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2041RE: [PrimeNumbers] Re: Cracking RSA: Relationship between prime numbers and quantum theory

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  • Paul Leyland
    Aug 1, 2001
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      > First Pauli exclusion principle states:
      > "In a closed system, no two electrons can occupy the same state."
      > http://theory.uwinnipeg.ca/mod_tech/node168.html

      No it does not! Just because that web page makes that claim that
      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
      supercoductivity.

      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 read
      > "exactly" what I said.

      Very well, I quote: "One of the postulate in quantum theory states that
      no two particle can occupy the same place at the same time."

      This statement is just plain wrong, for the reasons I went into
      previously.

      > Because when you say "occupy exactly" ... I'm very
      > suspicious whether
      > you've figured a way to violate Heinsberg uncertainity principle.
      > http://www.srikant.org/core/node12.html

      For a start, Heisenberg's uncertainty principle only applies to
      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
      accuracy.

      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". Having
      > bad assumption leads to bad argument.

      But that is precisely what you did write!

      > Working for your employer really makes you *think* you are
      > making progress. :)

      I don't think I understand that comment. Don't bother elucidating, as
      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.


      Paul
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