Cosmological Redshift and Expansion

[Mohdje]

The ultimate cause is always that the inner product of the light's four momentum with the four velocity of the emitter is different from that with the four velocity of the receiver. In curved spacetime this is usually all the cause that there is - there is no non-arbitrary way to divide the frequency change into different "causes".

However, in some spacetimes with symmetries it is possible to divide this effect into components. For example, in Schwarzschild spacetime it is possible to identify hovering observers, and then to divide the frequency change into a part due to the altitude difference ("gravitational redshift") and a part due to velocity relative to the hovering observers ("kinematic redshift"). And in the FLRW spacetimes used in cosmology you can pick out comoving observers who see the CMB as uniform, then separate the frequency shift between any two observers into a shift due to their motion relative to their nearby comoving observers (their "peculiar velocity") and the frequency shift between those comoving observers (the cosmological recession velocity or expansion of the universe, depending on how you want to see it).

I don't know of any other relevant breakdown of the frequency shift.

And I don't know either. All I meant was that Doppler shift and cosmological redshift lead to the same results, but they have different mechanisms. The first works on the motion between the observer and the observed, while the second works on the wavelength of light in spacetime. They are both different because they complement each other. If we say that the shift is the same, I agree with you here because it has the same results, which is the effect of objects receding. But I also disagree with you because the mechanisms are different, and here we are talking about known models, not new ones.

 

[Ibix]

All I meant was that Doppler shift and cosmological redshift lead to the same results, but they have different mechanisms.

But they don't, really. That's my point. Both are due to the different inner products between four vectors, and you can only divide the cause of that difference by imposing a definition of "at relative rest" that is a personal choice.

 

[Mohdje]

But they don't, really. That's my point. Both are due to the different inner products between four vectors, and you can only divide the cause of that difference by imposing a definition of "at relative rest" that is a personal choice.

If it's a personal definition, do you have any proof of it?

 

[Ibix]

If it's a personal definition, do you have any proof of it?

Proof of what?

 

[Mohdje]

Proof of what?

Didn't you say it was a personal definition? If so, you must have proof of its validity.

 

[Ibix]

Didn't you say it was a personal definition? If so, you must have proof of its validity.

The personal choice I was referring to is the choice of what "not moving relative to each other" means. That is a part of a choice of coordinate system, which is not a thing that can be proved, any more than you can prove that a metre is the correct unit of distance. It also has no effect on measurements or predictions of measurements - in this context it's simply a choice of how much of a given object's redshift to ascribe to motion and how much to the passage of the light through spacetime.

If you make a decision to use co-moving coordinates (which everyone does in a cosmological context) then that fixes the split of the redshift. But you could choose a different coordinate system and you'd get a different split. It's no more mysterious than you and I facing each other across a table. If it's a long table and we're near one end, I would say the bulk of the table is on the right while you'd say it's on the left. Neither of us is wrong, and neither of us can prove our choice right. We're just using different coordinates.

 

[Mohdje]

The personal choice I was referring to is the choice of what "not moving relative to each other" means. That is a part of a choice of coordinate system, which is not a thing that can be proved, any more than you can prove that a metre is the correct unit of distance. It also has no effect on measurements or predictions of measurements - in this context it's simply a choice of how much of a given object's redshift to ascribe to motion and how much to the passage of the light through spacetime.

If you make a decision to use co-moving coordinates (which everyone does in a cosmological context) then that fixes the split of the redshift. But you could choose a different coordinate system and you'd get a different split. It's no more mysterious than you and I facing each other across a table. If it's a long table and we're near one end, I would say the bulk of the table is on the right while you'd say it's on the left. Neither of us is wrong, and neither of us can prove our choice right. We're just using different coordinates.

Your point is valid, and I agree with you, but you're explaining a completely different idea. Scientists always rely on Earth as an observer, but you're explaining the idea of observer independence, meaning every celestial body can be considered an observer. This is difficult to implement with current models. Regarding the relative differences in orientations, as you mentioned, there's the redshift and the blueshift, and you're talking about something that's very difficult to confirm. So I agree with you here, but that's not the only reason for the shift in the end.