I had thought that it had been done long ago, but this was published on the 13th March 2013.
gives a bunch of references
takes it back to 1973 for electrons (but they might not be guaranteed single), It has also been done with buckyballs (C60 buckmeisterfullerene molecules).
though again there doesn't seem to be any guarantee that there was only one molecule going through the slits at any time.
-- Bill Sloman, Sydney
I wonder what Jim had in what passes for his mind. If he wasn't senile, he too could have used google to find the reference.
-- Bill Sloman, Sydney
The issue isn't only one of causality violation, straight Fick's law and anything derived from it also implies that the current is equal to the diffusive flux, always, but it's not hard to think up hypothetical macroscopic mediums/domains that don't themselves violate any classical physics where that cannot be the case. They're macroscopic and even non-relativistic though, shouldn't one be able to use a classical physics equation to describe their behavior?
The "outside domain of validity" objection is fine in moderation but IMO when one starts applying it with regularity to many situations and using it to handwave away all the "corner cases" it becomes just a synonym for "we don't really understand what's going on here" like e.g. why relativity and QM are incompatible.
What I was trying to suggest wasn't that you could use heat transfer to actually transfer information faster than light, it was that there are probably domains still within the purview of classical physics where The Heat Equation predicts that would occur, it is invalid in those domains for that reason, but might still want to say something about using a classical equation.
There's no guarantee that equation will be first order in time or anything else for that matter, but if it predicts observed behavior is it still somehow "lesser in stature" than the undergrad textbook equation?
Depends. If it comes from a first-principles derivation based on different but physically reasonable principles, so that it extends the region of vali dity of the heat equation, fair enough. If it extended it enough to predict striking new results, and these were experimentally verified, the folks in volved might well become famous.
OTOH if it were merely phenomenological, there'd be no new physics in it, s o basically nobody would care.
I don't disagree that there are some pretty obvious areas for improved unde rstanding in ordinary heat transfer. The one that's on the top of my mind i s interfacial thermal resistance. There are theories for this, based iiuc b asically on impedance mismatches in the electron and phonon wave functions at material boundaries, but they all have horribly wrong temperature depend ances. Horribly wrong as in predicting T**3 behaviour as T->0 when experim ent is T**0.
Cheers
Phil Hobbs
Well ...(more thread shift).. QM and relativity are compatible. It was Dirac who got that started and 'discovered' antimatter. Quantum gravity is what no one can do.
George H.
The general continuity equation seems axiomatic enough that it must hold in some form or other in all domains or more or less everything we know about physics is wrong. You have some kind of stuff, you cant create the stuff out of nothing, it can't vanish into nothing, what "goes in" must "come out."
Fick's law is a special case of the continuity equation which implies things that are non-physical in some domains.
I'm stretching the limits of what I know about theoretical physics here (which isn't a heck of a lot), but in the case of relativistic heat transfer it seems the continuity equation can still hold fine if you assume the "matter current" vector and "entropy current" vector don't necessarily have to be aligned.
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