**From:** John K Clark (*johnkclark@fastmail.fm*)

**Date:** Mon Feb 09 2009 - 10:32:08 MST

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On Mon, 9 Feb 2009 "Stuart Armstrong"

<dragondreaming@googlemail.com> said:

*> > On the
*

*> > Extropian List I used nothing but
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*> > The Identity of Indiscernibles and high school algebra to derive The
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*> > Pauli Exclusion Principle; and that is the root of chemistry, and that
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*> > is the root of biology. By the way I'm rather pleased with that
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*> > derivation.
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*>
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*> Sounds rather impressive - do you still have the derivation? And what
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*> assumptions do you put into it - basically how did you distinguish
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*> bosons (which don't obey the exclusion principle) from fermions?
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*> Indiscernibles wouldn't be enough.
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=========================================

*>From my post to the Extropian list:
*

In about 1690 the philosopher Leibniz discovered something called "The

Identity Of Indiscernibles". He said that things that you can measure

are

what's important, and if there is no way to find a difference between

two

things then they are identical and switching the position of the objects

does not change the physical state of the system.

Leibniz's idea turned out to be very practical, although until the 20th

century nobody realized it, before that his idea had no observable

consequences because nobody could find two things that were exactly

alike. Things changed dramatically when it was discovered

that atoms have no scratches on them to tell them apart.

By using The Identity Of Indiscernibles you can deduce one of the

foundations of modern physics the fact that there must be two classes of

particles, bosons like photons and fermions like electrons, and from

there

you can deduce The Pauli Exclusion Principle, and that is the basis

of the periodic table of elements, and that is the basis of chemistry,

and

that is the basis of life. If The Identity Of Indiscernibles is wrong

then

this entire chain breaks down and you can throw Science into the trash

can.

The Schrödinger Wave Equation proved to be enormously useful in

accurately

predicting the results of experiments, and as the name implies it's an

equation describing the movement of a wave, but embarrassingly it was

not at

all clear what it was talking about.

Exactly what was waving? Schrödinger thought it was a matter wave, but

that didn't seem right to Max Born. Born reasoned that matter is not

smeared

around, only the probability of finding it is. Born was correct,

whenever an

electron is detected it always acts like a particle, it makes a dot when

it

hit's a phosphorus screen not a smudge, however the probability of

finding

that electron does act like a wave so you can't be certain exactly

where that dot will be. Born showed that it's the square of the wave

equation that describes the probability, the wave equation itself is

sort of

a useful mathematical fiction, like lines of longitude and latitude,

because

experimentally we can't measure the quantum wave function F(x) of a

particle, we can only measure the intensity (square) of the wave

function

[F(x)]^2 because that's a probability and probability we can measure.

Let's consider a very simple system with lots of space but only 2

particles

in it. P(x) is the probability of finding two particles x distance

apart,

and we know that probability is the square of the wave function,

so P(x) =[F(x)]^2. Now let's exchange the position of the particles in

the system, the distance between them was x1 - x2 = x but is

now x2 - x1 = -x.

The Identity Of Indiscernibles tells us that because the two particles

are

the same, no measurable change has been made, no change in probability,

so

P(x) = P(-x). Probability is just the square of the wave function so

[ F(x) ]^2 = [F(-x)]^2 . From this we can tell that the Quantum

wave function can be either an even function, F(x) = +F(-x), or an odd

function, F(x) = -F(-x). Either type of function would work in our

probability equation because the square of minus 1 is equal to the

square

of plus 1. It turns out both solutions have physical significance,

particles

with integer spin, bosons, have even wave functions, particles with half

integer spin, fermions, have odd wave functions.

We MUST assume that atoms are interchangeable and have no individuality

or

modern Physics becomes incomprehensible. If we put two fermions like

electrons in the same place then the distance between them, x , is zero

and

because they must follow the laws of odd wave functions, F(0) = -F(0),

but

the only number that is it's own negative is zero so F(0)=0 .

What this means is that the wave function F(x) goes to zero so of

course [F(x)]^2 goes to zero, thus the probability of finding two

electrons

in the same spot is zero, and that is The Pauli Exclusion Principle. Two

identical bosons, like photons of light, can sit on top of each other

but

not so for fermions, The Pauli Exclusion Principle tells us that 2

identical

electrons can not be in the same orbit in an atom.

If we didn't know that then we wouldn't understand Chemistry, we

wouldn't

know why matter is rigid and not infinitely compressible, and if we

didn't

know that atoms are interchangeable we wouldn't understand any of that.

Bottom line: Atoms have no individuality and If they can't even give

themselves this property they can't give it to us.

John K Clark

-- John K Clark johnkclark@fastmail.fm -- http://www.fastmail.fm - Choose from over 50 domains or use your own

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