Duda Jarek

I also think it should remain valid in macroscopis physics - just imagine building larger and larger Feynman diagrams. However, CPT naively reverses causality direction, like in this hypothetical rocket which traveled through Klein-bottle-like wormhole - what seems highly controversial. Taking a setting with clear causality direction e.g. this laser causes excitation of its target later, if constructing CPT analogue of this situation, should CPT(laser) cause deexcitation of target earlier? While building CPT analogue of laser seems technically extremely challenging, at least for free electron laser(FEL) it seems realizable: just replace electrons with positrons traveling in the opposite direction. To test if it can cause deexcitation of target, we could use e.g. a gas-discharge lamp continuously exciting its atoms as the target - the big question is if such CPT(FEL) could increase deexcitation rate in this direction? (what could be measured monitoring lamp's energy balance) I don't know and believe only experiment could really answer this question (?) - I would love to conduct (if only getting allowance to place such lamp e.g. in synchrotron?)

CPT symmetry (charge, parity, time) is at heart of modern physics: However, it seems treated seriously only in scale of Feynman diagrams with a few particles - is it still valid for macroscopic physics? Feynman diagrams of Avogadro's scale numbers of particles? In other words, if preparing CPT(initial conditions), should they lead to CPT(their evolution) ... including time reversed causality direction? While it seems technically challenging to prepare CPT(initial conditions), in theory general relativity allows to prepare T(initial conditions) - by hypothetical Klein-bottle-like wormholes ( https://en.wikipedia.org/wiki/Non-orientable_wormhole ) e.g. rotating 180 deg. light cones - while standard laser causes excitation of its target, would laser in a rocket traveled through such wormhole cause deexcitation of target?

Fully synthetic cells are already created and working (e.g. https://en.wikipedia.org/wiki/Artificial_cell , https://www.nist.gov/news-events/news/2021/03/scientists-create-simple-synthetic-cell-grows-and-divides-normally ) - for simple microbes it is just a matter of putting what's needed into phospholipid bag ... and there are financial motivations: to cheaply synthesize mirror chemicals e.g. for drugs. It is quite likely there will be first mirror microbes in a decade - it is now time to prepare for that: understand the dangers (e.g. taking over ecological niches while being toxic), try to prevent them ...

Thanks, added to https://en.wikipedia.org/wiki/Mirror_life ... mirror microbe by 2040?

Radiation of linear antenna is probably detected everyday, the question is minimal size of rotating dipole to still radiate EM waves? So what is the minimal number of atoms building a dipole, such that the radiation power formula from the first post still works?

Indeed, while both calculations suggest alignment already for classical magnets, they seem to lead to essentially different times for such process - bringing interesting question of which is more appropriate, has better agreement with experiment.

So please take a look in the attached article - calculations for classical magnet in external magnetic field - satisfying below equation (3), do you disagree with it? Sure such magnet is built of atoms, but I don't think atomic physics is a proper description for antenna (?)

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 ...

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 ...

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?

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?

I completely agree that quantum mechanically the spin alignment is never perfect, however, often is nearly perfect - e.g. in Stern-Gerlach, NMR, ferromagnets. If you could elaborate on my questions regarding classical magnet - should it precess in external magnetic field? If so radiating energy as EM waves? Until reaching nearly perfect alignment?

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

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. 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. 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. 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.

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. 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.

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.

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

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? 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. 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?

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? 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 ...

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?

So how do you understand/explain Stern-Gerlach experiment: why these atoms align in parallel or anti-parallel way (as "classical magnets" would through radiation of abundant kinetic energy)? What happens with the difference of energy and angular momentum (between initial random and final aligned spins) if it is not radiated as EM wave?

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?

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.

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?

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/