All of the matter in the universe -- everything we see, feel and smell -- has a certain predictable structure, thanks to the tiny electrons spinning around their atomic nuclei in a series of concentric shells or atomic levels. A fundamental tenet of this orderly structure is that no two electrons can occupy the same atomic level (quantum state) at the same time—a principle called the Pauli exclusion principle, which is based on Albert Einstein's theory of relativity and quantum theory.

However, a team of Syracuse University physicists recently developed a new theoretical model to explain how the Pauli exclusion principle can be violated and how, under certain rare conditions, more than one electron can simultaneously occupy the same quantum state.

Their model, published July 26 in *Physical Review Letters* (vol. 105) may help explain how matter behaves at the edges of black holes and contribute to the ongoing scientific quest for a unified theory of quantum gravity. Physical Review Letters is a publication of the prestigious American Physical Society.

"Transitions of electrons from one atomic shell to another that violate the Pauli principle challenge the foundations of physics," says A.P. Balachandran, the J.D. Steele Professor of Physics in SU's College of Arts and Sciences. "For this reason, there is strong experimental interest in looking for such transitions. Until now, there were few viable models able to explain how such transitions can occur. Our theory provides such a model."

Balachandran is the lead author on the paper with Ph.D. candidates Anosh Joseph and Pramod Padmanabhan.

The orderly way in which electrons fill up atomic levels provides stability and structure to matter, as well as dictates the chemical properties of elements on the Periodic Table. Underlying this stability is the ability to pinpoint the location of objects (electrons, protons and neutrons) almost exactly in space and time. The new model posits that at the level where quantum gravity is significant, this picture of space-time continuum breaks down, deeply affecting the rotational symmetry of the atoms and triggering electron transitions (movement from one shell to another) that violate the Pauli principle.

"The Pauli principle is not obeyed in the model we built," Balachandran says. "We then used existing experimental evidence to put limits on when these violations in transitions can occur."

According to the model, violations of the Pauli principle would theoretically occur in nature in a time span that is longer than the age of the universe—or less frequently than once in the proverbial "blue moon."

"Though this effect is small, scientists are using high-precision instruments to try to observe the effect," Balachandran says. "If found, it will profoundly affect the foundations of the current fundamental physical theories. "

"Additionally, chemistry and biology in a world where such violations occur will be dramatically different," adds co-author Padmanabhan.

The fact that the Pauli principle can be violated may also help explain how matter behaves at the edge of black holes, Joseph says: "While we don't know what happens to matter in a black hole, our model may give hints about how matter behaves as atoms collapse from the gravitational pull of black holes."

**Explore further:**
K-State Mathematician Receives Grant to Study Gravity, Black Holes, Possible Future Space Travel

**More information:**
prl.aps.org/abstract/PRL/v105/i5/e051601

## Skeptic_Heretic

The Exclusion pricinple wouldn't have been developed, at least not by Pauli, without the knowledge of relativity and the rise of particulate masses based upon energy content within relativity. They're related, but only in the most distant of manners.

The author isn't wrong, just inaccurate.

## Jarek

After that they became 'bosons' - like grouping - but also not in the idealized by QM way, but e.g. BEC is just a liquid of clearly nonzero volume...

And I also don't like mixing it with relativity ...

About the situation in the middle of black hole - besides that I don't think we have good enough basis for such considerations, many particle models like supersymmetry requires proton decay, which is also useful to explain nonzero baryonic number of our universe - it would be nature's failsafe to prevent infinite densities - this matter would be just transformed into energy earlier ...

## Jigga

You're right, but this is a part of mainstream propaganda - to induce and illusion in laymans, mainstream theories explain everything. Actually it's a completelly empirical stuff, which was originally ad-hoced as a way to explain the arrangement of electrons in an atom.

## yyz

Thanks for the link to the paper. I see that it is an elaboration of computations from their earlier paper, which fully describes their model: http://lanl.arxiv...003.2250

jarek,

I was thinking of the similar use of proton decay in theory too, especially wrt the timescales discussed(i.e. 'longer than the age of the universe').

