Re: [PrimeNumbers] Re: Cracking RSA: Relationship between prime numbers and quantum theory
- On Wednesday 01 August 2001 13:01, Paul Leyland wrote:
> > > Not true in general. It is true for fermions (particles with spinFirst Pauli exclusion principle states:
> > > (2i+1)/2) and is known as the Pauli exclusion principle. For bosons
> > > (particles with integral spin) particles can, and do, occupy
> > > the same state at the same time. It's why lasers, superfluids and
> > > superconductors have such interesting properties.
> > "occupy precisely" ... can you elaborate? Why don't you use
> > the word "occupy exactly"?
> You're quibbling. If you prefer it, I'm equally happy with "occupy
> exactly". If you really want to get pedantic, I'd be even happier with
> phrasing along the lines of "there is no constraint on the occupancy
> number of an eigenstate of a system of bosons" but that seems unduly
"In a closed system, no two electrons can occupy the same state."
Note Pauli only states for occupance of same state not same time.
This isn't "exactly" what I'm saying. Go back and read "exactly" what I
said. Because when you say "occupy exactly" ... I'm very suspicious whether
you've figured a way to violate Heinsberg uncertainity principle.
>You don't have to be generous. You need to understand what I wrote. You are
> If we're being pedantic, your original statement is unequivocably false.
> It's not even strictly true for fermions in that the Pauli exclusion
> principle is not really a postulate of quantum mechanics (in the sense
> of a presupposed truth which is not amenable to question) but rather a
> consequence of the anticommutativity of operators acting on fermion
> quantum fields. I was being generous and assumed you meant
> "consequence" or "feature" where you wrote "postulate".
assuming what I wrote is "Pauli exclusion principle". Having bad assumption
leads to bad argument.
>Working for your employer really makes you *think* you are making progress.
> If you really want to make progress, I suggest that you consult an
> introductory text or two on quantum field theory. It's 19 years since I
> last studied QFT so the references I can quote from memory are now
> outdated and possibly unavailable, but I'm sure there must be
> contemporary works available.
>Thanks for using amazon.com, it's better than bn.com don't you think? :)
> (Just checked on Amazon: a search on Quantum Field Theory yields 596
> hits, so you ought to be able to find something. Further, the book I
> own, Elements of Advanced Quantum Theory written by John M Ziman in
> 1975, is still in print.)
> 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.
> I'm becoming ever more convinced that this thread has very little, ifYou miss the point of the relation to prime number.
> anything, to do with prime numbers. I've probably already bored the
> majority of readers, so I'll drop out of it here.
Cracking the RSA code is a linear problem, thus a one-dimensional problem.
You come and talk about the 4th dimension, which to me doesn't seem relevant.
So you ya, you convince yourself.
As I've said before, there exist a very close spectra that resemble prime
My equation with two variables:
Assume = C1 = P1*P2
f(x) = x^2 - (P1 + P2)*x + C1 = 0
I only have one equation with two variables. I need another equation to
solve for P1 and P2. That's what lead me to quantum mechanic in trying to
find the wavefunction that describes prime number sequence.
If P1 = P2, I can use the quadraic formula to solve for x. Resulting in
If P1 < P2 or P1 > P2, it's a more difficult situation.