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

if speed of light were not 3*10 ^8 m/s and something else would it affect the reality ?

No

• Dale
Ibix
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.

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but if doesnt change anything how would we know that the speed of light was constant over the time ? and it was changing over the time as the universe was expanding

Dale
Mentor
2021 Award
but if doesnt change anything how would we know that the speed of light was constant over the time ?
We can just define the speed of light to be constant over time.

What physicists are actually interested in is whether the fine structure constant is constant over time. That is a matter of real physics, not just unit choices.

• Sorcerer
CWatters
Homework Helper
Gold Member
if speed of light were not 3*10 ^8 m/s and something else would it affect the reality ?
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).

pervect
Staff Emeritus
if speed of light were not 3*10 ^8 m/s and something else would it affect the reality ?
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.

Buzz Bloom
Gold Member
We can just define the speed of light to be constant over time.
What physicists are actually interested in is whether the fine structure constant is constant over time. That is a matter of real physics, not just unit choices.
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

PeterDonis
Mentor
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

This is a meaningful question, yes.

and the values of e and h are unchanged

But this is not. If the fine structure constant changes, it is entirely up to your choice of units which of c, e, and h you want to change; you could choose for any one of them to change, or any two, or all three. So there is no physical meaning to asking which one of c, e, and h "actually" changed. The only physically meaningful question is whether the fine structure constant changed.

• Sorcerer
Buzz Bloom
Gold Member
So there is no physical meaning to asking which one of c, e, and h "actually" changed. The only physically meaningful question is whether the fine structure constant changed.
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
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

PeterDonis
Mentor
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.

Who said it did?

I am assuming that it is not a problem to measure the frequency f of a photon without knowing the speed of light.

How would you measure the frequency of a photon?

If both h and f can be measured without knowing c

The usual way of "measuring" the frequency of a photon is to measure its energy and divide by Planck's constant.

which seems to be measuring e without requiring knowledge of c

Yes. So what?

I was not able to find on the Internet what the method is for establishing the standard for the volt unit

Buzz Bloom
Gold Member
Who said it did?
Hi Peter:

Obviously I misunderstood the meaning of:
So there is no physical meaning to asking which one of c, e, and h "actually" changed. The only physically meaningful question is whether the fine structure constant changed.
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

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PeterDonis
Mentor
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.

Please go back and read my post again, carefully. This is not what I said.

If that is correct

It isn't. Go back and read my post again, carefully.

what is the meaning of: "So there is no physical meaning to asking which one of c, e, and h 'actually' changed,"?

You are confusing yourself by thinking that you measure h, e, and c. You don't. You measure ##\alpha##. (More precisely, you observe and record physical events whose relationships depend on ##\alpha##.) The formula ##\alpha = 2 \pi e^2 / h c## does not tell you how to calculate ##\alpha## once you've measured h, e, and c. It tells you how your measurement of ##\alpha## is related to other measurements. Summarizing the results of lots of different measurements in constants like h, e, and c, which have units, is a matter of convenience (and historical practice), not physics; all of the actual physics is in dimensionless numbers like ##\alpha##.

Buzz Bloom
Gold Member
The usual way of "measuring" the frequency of a photon is to measure its energy and divide by Planck's constant.
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

Buzz Bloom
Gold Member
Please go back and read my post again, carefully. This is not what I said.
Hi Peter:

I did not say that this
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
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.
Obviously I misunderstood the meaning of:

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.
You are confusing yourself by thinking that you measure h, e, and c. You don't. You measure α\alpha. (More precisely, you observe and record physical events whose relationships depend on α\alpha.) The formula α=2πe2/hc\alpha = 2 \pi e^2 / h c does not tell you how to calculate α\alpha once you've measured h, e, and c. It tells you how your measurement of α\alpha is related to other measurements. Summarizing the results of lots of different measurements in constants like h, e, and c, which have units, is a matter of convenience (and historical practice), not physics; all of the actual physics is in dimensionless numbers like α\alpha.

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

Buzz Bloom
Gold Member
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

Ibix
If h, e, and c, can be measured independently of knowing the value of α,
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.

• Buzz Bloom
PeterDonis
Mentor
I was able to satisfy myself that a voltage value could be determined without any knowledge of values for α, e, h, and c.

