You got it. Time is part of the Universe, and did not preëxist it.
As for the surface of last scatter, that does put a practical limitation on how far back we can see, that’s more restrictive than the age of the Universe. It’s not very much more restrictive, though… The Universe became transparent to light only a few hundred thousand years after the Beginning. And the surface of last photon scattered is not an absolute barrier: If we had the instruments (we’re building some of them right now), we could see somewhat further back in neutrinos, and much, much further back in gravitational waves (down to about 10[sup]-26[/sup] of a second, or so).
I’m not sure why this is so puzzling. Thanks to all of the smart folks who worked it out for us it seems pretty straightforward.
The velocity with which objects are receding from us is computed from the red shift, z, by the formula:
v = c*{(1+z)[sup]2[/sup] - 1}/{(1 + z)[sup]2[/sup] +1}
It’s pretty clear that as z gets bigger and bigger the fraction on the right that multiplies c gets closer and closer to 1 as a limit. So the maximum recessional velocity we can measure is c.
If we divide this velocity, c, by Hubble’s constant, H, we get the distance to the object in light years and the age of the universe in years.
Squink gave a value for H of 73500 ± 3.2 km/sec/parsec in Post #47/
Using that value for H and converting it to m/sec/light year and c = 3*10[sup]8[/sup] meters/sec we get for the smallest H
H = 0.0216
age in years = 13.92 billion
and for the biggest H
H = 0.0235
age in years = 12.76 billion years.
which is the maximum age we can measure unless Hubble’s constant changes.
According to Wiki the highest red shift measured so far is a quasar with a shift of 6.4. That object is receding from is at 0.964 c.
It’s a little more complicated than that, David. First off, Hubble’s “constant” does change over the life of the Universe, and not necessarily in a straightforward way. If we divide c by H, it give a decent first-order estimate of the age of the Universe, but that’s assuming that everything has always been moving at the same speed it is now. But it hasn’t: Gravity is slowing everything down, and the dark energy is speeding everything up, and which is more significant changes over the evolution of the Universe (currently, and presumably for the rest of time, the dark energy appears to be dominant, but at an earlier stage, normal gravity would have been). In order to get the age from H, you need to know what H was at every stage of the Universe’s development (which probably takes a bunch of other cosmological modelling), and then throw some calculus at it.
Second, just because the Universe is 13.7 billion years old, doesn’t mean that the most distant objects we can see are 13.7 lightyears away. The light from them has travelled a distance of 13.7 billion lightyears, but meanwhile, they and we have continued to move apart. When the light was emitted, the distance was significantly less than 13.7 ly, and now when it’s received, the distance is significantly greater than 13.7 ly.
All true which was my motivation in putting in the cowardly statement that 13.7 billion years is the maximum we can measure unless Hubble’s constant changes.
Humans living in the future time just before the sun starts to swell to a red giant might very well make entirely different measurements.
I think you’re still misinterpreting. It doesn’t just matter what H is now; the entire history of what H has ever been is important. There are actually cosmologies, for instance, in which H really is a constant, and in which the universe has an infinite age. Our own Universe does not appear to be governed by such a cosmology, but it does seem to have some features in common (such as the existance of a cosmological constant or vacuum energy), so it’s still quite possible that our Universe is currently older than one over the current value of the Hubble constant. For that matter, it’s also possible that it’s younger, too, although that does not currently appear to be the case.
