Here is an excerpt from the Wikipedia entry on physical constants:
To me, in a somewhat roundabout way, this says (among other things) that no one knows why dimensional constants such as the speed of light are the values they are measured to be. Chronos said it best in post #11 when he said that “Why” questions do not really fall under the purview of science.
Light does travel at different speeds in different transparent media. Light can and has been slowed to a crawl in various experimental settings. In vacuum, the speed of light is what it is. Asking “Why” really says more more about you and nothing about the constant.
In special relativity where c is the only physical constant and it has units, changing the value of c doesn’t change the theory at all as it is just like a change of units, so essentially the numerical value of c is simply defined by the units it is measured in. If you don’t believe me simply try comparing a change of value of c and a change of units of c in SR yourself and try to see how it would be possible to differentiate between the two (i.e. it isn’t possible).
In more complicated theories/pictures where you have fundamental dimensionless physical constants (e.g. the fine structure constant) changing the value of such constants does change the theory. Just like Cartesian geometry would be fundamentally altered if the ratio of a circle’s radius to its circumference were some other value than 2pi. Now it may be that there is an uber theory that contains no dimensionless fundamental constants, from which all dimensionless constants like the fine-structure constant can be derived, but if there is we don’t know it.
If the length of the rod changed then your height changed, the diameter of the Earth changed, etc. Every length scale in the universe scaled up appropriately? Does the Sun collapse into a black hole if the increase would bring its mass to the appropriate level?
If we cannot talk about changing speed of light, how is it we can talk about it slowing down when it travels through different media?
Why is it so hard to believe that every length scale in the universe changed, but easy to believe that c changed?
The point is, saying one is just as easy as saying another. Or to put it another way, suppose the length of a second changed. How would you know? How would you measure that yesterday a second took thiiiiis long, and today it takes thiiiiiiiiiiis long? Not that we’ve redefined the second, but time itself has changed. But we measure time by using instruments that depend on the passage of time. If it takes them twice as long to tick out one second tomorrow, the physical processes in our brains will take twice as long to notice one second, and it will seem exactly the same.
I was referring to the length standard not meeting the definition of number of wavelengths in an earlier question. My answer would be that someone has substituted a different rod, or your equipment is broken. Not that all lengths have changed.
As to light slowing down in different media - that is why I suggested earlier that we should change the name of c. c isn’t the speed of light directly. It is the speed of causality. Because the force carrier of EM is massless theory requires that it travel at c. So photons travel at c. It is just unfortunate that the particular speed was named for light first.
If photons are not travelling directly to you, but are being interacted with on the way, such as passing through a medium, the effective sum of possible paths they take (as described by QED) means that their velocity to you is less. The speed the photons have in between all the possible interactions in the media is still c.
Imagine you have a telephone that you can phone and alien in another Universe with. Luckily he speaks perfect English (with a heavy Zfolgian accent) and is au fait with scientific concepts. From speaking to him about physics he describes the theory of relativity, except he describes c as 2.6 vlargs. Is there any experiment you could ask him to perform that would determine whether c is different in his Universe or if he is just using different units to describe the same c as in our Universe? The answer is no there isn’t.
Now in the situation you describe (i.e. changing c so that the Sun collapses into a black hole) is also equivalent to changing its radius and so is equivalent to describing two different situations using the same value of c, using different units for each description.
The speed of light through some medium depends on the properties of the medium, so it is no different from describing those properties of the medium.
I’m asking about the ramifications. It seems that people are in agreement that c having a different value would not be noticeable.
Ok, so we take the platinum rod example. c is twice as fast, but we don’t know because the rod is twice as long. Is it now 8 times as massive? Or is it 1/8th as dense to preserve mass? Would that affect anything we observe?
I’m much too dumb to have anything but the most rudimentary understanding of any of this but thought I’d share this video that made a timely appearance in my feed today. It goes through the math of why the speed of light (or causality if you prefer) is what it is. I thought it was a good explanation as my non-math mind could actually catch a glimpse of what he was saying.
Light travels at the speed it does because it’s massless, and everything massless has a speed equal to 1. The next “why” question can, so far as I can tell, take one of three forms:
1: Why is light massless?
2: Why do massless things have a speed equal to 1?
3: Why is 1 equal to 1?
Is your question one of those, or does it have some other form?
How can 1 be equal to 1, when everyone knows (well, at least everyone on this board knows) that 1 equals 0.999… ?
ETA: Okay, I’ll add a real question, which may or may not be stupid: Is even the theory of relativity itself thought to be a constant across all possible universes? If we tried to discuss relativity with that Zfolgi dude, would he even necessarily know what we’re talking about? Is it certain that time and space are necessarily connected in the Einsteinian model in all universes? Might not some other universe be strictly Euclidean and Newtonian, or some other unimaginable model?
Well, that depends on just what one means by “all universes”, as well as what one means by “relativity”. One can envision and mathematically describe universes where relativity (at least, the interesting parts of it) isn’t relevant, but such universes tend to be radically different from our own: Does it really count as a universe if there’s no time in it, for instance?
Ok, so impedance of free space is ~= 376 ohm = c*mu. Is asking what would happen if it was 380 ohms instead a question that has any meaning? If not, why not? If so, how is that different than asking about a changing c?
Well, I’ve read some of those speculative articles about what universes might be like if some of the fundamental constants were just a leetle bit different. They all seem to be obsessively focused on the idea that such universes might be incapable of having life (at least as we think we know it) – when in fact, some descriptions seem to say that such universes might be incapable of having anything at all.
I’ve seen it suggested, for example, that quarks might not be able to coalesce into stable protons and neutrons, meaning that no matter could exist. What a depressing universe to live in! :rolleyes: Imagine an entire universe chock-full of complex probability wave functions and nothing else – no matter, no energy, and maybe not even time. What a waste of a universe. Does that count as a universe (time or no time)?
You have mass even when stationary. If you travel at “the speed of light” you will have infinite mass.
Light has mass when traveling at “the speed of light”. If it stops, it has infinitesimal (zero) mass.
Light travels at a speed of 1 because that is the value you get when you divide the momentum of light by the mass of light. If you measure those two things (they are measurable), you get numbers, and the ratio gives you the speed of light in whatever scale you are using.
Generally when people say “mass” without qualifier they generally mean “rest mass”. And it’s true that light has no rest mass. That light has momentum that can be used to construct a 4-vector “mass” is not relevant to the point that particles with no rest mass must move at the speed of light. You’re picking nits that anyone reasonably informed in the subject knows about.
Melbourne, you are using the word “mass” in a different way than it is used by physicists. I can’t blame you for that, since unfortunately a lot of physics textbooks do the same thing, but when physicists say “mass”, we mean “rest mass”.
According to Poul Anderson’s Operation Chaos, Hell/Hadesis very non-Euclidean - thus it is advisable to bring an expert or two on non-Euclidean geometry on any expeditions there (Operation Chaos (novel) - Wikipedia)
