2 ms·
If you consider both the strength of vacuum permittivity, ε0, (aka permittivity of free space/electric constant) and the vacuum permeability, μ0, (permeability
by hilbert42 6y ago
If you consider both the strength of vacuum permittivity, ε0, (aka permittivity of free space/electric constant) and the vacuum permeability, μ0, (permeability of free space/magnetic constant) determine the speed of light in vacuum as per the following relationship:
c = 1/(μ0 ε0)^0.5
0 being the vacuum case
then it follows that c will change when either or both values of μ and ε change. (The value of both the vacuum permittivity and vacuum permeability, along with the Fine Structure Constant‡, alpha, α, which is closely related and involves the electric constant, are now precisely known).
Normally, the speed of light decreases when it encounters a medium or dielectric (as we observe when it propagates within a coaxial cable or through glass etc.) but in photon tunneling it's not necessarily so. Thus the question to ask is what are the effective values of μ and ε at the instant of tunneling. If the effective μ and ε coupling from photons to the surrounding medium, is 'lost' or reduced at this instant through quantum coupling effects—or the lack thereof—then one can see how c could exceed c0 — the vacuum/free space figure.
OK that's the photon case, but if the same were to apply to the 'coupling' of an electron [which has mass] at the very instant of tunneling, then its mass might not be 'seen' thus we might end up with the electron exceeding c0 (but only for the duration of its tunneling).
I'm saying first thoughts out loud here (not a wise thing to do), so I've more thinking before I come to any conclusions, and clearly energy, conservation laws and possibly time constants have to be considered with an electron. That said, I've just looked at Thomas Hartman's equation and I've not come to any opinions, as I don't know enough about it at this point. All I'm saying now is that his equation shouldn't conflict with the one I've given above.
Would the real experts among us like to comment or offer various alternative explanations?
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† Presumably, c could also 'legitimately' exceed c0 if it were to travel through some medium with 'meta' properties (if one were ever found).
‡ Alpha is defined by various relationships (hence different equations). This specific eqn. defines alpha in terms of the electric charge, e, and vacuum permittivity: α = e^2/(4πεħ0c).