently part of a perturbative approach to quantising general relativity. You should think (loosely) of the gravitons as fluctuation in the local geometry. So really, gravitons are not "in conflict" with the notion of local geometry as gravity. They are the quanta just as photons are teh quanta of the EM field.

[Duda Jarek]

But we can also think about GR that we have flat spacetime with some interacting fields.

It allows to understand how it is a result of microscopic physics (like photon-graviton scatterings) and we avoid huge amount of philosophical questions for internal curvature interpretation.

 

The maximum time travel possibility this picture allows is to turn our reason-result line into opposite time direction and after some (minus) time turn back.

It would create some loop which cannot spoil actual situation (like killing grandfather) - so it suggests that the future is already somehow set - eternalism (which assumption creates QM (see link)).

 

Oh I've forgot to mention that such causality loop would create some very strange topological singularity ... so probably all time travels are forbidden ... ?

Edited December 14, 2008 by Duda Jarek

[north]

When light goes through different materials, it chooses path to locally minimalize distance - it's trajectory is geodesic of some metric (usually diagonal - isotropic) . It is the result of that microscopic structure of the material can reduce wave propagation speed.

 

Microscopic models of physics usually assume that we have some field everywhere and it's fluctuations transfer interactions/energy/momentum.

So maybe these microscopic structure can reduce waves propagation speeds?

Reciprocals of these velocities creates (anisotropic) metric tensor (g) and so for example particles travel through geodesics like in general relativity theory.

 

Standard interpretation of general relativity says that particles goes through geodesics because of space time internal curvature: theory, experiments suggest some equations, which looks like being a result of internal curvature of spacetime.

But if we live on some curved manifold, it intuitively should be embedded somewhere(?) (and for example black holes are some spikes)

So why our energy/matter is imprisoned on something infinitely flat?

Why we doesn't interact with the rest of this something?

What happen if our manifold will intersect with itself? (optimists say that it would allow for time travel/hyperspace jumps?...)

And less philosophical, but most fundamental (to connect GR and QM) question is: how energy/momentum density can create curvature?

 

Maybe it's not the only possible interpretation.

Maybe we live in flat R^4 and GR is only the result of reducing the speed of wave propagation by microscopic structure of some field, which somehow is ruled by similar equations to Einstein-Hilbert.

This interpretation doesn't allow for instant time/space travel, but it get rid of some inconvenient questions ... and creates a chance to answer to the last one.

 

So how should look such connection of QM(QFT?) and GR?

What are particles? From spacetime point of view, they are some localized in some three dimensions and relatively long in the last one, solutions of let say some field to some equations. These solutions want to be more or less straight in four dimensions (constant velocities), but they turn accordingly to interactions transferred by the field.

Many of them were created in big bang (boundary conditions), so their long dimension is similarly directed - creating local time arrow (GR).

Bolzman distribution among such trajectories, can purely classically create QM like statistical behavior ( http://www.scienceforums.net/forum/showthread.php?t=36034 ).

 

Are there any arguments for spacetime internal curvature other than that the equations looks like being be a result of it?

What do you think about these interpretations?

If the curvature is the only option, is spacetime embedded somewhere... ?

 

space nor time is " curved "

 

since neither has any fundamental substance associated with them , independent of all other substances

[Martin]

space nor time is " curved "

 

since neither has any fundamental substance associated with them , independent of all other substances

 

I understand the point you are making, north. But I think it involves a questionable unstated assumption.

 

You seem to be saying that space cannot have any geometric properties because it is not a substance.

 

I agree that space has no fundamental substance. But it can still have geometry.

 

For example the sum of angles of a triangle can either be 180, or it can be something else. If it is always 180 then space has a flat or Euclidean geometry. It can have this geometry even though it is not made of substance. If it is different from 180, then space has a non-flat or non-Euclidean geometry, which also does not require substance.

 

Likewise with radius and volume. If the volume of a sphere always increases as the cube of the radius then space has a flat or Euclidean geometry, and it can have this even though it is not made of any substance! Likewise the volume can increase as some other function of the radius.

 

In cosmology, using redshift surveys, CMB and BAO (baryon acoustic oscillations) data what people are doing in effect is measuring the angles of very large triangles or comparing large radii and volumes. The data show that curvature in largescale geometry cannot be ruled out, not yet anyway.

 

I do not think your claim is based on logic.

It seems to me that geometry can be curved, or not.

And space is nothing but geometry.

Therefore space can be curved, or not.

 

If space has no substance, then what does it consist of besides the sum total of all geometric relations? The catalog of all the distances, areas, angles etc.

This has been a traditional view of what space is, in Western philosophy, going back as far as Aristotle. So what I'm telling you is pretty ordinary stuff.

Einstein's special contribution was to equate the gravitational field with geometry itself. The gravitational field is nothing else but the geometry of spacetime (in his 1915 GR theory.) So he was the first to give a dynamical explanation of geometry---to discover that it has causes, and can change, and even oscillate. He began the effort to explain what determines where it is going to be flat and where and when it will be curved. In this way, he made geometry a real part of physics.

Edited December 16, 2008 by Martin

[Duda Jarek]

There is a problem with measuring angles - they depends on the reference frame.

GR rotates locally light cones - solutions for waves of interaction, which makes that it looks like we are living in Minkowski space.

