Quantum Tunnels Show How Particles Can Break the Speed of Light
quantamagazine.org
quantamagazine.org
That was brought on in my third semester of physics in college where we dove into quantum mechanics and the whole question of why you can't travel faster than the speed of light revolved around the fact that at the speed of light, time stopped. (insert mind blown gif) That was me, struggling with that idea.
When I went to work at Intel I learned all about 'electron tunneling' as something that caused EPROMs to fail and gates to change state, and why semiconductors with smaller than 1 micron features probably wouldn't work (smirk). But I had not seen the Hartman paper[1].
What I found most interesting about the Quanta article is the discussion about how to measure time at these scales. And just recently there was this article on zeptoseconds[2].
I can't help but think something amazing is going to come out of all this work. It may be a parlor trick but it is going to be a really cool parlor trick.
[1] Tunneling of a Wave Packet -- https://sci-hub.do/10.1063/1.1702424
[2] https://scitechdaily.com/zeptoseconds-new-world-record-in-sh...
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).