Is space an entity, a relationship or a concetual framework?

[dougy]

The only possible velocity function that is the same for multiple observers at different locations is one that is proportional to distance.

This is wrong. Consider v(D) = c*tanh(HD/c). Assuming the constancy of the speed of light the relativistic addition of velocities holds, then you can check that (v(D+d)-v(D))/(1-v(D)v(D+d)/c²) = v(d), and the cosmological principle is obeyed. You may want to argue that the constancy of the speed of light does not hold on cosmological scales, but that's only if you assume v(D) = HD in the first place and/or that the observable universe is not flat (it is up to measurement error).

Yes, it is. Because there is simply no way to be sure of what a theory predicts other than performing the math.

The mathematical framework of a theory is not the only framework that allows to reach predictions consistent with observations. I am sure it is possible to formulate a theory consistent with the observations that are considered tests of general relativity (or of any other theory) without the notion of differentiable function, integral, differential geometry or anything more complicated than basic maths everyone can grasp. You will probably disagree, and by giving many examples I may be able to convince you otherwise, but it is not as self-evident as you think that you need to use complicated mathematical structures to have a theory consistent with observations. While you do need to perform the maths to know what say general relativity predicts numerically, you don't necessarily need it to have a clear understanding of how the universe behaves (which does not necessarily require the use of a 4-dimensional pseudo-Riemannian manifold which is a mathematical tool and not a physical thing).

I don't think this is a good example. There is really no way to say whether or not space is an "entity" because "entity" isn't well-defined. Space-time does, after all, carry momentum and can transfer energy from one system to another (through gravity waves). Furthermore, there are a number of metrics that we can write down which have no matter but nevertheless have thermodynamic properties. There's every reason to believe space-time just as much a physical thing as the electromagnetic field.

By "entity" is meant something physical, something that can be perceived in some way, with or without the use of some instrument. If you can't perceive something but it is the only possible explanation for what you perceive, then it's safe to say that this thing exists. If however that thing is a mathematical tool, one of many ways to explain what you perceive, then it's safe to say it is nothing more than a tool.

I would say space is likely some physical thing but for different reasons (quantum fluctuations, the medium guiding waves would be made of in the deBroglie/Bohm interpretation of quantum mechanics, ...). And the electromagnetic and gravitational fields some disturbance in that medium. But neither these nor the ability to transfer energy necessitate space and time to be part of a single 4-dimensional entity that gets curved, nor does it necessitate space to physically expand and be the cause of galaxies receding from each other.

I doubt this question is actually relevant in cosmology. Space is no more, or less, than a coordinate system that spatially separates globs of matter.

Indeed it should be the case, and yet in cosmology space is reified to the point that the density of matter dictates whether the universe is "open" or "closed", i.e. whether one would go back to his starting point by always traveling in the same direction. Which cannot happen unless space is a physical thing being physically curved, which is an untested (and probably untestable) aspect of general relativity.

 

[Chalnoth]

This is wrong. Consider v(D) = c*tanh(HD/c). Assuming the constancy of the speed of light the relativistic addition of velocities holds, then you can check that (v(D+d)-v(D))/(1-v(D)v(D+d)/c²) = v(d), and the cosmological principle is obeyed. You may want to argue that the constancy of the speed of light does not hold on cosmological scales, but that's only if you assume v(D) = HD in the first place and/or that the observable universe is not flat (it is up to measurement error).

This isn't a valid thing to do. Special relativity doesn't hold for a curved space-time, and an expanding universe represents a curved space-time.

The point is that you can write down the behavior of an expanding universe without any mention of velocity and just have it obey homogeneity and isotropy. Those assumptions alone inevitably lead to recession velocities which increase linearly with distance.

The mathematical framework of a theory is not the only framework that allows to reach predictions consistent with observations. I am sure it is possible to formulate a theory consistent with the observations that are considered tests of general relativity (or of any other theory) without the notion of differentiable function, integral, differential geometry or anything more complicated than basic maths everyone can grasp. You will probably disagree, and by giving many examples I may be able to convince you otherwise, but it is not as self-evident as you think that you need to use complicated mathematical structures to have a theory consistent with observations. While you do need to perform the maths to know what say general relativity predicts numerically, you don't necessarily need it to have a clear understanding of how the universe behaves (which does not necessarily require the use of a 4-dimensional pseudo-Riemannian manifold which is a mathematical tool and not a physical thing).

