On Monday, February 2, 2015 at 3:20:20 PM UTC-5, Phil Hobbs wrote:
> On 2/2/2015 10:33 AM, Tim Williams wrote:
> > "Phil Hobbs" <pcdhobbs@gmail.com> wrote in message
> > news:c57edc71-7cf5-43a3-ab5d-d1b203cffe82@googlegroups.com...
> >> That's not what the Pauli principle states, and it only applies to
> >> fermions anyway.
> >>
> >> Splitting of coupled quantum oscillators is what gives rise to the
> >> band structure of solids. Photons and other bosons don't behave the
> >> same way. (That's why there are lasers, among other things.)
> >>
> >
> > Well, obviously it's a gross simplification.  But I don't think
> > unreasonable.
> >
> > If you look at the characteristics of the phenomena, quanta are well
> > defined, give or take externalities: the line width of an atomic
> > transition is for all intents and purposes infinitessimal, minus
> > splitting (fine structure, fields, etc.), doppler and such (properties
> > of a gas, etc.). Whereas the classical peak is fully described by a
> > continuous function of amplitude, with the "line" width determined by Q.
> >
> > Likewise, where you have systems containing fermions, coming together,
> > you get exclusion, and you get splitting of energy levels.  Two isolated
> > hydrogen atoms have identical spectra, but two hydrogen atoms in
> > relative proximity experience a splitting and shift.  The effect is not
> > un-analogous, at least on a grossly descriptive level.  When things like
> > this happen, there's often some underlying theoretical truth to it, that
> > it doesn't happen for mere coincidence.
> 
> The Pauli principle has nothing to do with splitting, it has to do with 
> wave function symmetry.
> 
> With indistinguishable particles, the wave function has to be symmetric 
> or antisymmetric, under the operation of interchanging particle A and 
> particle B.
> 
> The reason for this is that it has to be invariant under the operation 
> of swapping them and then swapping them back.
> 
> If the particles are indistinguishable, though, swapping one way is 
> indistinguishable from swapping  back.  That means that the eigenvalue 
> of the transformation has to be +- 1.  (It can't have a magnitude other 
> than unity, because the normalization sets the number of particles.)

Fun, thanks.
 I'd never heard the double swap  gets you back to where you 
started, argument before. (though kinda obvious in retrospect.)  
So there can be two, and only two, types of indistinguishable particles.

George H.

> 
> Bosons are particles for which the eigenvalue is +1, and fermions are 
> those for which the eigenvalue is -1.
> 
> With two or more bosons in a single state, interchanging them doesn't 
> change anything, so it's the more, the merrier.
> 
> With two fermions in a single state, interchanging them has to make the 
> wave function invariant under a multiplication by -1.  That is, its 
> magnitude has to be 0--which means there's no such state.
> 
> _That's_ the Pauli principle.
> 
> >
> > No, photons and phonons and such don't behave the same way, but their
> > interactions -- mediated by electronic transitions -- often are.  So,
> > we're talking about the fermionic structure that's probed by bosons, not
> > the statistics of bosons themselves.  Which would be boring -- like
> > talking about only superposition in linear classical systems. :)
> 
> Cheers
> 
> Phil Hobbs
> 
> -- 
> Dr Philip C D Hobbs
> Principal Consultant
> ElectroOptical Innovations LLC
> Optics, Electro-optics, Photonics, Analog Electronics
> 
> 160 North State Road #203
> Briarcliff Manor NY 10510
> 
> hobbs at electrooptical dot net
> http://electrooptical.net

On 2/2/2015 10:33 AM, Tim Williams wrote:
> "Phil Hobbs" <pcdhobbs@gmail.com> wrote in message
> news:c57edc71-7cf5-43a3-ab5d-d1b203cffe82@googlegroups.com...
>> That's not what the Pauli principle states, and it only applies to
>> fermions anyway.
>>
>> Splitting of coupled quantum oscillators is what gives rise to the
>> band structure of solids. Photons and other bosons don't behave the
>> same way. (That's why there are lasers, among other things.)
>>
>
> Well, obviously it's a gross simplification.  But I don't think
> unreasonable.
>
> If you look at the characteristics of the phenomena, quanta are well
> defined, give or take externalities: the line width of an atomic
> transition is for all intents and purposes infinitessimal, minus
> splitting (fine structure, fields, etc.), doppler and such (properties
> of a gas, etc.). Whereas the classical peak is fully described by a
> continuous function of amplitude, with the "line" width determined by Q.
>
> Likewise, where you have systems containing fermions, coming together,
> you get exclusion, and you get splitting of energy levels.  Two isolated
> hydrogen atoms have identical spectra, but two hydrogen atoms in
> relative proximity experience a splitting and shift.  The effect is not
> un-analogous, at least on a grossly descriptive level.  When things like
> this happen, there's often some underlying theoretical truth to it, that
> it doesn't happen for mere coincidence.

The Pauli principle has nothing to do with splitting, it has to do with 
wave function symmetry.

With indistinguishable particles, the wave function has to be symmetric 
or antisymmetric, under the operation of interchanging particle A and 
particle B.

