B Is the concept of true distance compatible with relativity?

[rede96]

I've spent quite a bit of time researching cosmology on here and various other sources (NOT pop science) and although I feel I have a much better understanding in general, there is one specific thing that I just can't get my head around. Is the space between galaxies expanding or is it just the distance between galaxies growing.

The reason this seems so confusing is that from posts I've made before I understood it as just the distance between galaxies growing. (at an accelerated rate due to dark energy) and not because there was some property of empty space the was 'expanding' causing the galaxies to move apart. But I read in many posts here that it's the space that is expanding.

One of the most popular references is related to photons from distant galaxies that are receding >c won't reach us because the 'space' in between is growing faster than c. Where I would have thought that if it is just the distances growing at a rate >c the photons would still reach us eventually.

So can someone help clear this up for me once and for all! I'm sure I'm missing something simple, but I just can't get it!

 

[Chalnoth]

I've spent quite a bit of time researching cosmology on here and various other sources (NOT pop science) and although I feel I have a much better understanding in general, there is one specific thing that I just can't get my head around. Is the space between galaxies expanding or is it just the distance between galaxies growing.

The average distance between galaxies certainly increases over time.

Whether you refer to this increasing distance as the expansion of space is more or less a matter of taste. The purpose of the "expanding space" description is to make it easier to grasp certain features of the expansion, namely that recession velocity can exceed the speed of light and that the expansion also affects the wavelengths of photons in the same way that it does the distances between galaxies.

One of the most popular references is related to photons from distant galaxies that are receding >c won't reach us because the 'space' in between is growing faster than c. Where I would have thought that if it is just the distances growing at a rate >c the photons would still reach us eventually.

It depends upon what the expansion does in the future. If the rate of expansion slows down sufficiently, yes, those photons will eventually reach us. But if the dark energy is indeed a cosmological constant (or acts like one in the future), then the rate of expansion won't slow down far enough for the light from many far-away galaxies to ever reach us.

 

[ogg]

Please explain the difference between the expansion of distance (in all directions) and the expansion of space. I am unable to understand why you think there IS a difference. Space is expanding. The distance "between galaxies" is not - unless the galaxies in question are NOT GRAVITATIONALLY BOUND. (Another way to put it is that the expansion rate is so small, that even the weakest force (gravity) is sufficiently strong to keep locally interacting objects bound.) So, it is on the scale of superclusters where you can observe the expansion of space VIA the increase in distance (as measured by red-shift). Our current model (theory) is that the expansion is the same for each point in space at a given time. (Please don't ask what I mean by "a given time"!). Our models predict that the rate of increase is increasing, but whether this will continue or not is unknown. IF the amount of space (distance) between two objects is increasing faster than the two objects are reducing that distance, and that remains true forever, then the two objects will never meet. If you are walking (against the flow) on a straight infinitely long moving walkway at a speed less than the speed of the walkway, you are "moving away" from fixed points in front of you, you will never reach them (unless something changes). To reiterate: objects in our local cluster of galaxies are NOT moving away from one another, more distant objects are moving away from us. So, we will not see (a cosmological) redshift from local galaxies, but will see red-shift with more distant ones. Space is expanding everywhere, distance isn't (in any meaningful way) if the objects are bound.

 

[rede96]

Whether you refer to this increasing distance as the expansion of space is more or less a matter of taste.

I'm not too sure I would agree with it being a mater of taste. I would have thought there is a fundamental difference between the 'space' between two distant galaxies expanding, causing the galaxies to move apart and the distance between those two distant galaxies getting larger due to the two galaxies moving apart.

expansion also affects the wavelengths of photons in the same way that it does the distances between galaxies.

Again, this would imply that because the 'space' the photon is traveling through is growing, it stretches or red shifts the photon. In the same way a pen mark on a piece of elastic would grow if the elastic was stretched. But from what I remember that isn't what is going on with cosmological red shift.

It depends upon what the expansion does in the future. If the rate of expansion slows down sufficiently, yes, those photons will eventually reach us. But if the dark energy is indeed a cosmological constant (or acts like one in the future), then the rate of expansion won't slow down far enough for the light from many far-away galaxies to ever reach us

Sure, I think for the purposes of this post I'd assumed the rate doesn't slow down in the future. So it makes sense to think if we are moving away from a distant source at a rate >c then a photon from that source would never catch up to us. However that statement causes confusion too. Because it's said that two distant objects can't move apart at speeds > c in a conventional sense as this would violate relativity. So I've heard it explained as the two distant objects are actually at rest wrt to each other, but the space grows between them. But what I thought I'd understood is that GR does allow objects at cosmological distances to move apart at speeds >c, it just doesn't allow things locally to pass each other at speeds >c.

So for me, I thought using the words 'space is expanding' is not only confusing but technically incorrect.

 

[Chalnoth]

I'm not too sure I would agree with it being a mater of taste. I would have thought there is a fundamental difference between the 'space' between two distant galaxies expanding, causing the galaxies to move apart and the distance between those two distant galaxies getting larger due to the two galaxies moving apart.

Nope.

The statement that the average distance between galaxies is increasing is the precise interpretation of the expansion.

General Relativity is interesting in that there are a lot of different ways of describing the exact same system that can sound very different from one another. You have to be really careful when making statements about how General Relativity describes the expansion (or other things) in order to avoid making ambiguous statements.

In this particular case, the ambiguity comes from time: before you can ask how far away two points are, you first have to find a way to synchronize your clocks between the two points. With an expanding universe, this is pretty easy: the same time at two different points is the time where they both measure the same CMB temperature. Once you've used the CMB to synchronize the clocks, the proper distance between any two points in the universe is well-defined, and the proper distance between any two points that are stationary with respect to the CMB increases with the expansion.

Other descriptions are used to try to get people to understand other interesting features of the expansion (as I mentioned), but they don't necessarily succeed. Many people on these forums tend to think that the "expanding space" description can be misleading. I don't know. Maybe it is, maybe it isn't. But either way, the "distance increasing" description is the most accurate way of describing it.

