What is the relative speed of two groups of quasars with different redshifts?

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SUMMARY

The discussion focuses on calculating the relative speed of two groups of quasars with different redshifts, specifically redshift 10 and redshift 6. The redshift 10 group is considered "at rest," while the redshift 6 group is moving towards the observer. To determine the speed, one must apply the Doppler shift formula, taking into account that both groups are at the same distance, which eliminates time dilation effects. The outcome will yield a minimal velocity expressed as a percentage of the speed of light or in kilometers per second.

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TL;DR
speed calculation between two groups at different redshifts : redshift 10 & redshift 6.
If many quasars are at redshift 10, and another group is at redshift 6, what is the speed of the second group relative to the first? The redshift 10 group can be considered "at rest", so the redshift 6 group is heading in our direction at what rate? For this scenario, let us assume all the quasars are at same distance (as suggested by zero time dilation difference). Answer in percent of lightspeed please, but kilometers per second is ok, I can handle that conversion.
 
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Cosmological redshift is effectively time dilation. You are asking for two mutually exclusive conditions at the same time. But if you want to put them at the same distance: Calculate the redshift from motion at this place (the relative frequencies stay the same), then plug that into the Doppler shift formula. You won't get a unique result because space is not one-dimensional, but you can get a minimal velocity.
 
Thanks for your time, mfb.
 

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