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Duda Jarek

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  1. You are focusing on internal atomic physics of these atoms, but please also take a look at the classical picture e.g. in calculation of this article.

    Imagine you have a nanonmagnet built of a thousand of atoms - I think you agree we can treat it as a classical magnet, so this classical calculation should be valid (?)

    EM radiated energy during such classical alignment might not necessarily be localized like photons (?) - rather as EM radiation of cylindrically symmetric antenna, suggesting such EM wave might be e.g. cylindrically symmetric ... I don't know if atomic physics describes well antennas?

    Now reduce the number of atoms one by one to a single atom ...

  2. Ok, maybe I should use e.g. "excessive" word instead - generally a system having excessive energy (larger than minimal), has tendency to release this energy.

    E.g. excited atom has tendency to release excessive energy as EM radiation (photon carrying the difference of energy, momentum, angular momentum) - deexciting to energy minimum of the ground state.

    I see unaligned "classical" magnetic dipole in external magnetic field analogously - this field causes precession, which means excessive kinetic energy - which can be released through EM radiation, leading to aligned magnetic dipole without this excessive energy.

    If you want more formal classical calculation, there is a deep analysis in the linked article.


    Sure this is different description than quantum, the big question is where is the boundary?

    Why cannot they be just different perspectives on the same systems? Like phonons which are both normal modes, and effects of creation operator in perturbative QFT ...


  3. 4 minutes ago, exchemist said:

    The passage you quoted is not a classical treatment, but a QM treatment. That's what the wave function integral is about.

    There is no way for a classical treatment to give you a series of beams, corresponding to discrete orientations. You would get a continuum, since all possible orientations are allowed - or just one spot if the particles had time to orient themselves with the field before exiting it.  

    The article ( https://www.preprints.org/manuscript/202210.0478/v1 ) uses classical electromagnetism - just a magnet in external magnetic field: should not only precess, but also finally align in parallel or anti-parallel way, what can be imagined e.g. as EM radiation of abundant (kinetic) energy, or direct calculation in this article.

    Please point mistake, problem in this derivation ... or if you cannot, the size boundary where it no longer works?

    As classical it should work for large magnets - made from how many of atoms? A million? A thousand? ... a single atom? electron?

    Experimentally it agrees also with the last two ... so where do you see the classical-quantum boundary here?

  4. I was pointed recent very nice article "Phenomenological theory of the Stern-Gerlach experimen" by Sergey A. Rashkovskiy with very detailed calculation of the alignment time getting ~10^-10s for Stern-Gerlach with atoms: https://www.preprints.org/manuscript/202210.0478/v1

    Instead of radiation, he directly uses formula for magnetic dipole in external magnetic field:


    My very approximated evaluation from radiation of abundant energy suggested a few orders of magnitude fasted alignment - bringing very interesting question if they are equivalent, how does energy balance looks above (?)

    Anyway, this is another confirmation that classical magnetic dipoles in external magnetic field have tendency to align in parallel or anti-parallel way.
    This "classical measurement" is deterministic and time-reversible: if recreating reversed EM, in theory one could reverse the process ...

    What is nonintuive here is that such EM radiation carrying energy difference here seems different than in "optical photon", might be delocalized (?).

    The big question is the minimal size to be able to apply this "classical measurement" - minimal size of such magnet: a million atoms? Thousand atoms? Single atoms? Electron?
    Experimentally in Stern-Gerlach they observe the same conclusion, such alignment is also well known for electrons (e.g. https://en.wikipedia.org/wiki/Sokolov%E2%80%93Ternov_effect ), for which they observe both Larmor precession, but also much more complex acrobatics in EM field: spin echo ( https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#Pulsed_electron_paramagnetic_resonance )

    So where is the classical-quantum boundary here?

  5. 13 minutes ago, exchemist said:

    Atoms "radiate abundant energy" is irrelevant, as well as being untrue. Atoms in the ground state do not and cannot radiate energy.

    Excited atoms have tendency to deexcite - releasing abundant energy as EM wave (photon), through dynamics of electrons in e.g. electric potential of the nucleus.

    The ground state e.g. of hydrogen is just the lowest energy state for proton+electron. In theory they could be taken closer down to zero distance (->neutron), but it would require investing ~782keV energy. This kind of orbit quantization is also observed in hydrodynamical QM analogs, e.g. double quantization: https://www.nature.com/articles/ncomms4219 - of distance R and angular momentum Lz:


    The discussion indeed starts going in circles, and I don't think I understand the problem.
    So do you agree classical magnet would precess in external magnetic field?
    That rotating, oscillating dipole radiates energy as EM wave like antenna?
    That radiating all the energy such classical magnet would align in parallel or anti-parallel way?
    That this is the same conclusion as observed in Stern-Gerlach?
    Do you have an alternative explanation of such alignment in Stern-Gerlach?