However that statement causes confusion too. Because it's said that two distant objects can't move apart at speeds > c in a conventional sense as this would violate relativity.

This isn't true in General Relativity, for the simple reason that in General Relativity, the relative velocity between two objects is only well-defined at a particular point. You can't actually subtract the velocity between two objects that are far away and get a single, definite answer. Because you can't get a definite answer for far-away objects, there can't be any speed limit for far-away objects.

The speed-of-light limitation in General Relativity instead is the statement that no object can outrun a light beam.

 

[rede96]

The statement that the average distance between galaxies is increasing is the precise interpretation of the expansion.

Once you've used the CMB to synchronize the clocks, the proper distance between any two points in the universe is well-defined, and the proper distance between any two points that are stationary with respect to the CMB increases with the expansion.

Thanks for the further explanation. This is basically how I understood it. But this still doesn't answer the question about whether the distances are increasing due to the galaxies moving through space wrt each other or if the distances are increasing because space itself is expanding and moving the galaxies apart. That is where I read so many contradictory things about expansion.

Even watching Leonard Sussskind's lectures on Cosmology he explains expansion something like "As space expands, imagine little bits of space filling in the gaps" I'll need to find the exact quote, but that is roughly what he implied. Space itself grows, not just distances getting bigger.

The speed-of-light limitation in General Relativity instead is the statement that no object can outrun a light beam.

Again still confusion here for me because if a distant galaxy emits a photon in our direction and we are far enough away (assuming no slowing down of expansion) then we will be moving away at a rate >c and thus the photon will never catch up to us. I think it is safe to say that is an accurate statement. Which then begs the question will we catch up with photons that had already passed us from that far away galaxy before our respective recession velocities were >c ?

 

[George Jones]

Again still confusion here for me because if a distant galaxy emits a photon in our direction and we are far enough away (assuming no slowing down of expansion) then we will be moving away at a rate >c and thus the photon will never catch up to us. I think it is safe to say that is an accurate statement.

Care is needed with respect to the definition of "speed" in a cosmological setting.

this isn't true. It is true that recession speeds of galaxies that we now see will eventually exceed c, but it is not true that we loose sight of a galaxy once its recession speed exceeds c. If we see a galaxy now, then we will (in principle) always see the galaxy, even when its recession speed exceeds c.

Suppose we now see galaxy A. Assume that at time t in the future, A's recession speed is greater than c, and that at this time someone in galaxy A fires a laser pulse directly at us. Even though the pulse is fired directly at us, the proper distance between us and the pulse will initially increase. After a while, however, the pulse will "turn around", and the proper distance between us and the pulse will decrease, and the pulse will reach us, i.e., we still see galaxy A.

This can happen because the Hubble constant decreases with time (more on this near the end of this post) in the standard cosmological model for our universe. Consider the following diagram:

O                                B        A        C
*                                *        *        **                    *     *     *
O                    B     A     C

The bottom row of asterisks represents the positions in space (proper distances) of us (O) and galaxies B, A, and C, all at the same instant of cosmic time, t_e. The top row of asterisks represents the positions in space of us (O) and galaxies B, A, and C, all at some later instant of cosmic time, t. Notice that space has "expanded" between times t_e and t.

Suppose that at time t_e: 1) galaxy A has recession speed (from us) greater than c; 2) galaxy A fires a laser pulse directed at us. Also suppose that at time t, galaxy B receives this laser pulse. In other words, the pulse was emitted from A in the bottom row and received by B in the top row. Because A's recession speed at time t_e is greater than c, the pulse fired towards us has actually moved away from us between times t_e and t.

Now, suppose that the distance from us to galaxy B at time t is the same as the distance to galaxy C at time t_e. Even though the distances are the same, the recession speed of B at time t is less than than the recession speed of C at time t_e because:

1) recession speed equals the Hubble constant multiplied by distance;

2) the value of the Hubble constant decreases between times t_e and t.

Since A's recession speed at time t_e is greater than c, and galaxy C is farther than A, galaxy C's recession speed at time t_e also is greater than c. If, however, the Hubble constant decreases enough between times t_e and t, then B's recession speed at time t can be less than c. If this is the case, then at time t (and spatial position B), the pulse is moving towards us, i.e., the pulse "turned around" at some time between times t_e and t.

If the value of the Hubble constant changes with time, what does the "constant" part of "Hubble constant" mean? It means constant in space. At time t_e, galaxies O, B, A, and C all perceive the same value for the Hubble constant. At time t, galaxies O, B, A, and C all perceive the same value for the Hubble constant. But these two values are different.

 

[rede96]

Care is needed with respect to the definition of "speed" in a cosmological setting.

Ok, I didn't mention speed in the section you quoted so could you elaborate a little more please?

And here we have it! Another contradictory statement. You statement:

this isn't true. It is true that recession speeds of galaxies that we now see will eventually exceed c, but it is not true that we loose sight of a galaxy once its recession speed exceeds c. If we see a galaxy now, then we will (in principle) always see the galaxy, even when its recession speed exceeds c.

Chalnoth's statement:

It depends upon what the expansion does in the future. If the rate of expansion slows down sufficiently, yes, those photons will eventually reach us. But if the dark energy is indeed a cosmological constant (or acts like one in the future), then the rate of expansion won't slow down far enough for the light from many far-away galaxies to ever reach us.

 

[George Jones]

And here we have it! Another contradictory statement.

No, the posts by Chalnoth and me are not contadictory. I dd not say that there do not exist galaxies whose light we will never be able to observe, I said that if we can observer a galaxy now (or at any time in the past), then we always be able to observe that galaxy, even if its proper recessional velocity exceeds c.

 

[rede96]

No, the posts by Chalnoth and me are not contadictory. I dd not say that there do not exist galaxies whose light we will never be able to observe, I said that if we can observer a galaxy now (or at any time in the past), then we always be able to observe that galaxy, even if its proper recessional velocity exceeds c.

Ah ok, sorry I missed read that. Although that still confuses me.

EDIT: However on one of Susskind's lectures he does say that in many billions of years to come the only stars we will see will be from our own milky way. So that does contradict you.