The reason for this is that it has to be invariant under the operation 
of swapping them and then swapping them back.

If the particles are indistinguishable, though, swapping one way is 
indistinguishable from swapping  back.  That means that the eigenvalue 
of the transformation has to be +- 1.  (It can't have a magnitude other 
than unity, because the normalization sets the number of particles.)

Bosons are particles for which the eigenvalue is +1, and fermions are 
those for which the eigenvalue is -1.

With two or more bosons in a single state, interchanging them doesn't 
change anything, so it's the more, the merrier.

With two fermions in a single state, interchanging them has to make the 
wave function invariant under a multiplication by -1.  That is, its 
magnitude has to be 0--which means there's no such state.

_That's_ the Pauli principle.

>
> No, photons and phonons and such don't behave the same way, but their
> interactions -- mediated by electronic transitions -- often are.  So,
> we're talking about the fermionic structure that's probed by bosons, not
> the statistics of bosons themselves.  Which would be boring -- like
> talking about only superposition in linear classical systems. :)

Cheers

Phil Hobbs

-- 
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510

hobbs at electrooptical dot net
http://electrooptical.net

"George Herold" <gherold@teachspin.com> wrote in message 
news:093b431f-176f-4bc3-8714-e832f3825d52@googlegroups.com...
>Hi Tim,  Just a fine point of correction.
Atomic transitions have a finite width that is set by the lifetime of the 
excited state.  For a typical ~10 ns lifetime, it's about a 10 MHz width... 
(there's a factor of 2 * pi in there.)  You can actually see this width with 
diode lasers.. and some tricks.  (search for saturated absorption 
spectroscopy.)
>

Ah yes, I should've remembered this.  Uncertainty and all.

Better phrasing; for being atomic transitions, they can be surprisingly 
sharp, much sharper than you'd expect for a frequency in the 600THz range!

Tim

-- 
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com

On Monday, February 2, 2015 at 10:33:18 AM UTC-5, Tim Williams wrote:
> "Phil Hobbs" <pcdhobbs@gmail.com> wrote in message 
> news:c57edc71-7cf5-43a3-ab5d-d1b203cffe82@googlegroups.com...
> > That's not what the Pauli principle states, and it only applies to 
> > fermions anyway.
> >
> > Splitting of coupled quantum oscillators is what gives rise to the band 
> > structure of solids. Photons and other bosons don't behave the same way. 
> > (That's why there are lasers, among other things.)
> >
> 
> Well, obviously it's a gross simplification.  But I don't think 
> unreasonable.
> 
> If you look at the characteristics of the phenomena, quanta are well 
> defined, give or take externalities: the line width of an atomic transition 
> is for all intents and purposes infinitessimal, minus splitting (fine 
> structure, fields, etc.), doppler and such (properties of a gas, etc.). 
> Whereas the classical peak is fully described by a continuous function of 
> amplitude, with the "line" width determined by Q.

Hi Tim,  Just a fine point of correction.  
Atomic transitions have a finite width that is set by the lifetime of the excited state.  For a typical ~10 ns lifetime, it's about a 10 MHz width... (there's a factor of 2 * pi in there.)  You can actually see this width with diode lasers.. and some tricks.  (search for saturated absorption spectroscopy.)  

George H. 
> 
> Likewise, where you have systems containing fermions, coming together, you 
> get exclusion, and you get splitting of energy levels.  Two isolated 
> hydrogen atoms have identical spectra, but two hydrogen atoms in relative 
> proximity experience a splitting and shift.  The effect is not un-analogous, 
> at least on a grossly descriptive level.  When things like this happen, 
> there's often some underlying theoretical truth to it, that it doesn't 
> happen for mere coincidence.
> 
> No, photons and phonons and such don't behave the same way, but their 
> interactions -- mediated by electronic transitions -- often are.  So, we're 
> talking about the fermionic structure that's probed by bosons, not the 
> statistics of bosons themselves.  Which would be boring -- like talking 
> about only superposition in linear classical systems. :)
> 
> Tim
> 
> -- 
> Seven Transistor Labs
> Electrical Engineering Consultation
> Website: http://seventransistorlabs.com

"Phil Hobbs" <pcdhobbs@gmail.com> wrote in message 
news:c57edc71-7cf5-43a3-ab5d-d1b203cffe82@googlegroups.com...
> That's not what the Pauli principle states, and it only applies to 
> fermions anyway.
>
> Splitting of coupled quantum oscillators is what gives rise to the band 
> structure of solids. Photons and other bosons don't behave the same way. 
> (That's why there are lasers, among other things.)
>

Well, obviously it's a gross simplification.  But I don't think 
unreasonable.

If you look at the characteristics of the phenomena, quanta are well 
defined, give or take externalities: the line width of an atomic transition 
is for all intents and purposes infinitessimal, minus splitting (fine 
structure, fields, etc.), doppler and such (properties of a gas, etc.). 
Whereas the classical peak is fully described by a continuous function of 
amplitude, with the "line" width determined by Q.