    Alignment known also e.g. in NMR: https://www.cis.rit.edu/htbooks/nmr/chap-3/chap-3.htm


    When a group of spins is placed in a magnetic field, each spin aligns in one of the two possible orientations


  6. 5 hours ago, exchemist said:

    No, that is wrong for this situation, because it is a bound system and therefore quantised. I pointed out to you earlier that electrons in atoms do not radiate and fall into the nucleus.

    But excited atoms radiate abundant energy - getting to the lowest energy: ground state?

    So why shouldn't unaligned spin radiate abundant kinetic energy - getting to the lowest energy: aligned spin? ... especially that this is exactly what they observe in Stern-Gerlach ... and EM says that oscillating dipoles should radiate energy.

    5 hours ago, exchemist said:

    Forget brehmsstralung. It's irrelevant. That is for free, i.e. unbound, particles.

    Indeed, and in Stern-Gerlach we have free unbounded objects - having magnetic dipole, in external magnetic field - as also e.g. electrons in synchrotron radiating energy as EM waves.

    4 hours ago, swansont said:

    Yes, this is what I asked you about. How did you arrive at this conclusion? I want your reasoning, not just a repetition of the statement.

    Magnetic dipole in external magnetic field gets torque - Larmor precession ... rotating dipole creates varying EM fields - like antenna radiating energy as EM waves, of power given by the used formula.

    4 hours ago, swansont said:

    But other effects are not classical (the deviation of the beam), so why should the alignment be classical? The discrete deviation is an indication that you do not have randomly-aligned spins that come into alignment over some period of time.

    Larmor precession comes from torque - works in all scales: from electron to macroscopic magnets.

    For non-polarized beam, the original direction of magnetic dipole is random, the final in Stern-Gerlach is aligned in parallel or anti-parallel way - exactly as we would expect for a classical magnet in external magnetic field.

  7. 3 hours ago, swansont said:

    You didn’t answer my questions, which don’t pertain to your calculation.

    There is this formula for power of rotating electric dipole: http://www.phys.boun.edu.tr/~sevgena/p202/docs/Electric dipole radiation.pdf


    Inserting k = 10^6 Hz and p ~ 10^-23, you get power ~10^-4 W ... proper calculations would require someone experienced with antennas, but generally we are talking about  ~femtosecond scales.

    2 hours ago, exchemist said:

    Why can't it just divert a proportion of the existing angular momentum - and kinetic energy - to the precession axis?

    My understanding is that is what happens in a lossless precessing gyroscope. (Though maybe a proper physicist can comment on whether that is the case.)

    We are talking about rotating dipole and acceleration of charges/dipoles generally leads to radiation of energy as EM waves, e.g. in bremsstrahlung.

    The above formula is for oscillating dipole, getting the details is difficult I will think about, but generally these are ~femtosecond scales.

    ... and this radiation says that magnetic dipoles should align in magnetic filed - what is exactly what they observe e.g. in Stern-Gerlach.

  8. 11 minutes ago, exchemist said:

    OK, why do you think precession means additional kinetic energy, rather than just partitioning the existing kinetic energy between motion about two axes? What work is done? Take me through the logic. 

    Imagine you have some object e.g. atom, and put it into precessing coordinates - it would introduce additional time derivative terms (kinetic), until stopping this precession.

  9. 6 minutes ago, joigus said:

    It only does that if you assume quantum mechanics is valid for the charged particles and classical field theory is valid for the EM field. If you combine quantum and classical attributes, it's possible to obtain relatively satisfactory models for some quantum behaviours. You have to put in QM by hand at some point.

    I have described classical radiation explanation leading to the same conclusion as Stern-Gerlach: of finally aligned spins.

    3 minutes ago, swansont said:

    Why femtoseconds? 

    If there was radiation why wouldn’t it be at the precession frequency?

    I have used the formula for EM radiation energy of antenna as oscillating dipole in the first post here.

    This is a complicated problem - it would be great if somebody experienced in antennas could make a better calculation.

    5 minutes ago, exchemist said:

    Ah but what kinetic energy of precession is this? On reflection I don't think there is any. I think the phenomenon of precession merely re-allocates the angular momentum into motion about 2 axes, doesn't it? 

