B Understanding the Expansion of Space: Galaxies Moving Away and Proving Expansion

[ObjectivelyRational]

The Einstein Field Equation is just what I said: it expresses the causal relationship between stress-energy and the geometry of spacetime.

Given the geometry of spacetime, yes, you can predict the trajectories of objects; but the Einstein Field Equation does not do that, it just tells you the geometry of spacetime.

Are there any observable effects caused by "the geometry of spacetime" besides causal effects on things (other than spacetime itself)?
Are there any observable effects on "the geometry of spacetime" caused by anything other than the energy mass distribution of things (other than spacetime itself)?

 

[ObjectivelyRational]

Graeme, I think you can take it from here.

Just a final parting thought:

If everything observable about the nature of "the geometry of spacetime" consists entirely in the direct linking of the relationship between causes, (specifically, mass-energy distribution) and their effects, (specifically, effects upon observable things in the universe), then "the geometry of spacetime" (using ocam's razor) is best thought of as only a mathematical device describing the relationship of cause and effect between real objects, which objects in the real world have a direct cause and effect relationship, there being no need to assume a reified spacetime also existing in and of itself.

Good luck Graeme!

 

[PeterDonis]

Are there any observable effects caused by "the geometry of spacetime" besides causal effects on things (other than spacetime itself)?

What does this even mean? What observable effects would you expect to see that aren't causal effects?

Are there any observable effects on "the geometry of spacetime" caused by anything other than the energy mass distribution of things (other than spacetime itself)?

I'm not sure what this means either. If you mean, is the stress-energy tensor the only source of gravity, per the Einstein Field Equation, then yes.

 

[Graeme M]

Thanks... I think! I will read the various linked references and see if that helps. Of course the fact that I don't know anything of relativity (beyond the usual basic grasp) or of advanced mathematics means I am up against it!

Some of the replies talk of "space-time", again in terms that suggest it is a thing. So I think a part of my conceptual difficulty is grasping what this means in a physical sense. I thought space-time referred to how the trajectories of phycial entities is affected over time by gravity (that is, for example, curved space describes how objects trajectories "curve" due to gravitational forces), rather than referring to anything through which objects move. The Einsteinian Field Effect equations referred to earlier seems to my naive eye to represent that physical fact by way of a mathematical abstraction that can be used to predict this effect for different physical scenarios (naive eye, I said - don't let the fact that I used the words Einsteinian Field Effect equation suggest I have any idea what I am talking about!).

If that were the case, then wouldn't we be describing not a place or a location but a relative motion that depends entirely for its force upon physical entities? And if space is not a physical entity, which to my mind it isn't, how can the equation, or the terms in the equation, describe anything about it?

I suppose I am not being clear here. I just am struggling to see what space, or space-time, actually IS. Or how its expansion has any effect on anything, again because to me, that can't happen if it doesn't have physical form (space is distance, not a physical and hence describable thing). I can totally understand that space and space-time, defined mathematically, can describe the behaviour of physical entities, but that's not space or space-time per se. When I think about this, it seems to me that objects, say galaxies, travel "through" fields (say gravity), but not through space. Their motions only exist relative to each other, which we can only describe in terms of some coordinate system that references the entities concerned. Are we really talking about a thing or rather relationships?

Sigh... what am I missing or is this just too hard for me?

 

[PeterDonis]

I thought space-time referred to how the trajectories of phycial entities is affected over time by gravity (that is, for example, curved space describes how objects trajectories "curve" due to gravitational forces), rather than referring to anything through which objects move.

You talk as if these are two different, distinct ways things could be. They're not. They're just two different ways of describing the same physics.

don't let the fact that I used the words Einsteinian Field Effect equation suggest I have any idea what I am talking about

Then rather than using the words, you should first learn what they actually mean, so you will know what you are talking about when you use them. Trying to ask the kinds of questions you are asking without that background knowledge is not a good strategy. When you have that background knowledge, many questions you think you have now will either answer themselves, or simply vanish when you understand that you were asking them only because you have the wrong conceptual foundation.

I just am struggling to see what space, or space-time, actually IS.

Physics doesn't tell you what anything "actually is". If you're worried about that, Dr. Tyree's philosophy class is right down the hall.

I can totally understand that space and space-time, defined mathematically, can describe the behaviour of physical entities, but that's not space or space-time per se.

Why not?

 

[rede96]

I just am struggling to see what space, or space-time, actually IS. Or how its expansion has any effect on anything, again because to me, that can't happen if it doesn't have physical form (space is distance, not a physical and hence describable thing).

Like you I am just an interested layman with no background in math or physics. And I struggled with the same questions. The conclusions I came to, and this is just my way of looking at it, is that space is just that... nothing. There is no experiment we can perform to measure it as a physical thing. It has no physical properties we can measure. And if space can't be a physical thing, then how can space-time? So personally, for all intents and purposes, I just ignore it when thinking about the physical aspects of the universe.

