chroot said:
The General Theory of Relativity indicates that time is an essentially local phenomenon. There is no consistent way of defining a specific moment in time -- "now" -- that applies everywhere in the universe.
- Warren
Warren is right, there no one single officially-approved way to slice the 4D loaf into slices of "now".
But practically speaking, astronomers
do have slicing that they tend to use a lot. It is only defined approximately and we don't know the ultimate extent of applicability, nevertheless it's quite handy, almost indispensable. Sometimes called "universe time" or "cosmic time".
It depends on the standard cosmo model, the Friedman model, that virtually everybody uses. Also can be called FLWR (Friedman, Lemaitre, Robertson, Walker). Derives from General Relativity after some simplifying assumptions are made like matter is approximately uniformly distributed. Or FWRL, whatever, or FRW. The standard expansion model universe.
The point is that the universe is full of microwave radiation which keeps getting cooler as the universe expands and so the
Background temperature can be taken as a clock.
Our "now" consists of all the observers who see the same temperature we do. Each observer sitting on his own rock somewhere in his own galaxy, holding a thermometer to the sky. (Or a microwave antenna measuring wavelengths, same thing.)
All the observers who measure 2.728 Kelvin, like we do, are part of our "now". They belong to our "slice". That is our timelike hypersurface---a 3D slice of the 4D loaf that gives a geometrical meaning to simultaneity.
Or maybe it is 2.726 Kelvin. The trouble is measurements are always fuzzy and approximate anyway.
And we have a criterion of
rest. An observer is at rest if he measures the approx. same Background temperature in all directions. If he is moving at some substantial speed he will see a Doppler hotspot ahead of him, where the microwave background temperature is hotter, or the wavelengths shorter, because of his motion relative to the Background.
The Hubble Law which is basic to standard cosmo uses these ideas of Now and Stationary Observer. It says that distances between stationary observers are now increasing at a rate which proportional to what the distance is now.
v = H d
d is the distance now. v is the current rate that the distance is increasing----in kilometers per second or whatever units are convenient. H is a proportionality factor (which is the same all over the universe now, but which changes gradually with time.)
Occasionally cosmic time or universe time is called "Friedman time" because it is the time according to which the standard universe model runs. And most often astronomers simply say "time" without clarifying----they just assume you know what they mean.
Like, "the light from that galaxy was emitted when the universe was 3 billion years old and has been traveling for 10 billion years, and it got here to our telescope yesterday". Statements like that typically assume we are using a Friedman clock.
So in pure General Relativity, with no simplifying assumptions and no nice Background radiation, there truly is no preferred time. Each observer has his own personal, or "proper" time, which is his own "property" so to speak. Which is great. Total anarchy. But for practical purposes, working cosmologists cheat and keep this informally preferred time around, and the corresponding idea of being at rest (with respect to the ancient matter and the ancient light of the universe) because it's so useful.
If you like simple differential equations and want to see one that governs the growth of largescale distance, the keyword would be "Friedman equations" or Friedmann with two Ns.
