Can Quantum Mechanics Explain the Expansion and Contraction of Space-Time?

[bapowell]

So the best way to describe expansion would be to not use pennies or specs. LOL No wonder it is such a stupid analogy.

I'm sorry you can't understand it, but I'm sure your attitude isn't helping.

 

[binbots]

I'm sorry you can't understand it, but I'm sure your attitude isn't helping.

Everyone else was saying how it is a bad analogy. Didn't realize I couldn't say it. Sorry. Plus a extra sorry in case that sorry came off as attitude :)

 

[phinds]

Everyone else was saying how it is a bad analogy. Didn't realize I couldn't say it. Sorry. Plus a extra sorry in case that sorry came off as attitude :)

You REALLY might find it helpful to read the full picture of the balloon analogy given in the link in my signature.

 

[bahamagreen]

What happens if you do use 3D for the analogy and take it step by step from scratch to account for theory and observations? Can we make a lucid 3D model? Here is how I'm thinking... my assumptions and questions are numbered so it may be easier to review and point out what might be really wrong with this approach...

First step - a 3D approximation using relativity...

The universe is a 3D sphere with the geometric properties that there is an apparent universal expansion of the interior space, there is no center, and the radius of the sphere is the distance at which distant objects' recession speed approaches c.

1- the far objects from any observer are increasingly distant and moving away faster
2- the distance at which their motion approaches c is the surface of the sphere
3- because of relativity (length contraction), the more distant objects are increasingly thin
4- approaching the limit at the interior surface, there is sufficient "room" for an arbitrary number of objects
5- there is no center because all locations see this the same way (our galactic super cluster is thin to those we see at what we call near the "edge")
6- basically, all interior observers see themselves surrounded by increasingly thinner Olbers shells to the limit where these shells become unlimitedly thin.

The expansion can be continued within this sphere unlimitedly because the distant objects just continue to approach the limit of the interior of the sphere and get thinner and thinner providing the right scale for distances those out there would measure between themselves, as well as their measures of distance to us.

So the size of this sphere has a definite radius but any distance measured from anywhere within it may be unlimitedly large for two reasons; all observers will infer an apparent "compression" of distance between increasingly distant objects, and all observers will see this compression around them as spherically symmetric so they always find themselves "in the center" which remains true no matter from what location they measure. This applies to those distant from us measuring us as well.

Step two - How to account for objects presumed >c beyond the horizon

7- is this necessary if we don't see them?
8- what do we do with red shifts due to expansion that imply >c?
9- can adjustments be included into this analogy to account for 7 and 8 without "bursting the bubble" (changing the "radius" of the sphere)?
10- could the v->c distance comprise an inner shell, with >c objects outside it, and would this mean the "radius" of the sphere must be bigger, or unlimitedly large?
11- if distant objects approaching the distance where v->c become unlimitedly thin, what must be the "thinness" of objects beyond this distance?

 

[bapowell]

Yes I was going to ask this as well. But i thought I was already pushing my luck. Can it be visualized?

Sure, the actual balloon's rubber surface is a pretty good approximation to a 2D surface mass density. But as I said earlier, the balloon analogy is not good for understanding the dynamics of massive bodies (inhomogeneities) within the universe since it models the isotropic expansion of a homogeneous density (this is essentially what Peter is saying above when he asserts that the analogy is about geometry not mass. I agree strongly and think that the balloon analogy is best for understanding how to visualize geometry and expansion, but point out that through the Friedmann Equations we can associate the isotropic geometry with an isotropic perfect fluid with some mass/energy density if we really want to.)

So it's not that it's a bad analogy, I think maybe you are expecting it to elucidate a problem it doesn't apply to?

 

[binbots]

The whole demonstration is set up to show how galaxies move away from each other. But a homogeneous model would not contain any galaxies. So what is the analogy showing?

 

[binbots]

You REALLY might find it helpful to read the full picture of the balloon analogy given in the link in my signature.

I did. Very informative. I wish all analogies came with one of these. Thanks

 

[bapowell]

The whole demonstration is set up to show how galaxies move away from each other. But a homogeneous model would not contain any galaxies. So what is the analogy showing?

It more adequately shows how points in general on the surface move away from each other. As I said, if you wish to draw small dots on the surface of the balloon and pretend they're galaxies, then you can do that. But really, the analogy works best on cosmological scales where homogeneity is a good property. In that case, the galaxies should be very small unless the balloon is *very* big. That was my point earlier about the "microscopic" galaxies but perhaps I'm just quibbling at this point.

