Duda Jarek

Photons are EM waves, antenna produces EM waves, wireless charger ... which carry energy proportional to |E|^2 without need for charged particles on the go.

Ok, you can skip r=0 case ... but such energy density should be continuous also there.

Regarding Heisenberg principle, notice that I am using "mean": what is mean energy density of electric field in distance r from electron? If one really needs a probe particle, e.g.: what is mean energy of electron - positron pair in distance r?

https://en.wikipedia.org/wiki/Electric_field#Energy_in_the_electric_field Or this F_munu F^munu in QED https://en.wikipedia.org/wiki/Quantum_electrodynamics#Mathematical_formulation

Regarding probing with other charged particle, there appears Coulomb potential V(r) ~ -1/r ... again having this infinity problem. There is scattering - extrapolating to energy of resting particles to remove Lorentz contraction contribution, we get ~100mb corresponding to size of electron in femtometers - we have discussed it here: But cannot we directly ask about field? Its mean energy density in r distance?

Ok, but in annihilation there are usually two (for para-positronium, +1 for ortho to reach zero angular momentum) ... e.g. used in PET imaging. Sure, in practice we need a bit larger energy to get pair in a distance ... ... but, this final energy also includes Coulomb potential V(r) ~ -1/r, again infinity in the beginning r=0 ... requiring some regularization. From one side, "subtracting infinity by hand" in renormalization is only mathematical trick - there still remains the question "what is mean energy density of electric field in distance r from electron?" Asymptotically ~|E|^2 = 1/r^4, but it leads to infinity - requires some deformation in the center. From the other, there are classical regularization methods. For example use Higgs potential V(u) = (|u|^2 -1)^2. It has |u|=1 vacuum (energy minimum), but e.g. in the center of topological singularity like hedgehog u(x) = x/|x|, to prevent discontinuity (infinite energy) it allows to get to v=0 by activating potential:

Energy conservation says that energy before and after should be the same. For 2gamma -> electron + positron pair creation: - energy before is 2x511keV in photons, which are EM waves - so this energy is initially in EM field, - energy after is, among others, energy of electric field of these two charges: integrating over energy density of E~1/r^2, we get infinite energy after this way. There is a problem, and just subtracting infinity in renormalization is only a mathematical trick without really understanding. We need to regularize this singularity: deform electric field to prevent E->infinity in the center. Running coupling ( https://en.wikipedia.org/wiki/Coupling_constant#Running_coupling ) can be seen as a consequence of such deformation: alpha increases e.g. to 1/127 in 90GeV - perfect point charges wouldn't need such deformation. Some discussion: https://physics.stackexchange.com/questions/386760/the-problem-of-infinite-energy-of-electron-as-point-charge Indeed the question of total energy of electric field of electron is extremely interesting - we only know the upper bound: 511keV. There are also other fields like magnetic of magnetic dipole: integrating energy density of all the fields, should we get 511keV or smaller? In other words: are particles more then just their fields? What more? Nice quote from 1961 Infeld "Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta.":

At least some of physicists believe in energy conservation, requiring source e.g. for hypothetical infinite energy. For example there is pair creation: of electron + positron from 2x511 keV only, so energy of electric field of such electron shouldn't exceed 511keV. But electric field of point charge is E~1/r^2, energy density is ~|E|^2, what integrates to infinite energy. So is there infinite energy in electric field of electron? QFT "repairs" this problem by just subtracting this infinity in renormalization procedure - successfully swept under the rug. But maybe it contains some regularization - deformation of electric field to indeed integrate to at most 511keV energy?

Especially in superconductors/superfluids there are observed so called macroscopic quantum phenomena ( https://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena ) - stable constructs like fluxon/Abrikosov vortex quantizing magnetic field due to topological constraints (phase change along loop has to be multiplicity of 2pi). There is observed e.g. interference ( https://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.094503 ), tunneling ( https://journals.aps.org/prb/pdf/10.1103/PhysRevB.56.14677 ), Aharonov-Bohm ( https://www.sciencedirect.com/science/article/pii/S0375960197003356 ) effects for these particle-like objects. It brings question if this similarity with particle physics could be taken further? How far? E.g. there is this famous Volovik's "The universe in helium droplet" book ( http://www.issp.ac.ru/ebooks/books/open/The_Universe_in_a_Helium_Droplet.pdf ). Maybe let us discuss it here - any interesting approaches? For example there are these biaxial nematic liquid crystals: of molecules with 3 distinguishable axes. We could build hedgehog configuration (topological charge) with one these 3 axes, additionally requiring magnetic-like singularity for second axis due to hairy-ball theorem ... doesn't it resemble 3 leptons: asymptotically the same charge (+magnetic dipole), but with different realization/mass?

Obviously many are coming, naturally selected especially for faster spread, now e.g. also from South Africa: https://www.cnbc.com/2021/01/06/south-africa-covid-strain-a-guide-to-what-you-need-to-know.html Again good interview:

good interview:

Tomorrow EU starts mass vaccination https://www.france24.com/en/europe/20201226-european-union-begins-coronavirus-vaccine-rollout-as-new-strain-spreads ... as the new strains like UK's are quickly spreading - what do we know about vaccine efficiency for them? It is great that there are lots of them - covering various mechanisms, hopefully allowing for effective war with mutations (https://www.nytimes.com/interactive/2020/science/coronavirus-vaccine-tracker.html 3 approved, 5 limited approved, 18 in phase III). Very nice explanation of Pfizer mRNA vaccine: https://berthub.eu/articles/posts/reverse-engineering-source-code-of-the-biontech-pfizer-vaccine/, especially: - it uses Psi (1-methyl-3’-pseudouridylyl) instead of U (uracil) - works the same, but with weaker immune response, - uses synonymous codons with increased numbers of C and Gs (e.g. CUU -> CUG both encode Leucine), which are converted more efficiently into proteins, - two amino acids are changed comparing to virus spike protein (K,V -> P) to handle the problem of difference between pre- and post-fusion spike protein - this exchange into Proline makes them fold into the proper shape without being mounted to a virus (known since 2017 thanks to work on SARS-CoV-1).