How?

PeterDonis
Mentor
I was able to satisfy myself that a voltage value could be determined without any knowledge of values for α, e, h, and c.

The fact that you can make a particular measurement without knowing the value of ##\alpha## does not mean that the process you are measuring does not depend on the value of ##\alpha##. This confusion seems to be a crucial one for you in this discussion.

Buzz Bloom
Gold Member
How?
Hi Peter:

Here is the URLs for the articles I was using for a reference.
Figure 1 in the 2nd reference has the following caption.
Fig. 1.One-volt NIST Josephson Junction array standard having 3020 junctions. The chip was designed and built by staff of the Electromagnetic Technology Division in Boulder in the cryoelectronic fabrication laboratory. It operates at liquid-helium temperatures; microwave energy is fed to four chains of junctions through the finguide structure at the left. The thin tapered structures at the end of each chain are terminations to prevent reflection of energy back up the chain.​
My understanding from what I perused (as best I could) is that NIST has produced (1991) a stable 1 volt standard apparatus.
In 1991 NIST conducted the first JVS laboratory comparison experiment using transportable 10 V Zener standards, in which five other U.S.industrial and military laboratories participated . Such comparisons are now carried out regularly under the auspices of the National Conference of Standards Laboratories, an industry trade association, with support from NIST as necessary.​
I conclude (perhaps erroneously) that this apparatus could be used to establish a Michelson setup with a controlled voltage to determine the value of e.

Regards,
Buzz

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PeterDonis
Mentor
My understanding from what I perused (as best I could) is that NIST has produced (1991) a stable 1 volt standard apparatus.

Ok, but does the behavior of this apparatus depend on the value of ##\alpha##? (Hint: the answer is yes.)

• Dale
Buzz Bloom
Gold Member
The fact that you can make a particular measurement without knowing the value of α\alpha does not mean that the process you are measuring does not depend on the value of α\alpha. This confusion seems to be a crucial one for you in this discussion.
Hi Peter:

Thanks for the post. I need to digest this quote for a while before I can determine if I can correctly understand its implications.

Regards,
Buzz

Buzz Bloom
Gold Member
Ok, but does the behavior of this apparatus depend on the value of α\alpha? (Hint: the answer is yes.)
Hi Peter:

I accept that your quote is correct, and that this means that the thought experiments I have been considering are flawed since it must be the case that efforts to measure a value for any of the four constants have hidden dependencies of the value of one or more other constants. I accept that for the present I am not able to understand the nature of these hidden dependencies. Thank you for making this clear to me.

Regards,
Buzz

PeterDonis
Mentor
it must be the case that efforts to measure a value for any of the four constants has hidden dependencies of the value of one or more other constants

It's not that: it's that there is really only one constant here, ##\alpha##. That is the only value with physical meaning in the set you give. The others are just choices of units.

Thinking about concrete examples might help. Consider the following collection of devices:

A standard 1 Volt Josephson junction array as described in your links.

A cesium clock such as those used in the SI definition of the second.

An oil drop experiment.

A photoelectric effect experiment.

(We could add more, but this should be enough for the point I'm going to make.)

You can think of these devices as devices for "measuring" physical constants like e or c or h. And you can think of then combining the results using the formula given earlier in this thread to "calculate" a value for ##\alpha##. But that gets things backwards. Actually, all of these experiments are experiments for measuring the value of ##\alpha##: more precisely, the value of ##\alpha## (and the values of other dimensionless constants--for example, the effect of gravity of the oil drop affects the result of the oil drop experiment, and ##\alpha## doesn't describe anything about gravity) governs the relationship between what is observed in all of these different devices. Different choices of units are just different ways of expressing that relationship, depending on which device we want to focus on.

Now let's go back to the original question in this thread: how would we tell if the values of any of these constants have changed over time? The point is that any such change won't just change one of these devices; it will change all of them. More precisely, if you just look at one of these devices, there is no way to tell if its behavior has "changed" over time. Suppose I told you that the value of a Volt was different a billion years ago. You interpret that as saying that the behavior of a standard Josephson junction array was different a billion years ago. But how would you tell? If all you look at is standard Josephson junction arrays, there is no way to tell. Those arrays define what you mean by a Volt. You have to look at multiple devices and the relationship between them to tell if anything has "changed"; and changes in those relationships are changes in ##\alpha## (and other dimensionless constants involved with whatever other interactions are present). There is no way to isolate the changes to just e, c, or h, because there is no way to tell that something changed by just looking at one device.

