How do we know the universe isn't collapsing ?

[Futobingoro]

How do we know the universe isn't "collapsing"?

Main questions:

-Is the conventional view of two galaxies moving away from each other in a uniform space correct?
-Or is it conceivable that two galaxies may be more or less stationary as the density of space increases?
-Does it matter?

Background:

I've been thinking of the balloon analogy of the expansion of the universe, whereby two dots of ink drawn on a deflated balloon will appear to move further apart as the balloon is inflated. I am somewhat confused by the coordinate system in use here:

-The two dots do indeed become more distant if you use a coordinate system not bound to the surface of the balloon. For example, a scientist in a lab observes the inflation of the balloon and uses a ruler or arc length tool to measure the distance.

but...

-The two dots remain the same distance apart if you apply a coordinate system to the balloon itself. An example here would be measuring distance based upon the amount of latex between the two points (assuming the line between them has tangible width). In other words, the balloon's coordinate system expands along with the balloon.

The latter is more analogous to our perspective of the universe. We have only our own conceptions of a coordinate system, lacking the outside view held by an observer looking at a balloon. Applying the balloon analogy to "our" universe, two galaxies that are on a common "shell" with negligible curvature (our equivalent to a balloon surface), with spacing of 10^20 km, will remain at that distance as the shell's coordinate system expands with them. The shell may be growing larger, but it still has the same amount of "latex."

Obviously, within our galaxy we can define distance by observing atomic phenomena and the speed of light in a vacuum, and then apply that to the distance between galaxies to show they are receding. However, in the balloon model, even these units would expand at the same rate as the distance between galaxies.

Thought experiment:

This FAQ site states that, according to the current models, "[The Big Bang] was an explosion of space, not an explosion in space." Going off of this I made some assumptions:

1. Two points exist that are equidistant from a hypothetical "center" of the Big Bang, and are not constrained to a given "shell" (made only to make comparison to the balloon analogy easier).
2. Space can flow around mass in much the same way gases from an explosion flow around a massive object (the converse of mass moving through space).
3. Space has finished expanding, and is now returning to its origin (i.e. the universe is shrinking)
4. There is a finite amount of space.

To illustrate this, assume the scientist I mentioned earlier replaces the balloon with a large sphere of latex (which can in this example be thought of as many concentric latex balloons) and has somehow stretched the sphere in all radial directions. If the scientist designates two different points within the sphere (which will remain stationary from his perspective) with a common radius and releases the forces keeping the sphere stretched, the sphere will shrink, placing more latex between the two points (again assuming the path between them has tangible width). A hypothetical observer on one of the points will have just observed the other point "accellerating away" as the sphere transitions from a stretched object with low density to a smaller object with a higher density.

This thought experiment, as it pertains to our universe, can be thought of as space contracting toward a hypothetical center as two galaxies remain relatively stationary. In our balloon model, this would equate to two points maintaining the same separation (in the lab frame) as the balloon is deflated. An observer on one of the points would measure an increase in the amount of latex between his dot and the other.

 

[pervect]

I favor "It doesn't matter" as the answer to your question, though the idea of the "density of space" is not, as far as I know, a standard idea.

The standard view does state that you can assign constant coordinates to points in the universe that are moving along with the so-called "Hubble flow". These constant coordinates are called comoving coordinates.

However, igiven the usual defintion of distance (either the current SI definition, or earlier definitions in terms of standard meter bars), it would be incorrect to say that these points maintain the same distance, Re-defining distance to mean something other than the standard definition is confusing (being an example of Humpty-Dumptyism), and furthermore doesn't seem to gain anything that I can see.

What one usually does is introduce a metric which converts the constant comoving coordinates into physical distances, a metric which changes with time.

There is then no need to consider anything like a "density of space" - one simply has comoving coordinates (which are constant), and a metric, which converts the comoving coordinates into distances. Strictly speaking, the metric gives us the distance only between nearby points, we actually have to integrate the distances between nearby points along some specific curve to get the cosmological distance.

