Why is the speed of light what it is?

[Johnnyallen]

I recently saw this question on a forum thread on The Guardian's website but was unable to follow it up.
Question: Why is the speed of light what it is? Could it have been another velocity?

 

[jedishrfu]

Our physical theories are pinned on assumptions, measurements and mathematical rules specific to our theories.

Light is example of a quantity of which we have measured it’s speed and found it to be the same for all observers in inertial reference frames regardless of their speeds relative to one another. Einstein took that fact as a postulate in Special Relativity to give us the notions of length contraction and time dialation.

Why is it this speed and no other we just don’t know. Perhaps some day a theory of theories will be discovered that explains it but that’ll just mean there will be other measured values for which there is no reason.

 

[sophiecentaur]

Question: Why is the speed of light what it is? Could it have been another velocity?

'That WHY? question is just not answerable, pretty much whenever it is asked in the context of Physics.
When you say you were unable to follow it up, have you been anywhere else but Physics Forums? The speed of light is fundamental to the way things interact and its value (in a vacuum) was measured with greater and greater accuracy over the centuries. JC Maxwell studied electromagnetic theory and he predicted that the speed of light relates directly to the Electric and Magnetic properties of empty Space. This is not an answer to 'why?' but it contributes to a very well founded model of the World - including Special Relativity. All we can help for is to find models that are closer and closer to what we can measure.
Try this wiki article. (Resist the urge to skim through it - it is heavy stuff.)

 

[Johnnyallen]

'That WHY? question is just not answerable, pretty much whenever it is asked in the context of Physics.
When you say you were unable to follow it up, have you been anywhere else but Physics Forums? The speed of light is fundamental to the way things interact and its value (in a vacuum) was measured with greater and greater accuracy over the centuries. JC Maxwell studied electromagnetic theory and he predicted that the speed of light relates directly to the Electric and Magnetic properties of empty Space. This is not an answer to 'why?' but it contributes to a very well founded model of the World - including Special Relativity. All we can help for is to find models that are closer and closer to what we can measure.
Try this wiki article. (Resist the urge to skim through it - it is heavy stuff.)

The Guardian posed the question soliciting answers from its readers. Going back to their site, I couldn't find the forum, so I came here thinking that this forum would be the best place to post the question.
I downloaded the wiki link you provided as a PDF and will jump into it tonight.
I've used Wikipedia to download PDF's on Special/General Relativity, Michleson-Morley (I live just up the hill from Case Western Reserve University, the site of the most famous failed Physics experiment), Fizeau-Foucault, time dilation (I get it) and length contraction(mind-boggling). Lorentz Transformation and Einstein Field Equations were too advanced for me.
I also subscribe to PBS Digital/Space Time on YouTube. Their short, rapid-fire videos are not that hard for me to follow. (FYI I don't have a degree in Physics. Just call me curious.)

 

[sophiecentaur]

The Guardian posed the question soliciting answers from its readers.

I take the (on line) Guardian and it is a fine newspaper. I do think they should have thought twice about presenting that question to their general readership because it's far to specialised for them to get (or be able to recognise) good answers.
But there's no substitute for a good old read about these things. I am sure that wiki article will cause you to think up further questions..

 

[phinds]

Try this wiki article.

BUT ... be aware that the early statement

According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of https://en.wikipedia.org/wiki/Physical_information in the universe can travel.

INCORRECTLY implies that conventional matter CAN travel at c, whereas really only massless particles / EM waves / gravitational waves can travel at c and conventional matter cannot.

 

[sophiecentaur]

BUT ... be aware that the early statement
INCORRECTLY implies that conventional matter CAN travel at c, whereas really only massless particles / EM waves / gravitational waves can travel at c and conventional matter cannot.

That's Wiki for you. But the whole article is not a bad overview of the whole topic. You can look in a lot of references and find the same gaff about massive particles and c.

 

[Dale]

Why is the speed of light what it is? Could it have been another velocity?

The value of c is not physically relevant. The value is merely an artifact of the units used.

