[Atomic-S (OP)]

According to the most current ideas, the universe is so many billion years old.  But according to Einstein, time is relative to the observer.  So the question arises:  according to what observer is this so?

[Pmb]

This age refers to time as measure in the frame of reference in which the net momentum density of matter as measured on a megascale has the value of zero. In our frame of reference this is the case. Our motion relative to that frame is so small as to make no relevant contribution to the estimated age. Think of it as the frame of reference in which the 3K background radiation is isotropic (i.e. has the same value no matterwhere you look). Our frame is very close to that. There is a very small bias towards one direction and that's accounted for by our motion in our galaxy which is moving relative to that frame.

[Bill S]

Pete, would you please explain "momentum density"?

[Pmb]

Pete, would you please explain "momentum density"?

It's what you'd thing it is, momentum per unit volume. Think of a stream of water. Select a portion of the water in the string. Find it's mass and its velocity. Divide the mass by the volume and you'll have the momentum density. There are two factors of gamma, one for mass increase and one for volume decrease. Therefore the momentum density, often represented by the vector g is defined as g = gamma^2 v. Hope that helps!

See also http://home.comcast.net/~peter.m.brown/sr/energy_momentum_tensor.htm

[Bill S]

Thanks Pete, it does help. I was quickly out of my depth with the link, but that is a feature of my major weakness - lack of maths.

Why couldn't I have got interested in something that didn't need so much maths?  Knitting, watching TV or "goin' dahn ther pub, perhaps.

[Pmb]

Thanks Pete, it does help. I was quickly out of my depth with the link, but that is a feature of my major weakness - lack of maths.

Then you're in luck. I'm looking for people just like you to advise me on learning new ways to help people understand math. Are you willing to help me by learning more math?

[Bill S]

Are you willing to help me by learning more math?

I would be glad to.  I'm quite heavily committed in a caring role, so time is often very short, but I'll certainly give it a go.

[Atomic-S (OP)]

Think of it as the frame of reference in which the 3K background radiation is isotropic (i.e. has the same value no matterwhere you look). Our frame is very close to that. There is a very small bias towards one direction and that's accounted for by our motion in our galaxy which is moving relative to that frame.

So does this mean that the universe, after all, does have a means for defining an absolute state of rest? That is a novel idea (and also an ancient one).

[Bill S]

As I understand it, it is possible to establish motion relative to the CMBR, and this will be related to the concept of comovement.

The rate of separation of the galaxy groups is proportional to the rate of expansion of the Universe.  Thus, if the distance between them is considered as a proportion of the size of the Universe, it remains constant.  The galaxy groups are, therefore, comoving.
 
A corollary of this is that everything in the Universe is comoving unless it is moving in such a way that its motion is independent of the expansion of the Universe.

The relevance of comoving coordinates to the CMBR is that a comoving observer will measure the CMBR as isotropic, whereas a non-comoving observer will see a blueshift in the forward direction and a redshift in the other.

In this way, an observer can claim to be stationary, or in motion, relative to the CMBR, but this says nothing about absolute motion or non-motion.

[flr]

According to the most current ideas, the universe is so many billion years old.  But according to Einstein, time is relative to the observer.  So the question arises:  according to what observer is this so?

If time is relative, the age of Universe is relative to observer. For us is 13.7 billions and for an extremely energetic 'o my god' particle the age of universe is (to my estimation) about 2 weeks.

[Bill S]

wait for it!  Someone's going to ask if, for a photon, the Big Bang is happening now. 

[yor_on]

I think you got a good point there Atomic. What would a thought up observer close to a event horizon define as the distance and age of a universe? Knowing about relativity he should be able to get a same answer as us, but not knowing? It depends on how you think of it, I think

If we assume a commonly shared universe in where time dilations and Lorenz contractions are solved through Lorentz transformation we also get a universe that only can exist in a theoretical description. If we go by 'what you see is what you get', though? Then a universes age should be observer dependent, as measured by your local arrow. This is assuming that we near a event horizon both will find a universe shrinking as well as time dilated. And that one is the equivalence principle to me, in where you can exchange the event horizon (non rotating black hole) for a constant uniform acceleration. Although there must be a difference in that constant acceleration as it brings with it a constantly added 'motion', just as different uniform motions should present us with different time dilations and Lorentz contractions, as I understands it then. The event horizon though does not have this effect of a continuously added 'motion', as far as I can see? But it must still shrink a universe as measured locally, and make that universe time dilated relative ones local clock (at the event horizon), to fit my thoughts and what I think of as the equivalence principle.

If I would assume that all clocks have one 'common rate', locally measured, as proven by you joining whatever frame of reference you find time dilated before merging with it, you get a definition of a arrow as the one thing locally unchanging, with what you measure between frames of reference (that 'outside' universe as it is here) becoming 'plastic', its parameters changing with relative motion and accelerations, mass 'energy'. And that would make the parameters distance (Lorentz contractions) as well as time dilations 'illusionary', if I instead define it from having a locally constant arrow, equivalent to 'c'. Alternatively you can define it as 'real'. (But that is just another way of saying the same, because if it is real, for you locally measuring, then a time dilation and a Lorentz transformation is a description from our preconception of that 'commonly same universe' in where we expect us all to exist.)

The other way to see it is to define it such as you with different mass would get a locally different arrow, your proper clock 'ticking' slower, distorting the universe you observe 'outside' your gravity well. But if you can't measure it locally, and you can't, then this view moves from the measurable to the theoretical. There are other objections one can make about that point of view but I find that one important. We measure locally.
=

Furthermore the first assumption (a constant arrow) makes uniform motion into something in its own right, making it something more than just a 'relative motion', in a binary system equivalent to being still depending on how you formulate that motion, as belonging to you or to the other object. So using the first definition 'motion' becomes something real, no matter if it is accelerating or not. But it also becomes something different than what we normally think of when something moves relative us, that as the binary description still is valid. You can define yourself as unmoving in any uniform motion, for example measuring a light bulbs red and blueshift inside a 'black box' (ignoring tidal forces), and there is no inertia informing you otherwise, no matter what 'speed' you define relative something else outside that box.