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How did we get here before light from this cluster did? Even given a few moments of hyper-expansion immediately after the Big Bang -- which may have given us a bit of a head start on the light -- how could all the mass in the Milky Way and beyond have gotten here before it, especially since, from "our" point of view, the light has been closing the gap at c, and started closing the gap 13.5 billion years ago when the universe was much smaller than it is today?

The trick is that the different observers will disagree on the size of the gap, thanks to relativity.

Let's start with a "neutral" observer, who is equidistant between the Earth and the distant cluster, and with respect to whom they are moving at equal and opposite velocities. What does he see?

At some distance between the Earth and the cluster, the cluster lets out a pulse of light. (We will also assume that the observer sees the Earth let out a pulse of light towards the cluster, at exactly the same moment.) The light moves towards the Earth at a velocity c. In the observer's rest frame, the time it takes is much larger than the initial distance divided by the velocity. This is because the Earth is moving away from the cluster; the light is trying to hit a moving target. By the time the light catches up to the Earth, it has moved a considerable distance. Even Newton would have understood this.

But what does it look like from the Earth's point of view? Well, that's very different. There are a number of post-Newtonian concepts at work here. I'll spare you the math, but trust me, it works out.

First of all, the distance from the Earth to the cluster, at the moment the Earth lets out its pulse, is actually shorter (yes, shorter) than what was observed by the "neutral" observer. (I'm assuming that all observers correct for the finite speed of light when making distance calculations, of course.) This is because of the Lorentz-Fitzgerald contraction along the direction of motion.

Also, as you know, the light is also moving at c with respect to the Earth, whereas Newton would have expected a smaller velocity (using Galilean relativity). Both of these factors make it seem like the light should get here in short order.

But that assumes that all observers will agree upon the time that the pulse is released. In reality, that isn't so. Two events that are simultaneous in one frame of reference will not be simultaneous in another. In this case, from the Earth's perspective, the pulse of light does not get emitted by the cluster until well after the Earth sends out its pulse.

From the Earth's point of view, events are unfolding much more slowly on the distant cluster, even after you correct for the Doppler effect (finite light speed). This effect is called "time dilation".

There are parts of the universe that are moving so quickly away from us that, even though we were only a tiny distance apart at one time, they haven't had time to begin forming material objects. In that part of the universe, from our point of view, the Big Bang is still going on. And in those references frames, at a time when there are galaxies and worlds in those places, the Earth hasn't yet had time to form.

(I stress that that isn't an illusion of perspective; I'm assuming that we compensate for the finite speed of light. What I'm making is a point about the nature of time itself.)

Thank you so much for taking the time to write such a thoughtful, and thought-provoking, answer to my question. I shall think long and hard about the things you've said.

The first thing I'll have to convince myself of (Aaargh! Shades of Halliday and Resnick!) is that there is a point midway between here and there for which Here and There's velocities are equal and opposite. When I think about two guys running in opposite directions, I don't automatically see that that is true. But I'm sure for galaxies, it is true since you said it, and it's up to me to work out the details.

Also it's very interesting to me that you've mentioned, in effect, the relativity of the time-order of events, which when I first saw the proof, almost destroyed my belief that the universe was a rational place. I mean, can everyone imagine, you can indentify a frame of reference for which John Kennedy died before Lee Harvey Oswald pulled the trigger? And that that frame of reference, and the view of the world you get from it, is as legitimate as our own? In other words, you can mathematically prove that Oswald is innocent!

Physics is truly, truly, a marvel. And I say that without an nanogram of sarcasm, only wonder.

Physicist, if you don't mind. Is this right? If 2 objects, Earths(E), are traveling apart at some speed v, then the clock frequency(or rate of the clock ticks), f₁ that one object E₁(our Earth) sees for the other clock,f₂ on E₂ is:

f₂=f₁1/sqrt(1-v²/c²)

If the doppler effect is thrown in to measure the clocks moving away from E₁, then the equation is:

Where f is now the frequency of light observed.

f₂=f₁sqrt(1-v/c/1+v/c).

In the early universe the rate of the debris flying apart must have been rather low, the debris was close together, the temperature was high and the light each particle of debris was not redshifted(because of the slow relative expansion and rough temp. equilibrium). The universe continued to expand and cool, but this must mean the debris has been continually accelerating from each other

That acceleration must occur along with the cooling that is occuring in order for the radiation seen from receding objects to redshift, or in other words the clocks on the receding debris appear to run slower. Since they both underwent the same acceleration the clocks on E₁ and E₂ actually run at the same rate, but to a person on one E, the other E's clock appears slow. LibW, light, or radiation has a frequency that depends on the rate of oscillation of some charges emitting the light. If the oscillator slows to a new rate(in quantized jumps), light is emitted at the difference of the 2 fs. Light is absorbed if it is the right f for a possible vibrational change. The oscillators are the clocks and their clock rate, vibration rate, depends on the temperature.

Because of the expansion and cooling the clock rate should appear to decrease and it does. The Lorentz time dialation eq above shows this means the Es are accelerating apart. That means as the universe ages and folks on E₁ look at E₂ they are looking back in time, since the clocks on E₂ appear to run progressively slower. The guy on E₂ sees the same for E₁. This effect of looking back in time is more than just the time lag for the light to travel the distance.

Since the universe is now ~4^oK, f₂ is about 10¹¹ and at the beginning of the universe it was 10¹⁷(guesses). From the Lorentz eq the relative speed the Es are receding now is ~0.999999999999c(c=speed of light). Such speeds would have been impossible in the early universe, or the temp. and energy exchange would have been much different. Although the debris must have picked up speed quickly and the temp. dropped the same way.

With the edge of the universe gaining mass like it is from continuous acceleration twords c, are we inside a friggin' black hole yet? LOL! I'm going to jump on my Harley now, it's the acceleration that keeps my clock slow and my heart young. Thanks