QM and electron orbits

This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless trying
to criticise a belief normally taught in such education. Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect and
obsolete model of the atom. As we know, the idea of fixed orbits is
not exactly correct, but that does not make it useless.

The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description. This
leads to the false belief that an electron's position is smeared out
over the orbital, and that the probability function is independent of
earlier observations. From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital. For all higher n, the relative uncertainty
becomes smaller, and the classical orbit becomes an increasingly
better approximation.

This explains the solar system, for example, where the quantum numbers
are very, very large and thus quantum effects are unobservable. The
solar system obeys the same physical laws as the atom. There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.

Andrew Usher

Andrew Usher wrote:
This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless trying
to criticise a belief normally taught in such education. Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

Since when do logic and QM have anything to do with each other? Especially when
you use a conventional (classic?) approach?

That's like trying to apply the rules of algebra to pig latin.

Andrew Usher wrote:

This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless trying
to criticise a belief normally taught in such education.

Res ipsa loquiter.

Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

Res ipsa loquiter ad nauseam.

[snip[]

This explains the solar system, for example,
[snip further crap]

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

"Andrew Usher" wrote in message
om...
This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless trying
to criticise a belief normally taught in such education. Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect and
obsolete model of the atom. As we know, the idea of fixed orbits is
not exactly correct, but that does not make it useless.

The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description. This
leads to the false belief that an electron's position is smeared out
over the orbital, and that the probability function is independent of
earlier observations. From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital. For all higher n, the relative uncertainty
becomes smaller, and the classical orbit becomes an increasingly
better approximation.

This explains the solar system, for example, where the quantum numbers
are very, very large and thus quantum effects are unobservable. The
solar system obeys the same physical laws as the atom. There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.

Andrew Usher

Shabby metaphysics, at best. Here's some Gems:

Placed properly, classical physics is isn't incorrect:
The Hamiltonian of Quantum Mechanics contains all
of classical physics.

The purpose of the QM wave equation is to place
Planck's constant in proper relationship to the classical
Hamiltonian.

[Old Man]

"Andrew Usher" wrote in message
om...
This message is a continuation of the discussion in the thread
'Neutrino mass'.

It is more like a reiteration of your position, already stated in that
thread.


I admit to not being formally educated in QM.

Neither am I.
But I try not to criticise things I don't understand.

I am nevertheless trying
to criticise a belief normally taught in such education.

If you're referring to the idea of the electron being "smeared" across the
orbital, then it is you who has misunderstood.
"In a general paper on quantum mechanics, Schroedinger discusses and rejects
the interpretation that a single quantum is somehow phyiscally "spread out"
or "blurred" among the different parts of a superposition ."
That is what is being taught.

Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect and
obsolete model of the atom. As we know, the idea of fixed orbits is
not exactly correct, but that does not make it useless.

It is very useful for chemistry and nuclear physics, but it is a model and
not meant to be taken as a true picture of the atom.


The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description. This
leads to the false belief that an electron's position is smeared out
over the orbital,

That's *your* false belief. The electron isn't "smeared out over the
orbital" (just as Schroedinger's cat isn't alive AND dead). It just doesn't
have a position until one has been measured (just as you don't know if the
cat is alive or dead until you open the chamber), and then that position is
one that is affected by the act of measuring, and is therefore not a true
representation of where the electron really was, if indeed it had a position
at all.
That's why such an innate position is done away with entirely; it is
meaningless since it can't be measured without interfering with it.

and that the probability function is independent of
earlier observations. From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital. For all higher n, the relative uncertainty
becomes smaller, and the classical orbit becomes an increasingly
better approximation.

What difference would it make?
If none, then what is the value of your version?


This explains the solar system, for example, where the quantum numbers
are very, very large and thus quantum effects are unobservable.

Which is exactly why QM doesn't explain it.

The
solar system obeys the same physical laws as the atom.

Because it looks like the classic atomic model?
You're not the first to see the similarity.
What happens inside an atom is very different from a solar system. Or do you
believe that the sun has a positive charge and the planets a negative
charge?

There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.