## Jarek

I thought about it while considering new soliton particle model (ellipsoid field - between too simple optical vertices and too abstract skyrmions) - strong/weak interaction appears there on effective(structural) level (what asymptotic freedom suggests) and its baryons (and nucleuses) are hold together by topology - so extremely high temperatures could destroy them (4th section of http://arxiv.org/pdf/0910.2724 ).

Anyway, my point is that time could be not enough for proton decay - it assumes that another idealization: Boltzmann distribution, behaves well far far away - that huge energies (like TeV) could appear spontaneously with nonzero probability in water tank they are testing it...

Better place to search for proton decay should be rather extremely hot like neutron star centers or quasars ... maybe huge energy they would produce could explain beyond GZK cosmic rays? (photons from one decay could stimulate others to do the same resulting in chain reaction?)

## Skeptic_Heretic

In a BEC the wave forms become congruent so that individual particles are indistinguishable from one another. They do not become a single particle.

Learn your WPD.

## Jigga

"...Related experiments in cooling fermions rather than bosons to extremely low temperatures have created degenerate gases, where the atoms do not congregate in a single state due to the Pauli exclusion principle. To exhibit Bose-Einstein condensation, the fermions must pair up to form compound particles (e.g. molecules or Cooper pairs) that are bosons..."

http://en.wikiped...ndensate

You know - I don't believe you a single word without linked reference. Actually it's apparent, the authors of this study forget the existence of BEC in the same way, like you. They predicted the phenomena, which was observed already many times.

## Jigga

Aether theory predicts instead, some new matter will be formed from interstellar dark matter during this, so that the total amount of observable matter inside of our universe will remain the same in similar way, like the entropy. Compare the new steady-state models of Universe here:

http://www.physor...806.html

http://www.physor...631.html

## Jigga

http://www.pnas.o...545.full

Actually we can see, how one group of physicists promotes concept, which were developed somewhere else - just under different name. Because physicists actually do not understand or even know about their theories mutually.

## Ethelred

Then in a masterpiece of fraudulent self-aggrandizement you rate yourself, under another name, a five. While giving ones, by multiple false names, to anyone that has had enough of your nonsense.

And then have the temerity to call others trolls and censorious.

You started this war and if you want the ones to stop YOU will have to start behaving yourself by using ONE name.

BECs do not violate the Pauli Exclusion Principle since it applies to electrons WITHIN atoms. Singularities, assuming they can exist, do not violate the PEP either since there are NO electrons in a singularity. As written that is self-contradictory. Perhaps you intended to say something else but since you think a singularity qualifies as a BEC you might really think that way.

Ethelred

## MustaI

## Skeptic_Heretic

Then continue using the wikipedia articles that I probably contributed on as a resource. I'd recommend you read the rest of it.

## MustaI

## Skeptic_Heretic

http://www.jupite...ein.html

Of course with no understanding of QM and rough Newtonian understanding you won't get it.

## MustaI

## Skeptic_Heretic

Your stance is that the bosons become a single particle. The statement above does not evidence this effect. They "overlap" which requires uncertainty. Uncertainty means wave action, not particle action. Learn your WPD.

## Jarek

Please explain what's so quantum about BEC?

Mathematical essence of thermodynamics: Boltzmann distribution itself says that in low temperatures there are chosen the lowest energy states - for quantum orbitals but also the same for classical e.g Bohr-like models...

Because of 'quantum bosons'?

It works for photons - somehow EM wave makes that excited states of the same energy difference deexcitate easier - kind of EM resonance (where is QM here?)

But BEC behaves differently - these atoms are spatially distributed creating liquid - loosely connected by EM interaction. And because of low thermal noise, it's (electrons) internal dynamics is so ordered that there is no transverse momentum transfer...

But where exactly do you need QM here?

People often use 'it's quantum' as cool and universal explanation of internal dynamics of processes they don't bother to try to really understand...

## Skeptic_Heretic

http://www.fortun...ose.html

That should clarify this for you.

## Jarek

Thanks anyway

## Skeptic_Heretic

What part of Did you not understand? Classical mechanics cannot speak to the stripping of information that occurs at extreme energy contents.