Except that in General Relativity, the real world actually is as complicated as the 4-dimensional manifold described by General Relativity. Even if you can come up with an explanation of a specific system using something much simpler, that explanation isn't going to generalize to other situations. So there will always be the danger that a person will take away some concepts that just aren't useful in other situations.

By "entity" is meant something physical, something that can be perceived in some way, with or without the use of some instrument. If you can't perceive something but it is the only possible explanation for what you perceive, then it's safe to say that this thing exists. If however that thing is a mathematical tool, one of many ways to explain what you perceive, then it's safe to say it is nothing more than a tool.

Gravity waves can be measured with the right instruments.

But neither these nor the ability to transfer energy necessitate space and time to be part of a single 4-dimensional entity that gets curved, nor does it necessitate space to physically expand and be the cause of galaxies receding from each other.

The success of General Relativity in predicting the outcomes of a wide variety of experiments necessitates this. It's certainly possible that there is some different quantum behavior that we don't yet understand, but that behavior must reduce to curved 4D space-time in the appropriate limit in order for current experiments to not rule it out.

 

[dougy]

This isn't a valid thing to do. Special relativity doesn't hold for a curved space-time, and an expanding universe represents a curved space-time.

The point is that you can write down the behavior of an expanding universe without any mention of velocity and just have it obey homogeneity and isotropy. Those assumptions alone inevitably lead to recession velocities which increase linearly with distance.

The cosmological principle is a statement that the universe appears the same to all observers, you can't infer the homogeneity of the universe from one sole vantage point without additional assumptions. Sure special relativity doesn't hold in the FLRW metric, which assumes homogeneity.

Except that in General Relativity, the real world actually is as complicated as the 4-dimensional manifold described by General Relativity. Even if you can come up with an explanation of a specific system using something much simpler, that explanation isn't going to generalize to other situations. So there will always be the danger that a person will take away some concepts that just aren't useful in other situations.

My point was precisely that the mathematics of general relativity are not the only way to arrive at predictions consistent with observations. While the much simpler explanation will not be equivalent to general relativity, what we are concerned about is whether it fits all the experimental evidence, not just one specific situation. And it is not necessary to invoke a 4-dimensional curved manifold to explain the evidence, as was done in this paper for the classical tests of general relativity: http://journals.aps.org/pr/abstract/10.1103/PhysRev.92.1557 (the same approach could be generalized to explain all the evidence, it could be formulated in a mathematically simpler way, other approaches could be used...the point is the facts of experience do not compel us to accept a 4-dimensional curved expanding manifold as a physical necessity)

Gravity waves can be measured with the right instruments.

Gravitational waves may be measurable, but their existence does not imply the existence of space being a physically curved expanding thing. Just like the bending of light does not imply space is physically curved unless you postulate in the first place that light travels in straight lines, and just like the precession of gyroscopes in orbit does not imply space is physically curved. What they do show is that what we observe can be interpreted in a mathematical framework where a mathematical space is curved.

 

[julcab12]

And the electromagnetic and gravitational fields some disturbance in that medium. But neither these nor the ability to transfer energy necessitate space and time to be part of a single 4-dimensional entity that gets curved, nor does it necessitate space to physically expand and be the cause of galaxies receding from each other.

But it is more intuitive with them getting in the mix. I wonder.. How can you facilitate a sensical framework without the spacetime mix?

what we are concerned about is whether it fits all the experimental evidence, not just one specific situation. And it is not necessary to invoke a 4-dimensional curved manifold to explain the evidence, as was done in this paper for the classical tests of general relativity:

... But it works and consistent that way (4D) --macro.

 

[dougy]

But it is more intuitive with them getting in the mix. I wonder.. How can you facilitate a sensical framework without the spacetime mix?

Well it is not necessary to invoke spacetime to derive the predictions of special relativity, the Minkowski framework was introduced after Einstein's original formulation. The predictions of general relativity follow from the equivalence principle, special relativity and some other assumptions. The structure of curved spacetime added on top of them comes from imposing the constraint that things subject to gravitation follow straight lines. The ability to impose such a structure comes from the equivalence principle, but it is not a necessity.