On Fri, 28 May 2004 23:00:20 -0500, "Old Man"
wrote:

"Andrew Usher" wrote in message
. com...
This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless trying
to criticise a belief normally taught in such education. Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect and
obsolete model of the atom. As we know, the idea of fixed orbits is
not exactly correct, but that does not make it useless.

The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description. This
leads to the false belief that an electron's position is smeared out
over the orbital, and that the probability function is independent of
earlier observations. From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital. For all higher n, the relative uncertainty
becomes smaller, and the classical orbit becomes an increasingly
better approximation.

This explains the solar system, for example, where the quantum numbers
are very, very large and thus quantum effects are unobservable. The
solar system obeys the same physical laws as the atom. There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.

Andrew Usher

Shabby metaphysics, at best. Here's some Gems:


Is anything beyond the equations 'metaphysics' to you? Do you think we
should make no effort to actually understand physics?

Placed properly, classical physics is isn't incorrect:
The Hamiltonian of Quantum Mechanics contains all
of classical physics.


This is actually what I am saying.

The purpose of the QM wave equation is to place
Planck's constant in proper relationship to the classical
Hamiltonian.

[Old Man]


Andrew Usher

"Old Man" wrote in message ...
"Andrew Usher" wrote in message
om...
This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless trying
to criticise a belief normally taught in such education. Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect and
obsolete model of the atom. As we know, the idea of fixed orbits is
not exactly correct, but that does not make it useless.

The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description. This
leads to the false belief that an electron's position is smeared out
over the orbital, and that the probability function is independent of
earlier observations. From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital. For all higher n, the relative uncertainty
becomes smaller, and the classical orbit becomes an increasingly
better approximation.

This explains the solar system, for example, where the quantum numbers
are very, very large and thus quantum effects are unobservable. The
solar system obeys the same physical laws as the atom. There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.

Andrew Usher

Shabby metaphysics, at best. Here's some Gems:


Is anything beyond the equations 'metaphysics' to you? Should we not
try to actually understand the physics?

Placed properly, classical physics is isn't incorrect:
The Hamiltonian of Quantum Mechanics contains all
of classical physics.


That this must be so is what I have been saying.

The purpose of the QM wave equation is to place
Planck's constant in proper relationship to the classical
Hamiltonian.

[Old Man]

Andrew Usher

"Andrew Usher" wrote in message
om...
This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless
trying
to criticise a belief normally taught in such education. Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect
and
obsolete model of the atom.

The idea that the Bohr-Sommerfeld orbits are an incorrect and an
obsolete model of the atom is in fact quite correct. That approach
led to a dead end and was entirely superceded by quantum mechanics
about seventy years ago.

As we know, the idea of fixed orbits is
not exactly correct, but that does not make it useless.

It is in fact a completely useless and misleading idea.

The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description.

There is no such thing as a time-independent wave function. A wave is
by defnition a function of space and time. The only reason why the
orbitals are written as time-independent functions is because each of
them has an additional implied factor
exp(iEt/hbar), where E is the energy. So the orbitals are actually
standing waves.

This
leads to the false belief that an electron's position is smeared out
over the orbital,

The probability density for finding the electron at a given position
*is* in fact determined by the orbital.

and that the probability function is independent of
earlier observations.

Those two lines carry no meaning that I can unambiguously discern.

From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital.

Unless you are trying to be clever by making a statement about the
fact that excited states are not stable, I can't follow what you are
driving at.

For all higher n, the relative uncertainty
becomes smaller,

The uncertainty relation relating momentum and position errors is
independent of the quantum number.

and the classical orbit becomes an increasingly
better approximation.

This explains the solar system, for example, where the quantum
numbers
are very, very large and thus quantum effects are unobservable. The
solar system obeys the same physical laws as the atom. There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.

Yes, the so-calle Rydberg states, with very high quantum numbers, do
begin to approximate to the classical situation. This is a
consequence of the corespondence principle.

Franz

On Sat, 29 May 2004 08:43:34 +0200, "Laura" wrote:


"Andrew Usher" wrote in message
. com...
This message is a continuation of the discussion in the thread
'Neutrino mass'.

