B What would happen if the speed of light were different?

No

 

This topic has come up several times. You'll often get a faster answer with a forum search.

You can't just change the speed of light, because the physical constants are linked. So you also have to specify what else you are changing and what you are not - and at least one other thing must change.

Generally, if you work through the consequences of such a change there is no effect. It turns out to be a Byzantine way of changing your units. Obviously we can halve the value of the speed of light by defining the metre to be twice what it is, and obviously this makes no difference to anything.

The exception turns out to be if you change the fine structure constant, which is a dimensionless number which relates the speed of light to the strength of the electromagnetic interaction. Since you (and everything else) are held together by electromagnetic interactions between your atoms, this changes the relationship between your size and the speed of light. In other words, this actually changes the relationship between monkey arm lengths (~1m), monkey heart beats (~1s), and the speed of light (a natural scale factor between distance and time units).

I don't think mucking around with the fine structure constant has any effect classically beyond changing the speed of light (or, at least, being interpretable as a change in the speed of light). My quantum (what I ever knew of it) is way too rusty to know if there are effects there - others may know.

 

In case you didn't know....

That's the speed of light in a vacuum. It's different in other media like water (about 25% slower).

 

As others have mentioned, experimental tests to see of the speed of light changes with time usually revolve around looking for changes in the fine structure constant.

The fine structure constant is something that one can measure that doesn't depend on one's units system. If you believe that plank's constant, the charge on the electron and the permittivity of free space are all constant, then detecting a change in the fine structure constant would be equivalent to saying the speed of light varies. Such experimental tests as have been done for changes in c really measure the fine structure constant (as far as I know), so if you want to look at the experimental literature, that's a good place to start.

Talking about changes in the fine structure constant eliminates trivial "changes" in the speed of light that amount to changes in units. For instance, the speed of light is about 9.8e8 feet/second. If one called a meter a foot, one might claim that the change of nomenclature "changed" the speed of light, but it was really just a changing in words, not a change in physics.

Considering only dimensionless quantities such as the fine structure constant eliminates this sort of confusion, because the units all cancel out and it's a pure number that's independent of one's choice of units.

 

Hi @Dale:

I think you (and others) misunderstood what the OP was asking. Suppose I rephrase the OP question as follow:

Suppose the fine structure constant, α = 2π e² / h c, actually had a different value some time in the past, t, than it does now, t₀, and the values of e and h are unchanged. This would imply that the speed of light in vacuum would also have had a different value at time t. Under this assumption, what astronomical measurements could be detected now that would confirm this had happen? ​

Obliviously the answer would depend on how large a change there was, so the most useful answer would assume the smallest changes, both + and -, that would result in some detectable measurements now.

Regards,
Buzz

 

Hi Peter:

I confess I find your post to be quite fascinating. I would much appreciate your explanation about how the energy E of a photon is measured, and why this measurement depends on knowing the speed of light. I am assuming that it is not a problem to measure the frequency f of a photon without knowing the speed of light. If both h and f can be measured without knowing c, then since E = h f, h could then be determined without knowing the value of c.

I may also be misunderstanding the description of the Millikan’s experiment

https://users.wfu.edu/~bonin/Intermediate_Lab_Phys_265/Millikan_Oil_Drop_Charge_electron.pdf​

which seems to be measuring e without requiring knowledge of c. I understand that measuring e requires measuring voltage, and I was not able to find on the Internet what the method is for establishing the standard for the volt unit. So, I may be mistaken, and the establishment of the volt unit might require knowing the speed of light.

Regards,
Buzz

 

Hi Peter:

Obviously I misunderstood the meaning of:

My interpretation was that given α = 2π e2 / h c, if α changes, and e does not change and h does not change, then the change is α must be due a change in c. If e can be measured without specifying a value for c, and e can be measured without specifying a value for c, then the changed value of c can be calculated: c = 2π e2 / h α.

That is, under the assumptions of h and e being measured and found to not change in value, then c changes inversely to α. If that is correct, what is the meaning of: "So there is no physical meaning to asking which one of c, e, and h 'actually' changed,"?

Regards,
Buzz

 

Hi Peter:

I get from this that the "usual" way of measuring frequency depends on knowing h, so using that method would not allow for the determination of h from E and f. Are you saying that all methods of determining frequency depend on the prior knowing h?

Regards,
Buzz

 

Hi Peter:

I did not say that this

is what you said. I said it was my interpretation of what you said, and I also indicated that I realized my interpretation was incorrect.

I confess that I am having difficulty understanding the meaning of you posts, and reading them again will not help me. You last paragraph did provide some help.

What is still a mystery to me is that I do not understand the reason that,
"The formula α=2π e²/ h c does not tell you how to calculate α once you've measured h, e, and c."
If h, e, and c, can be measured independently of knowing the value of α, what prevents the value of α from being calculated in this manner? I understand that this is not the "usual" way α is measured, but if this calculated determination of α is significantly different than the "usual" determination of α, wouldn't this result be of interest to physicists?

Regards,
Buzz

 

Hi Peter:

Thank you for the reference. I did previously look at this Wikipedia article but skipped over the discussion about the Josephson junction since it was way over my head. After your citing the reference I found some more detailed references with somewhat understandable discussions. I was able to satisfy myself that a voltage value could be determined without any knowledge of values for α, e, h, and c. From this I concluded that the value of e could be determined using the Michelson method without any knowledge of values for the other 3 constants.

Regards,
Buzz

 

They can't. Or, more precisely, there's a hidden assumption somewhere in any experiment that purports to measure them. For example, if you try to measure the speed of light you'll need a meter rule somewhere and its length depends on the strength of the interaction between atoms, which depends on e. I seem to recall @Dale worked this out in more detail recently, but I can't find the post at the moment.