## MustaI

Why not? BTW Where you got "extreme energy contents" from at the case of boson condensate?

## Jarek

That their dynamics is 'quantum-connected'?

For example some electron on Earth from some electron on Sun?

About choosing the lowest possible state - but we have it also in classical thermodynamics ...

Imagine abstract world without QM: atoms are made as Bohr-like models - thermodynamics says that in low temperature they would be in the energetically lowest states/orbits/trajectories, doesn't it?

## Skeptic_Heretic

Bohr's model is flawed, this is evidenced by observation and the lack of sync radiation produced by "orbiting" electrons. Your statement on electrons is faulty. Electrons are not bosons and are subject to Pauli's Exclusion.

You should already know. The extremes of energy content. Extremely high and extremely low. This is extremely low.

## Jarek

I haven't looked at it closer yet, but electron's magnetic moment makes that fast electrons are repelled near proton by Lorentz force - it allows for different falling-ascending like periodic trajectories. Models of this professor were published in best journals a few decades ago as better corresponding to experiment, here are his lectures:

http://www.cyf.go...ang.html

I don't understand how your comment about electrons not being bosons is connected to my question if electrons being in different places are distinguishable by physics?

BEC has nonzero volume and so many 'electrons in different places' - I would think that physics distinguish between e.g. electric fields created by them?

Until you are completely sure that you really understand whole QM, please try to use classical picture as long as you can ..

## Skeptic_Heretic

## MustaI

http://www.physor...511.html

http://prl.aps.or.../e240401

If we can explain the iconic experiments of QM, like the quantum tunneling and/or double slit experiment by water surface model, why not the rest of whole QM?

Of course, physicists aren't interested very much in popularization of these experiments and models from the same reason, like shamans of ancient era - it would make their jobs transparent for layman public.

## Jarek

I agree - and because there should be a difference between science and religion, I believe it should bother scientists...

For example that they at least should take intuitive noncontroversial classical picture as far as it is possible ... while it is practically silenced that there are better models than Bohr's - look and check the list of publications below http://www.ipj.go...tom.html

And what thermodynamics generally says about particle behavior?

That when we don't know which trajectory particle has chosen, we should assume Boltzmann distribution among these scenarios, untrue?

Please do the math yourself (or look to 2nd section of http://arxiv.org/pdf/0710.3861 ) - it doesn't lead to Brownian motion as is generally believed, but gives going to square of coordinates of dominant eigenfunction of Hamiltonian - 'quantum' decoherence.

Where exactly is the classical-quantum boundary?

## Skeptic_Heretic

Classical physics explains reality jsut as well as the naked eye discovers astronomy. You can see many stars, you can see they move, you can differentiate planets from stars by motion, etc.

If you want to learn about other galaxies you need a better tool. QM is that tool for physical interaction. QM doesn't stop being relevant. There's no boundary condition under which Classical works and quantum doesn't. Quantum replaces Classical just as the telescope replaces the naked eye. We can do everything that classical physics does with quantum mechanics and more.

## MustaI

In dense aether theory only boundary between relativity and quantum mechanics can be defined and it's observer size/mass energy density dependent. Classical model is universally valid here.

## Skeptic_Heretic

## MustaI

## MustaI

You cannot make QM more exact, because it doesn't support gravity and it predicts, all particles of observable matter will spread into infinity. It will always remain biased in such a way.

But you can make classical physics models more exact just by increasing of number of particles involved. Classical mechanics is extendable ad-infinitum.

## Skeptic_Heretic

Classical physics states the exact same thing. I'm not sure where you're headed with this line of reasoning. As for gravity, quantum mechanics is not complete, we all know this. Classical mechanics cannot describe gravity either so you're incorrect in your statement.

## Jarek

I agree - they are just different points of view - classical mechanics usually works on corpuscular picture, while QM usually operates on waves - like momentum picture after Fourier transform - eigenfunctions of linearized evolution operator given by Euler-Lagrange equations - because in fields governed by Lagrangian mechanics basic excitations are waves: on water, EM, gravitational ... or more generally: periodic behavior, like precessive motion of electron in EM field ...

