# How to rule out that the speed of light was different in the past?

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victorvmotti
The constancy of the speed of light is a fundamental principle in modern physics, and it is supported by a wide range of current experimental evidence.

There is no evidence to suggest that the speed of light was different in the past, and the idea that it could have been different is at odds with current scientific understanding.

But how can we test and experiment in the present and definitely rule out that the speed of light was differenet in the past?

Mentor
Under the current definition of the meter it is logically impossible for the speed of light to be different in the past when written in units of meters per second.

Perhaps you are interested in whether the fine structure constant has changed over time instead.

PeroK and FactChecker
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Gold Member
Under the current definition of the meter it is logically impossible for the speed of light to be different in the past when written in units of meters per second.
But might that just imply that the current definition of the meter based on the speed of light is not wise in general?
Perhaps you are interested in whether the fine structure constant has changed over time instead.
That does sound interesting. It's my (admittedly amateur) understanding that this is one factor that determines the speed of electromagnetic wave propagation.

victorvmotti
Under the current definition of the meter it is logically impossible for the speed of light to be different in the past when written in units of meters per second.
So you are saying that we do not need a test, and it can be shown logically, but how, that is the question, any hint, still not clear, why it is logically impossible to say that the speed of light was either smaller or larger in the past than the current measurment?

2022 Award
So you are saying that we do not need a test, and it can be shown logically, but how, that is the question, any hint, still not clear, why it is logically impossible to say that the speed of light was either smaller or larger in the past than the current measurment?
The speed of light is a defined constant, not a measurement. It can't be anything other than what it is until the SI standards board next meets. More generally, any constant with units can be made to have any value you like by fiat. You need to look at the dimensionless constants for evidence of physically meaningful change. The fine structure constant is the relevant one for electromagnetism.

vanhees71, DaveE, PeterDonis and 3 others
why it is logically impossible to say that the speed of light was either smaller or larger in the past than the current measurment?

Light moves with the invariant speed, that is defined via the SI unit system as follows:
Wikipedia said:
From 1983 until 2019, the metre was formally defined as the length of the path travelled by light in a vacuum in ##\frac{1}{299792458}## of a second. After the 2019 redefinition of the SI base units, this definition was rephrased to include the definition of a second in terms of the caesium frequency ##\Delta \nu_{Cs}##.
Source:
https://en.wikipedia.org/wiki/Metre

Chenkel, vanhees71 and Dale
Mentor
But how can we test and experiment in the present and definitely rule out that the speed of light was differenet in the past?
As Dale has already pointed out, you are actually asking whether the value of the fine structure constant has changed over time. Observations of spectral lines in radiation emitted by distant objects tell us about the value of the fine structure constant at the time that the radiation was emitted - and for distant objects that can be billions of years ago.

vanhees71, hutchphd, Ibix and 1 other person
Staff Emeritus
The speed of light is a defined constant

How do we know that a dozen was twelve in the past?

martinbn, vanhees71, malawi_glenn and 1 other person
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How do we know that a dozen was twelve in the past?
We dozent!

pinball1970, martinbn, vanhees71 and 7 others
victorvmotti
The speed of light is a defined constant, not a measurement. It can't be anything other than what it is until the SI standards board next meets.
I believe that I get it now. So speed of light is actually a strcutural constant of the spacetime geometry. And the unit of measurement of distance, meter, is actually defined using this constant which relates time to space. So logically it does not make sense to say if the speed of light was different in the past or not. Right?

vanhees71 and PeroK
2022 Award
So logically it does not make sense to say if the speed of light was different in the past or not. Right?
As currently defined, yes.

There's nothing to stop us switching to another standard (e.g. the standard meter in Paris again, although that's a bad idea), in which case the speed of light might again become measurable. But you'd still be unable to detect any changes - because changes in the speed of light mean changes in the electromagnetic field strength which mean changes in the length of the standard meter which cancel out the changes in the speed of light so it remains the same number of (revised) meters per second.

It's changes in the fine structure constant you need to look for.

vanhees71, Dale, victorvmotti and 1 other person
victorvmotti
because changes in the speed of light mean changes in the electromagnetic field strength which mean changes in the length of the standard meter which cancel out the changes in the speed of light so it remains the same number of (revised) meters per second.
I cannot follow, how about showing/writing the calculation you are doing so that I see what is cancelling out?

