Lorentz Transformations (split from why nothing >c)

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Sorry

This isn't the main issue.

We discuss on linearly speed at GR.

Therefore, the following example of rockets over rockets should work O.K.

At t=1 we get:

A-B-C-D-E-F-G-H-I-J-K-L-M

At t=3 we get:

A---B---C---D---E---F---G---H---I---J---K---L---M

I'm not sure what this is supposed to show, but I bet it is wrong.

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Because, if there is expansion of space and the galaxies are far enough away that this is significant, then you cannot compare their velocities without using GR to take the expansion into account. Therefore you cannot add velocities as you are doing.

Let's look again on that example:

B is located at a distance of 2571 Mpc from A and therefore, it is receding at a speed of 0.6c (from A).

C is located at a distance of 2571 Mpc from B and therefore, it is receding at a speed of 0.6c (from B).

Hence, the distance between A To C is 5142 Mpc.

The outcome is that the relative speed between A to C is 1.2c

What is wrong with that?

Edited by David Levy
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Let's look again on that example:

B is located at a distance of 2571 Mpc from A and therefore, it is receding at a speed of 0.6c (from A).

C is located at a distance of 2571 Mpc from B and therefore, it is receding at a speed of 0.6c (from B).

Hence, the distance between A To C is 5142 Mpc.

The outcome is that the relative speed between A to C is 1.2c

What is wrong with that?

OK. Looking at it again, your numbers are approximately correct. (This could be a first. We should have some sort of celebration.) I apologise for assuming that every calculation you post would be wrong, based on past experience.

The recessional speed is 71 km/s/Mpc and so at 2571 Mph it is 182,500 km/s or 06.c. At double that distance, it is 1.2c.

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However this calc is the seperation distance. Based upon a linear equation of Hubbles law. GR kicks in when you look at redshift values for those distances. You will find that z is not linear with seperation distance. Though it is approximately linear up to a point.

Recall as well GR doesn't apply to Hubbles law. It is not inertial based.

Nothing is truly violating the speed limit c.

Edited by Mordred
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I think a lack of clarity in the original question has led to conflicting answers here.

If the distance between our target galaxies is comparatively small and they are each moving through space with respect to A at 0.6c then the relative velocity between B and C will necessarily be less than c and they will be able to see each other. At relativistic speeds spacetime is distorted.

If however the distance between all galaxies is vast and their apparent speed is due to the expansion of space between them then they will not be able to see each other and their relative speed is meaningless. Any distortion in spacetime due to their speed through space is voided by the expansion of spacetime between them.

That's my thoughts

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I think a lack of clarity in the original question has led to conflicting answers here.

If the distance between our target galaxies is comparatively small and they are each moving through space with respect to A at 0.6c then the relative velocity between B and C will necessarily be less than c and they will be able to see each other. At relativistic speeds spacetime is distorted.

If however the distance between all galaxies is vast and their apparent speed is due to the expansion of space between them then they will not be able to see each other and their relative speed is meaningless. Any distortion in spacetime due to their speed through space is voided by the expansion of spacetime between them.

That's my thoughts

That is a good attempt to clarify. Except ... we can see galaxies that are receding because of the expansion of space. More than that, we can see galaxies that are receding at more than c!

But the key point you make is that you can no longer (directly) compare their relative speeds.

Edited by Strange
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... More than that, we can see galaxies that are receding at more than c!

I did not know that

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OK. Looking at it again, your numbers are approximately correct. (This could be a first. We should have some sort of celebration.) I apologise for assuming that every calculation you post would be wrong, based on past experience.

The recessional speed is 71 km/s/Mpc and so at 2571 Mph it is 182,500 km/s or 06.c. At double that distance, it is 1.2c.

Thanks

I do appreciate the excellent support which I have got from all of you.

We all share the ambition to get better understanding about our complex universe.

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