A common objection to the Big Bang model is that redshifts do not
measure distance.  The logic is that if redshifts do not measure
distance, then maybe the Hubble relation between velocity and distance
is all wrong.  If it is wrong, then one of the three pillars of
observational evidence for the Big Bang model collapses.

One way to show that redshifts do not measure distance is to find two
(or more) objects that are close together on the sky, but with vastly
different redshifts.  One immediately obvious problem with this
approach is that in a large Universe, it is inevitable that some very
distant objects will just happen to lie behind some closer objects.

A way around this problem is to look for "connections"---for instance,
a bridge of gas---between two objects with different redshifts.
Another approach is to look for a statistical "connection"---if high
redshift objects tend to cluster about low redshift objects that might
suggest a connection.  Various astronomers have claimed to find one or
the other kind of connection.  However, their statistical analyses
have been shown to be flawed, or the nature of the apparent "bridge"
or "connection" has been widely disputed.

At this time, there's no unambiguous illustration of a "connection" of
any kind between objects of much different redshifts.

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