 

[yogi]

From New Pathways in Science by Eddington at p 223:"...but if the universe is expanding relative to these standards, all the standards are shrinking relative to the universe. The theory of the expanding universe is also the theory of the shrinking atom"

 

[Futobingoro]

I think the matter remains:

Imagine that by some strange happenstance there are an extraordinary number of meter sticks (as we know them on Earth) laid end-to-end between two galaxies, and they are not disturbed.

If the space between the two galaxies expands, the meter sticks will also expand, leaving no gaps.

There needs to be an addition of space between the two points, rather than a stretching of the existing space. For instance, gaps would appear between the ends of the sticks and more would need to be inserted to recreate the end-to-end arrangement. There are of course other factors to consider, like on what scale the addition of space would manifest itself (making atoms more closely spaced to create said gaps or having space appear between the ends of the sticks, etc).

There are many possibilities for a mechanism of adding space between two points, among them the contracting universe example I proposed whereby the fabric of the universe is contracting, fitting more space between galaxies.

 

[pervect]

You might want to take a look at http://arxiv.org/abs/0707.0380, which talks about these issues.

The short answer to :

Imagine that by some strange happenstance there are an extraordinary number of meter sticks (as we know them on Earth) laid end-to-end between two galaxies, and they are not disturbed.

If the space between the two galaxies expands, the meter sticks will also expand, leaving no gaps.

is that meter sticks do not expand when "space expands" - this is not what is meant when cosmologists say that "space expands", it is a misinterpretation/misunderstanding of the basic idea.

For instance, the previously mentioned http://arxiv.org/abs/0707.0380 says

This result tells us how not to understand expanding space. Expanding space does not stretch rigid rulers — how could it? It is just a trick with inertial
frames. The internal, interatomic forces in rigid objects are able to maintain the object’s dimensions; Dicke & Peebles (1964) [see also Carrera & Giulini (2006)]
argue that EM forces do just this. Objects are held together by forces that pull their extremities through a succession of rest frames.

Thus concept of expanding space that the cosmologists are using is not the same one that you are thinking of.

Despite (and perhaps in part because of) its ubiquity, the concept of expanding space has often been articulated poorly and formulated in contradictory ways.
That addressing this issue is important must be placed beyond doubt, as the phrase ‘expansion of space’ is in such a wide use—from technical papers, through to
textbooks and material intended for school students or the general public—that it is no exaggeration to label it the most prominent feature of Big Bang cosmologies.
In this paper, we have shown how a consistent description of cosmological dynamics emerges from the idea that the expansion of space is neither more nor less
than the increase over time of the distance between observers at rest with respect to the cosmic fluid. This description of the cosmic expansion should be considered a teaching and conceptual aid, rather than a physical theory with an attendant clutch of physical predictions.

 

[Futobingoro]

I may not have have expressed my ideas well enough. Nevertheless, I benefitted from the work you linked to:

Since two bodies, both at rest with respect to the fluid defining the FRW metric, find the distance between them has increased after a certain time interval, it seems sensible to suggest that there is more space between them than there was previously. It may be misleading to suggest that the space that was there stretched itself as the universe expanded. Perhaps a better description, in simple terms, is to suggest that more space appeared, or ‘welled up’ between the two observers, however this is a largely semantic distinction.

I believe this speaks to the same concept I was talking about when I said that space doesn't stretch, that "there needs to be an addition of space between the two points."

I know I've used out a lot of analogies in this thread, but I have another that I think addresses the provisions needed for reference frames.

There are three people on a beach at low tide, spaced 100 feet from each other in a straight line parallel to the wavefronts moving toward the beach. If the water is an analogy for the fabric of space, and the three people are galaxies, more space will "well up" or appear between them as the tide comes in. This happens even though they are at rest with respect to the beach and the water (along the axis between the people). If the tide rises at a rate of 1 foot/hour, and the space between two adjacent people is defined as the amount of water above a 1x100 foot rectangle that runs along the sand between them, two adjacent people will gain 100 cubic feet of space between them each hour. The two outer people will gain 200 ft^3/hour.

