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

[wolram]

Is it true that the speed of light is only dependent on the size of the universe, if the universe were much smaller would the speed of light be faster?

 

[rishivashista13]

How speed of light is dependent on size of universe ?

 

[BiGyElLoWhAt]

https://en.wikipedia.org/wiki/Variable_speed_of_light
I'm assuming this is what you're referring to?

 

[PeterDonis]

Is it true that the speed of light is only dependent on the size of the universe

Not according to our best current measurements. As far as we can tell, the speed of light is constant and does not depend on the size of the universe.

 

[PeterDonis]

https://en.wikipedia.org/wiki/Variable_speed_of_light

These models are speculative and do not have any experimental data in their favor at this point.

 

[BiGyElLoWhAt]

Yea, I just found them, and hadn't heard of them before. OP inspired me to look into it, as I didn't know much about it.
That is what I'm gathering, however.

 

[Drakkith]

Is it true that the speed of light is only dependent on the size of the universe, if the universe were much smaller would the speed of light be faster?

Where did you read this?

 

[Chronos]

Ranks right up there with the green cheese moon theory.

 

[rootone]

This would mean that special and general relativity are based on a false assumption, (that 'c' is constant)
So somebody would need to propose an alternative to those theories which lead to the same predictions and explanations.
It won't be me.

 

[Chronos]

The basis for your premise is unclear.

 

[1oldman2]

Ranks right up there with the green cheese moon theory.

This particular theory was debunked by Bill Anders.
"Is the Moon made out of green cheese?
No, it's American cheese".

-Bills Anders, Apollo 8 Commander,

Two lines from the Wiki article.
"refers to a family of hypotheses"
"many of them non-mainstream."

 

[rootone]

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

 

[1oldman2]

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

Has the wavefunction collapsed yet?

 

[rootone]

Has the wavefunction collapsed yet?

It will in about 10 minutes, my girl friend has advised me so. Goodnight.

 

[BiGyElLoWhAt]

I don't know if that would actually violate sr, or gr for that matter. Sure, there are based on the constancy of light, however, in the sense that any observer would measure the same speed of light no matter their direction or speed of motion. If the value of c changed, but was the same throughout the universe over small ranges of time, meaning any experiment I could do would return 'c' as the speed of light, we would end up with the same lorentz transformation and same consequences, just with a different value for gamma.

 

[PeterDonis]

If the value of c changed, but was the same throughout the universe over small ranges of time, meaning any experiment I could do would return 'c' as the speed of light, we would end up with the same lorentz transformation and same consequences, just with a different value for gamma.

This doesn't make sense as you state it, because the "consequences" of a Lorentz transformation depend on the value of $\gamma$. Different $\gamma$, different consequences.

The real issue here is that $c$ is not a fundamental dimensionless physical constant; you can change its value by changing your choice of units. What we really need to look for is evidence that fundamental dimensionless physical constants, whose values are independent of the choice of units, have changed. The one most closely related to $c$ is the fine structure constant $\alpha$. So far we have found no evidence that $\alpha$ has changed over the life of the universe (or any other fundamental dimensionless constant).

 

[BiGyElLoWhAt]

I didn't mean the consequences of the lorentz transformation, I meant the consequences of SR, which is (IMO) slightly different. The consequences of SR are the lorentz transformations, which warrant that t/t' \neq 1. The same with l/l', assuming a non zero velocity between frames. If c changes, then so will the numerical value of gamma, but time dilation between frames is still a thing. That is what I meant.

Interestingly, though, is that this implies a "god frame" so to speak. An "absolutely stationary" frame in which the size of the universe is measured in order to determine c.

 

[PeterDonis]

If c changes, then so will the numerical value of gamma, but time dilation between frames is still a thing.

Unless you have an actual acceptable reference describing a theory that shows this, I would be very careful making such claims. Certainly standard SR (or GR) is not such a theory.

Interestingly, though, is that this implies a "god frame" so to speak. An "absolutely stationary" frame in which the size of the universe is measured in order to determine c.

Same comment as above. Please bear in mind the PF rules about personal theories.

Also, you don't seem to have grasped the other point I made in my previous post, regarding which constants are actually "fundamental".

