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

[AndyFin]

Hi, the first paragraph in the Wikipedia entry to space contains a sentence saying there is disagreement between PHILOSOPHERS whether space is an entity, a relationship or a conceptual Framework. I am interested in what PHYSICISTS think about this.

My personal view is that it is an entity as it is something that has physical PROPERTIES. It therefore can and should be investigated by physicists. I think the business of physics is the investigation of changes to matter and energy and as space has an energy momentum Tensor, it therefore has properties and should be considered as an entity.
Id like to make a small unrepresntative survey on your view so could I ask anyone reading this to let me know what their view is by just making a small comment like

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

If you could also leave an indication of what you have studied, it woud help me like -

p for trained physicist,
e for engineer,
m for mathmatician, and
o for other)

Of course if you want to give arguments for one view or the other, it would also be most welcome.Thanks

Id appreciate it, thanks

 

[phinds]

I think that the consensus among physicists is that space-time is a framework in which things happen. As has been said, time is what keeps everything from happening all at once and space is what keeps it from all happening to me.

The pop-science concepts of "expanding" space, "fabric" of space, ""bending" space are not taken seriously as they are an attempt to render in English things that really only render in math.

 

[Chalnoth]

Trained physicist here (though I'm no longer working in the field).

From my experience with physicists, not very many worry very much about this sort of question. Many are even pretty hostile to the idea of spending time thinking about this kind of question.

As far as most physicists are concerned (from my experience), space-time is a mathematical structure which is a component of various theories that describe how the universe works. They usually aren't worried with questions like, "Is this an entity or a framework?" but instead, "Does this mathematical structure provide predictions which can be tested experimentally?" They tend to get really frustrated with philosophical questions like the above because they don't see that there's any way to answer them definitively. But when there's an experiment you can do, then it becomes really easy to come to a solution.

There are physicists who are much more friendly to philosophical questions like this, but they seem to be pretty rare.

 

[jtbell]

Also note that here on Physics Forums, we have limited tolerance for philosophical discussions, because they usually end up going round and round without really going anywhere.

 

[AndyFin]

Exactly what I expected. But here is the thing. I think that at the minimum there is the need for a new vocabulary or nomenclature.

If physicists use words like expanding, contracting etc. it leads the "public" to think of "movement" or "velocity" of space. Here are some suggestions: You can take them seriously, or with a pinch of humour.

Space is "hubbling" - Hubbling refers to the expansion of the framework that is called space.

A recession velocity of a galaxy that is moving faster than the speed of light should be called a " Quasi- velocity" to differentiate between what is a velocity (with a maximum velocity of the speed of light) and the quasi-velocity which is greater than the speed of light.Anyone agree?

 

[Chalnoth]

I think expanding is a pretty good description. There are lots of analogies available to explain the expansion. Adding special new terminology just complicated matters because now that new terminology needs to be explained.

I think the simplest explanation is that the expansion means that galaxies tend to move away from one another, and the further they are, the faster they move.

 

[phinds]

Anyone agree?

No. Your ideas are not wrong or even wrong-headed, it's just that they are impractical to the point of being useless. We've had a lot of discussions here about changing the terminology in physics because much of it is so badly representative of what's really going on. The problem is that any "decision" we make here on PF is utterly meaningless in the wider world and it's just a waste of time to worry about it.

 

[AndyFin]

Perhaps terminology is the wrong word. Perhaps the word should be concept

Would you say the use of velocity of a body as used in special relativity and the use of velocity of a body when used in reference to a galaxy beyond the cosmic event horizon are the same animals?

Is velocity always the same thing in physics or not? Is it always used the same way and always follows the same rules?

I think that where there are differences, these are different concepts and should also have different terminology

 

[phinds]

Would you say the use of velocity of a body as used in special relativity and the use of velocity of a body when used in reference to a galaxy beyond the cosmic event horizon are the same animals?

No, I would not. They have nothing to do with each other. Local velocity means something is moving. With cosmic recession, nothing is moving, things are just getting farther apart.

 

[Chalnoth]

Perhaps terminology is the wrong word. Perhaps the word should be concept

Would you say the use of velocity of a body as used in special relativity and the use of velocity of a body when used in reference to a galaxy beyond the cosmic event horizon are the same animals?