What is physically relevant is the value of dimensionless constants. In this case it would be the fine structure constant.

 

[Nugatory]

Question: Why is the speed of light what it is? Could it have been another velocity?

The meter is defined to be the distance that light travels in 1/299792458 seconds (or equivalently 1/299792458 of the distance that light that light travels in one second) so the speed of light pretty much has to be 299792458 m/sec. If I were ever to get a different answer when I tried to measure the speed of light, I would have to conclude that one or both of my clock and my meter stick were somehow defective.

So asking whether the speed of light could be anything other than 299792458 meters/sec doesn't make much sense - it will always be that unless we've made a mistake. To get an interesting "what would be different?" question we need to work with something whose value is unrelated to the way that we define our units. In this particular problem we want the "fine structure constant" (Google for it), which is equal to 1/137 no matter what units we use - meters, furlongs, miles, smoots, feet, fathoms, whatever - and relates the speed of light to various other quantities.

So your question comes down to: Why is the fine structure constant equal to 1/137? Physics, being an experimental science, offers a rather unsatisfying answer: Because that's how the universe we live in works. It has to have some value, that's the value it has, and everything else follows from that.

We often accept that "because that's how he universe we live in works" answer without even noticing when it's consistent with our intuition and life experience. For example, Newton's law of gravity ($F=Gm_1m_2/r^2$) completely and magnificently explains why the planets move the way they do. But if we were to ask why it's $1/r^2$ instead of, for example, $1/r^3$ (which would lead to a completely different solar system)... Well, that's how the universe we live in works.

[Edit: corrected the value and thanks to @phinds for the catch]

 

[phinds]

In this particular problem we want the "fine structure constant" (Google for it), which is equal to 1/237

Actually, it's 1/137

 

[Nugatory]

Actually, it's 1/137

Oops - of course you're right. I'm fixing it above and thanks for the catch.

 

[Johnnyallen]

The meter is defined to be the distance that light travels in 1/299792458 seconds (or equivalently 1/299792458 of the distance that light that light travels in one second) so the speed of light pretty much has to be 299792458 m/sec. If I were ever to get a different answer when I tried to measure the speed of light, I would have to conclude that one or both of my clock and my meter stick were somehow defective.

So asking whether the speed of light could be anything other than 299792458 meters/sec doesn't make much sense - it will always be that unless we've made a mistake. To get an interesting "what would be different?" question we need to work with something whose value is unrelated to the way that we define our units. In this particular problem we want the "fine structure constant" (Google for it), which is equal to 1/137 no matter what units we use - meters, furlongs, miles, smoots, feet, fathoms, whatever - and relates the speed of light to various other quantities.

So your question comes down to: Why is the fine structure constant equal to 1/137? Physics, being an experimental science, offers a rather unsatisfying answer: Because that's how the universe we live in works. It has to have some value, that's the value it has, and everything else follows from that.

We often accept that "because that's how he universe we live in works" answer without even noticing when it's consistent with our intuition and life experience. For example, Newton's law of gravity ($F=Gm_1m_2/r^2$) completely and magnificently explains why the planets move the way they do. But if we were to ask why it's $1/r^2$ instead of, for example, $1/r^3$ (which would lead to a completely different solar system)... Well, that's how the universe we live in works.

[Edit: corrected the value and thanks to @phinds for the catch]

I realize that our systems of measurement are arbitrary or subjective. So consider the following:
I read that some physicists propose that the speed of light was different in the past. perhaps going back to the early history of the universe after the Big Bang. The article I read also said that as of now, no research has produced any evidence of this.

 

[Dale]

I read that some physicists propose that the speed of light was different in the past.

Some scientists are confused then. That is a physically meaningless proposal.

 

[Nugatory]

I read that some physicists propose that the speed of light was different in the past. perhaps going back to the early history of the universe after the Big Bang. The article I read also said that as of now, no research has produced any evidence of this.

Do you have a link to that article? Without that link, we can't tell whether you misunderstood the article, or whether the writer of the article misunderstood the underlying proposal - although I'd bet it's the latter if you were reading a popularization instead of a peer-reviewed paper in a serious professional journal.