 

[BiGyElLoWhAt]

I'm not trying to make my own theory, I linked to "variable speed of light theories" previously, and that is what this thread is about, no?
SR assumes that all observers (at least the ones that are capable of observing each other, all of the derivations I have seen utilize this concept) that measure "c" will agree on it's value. Generally, it assumes that the experiments are "close togwther in time". I.e. in my frame, they are happening simultaneously. Again, all of the derivations that I have seen are setup as such. Despite the value of c, you will end up with the same transformations. If the changea were small enough for some mystical c (t), then we would never even notice it.
In order for c to be a function of the size of the universe, and for all observers to agree on c, then either a) all observers would have to agree on the size of the universe, or b) there would have to be an absolute size to the universe. Is there a 3rd option that can keep these consistent that I'm overlooking? I'm not advocating for the theories, I just find them interesting as they seem to shake things up, but they would still have to be consistent with observations.

 

[PeterDonis]

I linked to "variable speed of light theories" previously, and that is what this thread is about, no?

The Wikipedia article you linked to earlier talks about speculative models predicting a variable speed of light (more precisely a variable fine structure constant). But we don't know if those are what the OP was asking about; he hasn't said.

But more importantly, the speculations you are making have nothing to do, as far as I can see, with the speculations referred to in the Wikipedia article. See below.

I'm not advocating for the theories

You're not even talking about them, as far as I can see. You're just waving your hands about what you think some imaginary theory in which $c$ varies might look like. What you should be doing, if you're really interested in the (speculative) theories along these lines already advanced, is to read the actual papers proposing them and see what they say, and then base your discussion on that (with references).

 

[Drakkith]

If c changes, then so will the numerical value of gamma, but time dilation between frames is still a thing.

Reminds me of a "game" some college students made where the value of c was much, much smaller. Something like 10 mph or something. The player controlled a character who had to walk/run around and perform some (usually) trivial tasks. But with the reduced speed of light, relativistic effects were very noticeable, making these trivial tasks not so trivial anymore.

 

[BiGyElLoWhAt]

But we don't know if those are what the OP was asking about; he hasn't said.

You're right, I just assumed and since I wasn't ever corrected, assumed that to be the case.

You're not even talking about them, as far as I can see. You're just waving your hands about what you think some imaginary theory in which $c$ varies might look like. What you should be doing, if you're really interested in the (speculative) theories along these lines already advanced, is to read the actual papers proposing them and see what they say, and then base your discussion on that (with references).

I suppose it is a little bit out there. I'm assuming that the observational consequences of SR still need to be intact. In the ways that I know how to derive the Lorentz transformations via light clocks and the like, at any value of t in some frame, if an observer measures c in that frame and then in another, nearly-simultaneously for the observer in question, they will notice that time and length are both distorted. The postulates of SR, in fact, do assume that "c is constant". However, in practice, it doesn't seem to be utilized as strongly. "c is constant" means, to me, constant through both space and time. It seems to be used meaning constant through space. This may or may not be the case with GR. I'm not very far into GR as of right now.
I might be spouting off again. I'll go look through some papers that I find and see what they say.

 

[PeterDonis]

I might be spouting off again.

Yes, you are. Please look at the actual papers.

 

[BiGyElLoWhAt]

Yes, you are. Please look at the actual papers.

In progress...

 

[BiGyElLoWhAt]

https://arxiv.org/abs/astro-ph/0305457
Here, this isn't necessarily about a specific theory, at least not yet. Just some general things about VSL theories, and apparently later he analyzes some of them.
He seems to be making comments about alpha similar to what you were doing. However, his argument which resembles what I interpreted you to be saying earlier, "A varying speed of light = a varying set of units" doesn't seem to hold much water. He says

This remark was clearly made by Bekenstein [11], who pointed out that the “observation” of a varying dimensional constant is at best a tautology, since it relies on the definition of a system of units.

...

it is always possible to define units such that c remains a constant.