Is velocity always the same thing in physics or not? Is it always used the same way and always follows the same rules?

I think that where there are differences, these are different concepts and should also have different terminology

Velocity behaves a bit differently depending upon whether you're talking about Newtonian physics, special relativity, general relativity, or quantum mechanics.

In Newtonian physics, velocity is very simple and intuitive: it's just the rate of change of the object's position.

Special relativity throws a wrench into the mix: every observer measures the speed of light to be c. This complicates math a bit, but it's conceptually not really different from the Newtonian case, except that now there's a speed limit.

General relativity really mucks things up. Locally, General Relativity works exactly like special relativity (so that velocity relationships for objects passing one another are the same). But for far-away objects, relative velocity becomes poorly-defined. Because space-time is curved in General Relativity, you can't directly compare the velocities of two objects: Imagine, as an example, two cars on exact opposite sides of the Earth on the equator that are both moving directly north at the same speed compared to the Earth. How fast is one car moving with respect to the other? If we compare the distance between the cars along the south, they're moving away. If we compare their distance along the north, they're getting closer. If we compare their distance east/west, they're not moving with respect to one another at all. You can come up with a convention to say what the velocity of each car is, but somebody else could just come up with a different convention. There's no way to say who is right. This is why far-away galaxies don't obey the speed of light limit when considering their velocity with respect to us: that speed limit can only apply at a single point, so that in GR the speed of light limit reduces to, "Nothing can outrun a light beam."

Quantum mechanics creates a separate problem because an object no longer has a single speed: as objects in QM are waves, they have a distribution of speeds, with some parts of the wave moving faster than others.

 

[Bandersnatch]

A recession velocity of a galaxy that is moving faster than the speed of light should be called a " Quasi- velocity" to differentiate between what is a velocity (with a maximum velocity of the speed of light) and the quasi-velocity which is greater than the speed of light.

First, you don't want a special word or a special phrase for recession velocities over c, because that'd suggest that there's some physics that changes once a galaxy recedes over that speed. You want a phrase to differentiate regular (local, special relativistic) velocity from any velocity associated with expansion (a general relativistic effect), as this does delineate different physics (Chalnoth explained the differences above). But we already have a phrase for that in cosmology - it's 'recession velocity'. I see no reason to change one noun modifier to another.

 

[dougy]

Trained physicist here (though I'm no longer working in the field).

From my experience with physicists, not very many worry very much about this sort of question. Many are even pretty hostile to the idea of spending time thinking about this kind of question.

As far as most physicists are concerned (from my experience), space-time is a mathematical structure which is a component of various theories that describe how the universe works. They usually aren't worried with questions like, "Is this an entity or a framework?" but instead, "Does this mathematical structure provide predictions which can be tested experimentally?" They tend to get really frustrated with philosophical questions like the above because they don't see that there's any way to answer them definitively. But when there's an experiment you can do, then it becomes really easy to come to a solution.

There are physicists who are much more friendly to philosophical questions like this, but they seem to be pretty rare.

The problem is it stops being just "philosophy" when statements such as "galaxies move away from each other because space expands" or "light is redshifted because of the stretching of space" are given unscrupulously everywhere. If space is a mathematical framework then it is false to state that the universe works the way it does because of how this mathematical framework behaves, this is the fallacy of reification. They get frustrated with philosophical questions, but they wouldn't have to if they used the proper terminology in the first place.

Why do galaxies move away from each other at a velocity proportional to the distance between them? If you consider space to be a mathematical concept and say because space expands or stretches between them, it's wrong. If you consider space to be an entity, then it is still wrong because this entity hasn't been detected. The valid answer to this question would be "we don't know", or if the big bang is assumed "because that's what they have been doing since the big bang", which then begs the question why that is the case. Explaining why in term of a mathematical concept gives the illusion of an explanation, at best it is an analogy.

In the end it is the non-physicists eager to understand who get frustrated with the misleading explanations given by the physicists. The honest attitude from the physicists then would be to clarify the misconceptions they are responsible for spreading in the first place, rather than getting frustrated with philosophical questions that spawned precisely from their misleading explanations.