So as such, it is meaningless to speak of 'space' expanding. How I like to view the universe and expansion is that in general the universe is made up of a lot of fields (QFT) of which some are responsible for matter of course. We know through observation that distant objects are all moving away from each other (with the exception of those locally bound by gravity.) And as the rate at which they are moving away from each other increases with distance, there must be some 'force' causing this. It can't be just natural momentum left over from the big bang.

So how I like to think of it (based on some reading / cosmology lectures) is that maybe there is some field that interacts with the other fields, (e.g. like the fields responsible for matter) in such a way that as this field expands, it causes other fields / objects that aren't bound by some local force, to move apart. And this would lead to the more distant objects moving away at an accelerating rate.

Like I said, I am not asserting this is actually what is going on. But personally I found it a good way to conceptually think of expansion that fits with what we see in observation and has some basis in physics. (E.g. QFT, the FRW equations, inflation theory etc.) And when people talk about 'space' expanding this is how I like to view it conceptually.

 

[timmdeeg]

We know through observation that distant objects are all moving away from each other (with the exception of those locally bound by gravity.) And as the rate at which they are moving away from each other increases with distance, there must be some 'force' causing this. It can't be just natural momentum left over from the big bang.

Here I disagree. There is no force acting due to which the galaxies are moving away from each other, they are in free fall. Matter is moving away from each other since the big bang and what we see today is just the continuation of that.

 

[jbriggs444]

is that space is just that... nothing

We have a model. Experiment agrees with the model. The model features something called space-time. That's not "nothing".

Requiring that it be a "physical thing" is superfluous.

 

[rede96]

Here I disagree. There is no force acting due to which the galaxies are moving away from each other, they are in free fall.

Can you define what being in “free fall” means?

 

[rede96]

Requiring that it be a "physical thing" is superfluous.

. Yes I agree.

 

[timmdeeg]

Can you define what being in “free fall” means?

If an object is in free fall its trajectory is a 'geodesic'. In this case the object doesn't feel a force acting on it. This is true for Galaxies, planets orbiting around a star and apples falling down to Earth.

 

[PeterDonis]

I found it a good way to conceptually think of expansion that fits with what we see in observation and has some basis in physics. (E.g. QFT, the FRW equations, inflation theory etc.)

As @timdeeg has pointed out, this does not fit with observation because your model predicts that galaxies should feel a force, and they don't.

The reason the concept of "space expanding" doesn't make sense is that "space" is frame-dependent, and the laws of physics are frame-independent. So whatever is going on in the universe, "space expanding" can't be a good description of it.

 

[rede96]

If an object is in free fall its trajectory is a 'geodesic'. In this case the object doesn't feel a force acting on it. This is true for Galaxies, planets orbiting around a star and apples falling down to Earth.

If I understood you correctly your saying that expansion is due to space time curvature. Correct?

 

[rede96]

As @timdeeg has pointed out, this does not fit with observation because your model predicts that galaxies should feel a force, and they don't

I was using ‘force’ in very loose terms just to indicate there was something going on to cause objects to move apart. I wasn’t implying they felt any force from acceleration. The way I thought about it wouldn’t be any different.

 

[PeterDonis]

I was using ‘force’ in very loose terms just to indicate there was something going on to cause objects to move apart.

Then you shouldn't use the word "force", because it will only lead to confusion. Not just for others, but for you. It leads you to think that "there was something going on to cause objects to move apart". There isn't. There is just the geometry of spacetime.

To illustrate what I mean, consider tidal gravity: two objects free-falling radially above a gravitating mass (like the Earth), starting from slightly different altitudes. These objects will move apart as they fall. Is there "something going on" that causes this? If so, what is this "something"? If not, how is this case different from the expansion of the universe?

 

[timmdeeg]

If I understood you correctly your saying that expansion is due to space time curvature. Correct?

Well, to know what geodesic means is not the clue to have a notion of what expansion means. But you can imagine two neighboring geodesics describing the trajectories of two objects. If the spacetime is curved then their geodesics accelerate relative to each other, in the case of an expanding universe they accelerate away from each other. Whereas if the spacetime is flat their relative acceleration is zero (which doesn't exclude of course that these particles move relative to each other with constant speed).

 

[PeterDonis]

If the spacetime is curved then their geodesics accelerate relative to each other, in the case of an expanding universe they accelerate away from each other.

This is not quite right. In a matter-dominated universe the expansion is decelerating, and the geodesics in question (the worldlines of comoving objects) are converging, not diverging. But the universe is still expanding.

