@krastanov
[First, to avoid confusion, I first mentioned this matter in my post to HN's story of several days earlier: https://news.ycombinator.com/item?id=24837545, unfortunately this story here is a duplicate, thus we've split posts.]
"The constants μ0 ε0 are not the fundamental constants setting the speed of light, rather they are historically the parameters we used at first when writing down the laws."
Well, it seems to me that depends on how one views the matter. It's not my idea, but μ0 are ε0 are actually defined as fundamental constants, so how do we bring this together? Clearly, some deep, still-far-from-understood, aspect of nature precisely relates these seemingly immutable constants to one another. Richard Feynman—and others (who likely go back as far as Sommerfeld's time)—seem to prefer the description when the equation is headed with the fine structure constant alpha α, (aka Sommerfeld's constant), presumably because α is a dimensionless constant:
α = e^2/(4πεħ0c), but also as c = 1/(μ0 ε0)^0.5. Now, if I've not screwed it up, that becomes:
α = (μ0/4π) ((e^2 c)/ħ)
Thus, now we've also tied in μ0, so we see they're all inextricably linked together with alpha being the kingpin (my words). Linking all these constants including c to α then allows all and sundry to wax lyrically over alpha's 'mystical' value, that of course being ≈1/137. Quoting from here: http://www.feynman.com/science/the-mysterious-137/
"If you have ever read Cargo Cult Science by Richard Feynman, you know that he believed that there were still many things that experts, or in this case, physicists, did not know. One of these ‘unknowns’ that he pointed out often to all of his colleagues was the mysterious number 137."
So how do we progress from here? If we don't understand what underpins the reason for the mysterious value of α then how can we say that c is intrinsically more important than the other constants herein? Clearly, the equation says c isn't intrinsically more significant than say Planck's constant, h or the electric charge, e. Thus, it seems to me that if we essentially stick to Maxwellian/Classical Electromagnetism as our reference then we cannot rank any one constant including c above any of the others, except to say their relationships are best summed up by using α as the reference, it being a dimensionless ratio/scalar.
To me, that explanation still seems to be unsatisfactory, so where to next? Moving along, I'll make a few observations that involve some related matters in the hope it will put things into perspective. It's probably best that I approach them more from an observational or philosophical standpoint, this way it's easier for me to discuss them without having to resort to a mathematical explanation, which, here, clearly would be impractical—moreover (and likely more importantly) I won't need to overtax my limited knowledge of physics in the process. ;-)
The first issue is that we know light travels in a vacuum at velocity c, but how and why does that occur, and what's the description of the underlying process? Leaving QED explanations aside for the moment, let's go back to the old now-discounted luminiferous aether theory which says that for light waves to travel then they must do so within some form of medium. Back when I was first leaning about this stuff, the luminiferous aether was considered a joke and we were told that it didn't exist, nevertheless that notion has never really ever gone away (but rather the understanding thereof has metamorphosed across many very different interpretations over the last 120 or so years). For instance, somewhat later, Lorentz came up with is his own Lorentz aether theory, still later others followed suit from the likes of de Broglie, Dirac to Einstein and others, all of which who had different views about the matter. Our present-day incarnation of the 'aether' now comes from quantum field theory; very loosely, it states that a vacuum is a condition wherein a quantum vacuum (minimum energy) state exists and that this manifests as a sea of foaming 'virtual' particle pairs that continually appear and then just as easily disappear out of existence.
What's relevant in this context is that we can now imply that light does travel in an aether and that its 'dynamics', its velocity etc., are determined by the values of the fundamental constants ε0 and μ0 which, ipso facto are also fundamental properties of that aether! Some even go on to suggest that an electromagnetic wave travelling though this 'vacuum' aether should also exhibit a minimum quantum noise (generated by its interaction with aether's virtual particles). We could imply that these virtual particles set the minimum 'granularity' of the quantum vacuum. Well, anyway, that's the basics of descriptive version (of course it's gets considerably more complicated when we go on to consider the full implications of QED and other matters that I mention below.