UK starts mass vaccination: https://www.bbc.com/news/uk-55218679

U.K. Approves Pfizer Coronavirus Vaccine, a First in the West https://www.nytimes.com/2020/12/02/world/europe/pfizer-coronavirus-vaccine-approved-uk.html

18th November Pfizer 95 percent https://www.theguardian.com/world/2020/nov/18/pfizer-covid-19-vaccine-95-effective-and-safe-further-tests-show Time for another bid for Sputnik and Moderna

9th November: Pfeizer "90 percent efficient" https://www.the-scientist.com/news-opinion/pfizers-covid-19-vaccine-90-percent-effective-initial-data-68138 11th November: "Sputnik V 92 percent" https://www.aljazeera.com/news/2020/11/11/russia-says-sputnik-v-covid-19-vaccine-is-92-percent-effective 16th November: "Moderna 94.5 percent" https://www.nytimes.com/2020/11/16/health/Covid-moderna-vaccine.html Who's next? ... in the meantime e.g. https://www.marketwatch.com/story/pfizers-ceo-sold-5-6-million-worth-of-shares-on-the-day-of-its-big-vaccine-news-so-what-11605280170

Sure, we can ask it using potential energy, e.g.: charged particle near atom behaves accordingly to superposition of Coulomb potential of electron being in all points, or maybe accordingly to single Coulomb potential: averaged over wavefunction?

Electron has associated electric field, so asking about electric field of atom/orbital, is it superposition of electric field of electron being in each point, or maybe mean? For example placing another atom nearby, should their electrons somehow synchronize (e.g. van der Waals force)? Don't it require superposition?

In other words: is electric field of orbital a superposition over electron being in all places, or rather mean?

While electron and proton being far apart are allowed to be imagined as nearly point particles, when they approach ~10^-10m (or much more for Rydberg atoms), electron is said "to become" this relatively huge wavefunction - orbital, describing probability distribution of finding electron (confirmed experimentally e.g. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165404 ). Can we specify in what e-p distance this qualitative change happens? How to think about this orbital from QM interpretations perspective - is it superposition of electron (indivisible charge) being in all these places? E.g. in Many Worlds Interpretation, should we imagine that electron has different position in each World? In such superposition each electron is staying or moving? If staying, where e.g. the orbital angular momentum comes from? If moving, why no synchrotron radiation?

Another very similar molecule is NH3 ... found e.g. on Pluto - not suggesting biological source only geological: https://advances.sciencemag.org/content/5/5/eaav5731 Detection of ammonia on Pluto’s surface in a region of geologically recent tectonism

Oxygen-free environments seem characteristic for geological processes (?), and PH3 is similar to CH4 released by our geology - if phosphorus dominates instead of carbon, couldn't phosphine by synthesized in oxygen-free geological environments? "Geologic emissions of methane to the atmosphere": https://pubmed.ncbi.nlm.nih.gov/12430657/ ps. SH2 can be produced by bacteria: https://en.wikipedia.org/wiki/Hydrogen_sulfide#Biosynthesis_in_the_body Phosphine also occurs in Earth atmosphere ... and Jupiter: https://en.wikipedia.org/wiki/Phosphine#Occurrence Can be generated by bacteria: https://www.researchgate.net/publication/12507095_Phosphine_generation_by_mixed-_and_monoseptic-cultures_of_anaerobic_bacteria

Here is their recent Lancet paper: https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)31866-3/fulltext https://www.reuters.com/article/us-health-coronavirus-russia-vaccine/russias-covid-19-vaccine-showed-antibody-response-in-initial-trials-idUSKBN25V1I2 Looks promising, but there are some suspicions: https://www.cnbc.com/2020/09/10/scientists-question-russian-vaccine-trial-data-on-unlikely-patterns.html Yesterday WHO vaccine report: https://www.who.int/publications/m/item/draft-landscape-of-covid-19-candidate-vaccines A worse news, probably the most promising (AstraZeneca) trial is on hold: https://www.nature.com/articles/d41586-020-02594-w

It is also crucial that it is local random choice: based on possible single steps, having characteristic length like use of single step. MERW can be seen as scale-free limit of GRW_k: using uniform (/Boltzmann) distribution of length k paths from given position: GRW = GRW_1 MERW = lim_{k->infty} GRW_k

Exactly, GRW is perfect e.g. for human wandering through the web, indeed performing local randomly looking decisions. MERW for electrons - having extremely complex EM&wave-based dynamics, expressing our limited knowledge through its entropy maximization, with Anderson-like localization property e.g. preventing semiconductor from being a conductor, like in below electron densities from STM (scanning tunneling microscope) from http://www.phy.bme.hu/~zarand/LokalizacioWeb/Yazdani.pdf The big question is what to choose between, like for this molecular dynamics? Practical difference is that only MERW has QM-like localization property - do we observe this kind of effects for molecules? Like entropic boundary avoidance, e.g. for [0,1] range GRW/diffusion/chaos would predict nearly uniform rho=1 stationary distribution, while QM/MERW predicts rho~sin^2 distribution avoiding boundaries - do we observe it for molecules?