God is sitting on a photon, straddling it and looking backward. Since He's God, He doesn't look in the traditional sense in that He doesn't require photons impinging on His retina to register an image; rather, He just focuses His omniscience on something. This is all a fancy way of saying that I don't want to hear arguments about the limitations of vision since they're irrelevant anyway.

Specifically, He's looking at another photon some distance behind Him traveling in the same direction as the one He's sitting on. Does He see the other photon catch up with Him?

Special relativity says that the speed of light in a vacuum is constant; Maxwell's equations don't allow electromagnetic radiation (and hence, photons) to travel at any speed other than the inverse of the square root of the product of the universal permittivity and permeability constants. So if God were sitting in His backyard (Heaven?) watching the photons pass overhead, He would know that they could never catch one another, since they have an initial separation and are bound by the mandate of Maxwell to go the same speed forever. But the thing is, He's not sitting in His backyard; He's riding one of them. According to His reference frame, the other photon must move at the speed of light relative to Him. That means it'll soon be catching up with Him.

So how do we reconcile the discrepancy? The obvious answer is time dilation: as we approach the speed of light, our observation of time itself will decrease to zero. That is, when we hit the speed of light, time in any non-speed-of-light reference frame passes infinitely faster. So, according to God, it may take only one second for the other photon to catch up with Him, but even a millionth part of that second will be eternity for the rest of the universe. The universe will close before the photon catches Him, perhaps the Big Bang will happen again and the universe will go through infinitely many cycles of explosion and collapse. God's one second is no small amount of time for the rest of us; the photon will, in fact, never reach Him. And that's consistent with the view from the backyard.

But it's not that simple. Let's suppose that the Devil is riding on the photon behind God, and that, as Milton tells us, he's also omniscient. He sees God's photon moving away from him at the speed of light: God sees the distance between them diminishing at the same time Satan observes it increasing. What gives? They're in the same inertial reference frame (since they're both moving at the same speed and neither one is accelerating), but they both see qualitatively different things happening.

One answer is vague and almost philosophical, but it's still about time dilation. See, since time passes infinitely slowly for both of them from the point of view of the rest of the universe, it will take an infinity of the universe's time before even God can recognize a net relative velocity. And infinity is an interesting place to be, whether you're there in time or in space; all such infinities look the same: when time reaches infinity, the rules break down. A rock might be perfectly stationary, but that's just one way of saying its velocity in any given axis is zero; what happens when you reach time T = infinity? Anyone can tell you that displacement is equal to the product of velocity and time, and when time is infinity and velocity is zero, we've got a sticky situation of indeterminacy. The point is, when the clock finally reaches infinity, all of the rules blow up like a wet turtle in a microwave.

Even that sounds like a cop-out, though, and to a large extent it is. We still have a single inertial reference frame that gives inconsistent results. To make a long story short, the entire scenario is inherently fallacious: you can't tie an inertial reference frame to a photon. If you could, the photon itself would be stationary relative to the reference frame, and Einstein would roll over in his grave. Inertial reference frames that move at the speed of light that aren't tied to a photon work, but to perform any real calculations with them, one would have to mess with all sorts of infinities and indeterminates that make them more trouble than they're worth.

The upshot? God just doesn't ride photons, or, when He does, He tells Physics to look the other way.

If He did, though, here's what it would look like:





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...except inverted, white on black.

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