 

[Chalnoth]

Thanks for the further explanation. This is basically how I understood it. But this still doesn't answer the question about whether the distances are increasing due to the galaxies moving through space wrt each other or if the distances are increasing because space itself is expanding and moving the galaxies apart. That is where I read so many contradictory things about expansion.

Even watching Leonard Sussskind's lectures on Cosmology he explains expansion something like "As space expands, imagine little bits of space filling in the gaps" I'll need to find the exact quote, but that is roughly what he implied. Space itself grows, not just distances getting bigger.

"Space is expanding" is one way of looking at it, and it isn't inaccurate. It's just that it's not really a precise statement.

The way I like to think of it is this: imagine you're driving down a road, and pass a telephone pole. It's completely accurate to say either that the pole passed by you and that you passed the pole. There's no right answer between those two choices: it's just a difference in reference frame.

Saying that space is expanding is sort of like that. You could describe it that way, but you can just as accurately describe it as objects getting further apart.

Again still confusion here for me because if a distant galaxy emits a photon in our direction and we are far enough away (assuming no slowing down of expansion) then we will be moving away at a rate >c and thus the photon will never catch up to us. I think it is safe to say that is an accurate statement. Which then begs the question will we catch up with photons that had already passed us from that far away galaxy before our respective recession velocities were >c ?

This isn't entirely accurate, because the rate of expansion changes over time. A photon that started traveling in our direction, but was still carried away from us due to how fast the expansion was, might eventually start to gain ground as the expansion slows over time. In fact, most of the galaxies visible from Earth are in this situation, because the expansion rate in the past was much, much faster than it is now.

The picture here is that the photon leaves the galaxy, traveling in our direction. But the expansion is so fast that the distance between us and the photon still grows as it moves at speed c away from its source galaxy. Over time, the expansion slows down enough that the photon starts to gain ground instead, eventually reaching us.

Note that the rate of expansion is now decreasing very slowly, and seems to be approaching a constant (the cosmological constant). So the limit beyond which we can no longer see galaxies is a little bit further than the point at which their recession velocity reaches c.

 

[Chronos]

See the article by Davis and Lineweaver ; http://arxiv.org/abs/astro-ph/0310808, Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe, for further discussion.

 

[George Jones]

However on one of Susskind's lectures he does say that in many billions of years to come the only stars we will see will be from our own milky way. So that does contradict you.

I have not seen any of Susskind's lectures, but he could mean in a "for all practical purposes sense". From

http://arxiv.org/abs/0704.0221

While objects will not be observed to cross the event horizon, light from them will be exponentially redshifted, so that within a time frame comparable to the longest lived main sequence stars all objects outside of our local cluster will truly become invisible.

The expansion of the universe in three ways diminishes the energy flux that we receive from distant galaxies.

1) a dimming due to increasing distance.

2) The energy of light is inversely proportional to its wavelength (energy of a photon is $E=hc/\lambda)$. As the light travels to us, the expansion of the universe expands the wavelength of the light by a factor of 1+z, where z is redshift.

3) Also, the expansion of the universe decreases the rate at which we receive photons, as compared to the rate at which photons left a source, by another factor of 1+z (gravitational time dilation).

This triple whammy means that we will lose contact in *practical* terms with most of the universe in the distant future.

 

[anorlunda]

I always thought the OP question was related to observational versus theoretical science. We can observe the light of distant galaxies, but not the intergalactic space. What happens in distant intergalactic space can be inferred but not observed. Therefore, if we stress what we know from observation, expansion of empty space is deprecated.

Where I think I sense disagreement among experts is if we consider a small region containing no mass, no photons,and no gravitational field. Does it expand? The answer would seem to depend on vacuum energy because to have a time evolution, the region needs a nonzero Hamiltonian. If I got it right, expert opinions on vacuum energy differ.

Another way to say it is that particles (massive and massless) and fields have properties. Take them away and we have nothing. It is meaningless to discuss the properties of nothing.

Is my description of the disagreement correct?

P.s. My spell checker just tried to correct "discuss" to "rickshaw". To me, that is an even deeper mystery.

 

[rede96]

See the article by Davis and Lineweaver ; http://arxiv.org/abs/astro-ph/0310808, Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe, for further discussion.

Thanks for the link. I've had a quick look but will review it in more detail over the weekend. However there is on thing that I'd like to mention, which comes from the quote below taken on page 5...

The general relativistic interpretation of the expansion interprets cosmological redshifts as an indication of velocity since the proper distance between comoving objects increases. However, the velocity is due to the rate of expansion of space, not movement through space, and therefore cannot be calculated with the special relativistic Doppler shift formula

...in particular where it states that separation velocities are due to expansion of space and not movement through space. This implies to me that expansion is due to 'empty space' growing, or in other words, some physical framework which energy and matter ect are embedded, is growing. Moreover that dark energy therefore isn't a force that is 'pushing' galaxies apart, it is a force acting on the expansion of empty space, causing that to accelerate.

That does make sense to me, but it is different to many things I've read about expansion. This is fundamentally what I am trying to clear up.

 

[rede96]

Where I think I sense disagreement among experts is if we consider a small region containing no mass, no photons,and no gravitational field. Does it expand?

That is pretty much where my confusion is. As I posted above, the article Chronos referred to would seem to suggest there is 'something' expanding.

 

[PeterDonis]

if we consider a small region containing no mass, no photons,and no gravitational field. Does it expand?

If there is no mass, no photons, and no gravitational field, then spacetime is empty and flat. So how could we possibly tell whether it was "expanding" or not? There is nothing to observe.

The way I would resolve the question raised by the OP is to say that the term "expansion", properly speaking, applies to a family of worldlines, not to "space". That is because "space" is not an invariant concept; what "space" is, and whether it is "expanding", depends on your choice of coordinates. But if we pick out a particular set of worldlines, then the question of whether those worldlines are "expanding" has an invariant meaning. Any set of worldlines has an invariant scalar associated with it called the "expansion scalar". If this scalar is positive, the set of worldlines is expanding; if the scalar is negative, it is contracting; and if the scalar is zero, the set of worldlines is not expanding or contracting.

