Precessive motion as the source of quantum uncertainty?

[Duda Jarek]

Imagine we hold a flat surface and there is a spinning top (gyroscopic toy) on it. While changing the angle of the surface, the top generally follows the change, but it additionally makes some complicated 'precessive sinusoid/cycloid like motion' around the expected trajectory.

 

Electron's spin is something different, but it sometimes is imagined as a spinning charge ... it's quantum mechanical phase rotates while time change ... there is Lamor precession ...

Let's look at Bohr model of atom - quantum mechanics made it obsolete, but it still gives quite a good predictions

http://en.wikipedia.org/wiki/Bohr_model

It's main (?) lack is that it says that the lowest energy state should be spherically asymmetric (an orbit), while quantum mechanics says that the ground state is symmetric.

Generally higher angular momentum states in Bohr model corresponds to quantum mechanical states with angular momentum lower by 1 as in this case.

 

What if we would extend Bohr model by treating electron as 'a top'?

Electron's spin projection while such precessive motion could be changing from -1/2 to +1/2, so intuitively it should 'fuzzy' angular momentum by 1 - exactly as in the difference between Bohr model and quantum mechanics, e.g. forgetting about the orbit for the ground state...

Quantum mechanical probability density of states can be seen as naturally appearing thermodynamically ( http://arxiv.org/abs/0910.2724 ). Deterministic, but chaotically looking precessive motion could be the main source of statistical noise this model require for this thermodynamical behavior.

 

What do you think about it?

Have you heard about extending Bohr model by considering electron precession?

---

Merged post follows:

Consecutive posts merged

There is so called (Bohr's) correspondence principle, which says that quantum mechanics reproduces classical physics in the limit of large quantum numbers:

http://en.wikipedia.org/wiki/Correspondence_principle

so for large orbits, especially in Rydberg atoms

http://en.wikipedia.org/wiki/Rydberg_atom

electrons looks like just moving on classical trajectories - this 'quantum noise' is no longer essential.

 

To extend Bohr mode to different angular momentums, there was introduced Bohr-Sommerfeld model: more 'elliptical' orbits

http://en.wikipedia.org/wiki/File:Sommerfeld_ellipses.svg

one source of loosing these simple orbits, can be found in something like Mercury precession, which allows such orbit to rotate. It doesn't only have to be seen as mass related effect, there are arguments that electric field can also cause GR related effects, like time dilation:

http://www.springerlink.com/content/wtr11w113r22g346/

 

The other source of nonstandard behavior and so this statistical noise can be precessive motion I mentioned - angular momentum conservation says that the total: orbital angular momentum + spin is conserved. Precession - rotating spin of electron is allowed and is compensated by electron's angular momentum to conserve 'j'. So such rotations should 'fuzzy' orbital angular momentum by 1, as in the difference between Bohr model and QM.

 

There is also e.g. very complicated magnetic interaction between particles in atom and finally the only practical model to work on such extremely complicated system could be through probability densities and so quantum mechanics...

[foodchain]

Imagine we hold a flat surface and there is a spinning top (gyroscopic toy) on it. While changing the angle of the surface, the top generally follows the change, but it additionally makes some complicated 'precessive sinusoid/cycloid like motion' around the expected trajectory.

 

Electron's spin is something different, but it sometimes is imagined as a spinning charge ... it's quantum mechanical phase rotates while time change ... there is Lamor precession ...

Let's look at Bohr model of atom - quantum mechanics made it obsolete, but it still gives quite a good predictions

http://en.wikipedia.org/wiki/Bohr_model

It's main (?) lack is that it says that the lowest energy state should be spherically asymmetric (an orbit), while quantum mechanics says that the ground state is symmetric.

Generally higher angular momentum states in Bohr model corresponds to quantum mechanical states with angular momentum lower by 1 as in this case.

 

What if we would extend Bohr model by treating electron as 'a top'?

Electron's spin projection while such precessive motion could be changing from -1/2 to +1/2, so intuitively it should 'fuzzy' angular momentum by 1 - exactly as in the difference between Bohr model and quantum mechanics, e.g. forgetting about the orbit for the ground state...

Quantum mechanical probability density of states can be seen as naturally appearing thermodynamically ( http://arxiv.org/abs/0910.2724 ). Deterministic, but chaotically looking precessive motion could be the main source of statistical noise this model require for this thermodynamical behavior.

 

What do you think about it?

Have you heard about extending Bohr model by considering electron precession?

---

Merged post follows:

Consecutive posts merged

There is so called (Bohr's) correspondence principle, which says that quantum mechanics reproduces classical physics in the limit of large quantum numbers:

http://en.wikipedia.org/wiki/Correspondence_principle

so for large orbits, especially in Rydberg atoms

http://en.wikipedia.org/wiki/Rydberg_atom

electrons looks like just moving on classical trajectories - this 'quantum noise' is no longer essential.