Dale
Mentor
2021 Award
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.
This one is very easy in SI units. In SI units the energy of a photon is measured in joules. 1 J is a derived unit which is equal to 1 kg m^2/s^2. So the meter is part of any measurement of energy in SI units. In SI units the meter is defined in terms of c. So to measure the energy of a photon in SI units does require knowing c in SI units also.

Note: this argument is specific to SI units and may not apply in other unit systems. That is the point, the dimensionful constants give you information about your unit system, not about physics.

Millikan’s experiment ... which seems to be measuring e without requiring knowledge of c.
It is not an issue of the experiment, it is an issue of the units.

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Buzz Bloom
Gold Member
There is no way to isolate the changes to just e, c, or h, because there is no way to tell that something changed by just looking at one device.
It is not an issue of the experiment, it is an issue of the units.

Hi Peter and Dale:

I think I may have come to an understanding of these above quotes, particularly with respect to c.
https://en.wikipedia.org/wiki/International_System_of_Units#Base_units
Second (Current as of 1967): The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
Meter (Current as of 1983): The distance traveled by light in vacuum in 1/299792458 second.​
https://en.wikipedia.org/wiki/Speed_of_light
The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 meters per second.​

This means that by definition the value of c (using any units) cannot change. In effect c is defined as 1 light-second per second. If it should (hypothetically) happen that the number of seconds (or picoseconds) it takes light to travel (in vacuum) over an actual specific physical distance is measured to have changed, c would not change. What would then change is the actually physical distance corresponding to a meter. What I would guess would likely happen then is that the International Bureau of Weights and Measures (BIPM, Bureau International des Poids et Mesures) and the International Committee for Weights and/or Measures (CIPM, Comité International des Poids et Mesures) would redefine the meter independently of the speed of light, since (by the hypothetical assumption of its change) the current definition would no longer be stable.

It the above a correct interpretation of the top two quotes?

Another possible interpretation would be that the speed of light cannot change because if it did, the actual lengths of physical things would also change so that the the number of seconds for light to travel the physical distance would remain unchanged. I find this interpretation too difficult conceptually for me to absorb.

I found the following quote from Dale at
https://www.physicsforums.com/threa...-meters-per-second.279798/page-3#post-2011753 .
I wanted to work out what would be the experimental result if the speed of light doubled but the fine structure constant was unchanged.​
Assuming α changes due to the change in c, but no other "constants" change (e and h), would this change in α change the time measured by the cesium clock which would make the measured time for light to travel the physical distance to be unchanged?

Regards,
Buzz

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PeterDonis
Mentor
This means that by definition the value of c (using any units) cannot change.

No, it just means the value of ##c## in SI units cannot change, because it's not measured any more, it's defined to be a specific number.

In effect c is defined as 1 light-second per second.

No, it isn't, because in those units, the numerical value of ##c## is ##1##, not ##299,792,458##. The only thing such units have in common with SI units is that the value of ##c## is defined, not measured.

If it should (hypothetically) happen that the number of seconds (or picoseconds) it takes light to travel (in vacuum) over an actual specific physical distance is measured to have changed

How would you measure this?

I wanted to work out what would be the experimental result if the speed of light doubled but the fine structure constant was unchanged.

You still don't appear to grasp the fundamental point: the fine structure constant is the one with physical meaning. If the fine structure constant is unchanged, all experimental results are unchanged. The only way for experimental results to change is if the fine structure constant changes.

Assuming α changes due to the change in c

But you just said the fine structure constant was unchanged. That's inconsistent with this sentence.

Also, again, you are missing the point that has already been made several times: if the fine structure constant changes, it is not "due to" a change in c, e, or h. Which of c, e, and h change if the fine structure constant changes is a matter of choice of units, not physics. The physics is all in the fine structure constant.

I think you are confusing yourself more and more instead of improving your understanding. I strongly suggest taking a step back and thinking carefully about the two sentences in italics above. Any time you find yourself saying or thinking something that is not consistent with those two sentences, you are doing it wrong and need to stop.