Stuff like this is the reason Physics Forums has its rule about acceptable sources.

 

[Nugatory]

That's Wiki for you. But the whole article is not a bad overview of the whole topic. You can look in a lot of references and find the same gaff about massive particles and c.

It's easy to lose the distinction between $\le$ and $\lt$ in natural language. I expect that it's worded that way because any attempt at more precise wording ("the smallest speed that soomething with non-zero rest mass cannot reach in an inertial frame"?) would just be clumsy and confusing.

 

[Johnnyallen]

Do you have a link to that article? Without that link, we can't tell whether you misunderstood the article, or whether the writer of the article misunderstood the underlying proposal - although I'd bet it's the latter if you were reading a popularization instead of a peer-reviewed paper in a serious professional journal.

Stuff like this is the reason Physics Forums has its rule about acceptable sources.

Using the word "article" may be a misnomer. It was Wikipedia's "Speed of Light" ( https://en.wikipedia.org/wiki/Speed_of_light )
"It is generally assumed that fundamental constants such as c have the same value throughout spacetime, meaning that they do not depend on location and do not vary with time. However, it has been suggested in various theories that the speed of light may have changed over time. No conclusive evidence for such changes has been found, but they remain the subject of ongoing research."
There was no footnote marker specifying the source.

 

[DrStupid]

Question: Why is the speed of light what it is? Could it have been another velocity?

What does "speed of light" mean in this question? The speed of light in general? The speed of light in vacuum? Or the invariant speed according to special relativity?

 

[Johnnyallen]

What does "speed of light" mean in this question? The speed of light in general? The speed of light in vacuum? Or the invariant speed according to special relativity?

The latter, but as Jedishfru stated, "Why is it this speed and no other we just don’t know." And Nugatory said, "So your question comes down to: Why is the fine structure constant equal to 1/137? Physics, being an experimental science, offers a rather unsatisfying answer: Because that's how the universe we live in works. It has to have some value, that's the value it has, and everything else follows from that."
From a layman's point of view no question is a dumb question. The fact that the question was asked shows, in my opinion, a curiosity in how the Universe works.

 

[Dale]

However, it has been suggested in various theories that the speed of light may have changed over time.

If you read the references you will see that they are actually discussing variations in the fine structure constant rather than variations in c. The scientists are not confused, but the people summarizing the scientists are.

 

[ZapperZ]

The latter, but as Jedishfru stated, "Why is it this speed and no other we just don’t know." And Nugatory said, "So your question comes down to: Why is the fine structure constant equal to 1/137? Physics, being an experimental science, offers a rather unsatisfying answer: Because that's how the universe we live in works. It has to have some value, that's the value it has, and everything else follows from that."
From a layman's point of view no question is a dumb question. The fact that the question was asked shows, in my opinion, a curiosity in how the Universe works.

Then please read this reference:

https://physics.aps.org/articles/v7/117

It should clearly provide the evidence that the starting premise is not valid based on the latest and most accurate measurement so far.

Zz.

 

[Albrecht]

Do you have a link to that article? Without that link, we can't tell whether you misunderstood the article, or whether the writer of the article misunderstood the underlying proposal - although I'd bet it's the latter if you were reading a popularization instead of a peer-reviewed paper in a serious professional journal.

Stuff like this is the reason Physics Forums has its rule about acceptable sources.

There is a paper of A. Albrecht and J. Magueijo about this: "A time varying speed of light as a solution to cosmological puzzles", Physical Review D, Band 59, 1999, 043516
It can be assumed that this article is peer-reviewed.

They say that the assumption of a higher speed of light at earlier times would explain the non-understood problem of cosmological inflation; and that this assumption is in no conflict with the essential rules and assumptions of today's physics.

Regarding the constancy of the speed of light I think we should be aware that the measured value is constant. The real value may be a different story. Because we know that our measurement tools change when we move, e.g. a clock runs more slowly. And by use of these changed tools we yield the constancy. That looks like being a different story.

