# Basic question on expansion

1. Jul 24, 2006

### MeJennifer

One what basis do we conclude or consider it plausible that the universe is expanding? I realize there is a set of observations about objects in the universe we try to fit in with our theories.

It seems to me that there are two paths to follow:

a) GR is correct + we have expansion of space
b) GR is wrong

Or do I make a logical fallacy here?

2. Jul 24, 2006

### marcus

in GR or many other models of spacetime, the continuum is represented by a smooth 4D manifold with a metric (a distance function). Personally I can't think of any serious model of spacetime where distances are not free to change.
All expansion means is that overall most distances are increasing (at rates roughly proportional to how long they already are)

it would be unusual for distances not to change with time-----in the basic situation there is nothing forcing them to stay the same.

maybe if there is any "logical fallacy" in your post, it is that (if I read you correctly) you seem to be expecting that distances normally would not change. I agree that lengths of objects ordinarily dont change much, I mean size of atoms, crystal bonds, molecules etc OK. but a distance between two galaxies is physically different from the length of a metal rod.

So intuitively there is no reason to expect distances between stationary points to be constant, in ANY model of spacetime whether it is GR or some other serious attempt to fit the data.

GR is basically just one possible differential equation that has been proposed to govern the evolution of the metric.

This differential equation has various different solutions. It has solutions where all the distances decrease (so space shrinks) and it has solutions where all the distances increase (so space expands) and it has solutions with some of both-----a mix of expanding and contracting. In some solutions both can be happening in different places at the same time! A basic question is: which solution to the GR equation do we happen to live in?
At least to a rough approxmation, it looks as if we are living in one of the expanding solutions.

GR checks out to high accuracy---extremely well whereever we can test it. with Mercury's orbit, with neutron stars, with GPS clocks, with Gravity Probe B gyroscopes on board a satellite etc etc. So the simplest thing is BELIEVE IT.

If you believe GR then it is natural to expect distances to change. It is just an elementary fact about distance----TYPICALLY IT CHANGES. And we seem to be approximately (but not exactly) in one of the solutions where distances are (almost) all increasing----an over-all expansion case.

Last edited: Jul 24, 2006
3. Jul 24, 2006

### MeJennifer

We are the results from Gravity Probe B gyroscope measurements?
I was under the impression that there is no data as of yet.

4. Jul 24, 2006

### marcus

funny you should ask, I just read some discussion this morning about preliminary results. I can't say! Dont have a link! I gather they are analyzing the data and that they havent noticed any big surprises, but i could be wrong.

Until further notice consider that part of what I said to be my own extrapolation
If I find the link to what i read earlier today, I'll post it in case you or anyone are interested.

5. Jul 24, 2006

### MeJennifer

So do I understand correctly that expansion of space-time (I assume it is space-time that expands not just time) is a possible solution to the Einstein field equations without any external explanations such as a cosmological constants, quintessence fields, de Sitter spaces etc?

How so?

I suppose we are not talking about the volume contracting properties of mass right?

Last edited: Jul 24, 2006
6. Jul 24, 2006

### marcus

"How so?" is a good question!

different people would respond differently. I don't consider myself an authority and I assume other people will want to jump in and give their view on this. However if you want my personal take, I would be delighted to give it.

the cosmological constant is something I consider to be PART OF THE EINSTEIN EQUATION

but in my view it does not explain expansion because expansion could occur as a solution EVEN IF THE CC WERE ZERO.
the CC only conditions the shape of the expansion

ALSO I am put off by what you say about "spacetime" expanding or "time" expanding. it seems to miss the main feature which is what people interpret as the expansion of SPACE.
when I think of the universe expanding, what comes to mind is the FRW metric which has a time parameter in it, and as time advances SPATIAL DISTANCES INCREASE.

so I would rather not talk about this as if it were "time expanding" or "spacetime expanding"
the simple phenomenon which everybody sees and wants to explain is just spatial distances increasing with time.

1. we should not expect spatial distances to stay constant, why should they? they are not tied by rigid bars or connecting cables made of stuff we normally experience to not change size.

2. and in fact distances across large voids of space are OBSERVED to increase---plenty of evidence

3. and the most successful theory, namely GR, teaches us to expect this or at least not be surprised by it----because expansion or contraction is predicted as likely in solutions of the equations.

============

hmmmmm

to me it is not surprising----because of points 1, 2, and 3, I find it not so remarkable or in need of further explanation.

but YOU DO and that is interesting. I like to learn other people's views on stuff.
=============

maybe you would like to know my viewpoint. To me, what is the greatest mystery is WHERE DOES THE EINSTEIN EQUATION COME FROM?
I think that this equation must have a quantum ground in the microscopic dynamics of spacetime and matter.

