How can we know that the universe is expanding

[abhi2005singh]

I don't know much about astrophysics and have never studied it. So, if I am wrong at any point, kindly correct me.
It is said the whole space-time fabric itself is expanding after the big-bang. If this is so then why do we at all feel the recession of the heavens?

I will try to elaborate my confusion. If the underlying space-time itself is expanding, all the corresponding ways to measure length-time should experience similar expansion. Like if you are on the surface of the balloon (neglect the curvature), and you draw a 1 cm line to define a cm, then you use that line to measure another object as 3 cm. Now let the balloon inflate and the standard line now becomes of 2 cm (say). The previously measured object will now be 6 cm (due to expansion). But using the standard line, the measured object will still be of 3 cm. So, staying within the universe of the balloon, it is not possible to know if the balloon is expanding or not. Similar arguments can be given for time also.

I hope the question is not stupid.

 

[sylas]

I will try to elaborate my confusion. If the underlying space-time itself is expanding, all the corresponding ways to measure length-time should experience similar expansion. Like if you are on the surface of the balloon (neglect the curvature), and you draw a 1 cm line to define a cm, then you use that line to measure another object as 3 cm. Now let the balloon inflate and the standard line now becomes of 2 cm (say). The previously measured object will now be 6 cm (due to expansion). But using the standard line, the measured object will still be of 3 cm. So, staying within the universe of the balloon, it is not possible to know if the balloon is expanding or not. Similar arguments can be given for time also.

Let us suppose you WERE on a balloon that was expanding. You wouldn't draw a line on the balloon. You would draw two points, and then use a ruler to measure whether they are moving apart.

Same with the universe. There's no implication that every ruler expands. The nature of expansion is basically that on large scales things are dispersing and the universe as a whole is becoming less dense. But a ruler which is held together by atomic forces or a galaxy that is held together by gravity doesn't get bigger. It is rather that galaxies which are a long way apart from each other, so that they are not gravitationally bound to each other, tend to be moving apart from each other, and we can measure that movement.

Cheers -- sylas

 

[abhi2005singh]

Thank you sylas for the reply. It helped but there are still some doubts.

1. Does this (your reply) mean that the space-time fabric is not expanding for the Earth (bound together) but it is expanding for the empty space between (say) milky way and some other distant galaxy?

2. Even if it is expanding for our Earth as well, do we have any means to know/measure it? (I think we don't.)

3. If we don't have any means to measure this expansion, then are we correct to say that the recession is due to the expanding space-time?

 

[sylas]

Thank you sylas for the reply. It helped but there are still some doubts.

1. Does this (your reply) mean that the space-time fabric is not expanding for the Earth (bound together) but it is expanding for the empty space between (say) milky way and some other distant galaxy?

Don't get hung up on the word "fabric". It's just empty space. If you want to get into full technical details then you do need general relativity, and that does things which are a bit outside what we are used to for empty space; but it all reduces to good old Newtonian physics and empty space on smaller scales. Specifically, the expansion of the universe doesn't "drag" anything along for the ride. It's just things moving apart from each other. And things that are not moving apart from each other are not expanding.

However, it is true enough that the GR description of space within a galaxy is not expanding. That is effectively the same thing as saying a galaxy is held together by gravity. It depends on whether you think of gravity as a force, in the Newtonian sense, or go to the full generality of GR and gravity as curved spaces.

2. Even if it is expanding for our Earth as well, do we have any means to know/measure it? (I think we don't.)

As I said before, you can measure expansion just fine. The Earth is not expanding. If it was expanding, it would be a lot different from what it is... it would be getting bigger and of course we could measure it, just like we could measure it if you were sitting on top of a large balloon that was expanding. There's nothing problematic at all about measuring when something is expanding... a universe, a planet, or a balloon.

Of course, if expansion is small enough it might not be detectable; but that is not the issue. The point is that there is no problem in principle with measuring expansion of things.

3. If we don't have any means to measure this expansion, then are we correct to say that the recession is due to the expanding space-time?

We certainly do have a way to measure the expansion of the universe, and you can describe it in terms of expanding spacetime if you get into GR. The problem appears to be that you are reading things into the notion of expanding spacetime that are not really there.

If you are thinking of expansion as some kind of undetectable change that alters all measuring methods to keep giving the same results regardless of expansion, then you are not thinking about what cosmologists talk about when they say the universe is expanding.

Cheers -- sylas

 

[abhi2005singh]

Consider the expansion of time (this will also avoid the word "fabric"). Consider we are in a place where there is expansion in time due to the expanding universe or due to some other reason. Does the expansion in the time means that the time taken for the transitions to take place between two atomic level will now be more/less than the non-expanding case?

 

[sylas]

Consider the expansion of time (this will also avoid the word "fabric"). Consider we are in a place where there is expansion in time due to the expanding universe or due to some other reason. Does the expansion in the time means that the time taken for the transitions to take place between two atomic level will now be more/less than the non-expanding case?

I have no idea what you might mean by expansion of time. The above is not even meaningful. Try again.