 

[PeterDonis]

The predictions of general relativity follow from the equivalence principle, special relativity and some other assumptions.

Do you mean you have a theory using a different mathematical framework from GR, that reproduces all of its predictions? If so, please give a reference.

Or do you just mean that you prefer to interpret the same math of GR that everyone uses, differently from the usual curved spacetime interpretation? If so, that's a question of philosophy, not physics.

 

[Chalnoth]

The cosmological principle is a statement that the universe appears the same to all observers, you can't infer the homogeneity of the universe from one sole vantage point without additional assumptions. Sure special relativity doesn't hold in the FLRW metric, which assumes homogeneity.

The question was whether the cosmological principle implies a linear distance/recession velocity relationship. It does.

This does require defining a specific reference frame (given by a time slicing of the universe). But the point is that if you have homogeneity and isotropy (the cosmological principle), then it's always possible to define a reference frame where the first derivative of the proper distance between any two galaxies at the same time (given by this time slicing) is a linear function of that proper distance.

As for other possible expansion histories that would be consistent with observations, well, so far no such models have been shown to be accurate. It's particularly difficult to fit any non-homogeneous model with measures of large scale structure such as baryon acoustic oscillation measurements.

My point was precisely that the mathematics of general relativity are not the only way to arrive at predictions consistent with observations. While the much simpler explanation will not be equivalent to general relativity, what we are concerned about is whether it fits all the experimental evidence, not just one specific situation. And it is not necessary to invoke a 4-dimensional curved manifold to explain the evidence, as was done in this paper for the classical tests of general relativity: http://journals.aps.org/pr/abstract/10.1103/PhysRev.92.1557 (the same approach could be generalized to explain all the evidence, it could be formulated in a mathematically simpler way, other approaches could be used...the point is the facts of experience do not compel us to accept a 4-dimensional curved expanding manifold as a physical necessity)

Not the only way, sure. Technically, there has to be a different way because General Relativity cannot be entirely correct (due to its prediction of singularities). But there is no simpler way that will fit with all of the evidence.

As for that paper, I no longer have access to an institutional subscription. But I highly doubt that it would be in any way easier to grasp than General Relativity (and it's probably either wrong or reduces to General Relativity in the appropriate limit).

Gravitational waves may be measurable, but their existence does not imply the existence of space being a physically curved expanding thing. Just like the bending of light does not imply space is physically curved unless you postulate in the first place that light travels in straight lines, and just like the precession of gyroscopes in orbit does not imply space is physically curved. What they do show is that what we observe can be interpreted in a mathematical framework where a mathematical space is curved.

Except that it fits your own definition of space-time being a physical entity.

 

[yogi]

Since the original question is more of a survey - I will weigh in with my own interpretation of space as a functional entity. My background is engineering - I have BS, MS and JD degrees. Einstein notably changed his position on space as an ether during the years spent developing GR, he believed space to be conditioned by matter - and while he had the wrong view of the universe as static, the equations admit dynamic solutions as shown by de Sitter, Friedmann and others. A mental image of dynamic space as motion is not necessary... anymore than an image of static space as bent by matter. Both concepts are mathematically useful and both have been used to derive physical results.

 

[Gigel]

Space may be a superfluid Bose-Einstein condensate with very little interaction with fields and particles (except maybe the gravitational field) - just an opinion I found in a few articles.

 

[jack476]

No, a "space" is just a set of objects where there is some concept of distance, direction, and position. Vector spaces, point sets, the xy-plane, your computer's RAM (in a more abstract sense), the search space of a search engine, the solution space of a differential equation...etc.

So I'm going to go with "conceptual framework". Quantities like distance and position are not necessarily inherent to the universe itself, they are ideas that were invented by humans to quantify phenomena in the universe in order to make it amenable to human understanding. It might well be that the universe itself is made out of some identifiable material, but calling the universe a space in which we can quantify distance and direction is entirely a human invention.

 

[Feeble Wonk]

"Entity" ,
"relationship" or
"Framework".

Leibniz would say "relationship".