 

[dougy]

No, I would not. They have nothing to do with each other. Local velocity means something is moving. With cosmic recession, nothing is moving, things are just getting farther apart.

"Things are just getting farther apart", which means they have a relative velocity. Unless you are treating space as an entity that expands between galaxies while galaxies remain at rest relative to that space, which is the fallacy of reification.

General relativity really mucks things up. Locally, General Relativity works exactly like special relativity (so that velocity relationships for objects passing one another are the same). But for far-away objects, relative velocity becomes poorly-defined. Because space-time is curved in General Relativity, you can't directly compare the velocities of two objects.

On the scale of the observable universe space-time is flat, why can't you compare their velocities then?

 

[phinds]

"Things are just getting farther apart", which means they have a relative velocity. Unless you are treating space as an entity that expands between galaxies while galaxies remain at rest relative to that space, which is the fallacy of reification.

If I pass you in a car, we are moving relative to each other. There is a frame of reference in which I am stationary and you are moving relative to me and there is a reference frame in which you are stationary and I am moving relative to you. If I toss an apple out of the car window as I pass you, and it hits you it is equally valid to say that the apple moved towards the stationary you or you moved towards the stationary apple. Either way, there is momentum that comes into play, as you will well notice when you and the apple meet up. There is NO momentum between galaxies that are receding from each other because they are not moving relative to each other in the way that you and I were moving relative to each other. They are just getting farther apart.

 

[dougy]

If I pass you in a car, we are moving relative to each other. There is a frame of reference in which I am stationary and you are moving relative to me and there is a reference frame in which you are stationary and I am moving relative to you. If I toss an apple out of the car window as I pass you, and it hits you it is equally valid to say that the apple moved towards the stationary you or you moved towards the stationary apple. Either way, there is momentum that comes into play, as you will well notice when you and the apple meet up. There is NO momentum between galaxies that are receding from each other because they are not moving relative to each other in the way that you and I were moving relative to each other. They are just getting farther apart.

If you never passed me but were always moving away from me you couldn't do that experiment with the apple. With your interpretation it seems you would say there is no momentum involved between two objects that never meet, and so with your interpretation that I couldn't measure the velocity of your car if you didn't pass me but were moving away from me at the beginning. That all I could say is that we are getting farther apart. Yet I'm sure you will agree I can measure the velocity of your car even if we never meet. What's the difference between the two situations then?

I would say that there is a practical difference, not a conceptual one. Practical in that I can measure your velocity almost instantaneously by exchanging light signals, while in the case of distant galaxies one would have to wait billions of years for the light to come back. But still if the distant galaxy is assumed to have a constant relative velocity throughout, its velocity could be measured in principle.

Regarding galaxies supposedly receding faster than light, do we really have any experimental evidence that they do so, besides assuming that Hubble's law applies on cosmological scales?

 

[Chalnoth]

The problem is it stops being just "philosophy" when statements such as "galaxies move away from each other because space expands" or "light is redshifted because of the stretching of space" are given unscrupulously everywhere. If space is a mathematical framework then it is false to state that the universe works the way it does because of how this mathematical framework behaves, this is the fallacy of reification. They get frustrated with philosophical questions, but they wouldn't have to if they used the proper terminology in the first place.

There's no question that a lot of physicists use sloppy terminology. I've been guilty of it myself. But when it comes down to evaluating ideas, this isn't a problem at all. All physical theories are approximations to the real behavior, and the primary job of physics is to find out where those approximations break down.

With regard to the expansion, for instance, the mathematical framework used (the FLRW metric) assumes that matter is perfectly evenly-distributed throughout space. This is clearly not completely accurate: the very fact that the solar system exists proves it to be false. But it turns out to work very well for describing the universe on large scales. There was also a flurry of work in the early 2000's where they tried to make sure that this approximation did work on large scales as well as was generally believed: some thought that the fact that the universe wasn't uniform might potentially lead to the illusion of an accelerated expansion (this turned out not to be the case).

