How did you get your post the number ’42′ – you do know that is the answer to ‘the Answer to Life, the Universe, and Everything’? According to the ‘Hitch Hikers Guide to the Universe’, by Douglas Adams.

The speed of light in a vacuum in Maxwell’s equations, is derived from 2 ‘constants’ εo (the dielectric permittivity of a vacuum) and μo (the magnetic permeability of a vacuum). Apart from the fact that no explanation is given as to why a vacuum has to have these particular values for those constants, there is also no explanation for why a changing electric field creates a changing magnetic field – AFAIK.

I said “However, you do need to consider Special Relativity when building a GPS system.” this is simply carelessness on my part – you need General Relativity to cope with the acceleration and differences in gravitational potential, associated with the orbit of a GPS satellite.

See
http://www.youtube.com/watch?v=NZ-ElsvYKyo&feature=related
for a series of lectures on String Theory by Leonard Susskind (he used to be plumber!).

The facts that light propagates through a vacuum and has a constant speed are found through observation. However, the interesting problem for me is what is the fundamental nature of Space & Time that makes this so. Hence, Maxwell’s equations are insufficient to explain why light travels through a vacuum.

I would not claim that electric fields can propagate in vacuum because of Maxwell’s equations (which I think is what you are implying that I said). However I would claim (and I did claim) that Maxwell’s equations embody all of the physics necessary to understand why waves can propagate in vacuum. And further, that no other physics (which implies: no other equations) are required.

That’s all I said. I think. And I stand by those statements, although I completely agree with your assertion that equations before phenomena is horse before cart.

Actually not quite true. The speed of light is a direct consequence of Maxwell’s equations. In fact Maxwell himself calculated the speed of light and was correct within a few percent, if I am remembering my history correctly. This is firmly in the realm of classical physics. Now, admittedly, Maxwell and his cohorts were not aware that this speed constituted an upper limit on the speed of information – but that is not a quantum effect, it is a relativistic effect. And it certainly is not relevant to the discussion at hand, which was “How do waves travel in a vacuum when there is nothing present to do any waving?” The answer to THAT question does not require an understanding of relativity (although that answer does IMPLY that special relativity must be true).

“Classical mechanics deals in rigid bodies”

My apologies for the use of jargon. Most physicists use the phrase “classical physics” when they mean “physics prior to the emergence of relativity and quantum mechanics”. What I (and most other physicists) mean by “classical physics” includes Maxwell’s equations. Thus, the nature of light propagating in a vacuum IS classical, according to this use of the term “classical”.

“However, you do need to consider Special Relativity when building a GPS system.”

In fact, if I am remembering correctly, it is GENERAL relativity that is relevant here. The speed of the satellites is not the key consideration. It is the fact that they are farther from the gravity well, so their clocks run at different rates. That is a general relativistic effect, not a consequence of special relativity. Quite different topics, despite the very similar names.

@Nigel #35 AND Gavin too:

My apologies, I should not have called string theory or M-theory ‘pseudo-science’. There is an active debate in the field as to whether it is science at all, seeing as many experts believe that it is fundamentally untestable by experiment (and therefore firmly in the realm of philosophy rather than science). Personally, I am agnostic on this question, since it’s not my field of expertise – my understanding of string theory comes from popularizations (e.g. Brian Greene), not from any actual technical source. However, I do tend to support the notion that predictions must be testable, at least in principle if not in practice, in order for them to be worth spending time (and research funding) on. If a prediction is fundamentally impossible to test no matter how big a machine you build, then it teaches us nothing about the world.

On the other hand, I do know a lot about E&M and about quantum mechanics, since I teach both subjects regularly. String theory, the fundamental nature of the vacuum at the quantum level, and the ultimate consequences of these facts for our perception of space-time may be interesting subjects, but they are all irrelevant to the question I was answering initially. That question can be answered fully and completely with no reference whatsoever to quantum mechanics.

Let’s remind ourselves that Maxwell’s equations are a perfectly accurate description of every phenomenon involving electromagnetism at any energy scale accessible to human experimentation (even the LHC). Relativity does not modify Maxwell’s equations at all, and neither does quantum theory. When light is acting like a wave (i.e., when you have enough field amplitude so that the classical treatment is valid), its behavior is perfectly predicted by this entirely classical theory. Of course, if the field is very small, so that you are working at the level of a single photon, you have to think differently – then quantum effects become important. But the question at hand was about fields, not photons. We weren’t talking about single photons. Yet

Strange to have deadly radiation sound so peaceful and sweet. So much like birdsong.

Fascinating clip. Surreal to hear our planet sing. Cheers!

Certainly, though, M-theory is Real Science – but that does not mean it has to fit what people feel is ‘Right & Proper’!

Agreed!

Classical physics was based on what people felt was right and proper, and it ended up in all sorts of trouble.