To cut to the chase, you have evidently heard about expanding space and expanding universe. I can only repeat, this does not have any of the associations you appear to be making. It is a measurable effect, which is why we can study it and speak meaningfully about it.

The unit of time (the second) is defined in terms of the frequency radiation from transitions of a caesium 133 atom. That time is not changing. Neither is the time it takes for transitions to occur.

Cheers -- sylas

 

[Chalnoth]

The expansion of our universe is a large distance average effect. It is not an accurate description of the behavior of our universe on the size of galaxies, let alone smaller. But it is an accurate description of what happens between the galaxies.

The main way this is studied directly is through the distance-redshift relation. Redshift is a measure of recession velocity: somewhat like the doppler effect, the faster something is moving away, the more its light is shifted towards longer wavelengths (caveat: this is only a reasonable description for the nearby universe, before we have to take General Relativity into account, but it's fair enough to get the basic idea of how these things are measured).

Once you have the recession velocity, the next step is to measure the distances to these galaxies. There are a variety of ways, but one of the ways is by using so-called "standard candles". A "standard candle" is an astronomical object that has properties such that we can determine how bright it is at the source. The brightness that we observe, then, tells us how far away it is.

Some of the earliest standard candles, and the ones used to first tease out the distance/redshift relation, are stars called cepheids. Cepheids have this interesting property that they oscillate in brightness: they get brighter, dimmer, then brighter again. And they do so very regularly. Furthermore, observations of nearby cepheids have shown that there is a direct relationship between how fast they brighten and dim and how bright they are. We use other measurements of distance to determine their intrinsic brightness, and then use that to determine how far away other galaxies are by measuring their cepheids (cepheids are extremely bright, and so are visible even in moderately far-away galaxies).

When we put this together, we find a very specific sort of relationship: things that are far away are, on average, moving away from us. And they are doing so in a way proportional to distance. That is, an object twice as far away from us is, on average, moving away at twice the velocity.

When we combine this with General Relativity, we find that this sort of behavior is the exact sort of behavior that we expect for a uniform universe, one that is the same everywhere (a uniform universe cannot ever be static and stable, but must be either expanding or contracting in exactly this way). But when we study GR, we also find that it also predicts that systems like galaxies (and smaller) will remain stable through the expansion. Thus it is that the distances between galaxies increases, but the galaxies themselves remain about the same size (until they collide with another galaxy).

 

[abhi2005singh]

My question was some thing else and Chalnoth you answered something else. But thank you very much for the information you have provided. Some of it was new to me.I have just two question which may solve my confusion on this issue:

1. Consider a 1 D space from x = -10 to x = 10.

My previous conception was that since the space-time is expanding this means that still the space is from x = -10 to x = 10, just the spacing between any two consecutive points is increasing.

Now it seems that I was wrong. The expanding space means that the space is now (say) from x = -20 to x = 20 and will be from x = -50 to x = 50 at some later time and so on.2. Since the galaxies are receding away from each other and their recession speed is proportional to the distance from us, will it happen at any time that they will move faster than c. I don't think that this will happen, but can't find reasons to disprove it. Even if the recession is due to the expanding space between us, still I don't think that the relative velocity can exceed the value of c.

 

[sylas]

1. Consider a 1 D space from x = -10 to x = 10.

My previous conception was that since the space-time is expanding this means that still the space is from x = -10 to x = 10, just the spacing between any two consecutive points is increasing.

Now it seems that I was wrong. The expanding space means that the space is now (say) from x = -20 to x = 20 and will be from x = -50 to x = 50 at some later time and so on.2. Since the galaxies are receding away from each other and their recession speed is proportional to the distance from us, will it happen at any time that they will move faster than c. I don't think that this will happen, but can't find reasons to disprove it. Even if the recession is due to the expanding space between us, still I don't think that the relative velocity can exceed the value of c.

These two points are related, in a way you might not expect.

When you speak of "points" moving apart from each other, what could that mean? A "point" is an abstract thing. We can assign co-ordinates to space and time so that we can identify points by four co-ordinates (usually three co-ordinates for space and one for time), but they are still not real "things". It is a convention to identify where actual physical things happen; for identifying the location of a galaxy at the time a supernova explodes, for example.

You can also talk about the distance between points.

Locally, this isn't a problem; everything is as you expect. But when you talk about the distance between things over cosmological scales, it isn't quite so clear. There are different ways of defining distances, and you can't really say one is more correct than another.

The limit of the speed of light is a limit on speeds locally. Nothing can move past you at greater than the speed of light. But as for how fast a distant galaxy is moving away... it depends on how you define distance co-ordinates.

I personally like what is called the "proper" distance co-ordinate. Roughly speaking, it is the distance you would get if you add up the length of a whole bunch of co-moving rulers. But then we have to define "comoving"... basically that means rulers that are all expanding away from each other in the same way as galaxies.

Galaxies most certainly can have the distance between us and them increasing at greater than the speed of light, and this is not in any conflict with relativity, because it isn't the velocity of one thing moving past another.