Why do galaxies move away from each other at a velocity proportional to the distance between them? If you consider space to be a mathematical concept and say because space expands or stretches between them, it's wrong. If you consider space to be an entity, then it is still wrong because this entity hasn't been detected. The valid answer to this question would be "we don't know", or if the big bang is assumed "because that's what they have been doing since the big bang", which then begs the question why that is the case. Explaining why in term of a mathematical concept gives the illusion of an explanation, at best it is an analogy.

Ultimately the fact that the expansion is uniform comes down to initial conditions. This isn't a completely worthless statement: it narrows the scope of the investigation into the causes. What we do know of the expansion is that our universe is pretty accurately described by the cosmological principle. And a universe that obeys the cosmological principle has recession velocity proportional to distance.

So the question then becomes, how was the universe started in such a way that the cosmological principle applies? For that, we don't yet know. The answer may have something to do with inflation, but that appears to just make it so that the cosmological principle needs to be assumed over a smaller region.

In the end it is the non-physicists eager to understand who get frustrated with the misleading explanations given by the physicists. The honest attitude from the physicists then would be to clarify the misconceptions they are responsible for spreading in the first place, rather than getting frustrated with philosophical questions that spawned precisely from their misleading explanations.

If you really want clarity, you have to study the math. It is fundamentally impossible to accurately translate physical theories into words alone. The full description only exists in the mathematical structures that make up the theories.

 

[AndyFin]

The above discussion is EXACTLY my point. A recession velocity is not the same as Newtonian velocity.

What the general non scientific public who speak english and do not understand the maths understand when physicists talk about a recession velocity. is something receding (moving) with Newtonian velocity. Which is incorrect right?

Who pays the majority of physicists salaries and for physics experiments. The general public.

Therefore physicists owe it to the general public to explain what they mean. Asking the general public to learn the maths to understand, is less good a suggestion than asking physicists to be more precise in the language they use when explaining

If it is obvious that commonly used terminology leads to misunderstanding, I would hope physicists would actually think about this. I certainly have.. I suggested a possible solution by suggesting a different terminology to underscore and make obvious to the general public that recession velocity is a different concept to Newtonian velocity. Of course physicists know what they mean, and physicists therefore don't need different terminology, but my point is that if you want to get non physicists on the "same page", rather than describing something that immediately conjures up the false idea, and then trying to explain it later. It would be better to describe the different concept at the beginning.

Again, I see physicists have no need when communicating between themselves of new terminology, but when communicating with the general public, I see a need for improvement. Thats all

 

[AndyFin]

And now for a bit of mischief on my side.

Gedanken experiment because it obviously can't actually be done so no need to comment that it is not possible.

Imagine you could attach a long rope to a faraway galaxy with recession velocity. The other end is in your lab on earth.

Will the end of the rope in your lab move?

Lets go a step further. We wrap the end of the rope around a flywheel attached to an electric generator.

Will the flywheel turn and can the generator produce electricity.

Please explain your reasoning for what you think would happen.

 

[dougy]

What we do know of the expansion is that our universe is pretty accurately described by the cosmological principle. And a universe that obeys the cosmological principle has recession velocity proportional to distance.

Wouldn't a universe where recession velocities are the same function of distance for each observer (i.e. not necessarily proportional) obey the cosmological principle too?

If you really want clarity, you have to study the math. It is fundamentally impossible to accurately translate physical theories into words alone. The full description only exists in the mathematical structures that make up the theories.

I wouldn't say fundamentally impossible, I'm sure it could be done but it would take much longer and in the end the explanation using words alone wouldn't be any clearer. But I meant clarifying the misconceptions that have been widespread, such that stating the expansion of space is the cause of galaxies moving away from each other. The vast majority of the public who has heard this explanation believes space to be a real entity that is actually being created or stretched between galaxies, and believe that this is why galaxies move away from each other. What science communicators could do to clarify this is to say that as far as we know space is not an entity, not a real thing, and so that there is no causal link between what we refer to as "space expanding" and galaxies moving away from each other, the former is not a cause of the latter, it is a description to aid visualizing the motion of these galaxies.

Imagine you could attach a long rope to a faraway galaxy with recession velocity. The other end is in your lab on earth.

Will the end of the rope in your lab move?

Lets go a step further. We wrap the end of the rope around a flywheel attached to an electric generator.