I think this equation (what you call the Einstein field equations) must be WRONG because it has singularities. The solutions have regions where they dont make sense---they say infinite density and curvature in some places. That does not happen in nature, I think. IMO nature does not have "singularities" which are really just failures in some theory.

So I think there is a deeper theory of microscopic spacetimematter dynamics which GIVES RISE to the einstein equation picture. And also it may explain something about where the CC comes from and where "dark matter" effects come from.

So I do not spend my time wondering why space EXPANDS. AFAIK that is just something that one naturally expects given the classical macroscopic theory and which obviously happens.
I am more apt to spend time wondering how the successful classical model arises from a microscopic model.

BTW Lee Smolin's generic QG models (going by various names) tend to have microscopic "moves" which occur with a certain amplitude or probability in the "path integral" or sum-over-histories picture of spacetime evolution. And some of these moves are called "exchange moves" and they just rearrange the web of relationships that is the quantum state of spatial geometry. and some of the moves are called "expansion moves" and they actually are accompanied by expansion of space at a microscopic level.

So if you are desperate for answers, grasping for straws, you could look at Smolin's recent paper "GENERIC PREDICTIONS OF QUANTUM THEORIES OF GRAVITY" http://arxiv.org/abs/hep-th/0605052
Athough these ideas come up in a number of different currently-studied models, they are as yet untested ideas.

Last edited: Jul 24, 2006
7. Jul 24, 2006

### MeJennifer

The usage of "time" was a slip of words, of course I meant space, sorry for that.

Now forgive my ignorance for GR, but my understanding was that the expansion or contraction or steady state had something to do with the amount of mass in the universe.

So the volume reduction properties of mass as predicted by GR has nothing to do with the expansion/contraction of space?
So does in fact only space expand and not time or do both expand?

By the way perhaps you missed this question:
How so? Or in other words, in what way is it different?

Last edited: Jul 24, 2006
8. Jul 24, 2006

### marcus

Admittedly my take on this is very simple and naive. I see an obvious difference.

When you compare a metal rod---say a meter stick---with the distance over, say, a billion lightyears of empty space what i see is a distinct physical difference.

On the one hand you have a metal object----a crystal lattice of, say, iron atoms---the meter length is a property of that object.

On the other hand you have a billion lightyears of almost empty space, with no material structure and only negligible material.

they are physically very different and they are governed by very different physical laws.

the metal meter stick is governed by a theory of crystal lattice bonds, and all its properties like
density, length, mass etc can be deduced from that and relevant stuff about the atoms comprising it.
by contrast the billion lightyear distance is governed by the EINSTEIN EQUATION because it arises from the metric, and the metric is a solution of the einstein equation.

to me it seems obvious that they are quite different things----one is material (in fact metallic) and the other is a purely GEOMETRIC entity, or purely spatial.

You ask How so? are they different. I think we may have reached a basic perceptual incompatibility. I see the two things as obviously different and have tried to explain. You may very well NOT see them as different and be indisposed to see it from my viewpoint. In that case, perhaps we should leave it there.

I expect other people will have different views, so in the end the contrast will not seem so stark.

Last edited: Jul 24, 2006
9. Jul 25, 2006

### Garth

Garth

10. Jul 25, 2006

### Garth

Space-time does not expand - expansion is a process in time that requires the time dimension already included in the space-time continuum.

Space-time suffers curvature, in the Friedmann solution of the cosmological case of Einstein's field equation this curvature causes space to expand and itself (as a slice or 'foliation' of space-time) to possibly suffer curvature (spherical, flat or hyperbolic). The expansion convoluted with the curvature of space cause distant objects to suffer red-shift, this may be thought of as an observed time-dilation, but not the "expansion of time", which is a phrase that does not make sense.

Note: time can only pass at the tautological 'one second per second', time dilation is an observed effect when one clock is compared to a laboratory clock. The curvature of space-time and any real relative motion cause the distant clock to appear to run slowly. (This is assuming that fundamental particle masses, charge, c and Planck's constant do not vary.)

Garth

11. Jul 25, 2006

### MeJennifer

Odd, because time definitly contracts due to mass, so why could it not expand as well?

Take for instance a sphere that reduces volume due to the curvature of space-time. Then not only the space but also the time contracts.
So why is it different?

So is this Friedmann's idea or does it directly derive from EFE that time plays no role in it?