 

[binbots]

It more adequately shows how points in general on the surface move away from each other. As I said, if you wish to draw small dots on the surface of the balloon and pretend they're galaxies, then you can do that. But really, the analogy works best on cosmological scales where homogeneity is a good property. In that case, the galaxies should be very small unless the balloon is *very* big. That was my point earlier about the "microscopic" galaxies but perhaps I'm just quibbling at this point.

By all means make the balloon as big as need be. Eventually these specs would show some sort of structure.

 

[bapowell]

There's nothing wrong with them "showing structure". The problem is with endangering the approximation of isotropy and homogeneity. In the real universe, we have galaxies and clusters and so on and we still have isotropy and homogeneity on large scales. The same is true of the balloon. I apparently cannot emphasize enough that the balloon is meant to illustrate the expansion and geometry of the isotropic universe: you can imagine that galaxies populate your balloon all you want and the analogy will still help you visualize how they move. But if you want the analogy to be a solid one, and you seem to be very critically appraising it on this level, then all I'm saying is that your galaxies must be scaled such that the cosmological approximations still hold.

 

[binbots]

We use many analogies to describe many different scales. We use baseballs, grains of sands, planets etc. to explain scale of galactic distances, atomic structure etc. So why can we not use the same balloon analogy to show scale? How big would you have to make this balloon in order to see galaxies with the naked eye? (for example)

 

[timmdeeg]

It isn't forbidden to use a microscope. Anyway, in my opinion the balloon analogy could be improved by having the structures, galaxies and clusters, glued on the balloon, to show that they don't participate in the expansion of the universe, because being gravitationally bound.

Altogether I think that the balloon analogy is very helpful, though one has to be aware of that it suggests a closed universe.

 

[Bandersnatch]

We use many analogies to describe many different scales. We use baseballs, grains of sands, planets etc. to explain scale of galactic distances, atomic structure etc. So why can we not use the same balloon analogy to show scale? How big would you have to make this balloon in order to see galaxies with the naked eye? (for example)

Let's assume a human eye can discern an object from an arm's length if it's about 0.1mm in diameter. Some of the larger galaxies can reach (and exceed) 1 Mly in diameter. Let's use that size as our standard galaxy.
For a 1Mly galaxy to be no smaller than 0.1mm, the patch on the balloon's surface corresponding to the visible universe (proper distance) would need to be at least 4.6 m across. But the balloon itself would need to be large enough for the curvature of the observable patch to match that of the actual universe. The last curvature estimate I saw (might be outdated; i.e., too low, considering the trend) was a ~220 Gly curvature radius. Assuming spherical topology (since we're using the balloon), it'd mean that the balloon would need to be 44 metres in diameter. Ten times larger if you'd also like to see smaller galaxies (like the MW and Andromeda).

Whether there is any pedagogical value in trying to explain the current state of cosmology by asking your interlocutors to imagine a rubber balloon comparable in size to the Hindenburg, and possibly infinitely larger, is a matter of opinion.

 

[binbots]

I am just trying to push this 2d analogy as far as it can go before thinking about it in 3d. Is that wrong?
I assumed these galaxies of 0.1mm on my Hindenburg balloon would all be of similar size and distribution. All separated by 4.6m forming a grid pattern since this is a model of a smooth universe. How would I be able to see smaller galaxies?

 

[ChrisVer]

How would you see the galaxies, if the galaxies don't expand? -.-

 

[gulfcoastfella]

How would you see the galaxies, if the galaxies don't expand? -.-

As you look at objects which are further and further away, you're looking back in time to when the universe was smaller. I'm not 100% on this, but since the earlier, smaller universe appears to encompass our older, larger one, wouldn't this cause distant objects to appear bigger than they actually were, bigger than if the image you see of them was comprised of light which traveled instantly from the distant galaxy to yourself (which it obviously doesn't).