Will the flywheel turn and can the generator produce electricity.

The distance between the galaxies increases so indeed if it was attached to the faraway one it would move away from ours and you could generate electricity from that motion, while slowing down the faraway galaxy a tiny bit. That's the way I see it.

 

[Chalnoth]

Wouldn't a universe where recession velocities are the same function of distance for each observer (i.e. not necessarily proportional) obey the cosmological principle too?

The only possible velocity function that is the same for multiple observers at different locations is one that is proportional to distance. To see this, imagine a single line of galaxies:
x--x--x--x

To make this simple, the nearest-neighbor distance is the same for all of them. So if there is some expansion, some time later it might look like this:
x---x---x---x

It should be relatively easy to see that the recession velocity is proportional to distance. But if the velocity was some other function of distance, at a later time the system might look like this instead:

x--x---x----x

...a situation which is decidedly not homogeneous any longer, and therefore not following the cosmological principle. Also note that the relative velocity of the nearby galaxies according to the observer on the far left would be very different from that seen by the observer on the far right.

I wouldn't say fundamentally impossible,

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

This doesn't mean that you have to learn the math, just that if you don't, you shouldn't expect any explanation to be completely clear.

What science communicators could do to clarify this is to say that as far as we know space is not an entity, not a real thing, and so that there is no causal link between what we refer to as "space expanding" and galaxies moving away from each other, the former is not a cause of the latter, it is a description to aid visualizing the motion of these galaxies.

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.

We don't yet know the full picture of what gravity is because we don't have an understanding of quantum gravity.

 

[AndyFin]

No, I would not. They have nothing to do with each other. Local velocity means something is moving. With cosmic recession, nothing is moving, things are just getting farther apart.

The Hubble constant is about 70 km / s per parsec and a parsec is about 3.3 million light years. so at 3.3 light years space expands at about 7 cm/s right? So to the right of my lab I have an atom initially at relative zero velocity to me at a distance of 3.3 light years, and due to space expansion it has moved 7cms one second later ( my reference frame) To my left, at 3.3 light years is another atom initial at rest relative to my reference frame of the same type, but here the gravitational constellation is such that space doesn't expand or contract. Now this atom there is accelerated so it has a velocity of 7 cm/s. Because the atom to my left has accelerated, it has an increase of mass and a time dilation as measured from my reference frame. So the question is do both the atoms still have the same mass in my reference frame? I now bring both atoms to my lab. Do they now have the same mass? If they are cesium atoms and I build clocks out of them do they tick at the same rate ?

 

[PeterDonis]

at 3.3 light years space expands at about 7 cm/s right?

No; at 3.3 light years, comoving objects--objects moving with the Hubble flow--are moving apart at 7 cm/s. See below.

to the right of my lab I have an atom initially at relative zero velocity to me

Then the atom isn't comoving. The initial condition you should be using, for the atom to be moving with the Hubble flow, is that it is moving at 7 cm/s away from you. That is what the Hubble constant means. It doesn't mean things that start out at rest relative to you are carried away from you. "Space expansion" is not a force and doesn't exert a force on anything.

The rest of your post is based on this misconception so you need to rethink your scenario in the light of the above.

 

[AndyFin]

Let me try again

The atom to the right is at a distance of 3.3 light years and moves with the Hubble flow of 7cm/s (no force appplied)

The atom to the left is 3.3 light years away and moves at 7cm/s because a force was applied to it. Space is not expanding on the left side due to the gravitational constellation on this side.

My questions are :

1) are they the same distance away from me?
2) Do they have the same mass? I would think the one on the left is heavier due to special relativity. Right?
3) They send light back to me and I observe their osculations. Are the signals identical? I would think the signal from the right is redshifted due to expansion, The signal from the left is redshifted due to the velocity from the force applied, But the signal from the left also has a time dilation component due to the velocity from the force applied, do I understand that correctly?

 

[PeterDonis]

The atom to the right is at a distance of 3.3 light years and moves with the Hubble flow of 7cm/s (no force appplied)

This part is ok.

The atom to the left is 3.3 light years away and moves at 7cm/s because a force was applied to it.

In other words, you are assuming that there is no Hubble flow to your left? See below.