 

[ZapperZ]

Regarding the constancy of the speed of light I think we should be aware that the measured value is constant. The real value may be a different story. Because we know that our measurement tools change when we move, e.g. a clock runs more slowly. And by use of these changed tools we yield the constancy. That looks like being a different story.

This last claim is very puzzling, and frankly, an assault on experimental physics.

First of all, this claim implies that all inertial reference frame are not equal, that by "moving", one is measuring something that is different than it should be. Secondly, we have a theoretical foundation for what we measure, and this understanding allows us to interpret the data. After all, why do you think we need relativistic correction for time measurements in GPS satellites?

Thirdly, what is a "real value" here? If the "real value" is not accessible via any experimental measurement, then the claim that it exists is purely unverified speculation.

And finally, many of the earlier claims of varying fine-structure constants, especially those made by J.K. Webb et al., have been superseded by significantly more accurate measurements that did not support the initial findings. So there is no experimental support at all for such a claim. I always find it puzzling when theorists ignore experimental evidence, or jump too quickly on something that hasn't been verified (Can we say superluminal neutrinos of OPERA?).

Zz.

 

[TeethWhitener]

But if we were to ask why it's 1/r21/r21/r^2 instead of, for example, 1/r31/r31/r^3 (which would lead to a completely different solar system)... Well, that's how the universe we live in works.

I thought that had to do with the fact that we live in 3-dimensional space, so that the total intensity of a field from a point source at distance $r_1$ (integrated over the surface area of a sphere with radius $r_1$) has to be the same as the intensity at distance $r_2$ (integrated over a sphere with radius $r_2$). Since it's dependent on the surface area of the sphere, the intensity at any given point goes as $1/r^2$.
Edit: if it were $1/r^3$, it would mean that the field were traveling through some homogeneous and isotropic absorbing medium.

 

[Albrecht]

This last claim is very puzzling, and frankly, an assault on experimental physics.

First of all, this claim implies that all inertial reference frame are not equal, that by "moving", one is measuring something that is different than it should be. Secondly, we have a theoretical foundation for what we measure, and this understanding allows us to interpret the data. After all, why do you think we need relativistic correction for time measurements in GPS satellites?

Thirdly, what is a "real value" here? If the "real value" is not accessible via any experimental measurement, then the claim that it exists is purely unverified speculation.

And finally, many of the earlier claims of varying fine-structure constants, especially those made by J.K. Webb et al., have been superseded by significantly more accurate measurements that did not support the initial findings. So there is no experimental support at all for such a claim. I always find it puzzling when theorists ignore experimental evidence, or jump too quickly on something that hasn't been verified (Can we say superluminal neutrinos of OPERA?).

Zz.

What we know about our world is what our measurements tell us. That is a basic result of epistemology and generally accepted. Why should this be an assault?

Yes, the result of our measurements is that all inertial systems are equal. That is the same as what I said about the speed of light. But on the other hand relativity tells us that our measurement tools change and work differently in different inertial systems. If we move a clock and let it come back then it indicates a different time than a clock which was not moved. I think, it's well understood. This slower clock is used when the speed of light is measured in a state of motion. So, what can we conclude about the result?

And the clocks in the GPS satellites have to be corrected according to their motion. They move in a different system. That tells us special relativity. Why do you ask? It is the same point.

There is another interesting point about the GPS satellites. If an observer would be residing in and moving with such satellite and he would try to synchronize the clocks of all satellites from his position, then he would run into problems. Because special relativity does not work according to Einstein in a rotating system. This case is not covert by SRT. And if such observer undertakes to measure the speed of light he will have a deviating result. -

Speed of light at earlier times: can we really conclude so much from the behavior of alpha? Isn't that model dependent? And on the other hand: cosmology and Lemaitre's interpretation of Einstein tell us that space is permanently expanding. Now, if space changes, what does it mean what we say about the speed of light? The notion speed is always related to space, otherwise it does not mean anything. If we now assume that the space has always changed, what does it mean when we say that c was constant all time?

