Does infinite one-way speed of light violate p conservation?

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We recently had a similar thread on this topic, but it was with respect to a crank's attempt to utilize this for religious purposes. The following question has nothing to do with that, but it could be related to it.

Basically, here's the deal: when we look at galaxies very, very far away, they all appear to be very young. This implies that light had to have taken a long time to reach us. If we could choose a coordinate system where their light got here instantaneously, wouldn't they appear as old as every other galaxy? Or in choosing such a synchronization convention, are we choosing a frame in which those galaxies just formed, and that is why they look so young?

https://imagine.gsfc.nasa.gov/features/cosmic/farthest_info.html

All these distant galaxies are viewed with light that was emitted around a few hundred years after the big bang (in the isotropic CMB frame), and all appear to be young when their light reaches our telescope. Why wouldn't they appear ancient if incoming light really traveled instantly to us? Or if we "chose" such a convention? Surely that is an argument against any arbitrary convention?


Or is it again simply choosing a frame where those galaxies really are that young?
 
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Ibix
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Or is it again simply choosing a frame where those galaxies really are that young?
This. The point is that "at the same time coordinate as you" is a concept that's up to you. You are free to define it any way you like, as long as you don't assign multiple coordinates to an event.

It would make sense to link it to something physical. That's what Einstein coordinates do in flat spacetime - they agree that two clocks are synchronised if they both literally see the other lagging by the same amount. That's also what FLRW coordinates do in an FLRW universe - here they pick observers who see the CMB as isotropic and who zeroed their clocks at the Big Bang singularity and define these clocks as synchronised.

But you don't have to do it. You can define anything you like as a time coordinate as long as it increases in a time-like direction. You will find that your notion of time usually doesn't correspond to anyone else's. You will also usually end up with more complex and opaque maths because you've sacrificed a direct correspondence between your core mathematical concepts and the physics. But if you want to do it, that's up to you.

An Earthbound example is latitude and longitude. Since the coordinate poles lie on the physical rotation axis, the coordinates are related to something physically meaningful and physically meaningful things (like the tropics and arctic circles) have simple representations. And since the magnetic field comes from the spin of the core we get a free way of measuring orientation relative to this coordinate system.

But we could pick anywhere on the Earth's surface as the coordinate pole. It's just a sphere. But it would be silly to do so because it's much harder to describe weather patterns (that are related to rotation) and compasses don't do anything relevant.
 
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This. The point is that "at the same time coordinate as you" is a concept that's up to you. You are free to define it any way you like, as long as you don't assign multiple coordinates to an event.

It would make sense to link it to something physical. That's what Einstein coordinates do in flat spacetime - they agree that two clocks are synchronised if they both literally see the other lagging by the same amount. That's also what FLRW coordinates do in an FLRW universe - here they pick observers who see the CMB as isotropic and who zeroed their clocks at the Big Bang singularity and define these clocks as synchronised.

But you don't have to do it. You can define anything you like as a time coordinate as long as it increases in a time-like direction. You will find that your notion of time usually doesn't correspond to anyone else's. You will also usually end up with more complex and opaque maths because you've sacrificed a direct correspondence between your core mathematical concepts and the physics. But if you want to do it, that's up to you.

An Earthbound example is latitude and longitude. Since the coordinate poles lie on the physical rotation axis, the coordinates are related to something physically meaningful and physically meaningful things (like the tropics and arctic circles) have simple representations. And since the magnetic field comes from the spin of the core we get a free way of measuring orientation relative to this coordinate system.

But we could pick anywhere on the Earth's surface as the coordinate pole. It's just a sphere. But it would be silly to do so because it's much harder to describe weather patterns (that are related to rotation) and compasses don't do anything relevant.
But we cannot transform out differential aging, or even the fact that in every reference frame, all the galaxies should never appear to be the same age, unless that frame was equidistant from all of them (and surely no such frame exists). Am I right on that one? That is, we can use a convention to choose time coordinates where distant galaxies have just recently been born, but we can't choose one where the previous is true AND the nearer galaxies which appear older have also just recently been born (because in our frame they clearly are old, regardless of how fast we choose the incoming speed of light).
 
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Ibix
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But we cannot transform out differential aging, or even the fact that in every reference frame, galaxies should never appear to be the same age, unless that frame was equidistant from all of them (and surely no such frame exists). Am I right on that one? That is, we can use a convention to choose time coordinates where distant galaxies have just recently been born, but we can't choose one where the previous is true AND the nearer galaxies which appear older have also just recently been born (because in our frame they clearly are old, regardless of how fast we choose the incoming speed of light).
Correct. If you look through a telescope at a co-moving clock then you see what you see - 12bn years since the Big Bang, for example. The FLRW explanation is that it's actually 1.9bn years away and light took 1.9bn years to get here, so the clock reads 13.9bn years now, same as ours. The explanation being touted in the other thread is that "now" is whatever the clocks appear to be reading to observers on Earth. So nearby clocks - for some reason - have been running longer than further away clocks. As long as you are willing to pay the mathematical and conceptual price of making that claim, that's fine.

The advantage to FLRW coordinates is that they reflect the symmetry of the physics. For example, any FLRW co-moving observer sees the universe looking the same (on cosmological scales) as any other when their own time-since-the-Big-Bang clock shows a specified time. Trivially, then, the owner of the clock in that distant galaxy will see our clock reading 12bn when his reads 13.9bn - because he's in the exact same situation as us. Using weird anisotropic coordinates completely obscures that. It's still true, but I would need a few hours and a symbolic maths package to prove it if I used the weird coordinates and didn't know a transform to the simple ones.
 

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