Space is not expanding on the left side due to the gravitational constellation on this side.

This won't work. First, as I said before, "expansion of space" is not a force and doesn't exert a force on anything. The same applies to the lack of "expansion of space"; in itself it doesn't make any difference.

What you appear to be trying to set up is a scenario where you and the atom on your right are comoving--moving with the Hubble flow--but the atom on your left is not, even though it is the same distance away and moving away from you at the same speed. That won't work. If there is enough gravitating mass in the region to your left to make the atom on the left not comoving, then there is enough to make the atom on the right not comoving either, since the distance scales in both cases are the same.

More generally, the way you are trying to envision "space expanding" won't work. The expansion of space is a way of describing the average motion of all the matter in the universe. It doesn't show up on the scale of individual objects; it shows up on scales much larger than the size of the largest gravitating systems, the galaxy clusters, which are at least tens of millions of light-years across. So you need to go to distance scales larger than that to think in terms of "expansion of space" and the Hubble flow.

Also, the concepts you are trying to use from SR--like relativistic mass, time dilation, etc.--don't work in an expanding universe, because, first, there is gravity present and SR isn't valid in the presence of gravity, and second, spacetime is not static, so the limited ways of extending concepts like those SR ones to situations where gravity is present don't work.

 

[rede96]

First, as I said before, "expansion of space" is not a force and doesn't exert a force on anything.

Just out of interest, as I understand it 'Expansion' itself may not be a 'force' but the acceleration of expansion caused by dark energy does produce a very tiny 'pressure' which does effect everything in a very tiny way. For example a gravitationally bound galaxy will be slightly 'bigger' due to the pressure from dark energy then it would if there were no dark energy.

I only mention this because when people talk about 'expansion' they often are talking about the net result of all the things that effect expansion.

 

[PeterDonis]

'Expansion' itself may not be a 'force' but the acceleration of expansion caused by dark energy does produce a very tiny 'pressure' which does effect everything in a very tiny way.

That's true, but the emphasis is on "very tiny". For any gravitationally bound system of the size of a galaxy cluster or smaller, and certainly for the scenarios proposed in this thread, this effect is negligible. It only becomes significant on the scale of the universe as a whole.

 

[AndyFin]

spacetime is not static,

Does this mean space time moves? Or just the energy within spacetime is dynamic, or both, or neither.

The way I understand is that there are three basic types of movement. Please correct all errors

1) The movement of a geodesic, As "gravitational acceleration" is a movement, but a falling body is on a geodesic ( is it a geodesic parallel to the mass?) then geodesics move.

2) energy within space has a flow and a momentum

3) The shape of space can change or space can expand, or a piece of space can rotate, or a piece of space can comove away from an observer

They all move accord to different rules.

Have I understood this correctly?

 

[PeterDonis]

Does this mean space time moves? Or just the energy within spacetime is dynamic, or both, or neither.

"Static" means, roughly speaking, that the curvature of spacetime does not change with time. Since the curvature of spacetime depends on the configuration of matter and energy, it also means that the configuration of matter and energy does not change with time. For example, an isolated, non-rotating planet or star is static. But the universe as a whole is not, because of expansion.

(A more precise definition would be that there exists a family of observers in the spacetime who observe spacetime curvature and configuration of matter and energy that does not change with time.)

there are three basic types of movement

I don't think this is a fruitful way of trying to understand what is going on. "Movement" (motion) of objects is relative, and the concept of "movement" really only applies to objects relative to each other; it doesn't apply to geodesics (which are geometric objects, curves in spacetime, and don't "move"--they just are, like spacetime itself), or to "space".

 

[Chronos]

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. I would arue on the grounds that not everything can happen in the same place at the same time in a loically consistent universe.

 

[timmdeeg]

Imagine you could attach a long rope to a faraway galaxy with recession velocity. The other end is in your lab on earth.

Will the end of the rope in your lab move?

I think it's motion would indicate the increase of proper distance between the two galaxies over time. However the locally measured relative velocity of the imagined rope and the galaxy wouldn't say anything about an assumed relative velocity of the two galaxies, as Chalnoth explained in post #10.

 

[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.