- #1

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## Main Question or Discussion Point

The formula for redshift according to the special relativity is

[tex]

f = \sqrt{\frac{c-v}{c+v}} f_0.

[/tex]

Here [tex]f\to 0[/tex] when [tex]v\to c[/tex]. So for arbitrarily strong redshift effect we can always solve the corresponding velocity [tex]v<c[/tex] of the emitter moving away. Why then does Carrol explain this:

"As an example of how you can go wrong, naive application of the Doppler formula to the redshift of galaxies implies that some of them are receding faster than light, in apparent contradiction with relativity."

[tex]

f = \sqrt{\frac{c-v}{c+v}} f_0.

[/tex]

Here [tex]f\to 0[/tex] when [tex]v\to c[/tex]. So for arbitrarily strong redshift effect we can always solve the corresponding velocity [tex]v<c[/tex] of the emitter moving away. Why then does Carrol explain this:

"As an example of how you can go wrong, naive application of the Doppler formula to the redshift of galaxies implies that some of them are receding faster than light, in apparent contradiction with relativity."