However, in his example, the meter was defined in terms of c. Of course c is constant if c is defined as a function of c!
If we define the meter in terms of c, so $1 \text{meter} = \frac{1}{299,***,***}\times c \times N_{\text{Cs}=1s} \times ( \text{duration of one excitation of cs} )$
What do you end up with? $1=1$ ? These quantities are linearly dependent on each other (the meter and c), and you will always get a constant c if you define the meter in terms of c. However, if you were to go old school, grab a meter stick, and define a meter to be that long, would you experience the same thing? Now we have value, c, which is linearly independent of both the definition of time (using current SI), and the definition of length. Does the same argument hold?
My hunch says no, but I might be missing something. I will continue to go through this article, but 2 sections later, he still hasn't clarified this.

 

[BiGyElLoWhAt]

Hmmm... That was a bad example, apparently. Unrelated to the thread. Feel free to delete, or annotate as needed.

We are now ready to define varying speed of light. VSL theories are theories in which you find yourself in a situation like the one in the last example, regarding the speed of light in vacuum. They are theories in which the dynamics is rendered more simple if units are chosen in which c is not constant.

So this is explicitly about units. I don't think this is what OP was asking about. "Is the speed of light dependent on the size of the universe?" Changing units of length would be arbitrary, which leaves only time to vary, and that gets weird with SR when I think about it.

 

[PeterDonis]

If we define the meter in terms of c, so $1 \text{meter} = \frac{1}{299,***,***}\times c \times N_{\text{Cs}=1s} \times ( \text{duration of one excitation of cs}$ )
What do you end up with? $1=1$ ?

No, you end up with a value of $c$ that is defined to be a constant numerical value, so that your units of length and time are both dependent on a single standard (in the case of SI units, the Cesium transition frequency standard). But there is no requirement that the constant numerical value that $c$ is defined to be must be 1. Obviously that's not the case for SI units, in which that value is 299,792,458 by definition.

if you were to go old school, grab a meter stick, and define a meter to be that long, would you experience the same thing?

No, because your value of $c$ in this case will not be a defined constant numerical value. It will be the outcome of a comparison between two measurement standards. In the case of SI units before the meter was redefined, it would be a comparison between the length standard for the meter and the time standard for the second--more precisely, a comparison of the behavior of light relative to both standards, in order to obtain a numerical value for $c$.

 

[PeterDonis]

So this is explicitly about units.

Not just about units, no. Read what he says carefully: "the dynamics is rendered more simple if units are chosen in which $c$ is not constant". There is still actual dynamics going on, which is there regardless of how you define your units. But it looks simpler (at least in the particular speculative theories he is discussing at this point) if we choose units in which $c$ is not constant (more precisely, is not defined to be constant--e.g., SI units before the meter was redefined, as opposed to after).

There is also a very important remark at the beginning of section 2.1 (bottom of p. 5):

"The speed of light is a quantity with units (units of speed) and in a world without constants there is no a priori guarantee that meter sticks are the same at all points and that clocks spread throughout the universe are identical."

In other words, the actual dynamics might cause standards of length and time (like meter sticks or Cesium clocks) to behave differently in different regions of spacetime. This must be ultimately expressible in terms of truly fundamental dimensionless constants (like the fine structure constant), regardless of what units we choose for length, time, etc. But it might look simpler with a judicious choice of units, just as certain spacetime geometries in GR look simpler with a judicious choice of coordinates.

 

[BiGyElLoWhAt]

I thought he was talking about, say Lagrangian or Newtonian mechanics as he was a shortly before that. As in the dynamics of motion.

 

[PeterDonis]

I thought he was talking about, say Lagrangian or Newtonian mechanics as he was a shortly before that. As in the dynamics of motion.

He's talking about how you describe the dynamics, whatever dynamics it is. In other words, he's talking about how your theory represents everything that it needs to represent in order to make predictions that can be compared with experiments. The experimental results are ultimately dimensionless numbers (this point is made in the article as well), so your theory needs to somehow crank out predictions in terms of dimensionless numbers. But there are various ways of doing that, some simpler than others, and sometimes the simpler way involves defining a system of units such that $c$, or other "physical constants" (the article mentions $G$ and $\hbar$) are not actually constant. Consider, for example, his discussion of electrodynamics and the speed of light in a dielectric medium.

 

[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.