So does time contraction make sense to you? If so the why not time expansion?

What do you mean by a laboratory clock?

Last edited: Jul 25, 2006
12. Jul 25, 2006

### Garth

No, time does not "contract due to mass". This is a very slipshod phrase.

As has been explained on these Forums many times, the idea of time going slowly or 'contracting' (whatever that means; are you measuring time with a ruler?) is an oxymoron, a contradiction of terms.

Time always 'passes' at the tautological 'rate' of 'one second per second'.

How do you measure a rate as 'slow' or 'fast' except by comparing the observed process with another clock?

In SR a moving clock is observed to run slowly when compared to a 'stationary' clock, i) because of a classical doppler effect and ii) because of the Minkowski metric effect. (Draw space-time diagrams with the two world-lines and light rays passing between the two)

In the 'Twin Paradox' the non-inertial twin ends up younger because the interval along her world line is actually shorter (measured in seconds) than that of her inertial 'stationary' twin.
Again what do you mean by "also the time contracts"?

Red shift is observed in gravitational time dilation because the null-geodesics of consecutive light signals, coming from a process deep in the gravitational well, traverse curved space-time and mutually diverge (think of the curved funnel analogy), and therefore arrive further apart.

Consider a thought experiment: Let an observer have two identical and sychronized clocks at the top of a high tower on a non-rotating massive planet. If she slowly lowers the second clock to the bottom and retrieves it sometime later, then the lowered clock will be found to be 'slow' relative to the first clock.

This is because less time has elapsed at the bottom of the tower. (Again think of the curved funnel analogy).

From the beginning of the experiment until its end the world-line of the second clock is actually shorter than that of the first.
It is a direct solution of the EFE. The universe either expands or contracts, it is observed to be actually expanding.

Time is the parameter by which space expands; that is all points in space are found to be further apart from each other at later times than they were at earlier times.
Neither makes sense to anyone, as I said, expansion and contraction require time for the process to take place. Space-time is static, conceptually 'observed' from 'outside' space and time.
Time dilation is the comparison of one clock with another.

If we observe red shift in a distant galaxy we are comparing the observation of the wavelength and frequency of light emitted/absorbed by an electron transition (energy level) in that distant object with the wavelength and frequency of light produced by the same electron transition in the local laboratory.

That frequency of the local electron transition is measured by the clock on the laboratory wall, that clock is the laboratory clock I was referring to, why are you confused ()?

Garth

Last edited: Jul 25, 2006
13. Jul 25, 2006

### MeJennifer

Gravitational contraction of space and time is nothing slipshod IMHO.

Yes I completely agree, but that is no what we are talking about here, we are talking about gravitational time contraction.
Gravitational time contraction and relativistic time effects are two different things.

Relativistic time effects are directly related to the paths taken in flat space-time, both in space and in time. You are correct there is no time contraction here, in fact it has nothing to do with time at all. Both observe a "slower clock" in the other frame due to relativistic effects. Factually both clocks run as fast as the other, and each clock's proper time is identical as well.

Again, I do not disagree here with you.
The world line in space-time is actually longer, but the proper time is shorter.
But again this is all special relativity, in flat space-time, it has nothing to do with gravitational contraction which is in curved space-time (and both space and time curve here).

Indeed they diverge due to the curvature of space and time in the gravitational well.
What I don't understand is that you see readily that space is contracting in this gravitational field but that you have trouble seeing that time is contracting as well.

That is correct.

That is correct as well.

I am not sure about that. The calculations are not trivial, since the second clock has to decelerate first to go deeper into the gravitational field and then accelerate back to the first clock. But it seems to me that the worldline in curved space-time of the second clock is actually longer not shorter.

Last edited: Jul 25, 2006
14. Jul 25, 2006

### Garth

The length of a world-line is the integrated interval along it.

Consider two stationary clocks in the situation above, one deep in the gravitational well and one 'at infinity'.

For the one in the well:

$$\tau = \int \sqrt{1 - 2GM/rc^2}dt$$

and the one at inifinity:

$$\tau = \int dt$$

The one in the well has a shorter interval along its world-line.

Garth

15. Jul 25, 2006

### MeJennifer

The wordline and proper time is not the same thing in relativity. Your formula shows the proper time not the worldline.

Last edited: Jul 25, 2006
16. Jul 25, 2006

### Garth

The proper time is the 'length' of the interval along the worldline measured in time units (rather than length units).

Garth

17. Jul 25, 2006

### MeJennifer

Yes, so that implies they are not identical.

Proper time and proper distance are related to the worldline but they are not the wordline itself.