 

[rootone]

This is similar to asking why the value of Pi happens to be what it is.
It simply is a universal constant, something which is not disputed.
Arguably Pi, c, and other constants might differ in some interpretation of a 'multiverse', (not something I am keen on),
However. even if that was the case, it makes no difference to the Universe we exist in.

 

[TeethWhitener]

But on the other hand relativity tells us that our measurement tools change and work differently in different inertial systems.

No, relativity tells us that our measurement tools work exactly the same in different inertial systems.

If we move a clock and let it come back then it indicates a different time than a clock which was not moved.

The clock that was moved is not an inertial reference frame.

This slower clock is used when the speed of light is measured in a state of motion.

Inertial reference frames maximize proper time.

 

[phinds]

This is similar to asking why the value of Pi happens to be what it is.
It simply is a universal constant, something which is not disputed.
Arguably Pi, c, and other constants might differ in some interpretation of a 'multiverse', (not something I am keen on),
However. even if that was the case, it makes no difference to the Universe we exist in.

Actually, the value of c is an artifact of whatever system of measurements you use. it is the fine structure constant that is the universal (dimensionless) constant

 

[sophiecentaur]

I always find it puzzling when theorists ignore experimental evidence, or jump too quickly on something that hasn't been verified (Can we say superluminal neutrinos of OPERA?).

Theorists are people and people are only human. We all like a bit of magic in our lives and think of the kudos of your theory turning out to be right.

 

[Dale]

There is a paper of A. Albrecht and J. Magueijo about this: "A time varying speed of light as a solution to cosmological puzzles", Physical Review D, Band 59, 1999, 043516

They are also very clear to point out that it is physically nonsense to talk about a variable speed of light and that what they are actually describing is a variation in the fine structure constant.

I think we should be aware that the measured value is constant. The real value may be a different story.

An unmeasurable “real” value is physically silly.

But on the other hand relativity tells us that our measurement tools change and work differently in different inertial systems.

No, relativity tells us exactly the opposite. It is the first postulate of relativity.

Speed of light at earlier times: can we really conclude so much from the behavior of alpha? Isn't that model dependent?

No.

 

[Albrecht]

They are also very clear to point out that it is physically nonsense to talk about a variable speed of light and that what they are actually describing is a variation in the fine structure constant.

According to the other contributions here, both statements are equivalent. And the topic of the paper is clearly the speed of light. - The assumption of a variation has fascinating consequences. It explains directly the (otherwise not understood) cosmological inflation (said by the authors). And even better: The problem of Dark Energy, which is such a mystery now, is immediately explained if a decrease of c with time is assumed. We can be very sure that the question of Dark Energy will never be solved on the basis of present understanding, i.e. a constancy of c.

An unmeasurable “real” value is physically silly.

We know that our measurement tools a cheating us (by dilation and contraction). So it makes sense to ask for the truth. - This was also an argument of Lorentz when he once discussed relativity with Einstein.

No, relativity tells us exactly the opposite. It is the first postulate of relativity.

The principle of relativity says that we observe the same physical laws in any inertial system. Contraction and dilation are on the other hand essential parts of Einstein's SRT. Which is not a logical conflict.

No, relativity tells us that our measurement tools work exactly the same in different inertial systems.

No, because dilation and contraction influence our tools.

The clock that was moved is not an inertial reference frame.

A clock moving with a (different) inertial frame is delayed. Take the following experiment:
You have a clock at rest in your system. Then move another clock by linear motion along this clock, and in the moment of passing by the moving clock is synchronized to the clock at rest. Then after a time of motion, another clock may move linearly along this clock into the direction of the clock at rest. And when passing the other clock the new clock shall be synchronized to the first moving clock. Then when the new clock passes the clock at rest compare both clocks. The moving one will show a delayed time, so dilation. All clock in this experiment move linearly, so they are all in inertial frames.
This shows that also clocks in linear motion are dilated.

Inertial reference frames maximize proper time.

What does "maximization of time" mean?