Re: Cosmological redshift

["Paul Camp" <pjcamp@coastal.edu>]

The metric *does* stretch. This is the mathematical embodiment of 
"expansion of space-time." However, I think what you are doing here 
is confusing local ideas with global ones. This is the most common 
source of conceptual difficulties with general relativity.

The definition of a centimeter belongs to us and is created by us 
based on local measurements. The equivalence principle tells us that 
locally spacetime is flat. Thus this local definition is not going to 
change.

Using that local definition to measure a global phenomenon such as 
spacetime expansion is another matter, however. You cannot speak of 
expansion of the universe except in the sense of comparing positions 
for objects at different locations as time passes. This is not a 
local measurement but a global one. So it isn't so much that the 
centimeter is being stretched (though that would make me happier when 
I buy pants) but that you are getting more of them. Think of it as 
new geometry coming into being rather than the existing geometry 
being stretched and you'll get the basic idea.

> If the universe is expanding as a cosmic microwave background photon is 
> travelling through space-time, then I am happy to accept that the 
> photon is "stretched" (if not, would it be blue 
> shifted?)  However as space is being stretched, why isn't the metric 
> being stretched too, in which case a photon whose wavelength was 
> once one centimetre, for example, would still measure a centimeter now?
> (Because today's 1 cm would be bigger than the original 1 cm by the same 
> factor as the amount by which the photon has been stretched.)
> Analogies such as the expanding balloon don't help, because a grid on the 
> balloon stretches the way I imagine the metric to stretch - wrongly, no 
> doubt.  
>
> Feel free to tell me that I am being dim, as long as you enlighten me in 
> the process!
>
> Cheers
> Margaret Mazzolini

Paul J. Camp                   "The Beauty of the Universe
Assistant Professor of Physics  consists not only of unity
Coastal Carolina University     in variety but also of 
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