Gold Member
Under the current definition of the meter it is logically impossible for the speed of light to be different in the past when written in units of meters per second.

Perhaps you are interested in whether the fine structure constant has changed over time instead.
OP did not ask about metres. That can be considered a red herring. So:

Is it possible to find evidence that light took longer to get from one side of Earth to the other side in the past?

victorvmotti
Mentor
OP did not ask about metres. That can be considered a red herring. So:

Is it possible to find evidence that light took longer to get from one side of Earth to the other side in the past?
The thing is that it isn’t a red herring. It is teaching an important principle:

Asking about a change in a dimensionful universal constant is not meaningful. Only the dimensionless universal constants are physically meaningful.

It just happens that the meaninglessness is most apparent with the speed of light and SI units. That is why the related physical question must be about the fine structure constant.

vanhees71, Motore and DaveE
Mentor
I cannot follow, how about showing/writing the calculation you are doing so that I see what is cancelling out?
To measure the speed of light you need to measure a distance and then time how long it takes for light to travel that distance.

So suppose you have a distance where it takes ##t=10\mathrm{\ ns}## for light to go. Now, to determine the length in meters then by the SI definition of the meter the distance is ##d=c \ t=2.99792458 \mathrm{\ m}##. So then you get exactly ##d/t=(c\ t)/t=c## for the speed. There is no way to get a different number for ##c## because the time and ##c## together determine the distance in meters.

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vanhees71
Staff Emeritus
The modern (post 1905) view is that c is an artifact of our system of units. It comes about because we traditionally measure space in meters and time in seconds, and this is the conversion factor. In this regard it is no different than in aviation, where x and z are measured in nautical miles, but y is measured in feet.

Asking if c was different in the past is exactly the same as asking if the number of feet in a nautical mile was different in the past.

Further, we know that two objects are the same size by placing them next to each other and seeing if they line up. If two objects are at different places, this is impossible. A similar argument can be made for durations. As such, there is no way to tell if the speed of anything were different in the past without a chain of inferences and assumptions, such as a "a metter then is the same length as a meter now".

Because of this, one can only compare dimensionless quantities over time. However, I disagree with my fellow forum members that a change in c means a change in α. Yesa, in some sets of units α = e2/ħc., and there's a c there. But in other units, α = e2/4π. The only thing that is always present is the e2, the electron's charge (coupling) so it makes much, much more sense to consider α a neasure of charge than a measure of speed.

People can and do look for variations in natural properties over time, In principle, one could discover that the time (measured in cesium transitions) for light to travel a distance (measured in krypton wavelengths) is different today than it was last Tuesday, but that doesn;t tell us whether the second has changed, the meter has changed, or c has changed, and for good and sound reasons, we decide that c is taken to be constant. (And also that the second is constant)

Dale, vanhees71 and PeroK
Mentor
I disagree with my fellow forum members that a change in c means a change in α
You are right that a change in ##c## need not imply a change in ##\alpha##, but your fellow forum members are making a weaker claim: When someone asks about the physical consequences of the speed of light being different, we should instead be talking about a change the value of ##\alpha##.

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Dale, vanhees71 and Motore
Mentor
I disagree with my fellow forum members that a change in c means a change in α.
It isn’t that a change in ##c ## means a change in ##\alpha##, at least in my view. It is that the dimensionless fundamental constant governing electromagnetism is ##\alpha##.

So if there were a physical change in electromagnetism it would be reflected in a change in ##\alpha##. How that physical change would be partitioned into units and dimensionful constants is purely a matter of convention.

PeroK and PeterDonis
victorvmotti
To measure the speed of light you need to measure a distance and then time how long it takes for light to travel that distance.

So suppose you have a distance where it takes ##t=10\mathrm{\ ns}## to go. Now, to determine the length in meters then by the SI definition of the meter the distance is ##d=c \ t=2.99792458 \mathrm{\ m}##. So then you exactly ##d/t=(c\ t)/t=c## for the speed. There is no way to get a different number for ##c## because the time and ##c## together determine the distance in meters.
So you use the "present" speed of light in the present to compute a distance and then compute the speed of light, having used the speed of light, by canceling out the time! Isn't this meaningless? Also, where did you compare with the past, when the same distance could have been travelled in larger time provided that speed of light was slower in the past? I still don't see the contradiction.

