After lots of thinking, and numerous cups of tea (which undoubtedly betrays my location as UK), I have come up with some thoughts I would like to share; i.e. have kicked around.
A photon is a quantum object. I suggest the use of Nick Herbert’s “quon” for a quantum object. (This definition found its way into Wikipedia yesterday.)
Quons are able to be in more than one place at a time, as long as they are not being observed. As far as I am aware, we have no evidence to indicate that the restriction to a single place, which we observe from our F of R, also applies in the F of R of the quon. In its own F of R it may still be everywhere at once. It may exist in infinity (=eternity).
Eternity is not an infinite expanse of time; in fact, it does not involve time, the two concepts are, incompatible. The concept of eternity as being in any way “temporal” arises from our limited ability to comprehend the nature of infinity. Like “Flatlanders” who cannot even imagine a third spatial dimension, we try to examine infinity using only our four dimensions of spacetime. Thus we find ourselves constantly falling back on temporal analogies and terminology, which are, at best, only of limited value, and, at worst, are downright unhelpful.
John Wheeler said that “Time is nature's way to keep everything from happening all at once”. This may sound like a flippant comment, but it is in fact quite a profound observation. We might say that eternity is the absence of time, and that in eternity everything must happen at once. However, even that statement is misleading: in order for something to happen there must be some passage of time. In eternity, everything just is.
Whatever one can do with mathematical infinities, it seems inescapable that any physical infinity must be immutable. The corollary of this is extremely important. An infinite cosmos cannot be multiplied nor divided. It can have nothing added to it, because there is nothing outside it that could be added. It can have nothing taken away, because to take something away would either make it less than infinite, or it would mean that there was something other than the all-embracing infinity, which would constitute a contradiction in terms.
If we were able to divide infinity, for example, by two, what would we be left with? One possibility seems to be that we would have two halves of infinity. Each half would be less than infinite, thus it would be measurable. Measure this quantity and multiply it by two and we have a measure of infinity, which is nonsense. The second possibility must be that each “half” somehow becomes infinite. Mathematically this seems reasonable; after all we can multiply or divide zero by any number we choose, and the outcome will be zero. Perhaps we also could do this, mathematically, with infinity, (Cantor almost certainly did), but practically there is the complication that anything that is truly infinity must contain everything; there cannot be two infinities, because each would have to contain the other.
This apparently intrinsic indivisibility of infinity leads one to wonder if any “part” of infinity can be distinct from any other “part”. Is it in any way meaningful to talk of parts of infinity? If it is not, and if our Universe is “part” of this infinite cosmos, then we seem to have a problem. However, the problem may not be as difficult to solve as it at first appears. Consider the following possibility. The cosmos is infinite; therefore every part of the cosmos is the whole cosmos. Everything, including our apparently finite Universe, is infinite. The birth of the Universe and perhaps its ultimate death exist together in infinity, along with all the things that seem to us to “happen” between those two points. It is all there, in eternity, in an all-embracing now. We perceive spatial differences, and the passage through time, because our minds need to make sense of the partial image to which we are restricted.
Consider events A, B and C. In linear time these might occur, one after the other, in that order. In eternity, though, they would all be present together. There could not have been a point in eternity when, for example, A had happened, but not B or C. The whole of eternity must contain A, B and C, in their entirety, for all eternity.
Just when you thought I had wandered infinitely far from the point, this brings us back to our photon travelling from A to B, via the Earth’s atmosphere. In our F of R there is a passage through time involved, but in the Photon’s F of R it is at A and B, and in the Earth’s atmosphere all at the same infinite point.