This can imply that the fabric of space is receding, that the "tide is coming in." However, while the people on the beach were at rest with respect to the axis along the beach, there was movement of space perpendicular to the beach (i.e. the tide was able to flow past them toward the beach). This would imply that for galaxies that are stationary laterally (as the people were) the increase in density wrought by the contraction of space would cause space to "appear" between them.

 

[pyrojelli]

When I was somewhere around 7-years-old I concocted the same idea and proposed this baffling theory to my parents: If everything were getting bigger every second how could we know it since the rulers are getting bigger too, and if everything were getting smaller how could we know it since the rulers are getting smaller too? Our universe by now might really be the size of an original atom or a single atom might be the size of our original universe, there's just no way to tell. I find this idea of the shrinking atom quite intriguing, but what if the universe (space) and the atom/quanta (matter) were BOTH shrinking, just at different rates. We would have breaches of e=mc^2 all around us and never know it. That would make all of our so-called laws of nature simply relative to our perception.

 

[Chronos]

Hmmm, so what are you saying is redshift = a shrinking universe? Can we talk about redshift, or do you consider it irrelevant? The concept works well in Earth bound experiments.

 

[pyrojelli]

Please expound on truth of falsity of "redshift=a shrinking universe"

 

[SpaceTiger]

Re-defining distance to mean something other than the standard definition is confusing (being an example of Humpty-Dumptyism), and furthermore doesn't seem to gain anything that I can see.

Comoving coordinates make it easier and more intuitive to track the deviations of the universe's contents from the Hubble flow. Unless one is measuring the Hubble parameter or energy contents of the universe directly (as with the Type Ia SNe), then all of the interesting large-scale physics are in the comoving distance distributions. Perhaps the most striking demonstration of this is the evolution of structure in cosmological N-Body simulations. See, for example, the images on the righthand side of this page:

http://chronicle.uchicago.edu/060713/darkmatter.shtml"

Imagine that progression being displayed in physical coordinates and perhaps you'll see why we sometimes want to study structure in a comoving coordinate system. On cluster scales or smaller we move back to physical distances because the Hubble flow becomes negligible for the system's dynamics.

For most pedagogical purposes, however (as in the OP's question), there is seldom need for comoving coordinates and I agree that it adds an unnecessary layer of complexity.

 

[Futobingoro]

I think this thread's focus has shifted to the definition of comoving coordinates and what it means for two points to move away from each other. I still don't think my main question has been answered, and I will try to keep it simple:

Can the observed phenomena (like the Hubble flow) also be ascribed to a contraction of space faster than the contraction of the galaxies in the observable universe?

The most common hypothesis can be thought of as people wading into deeper water on radials from the center of a small island. A higher volume of water is appearing between them, and at an accelerating rate. The other possibility that I have suggested involves the same people remaining stationary in the water as the tide comes in.

Both create the impression that water is "welling up" between the people.

I have read that the hesitance of physicists to ever use "absolute velocity" stems from the fact that velocity depends on one's perspective. One doesn't know whether an object is moving toward oneself at 100 km/s or if he/she is moving toward it, or some combination of the two. Is there a possibility that the observed "expansion" of the universe also depends on one's perspective, as detailed above?

 

[pervect]

"Contraction of space" doesn't make a lot of sense to me. One of the standard explanations (that I personally don't care for, but it is standard in the sense that it's used a lot) is the expansion of space, not the contraction of space. That's what the paper I mentioned earlier talks about in more detail - how to make the idea of "expanding space" actually work right.

You can also view the expansion of space-time as the contraction of rulers (as yogi mentioned much earlier), i.e. you say that all standard meter sticks, everywhere in the cosmos, are shrinking. Then the re-defined rulers measure re-defined distances, which stay constant. (These re-defined rulers then measure the comoving coordinates I mentioned earlier - ST thinks I'm getting overelaborate by talking about them, but I find them too handy to ignore. YMMV.).