When cosmologists say "the universe is expanding", what they actually mean, put in precise technical language, is that the expansion scalar of the set of "comoving" worldlines--that is, the worldlines of observers who see the universe as homogeneous and isotropic--is positive. That is an invariant statement and does not depend on any choice of coordinates, nor does it require one to say that "space" is expanding, or that it isn't, for that matter. Whether "space" is expanding is simply not a meaningful question as far as the physics is concerned.

The expansion scalar is actually one piece of a very useful mathematical tool in GR, called the "kinematic decomposition" of a set of worldlines (the more precise technical term is a "timelike congruence"). Some more information about that can be found here:

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

 

[Chronos]

The concept of distance has no intrinic meaning under GR, which is a theory only of 'space-time coincidences'. This means all such measurement can only be local (at an event) . This destroys the notion of length and time co-ordinates as observables. To quote Einstein "All our space-time verifications invariably amount to a determination of space-time coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meeting of two or more of these points. Moreover, the results of our measuring are nothing but verifications of such meetings of the material points of our measuring instruments with other material points, coincidences between the hands of a clock and points on the clock dial, and observed point-events happening at the same event. The introduction of a system of reference serves no other purpose than to facilitate the description of the totality of such coincidences." So, in this light it is no more meaningful to say that space-time is expanding than it is to say the distance between far away galaxies is increasing. It is strictly a frame dependent convenience to characterize the relationship between non-local events and space-time. Some users prefer to talk in terms of an expanding coordinate system to characterize expansion. This too, however, is little more than a convenient illusion.

 

[rede96]

The way I would resolve the question raised by the OP is to say that the term "expansion", properly speaking, applies to a family of worldlines, not to "space". That is because "space" is not an invariant concept; what "space" is, and whether it is "expanding", depends on your choice of coordinates.

For me personally, my question isn't about how we describe expansion. In the context of the questions I guess the words we use or choice of coordinates etc are for the most part irrelevant.

What I am asking is much more fundamental. Another way of putting this would be as the universe expands, is new 'space' being created? Are quantum fields, such as the quark field or higgs field etc being constantly created OR do they already exist and the universe is just 'moving' into those pre-existing fields?

 

[PeterDonis]

Another way of putting this would be as the universe expands, is new 'space' being created?

I don't know what "new space being created" means.

Are quantum fields, such as the quark field or higgs field etc being constantly created OR do they already exist and the universe is just 'moving' into those pre-existing fields?

I don't know what it would mean for new fields to be "created" vs. the universe "moving into pre-existing fields".

I understand that these seem to you like meaningful questions. But they don't correspond to anything in the actual models we use. That was part of my point.

 

[rede96]

I don't know what "new space being created" means.

This was something I picked up on from Suskind's lectures on cosmology. He explained expansion as new space being created, but I didn't really follow what he meant.

I don't know what it would mean for new fields to be "created" vs. the universe "moving into pre-existing fields".

Simply, if I take any two galaxies at some large distance moving apart, when they are at some certain distance apart there is a finite amount of energy (from some quantum field for example) between them. As the distance between them gets larger, if the energy density stays the same, then there must even more energy between them. This could be because the energy density of that field is the same everywhere in the universe, and those two galaxies are simply separating into that existing energy field (e.g. moving through the field), hence there is more energy between them, or if could be because that energy field is actually expanding with the universe, so the energy density is going down but as they separate, more energy is being created in the space between the galaxies.

From what I understand it doesn't really make a difference to the predictions of current models which one of those situations we imagine. But they are at least to me two different fundamental processes.

I understand that these seem to you like meaningful questions. But they don't correspond to anything in the actual models we use. That was part of my point.

I guess that is where I am struggling. GR, Eisenstein's field equations etc. tell us very well how gravity works and operates through the interactions of spacetime and energy/matter. But they don't tell us what gravity actually is.

I suppose it's the same with expansion. Current cosmological models tell us very well what is happening, we can do the math, make predictions etc but for me at least, they don't tell me just what expansion actually is, or what does indeed 'expand'. Moreoever, unlike GR, there is a lot more ambiguity in the words used in explaining expansion.

 

[PeterDonis]

He explained expansion as new space being created, but I didn't really follow what he meant.

That's because there isn't really anything in the actual physical model that corresponds to what he meant. The words he used are commonly used when describing the model to lay people, but they're not meant to actually describe the model in technical terms that you can use to draw inferences. You are finding that out because you are trying to draw inferences from those words, and the inferences aren't working.

if I take any two galaxies at some large distance moving apart, when they are at some certain distance apart there is a finite amount of energy (from some quantum field for example) between them. As the distance between them gets larger, if the energy density stays the same, then there must even more energy between them.

This reasoning applies to dark energy, but not to other quantum fields. Even for dark energy, though, it is coordinate-dependent, because "distance" and "space" are coordinate-dependent. If you look at invariants, there aren't any that change in the way you are describing. The energy density is an invariant (when correctly defined), but the "energy contained in a given distance" is not.

From what I understand it doesn't really make a difference to the predictions of current models which one of those situations we imagine.

Yes, it does. The energy density is an observable, so predicting that the energy density is constant everywhere and at all times is observably different from predicting that the energy density goes down with time. The first of the two is the correct prediction, as far as we can tell from our best current observations. (More precisely, it's the correct prediction for dark energy. For all other quantum fields, the observed energy density in empty space is zero.)

they don't tell us what gravity actually is.

In the sense you appear to mean that term, no physical theory tells you what "actually is". Physical theories tell you how to make predictions that will match observations.

there is a lot more ambiguity in the words used in explaining expansion.

There is plenty of ambiguity in the words used to describe GR in general. "Gravity", for example--there are at least three things in the math of GR that I can think of off the top of my head that that word can refer to (the metric tensor, the Christoffel symbols, and the Riemann curvature tensor). This is why, to be precise, you shouldn't use ordinary language; you should use math.

 

[rootone]

Yes, astronomical observations confirm that stuff is getting more distant from 'us' all the time.

