Hubble's law at current time is as follows.


But if you look at the explanation in the next link,


“ Strictly speaking, neither v nor D in the formula are directly observable, because they are properties now of a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it.

For relatively nearby galaxies (redshift z much less than unity), v and D will not have changed much, and v can be estimated using the formula v=zc where c is the speed of light. This gives the empirical relation found by Hubble.

For distant galaxies, v (or D) cannot be calculated from z without specifying a detailed model for how H changes with time. The redshift is not even directly related to the recession velocity at the time the light set out, but it does have a simple interpretation: (1+z) is the factor by which the universe has expanded while the photon was travelling towards the observer.”

My question is as follows.

Current proper distance indicates where the galaxy should be by expansion when photons from the past start and reach us now.

In the expression of Hubble's law, Hubble's law has a current proper distance. Therefore, Hubble's law at current time already has a meaning that implies information about photons in the past. It's strange to say that Hubble's law only holds close distance because of the inability to observe current information.

Why does cz=Hd exist only at a close distance?



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