Analogy for recession of galaxies > the speed of light

[osotou]

For a lay person such as myself, it's very easy to get confused and stumble around a bit, trying to understand how galaxies can be receding greater than the speed of light when the speed of light is the cosmological speed limit. It's easy to make the mistake of saying 'Ha! There are whole galaxies breaking the law'. I'm trying to develop a bit of intuition for this. I take it that I should understand that expansion doesn't grant motion. I like the balloon analogy, it's helpful but I have trouble getting past the roundness of a balloon. So, I tried imagining something flatter and went for a pair of nylon stockings in the wife's bureau. Imagining grains of sand stuck to the threads as galaxies and stretching the fabric, it's easy to get a sense for how celestial bodies keep their coordinates and the laws of physics are preserved. It's just the metric of those coordinates that is changing .. no 'new' energy or motion. Am I on the right track, or just out there flapping?

 

[Bandersnatch]

No, it's good. Like all analogies it's got its problems if you can't get past the unimportant bits (like the existence of the edges, or what is pulling on the edges, or the rate of expansion), but to visualise the expansion as such it's all right. It's even got the threads in the stockings acting like comoving coordinates.

To get one's head around the speed of light issue, one can always consider a light beam traveling through the expanding space in either analogy. There's never any possibility of any other object traveling through such space to overtake the light beam - it's the local speed limit. That some faraway galaxies recede faster than the beam could ever move has got nothing to do with travelling, but, as you said, is just a matter of changing metric.

 

[osotou]

No, it's good. Like all analogies it's got its problems if you can't get past the unimportant bits (like the existence of the edges, or what is pulling on the edges, or the rate of expansion), but to visualise the expansion as such it's all right. It's even got the threads in the stockings acting like comoving coordinates.

To get one's head around the speed of light issue, one can always consider a light beam traveling through the expanding space in either analogy. There's never any possibility of any other object traveling through such space to overtake the light beam - it's the local speed limit. That some faraway galaxies recede faster than the beam could ever move has got nothing to do with travelling, but, as you said, is just a matter of changing metric.

I guess to make my analogy more clear, I'll liken the threads to transmission cables that can be infinitely stretched and infinitely woven. The 'stretching'? is the metric - all bodies keep their cosmic address within the region of their local motion upon the fabric. Information about the energy of these bodies, in the form of light is transmitted across the network at a constant speed and happens regardless of the rate of expansion of the transmission cables. So the cables, or threads may stretch such that it would take an eternity to receive the signal?

 

[rootone]

Think of a duck swimming downriver.
The duck definitely has a maximum speed at which it can swim through water.
The water in the river is also moving at a given speed relative to you standing on the riverbank watching this.
From your perspective the duck might appear to moving impossibly fast, but it is not in fact exceeding the maximum speed of a duck.

 

[Chalnoth]

For a lay person such as myself, it's very easy to get confused and stumble around a bit, trying to understand how galaxies can be receding greater than the speed of light when the speed of light is the cosmological speed limit. It's easy to make the mistake of saying 'Ha! There are whole galaxies breaking the law'. I'm trying to develop a bit of intuition for this. I take it that I should understand that expansion doesn't grant motion. I like the balloon analogy, it's helpful but I have trouble getting past the roundness of a balloon. So, I tried imagining something flatter and went for a pair of nylon stockings in the wife's bureau. Imagining grains of sand stuck to the threads as galaxies and stretching the fabric, it's easy to get a sense for how celestial bodies keep their coordinates and the laws of physics are preserved. It's just the metric of those coordinates that is changing .. no 'new' energy or motion. Am I on the right track, or just out there flapping?

First, the speed of light limitation is a local limitation: no object can outrun a light beam.

That said, here's a picture of precisely how this occurs.

1. In the early universe, the rate of expansion was much faster. This meant that objects had to be much less far away to have a recession velocity faster than light.
2. For any object with an FTL recession velocity, the light ray traveling in our direction will be getting further away over time, as more space will be created between us and the light beam than the light beam can traverse.
3. However, the rate of expansion slows down: after the light ray has been traveling for long enough and is close enough to us, then the slowing rate of expansion will allow the light ray to start gaining ground, eventually reaching us (that is, it will make it past matter that is no longer receding from us faster than light). The recession velocity of the galaxy at this point is irrelevant, because the light ray left that galaxy long ago and its behavior isn't dependent upon what the galaxy did after it left.

The slowing of the rate of expansion is a critical point here: if the rate of expansion had never slowed, then we could not observe any objects receding at faster than the speed of light.

 

[phinds]

You might try the balloon analogy discussion linked to in my signature. I think it's more helpful than the raw analogy.

 

[osotou]

You might try the balloon analogy discussion linked to in my signature. I think it's more helpful than the raw analogy.

Yes, and Thank you! I read it and it was very helpful. And I'll for the moment (hopefully wisely) shy away from exploring metric expansion, although I was reaching for it in my analogy. It's enough to know that it's there for the moment ... I've a deep dread that the metric itself is fractal, so yeah, I'll wave my hands furiously at it for now. It's enough for me to think of a penny stuck to a balloon or grains of sand glued to the threads of the wife's stockings.

 

[rootone]

You might need to get your wife's opinion about that.

 

[osotou]

You might need to get your wife's opinion about that.

Funny! No stockings were actually harmed. I didn't glue any sand on them, honest! As a matter of fact all the stockings she has in her drawer have runs in the fabric .. well that would require a new thread altogether! Don't know why she keeps them, why does she keep them?