Is the Speed of Light Dependent on the Size of the Universe?

[PeterDonis]

Aren't we making assumptions about light as it is, by defining the meter in terms of the speed of light?

We're making a bet that defining our standard of length using light and our standard of time will turn out to be a good idea--that it will help to make physics look simple. That bet might turn out wrong (though it certainly seems to work well in our local region of spacetime). But it doesn't require making any assumptions about how the apparent size of distant objects in our telescopes will correlate with their actual size in terms of our meter sticks (or whatever our local standard of length is). We can still investigate the latter and consider various possible relationships, including ones that imply that the geometry of space is not Euclidean and that light paths are not always Euclidean straight lines. (Cosmologists call this general method "angular size distance", and it is not by any means a straightforward process.)

 

[Chronos]

How do you avoid making measurements comparative? It was bigger than my left foot is not very useful. We cannot make sense out of anything without making comparisons to something that qualifies as a 'standard'. Otherwise, we cannot avoid conceding we reside in a nonsensical universe. I fail to see how that advances our knowledge, or survivability potential.

 

[timmdeeg]

But it doesn't require making any assumptions about how the apparent size of distant objects in our telescopes will correlate with their actual size in terms of our meter sticks (or whatever our local standard of length is). We can still investigate the latter and consider various possible relationships, including ones that imply that the geometry of space is not Euclidean and that light paths are not always Euclidean straight lines. (Cosmologists call this general method "angular size distance", and it is not by any means a straightforward process.)

Cosmologists seem to consider as proven that the universe is (almost) flat, because this follows from the angular scale of the first peak of the power spectrum of the CMB. Does this mean that they don't doubt that the size of their meter stick now is identical with the size of a meter stick then?

 

[PeterDonis]

Does this mean that they don't doubt that the size of their meter stick now is identical with the size of a meter stick then?

The size of a meter stick now vs. then doesn't depend on whether or not the universe is spatially flat. It depends on the construction of the respective meter sticks and the forces (if any) that they are being subjected to. Two meter sticks of identical construction and both in free fall, one now and one billions of years ago, would have the same size, at least according to our best current understanding, whether the universe is spatially flat or not.

 

[timmdeeg]

Two meter sticks of identical construction and both in free fall, one now and one billions of years ago, would have the same size, at least according to our best current understanding, whether the universe is spatially flat or not.

Yes. Let me rephrase my question. The angular scale of the first peak of the power spectrum, which is one degree, corresponds to a certain distance then. Does this 'meter distance' then (measured using light then, etc.) correlate to 'meter distance' now (measured using light now, etc.)? Or is this an assumption, which isn't necessarily true, but fits to the data?

 

[PeterDonis]

The angular scale of the first peak of the power spectrum, which is one degree, corresponds to a certain distance then.

Yes, but exactly what distance then it corresponds to depends on by what factor the universe has expanded from then to now, which is model-dependent.

Does this 'meter distance' then (measured using light then, etc.) correlate to 'meter distance' now (measured using light now, etc.)?

Experimentally, this question is unanswerable, because we have no way of using "light then" to measure "distance then". All we can do is look at angular separations then and use our best current model to translate those into distance then. In our best current model, the answer to your question is yes.

Or is this an assumption, which isn't necessarily true, but fits to the data?

It's not an "assumption" in the sense of being made ad hoc. It's part of our best current model, which says that, since all of the physical factors determining the propagation of light, the structure of meter sticks, etc., were the same then as now, a "meter" then is the same as a "meter" now. Our best current model says that because we have looked for variations in the physical factors, such as the fine structure constant, that would affect the propagation of light, etc., and have found none.

It's not inconceivable that someone could construct a different model, one which included changes in those physical factors from then to now, so that a "meter" then would not be the same as a "meter" now, but still matched our observations. But AFAIK no one actually has such a model.

 

[timmdeeg]

PeterDonis, thanks for your clear answer!

 

[Burnerjack]

Surely the cheese could be both American and green without violating any known laws?

My refrigerator has achieved this while not violating any known laws. Eating it however, could violate the Law of General Gastronomic Nirvana.
Being more of a theorist than pragmatist, I have never endeavored to ascertain the result of such ingestion. Call it a hunch.