3 ms·

This page is proving that Maxwell's equations _predict_ that the speed of light is constant. This prediction is dependent on assuming that the vacuum permeabili

This page is proving that Maxwell's equations _predict_ that the speed of light is constant. This prediction is dependent on assuming that the vacuum permeability and permittivity are constant numbers. This is an axiom of classical electrodynamics, specifically that free space is homogeneous and isotropic [1]. Therefore, measuring the speed of light is a check on this axiom. [1] homogeneity means that translating your experimental setup to a different location will not change the results of your experiment. Isotropy means that rotating your experimental setup will not change the results of your experiment.

vegedor 12y ago
>the speed of light is constant ... in a vacuum. I was surprised when I was told so for the first time, because it seems like a notable limitation, the omission of which leads to an opposite assumption.
sytelus 12y ago
Exactly, it doesn't prove "constancy" of c unless you assume constancy of other constants. Even the isotropic and homogeneous assumption is incomplete because it doesn't make any assertions on values through time. Is it possible that u0 or E0 or c had a different value at very start of the big bang? It's a very tempting thought although professional physicists seem almost universally consider those ideas a giant crackpot.
- weland 12y ago
  I don't know why you are getting downvoted. I haven't had my morning coffee yet, so I am cynically going to presume a bunch of folks think you're nitpicking on the words, but you're not. The derivation is correct, but it is not a proof of anything. Maxwell's equations aren't textbook PDEs that exist in a vacuum, devoid of any connection with the surrounding world. They are quantitative approximations of real-life phenomenae, that hold only under very specific circumstances, and break when those conditions (about e.g. distances) aren't met. The proof that the speed of light in vacuum (which the article "helpfully" fails to mention) is constant is experimental. If the experiment would fail, Maxwell's equations would have to be modified. Any predictions they make are tested against the reality, not vice-versa. Oh yes: I'm not nitpicking about their failure to mention it's the speed of light in vacuum. The final expression is constant only because \mu and \varepsilon are (supposed to be) constant in vacuum. Precisely the same expression predicts the (correct!) fact that the speed of light is not constant, but depends on the properties of the material it is travelling through. Edit: this should be very obvious from the fact that the derivation is based entirely on the four laws that constitute Maxwell's equations, not on theorems. Laws are not deduced mathematically, but formulated by experiment. Their predictions cannot constitute a proof. It may be tempting to treat their predictions as such, because in mathematics any correct result obtained by derivation can constitute a proof, but this is not the way to look at a set of physical laws. Maxwell's equations also "prove" that things like squeezed light cannot exist -- despite the fact that it clearly does, since we can generate it. These incorrect predictions are not onthologically different from correct ones.
acjohnson55 12y ago
If I recall correctly, we measure ϵ0 and c experimentally, and then define µ0 accordingly. That aside, is there any specific reason to believe homogeneity holds?
- widdma 12y ago
  Nowadays, in SI, they're defined as constants: c is exactly 299,792,458 m/s, µ_0 = 4π×10^−7 H/m, ε_0 = 1/(µ_0*c^2). But these were chosen, based precise measurements, to ensure the (old) metre and the Ampere remained relatively unchanged. As for your question, homogeneity is considered the simplest assumption you could make: you can't get simpler than a no-parameter model. It's also easy to disprove, if you can get data, making it a good scientific hypothesis. There's some astronomers trying to measure the various fundamental constants in other regions of the galaxy via maser emissions. There was some interesting results a few years ago, but I don't think they're considered definitive. Still, lots of fame if they can do it!
  - carlob 12y ago
    > homogeneity is considered the simplest assumption you could make: you can't get simpler than a no-parameter model. Ehm… one-parameter…
    - widdma 12y ago
      Whoops, zero dependence on spatial variables was thinking.

vegedor 12y ago

>the speed of light is constant ... in a vacuum. I was surprised when I was told so for the first time, because it seems like a notable limitation, the omission of which leads to an opposite assumption.

sytelus 12y ago

Exactly, it doesn't prove "constancy" of c unless you assume constancy of other constants. Even the isotropic and homogeneous assumption is incomplete because it doesn't make any assertions on values through time. Is it possible that u0 or E0 or c had a different value at very start of the big bang? It's a very tempting thought although professional physicists seem almost universally consider those ideas a giant crackpot.

weland 12y ago
I don't know why you are getting downvoted. I haven't had my morning coffee yet, so I am cynically going to presume a bunch of folks think you're nitpicking on the words, but you're not. The derivation is correct, but it is not a proof of anything. Maxwell's equations aren't textbook PDEs that exist in a vacuum, devoid of any connection with the surrounding world. They are quantitative approximations of real-life phenomenae, that hold only under very specific circumstances, and break when those conditions (about e.g. distances) aren't met. The proof that the speed of light in vacuum (which the article "helpfully" fails to mention) is constant is experimental. If the experiment would fail, Maxwell's equations would have to be modified. Any predictions they make are tested against the reality, not vice-versa. Oh yes: I'm not nitpicking about their failure to mention it's the speed of light in vacuum. The final expression is constant only because \mu and \varepsilon are (supposed to be) constant in vacuum. Precisely the same expression predicts the (correct!) fact that the speed of light is not constant, but depends on the properties of the material it is travelling through. Edit: this should be very obvious from the fact that the derivation is based entirely on the four laws that constitute Maxwell's equations, not on theorems. Laws are not deduced mathematically, but formulated by experiment. Their predictions cannot constitute a proof. It may be tempting to treat their predictions as such, because in mathematics any correct result obtained by derivation can constitute a proof, but this is not the way to look at a set of physical laws. Maxwell's equations also "prove" that things like squeezed light cannot exist -- despite the fact that it clearly does, since we can generate it. These incorrect predictions are not onthologically different from correct ones.

acjohnson55 12y ago

If I recall correctly, we measure ϵ0 and c experimentally, and then define µ0 accordingly. That aside, is there any specific reason to believe homogeneity holds?

widdma 12y ago
Nowadays, in SI, they're defined as constants: c is exactly 299,792,458 m/s, µ_0 = 4π×10^−7 H/m, ε_0 = 1/(µ_0*c^2). But these were chosen, based precise measurements, to ensure the (old) metre and the Ampere remained relatively unchanged. As for your question, homogeneity is considered the simplest assumption you could make: you can't get simpler than a no-parameter model. It's also easy to disprove, if you can get data, making it a good scientific hypothesis. There's some astronomers trying to measure the various fundamental constants in other regions of the galaxy via maser emissions. There was some interesting results a few years ago, but I don't think they're considered definitive. Still, lots of fame if they can do it!
- carlob 12y ago
  > homogeneity is considered the simplest assumption you could make: you can't get simpler than a no-parameter model. Ehm… one-parameter…
  - widdma 12y ago
    Whoops, zero dependence on spatial variables was thinking.