    If it would be a macroscopic magnet, torque should lead to precession. Exactly the same argument is used for electron in https://en.wikipedia.org/wiki/Larmor_precession

    So why there shouldn't be precession in intermediate scale: of atom?

    And precession means additional kinetic energy - contributions with time derivative, which can be minimalized by just aligning spin - what they experimentally observe e.g. in Stern-Gerlach.

  10. 4 minutes ago, exchemist said:

    I don't think there is any need to presume they have to radiate. 

    Such need is suggested by conservation laws - especially of energy and angular momentum.

    Magnetic dipole of random direction in external magnetic field has abundant energy (kinetic of precession) - in Stern-Gerlach somehow lost by aligning, so what happens with this energy difference? Could turn into heat, through EM interactions.

    Also angular momentum is different for a random initial spin and aligned final spin - what has happened with this difference?


    linearly polarising magnetic potential as well

    There are two effects here - "V cdot mu" energy as in Zeeman effect, and kinetic energy from precession of unaligned spin.

    In Stern-Gerlach the latter seems to dominate, but there should be also statistical difference of population of two beams (?) - although, it might be extremely tiny.

    5 minutes ago, joigus said:

    The whole point of the Stern-Gerlach experiment is to disprove the classical theory of radiation.

    The problem is that classical theory of radiation predicts exactly the same outcome - magnetic dipole in external magnetic field gets torque, additional kinetic energy of precession - as oscillating dipole should should EM radiate energy, until reaching minimum: when it is aligned ... exactly as seen in Stern-Gerlach.

    So what is the difference between such classical behavior of magnet in magnetic field, and what they observe in Stern-Gerlach?

  11. Textbook explanation of this kind of quantum effects is usually "unitary evolution ... magic happens ... unitary evolution" ... I would gladly see a better one, getting inside this magic, and experimentally it slowly becomes accessible - e.g. they measured ~20 attosecond delay of photoemission: https://www.science.org/doi/10.1126/science.1189401 ... what is happening during such 20as?

    If atom has magnetic dipole moment e.g. due to angular momentum, then in external magnetic field it gets torque, hence its axis should precess - what means additional kinetic energy. There is tendency to release abundant energy, and mechanism for oscillating dipole - due to acceleration of charge/dipole, as e.g. for electron in bremsstrahlung.

    However, there appears question, issue of quantization of such released EM energy - I completely agree it can directly manifest as heat ... but what if they are single atoms in vacuum?


    Non-radiative relaxation will manifest itself as heat in the material.

    The belief that everything EM related is through quantized photons probably comes from pertubative approximation of QFT e.g. seeing Coulomb interaction through photon exchange ... but this is our approximation - fundamental question should be for non-perturbative.

    A common alternative is quantization through emitter/absorber - usually being atoms of quantized energy states. E.g. cosmic microwave background radiation seems just a thermal noise of EM degrees of freedom - quantized when absorbing its energy by atoms.

    The problem starts with antennas e.g. linear - producing cylindrically-symmetric EM waves. Assuming such wave consists of a finite number of photons, going with distance to infinity such discrete photons would become infinitely diluted, large ...

  12. Conservation laws e.g. Noether theorem say that change of energy, momentum, angular momentum - has to be compensated with opposite change e.g. in EM field, for example:

    excited atom <-> deexcited atom + EM wave carrying difference of energy, momentum and angular momentum

    From the other side, accelerating charges/dipoles leads to radiation of some energy as EM waves ... and e.g. spin echo in pulsed EPR shows everything works down to electron scale.

    I think you agree that classical magnet in magnetic field should EM radiate energy and finally align (to zero torque μ×B=0) ... they also see it for atoms in Stern-Gerlach ... if you claim these are different mechanisms, please elaborate on the mechanism seen in Stern-Gerlach?

    Cannot we see it as

    unaligned "random" spin <-> aligned spin + EM wave carrying difference of energy, momentum and angular momentum?

  13. Precession is not just "a classical concept" - it applies also to electron, even for much more complex acrobatics in spin echo: https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#Pulsed_electron_paramagnetic_resonance



    I think you agree that macroscopic magnet in external magnetic field would get torque, precession ... undergo "classical EM radiation" down to minimal energy μ×B=0 ... as also observed in Sterin-Gerlach.

    So how small could such magnet be? What happens when this magnet becomes extremely tiny: of size of atom ... electron?

  14. For atom the dominating magnetic dipole moment can come e.g. from angular orbital momentum - in which case shouldn't Larmor precession be of angular momentum direction?