PeroK
Mentor
So you use the "present" speed of light in the present to compute a distance
No, I use the SI definition of the meter to measure a distance.

and then compute the speed of light, having used the speed of light, by canceling out the time! Isn't this meaningless?
Yes, that is the point. In SI units that is the only possible outcome.

It turns out that this is not a weakness of SI units, it is just more obvious in SI units. If you use a different standard of length, say a physical object, then you still wind up in a similar situation. A change in ##c## that leaves ##\alpha## unchanged produces no change in an experiment designed to measure the speed of light. In contrast, a change in ##\alpha## without a change in ##c## does produce a change in such an experiment.

Mentor
So you use the "present" speed of light in the present to compute a distance and then compute the speed of light, having used the speed of light, by canceling out the time! Isn't this meaningless?
You have just identified the reason why asking about the speed of light is unhelpful - we can never get away from the tautology that the speed of light is one light-second per second, one light-year per year, 186000 miles per second after we've learned that a mile is 1/186000 the distance that light travels in a second, ....

That's why we're saying that you want to be asking about the fine-structure constant ##\alpha## instead. If the physics of light propagation were different, the fine structure constant would have a different value. And as I said in post #7 above, we can measure the value of the fine structure constant both now and as it was billions of years ago.

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The constancy of the speed of light is a fundamental principle in modern physics, and it is supported by a wide range of current experimental evidence.

There is no evidence to suggest that the speed of light was different in the past, and the idea that it could have been different is at odds with current scientific understanding.

But how can we test and experiment in the present and definitely rule out that the speed of light was differenet in the past?
You need to be a bit more specific and we need to be more careful. If you mean: what if the value of the constant c changes in time then these answers are correct.
But if you mean: what if red light used to be slower than green light than the crap will hit the fan.
In order to measure a quantity you must compare it to a like quantity. This means you will measure a ratio no matter how circuitously you make the measurement. So the value of one of the dimensionless constants would also change.

victorvmotti
we can never get away from the tautology
Now fully clear, if in the present the speed of light is one light-second per second then in the past it was again one light-second per second. No different!

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Dale and PeroK
I cannot follow, how about showing/writing the calculation you are doing so that I see what is cancelling out?
This can be argued via the Bohr radius.

The length of the old meter prototype ##L_1## is a multiple (factor := ##k##) of the Bohr radius ##a_0##:
##L_1 = k * a_0 = k * \frac {\hbar}{m_ec\alpha}##.

Source:

=> ##\ \ \ c = k * \frac {\hbar}{m_e L_1 \alpha}##

So, if ##L_1## is assumed to be "constant with time", then you will measure a constant ##c##.

Gold Member
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You can as well argue in the same way you argued about the meter with the fine structure contant since it also
You are right that a change in ##c## need not imply a change in ##\alpha##, but your fellow forum members are making a weaker claim: When someone asks about the physical consequences of the speed of light being different, we should instead be talking about a change the value of ##\alpha##.
I think one can make the point clear from this example, using the new SI. In fact the new SI is the (almost) most transparent definition of a coherent set of (base) units we have, given our current fundamental natural laws. Of course we need the fundamental natural laws as far as we know them to define our units.

The new SI is based on a set of general fundamental constants, except the second for practical reasons, i.e., because we still cannot determine the value of the gravitational constant given the present definition of the base units to also use its value as defining the SI units completely with fundamental constants.