 

To extend Bohr mode to different angular momentums, there was introduced Bohr-Sommerfeld model: more 'elliptical' orbits

http://en.wikipedia.org/wiki/File:Sommerfeld_ellipses.svg

one source of loosing these simple orbits, can be found in something like Mercury precession, which allows such orbit to rotate. It doesn't only have to be seen as mass related effect, there are arguments that electric field can also cause GR related effects, like time dilation:

http://www.springerlink.com/content/wtr11w113r22g346/

 

The other source of nonstandard behavior and so this statistical noise can be precessive motion I mentioned - angular momentum conservation says that the total: orbital angular momentum + spin is conserved. Precession - rotating spin of electron is allowed and is compensated by electron's angular momentum to conserve 'j'. So such rotations should 'fuzzy' orbital angular momentum by 1, as in the difference between Bohr model and QM.

 

There is also e.g. very complicated magnetic interaction between particles in atom and finally the only practical model to work on such extremely complicated system could be through probability densities and so quantum mechanics...

 

I think bells inequalities meant that quantum mechanics was not just statistical mechanics by another name.

[Duda Jarek]

Bell inequalities based argumentation says that quantum mechanical 'squares' cannot be a result of some 'hidden variables' which would give QM as statistical result.

Imagine two charged points idealized systems - if they are macroscopic, they can be described deterministically, while if they are microscopic - because of these 'squares' they cannot be described deterministically ?

So while rescalling these 'squares' would have to somehow emerge ... how?

 

I have seen only one trial to create probabilistic model for macroscopic system about which we can measure only some of its properties (for example because of distance) - and in this model: thermodynamics among trajectories, these 'squares' appears naturally in any scale (see my paper).

[foodchain]

Bell inequalities based argumentation says that quantum mechanical 'squares' cannot be a result of some 'hidden variables' which would give QM as statistical result.

Imagine two charged points idealized systems - if they are macroscopic, they can be described deterministically, while if they are microscopic - because of these 'squares' they cannot be described deterministically ?

So while rescalling these 'squares' would have to somehow emerge ... how?

 

I have seen only one trial to create probabilistic model for macroscopic system about which we can measure only some of its properties (for example because of distance) - and in this model: thermodynamics among trajectories, these 'squares' appears naturally in any scale (see my paper).

 

One of the big advances in QM was the Schrodinger equation, which of course has statistics as part of it.

 

As for the squares aspect, I think that sort of boils down to the interpretation level somewhat. I like to go along with quantum decoherence, but of course today or a hundred years from now someone might come along and revolutionize everything. Quantum deocherence also tends to deal with thermodynamics, which is another reason I like that framework over others.

 

Here is a link you might find of some interest, and for your sake I study this stuff as hobby only.

 

http://books.google.com/books?id=MqDUIvOCIgoC&dq=quantum+thermodynamics&printsec=frontcover&source=bn&hl=en&ei=hsRES9W_D4fmMbWmvfEB&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBgQ6AEwAw#v=onepage&q=&f=false

 

There is a few books to skim through on the link.

[Duda Jarek]

Thanks for the book, I'll look at it.

In approach from my paper we just take thermodynamics among trajectories (Boltzmann distribution) and we automatically get thermodynamical behavior of quantum mechanics - that everything wants to deexcitate to the ground state - we get concrete trajectories which statistically average to quantum mechanical probability distribution of the ground state.

[foodchain]

Thanks for the book, I'll look at it.

In approach from my paper we just take thermodynamics among trajectories (Boltzmann distribution) and we automatically get thermodynamical behavior of quantum mechanics - that everything wants to deexcitate to the ground state - we get concrete trajectories which statistically average to quantum mechanical probability distribution of the ground state.

 

Also its not statistical, its probability, which is something apart from just statistics. This is in reference to the Schrodinger equation thing I said.

[Duda Jarek]

Yes, it occurs that pure Boltzmann distribution among trajectories leads to probability densities exactly as squares of eigenfunctions of Schrödinger operator.

In this thermodynamic picture time propagator is not unitary, but stochastic - thermodynamically everything wants to deexcitate as in QM. To introduce interference to this picture, there is required some rotation of some integral degree of freedom of particles (in ellipsoid field it's caused by particle's electric charge)

[foodchain]

Yes, it occurs that pure Boltzmann distribution among trajectories leads to probability densities exactly as squares of eigenfunctions of Schrödinger operator.