It is more like a reiteration of your position, already stated in that
thread.


I admit to not being formally educated in QM.

Neither am I.
But I try not to criticise things I don't understand.

I am nevertheless trying
to criticise a belief normally taught in such education.

If you're referring to the idea of the electron being "smeared" across the
orbital, then it is you who has misunderstood.
"In a general paper on quantum mechanics, Schroedinger discusses and rejects
the interpretation that a single quantum is somehow phyiscally "spread out"
or "blurred" among the different parts of a superposition ."
That is what is being taught.


What do you believe we should picture?

Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect and
obsolete model of the atom. As we know, the idea of fixed orbits is
not exactly correct, but that does not make it useless.

It is very useful for chemistry and nuclear physics, but it is a model and
not meant to be taken as a true picture of the atom.


The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description. This
leads to the false belief that an electron's position is smeared out
over the orbital,

That's *your* false belief. The electron isn't "smeared out over the
orbital" (just as Schroedinger's cat isn't alive AND dead). It just doesn't
have a position until one has been measured (just as you don't know if the
cat is alive or dead until you open the chamber), and then that position is
one that is affected by the act of measuring, and is therefore not a true
representation of where the electron really was, if indeed it had a position
at all.

True, as a matter of logic, not physics.

That's why such an innate position is done away with entirely; it is
meaningless since it can't be measured without interfering with it.

and that the probability function is independent of
earlier observations. From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital. For all higher n, the relative uncertainty
becomes smaller, and the classical orbit becomes an increasingly
better approximation.

What difference would it make?
If none, then what is the value of your version?


That it avoids the implicit belief that the atom obeys different
physical laws.


This explains the solar system, for example, where the quantum numbers
are very, very large and thus quantum effects are unobservable.

Which is exactly why QM doesn't explain it.


QM is not necessary to explain it.

The
solar system obeys the same physical laws as the atom.

Because it looks like the classic atomic model?
You're not the first to see the similarity.
What happens inside an atom is very different from a solar system. Or do you
believe that the sun has a positive charge and the planets a negative
charge?

There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.


I think you should read my last paragraph again.

Andrew Usher

Franz Heymann wrote:
"Andrew Usher" wrote in message
om...

This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless

trying

to criticise a belief normally taught in such education. Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect

and

obsolete model of the atom.


The idea that the Bohr-Sommerfeld orbits are an incorrect and an
obsolete model of the atom is in fact quite correct. That approach
led to a dead end and was entirely superceded by quantum mechanics
about seventy years ago.

As we know, the idea of fixed orbits is

not exactly correct, but that does not make it useless.


It is in fact a completely useless and misleading idea.


The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description.


There is no such thing as a time-independent wave function. A wave is
by defnition a function of space and time. The only reason why the
orbitals are written as time-independent functions is because each of
them has an additional implied factor
exp(iEt/hbar), where E is the energy. So the orbitals are actually
standing waves.


This
leads to the false belief that an electron's position is smeared out
over the orbital,


The probability density for finding the electron at a given position
*is* in fact determined by the orbital.


and that the probability function is independent of
earlier observations.


Those two lines carry no meaning that I can unambiguously discern.


From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital.


Unless you are trying to be clever by making a statement about the
fact that excited states are not stable, I can't follow what you are
driving at.


For all higher n, the relative uncertainty
becomes smaller,


The uncertainty relation relating momentum and position errors is
independent of the quantum number.


and the classical orbit becomes an increasingly
better approximation.

This explains the solar system, for example, where the quantum

numbers

are very, very large and thus quantum effects are unobservable. The
solar system obeys the same physical laws as the atom. There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.


Right.
Unless they all have the same direction
magnetic field at the same time.
The electrons must all lie in concentric,
co-rotating rings for them not to
interfere with each other yet still
exert over the volume:
http://www.petcom.com/%7Ejohn/H.GIF
http://www.petcom.com/%7Ejohn/He.GIF
http://www.petcom.com/%7Ejohn/Li.GIF
http://www.petcom.com/%7Ejohn/Be.GIF
John