With this point of view, the universe is "really" static (in terms of the re-defined, nonstandard rulers).

I'm not aware of anybody who talks about space shrinking as you do that has a published paper. This means that you're on your own as far as making this idea work. If you re-read our guidelines, you'll notice that its our policy not to talk overmuch about private theories, but to try and explain science as mainstream scientists practice it. And since mainstream scientists publish, this means that we talk about ideas that are published.

 

[SpaceTiger]

These re-defined rulers then measure the comoving coordinates I mentioned earlier - ST thinks I'm getting overelaborate by talking about them, but I find them too handy to ignore.

The passage that I quoted suggested you were saying the opposite, didn't it? I responded to explain why I thought comoving coordinates weren't useless.

Anyway, on the OPs question, "contraction of space faster than the contraction of galaxies" sounds like it would require an additional, non-gravitational force between galaxies. As such, it would definitely fall into the category of a personal theory and not be appropriate for this forum.

 

[hellfire]

You can also view the expansion of space-time as the contraction of rulers (as yogi mentioned much earlier), i.e. you say that all standard meter sticks, everywhere in the cosmos, are shrinking.

But in the same way that you need a physical mechanism to explain expansion in this new picture you would need some physical mechanism to explain contraction of rulers. You would need some kind of field that couples to matter and shrinks it. Both descriptions are not completely equivalent in general relativity. I think that in some modifications like former Garth's theory both descriptions are actually equivalent. Am I wrong?

 

[jcsd]

But in the same way that you need a physical mechanism to explain expansion in this new picture you would need some physical mechanism to explain contraction of rulers. You would need some kind of field that couples to matter and shrinks it. Both descriptions are not completely equivalent in general relativity. I think that in some modifications like former Garth's theory both descriptions are actually equivalent. Am I wrong?

These sort of relativistic cosmologies start off by postulating that there exists a frame in which the universe is homogenous and isotropic - this the so-called cosmological principle (which is of course an approximation, but one which is thought to be a very good one when dealing on cosmological scales).

Because of this assumtpion standard cosmologies have a 'preferred' frame (I use preferred in a weak sense). When people talk about the expansion/contraction of space/universe they are talking about the way that distances between two spatial points in this preferred frame change in relation to time (and given that the universe is always isotropic and homogenous in this frame all distances change in the same way in this frame).

 

[hellfire]

I am aware of that. Cosmological spacetimes can be described in different ways from different frames, that have however one thing in common: spacetime changes in some way. The question is that, as mentioned above, there is a kinematical equivalence between a changing spacetime with constant matter rulers and changing rulers with static spacetime. However, general relativity only provides a dynamics to explain the first phenomenon but not the second. Or are you suggesting that there exists in GR change in coordinates that allows you to describe a cosmological static spacetime with changing matter? I don't think so. For this second option to be explained, and to have a full equivalence between both options, you need to modify GR (scalar-tensor theories?). This is what I tried to say, although I am not completely sure in what extent it is generally correct.

 

[jcsd]

I am aware of that. Cosmological spacetimes can be described in different ways from different frames, that have however one thing in common: spacetime changes in some way. The question is that, as mentioned above, there is a kinematical equivalence between a changing spacetime with constant matter rulers and changing rulers with static spacetime. However, general relativity only provides a dynamics to explain the first phenomenon but not the second. Or are you suggesting that there exists in GR change in coordinates that allows you to describe a cosmological static spacetime with changing matter? I don't think so. For this second option to be explained, and to have a full equivalence between both options, you need to modify GR (scalar-tensor theories?). This is what I tried to say, although I am not completely sure in what extent it is generally correct.

These spacetimes we're tlaking about are not static and as staticity is a quality of a spacetime itself rather than of a particular cooridnate system, no coordinate change will make them static. So yes you are correct.

I think maybe lost here is the distinction between spaectime and time and space though.