We can for example look at BEC through normal modes of this 'generalizes pendulum' ... but also simultaneously through concrete movement of EM interacting particles creating it.

## Skeptic_Heretic

## MustaI

http://en.wikiped...vitation

Le-Sage gravity is a special example of the recent Erik Verlinde's entropic model of gravity (surface tension pseudoforce inside of black hole). Entropy is classical physics model too, being based on Boltzmann gas concept.

## MustaI

The causal superiority of classical physics over QM (and GR) is quite apparent here.

## Jarek

But similar situation we have in a gas tank - so there thermodynamics come - mathematical theorems like maximum uncertainty principle says that in such situations we should assume some (canonical) statistical ensemble among all possible scenarios - it leads to that we should assume some fluctuations around quantum ground state (Maximal Entropy Random Walk and extensions).

And quantum mechanics works well (unitary) until decoherence - now simplifications of this picture comes out and it only can predict probability distribution among outcoming situations.

Like that thermodynamical model can say only probability distribution among the number of particles escaped while specific valve opening of the gas tank.

## Skeptic_Heretic

With QM you can model each and every known interactions and derive a more accurate picture than classical computation will allow for. The reason why we still use classical mechanics is because, going back to the astronomy example, it's good enough for our purposes to see the moon with the naked eye to determine that it is there. Decoherence is simply when we reach a state under which we do not know what is governing the actions. This is the incompleteness of QM.

As for the Lesage gravitational mechanic, Alizee, it has been conclusively discredited.

## Jarek

I agree, but both pictures have own advantages so we should work on both of them, because there is a chance that they are just equivalent ... and classical one is intuitive and understandable, what is very important for scientific models.

peace

## Skeptic_Heretic

I greatly doubt this is the case. Thanks for the chat.

Alizee, take notes, this is how two people, with opposing views debate a topic.

## MustaI

Can you provide some evidence against Le-Sage model - or do you just feel, you would have no chance in such discussion?

It isn't, as QM predicts different results, then the Newtonian physics and observation - in QM all objects (free particle wave packet) expand into infinity - in classical mechanics they're remaining unchanged.

## Jarek

Fortunately some scientists don't give up so easily and use the scientific way: go back to what we can be really sure and try to consequently expand it ... instead lack of safe basis allowed modern physicists for limitless creative expression and so the right has who shouts louder :/

Thanks for the chat

## MustaI

Aug 05, 2010## Skeptic_Heretic

## Jigga

## Skeptic_Heretic

So be it, I won't cry about it if you don't.

## Jigga

I've no problem with my easy identification of course, as it partially removes the effect of the lost of identity after account ban. If everyone will downvote others here, it will just lead readers to disable voting filter completely - which will improve the readability of thread significantly - and everyone will remain happy.

## Skeptic_Heretic

## Jarek

It made me think that it's a shame that such natural atomic model, which in dozens of peer-review papers (see citation numbers) was shown to correspond well to experiment (at least much better than Bohr model) ... is just unknown ...

Please help expand this mini-stub: there are especially some really concrete comments needed...

http://en.wikiped....224.239

## MustaI

http://xenophiliu...hr-atom/

But electron is making vacuum foam more dense around itself during motion too (in similar way, like the swimming duck is expanding water surface with its undulations) - which is the effect, which Bohr's model doesn't describe well (if at all) at the case of more complex atoms and which makes path of electrons more complex at the proximity of atom nuclei.

## Jarek

For large radius these Bohr orbits are fine, but closer Lorentz force becomes essential - it pull or push electron radially, making such orbits unstable.

For small atomic numbers more physically looks these almost radial falling-ascending type trajectories.

## MustaI

http://superstrun...anim.gif

## Jarek

These practically unknown (but which passed many peer-reviews) models have different behavior - almost completely radial free-falling, which is bent in the last moment by Lorentz force - there are nice animations in his lectures:

http://www.cyf.go...ang.html

## Skeptic_Heretic

I disagree with the free fall model. I don't think we can state empirically that electrons exist as a particle in the orbitals of atoms.

The atomic model I'm most familiar with is the wave shell model.

Effectively each valence level is simply made more "solid" by the presence of greater quantities of electrons. Tough to explain when character limited.

