- #1

tom.stoer

Science Advisor

- 5,766

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## Main Question or Discussion Point

In http://arxiv.org/abs/0808.1081 / Am.J.Phys.77:688-694,2009 Bunn and Hogg explain how cosmological redshift can be interpreted as accumulation of infinitesimal Doppler shifts. This suggested to invert z = z(v) and interpret v(z) as relative velocity of two objects with redshift z.

It seems that this view has become popular over the last years, however I still have doubts whether this interpretation does make much sense.

Relative velocities as used in the Doppler shift formulas must be defined w.r.t. a common (i.e. globally defined) inertial frame - which does not exist. So using such a v(z) still means that v(z) is not a relative velocity (even so it has been constructed from infinitesimal relative velocities).

In an expanding universe there may exist objects P and Q which cannot be connected by a light-like geodesic. It may even be the case that there are objects for which such a geodesic will never exist. So for these objects there will never be a redshift nor a velocity v(z) defined a la Bunn and Hogg. However these objects somehow "recede" from each other which can be understood using the picture of expanding space, but not a picture relying on a geodesic that does not exist by construction. So the kinematical interpretation breaks down for cosmological horizons.

However it seems that all this could be a rather academic discussion resulting from "intuitive pictures" instead of well-defined math only ...

It seems that this view has become popular over the last years, however I still have doubts whether this interpretation does make much sense.

Relative velocities as used in the Doppler shift formulas must be defined w.r.t. a common (i.e. globally defined) inertial frame - which does not exist. So using such a v(z) still means that v(z) is not a relative velocity (even so it has been constructed from infinitesimal relative velocities).

In an expanding universe there may exist objects P and Q which cannot be connected by a light-like geodesic. It may even be the case that there are objects for which such a geodesic will never exist. So for these objects there will never be a redshift nor a velocity v(z) defined a la Bunn and Hogg. However these objects somehow "recede" from each other which can be understood using the picture of expanding space, but not a picture relying on a geodesic that does not exist by construction. So the kinematical interpretation breaks down for cosmological horizons.

However it seems that all this could be a rather academic discussion resulting from "intuitive pictures" instead of well-defined math only ...

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