 

[gulfcoastfella]

I have a question of my own. How is space-time curvature measured? It seems like it would be different than measuring 3-sphere curvature. If a 2-D being living "in" the surface of a sphere tried to measure the 3-D curvature of the sphere, how would they go about it? They couldn't detect the curvature by looking for curvature in the paths of signals, because if the surface of their sphere was as transparent, isotropic, and homogeneous as our universe is, then wouldn't any signal they emit show no deviation from a geodesic when viewed on a cosmological scale, and we would see any 4-D geodesic in our universe as a straight line, the path followed by an "unperturbed" particle? The only way I can think of to detect higher-dimensional curvature would be to examine the effect on particles which have been traveling for a cosmological time-scale. Since particles have non-zero dimension, then absent some kind of resistance by the particle or a field, they would tend to be stretched out more and more the further they traveled. (Two sides of the particle on opposite sides of it's geodesic path would tend to follow slightly different geodesics, leading to a "spreading out" of the particle as it traveled, assuming, again, that the particle or a field didn't counteract this somehow.) I remember from a quantum mechanics course I took in college that photons tend to spread out more and more the further they travel. I understood, however, that this phenomenon was explained by quantum mechanics and didn't require curvature of space in higher dimensions.

 

[ChrisVer]

As you look at objects which are further and further away, you're looking back in time to when the universe was smaller. I'm not 100% on this, but since the earlier, smaller universe appears to encompass our older, larger one, wouldn't this cause distant objects to appear bigger than they actually were, bigger than if the image you see of them was comprised of light which traveled instantly from the distant galaxy to yourself (which it obviously doesn't).

My problem with this, is that the expansion happens at a cosmological scale, which (due to the Cosmological Principle) is isotropic. If you start being able to see structure in it, as for example distinct galaxy here and there, you are destroying the isotropy. However I may be wrong in the way I imagine it...

 

[Rocky9242]

I don't mean to imply that the universe is necessarily spherical just because the balloon analogy suggests this.

Maybe we need an inflatable potato chip.

 

[PeterDonis]

How is space-time curvature measured?

Spacetime curvature is tidal gravity, so by measuring tidal gravity you are measuring spacetime curvature. The basic way you measure tidal gravity is to look at nearby objects that are freely falling, i.e., moving along geodesics. If they do not have a constant speed relative to each other, then tidal gravity is present.

In the case of the expanding universe, the easiest geodesics to use to see the tidal gravity are the worldlines of nearby "comoving" observers, i.e., observers who see the universe as homogeneous and isotropic. Such observers are moving away from each other, but that alone doesn't show tidal gravity; what shows tidal gravity is that the speed at which they move away from each other varies with time. Up to a few billion years ago, that speed was decreasing with time; now it is increasing with time. That means the spacetime of our universe is curved, even if the spatial slices of constant time for "comoving" observers are flat.

 

[binbots]

If we could take a step back from this balloon we would see the surface populated by galaxies that are very similar to ours. They would all share our present moment in time. But do to the expansion of our surface and the finite speed of light we will never observe anything at the same moment of time in our 2d universe. We can only see past events from our perspective which means we can only gather information from past events. This information can only be seen inside the balloon. Now I know nothing can exist inside the balloon, but these objects don't exist anymore. All measurement we take are measurements of the past, never our present. Our future on the other hand is behind us which we can not see as we are expanding into it. We are backing into expanding space. Until we expand into it we can only make predictions of future events. Everything in our universe only exist on one 2d plane at a time. Distance and time are a result of our velocity through them.

 

[TEFLing]

I understand that the balloon analogy is misleading

Space is not expanding

Moment by moment, we leave behind a smaller space like slice, of the fabric of space-time...

And evolve into another, new, larger space like slice, of the fabric of space-time...

It's NOT like one balloon stretching...
Rather it's like a stack of balloons of increasing size...

To change the analogy, it's not one loaf of raisin bread rising... But a stack of slices of increasing size... Like a sliced loaf of artisan olive bread... The first slice is tiny, the next a bit bigger, and so on, up to the largest slices near the center middle...

The olives in the first few slices represent our galaxy in an ancient past life, the way it was billions of years ago...

The olives in the middle represent galaxies as they exist today

Olives towards the other end represent those same galaxies at future times

Please remember, Relativity says we are 4D beings, having "world volumes" as it were

Our past selves CONTINUE to exist in past space like slices, of the fabric of space-time...

And our future selves ALREADY exist, in future space like slices, of the fabric of space-time

The fabric of space-time is NOT expanding...

What is happening, is that what we for some reason perceive of as NOW, is a space like slice, of the fabric of space-time...

