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The notion of there being a direction of time is presupposing the existence of time, and you go back and forth on whether you talk about time being a property of the Universe. The fact that you're asserting what time must be in order to satisfy your hypothesis is fine, but keep an eye on that assumption.
Good point, noted. I'm not sure time is a property of the universe, rather a property of mass.
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I.e. the Big Bang may be an exponential expansion that goes back into infinite time
Sure, but it certainly appears that the universe was once very small, at least in terms of the Plank scale. I know we've discussed the Plank unit before and you didn't seem to think it was an important threshold, but everything I have read about it seems to imply it is. That is, if everything occupies a single Plank volume, then we might as well call it a singularity. The significance of the Plank scale is related to it being smaller than the shortest wavelength of light. So even to a photon, it's a significant measure. If the universe is less than a Plank volume, then light cannot even propagate. That is, it no longer a wave.
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...nor what failed to turn the Big Bang into a black hole.
How do we know we're not inside a black hole? I mean, cosmic expansion is indistinguishable to the accelerating spacetime within a black hole.
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That Universe does not have a "beginning" as you describe.
Again, Plank units come into play here. If light cannot exist as a wave, then nothing exists that is slower than light. So again we come to the problem of what time actually means in this world. It seems to me that a beginning of time is inevitable, it emerges when something moves slower than light. That can't happen until light can actually move. But of course there's a paradox here... it takes time for this process to happen. I have no idea how to resolve this paradox.
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Physics doesn't actually care if anyone is there to observe anything, it only describes what you would observe if you were there.
I understand this, but in a universe of photons, a physical observer appearing radically changes the entire landscape of the universe. How can we possibly imagine what the universe would be like if we were a non-physical (imaginary) observer?
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If you were an inertial observer in the Heat Death universe, you would see photons moving at c.
Indeed, because you exist. But if you're, idk, an observer from another universe somehow peering into this universe, things could be very different. If only photons exist, what does it mean to move at c? Does a photon move at c relative to another photon? Or does it move at 0?
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Whether or not there is an observer to observe doesn't change the physics of what an observer would observe if they are there.
I think this is only true in a universe with mass. A massless universe is a different ball game altogether. An observer appearing introduces gravity to the universe. Without mass, there is no gravity. Like I say, a radical change of landscape.
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Which is why I'm saying that if your specific hypothesis is that we rule out anything depending on an observer, then I have nothing to comment on that as a physicist.
I appreciate physics cannot answer these question, not now and probably never, because we're talking about things that can never be measured. Ultimately, we're talking here about what time actually is, not how we observe it and measure it. And we're talking about a massless universe, something that will never exist while we exist. So it's always going to be philosophy.
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What all observers will agree on is whether or not event A could have caused event B (or vise versa), based on applying relativity correctly and determining the "light cones" of each event, and seeing if one event lies inside or outside the other event's light cone.
I'm pretty sure that here you imply that all observers have mass. A photon is clearly a different kind of observer to a human, or a cat, or a hydrogen atom. How does a photon observe causality? To the photon, the past, present and future are all the same thing. A photon can say "A could have caused B, but B could have caused A", because the photon observes everything happening at the same time. In fact it's absurd to even say the A could have caused B, or B caused A, rather the photon would say A and B are the same thing because they happened at the same time in the same place. The universe is a completely different world to a photon, due to infinite time dilation and length contraction.
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The only way for both events to be able to "cause" each other, is if both events happened at the identical same point in space-time. I.e. that it was indistinguishable from a single event.
Exactly! I didn't read this before making that last comment! The difference between an observer with mass and an observer without mass is not to be ignored. If you don't have mass, then you're moving at c. It's absurd to assume an observation from the FoR of something that has no mass yet doesn't move at c.
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There's isn't 1 FoR, there's a unique non-inertial FoR for each photon.
This feels like as much an assumption as saying the opposite, that a photon's FoR is indistinguishable from another photon's FoR. Only the latter seems to make more sense to me, because it experiences no time, and therefore no space. It exists in a singularity for all existence. That's its FoR. Only things that move slower than it will disagree.
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If we have a universe of photons, it would be something like the total mass-energy of the photons is exactly enough to create exactly the right spacetime curvature to drive all photons to infinite red-shift, but only given infinite time.
I don't see why it would be an infinite red shift. The universe seems to be quantum. There's a minimum unit of energy, there's a minimum wavelength of light, so there comes a point where something can't red shit any more because it's already at the minimum "colour".