# Gravitational waves, distance and space-time

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1. Feb 17, 2016

### tim9000

So the discovery of gravitational waves observed a contraction and stretching of space-time, and I've been trying to understand how the expansion of the universe means that space itself is growing.
I want to understand how this actually works in relation to 'things' like a photon and an atom.
Like take an atom at a fixed point in time.
I understand that a photon has no concept of time from it's reference frame.
But as space expands how does this affect 'distance' as we understand it in relation to the atom? I imagine that sub-atomic particles are of a fixed size and do not grow with space-time as the universe expands. So does a planck length inside an atom grow, or stay the same? Because as far as I'm aware light gets stretched as the universe expands, and I know that a planck length is based off light and time, but I don't know the end ramifications.

Thanks!

2. Feb 17, 2016

### andrewkirk

Things don't get bigger under the expansion of the universe (google 'Brooklyn isn't expanding'). They just get farther apart.

In some cases they don't even get further apart - for instance if they are tied together by electromagnetic forces or string. But galaxy clusters are tied to each other by neither of those, so they get further apart.

We can't talk meaningfully about units of length like a Planck length getting bigger. For that to mean anything, we'd need to measure them 'before' and 'after', and what can we use to measure them other than a unit of length? An object or wavelength cannot be longer than itself.

3. Feb 17, 2016

### tim9000

I'm somewhat familiar with 'recession' and 'proper movement', and bound systems.

But the light gets red-shifted between leaving the galaxy and reaching us, presumably the light is the same frequency as far as it's concerned, but the distance got bigger?
I understand you want to compare instants in time, but I mean like the equation that denotes a planck length, there must be term(s) in it changing due to the expansion of the universe?

Thanks

4. Feb 17, 2016

### andrewkirk

No. The Planck length is defined as the wavelength of light with a specified frequency. Light which is emitted at that frequency and, after a long journey undergoes significant cosmological redshift, is no longer at that frequency and hence no longer corresponds to the Planck length.

5. Feb 18, 2016

### tim9000

Sorry, just humour me, so is that to say A planck length has a value when the light leaves, then much later when the light arrives cosmologically red-shifted, a planck length is different in reference to the length when it first left? For us a Planck length isn't changing, but for the ancient light it is?

I don't understand how 'the vacuum' of space-time is expanding cosmological, but what does that mean? Theoretically more weird particles like gravions and the thing of whatever the 'time' part of space-time, is/are stretched into existence?

6. Feb 18, 2016

### andrewkirk

Reflect on what you mean when you use the words 'a Planck length' in this quote. It sounds like you are thinking of 'a Planck length' as a physical object, like a stick or an atom or part of a beam of light. It isn't any of those. A Planck length is a unit of length, with the same status as a metre or a second. It is an abstract, non-physical concept. To ask what is the length or value of a planck length is like asking what is the name of my name. Remember that marvellous scene in Through the Looking Glass when Humpty Dumpty tells Alice in succession, what the name of the song is called, what the name of the song is, what the song is called, and what the song is, and each of them is different?

What we can say is that, when light is emitted, with a wavelength of say $10^{25}$ Planck lengths, many thousands of years later, its wavelength will be longer than that, say $1.5\times 10^{25}$ Planck lengths, and the frequency is commensurately lower.

7. Feb 18, 2016

### tim9000

Unfortunately I only saw the first scene of through the looking glass, and I've never read it.

I'm so confused I don't even understand my own question, let alone how to contextualise it. I accept that a Planck length or the meter itself isn't changing, but
If the universe was perfectly stationary than the frequency of the light wouldn't change (I assume) on it's way. But it does as the universe expands. Somehow some distance has gotten longer, apparently not the units we measure distance with, but the vacuum itself. If you had a big blob of jelly/'jello' and you induced a ripple in it, and you stretch the big blob I suppose you'd stretch the ripple too. So doesn't that indicate something related to 'space' or space-time is actually growing, rather than 'the nothing is getting bigger'?

8. Feb 18, 2016

### Chalnoth

The Planck length is defined in terms of the fundamental constants, which are measured in a wide variety of ways. So far as we can tell, all of the fundamental constants have remained constant to well within a percent for the history of our universe.

9. Feb 18, 2016

### rede96

I think your confusion might be because you are thinking of 'space' as something that expands. It doesn't. 'Space' is not a physical thing. People often use the term space is expanding, but what they really mean is the distances between things such as galaxies is getting larger due to them moving apart from each other.

Another thing that used to really confuse me is when I hear things like 'the wave length of a photon gets stretched with the expansion of space' as it doesn't. At least not in the way you are thinking about it as expanding space having an effect on the photon.

As I understand it, the wave length a photon doesn't change as it travels through space. (I am leaving out dark energy for now) The cosmological redshift you mention is caused by something different. In very layman's terms cosmological redshift is because of the different direction of two distant objects in space-time.

Have a read of these two posts here and here, they might help.

10. Feb 19, 2016

### Jorrie

I think this is a matter of interpretation; the physical fact is that the photon at the receiver is measured to have a longer wavelength than the photon had as measured by the emitter. Another, perhaps more 'natural' interpretation, is that the two observations are made in different inertial frames and in the cosmological case the difference depends on the spacetime curvature. Dark energy would not make a difference to either interpretation, I think.

11. Feb 19, 2016

### rede96

Thanks for that, I'm really just a layman so don't fully understand the workings, but guess the point I was trying to make is that 'space' isn't responsible for cosmological red shift and that if two distant objects were at rest wrt each other, then there would be no red shift for a photon transmitted between them as I understand it.

I really have no idea if dark energy would make a difference or not. My rationale was that it might. Dark energy does effect mass of course, in that it has a repulsive force causing the rate of acceleration to speed up. So therefore I assumed it must effect energy too and hence may have some small effect on a photon travelling through space.

12. Feb 20, 2016

### Chalnoth

The only effect of dark energy comes through how it impacts the curvature of space-time. There are two main ways it does this:
1. It impacts the rate of expansion. The rate of expansion today is faster than it would have been without dark energy. The photon is affected by the total amount of expansion between us and the source.
2. It causes large gravity wells to slowly decay. A photon entering such a gravity well picks up a blueshift, and then is redshifted as it leaves. But since the gravity well is shallower by the photon leaves, there's a net blueshift. This is known as the Sachs-Wolfe Effect. It's mostly only relevant for CMB photons.