## Jarek

I'm just saying that physicists should be aware that the history of classical models doesn't end on Bohr and Sommerfeld.

## Skeptic_Heretic

## MustaI

http://snelsonatom.com/?p=6

In Snelson's atom model the electrons are moving only tangentially(?) around atoms along so-called "cyclospheres". Such "crazy" model is still able to predict correct sequences of quantum numbers reliably. It's evident, both later models are related mutually via T-duality.

Of course, classical Schrodinger's model of atom is still the most universal one, as it can predict the behavior of particles in more asymmetric complex arrangement (double slit, for example). It still suffers with instability for free moving particle, though, as it predicts its evaporation into infinity. It works well only in space-time curved by presence of Coulomb fields - whereas the previous models suffer with radiation of electron along "curved path", instead.

## MustaI

Dense aether theory is somewhere in the middle of the discrete and fuzzy model of electron, as it predicts, every moving particle is surrounded with less or more dense "cloud" of vacuum represented by de Broglie wave, which gets more compact and dense with increased speed of particle.

When the energy density exceeds certain limit, the particle will literally dissolve in its own deBroglie wave into boson - but such energy density is close to energy density inside of atom nuclei. So we can estimate rather safely, inside of atom orbitals electrons are moving both like waves, both like particles.

The ionization energy of electrons increases with number of protons inside of atom nuclei, so that the electrons inside of low quantum numbers orbitals of large atoms are delocalized heavily.

## Skeptic_Heretic

## Jarek

http://www.mizozo...tom.html

About synch radiation - this argument is a complete nonsense!

It appears in synchrotron because of momentum conservation - to compensate electron's acceleration ... but the center of mass of atom doesn't have to move - 'electron and proton exchange virtual photons'.

And again - where energy of these photons would come from?

I understand falling on positron (about 142ns) ... but on proton? to create neutron? :)

Periodic trajectories are themselves because of being in some energetic optimum - cannot decrease it just like that to produce photon.

## Jigga

## Jarek

I agree - in classical picture point-like electron starts moving on some trajectory around, stabilizing thermodynamically own statistics (using some complicated deterministic motion) to expected probability density (maximizing entropy) and finally is tear off by potential - natural thermodynamical model: Boltzmann distribution among possible trajectories says that this stabilized probability density (time average) is exactly the same as for the lowest quantum state.

## Skeptic_Heretic

Is this another of your aliases Jigga?

## Jarek

I understand - 'it's quantum' - everything is explained, end of discussion ... and it doesn't bother you that wavefunction - 'smeared electron' just gathered into a corpuscle in one moment because ... there is duality? - we can have only one physics in one moment: quantum or classical? ... (what about Afshar experiment? http://en.wikiped...periment )

... but classical is a result of quantum (like Ehrenfest theorem)...

But you are completely sure it doesn't work in the opposite way: that they are not just equivalent - that common classical picture couldn't get neat inconceivable quantum ... ?

Please explain why??

## Jarek

ALL WAVES ARE OSCILLATIONS, BUT NOT ALL OSCILLATIONS ARE WAVES!

Modes of conjugated pendulum, quantum orbitals - are periodic motions, oscillations - but not plane waves!

'Waves' in the duality denotes not plane wave, but 'rotation of quantum phase' - something much more general: oscillation.

Now look at electron - it behaves similarly to a gyroscope - there is precessive motion involved (called zitterbewegung in QM) - after each period it returns to given state.

So such 'classical' electron is both corpuscle and has 'internal periodic motion' - oscillation - is 'wave'.

In some situations it's essential for it to just be somewhere and in another it has to 'fit well with own phase' to the situation - duality.

So this poor little particle doesn't have to constantly worry to which kingdom he has to magically jump now, but is in both simultaneously.

## Jigga

## Jigga

Aug 08, 2010## james11

## MustaI

## Skeptic_Heretic

So technically we agree and we're looking at it from irreconcilable opposite sides of the same problem.

## Jarek

Look at conjugate pendulums - we can see it through positions (classically), or as 'superposition of rotations of normal modes phases' (quantum).

