Re: The frame of reference concerning the timeline of the big bang

Hmm - that's a good question!

There's no need to go back to the Big Bang to think about it; the Universe is still expanding today, and so we could look at modern galaxies (we've observed quasars that are moving away from us at 95% of the speed of light!), and indeed "time passes slower" in those galaxies, as seen from Earth. Astronomers can see this time dilation in the form of slower types of radiation; an atom that would emit blue light on Earth will appear red or infrared when it is time-dilated like this, so astronomers call the effect "redshift," and it's ultra-important in all types of astronomy. So time dilation indeed occurs; how to we deal with timelines?

The timeline you've described would apply to every point in space, in the "local rest frame" of that point. To illustrate: Bob can sit in his spaceship with a thermometer and a stopwatch; he can watch time go by (in his local rest frame) and watch the temperature go down. Sally can sit somewhere else in the Universe and watch her own local clock, and her own local thermometer, and draw the same timeline. Both timelines will be the same!

What if Sally looks over and tries to observe Bob's ship? She'll see his clock apparently running slowly, due to the redshift---but she'll also see the temperature of Bob's ship drop slowly. The local patch of space that Bob's ship is sitting in---including any gas, or radiation, or whatever, that he can measure the temperature of---is moving right along with Bob's ship, and will be redshifted and slowed in the same way. (She should not, of course, compare Bob's temperature drop with her own clock! But she doesn't need to, she has her own temperature to measure.)

This is an important feature of the expansion nature of the Big Bang; Bob doesn't have to accelerate his ship to "keep up with" gas and radiation rushing past him. Rather, he sits still among the gas and radiation, and the Big Bang causes the space around him to expand. So any given patch of space will have a perfectly-reasonable local rest frame, and a consistent set of measurements of stuff within that rest frame. You can measure the temperature, you can measure particle densities and ionization states. You can measure (with your local stopwatch) how long it has been since the big bang---and of course you're not time-dilated with respect to yourself, so you do not need to think twice about your watch. This would be the "age of the Universe" ... that's an oft-discussed quantity, but it can be confusing to describe, if you compute it by looking at very distant galaxies (redshifted, time-dilated, and giga-light-years away).

Now, these may sound like impractical thought-experiments, a la "imagine you're in a windowless elevator with a rotating black hole," but let me assure you they are not.

For example, is the Earth in its own big-bang local restframe? No! Whereas the particles that now make up the Earth were originally co-moving and "at rest" with respect to the expansion of space, since then they have been buffeted by many forces (gas pressure, radiation pressure, gravity) and we're now moving slowly with respect to our Big Bang rest frame. How can we tell? By doing a local measurement---sticking a thermometer out the window, so to speak. We're surrounded by photons, photons which have not been buffeted by any forces, not since shortly after the Big Bang. We can do a local measurement of these photons (known as the "cosmic microwave background" or CMB photons), which tell us the current local temperature. A small asymmetry in the photons---they're a bit hotter towards Constellation Virgo, a bit cooler opposite---tell us that the Earth is moving at 600 km/s through the local CMB! (The CMB is one of the hottest fields of cosmology today!)

Hope this helps!

-Ben Monreal

[One might wonder, though, how do we go about finding out the temperature of the CMB photons at other places in the Universe? We can look at distant clouds of gas. The spectrum that we see from these distant clouds of gas depends in part upon their temperature. If we know how far away these clouds of gas are, we can calculate how hot the CMB photons should be. (Remember looking out into space also means looking back in time! so at large distances the CMB photons should be hotter, if the Big Bang model is correct.) We find that, indeed, in other parts of the Universe the CMB photons are a temperture consistent with what we measure in our local reference frame. An example is some recent observations toward the quasar PKS 1232+0815. Moderator]