In this thermodynamic picture time propagator is not unitary, but stochastic - thermodynamically everything wants to deexcitate as in QM. To introduce interference to this picture, there is required some rotation of some integral degree of freedom of particles (in ellipsoid field it's caused by particle's electric charge)

 

Is your use of deexcitate somewhat similar to dephasing? As from what I know no quantum system is ever something just to itself ultimately, as in one particle like an electron is constantly bombarded from the environment via entanglement for example. I would also guess this is why so much information can be produced about a particles behavior, but I could be very wrong.

 

What I like to wonder is about phonon behavior. If sound in a general sense is phonons, why is it regular, like metal on metal making a certain sound as opposed to rubber on metal, or is that one of those cat in a box questions?

 

*This may seem an odd question but you seem to know a lot more about this then I. Is it because quantum mechanics relies on the Planck constant that squares have to be used? I am unsure if equations in quantum mechanics deal with all real numbers, but again I am just wondering if the square is a product of somehow needing to return a positive value to satisfy the Planck constant?

[Duda Jarek]

While deexcitating into the ground state e.g. electrons just take the lowest orbitals and they are indistinguishable from QM point of view - we also loose entanglement - it's thermodynamical process.

 

About phonons - mechanical waves of atoms, they are qualitatively very similar to photons ("mechanical waves of electromagnetic field").

Metals have crystalic - periodic structure - transmit sound well and generally what You hear are resonances, while rubber is random structure of long organic chains - diffusing phonons ... there is also large difference in sound velocity and so resonant frequencies ...but generally it's not for this discussion and You should look at some solid matter book ...

 

About the 'squares' in probabilistic theories ...

If for given Markov process we would focus on infinite in one direction chains - probability distribution would be the eigenstate of the stochastic matrix (without the squares).

When we focus on a position inside chains infinite in both directions, we get the squares - intuitively: it's because there meet two random variables (chains) - from past and from future and while this gluing they have to give the same - the square is because of multiplying both probabilities.

 

Please look at my paper - there is expanded this argument that it's just a natural result of 4D nature of our world ... generally while trying to predict 'charged points' idealization using some measurements - in any scale: microscopic(QM) or macroscopic(deterministic) there should appear these squares ...

The simplest model - maximal entropy random walk on graph in opposite to standard random walk

http://demonstrations.wolfram.com/GenericRandomWalkAndMaximalEntropyRandomWalk/

has strong localization properties as quantum mechanics (Anderson localization)

[Duda Jarek]

While argumenting quantification of magnetic flux going through superconducting ring, we say that 'quantum phase' has to 'enclose itself' - make some integer number of 'rotations' along this ring.

But in such considerations (or e.g. Josephson junction) nobody rather thinks about this phase as really the quantum phase of these single electrons, but as ORDER PARAMETER - some local value of statistical physics model, describing relative 'quantum' phase - or more generally phase of some periodic motion (e.g. http://rmf.fciencias.unam.mx/pdf/rmf-s/53/7/53_7_053.pdf ).

 

So what about solutions of Schroedinger equation for hydrogen?

We know well that there are better approximation of physics, like Dirac equations ... which still ignores internal structure of particles ...

So doesn't it make Schroedinger's phase also only just an order parameter of some approximate statistical model?

... describing relative phase of internal periodic motion of electrons ("zitterbewegung") ...

 

What I'm trying to convince is that when we get below these statistical models - to 'the real quantum phase' (which for example describes the phase of particle's internal periodic motion) - we won't longer have to 'fuzzy' everything, but will be able to work on deterministic picture.

These statistical models works only on relative phase of some periodic motions - cannot rather distinguish absolute phase ... but generally we should be careful about implying this gauge invariance as fundamental assumption - that physics doesn't really cares about its local values.

 

I was recently told that prof. Gryzinski also didn't like the approach that physicists couldn't handle with some problems, so they have hidden everything behind mystical cape of quantum mechanics and said that it's the fundamental level.

He spent his life (died in 2004) explaining atomic physics, 'problems' which lead to the belief that QM is the lowest level using classical physics. There are many his papers in good journals.

Here can be found his lectures: http://www.cyf.gov.pl/gryzinski/ramkiang.html

 

Another argument are recently mapped electron densities on the surface of semiconductors:

http://physicsworld.com/cws/article/news/41659

So we have some potential wells and electrons jumping between them.

These wells create lattice with defects - we can approximately model it using graph on which these electrons make some 'walks'.

There are huge amount of small interactions there, so we should rather look for statistical model - some random walk on this graph.

Which random walk? Standard (maximizing entropy locally) gives just Brownian motion - without localization properties ...

From quantum mechanics we should also expect going to the quantum ground state of this lattice ... and random walk maximizing entropy globally also gives such quantum ground state probability density ... and similar 'fractal patterns' as on the pictures from experiment.

Edited March 6, 2010 by Duda Jarek