2041RE: [PrimeNumbers] Re: Cracking RSA: Relationship between prime numbers and quantum theory
- Aug 1, 2001
> First Pauli exclusion principle states:No it does not! Just because that web page makes that claim that
> "In a closed system, no two electrons can occupy the same state."
doesn't mean that the PEP is as stated. The PEP states that no two
fermions can occupy the same quantum state. Electrons are fermions,
indeed, but electrons can pair up to form "Cooper pairs" which
themselves are bosons. These bosons can indeed occupy the same quantum
state and, when they do, give rise to the phenomenon of
The web page itself goes on to state "actually, protons and neutrons
obey the same principle, while photons do not)" something you seem to
have missed. Lasers function precisely because photons do not obey the
same principle. Protons and neutrons are spin-half particles and thus
fermions; photons are spin-zero bosons. Photons, as far as we know,
have no sub-structure but both protons and neutrons are composite
particles (as are Cooper pairs and helium nuclei). The helium-4 nucleus
is a spin-zero boson and so can violate the PEP. When it does, bulk
helium-4 becomes superfluid. The helium-3 nucleus is a spin-half
fermion and so liquid helium-3 doesn't become superfluid until the
temperature is low enough for pairs of nuclei to form spin-zero bosons,
whereupon it too shows superfluidity.
> This isn't "exactly" what I'm saying. Go back and readVery well, I quote: "One of the postulate in quantum theory states that
> "exactly" what I said.
no two particle can occupy the same place at the same time."
This statement is just plain wrong, for the reasons I went into
> Because when you say "occupy exactly" ... I'm veryFor a start, Heisenberg's uncertainty principle only applies to
> suspicious whether
> you've figured a way to violate Heinsberg uncertainity principle.
conjugate quantities, such as energy/time and linear momentum/position
(these two quantities are, of course, special cases of the more general
4-momentum / spacetime coordinates). It does *not* apply to
non-conjugate measurements, such as the x-component of momentum and the
y coordinate, which can be simultaneously measured to arbitrary
In general, if the operators corresponding to observables anti-commute,
HUP applies. If they commute, they do not.
Please read some real books on quantum theory.
> assuming what I wrote is "Pauli exclusion principle". HavingBut that is precisely what you did write!
> bad assumption leads to bad argument.
> Working for your employer really makes you *think* you areI don't think I understand that comment. Don't bother elucidating, as
> making progress. :)
the smiley suggests that it's probably not that important.
I'm becoming ever more convinced that this thread has very little, if
anything, to do with prime numbers. I've probably already bored the
majority of readers, so I'll drop out of it here.
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