Main Question or Discussion Point
This may be a dumb question, but if the universe is expanding and time can be treated as just another dimension, does this mean that time is 'expanding'? And if so, what the heck does that mean?
Fair enough, I'm still puzzling over the time dilation thing, and I thought this might be related.In standard cosmological coordiantes, time is not expanding. You could use coordinates in which one interval of coordinate time corresponded to different amounts of clock time, but there is no reason to do so.
Hmm. I thought maybe the... rate of expansion with regards to space might be related to an 'expansion' of time. But now I guess I'm muddling in the whole time slowing down as you get closer to the speed of light thing. Damn its easy to get bogged down in analogies.There is a good reason to use coordinates in which an object from which the universe appears to be stationary with respect to the CMB has constant spatial coordinates, however. These sorts of coordinates have the property that the distance between objects with static coordinates expands as a function of time.
Not a dumb question, but let’s split it into 3 parts.
Part 1 - ignoring expansion of universe, time dilation and quantum mechanics:
1 and 3 are agreed.Part 2 - concentrating on spatial expansion of universe
Yes, but this example is not really 2d, if you're talking about a balloon. Maybe I'm abusing the example, but if the 2d space is expanding and the galaxies are moving apart, isn't the air filled part of the balloon equivalent to the past points in 'time'. The galaxies move apart as time progresses, as the balloon expands, but if the past still exists.... I suppose maybe in your example the present is all that exists... hmmm... that 3rd 'balloon dimension' is I guess what I'm thinking of.2. The 2d analogy (or parable) is that of an expanding balloon with small paper discs stuck on the surface. The discs are the galaxies (held together by their own gravity) that do not expand, while the space between them expands. So the recession of further galaxies is faster than that of nearer galaxies (Hubble effect or cosmological red-shift).
Yeah, this part I need to read more on for sure.Part 3 - time dilation due to observing receding objects.
1. This is the stuff of standard Special Relativity course. There is an analogy with the Doppler effect with sound in air - but be careful as there is no corresponding medium for light (other than space-time itself). You may find the following helpful http://www.csupomona.edu/~ajm/materials/twinparadox.html [Broken]
2. The above red-shift is nothing to do with the cosmological red-shift of part 2 which is a GR effect.
3. Neither is it anything to do with gravitational red-shift due to light ‘climbing out’ of the sun or massive body - which is yet another GR effect.
Heheh, regardless, thanks a lot. I'll be thinking about this for a while.Cautionary note: I have had these ideas so long now that they have become ‘common sense’ to me - and you know that Einstein did not think too highly of that.
This makes me think of it more as an expanding ripple of water, that is flattening at the same time, ultimately causing a loss of surface tension and therefore accelerated expansion.6. Since the 1990’s there has been evidence that the universe expansion is not slowing down, but accelerating. This implies an ‘open’ universe. I gather the problem of the no-boundary is explained by it being beyond the ‘visible’ universe (i.e. light can’t reach us from beyond this ‘boundary’ anyway) - again I am out of my depth. It turns out that even in this open (parabolic) universe - forget the balloon, just consider 3 ordinary dimensions expanding - the further away galaxies are, the faster they separate. The Hubble ‘radius’ is then a bit more abstract.