 

[rede96]

That's because there isn't really anything in the actual physical model that corresponds to what he meant. The words he used are commonly used when describing the model to lay people, but they're not meant to actually describe the model in technical terms that you can use to draw inferences. You are finding that out because you are trying to draw inferences from those words, and the inferences aren't working.

But just to clarify once and for all... Is it correct to say that when we talk about expansion, as far as we know, all that is physically happening is the distances between matter which isn't bound in any way, are simply getting bigger, or in other words moving apart, due to the pressure from dark energy pushing matter apart? And that there is no physical thing (e.g. space, space time, energy fields etc.) that is 'stretching'?

This reasoning applies to dark energy, but not to other quantum fields.

What about the higgs field? Is that just another type of scaler field like dark energy?

 

[PeterDonis]

Is it correct to say that when we talk about expansion, as far as we know, all that is physically happening is the distances between matter which isn't bound in any way, are simply getting bigger, or in other words moving apart

Yes, this is fine, as long as you are aware that "distance" here is coordinate-dependent. An invariant way of describing what is going on is to say that the congruence of "comoving" worldlines has a positive expansion scalar.

due to the pressure from dark energy pushing matter apart?

This only applies to the acceleration of the expansion; it does not apply to expansion in itself. If there were no dark energy, the universe would still be expanding, but the expansion would not be accelerating.

And that there is no physical thing (e.g. space, space time, energy fields etc.) that is 'stretching'?

Yes--that is, there is nothing in the actual model that corresponds to any physical thing "stretching".

What about the higgs field? Is that just another type of scaler field like dark energy?

The Higgs field is a scalar field, but it does not have the same effect in cosmological models as dark energy. AFAIK the Higgs field plays no role in cosmological models at all. (I believe there have been some speculations that the Higgs field might be what produces dark energy, but AFAIK those speculations have not worked out; the Higgs field doesn't have the right properties.)

Btw, we don't know that dark energy is a scalar field at all; that is just one possibility.

 

[PAllen]

See the article by Davis and Lineweaver ; http://arxiv.org/abs/astro-ph/0310808, Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe, for further discussion.

And this gets at those 'more than one valid way of interpreting the same mat' that Chalnoth referred to. Co-author Tamara Davis of this paper wrote a later paper arguing for the view that recession speed is highly misleading, and that the GR analog (ambiguous though it is) of relative velocity is always subluminal; and that it is completely valid to view cosmological redshift as a generalization of Doppler; and that 'the universe losing energy' is misleading and better phrased as 'there is no such thing as total energy of the universe'.

 

[PAllen]

Observation: in the limit of decreasing density without dark energy, the FLRW cosmology has increasing expansion rate while approaching flat Minkowski space geometrically. Thus, we have maximal expansion rate as the manifold becomes static and flat! That's why I strongly prefer Peter's terminology of expanding comoving congruence, or the popular phrase, 'expanding universe' rather than expanding space.

Also, note that the closest SR analog of recession rate is a celerity (not a relative velocity), which has no upper bound at all even in SR. And recession rate as function of distance is maximal in the flat spacetime limit of FLRW - i.e. when there is no curvature at all.

 

[bahamagreen]

Maybe I can help because I've been puzzled here before about the same question.

What concerned me about distinguishing increasing distance and space expansion was that both the increasing distance and space expansion ideas present that there is a mutual acceleration between objects...but these objects don't seem subject to inertial effects of this acceleration. My coffee stays in my cup without sloshing out!

The idea that helped me reconcile comoving objects as both inertial and yet accelerating was to consider a similar familiar situation of two "co-falling" objects in the Earth's gravitational field - both are inertial in free fall, yet both are accelerating towards each other because their individual fall lines point toward the center of the Earth's mass and converge.

For me, once I understood comoving as co-falling, the distinction between more distance and more space seems ill-formed and irrelevant.

 

[rede96]

Yes, this is fine, as long as you are aware that "distance" here is coordinate-dependent. An invariant way of describing what is going on is to say that the congruence of "comoving" worldlines has a positive expansion scalar

I understood how we measure distance may be coordinate-dependent, but I thought if a distance increases or not is fairly absolute? My simple logic tells me there are only three physical possibilities. Two objects are either moving closer together, are at rest wrt each other or are moving further apart. We know they are moving further apart. Isn't that correct or have I misunderstood something?

This only applies to the acceleration of the expansion; it does not apply to expansion in itself. If there were no dark energy, the universe would still be expanding, but the expansion would not be accelerating.

Yes sure, and in that case I'd just replace 'due to dark energy' with 'due to the initial inertia from inflation' is that correct?

Yes--that is, there is nothing in the actual model that corresponds to any physical thing "stretching".

Just as an aside, is there anything in the cosmological models that prevents us from describing expansion in just 3 dimension, such as a field growing as opposed to describing expansion using the 3 sphere analogy?

The Higgs field is a scalar field, but it does not have the same effect in cosmological models as dark energy.

Ok, thanks. I was thinking more that the energy density of the Higgs field would have to remain constant, i.e. not dilute with expansion or there would be an effect on the mass of objects.

 

[PeterDonis]

I thought if a distance increases or not is fairly absolute?

A congruence of worldlines having a positive expansion scalar is an invariant way of having distance increasing. But having a coordinate-dependent distance that increases in one set of coordinates does not guarantee that the coordinate-dependent distance between the same objects will be increases in all sets of coordinates.

in that case I'd just replace 'due to dark energy' with 'due to the initial inertia from inflation' is that correct?

The "initial inertia from inflation" is really the inertia from reheating--from the transfer of energy from the inflaton field to the Standard Model matter and radiation fields at the end of inflation. That process does not continue to push things apart; it's just a one-time event that creates the hot, dense, rapidly expanding "Big Bang" state.

is there anything in the cosmological models that prevents us from describing expansion in just 3 dimension, such as a field growing as opposed to describing expansion using the 3 sphere analogy?

I'm not sure what you mean here.

I was thinking more that the energy density of the Higgs field would have to remain constant, i.e. not dilute with expansion or there would be an effect on the mass of objects.