Which slices are becoming bigger and bigger, larger and larger

It's not that something is expanding or stretching...

Rather, space like slices, of the fabric of space-time, USED to be small...

And are GOING to be big...

And we're ON (relatively) medium sized slices

In a nutshell, that is what Relativity really says ... Not ONE thing stretching, but a STACK of thingS which are larger and larger

 

[PeterDonis]

Space is not expanding

Moment by moment, we leave behind a smaller space like slice, of the fabric of space-time...

And evolve into another, new, larger space like slice, of the fabric of space-time...

Relativity says we are 4D beings, having "world volumes" as it were

Our past selves CONTINUE to exist in past space like slices, of the fabric of space-time...

And our future selves ALREADY exist, in future space like slices, of the fabric of space-time

Each of these two quotes is basically ok by itself (though what you are describing are not physical facts but interpretations--see further comments below). But they contradict each other, so you need to decide which interpretation you are trying to describe.

that is what Relativity really says ... Not ONE thing stretching, but a STACK of thingS which are larger and larger

This, taken by itself, is much closer to just a straight description of what the mathematical model of the universe in relativity says (more precisely, what it says when you adopt a particular coordinate chart, the "comoving" chart).

Notice, however, that in this quote, there is no assertion about what "exists", and there are no words implying change, like "leave behind" or "evolve", or time relationships outside the time dimension of spacetime itself. Those kinds of assertions or words are what make your other quotes interpretations, rather than just descriptions.

 

[TEFLing]

It's very hard to take the time to be properly precise

Humans have a perception of now which is so unique as to psychologically seem separate and distinct from both the past and the future

We feel ourselves to be evolving from one moment to the next, so I want to humor that popular perception

Yet Relativity implies that we are 4D beings, whose present selves connect continuously from our past selves through our sense of now forward to our future selves

In some sense, vaguely reminiscent of the Law of Biogenesis ( life only from prior life ), Relativity would connect our world lines to those of our parents...

To those of our ancestors...

Back ultimately ~4Gyr to the first Earth protocellular life form

 

[gulfcoastfella]

I feel like there's an elephant in the room which no one has brought up yet. 4 spatial dimensions and space-time are not the same thing. It's almost more appropriate to refer to the former as "4 D" and the latter as "3+1 D". If you considered space-time to exist in the balloon analogy, then the two spatial dimensions and one time dimension would NOT be the 3 dimensions in which the sphere exists. For the purposes of the analogy, the balloon exists in 3 spatial dimensions and one time dimension, with 2 spatial dimensions and one time dimension interacting to create the 2D surface of the sphere's relativistic effects.

 

[TEFLing]

I feel like there's an elephant in the room which no one has brought up yet. 4 spatial dimensions and space-time are not the same thing. It's almost more appropriate to refer to the former as "4 D" and the latter as "3+1 D". If you considered space-time to exist in the balloon analogy, then the two spatial dimensions and one time dimension would NOT be the 3 dimensions in which the sphere exists. For the purposes of the analogy, the balloon exists in 3 spatial dimensions and one time dimension, with 2 spatial dimensions and one time dimension interacting to create the 2D surface of the sphere's relativistic effects.

In the olive artisan bread loaf analogy, each slice represents 2D of space ... And the stack of slices represents the passage of +1D of time

 

[ChrisVer]

(more precisely, what it says when you adopt a particular coordinate chart, the "comoving" chart)

I am having some conceptual problems with this, if you can enlighten me...
Why should it depend on the coordinate system itself,since coordinate systems are all equivalent ? I mean why would someone have to adopt a particular chart [the one named comoving] to get that?

 

[bapowell]

For the purposes of the analogy, the balloon exists in 3 spatial dimensions and one time dimension, with 2 spatial dimensions and one time dimension interacting to create the 2D surface of the sphere's relativistic effects.

I don't think there's a good reason to bring time into the analogy as a dimension. The balloon exists in 3D (ambient) space, and its surface is idealized to be 2D (the surface of a 2-sphere). In making the analogy with the universe, only the surface of the balloon carries over: space is the 3D surface of a 3-sphere. The ambient 3D space of the balloon does not carry over in the analogy -- there is no 4D space within which the 3D "surface" of the universe is imbedded.

 

[gulfcoastfella]

Thanks bapowell. Why is it believed that there can't be a 4D space for which our universe is a surface?