[My personal view is that often textbooks do not pay sufficient attention to the importance of the fundamental constants vacuum permittivity, ε0, and vacuum permeability, μ0, and how they relate to the speed of light through the relationship c = 1/(μ0 ε0)^0.5. Moreover, the emphasis placed on various aspects and understandings of this relationship often differs substantially between physics and electrical engineering texts.]
Moreover, the above explanation of a vacuum is not the only instance in electrodynamics wherein Classical Electromagnetic theory breaks down and fails to describe the phenomenon adequately; others involve potentials and static electric and magnetic fields, the theoretical underpinnings of which are difficult and tricky matters to understand. Simply, how do we explain why one's fridge magnets stay put—or slightly more precisely—what exactly is going on within these static electric and magnetic fields—that allows them to remain static (fields) but that they're also able to radiate their 'influence' away from the source at the speed of light and in accordance with the inverse square law? (Superficially, it looks as if we've perpetual motion, as it seems we've 'surplus' energy that we can't account for, but no such luck, that's not what happens.)
Perhaps if we look at the following simple but excellent example then we'll gain a better understanding. That is to compare your fridge magnet with say that of a normal wax candle. Your magnet conveniently remains static in one place and it does so indefinitely. Effectively, it's in stasis and 'stuck' to your fridge until you apply external force to move it—and it continues in this state without ever running out of energy (as with a battery going flat). At the same time, as mentioned, any unconstrained 'field' 'radiates' away from the magnet at the speed of light. Whereas for the candle to radiate electromagnetic energy in the form of heat and light, it actively has to consume energy contained within the wax. As both of these examples are electromagnetic phenomena, then what's the explanation for the difference?
If we want a reasonable description of why the magnet doesn't run out of energy (one which is consistent and in harmony with other physical laws) then, to say the least, the explanation gets very tricky. And for that we need to enter the depths of QED to find an explanation, and it comes by way of a complex mathematical explanation that involves potentials and virtual photons, etc.: it shows that whilst the field remains static, only the influence of the 'field' 'radiates' out from the magnet at the speed of light (note I've used 'field' in inverted commas for this reason).
If that explanation still doesn’t make much sense then it's because it doesn’t! The trouble is that to understand physics at this level we cannot use our usual real-world/pictorial analogies as they break down and no longer make any sense. Thus, for a full and proper explanation, we have to rest content with the mathematical description, and often that's either very difficult to understand and interpret or it's impossible to do so. Moreover, it gets worse as one gets deeper into the mire, eventually we need to consider QED and its relationship to both QCD and the Standard Model, etc.
(It's somewhere about here along this road that my understanding gets sketchy, and its mathematics gets so intense that my brain goes into meltdown—note, this it's not my day job)!
Next comes quantum gravity etc., and already we know the propeller-heads have been struggling with that for years and are still doing so. Just on that point it's worth trying to work through raattgift's two post below (near the end). They're quite remarkable in that they're both succinct and very broad in coverage and also for the fact that he discusses just about every aspect of theoretical physics that's in anyway related to these matters.
The second issue I've already mentioned elsewhere in another post, which is that if the experimental evidence is eventually verified that an electron can actually be seen to exist in two states whilst it simultaneously moves from one state to another in a smooth and deliberate manner and that it does so over a finite (measurable) time, then this seems to imply that quantum states such as an electron's transitions between orbitals, and when in quantum tunnelling, etc. may actually occur within spacetime itself (it's just that the process is incredibly fast). It may also follow that these particles may mot be fully isolated and confined during quantum transitions. In other words, if true, then it's possible that couplings may exist between spacetime and the quantum state, and that they too actually may be measurable.
Right, that sounds quite outrageous, as it would put an altogether different view and complexion about the way we explain light travelling within and though dielectrics, as well as why dielectric constants are the way they are, it may also provide us with more nuanced explanations of tunnelling, the Casimir effect, solid state physics and condensed matter physics, etc.
Now we'll all just have to wait and see what happens next.