The Higgs field effect on the mass of objects is not, as I understand it, due to the Higgs field having a nonzero energy density. It's due to interaction between the Higgs field and other Standard Model fields, but I don't think that interaction has a simple description as a nonzero energy density.

 

[Dale Tortorelli]

I have always had difficulty with the big bang theory as the cause of the expansion of the universe. Our perception of the expansion could be the result of a spinning universe, or light having a time dependant redshift as a part of its nature. We really do not have enough information to claim the knowledge of either.

 

[Chronos]

The ideas of a 'spinning' universe or one with time dependent redshift have long since been discredited.

 

[rede96]

A congruence of worldlines having a positive expansion scalar is an invariant way of having distance increasing. But having a coordinate-dependent distance that increases in one set of coordinates does not guarantee that the coordinate-dependent distance between the same objects will be increases in all sets of coordinates.

I'm not disagreeing with this of course, but I am finding it difficult to understand how a spatial 'separation' between two objects can be coordinate dependent. Are there any simply examples you could point me to that show where this is the case? Thanks.

That process does not continue to push things apart; it's just a one-time event that creates the hot, dense, rapidly expanding "Big Bang" state.

Yes, understood. I sometimes generalize reheating as part of the inflation process.

I'm not sure what you mean here.

The balloon analogy is often used to describe how everything moves away from everything else in an expanding universe. As I understood it, this is a 2 sphere. So mathematically it follows that the 3 sphere describes how everything moves apart in the 3 spatial dimensions of our universe.

The problem I have conceptually with this explanation, taking the 2 sphere as an example, is that implies an extra dimension for the sphere to 'grow' in to. Which would be the same with the 3 sphere, it implies there is another dimension for our universe to expand in to. I know this isn't the case, it's not embedded in another dimension but still confuses me. So I was wondering if it were possible to model the movement of matter in an expanding universe just in a 3 spatial dimensional context? Hope that makes sense.

 

[PAllen]

The problem I have conceptually with this explanation, taking the 2 sphere as an example, is that implies an extra dimension for the sphere to 'grow' in to. Which would be the same with the 3 sphere, it implies there is another dimension for our universe to expand in to. I know this isn't the case, it's not embedded in another dimension but still confuses me. So I was wondering if it were possible to model the movement of matter in an expanding universe just in a 3 spatial dimensional context? Hope that makes sense.

A 3-d analog of the balloon analogy is the raisin bread analogy. As cooking loaf rises, the distance between all the raisins increases isotropically and homogeneously (in the ideal) except near the edges. If you imagine there is no edge, you have a model of 3-d expanding congruence.

 

[Hernik]

Now I'm not a physicist and might get some slamming for this, so please correct me if this is wrong - but I was once told to think of the expansion of space as an increase in distances between objects without movement.

That helped me a lot because it delivers an easily understandable explanation for why special relativity does not apply. There is nothing moving apart faster than the speed of light, just distances increasing - and for particles, stars or galaxies separated by a very large distance the increase can be more than 300.000 km/s.

It kind of helped me to understand what goes on in inflation also. Nothing moves. No inertia. Just distances suddenly grow enormously.

Henrik

 

[PAllen]

Now I'm not a physicist and might get some slamming for this, so please correct me if this is wrong - but I was once told to think of the expansion of space as an increase in distances between objects without movement.

This has been written by some cosmologists, but it is not remotely justifiable in the math of GR. Given two 4-velocities of of separated bodies, there is nothing in the math of GR that distinguishes 'relative motion' from 'increase of distance without motion'. Nothing at all.

That helped me a lot because it delivers an easily understandable explanation for why special relativity does not apply. There is nothing moving apart faster than the speed of light, just distances increasing - and for particles, stars or galaxies separated by a very large distance the increase can be more than 300.000 km/s.

This also a common but strictly false statement. This is shown by the argument I gave earlier where maximal superluminal recession rate occurs in the special relativity limit of cosmological models. In particular, it shows that recession rate corresponds the special relativity quantity called celerity not relative velocity. In special relativity, celerity has no upper bound at all - it can be a thousand times c.

It kind of helped me to understand what goes on in inflation also. Nothing moves. No inertia. Just distances suddenly grow enormously.

Henrik

Inflation is a separate model than generic big bang cosmology (FLRW solutions in GR). In classical GR, inflation may be modeled by an initial, large, cosmological constant that then decreases to almost zero. However, viewed in classical GR terms, it remains true that there is nothing you can identify about two separated 4-velocities to say they do not represent motion.

 

[PeterDonis]

I am finding it difficult to understand how a spatial 'separation' between two objects can be coordinate dependent.

Because "space" itself is coordinate dependent.

Are there any simply examples you could point me to that show where this is the case?

Specific examples are going to be hard to find, because for practical purposes physicists like to choose coordinates that are convenient to use. If we have a congruence of worldlines with a positive expansion scalar (for example, the congruence of "comoving" worldlines in expanding FRW spacetime), it's much more convenient to choose coordinates in which the spatial distance between comoving objects increases. But "convenient" is not a statement about the physics; it's a statement about us humans and how we choose to model the physics. If you want to focus on the physics, the best thing is to forget about coordinates and look at invariants, such as the expansion scalar.

I sometimes generalize reheating as part of the inflation process.

That might not be a good idea, if only because it is likely to cause confusion since it is not standard terminology (at least, not as I understand it).

The problem I have conceptually with this explanation, taking the 2 sphere as an example, is that implies an extra dimension for the sphere to 'grow' in to.

No, it doesn't. The extra dimension helps us to visualize what is going on (at least in the 2-sphere case). But it is not logically required by the model.

I was wondering if it were possible to model the movement of matter in an expanding universe just in a 3 spatial dimensional context?

I'm still not understanding what you are trying to say here. The standard 4-dimensional spacetime model of the universe, including all movement of matter in it, does have 3 spatial dimensions. But you seem to be talking about something different from the standard 4-dimensional spacetime model. So I'm confused about what you mean.

 

[Hernik]

This has been written by some cosmologists, but it is not remotely justifiable in the math of GR. Given two 4-velocities of of separated bodies, there is nothing in the math of GR that distinguishes 'relative motion' from 'increase of distance without motion'. Nothing at all.