We're talking about the expansion of space. Or more specifically how distance increases between two co-moving obserevres in our preferred cooridnate system.

What pervect is talkign about is simply changing how we interpret our cooridnate system. Really it's a matter of philosophy/pedagogics whether we choose to interpret the change in distances between co-moving observers as the expansion of space or the shrinkage of rulers.

At the end of the day we're delaing with the same objective predictions whatever way we like to think about them in our heads.

 

[hellfire]

We're talking about the expansion of space. Or more specifically how distance increases between two co-moving obserevres in our preferred cooridnate system.

That's what is actually matter of coordinate choice IMHO. With a proper definition of expansion you can talk about expansion of space in the usual comoving coordinates or about expansion of spacetime in e.g. conformal coordinates.

What pervect is talkign about is simply changing how we interpret our cooridnate system. Really it's a matter of philosophy/pedagogics whether we choose to interpret the change in distances between co-moving observers as the expansion of space or the shrinkage of rulers.

I cannot agree. You have agreed with me above that there is not an equivalent description between both options within general relativity. So it would be only a matter of philosophy if the correct (in a classical limit) theory of gravitation would allow for both descriptions to be kinematically and dynamically equivalent. This is not the case for GR.

 

[sysreset]

Regarding "Expansion of Space" vs "Shrinkage of Rulers":

These do not appear to be mathematically equivalent because with expansion of space, space expands but matter doesn't expand with it. But with "shrinkage of rulers", your actual measurement standard changes, so space and matter would both have to be affected. These are not mathematically equivalent scenarios.

 

[pervect]

Regarding "Expansion of Space" vs "Shrinkage of Rulers":

These do not appear to be mathematically equivalent because with expansion of space, space expands but matter doesn't expand with it. But with "shrinkage of rulers", your actual measurement standard changes, so space and matter would both have to be affected. These are not mathematically equivalent scenarios.

Let's start off by saying that physics doesn't change fundamentally if you measure distances in inches, or in feet. Note that various "fundamental constants" will change in their numerical values, but physics itself does not change.

But "the same" distance is associated with a larger number of inches and a smaller number of feet.

So, if we redefine our basic measure of distance so that they are variable with time, some of our fundamental constants will now be variable as a function of time (for example, the speed of light.)

The physics, however, will still not change. It's just a change in how we describe things, there is not a fundamental change in the actual physics. And in our new unit system, the universe will not be expanding, while the meter bar in paris will be shrinking.

Note: this topic (of the expansion of space) has been discussed before at length. One of many past threads that is very similar is

https://www.physicsforums.com/showthread.php?t=69509. See in particular post #27 by Garth for the specific point about shrinking rulers.

If you don't find "shrinking rulers" intuitive, don't use them - it's not a particuarly common idea, though it has been published.

The main point I want to make is semi-philosophical. This point is that operationally, space is defined by what me measure with a rulers. People seem to be attributing excess philosophical baggage to the idea of "space" that do not really (IMO) belong to the concept.

From an operational point of view, space is an abstract concept that describes our conception of how rulers behave, i.e. the set of rules that distances follow. And that's really all there is to it.

 

[sysreset]

Is it even possible to come up with a meaningful "ruler" that applies to space across cosmologic distances??

You can try "one meter" but the length of one meter depends on your frame of reference. The same with one AU or one light-second...

 

[pervect]

Is it even possible to come up with a meaningful "ruler" that applies to space across cosmologic distances??

You can try "one meter" but the length of one meter depends on your frame of reference. The same with one AU or one light-second...

What's really constant across cosmological distances is the Lorentz interval. This is the same for all observers, independent of frame of reference.

To actually compare distances, rather than Lorentz intervals, one has to split space-time into space+time. This does involves making a choice of a reference frame to split space-time into space+time.

In cosmology, choosing "cosmological time" or equivalently choosing a frame comoving with the Hubble flow is a "standard" way of making this split. But making such a split is a choice or convention.