The correct definition of "expanding" for the universe is that the congruence of worldlines of comoving objects has a positive expansion scalar. Unfortunately, that's already getting beyond the "B" level of this thread. But you can find more information here:

https://en.wikipedia.org/wiki/Congr...atical_decomposition_of_a_timelike_congruence

 

[PeterDonis]

your saying that expansion is due to space time curvature.

The expansion is due to the positive expansion scalar of the congruence of comoving worldlines (see my previous post). But the fact that such a congruence exists and has the properties it has (not just positive expansion, but every comoving observer sees the universe as homogeneous and isotropic) is due to the particular geometry of the spacetime in question (FRW spacetime).

 

[timmdeeg]

This is not quite right. In a matter-dominated universe the expansion is decelerating, and the geodesics in question (the worldlines of comoving objects) are converging, not diverging. But the universe is still expanding.

Ah yes, it follows from the second Friedmann equation that the second derivative of the scale factor is negative in this case (what I didn’t take into account). Thanks for correcting and for the link.

 

[Dan White]

This is an old thread but my understanding is that there is an idea from quantum physics that says that empty space may be teeming with activity at a quantum level. I thought this might be of interest to the OP if he is still around.

 

[PeterDonis]

This is an old thread but my understanding is that there is an idea from quantum physics that says that empty space may be teeming with activity at a quantum level.

This appears in our current cosmological model as dark energy. We don't fully understand why its density is so small (about 120 orders of magnitude smaller than the value that the basic quantum physics calculation you refer to gives), but it is there in the model.

 

[Orodruin]

This appears in our current cosmological model as dark energy. We don't fully understand why its density is so small (about 120 orders of magnitude smaller than the value that the basic quantum physics calculation you refer to gives), but it is there in the model.

I think that is taking things for granted a bit too far. In the cosmological model the cosmological constant is just a parameter without any particular origin. In the quantum zero point energy could theoretically contribute to this but is, as you say, 120 orders of magnitude off which if anything is an indication that the connection to the cosmological constant is not well understood. Ideally a theory of quantum gravity should of course address this.

 

[PeterDonis]

In the cosmological model the cosmological constant is just a parameter without any particular origin.

True, but any "activity of empty space" of the sort the poster I responded to was describing would have to appear in our cosmological model in this parameter. So our cosmological model already takes into account the possibility that such a thing exists. The value we use in our model is based on empirical observation and we don't have a good theoretical understanding of why that is the value we observe, but that doesn't mean our model doesn't take the possibility into account.

 

[vanhees71]

I think that is taking things for granted a bit too far. In the cosmological model the cosmological constant is just a parameter without any particular origin. In the quantum zero point energy could theoretically contribute to this but is, as you say, 120 orders of magnitude off which if anything is an indication that the connection to the cosmological constant is not well understood. Ideally a theory of quantum gravity should of course address this.

Well, in principle our Standard Model of HEP doesn't tell us at all what the absolute value of the vacuum energy (density) is. In the usual perturbative treatment it's set to 0 by imposing "normal ordering" or equivalently by renormalization of the vacuum diagrams. This introduces a renormalization scale, and when using the renormalization group to go from the low-energy scale to very high scales (GUT scale or even the Planck scale) you get these huge 120 orders of magnitude discrepancies.

I think in this sense the vacuum-energy/cosmological-constant problem is the least understood "today observable part" on the crossroad between GR and QT. Maybe it's solved one day when a consistent formulation of "quantum gravity" is found.

 

[timmdeeg]

I think in this sense the vacuum-energy/cosmological-constant problem is the least understood "today observable part" on the crossroad between GR and QT.

Do we have at least a hint why it acts as "repelling" gravity?

 

[PeterDonis]

Do we have at least a hint why it acts as "repelling" gravity?

We have more than a hint. What you are calling "repelling gravity" is what the Einstein Field Equation says you get when you have the stress-energy of a perfect fluid with an equation of state $p = - \rho$. And that's exactly what you have with a cosmological constant.

 

[timmdeeg]

We have more than a hint. What you are calling "repelling gravity" is what the Einstein Field Equation says you get when you have the stress-energy of a perfect fluid with an equation of state $p = - \rho$. And that's exactly what you have with a cosmological constant.

Thanks. I have another question in this context.

The value of the Cosmological Constant according to the Quantum Field Theory is much to high. But apart from this it's sign due to QFT seems correct. In other words QFT having no link to General Relativity doesn't just predict a vacuum energy density, it predicts the vacuum energy density with the correct sign to act like the CC. Is that correct?

 

[PeterDonis]

QFT having no link to General Relativity doesn't just predict a vacuum energy density, it predicts the vacuum energy density with the correct sign to act like the CC. Is that correct?

AFAIK yes, QFT predicts a positive sign for the vacuum energy density.

 

[StandardsGuy]

Space without matter still has fields: electromagnetic field, gravitational field, Higgs field, etc. It also has energy, so "empty" space isn't nothing.