Likewise, where you have systems containing fermions, coming together, you 
get exclusion, and you get splitting of energy levels.  Two isolated 
hydrogen atoms have identical spectra, but two hydrogen atoms in relative 
proximity experience a splitting and shift.  The effect is not un-analogous, 
at least on a grossly descriptive level.  When things like this happen, 
there's often some underlying theoretical truth to it, that it doesn't 
happen for mere coincidence.

No, photons and phonons and such don't behave the same way, but their 
interactions -- mediated by electronic transitions -- often are.  So, we're 
talking about the fermionic structure that's probed by bosons, not the 
statistics of bosons themselves.  Which would be boring -- like talking 
about only superposition in linear classical systems. :)

Tim

-- 
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com

On Sunday, February 1, 2015 at 3:05:25 AM UTC-5, Bill Beaty wrote:
> In classical physics, search "line splitting" of coupled oscillators.   It's the chassical version of QM's Pauli Exclusion principle, where two oscillators aren't allowed to be in the same state (have the same freq.)   Note that as oscillations "slosh" between the resonators, the sloshing period is the same as the separation between peaks in the frequency domain.

I would just call them (the oscillations) the normal modes of the system. 
If you can excite the system in one of it's normal modes, then it will stay
 in that mode and not have the energy sloshing back and forth.

George H.    
> 
> Make a big square array of resonators, and you've got a 2D crystal, and so much line-splitting that we end up with an "energy band" which is actually a large number of closely-spaced peaks.   Hmmm, if we could plot the absolute value amplitude of every oscillator as a raster, then slam single elements (or groups) with transient spikes, what's that look like?   For low coupling, it's thermal vibrations in solids.   With high coupling it's just a patch of 2D waveguide with 2D waves bouncing around inside.   Make a low-coupling "wave tank" where the "liquid' only passes slowly-moving oscillations along, rather than propagating waves.

John Larkin <jlarkin@highlandtechnology.com> wrote:
> On Sun, 1 Feb 2015 00:05:20 -0800 (PST), Bill Beaty <billb@eskimo.com>
> wrote:
> 
>> In classical physics, search "line splitting" of coupled oscillators.  
>> It's the chassical version of QM's Pauli Exclusion principle, where two
>> oscillators aren't allowed to be in the same state (have the same freq.)
>>   Note that as oscillations "slosh" between the resonators, the sloshing
>> period is the same as the separation between peaks in the frequency domain.
>> 
>> Make a big square array of resonators, and you've got a 2D crystal, and
>> so much line-splitting that we end up with an "energy band" which is
>> actually a large number of closely-spaced peaks.   Hmmm, if we could
>> plot the absolute value amplitude of every oscillator as a raster, then
>> slam single elements (or groups) with transient spikes, what's that look
>> like?   For low coupling, it's thermal vibrations in solids.   With high
>> coupling it's just a patch of 2D waveguide with 2D waves bouncing around
>> inside.   Make a low-coupling "wave tank" where the "liquid' only passes
>> slowly-moving oscillations along, rather than propagating waves.
> 
> OK, here are three resonators in-line.
> 
> https://dl.dropboxusercontent.com/u/53724080/Circuits/Oscillators/Coupled_Resonators_Three.jpg
> 
> The waveforms are sort of beautiful, and vary radically as the
> coupling caps are changed, especially if C3<>C6.
> 
> 
> 
> 
> 


I've got some very similar waveforms at work from a 230 kV, 3 phase cable
circuit which had a 45 MVAR shunt reactor hanging off it when the line was
tripped. All three phases resonated at nearly equal frequencies and you had
energy transfer via the inter-phase capacitance and mutual inductance of
the overhead portion of the line.

On Sun, 1 Feb 2015 00:05:20 -0800 (PST), Bill Beaty <billb@eskimo.com>
wrote:

>In classical physics, search "line splitting" of coupled oscillators.   It's the chassical version of QM's Pauli Exclusion principle, where two oscillators aren't allowed to be in the same state (have the same freq.)   Note that as oscillations "slosh" between the resonators, the sloshing period is the same as the separation between peaks in the frequency domain.
>
>Make a big square array of resonators, and you've got a 2D crystal, and so much line-splitting that we end up with an "energy band" which is actually a large number of closely-spaced peaks.   Hmmm, if we could plot the absolute value amplitude of every oscillator as a raster, then slam single elements (or groups) with transient spikes, what's that look like?   For low coupling, it's thermal vibrations in solids.   With high coupling it's just a patch of 2D waveguide with 2D waves bouncing around inside.   Make a low-coupling "wave tank" where the "liquid' only passes slowly-moving oscillations along, rather than propagating waves.

OK, here are three resonators in-line.

https://dl.dropboxusercontent.com/u/53724080/Circuits/Oscillators/Coupled_Resonators_Three.jpg

The waveforms are sort of beautiful, and vary radically as the
coupling caps are changed, especially if C3<>C6.






-- 

John Larkin         Highland Technology, Inc
picosecond timing   laser drivers and controllers

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com