# I Why is the speed of light what it is?

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1. May 31, 2018

### Johnnyallen

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

2. May 31, 2018

### Staff: Mentor

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 irregardless 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.

3. May 31, 2018

### sophiecentaur

'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.)

4. May 31, 2018

### Johnnyallen

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'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 dialation (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.)

5. May 31, 2018

### sophiecentaur

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..

6. May 31, 2018

### phinds

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.

7. May 31, 2018

### sophiecentaur

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.

8. May 31, 2018

### Staff: Mentor

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.

9. May 31, 2018

### Staff: Mentor

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]

Last edited: May 31, 2018
10. May 31, 2018

### phinds

Actually, it's 1/137

11. May 31, 2018

### Staff: Mentor

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

12. Jun 1, 2018

### Johnnyallen

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.

13. Jun 1, 2018

### Staff: Mentor

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

14. Jun 1, 2018

### Staff: Mentor

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.

15. Jun 1, 2018

### Staff: Mentor

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.

16. Jun 2, 2018

### Johnnyallen

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.

17. Jun 2, 2018

### DrStupid

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?

18. Jun 2, 2018

### Johnnyallen

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.

19. Jun 2, 2018

### Staff: Mentor

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.

20. Jun 3, 2018

### ZapperZ

Staff Emeritus

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.

21. Jun 6, 2018

### Albrecht

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 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.

22. Jun 6, 2018

### ZapperZ

Staff Emeritus
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.

23. Jun 6, 2018

### TeethWhitener

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.

24. Jun 6, 2018

### Albrecht

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?

25. Jun 6, 2018

### 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.