I Problem interpreting a Distance-Redshift Plot

[JohnnyGui]

This has been an interesting thread for me and I have had to re-examine the assumptions that the graph of magnitude v red shift make which has been a large part of the discussion. I still think that your graph is very similar to the one Saul Pelmutter used in his famous paper and this was taken as a true reflection of distance v receding velocity. I did come to a similar conclusion to yourself wrt this graph and I still don't quite know what the answer is.

The way I understood it is by realising that the graph in my OP is a measure of redshifts at one moment in time (all redshifts measured at once).
Therefore, one would have to consider a scenario in which you measure the 2 redshifts of 2 lights both at once, one from a nearby star $A$ and another from a very far star $B$. To be able to measure them at once, you'd first have to calculate the new distance and velocity of star $A$ at the time at which the light of star $B$ passes star $A$ itself, during an acceleration. It's a quadratic formula in which you have to solve for the time duration until the light of star $B$ passes star $A$ (let's call that moment $T_A$). So star $A$ is approaching the light of star $B$ while accelerating while star $B$'s light is approaching star $A$ at $c$

Once you have calculated the new velocity and distance of star $A$ at $T_A$, you can calculate star $A$'s redshift by calculating how much distance star $A$ has traveled from $T_A$ (with acceleration) until its light reaches the Earth and divide that by the distance of star $A$ at $T_A$. Also, you can calculate the redshift of star $B$'s light that was emitted before $T_A$ (it's the light that passed star $A$ at $T_A$) at $T_B$ by calculating how much distance star $B$ has traveled from $T_B$ all up until it reached the earth, divided by the initial distance of star $B$.

You should get 2 redshifts that are not proportional with distance, such that the redshift of star $B$ is actually less than one would expect with the Hubble value deduced from star $A$'s redshift. I'm aware there are many factors into play but this is a basic concept that shows a simple case of the relation between redshift and acceleration. For more info on the calculation, see my post #15.

 

[Adrian59]

I would agree with this interpretation as I have now found the right expression for cosmological red shift as
1 + z = R(t ob ) with R being the scale factor,
R(t em)
which I think is the same as in your example.

 

[JohnnyGui]

I was wondering about the factors that cause redshift in our universe. So far I've concluded the following:

1. Redshift caused by leaving and/or approaching a gravity source
2. Redshift caused by expansion of the universe
3. Redshift caused by the own velocities of galaxies/stars/etc.

Am I missing something else? Is there a redshift that is caused by a different curvature of space far away from us or is this a physical meaningless conclusion since it's dependent on the choice of coordinates?

 

[PeterDonis]

I was wondering about the factors that cause redshift in our universe.

There are two: relative velocity (your #3--though it should be stated more carefully) and spacetime curvature (your #1 and #2).

Is there a redshift that is caused by a different curvature of space far away from us or is this a physical meaningless conclusion since it's dependent on the choice of coordinates?

"Curvature of space" itself depends on your choice of coordinates. But "different curvature of space far away" could also be a way (an imprecise way) of referring to being in a curved spacetime, which is one of the two factors above.

 

[JohnnyGui]

Thanks for the clarification.

"Curvature of space" itself depends on your choice of coordinates.

Correct me if I'm wrong, but if curvature of space itself is merely dependent of coordinates and have no physical meaning, then I have a hard time accepting that there are actual physical phenomena that result from this curvature of space, if there are any. I think I can accept that the angles of a triangle in a curved space would not equal 180 degrees if one uses a particular coordinate system. But are you saying that there isn't any redshift or time dilation caused by curvature of space itself if one uses a particular coordinate system that is not invariant to curvature?

 

[PeterDonis]

if curvature of space itself is merely dependent of coordinates and have no physical meaning, then I have a hard time accepting that there are actual physical phenomena that result from this curvature of space, if there are any.

The physical phenomena don't result from "curvature of space", they result from picking out particular physical events or sets of events. The events themselves, and the relationships between them, don't depend on your choice of coordinates.

I can accept that the angles of a triangle in a curved space would not equal 180 degrees if one uses a particular coordinate system.

The angles of a triangle are invariants; they don't depend on your choice of coordinates. But in order to define a triangle in the first place, you have to pick out three events (points in spacetime), and three sides (three curves in spacetime, each one connecting two of the points). Once you've picked out three points and three sides, the angles of the triangle, and the lengths of the sides, are invariants; they don't depend on your choice of coordinates. But whether all of the events and sides taken together, i.e., all of the points in a particular set of points that is the union of three points and three curves connecting them, are properly called a "triangle of points in space at a constant time" does depend on your choice of coordinates. They might not all have the same time coordinate in some choices of coordinates.

are you saying that there isn't any redshift or time dilation caused by curvature of space itself if one uses a particular coordinate system that is not invariant to curvature?

No. I'm saying that redshift and time dilation (assuming that by "time dilation" you mean some invariant such as the observed difference in elapsed proper time between two twins in a "twin paradox" scenario when they meet up again), since they are invariants, aren't caused by "curvature of space"; they are caused by something else. (The obvious cause in general is curvature of spacetime--not space--plus a choice of particular points and curves in spacetime, whose properties, like lengths and angles, are invariants.)