We are getting into deep water here, and this may not have been the clearest way to explain it. When you say recession speed is proportional to distance, you are in fact using the proper distance co-ordinate... though it is the distance to where the galaxy is right now (same proper time) rather than where the galaxy was when the light left it. This relation, as you note, does indeed mean that galaxies are receding faster than the speed of light. This is true for most of the galaxies we can see out into deep space.

(And yes, light from these galaxies does eventually reach us, because the photons keep moving into regions where the recession velocity is less, and eventually into regions where the recession velocity is less than light speed... and from then is the approaching light actually getting closer, in the sense of being at a reducing proper distance.)

Cheers -- sylas

 

[Chalnoth]

2. Since the galaxies are receding away from each other and their recession speed is proportional to the distance from us, will it happen at any time that they will move faster than c. I don't think that this will happen, but can't find reasons to disprove it. Even if the recession is due to the expanding space between us, still I don't think that the relative velocity can exceed the value of c.

Well, the main thing to bear in mind here is that in General Relativity, the speed of light limitation is only a local limitation: no galaxy will ever outpace photons moving by it. But it turns out that far-away speeds are quite arbitrary, and you can define them however you want, so that you can pull up a velocity of a far-away object that is faster than c no problem. Or, you can change to a different coordinate system, and have that same velocity be zero. It is only locally that relative velocities are well-defined.

So yes, if you take the sort of "natural" coordinate system, with velocity being proportional to distance, eventually you reach a point where the typical recession velocity is greater than the speed of light. In fact, in this coordinate system, most of the galaxies we can see today are now and always have been receding at faster than the speed of light!

What this means physically is not that they've done something weird, but rather that a photon leaving such a galaxy, even though it travels towards us at the speed of light, has its speed outpaced by the expansion: it traverses some distance, but the remaining distance has already expanded by a greater amount, and so the photon actually loses ground. This explains why, for instance, the portion of the CMB that we can see today was emitted a mere 45 million light years away or so, and yet has taken some 13.7 billion years to get here. For a long time the expansion of the space between us and the photon was much more rapid than the photon could traverse said space. But, after it traversed enough distance, and after the expansion slowed enough, it started making ground, until it arrived here 13.7 billion years later.

 

[abhi2005singh]

This helped in the second question:
http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope"

But still the first one remains.

 

[abhi2005singh]

Actually from the above link, it seems that second option is the correct solution to my first question. Comments/suggestions/improvements from anyone?

 

[sylas]

Actually from the above link, it seems that second option is the correct solution to my first question. Comments/suggestions/improvements from anyone?

Yes, I think you are on the right track here.

But just as a caution... did you get the point that defining co-ordinates is a somewhat arbitrary? There are various ways to define co-ordinates and distances, and what numbers do depend on what co-ordinates you decide to use.

The rubber hose example can sometimes be misleading, if you end up thinking of space as being like the fabric of a hose dragging things along for the ride; but apart from that it can be useful. Previously I spoke of the "proper distance" co-ordinate. This would be the normal sense of distance which is used to measure the length of parts of a hose as it is being stretched. An ant traveling at a fixed speed relative to the hose is a lot like a photon moving at speed c as measured at at any given point along its journey from one galaxy to another.

So yes, when you use the proper distance co-ordinate, the second option is correct. Points (attached to galaxies) which were at x = -10 and x = 10 will in time be at x = -20 and x = 20, and so on. The distances increase as the universe expands.

Furthermore, as you have correctly observed, this means that the distance to some galaxies is increasing at greater than the speed of light. This also means that a photon coming towards us from that galaxy is actually getting further and further away, as measured using "proper distance", because although the photon is moving at c, it is in a region of space where the proper distance to that region is increasing at MORE than c, so the photon is actually getting further away. However, like the ant on the hose, the photon will still get here eventually. Mathematical analysis is given in your link.

At the risk of confusing you, there is also another co-ordinate called "co-moving distance", and by that measure, galaxies remain at the same co-moving distance, so using that co-ordinate points at x = -10 and x = 10 remain at that co-ordinate distance as expansion occurs. The co-moving distance co-ordinate is analogous to a grid marked out on the stretching hose, and so points "on the hose" (or points attached to galaxies that are receding with the Hubble flow) remain at a fixed co-ordinate. That gives your other solution, but now velocities defined using this co-ordinate may be unexpected.

The velocity of the ant, if defined using this co-ordinate, is no longer fixed. Using the usual notion of time, the velocity as change in co-moving distance per unit time is continually reducing. Cosmologists sometimes also use a special time co-ordinate called "conformal time", which keeps the speed of light the same. I do not recommend using such co-ordinates until you learn a lot more about the details of maths of expanding spaces and the FRW solutions and so on.

For the time being, you are on the right track to think of points in space at x = 10 and x = -10 later being at x = 20 and x = -20 as the universe expands. Proper distances are increasing.

Cheers -- sylas

 

[abhi2005singh]

To sylas and Chalnoth.
Thanks a lot to both of you for your clarifications of my doubts. It helped a lot.