But in this link, provided by Chronos in post 12 as a paper that debunks misconceptions on the expansion of space: http://arxiv.org/abs/astro-ph/0310808 the following sentences page 5 seem excactly to claim that expansion is simply distances changing and not a process initially involving motion:

"The general relativistic interpretation of the expansion interprets cosmological redshifts as an indication of velocity since the proper distance between comoving objects increases. However, the velocity is due to the rate of expansion of space, not movement through space, and therefore cannot be calculated with the special relativistic Doppler shift formula."

Of course the result is relative motion, I understand that - but I understand from the text that objects in space are not moved away from each other by the expansion of space. Distances only grow. Where do I go wrong when I read that text?

Henrik

 

[PAllen]

But in this link, provided by Chronos in post 12 as a paper that debunks misconceptions on the expansion of space: http://arxiv.org/abs/astro-ph/0310808 the following sentences page 5 seem excactly to claim that expansion is simply distances changing and not a process initially involving motion:

This paper pushes a particular interpretation of the math that is not at all universally shared. As I noted in an earlier post, one of its co-authors distanced herself from this interpretation later (Tamara Davis). Steven Weinberg has also argued against this interpretation (even calling it the root of evil). I do not claim this interpretation is wrong (that is a category error unless an interpretation is internally inconsistent); what is wrong is not to recognize that it is just one interpretation, and is not mandated by the math of GR. In particular, this interpretation gives meaning to coordinate dependent quantities (technically, foliation dependent quantities). Since a key feature of GR is coordinate invariance, it is an error to overvalue such coordinate dependent quantities, let alone claim they are the 'truth'.

"The general relativistic interpretation of the expansion interprets cosmological redshifts as an indication of velocity since the proper distance between comoving objects increases. However, the velocity is due to the rate of expansion of space, not movement through space, and therefore cannot be calculated with the special relativistic Doppler shift formula."

The objectively true part of this statement is that the pure SR Doppler formula does not apply to distant objects in GR (this statement is true in general, not just for cosmology). However, GR generalizations of Doppler expressed in terms of invariant procedures do not distinguish two sources of Doppler. There are several formulations of general redshift in GR; none involve expansion of space in the expression. One example is to parallel transport one 4-velocity to the other along the null geodesic connecting the emission event and the reception event, and then apply the SR doppler formula locally. This procedure applies universally in GR. Note the complete absence of factoring into different causes. Note also, that the SR doppler formula is involved, but not just the SR doppler - the parallel transport on the null geodesic is a required feature of this generalization to GR, bringing in the effects of curvature. Another universal procedure is to follow two very nearby null geodesics from one world line to another, and find the ratio of the proper time difference. Again, no factoring into separate causes appears in this universal generalization of SR doppler.

Factoring redshift into different components requires a choice of coordinates, and is different for different choices.

Of course the result is relative motion, I understand that - but I understand from the text that objects in space are not moved away from each other by the expansion of space. Distances only grow. Where do I go wrong when I read that text?

Henrik

The error is by the authors in overstating their case.

 

[PAllen]

This has been written by some cosmologists, but it is not remotely justifiable in the math of GR. Given two 4-velocities of of separated bodies, there is nothing in the math of GR that distinguishes 'relative motion' from 'increase of distance without motion'. Nothing at all.

This quote of mine would more precisely be "nothing in the math of GR except choice of coordinates + interpretation". That is, there is no invariant in GR defining 'expansion of space'. Given a congruence of world lines (e.g. the comoving congruence, in the case of cosmology), there is an invariant definition of the expansion of that congruence. However, the steps from here to the notion of expanding space are:
- pick a coordinate system where spatial position is defined by this congruence (typically with other desirable properties, if possible, e.g. hypersurface orthogonality)
- Name the growth of distance between members of the congruence, in these coordinates, expansion of space.

The last step, in particular, is not part of the math or normal use of GR. It is an interpretation added to GR by many cosmologists. This is basis of my statement "nothing in the math of GR makes the claimed distinction". Some find this added interpretation useful, some do not.

[edit: to emphasize yet again, the conventionality of this, you can do this in flat, static, Minkowski space with the Milne congruence of inertial world lines. You then end up claiming extreme superluminal expansion of space for a static flat manifold.]

 

[rede96]

A 3-d analog of the balloon analogy is the raisin bread analogy. As cooking loaf rises, the distance between all the raisins increases isotropically and homogeneously (in the ideal) except near the edges. If you imagine there is no edge, you have a model of 3-d expanding congruence.

I'm still not understanding what you are trying to say here. The standard 4-dimensional spacetime model of the universe, including all movement of matter in it, does have 3 spatial dimensions. But you seem to be talking about something different from the standard 4-dimensional spacetime model. So I'm confused about what you mean.

Sorry for the confusion and not explaining this very well. In essence the balloon analogy or 2 sphere just never sat right with me personally. Partly because it implies a bound universe but mainly because in order for 'galaxies' to move apart on the surface of the balloon, the 'balloon' or sphere itself must grow into a dimension the wouldn't exist in just a two dimensional space. So mathematically, if I extend the 2 sphere to a 3 sphere, I get the same problem.

So instead of the surface of a balloon being used it it would make more sense to me to have a flat 2 dimensional area and just show everything moving away from everything else. Or for 3 dimensional space (ignoring the time dimension) the raisin bread analogy form PAllen above (thank you by the way) seems to make more sense to me. If I just imagine how the raisins move, ignoring the bread and edges etc, then this is how I imagined matter to be moving apart.

The only problem with thinking about it in this way is, unless the universe is infinite, then I can collapse the raisin bread example to a central point. Using the balloon analogy that doesn't happen.

 

[rede96]

Because "space" itself is coordinate dependent.

I'm probably looking at this in a very elementary way in that coordinates are only there for us to make measurements. So space is still space and does what it does independently of how we measure it. For example if I take two objects which are touching, then start them moving apart in such a way that they will always be moving apart, then I would have thought if one frame of reference can measure they are moving apart, all frames of reference will measure they are moving apart. They may measure different distances or different rates, but no one will say they measured them to be moving together or static wrt each other.

