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

[BiGyElLoWhAt]

I think I see what you're saying. However, I think I am missing something.
One of his big points is that "The wand chooses the wizard"... I mean... "The theory chooses the units" out of convenience. OK. I suppose that might be the case, as I've never sat and worked through an original theory and tried to decide which units were most acceptable. I have worked in natural units in relativity, though, and it does seem to simplify things somewhat.

Going back to the meter stick idea, however, if we rigidly fixed our units, a meter stick = 1 meter, 9 billion-some-odd number of cycles of Cs excitations for time, some particular amount of charge required to exert a force of 1N on an electron from 1 meter (or something similar), and the kg as something similar (I'm having a hard time coming up with an example for mass) - Wouldn't that sort of solve the whole problem of allowing it to be "chosen" instead of us having to determine which of the fundamental "constants" are changing?

Give me a very accurate clock, and a meter stick. I will test to see if c is still equal to 299,792,458 m/s (within experimental error, but let's toss that aside for a second [ba dum])
Measure mass via some good method that I can't come up with right now, check the electron mass.
Give me a meter stick, an accurate clock, and the notion that electron mass is the same, and I can check to see if e is the same. If both of those are the same, but alpha varies, it must be in hbar. With a constant, non varying unit for kg, m, s, and C, you would also be able to check h, if you wanted.

Seeing as how you seem to be more on page with the author than I am, can you explain to me why (in theory) this isn't feasible for determining the constancy (or lack thereof) of "constants"? (I understand the problems with keeping a meter stick in a vault, etc.)

To add:
I'm referring to this comment:
"Hence the dynamics associated with each varying α theory “chooses” the units to be used, on the grounds of convenience, and this choice fixes which combination of e, c and ¯h is assumed to vary."

This seems like a very bad way to do things, in my opinion. "Oh, it's easier to say that e changes, so we'll roll with that."

 

[PeterDonis]

Give me a meter stick, an accurate clock, and the notion that electron mass is the same, and I can check to see if e is the same. If both of those are the same, but alpha varies, it must be in hbar.

You can't have the same meter stick everywhere in spacetime. You can't have the same clock everywhere in spacetime. You can't have the same electron everywhere in spacetime. So you can't possibly say for sure that a meter stick in a quasar a billion light-years away is "the same" as the meter stick in your laboratory right now; or that a clock in the early universe is "the same" as the clock in your laboratory right now; or even that an electron in a faraway galaxy is the same as the electron in your laboratory right now. You can test that things seem to stay "the same" in your laboratory; but you can't directly test that they are "the same" everywhere in spacetime. You have to make assumptions, and those assumptions will have to include some choice of units--which means some choice of how you are going to define what a "meter" is in a faraway galaxy that you can't measure directly with your meter stick (and similarly for other units).

 

[BiGyElLoWhAt]

Why can't we use a meter stick and do trig on our fancy telescopes to determine a meter? It's not like we can observe photons traveling from a to b in some galaxy, anyways. We can only see light that travels from a to our telescope and from b to our telescope. We have to do trig anyway if we want to use that method, so what's to keep us from using our meter stick and calibrating our telescope? Given 3 telescopes that we know the arc distance between and their respective measurements of the arc length between 2 points in some galaxy, (using the distance between 2 rays of light coming from those 2 points) I don't see why we couldn't reflect that back onto our meter stick, or why it's necessary to choose 1/299,792,458 * c to do so, especially if we doing something like checking for the constancy of c. It just feels theoretically problematic, which is worse than keeping a meter stick in a vault under lock and key, which is realistically problematic.

 

[PeterDonis]

Why can't we use a meter stick and do trig on our fancy telescopes to determine a meter?

Because then we are making assumptions about the geometry of space and the behavior of light. Or, to put it another way, we are choosing our units in such a way that changes in the geometry of space and the behavior of light in different parts of the universe and different times will appear to us in a certain way, as changes in certain quantities and not others.

 

[BiGyElLoWhAt]

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

 

[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.