    For any (also macroscopic) magnet in external magnetic field there is τ=μ×B torque leading to precession, what means oscillating dipole - type of antenna, radiating energy with power as the above formula ... until reaching the lowest energy state: μ×B=0 having minimal kinetic terms.

  15. Stern-Gerlach experiment is often seen as idealization of measurement. Using strong magnetic field, it makes magnetic dipoles (of e.g. atoms) align in parallel or anti-parallel way. Additionally, gradient of magnetic field bends trajectories depending on this choice.

    Magnetic dipoles in magnetic field undergo e.g. Larmor precession due to τ=μ×B torque, unless μ×B=0 what means parallel or anti-parallel alignment.

    Precession means magnetic dipole becomes kind of antenna, should radiate this additional kinetic energy. Thanks to duality between electric and magnetic field, we can use formula for precessing electric dipole, e.g. from this article:


    Using which I get power like 10^−3 W, suggesting radiation of atomic scale energies (∼10^−18 J) in e.g. femtoseconds (to μ×B=0 parallel or anti-parallel).

    So can we see spin alignment in Stern-Gerlach as a result of EM radiation of precessing magnetic dipole?

    Beside photons, can we interpret other spin measurement experiments this way?

  16. Just prepared: https://arxiv.org/pdf/2112.12557

    While textbook explanation of p-n junction ( https://en.wikipedia.org/wiki/P–n_junction ) looks quite heuristic, this is just using statistical mechanics - no "holes", only electron dynamics.

    Lattice 60x30 atoms below, dopants of different potentials are presented as red/green dots, grayness shows calculated electron densities, arrows show local currents.
    The model is:
    - use 3 types of potentials: of individual atoms + from external voltage + mean-field self interaction (from found charge density),
    - apply entropy maximizing diffusion ( https://en.wikipedia.org/wiki/Maximal_entropy_random_walk ),
    getting e.g. below diagrams.

    Are there there others atomic-scale conductance models?
    What applications could they have, e.g. some technology optimization?

    ps. simpler simulator: https://demonstrations.wolfram.com/ElectronConductanceModelsUsingMaximalEntropyRandomWalks/

    reddit discussion: https://www.reddit.com/r/electronics/comments/rmxjd4/inexpensive_atomicscale_conductance_model/


  17. Some updates - interactive demonstration to play with such topological charges of liquid crystal biaxial nematic - of 3 types resembling 3 leptons, requiring magnetic dipoles, with analogy of quantum phase evolution: https://demonstrations.wolfram.com/TopologicalChargesInBiaxialNematicLiquidCrystal/

    Derivation of Klein-Gordon-like equation for this evolving phase (slide 15 of https://www.dropbox.com/s/9dl2g9lypzqu5hp/liquid crystal particles.pdf )


  18. Paper: https://arxiv.org/pdf/2108.07896

    Slides: https://www.dropbox.com/s/9dl2g9lypzqu5hp/liquid crystal particles.pdf

    Hypothesized further particles, e.g. proton lighter than neutron - because baryons structurally require charge here, neutron has to compensate it what costs energy ... in deuteron two baryons hare single charge - getting electric quadrupole moment and aligned spins as in physics:




  19. I have finally worked out mathematical framework up to Euler-Lagrange for this ellipsoid field/liquid crystal like approach:

    - field of 3 distinguishable axes using 3x3 matrices preferring fixed set of eigenvalues,

    - hedgehog of one of 3 axes for 3 leptons - charges governed by Maxwell equations, with magnetic dipole moment due to hairy ball theorem,

    - then expanding to 4x4 matrices we get second set of Maxwell equations for GEM ( https://en.wikipedia.org/wiki/Gravitoelectromagnetism ).


    The approach generalizes Faber's from vector to matrix field.

    Electromagnetic (A vector, F tensor) are no longer just (connection Gamma, curvature R), but additionally include dependence of rotated shape (eigenvalues).

    This way we can get vacuum dynamics of 3 strengths: EM >> pilot wave >> GEM.


    Below is the main diagram with concepts.

    I have submitted to arxiv but is "on hold" as usual, so I have put it here: https://www.researchgate.net/publication/353932148_Framework_for_liquid_crystal_based_particle_models

    It is initial version I will work on especially:

    - the details of potential to choose is the main open question, and very difficult one - it contains weak/strong interactions,

    - explaining gravitational mass - spatial curvature caused e.g. by energy density, activation of potential,

    - finally numerics first aiming agreement with electron, 3 leptons, hopefully enforcing intrinsic periodic process: de Broglie clock.

    Would gladly discuss/collaborate.


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