So relating that to expansion, I can imagine different coordinate systems will tell us different things, but I would thought measuring increasing distances is absolute. Is that not the case?

 

[PAllen]

I'm probably looking at this in a very elementary way in that coordinates are only there for us to make measurements. So space is still space and does what it does independently of how we measure it. For example if I take two objects which are touching, then start them moving apart in such a way that they will always be moving apart, then I would have thought if one frame of reference can measure they are moving apart, all frames of reference will measure they are moving apart. They may measure different distances or different rates, but no one will say they measured them to be moving together or static wrt each other.

So relating that to expansion, I can imagine different coordinate systems will tell us different things, but I would thought measuring increasing distances is absolute. Is that not the case?

Touching is invariant. Moving apart or together is coordinate dependent. This could even happen in SR. Consider two rockets accelerating uniformly, consistent with the Rindler congruence, such that each perceives their mutual distance constant (possibly surprisingly, this means the front rocket's proper acceleration must be slightly smaller). In an inertial frame, these rockets appear to be approaching each other rather than static. If you then have the front rocket accelerate a tiny bit more, but still less than the back, each rocket's standard accelerating frame would have them separating. However, an inertial frame would have them approaching. Each of these coordinate statements corresponds to the most natural measurements that may be made by the corresponding observer.

[edit: To add what you can say about this from an invariant perspective: if you treat the rockets that are receding in their frames, while approaching in the inertial frame, as part of a congruence, using the simplest way to fill in the congruence, you would find that the congruence has positive expansion scalar. While expansion of the congruence is invariant, the remarkable fact remains that in this case, as natural coordinates as Minkowski coordinates treat the world lines of the congruence as approaching each other. ]

 

[rede96]

Touching is invariant. Moving apart or together is coordinate dependent. This could even happen in SR. Consider two rockets accelerating uniformly, consistent with the Rindler congruence, such that each perceives their mutual distance constant (possibly surprisingly, this means the front rocket's proper acceleration must be slightly smaller). In an inertial frame, these rockets appear to be approaching each other rather than static. If you then have the front rocket accelerate a tiny bit more, but still less than the back, each rocket's standard accelerating frame would have them separating. However, an inertial frame would have them approaching. Each of these coordinate statements corresponds to the most natural measurements that may be made by the corresponding observer.

I'm still not sure I understand this. Imagine we tie a rope taut between the two rocket ships as they accelerated. The rope can only do one of three things. It can stay taut, it can become loose or it can stretch and snap. This is not coordinate dependent but still decribes how the distance between the two rocket ships changes.

 

[PAllen]

I'm still not sure I understand this. Imagine we tie a rope taut between the two rocket ships as they accelerated. The rope can only do one of three things. It can stay taut, it can become loose or it can stretch and snap. This is not coordinate dependent but still decribes how the distance between the two rocket ships changes.

Your question anticipates my addendum above. This is basically a way to measure expansion scalar in the case of a simple one parameter congruence.

 

[rede96]

Your question anticipates my addendum above. This is basically a way to measure expansion scalar in the case of a simple one parameter congruence.

I'll be honest I don't fully understand the terminology you are using in your Edit, so will need to do a bit of reading. But I take it you agree that the rockets can't both be receding and approaching simultaneously. In the same way that galaxies can't be both receding and approaching simultaneously. So how the actual distance changes between them is invariant (as in the rope example) but how we measure isn't.

 

[PAllen]

I'll be honest I don't fully understand the terminology you are using in your Edit, so will need to do a bit of reading. But I take it you agree that the rockets can't both be receding and approaching simultaneously. In the same way that galaxies can't be both receding and approaching simultaneously. So how the actual distance changes between them is invariant (as in the rope example) but how we measure isn't.

No, I don't agree unless you define receding as positive expansion scalar. Normally, receding is simply defined as increase in proper distance measured in a specified slicing of spacetime into space and time (called a foliation). This can call the same objects receding in one foliation and approaching in another. I gave you an example where both foliations that disagree are exceedingly natural, and this all happened in SR, not even GR.

 

[PeterDonis]

in order for 'galaxies' to move apart on the surface of the balloon, the 'balloon' or sphere itself must grow into a dimension the wouldn't exist in just a two dimensional space.

Once again: this does not logically follow. It is an artifact of the way you are visualizing the expanding balloon. It is not a logical implication of the actual model. If the balloon analogy bothers you because you feel forced to visualize it this way, the correct response is to discard the balloon analogy. It is not to try to make up alternate models that are incorrect. See below.

it would make more sense to me to have a flat 2 dimensional area and just show everything moving away from everything else.

It might seem like it makes sense to you, but this model does not match observations. Nor is it how FRW spacetime actually works. FRW spacetime is 4-dimensional, not 3 dimensional (and a "reduced" version of it with 2-spheres as spatial slices would be a 3-dimensional spacetime, not a 2-dimensional one).

 

[PeterDonis]

I would thought measuring increasing distances is absolute. Is that not the case?

No.

 

[rede96]

No, I don't agree unless you define receding as positive expansion scalar. Normally, receding is simply defined as increase in proper distance measured in a specified slicing of spacetime into space and time (called a foliation). This can call the same objects receding in one foliation and approaching in another. I gave you an example where both foliations that disagree are exceedingly natural, and this all happened in SR, not even GR.

If we take the SR example of the 2 rocket ships mentioned, if there is a taut, thin rope tied between them, if the rocket ships recede, the rope breaks. This is invariant in that every FoR will see the rope break. There is no FoR that will see the rope slacken. The rope, in the way I am understanding this, represents the proper distance between the two ships. In that if all frames of reference took turns in measuring the rope in their own FoR, they would all measure the same length.

So if there is a FoR that uses a specific coordinate system which measures the 2 rocket ships to be approaching each other, but observe the rope breaking, then it seems to me that the way the rockets are being measured is in error. If there are many ways to measure something but they all give a different result, they all can't be correct in terms of the proper distance.

Is that not correct?