Now create a lattice of such pendulums (crystal with phonons), make infinitesimal limit - and you get some classical field theory (like water surface, EM, Klein-Gordon) - we can look at it through some concrete field valuations (classically), but also in eigenbase of differential Euler-Lagrange evolution operator - getting 'superposition of rotations' - unitary evolution.

For linear operator this eigenbase are plane waves, but we know that physics isn't linear - and so some nonlinearities allows for solitons - localized defects:

http://en.wikiped...l_defect

They are both corpuscular and often have some 'internal phase rotation' - wave nature, which allows for interference stuff.

And their thermodynamics leads to decoherence also classically.

## Skeptic_Heretic

## Jarek

Their picture is clear and completely deterministic: we live in space-time, move with 4D entropy gradient(time arrow), created for example by relatively low entropy of big bang - in static action optimizing four-dimensional solution - which each point is in equilibrium with its 4D neighborhood: space-time is kind of 4D jello - what e.g. :

- is literally seen in Wheeler's delayed choice experiment,

- makes that to choose given event, it had to be chosen on ends of both past and future halves of spacetime (tension in jello works in all directions) - their correlations are related by squares against Bell's intuition,

- allows for quantum computers ( http://www.thesci...936t.php ),

- diagonalized linearized evolution operator is 'superposition of rotations',

...

Dear Skeptic, what better alternative for Lagrangian mechanics do you have?

## Skeptic_Heretic

Overall, the two fields have some fundamental discrepancies especially when addressing the very small where Qm wins out for accuracy, and on the very large, where classical mechanics appear more descriptive.

The two are largely describing the same aspects of reality and missing the corrolary pieces that unite the two halves of the whole.

Currently, nothing as accurate or complete in overall understanding. I think you have me painted as an opponent of classical mechanics, that'd be an incorrect assumption.

## Jarek

I just give up. I'm only a simple (widely educated, but) mathematician ... talking with modern physicist is kind of talking with creationists - they can nod for a single arguments, but while trying to join them into a coherent picture ... logic, reasoning, arguments ... they just no longer applies ??? ...

Guessed by Schroedinger formula was inconceivable and so it had to become a dogma, started an age in which intuition, logic no longer applies and so you can trust only authorities and their new exciting ideas ...

You can return to your infinitely quickly branching parallel alternative entropic realities in fractal number of curved dimensions ...

Cheers

## Jarek

Mathematics is about finding as SIMPLE as possible, really COHERENT deep UNDERSTANDABLE picture of what is actually going on ... while modern physicist doesn't even look at theories without a scent of mysticism ...

Like that using just Coulomb and Lorentz force we can get really good agreement with experiments on atoms, even after being verified and approved by many reviewers of world class journals ... is just called controversial and ignored http://en.wikiped...ic_model

Or that while doing thermodynamics right: assume Boltzmann distribution among trajectories (similar to Feynman path integrals) - we don't get Brownian motion, but exactly 'quantum' decoherence ... who cares?

Dear physicists,

Please gain really DEEP UNDERSTANDING of LAGRANGIAN MECHANICS, their CONSEQUENCES, THERMODYNAMICS ... before going to new exciting theories.

## Skeptic_Heretic

I applaud you for being a rather skilled mathematician and having the introductory mathematical disciplines in order to have a rather deep understanding of a complex but small field of physics.

## Jarek

I had dozens of QM lectures on theoretical physics studies, read more books about it ... but as a mathematician I could find satisfaction with finally some coherent its picture ... after throwing away most of its mysticism hidden behind complicated formulas ...

Look precisely what using field theories governed by Lagrangian really means ... and QM emerges itself - clear, simple mathematical picture ... unfortunately it would hurt feeling of quantum worshipers and so is called controversial ...

nice 'discussing' with you, bye

## Skeptic_Heretic

At what point in time did I call it controversial, or state that your linking lagrangian mechanics to QM was in error? QM came from Lagrangian formulae and then went further into the elementary particle boundaries and internal structures that lagrangina mechanics cannot speak to, nor can thermodynamics give an accurate picture.