That's why the SI still uses ##\Delta \nu_{\text{Cs}}## to define the second, i.e., the frequency of the em. wave emitted due to the groundstate hyperfine transition of Cs-133:
The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, ##\Delta \nu_{\text{Cs}}##, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to ##\text{s}^{−1}##.
All the other (physical) base units define the values "fundamental constants of Nature", according to our current understanding of these laws. So, indeed, the metre is defined by just choosing a value for the limiting speed of relativity, which empirically is to a very high accurcy the phase velocity of electromagnetic waves in a vacuum:
The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum ##c## to be 299792458 when expressed in the unit ##\text{m} \cdot \text{s}^{-1}##, where the second is defined in terms of the caesium frequency ##\Delta \nu_{\text{Cs}}##.
Then to define the kg the Planck unit of action (not the modified Planck constant!) is used:
The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant ##h## to be ##6.62607015 \cdot 10^{−34}## when expressed in the unit J⋅s, which is equal to ##\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-1}##, where the metre and the second are defined in terms of ##c## and ##\Delta \nu_{\text{Cs}}##.
Finally for this argument we need the definition of the unit of electric charge or, equivalently, of the electric current:
The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be ##1.602176634 \cdot 10^{-19}## when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of ##\Delta \nu_{\text{Cs}}##.
Now we have the four base units defined needed for the argument, why it makes sense to ask and to decide empirically, whether the fine structure contant has changed over time. The finestructure constant is a dimensionless quantity defined by
$$\alpha=\frac{e^2}{4 \pi \epsilon_0 \hbar c}.$$
Here everything has defined values, except ##\epsilon_0##, which must be measured, given the values of ##\hbar=h/(2 \pi)##, ##c##, and ##e##, which are all defined values when expressed in the SI units according to the above quoted 2019 definition of the SI base units (s, m, kg, and A).

The current state of the art is ##k_e=1/(4 \pi \epsilon_0)= 8.9875517923(14) \cdot 10^9 \text{N} \cdot \text{m}^3 \cdot \text{s}^{-4} \cdot \text{A}^2##. It's determined (according to the CODATA-2018 paper) by measuring the anomalous magnetic moment of the electron or recoils of atoms when emitting em. radiation.

Sagittarius A-Star, Vanadium 50 and LittleSchwinger
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vanhees71
Lluis Olle
Under the current definition of the meter it is logically impossible for the speed of light to be different in the past when written in units of meters per second.

Perhaps you are interested in whether the fine structure constant has changed over time instead.
Yes, but then do the permittivity and permeability ratio of vacuum (free space) could be different some billions of years ago?

PeroK
Staff Emeritus
I think the definition of the Hartree atomic units may shed particular light on this subject.
I think it makes it worse and not better. It mixes the fundamental with the practical.

Staff Emeritus
@victorvmotti , for your question to make sense in a scientific sense, there must be some way to measure it. Please tell us how to measure what the sped of light was 2000 years ago, or 2 million, or 2 billion. Take your pick.

vanhees71
Mentor
@victorvmotti , for your question to make sense in a scientific sense, there must be some way to measure it. Please tell us how to measure what the sped of light was 2000 years ago, or 2 million, or 2 billion. Take your pick.
To be fair, his question is basically "How can we be so sure it hasn't changed if we can't measure it?"

Staff Emeritus
α is absolutely not the speed of light morphed into a dimensionless form.
Insofar as it is anything at all besides α, it is the charge of the electron morphed into a dimensionless form.

c is a factor that comes about because we historically measured time in seconds and length in meters. (And is equal to a dimensionless 1 in sane units). It's a conversion factor, like the dozen. No more, no less. It tells us about spacetime, not electromagnetism.

Mentor
Yes, but then do the permittivity and permeability ratio of vacuum (free space) could be different some billions of years ago?
This runs into the same problem that I mentioned previously, it is just not so obvious:

A change in c that leaves α unchanged produces no change in an experiment designed to measure the speed of light. In contrast, a change in α without a change in c does produce a change in such an experiment.
The same thing happens with ##\epsilon_0## or any other dimensionful universal constant for EM.

victorvmotti
@victorvmotti , for your question to make sense in a scientific sense, there must be some way to measure it. Please tell us how to measure what the sped of light was 2000 years ago, or 2 million, or 2 billion. Take your pick.
After reading the responses here and elsewhere, and noting the repeated emphasis on the fine structure constant by the Physics Forums community mentors, I'd say we can measure it in the past indirectly. So, assuming that other dimensionful constants involved in this particular ratio known as ##\alpha## were not different in the past, say in 2 billion years ago, we can refer to the data from the Oklo mine natural nuclear reactor. And it looks like we have experimental evidence here on our planet from at least 2 billion years ago, ruling out that the speed of light was different in the past!