These rotations of solutions can be caused by some field. So even when they will be confirmed by an observation, the internal curvature won't be needed.

[Severian]

So maybe it only looks like it was a result of a curvature?

 

I have a certain sympathy with that notion, but I would say if it "looks like it was a result of a curvature" then it is curvature by definition. For example, if two people head off in parallel directions (that is, at right angles to the line between them) and after a while they find that they are getting closer together or further apart, then the space is curved by definition.

 

Ironically, I often think that the understanding of General Relativity becomes muddled by thinking too much about geometry.

[Duda Jarek]

if it "looks like it was a result of a curvature" then it is curvature by definition

I cannot agree - there is qualitative difference.

Light 'thinks' that geometry changes/the world is curved when it goes through different materials.

If it would be really geometry, X-rays would also 'think' so

People going in parallel direction can be getting closer, because of positive curvature of the space OR because solutions of the field they are build of would have energetic tendency to bend so.

[ajb]

 

Ironically, I often think that the understanding of General Relativity becomes muddled by thinking too much about geometry.

 

I take a different point of view and think that just about all physics can be understood in terms of geometry.

[north]

I understand the point you are making, north. But I think it involves a questionable unstated assumption.

 

You seem to be saying that space cannot have any geometric properties because it is not a substance.

 

no this is not what I'm saying

 

space by its very nature will have a geometry(s) associated within it . it is SPACE after all

 

it just that you can't use space in and of itself by itself to change the geometry of a particular angle

 

the angle can only be changed by calculation

 

 

 

 

 

I agree that space has no fundamental substance. But it can still have geometry.

 

agreed

 

For example the sum of angles of a triangle can either be 180, or it can be something else. If it is always 180 then space has a flat or Euclidean geometry. It can have this geometry even though it is not made of substance. If it is different from 180, then space has a non-flat or non-Euclidean geometry, which also does not require substance.

 

Likewise with radius and volume. If the volume of a sphere always increases as the cube of the radius then space has a flat or Euclidean geometry, and it can have this even though it is not made of any substance! Likewise the volume can increase as some other function of the radius.

 

above

 

In cosmology, using redshift surveys, CMB and BAO (baryon acoustic oscillations) data what people are doing in effect is measuring the angles of very large triangles or comparing large radii and volumes. The data show that curvature in largescale geometry cannot be ruled out, not yet anyway.

 

again above

 

 

 

 

I do not think your claim is based on logic.

 

my claim is not based on logic but reason

 

 

 

 

It seems to me that geometry can be curved, or not.

And space is nothing but geometry.

Therefore space can be curved, or not.

 

again above

 

 

 

 

 

 

If space has no substance, then what does it consist of besides the sum total of all geometric relations? The catalog of all the distances, areas, angles etc.

This has been a traditional view of what space is, in Western philosophy, going back as far as Aristotle. So what I'm telling you is pretty ordinary stuff.

Einstein's special contribution was to equate the gravitational field with geometry itself. The gravitational field is nothing else but the geometry of spacetime (in his 1915 GR theory.) So he was the first to give a dynamical explanation of geometry---to discover that it has causes, and can change, and even oscillate. He began the effort to explain what determines where it is going to be flat and where and when it will be curved. In this way, he made geometry a real part of physics.

 

Martin

 

I see your point

 

but what Einstein didn't include was the WHY

 

the WHY being while the geometrics said this or that and then came to a conclusion

 

he forgot or didn't include or couldn't include( because of the knowledge then known ) the physical dynamics of objects and their interactions, which is the essence of the geometrics

 

for the most part Einstein was right he just did not understand fully WHY he was right

 

for instance can we fully explain beyond geometrics why Mercury does what it does ?

 

not that I know of

[Martin]

North,

If you want to respond to points of mine which you quote, please give a explicit responses. Here you just say "above". This apparently refers to some sentences above which don't make sense to me.

"it just that you can't use space in and of itself by itself to change the geometry of a particular angle the angle can only be changed by calculation"*

 

And it isn't clear what your reaction is when you say "above", or how the earlier sentences are suppose to respond to what I said.

 

If you really intended to respond to my earlier post, please give it another try and spell out more clearly what you mean. I will await your reply.

 

Also if you want to state a position, please go right ahead and make it clear what you think on this topic.

 

*I didn't propose any such thing---I don't propose "changing" angles. One observes angles, and measure angles. I don't believe angles that you measure can be changed by calculation or any other means. So you are not objecting to anything I said! Yet it sounds as if you are unhappy about something and are protesting----you can't use space...etc etc. So I couldn't see the point of your "above" passage.

Edited December 25, 2008 by Martin

[north]

North,

If you want to respond to points of mine which you quote, please give an explicit response. Here you just say "above". This apparently refers to some sentences above which don't make sense to me.

 

And it isn't clear what your reaction is when you say "above", or how the earlier sentences are suppose to respond to what I said.

 

" above " is in reference to my first response in post # 22

[Phi for All]

" above " is in reference to my first response in post # 22

[moderation]

 

Am I correct in saying that all your references in posts #22 and #24 to "above" and "again above" mean "agreed"? If so, please don't do this again, just say "agreed". Agreeing shouldn't be so disagreeable that you have to mask it in confusion.

 

[/moderation]