If you really want to get into a complex discussion of the likeness of primordial atoms to singularities and the regression problem within QM as compared to the regression problem within Classical, I'd be happy to do it somewhere that doesn't have a 1000 character limit and can handle plus signs.

## Jarek

I'm saying that QM emerges naturally in Lagrangian mechanics - we don't have to assume any additional inconceivable dogmas - just pure clear math and natural picture it presents - linearized evolution differential operator in its eigenbase makes literally 'superposition of rotations' - unitary evolution - we get interference also on 'classical' water surface.

When we don't know where particle go, we should assume Boltzmann distribution among possible scenarios (trajectories), what leads literally to 'quantum' decoherence also classically (in 'pure QM' it had to be additionally assumed).

I'm asking why do you believe that these pictures - classical and quantum cannot be just equivalent - that there are just needed some additional inconceivable quantum dogmas ...

To be able to respond, I need to finally see at least one concrete argument ...

## Skeptic_Heretic

Where they fall apart is further down the chain. Go ahead and produce a solution to the microscopic many body problem. Oh that's right, you can't. You need to use pure QM to do so as the Faddeev and Faddeev-Yakubovsky equations will not solve out. Where QM shines and classical fails, where they are irreconcilable, is illustrated when dealing with a boundless interaction problem, such as "entanglement".

## Jarek

As many reviewers verified and approved - Gryziński's model successfully produces solutions to concrete 'microscopic many body problems'... ?

When we cannot trace them, natural thermodynamics leads to 'wavefunction collapse' ... ?

Could you e.g. give some paper explaining this argument?

Hamiltonian is energy density in field theories - with kinetic part like

sum_{i=0..3}(d_i f)^2

the interesting about this really fundamental property is that it completely doesn't emphasize any (time) direction in spacetime - it has full 4D symmetry ('4D jello').

We break it while choosing direction we want to consider evolution along - making mathematical transformation 'Wick rotation' of this selected time direction to get Lagrangian density - less fundamental than energy density.

So in Lorentz invariant theories, spacetime is just completely symmetric R^4 - pure and simple deterministic picture.

## Jarek

Living in a field theory solution goes with qualitatively different picture - 'static 4D' - '4D jello' in which there is minimalized tension towards all directions, also to past and future (kinetic terms) - it leads to qualitatively different probabilistic theories (with squares against Bell).

To feel this difference, make simple combinatorics exercise: derive formulas for Maximal Entropy Random Walk - just uniform distribution among paths on graph - see where the 'squares' of coordinates of dominant eigenvector of 'discrete Hamiltonian' (minus adjacency matrix) as stationary probability density appears here from ...

## Skeptic_Heretic

The Microscopic Many Body problem is effectually continual interaction with a time basis set in a single direction. As you state, when bound it can be solved by classical mechanics, however, reality is unbound which is why you need non-directional QM, based on the tenets of Hamiltonian non-specific time equations.

## Jarek

In linear field theories situation is simple: eigenbase of evolution operator are just plane(/circular...) waves, like on water surface.

But in nonlinear physics, eigenfunctions which 'superposition of rotations' evolution is - are much more complicated and constructing them from plane waves in perturbative picture doesn't really present the situation well - like when eigenfunctions are localized solitons.

It becomes subtly hidden, but the evolution is still superposition(entanglement) of rotations - with qualitatively much more complicated full interference capability (just QM)

Ok, taking entanglement to the limits is used in quantum computers.

In '4D jello' picture, QM allows us to simultaneously 'mount trajectories' of particles in both past (initialization) and future (measurement):

http://www.thesci...936t.php

Is something wrong with such understanding?

## Skeptic_Heretic

## Jarek

For both quantum mechanics and field theories (linearized), the basic evolution is unitary, untrue?

But QM has additionally decoherence ... which in modern view is believed not to be out of unitary picture, but thermodynamical consequence of interaction with environment, untrue?

Classical thermodynamics: that when we cannot trace particle, we should assume Boltzmann distribution among possible trajectories, leads to going to the lowest Hamiltonian eigenfunction (with nonzero projection), untrue?

It explains decoherence and for example makes that stable orbits while stochastic perturbation shifts toward the nearest quantum state...

Talking to a wall... bye