Imagine a firefly drifting in an empty universe that can only do three things: remember, detect photons and emit photons. If you follow the principle of Mach that 'if it can't be measured in principle, then it doesn't exist', as I do, then as far as the lonely firefly is concerned there is no time or space since it has no way of measuring them. It could emit a photon of light to try and explore its environment, but the photon will never come back so neither will any information. My intention here is not to make spacetime subjective but to apply the same idea to inanimate objects, and say that if time/space are fundamentally unmeasurable by a system then these abstract quantities don't exist.
Now imagine that suddenly another firefly appears and there are two things in the universe. Now firefly A can emit light and firefly B can respond to A with its own flash. Suddenly A and B have a way to measure time. They can't do this by measuring the time taken for a signal to return because we've already assumed that time without the return of a signal doesn't exist, but if A and B have memories then they can count the number of times they receive a reply and call this time. This begs the questions: does time only exist with interactions? Does it speed up if you have more interactions? I think so, because this suggests a way to resolve the Einstein, Podolsky & Rosen (1935) (EPR) paradox.
In the EPR problem there is a particle with zero spin that splits into two particles, one going left, one right. Quantum mechanics, not to be pinned down, only says that both are spinning both up and down, but if someone measures particle A and finds it spinning up, by conservation of angular momentum we know immediately that particle B must spin down. Since quantum mechanics says there was no information on spin before the particles were measured, and Bell's inequality has allowed people to experimentally confirm this, then this implies that A and B communicate apparently faster than light, in violation of special relativity.
Well, I'd like to suggest these particles are a bit like the fireflys: while they're diverging they can't interact with anything, and so, as above, time cannot exist for them, so at the time (from our external point of view) that they seperated they already knew what would happen at the later measurement time (Being complex beings we have lots of interactions going on so we have a finer measure of time). I've been vaguely thinking this for years (inspired just after my physics degree by reading the Emperor's New Mind by Roger Penrose), but recently I've got stuck in and I've finally worked out a way to justify and quantify this using information theory. I am just about to submit a paper on it..
PS: The brilliant Transaction Interpretation of Quantum Mechanics of Cramer (1986) says something similar, but involves waves sending signals 'through' time rather than, as here, having time itself dissapear.
PPS: The bleak but deep novel by Greg Bear 'The City at the End of Time' involves a sort of collapse of time so different events in history suddenly end up simultaneous.
Einstein, A., B. Podolsky, N. Rosen, 1935. Can quantum mechanical description of physical reality be considered complete? Phys. Rev., 41, 777.
Cramer, J., 1986. Reviews of Modern Physics, 58, 647-688.
Penrose, R., 1989. The Emperor's New Mind.
Throw in space as well and maybe it's space-time that arises from interaction...
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