> > Not true in general. It is true for fermions (particles with spin

precisely

> > (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

You're quibbling. If you prefer it, I'm equally happy with "occupy

> > superconductors have such interesting properties.

>

> "occupy precisely" ... can you elaborate? Why don't you use

> the word "occupy exactly"?

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

wordy.

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".

Even being that generous, your statement "no two particle (sic) can

occupy the same place at the same time" is false, if by "place" you mean

spatial location. For a start, two fermions differing only in spin can

occupy the same energy state. Further, from Heisenberg's uncertainty

principle, the spatial location of each of two particles can only be

precisely determined if their momenta are completely undetermined. If

you know anything about the momenta of the particles, their wave

functions *will* overlap in space. Trying to nail down "the same time"

is equally difficult: the particle's energy is then the conjugate

quantity. But I'll be generous again and assume that by "particle" you

meant fermion and that by "place" you meant eigenstate.

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outdated and possibly unavailable, but I'm sure there must be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.

(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.)

Paul- On Wednesday 01 August 2001 13:01, Paul Leyland wrote:
> > > Not true in general. It is true for fermions (particles with spin

First 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

>

> precisely

>

> > > 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

> wordy.

"In a closed system, no two electrons can occupy the same state."

http://theory.uwinnipeg.ca/mod_tech/node168.html

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.

http://www.srikant.org/core/node12.html

>

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.)

--kent > 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."

> http://theory.uwinnipeg.ca/mod_tech/node168.html

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

Very 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

previously.

> Because when you say "occupy exactly" ... I'm very

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

> suspicious whether

> you've figured a way to violate Heinsberg uncertainity principle.

> http://www.srikant.org/core/node12.html

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

But that is precisely what you did write!

> bad assumption leads to bad argument.

> Working for your employer really makes you *think* you are

I 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.

Paul> I'm becoming ever more convinced that this thread has very little, if

You 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

number sequence.

http://www.maths.ex.ac.uk/~mwatkins/zeta/physics1.htm

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

sqrt(C1).

If P1 < P2 or P1 > P2, it's a more difficult situation.

--kent