 

[bapowell]

It's not that there cannot be such a space, only that such a space is not actually necessary. Though perhaps counter-intuitive, the surface of a 2-sphere, for example, is well-defined in 2D (i.e. the geometric properties that make it a 2-sphere don't care about any additional dimension). You can think of the geometry of the surface as being "encoded" within the surface.

 

[gulfcoastfella]

Oh, yeah, that's very cool; I haven't heard that before, even though I'm reading a book on the Calculus of Variations, and it talks about describing a 3-dimensional coordinate system constrained by a surface as really only needing 2 dimensions. Very cool.

 

[PeterDonis]

Humans have a perception of now which is so unique as to psychologically seem separate and distinct from both the past and the future

Yes, but this is a fact about human psychology, not about physics. This thread is about physics.

We feel ourselves to be evolving from one moment to the next, so I want to humor that popular perception

Why? What does it have to do with physics?

Relativity implies that we are 4D beings, whose present selves connect continuously from our past selves through our sense of now forward to our future selves

This is one way of interpreting what the mathematical model of relativity says, yes. But it could equally well be put forward as an interpretation of non-relativistic physics.

Relativity would connect our world lines to those of our parents...

To those of our ancestors...

Back ultimately ~4Gyr to the first Earth protocellular life form

None of this requires relativity. The fact that we are causally connected to our ancestors is perfectly explicable with non-relativistic physics.

 

[PeterDonis]

4 spatial dimensions and space-time are not the same thing

This is true; when we speak of "4-D" in a relativistic context, we mean "a four-dimensional manifold with three spacelike and one timelike dimension", not "a manifold with four spacelike dimensions". The difference shows up in the metric; the metric of spacetime is indefinite (squared intervals can be negative, or zero even between different points), whereas the metric of a four-dimensional space would be definite (squared intervals between different points must be positive).

For the purposes of the analogy, the balloon exists in 3 spatial dimensions and one time dimension

But one of the spatial dimensions does not represent an actual physical dimension of spacetime; it is an unphysical feature of the analogy only.

 

[Rocky9242]

I understand that the balloon analogy is misleading
Space is not expanding
Moment by moment, we leave behind a smaller space like slice, of the fabric of space-time...
And evolve into another, new, larger space like slice, of the fabric of space-time...
It's NOT like one balloon stretching...
Rather it's like a stack of balloons of increasing size...
To change the analogy, it's not one loaf of raisin bread rising... But a stack of slices of increasing size... Like a sliced loaf of artisan olive bread... The first slice is tiny, the next a bit bigger, and so on, up to the largest slices near the center middle...
The olives in the first few slices represent our galaxy in an ancient past life, the way it was billions of years ago...
The olives in the middle represent galaxies as they exist today
Olives towards the other end represent those same galaxies at future times
Please remember, Relativity says we are 4D beings, having "world volumes" as it were
Our past selves CONTINUE to exist in past space like slices, of the fabric of space-time...
And our future selves ALREADY exist, in future space like slices, of the fabric of space-time
The fabric of space-time is NOT expanding...
What is happening, is that what we for some reason perceive of as NOW, is a space like slice, of the fabric of space-time...
Which slices are becoming bigger and bigger, larger and larger
It's not that something is expanding or stretching...
Rather, space like slices, of the fabric of space-time, USED to be small...
And are GOING to be big...
And we're ON (relatively) medium sized slices
In a nutshell, that is what Relativity really says ... Not ONE thing stretching, but a STACK of thingS which are larger and larger

I _really_ don't understand this slice business. I thought space was expanding at the rate of the Hubble Constant. If space is not really expanding, what is the explanation of red shift?

Saying that our past selves continue to exist and our future selves already exist is a non-scientific statement. It is all right to make non-scientific statements, but we need to keep in mind that the current existence of the past and future is not subject to observation or experiment, and therefore is not scientific.

 

[PeterDonis]

I thought space was expanding at the rate of the Hubble Constant. If space is not really expanding, what is the explanation of red shift?

The redshift is evidence that distant galaxies are moving away from us, and that how fast they are moving away depends on their distance from us. (The Hubble constant, btw, is the proportionality constant between those two things; you have to multiply it by a particular galaxy's distance from us to get that galaxy's speed of recession from us.)

Whether you attribute the fact that distant galaxies are moving away from us to "space expanding" is a matter of interpretation, not physics.