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Has evolution been experimentally observed? If not, could it be experimentally verified and how?

Has evolution been experimentally observed? If not, (how) could it be experimentally verified?Thanks for the A2A, I hope my answer helps. Feel free to click on any or all of the links below.Below, please find all of the evidence for creationism and (a small amount of) the evidence for evolution. From here, you can decide for yourself which is more compelling, is better proven and makes more sense to you…First here is all of the evidence that can be found for Creationism:A small amount of the evidence available for the Science of Evolution:Mount, D.M. (2004). Bioinformatics: Sequence and Genome Analysis (2nd ed.). Cold Spring Harbor Laboratory Press: Cold Spring Harbor, NY. ISBN 978-0-87969-608-5.Penny, David; Foulds, L. R.; Hendy, M. D. (1982). "Testing the theory of evolution by comparing phylogenetic trees constructed from five different protein sequences". Nature. 297 (5863): 197–200. Bibcode:1982Natur.297..197P. doi:10.1038/297197a0. PMID 7078635."Eukaryotes". Tree of Life Web Project. Retrieved 23 June 2018.Max, Edward (5 May 2003). "Plagiarized Errors and Molecular Genetics". The Talk Origins Archive. Retrieved 4 May 2018.Futuyma, Douglas J. (1998). Evolutionary Biology (3rd ed.). Sinauer Associates. pp. 108–110. ISBN 978-0-87893-189-7.Haszprunar (1995). "The mollusca: Coelomate turbellarians or mesenchymate annelids?". In Taylor (ed.). Origin and evolutionary radiation of the Mollusca : centenary symposium of the Malacological Society of London. Oxford: Oxford University Press. ISBN 978-0-19-854980-2.Kozmik, Z.; Daube, M.; Frei, E.; Norman, B.; Kos, L.; Dishaw, L.J.; Noll, M.; Piatigorsky, J. (2003). "Role of Pax genes in eye evolution: A cnidarian PaxB gene uniting Pax2 and Pax6 functions" (PDF). Developmental Cell. 5 (5): 773–785. doi:10.1016/S1534-5807(03)00325-3. PMID 14602077.Land, M.F. and Nilsson, D.-E., Animal Eyes, Oxford University Press, Oxford (2002) ISBN 0-19-850968-5.Chen, F.C.; Li, W.H. (2001). "Genomic Divergences between Humans and Other Hominoids and the Effective Population Size of the Common Ancestor of Humans and Chimpanzees". American Journal of Human Genetics. 68 (2): 444–56. doi:10.1086/318206. PMC 1235277. PMID 11170892.Cooper, G.M.; Brudno, M.; Green, E.D.; Batzoglou, S.; Sidow, A. (2003). "Quantitative Estimates of Sequence Divergence for Comparative Analyses of Mammalian Genomes". Genome Res. 13 (5): 813–20. doi:10.1101/gr.1064503. PMC 430923. PMID 12727901.The picture labeled "Human Chromosome 2 and its analogs in the apes" in the article Comparison of the Human and Great Ape Chromosomes as Evidence for Common Ancestry Archived 2011-08-20 at WebCite is literally a picture of a link in humans that links two separate chromosomes in the nonhuman apes creating a single chromosome in humans. Also, while the term originally referred to fossil evidence, this too is a trace from the past corresponding to some living beings that, when alive, physically embodied this link.The New York Times report Still Evolving, Human Genes Tell New Story, based on A Map of Recent Positive Selection in the Human Genome, states the International HapMap Project is "providing the strongest evidence yet that humans are still evolving" and details some of that evidence.Alberts, Bruce; Johnson, Alexander; Lewis, Julian; Raff, Martin; Roberts, Keith; Walter, Peter (March 2002). Molecular Biology of the Cell (4th ed.). Routledge. ISBN 978-0-8153-3218-3."Converging Evidence for Evolution." Archived 2010-12-01 at the Wayback Machine Phylointelligence: Evolution for Everyone. 26 November 2010.Petrov, D.A.; Hartl, D.L. (2000). "Pseudogene evolution and natural selection for a compact genome". The Journal of Heredity. 91 (3): 221–7. doi:10.1093/jhered/91.3.221. PMID 10833048.Xiao-Jie, Lu; Ai-Mei, Gao; Li-Juan, Ji; Jiang, Xu (1 January 2015). "Pseudogene in cancer: real functions and promising signature". Journal of Medical Genetics. 52 (1): 17–24. doi:10.1136/jmedgenet-2014-102785. ISSN 0022-2593. PMID 25391452.Vanin, E F (1985). "Processed Pseudogenes: Characteristics and Evolution". Annual Review of Genetics. 19 (1): 253–272. doi:10.1146/annurev.ge.19.120185.001345. ISSN 0066-4197. PMID 3909943.Gerstein, Mark (2006). "Pseudogenes in the ENCODE Regions: Consensus Annotation, Analysis of Transcription and Evolution" (PDF). Gerstein Lab. Retrieved 23 June 2018."What is Junk DNA?". Medical News | Medical Articles. 7 May 2010. Retrieved 23 June 2018.Okamoto, N.; Inouye, I. (2005). "A secondary symbiosis in progress". Science. 310 (5746): 287. doi:10.1126/science.1116125. PMID 16224014.Okamoto, N.; Inouye, I. (2006). "Hatena arenicola gen. et sp. nov., a katablepharid undergoing probable plastid acquisition". Protist. 157 (4): 401–19. doi:10.1016/j.protis.2006.05.011. PMID 16891155.MacAndrew, Alec. Human Chromosome 2 is a fusion of two ancestral chromosomes. Accessed 18 May 2006.Evidence of Common Ancestry: Human Chromosome 2 (video) 2007Yunis, J.J.; Prakash, O. (1982). "The origin of man: a chromosomal pictorial legacy". Science. 215 (4539): 1525–1530. Bibcode:1982Sci...215.1525Y. doi:10.1126/science.7063861. PMID 7063861.Human and Ape Chromosomes Archived 2011-08-20 at WebCite; accessed 8 September 2007.Avarello, Rosamaria; Pedicini, A; Caiulo, A; Zuffardi, O; Fraccaro, M (1992). "Evidence for an ancestral alphoid domain on the long arm of human chromosome 2". Human Genetics. 89 (2): 247–9. doi:10.1007/BF00217134. PMID 1587535.Ijdo, J. W.; Baldini, A; Ward, DC; Reeders, ST; Wells, RA (1991). "Origin of human chromosome 2: an ancestral telomere-telomere fusion". Proceedings of the National Academy of Sciences. 88 (20): 9051–5. Bibcode:1991PNAS...88.9051I. doi:10.1073/pnas.88.20.9051. PMC 52649. PMID 1924367.Amino acid sequences in cytochrome c proteins from different species, adapted from Strahler, Arthur; Science and Earth History, 1997. page 348.Lurquin, P.F.; Stone, L. (2006). Genes, Culture, and Human Evolution: A Synthesis. Blackwell Publishing, Incorporated. p. 79. ISBN 978-1-4051-5089-7.Theobald, Douglas (2004). "29+ Evidences for Macroevolution; Protein functional redundancy]". The Talk Origins Archive.Castresana, J. (2001). "Cytochrome b Phylogeny and the Taxonomy of Great Apes and Mammals". Molecular Biology and Evolution. 18 (4): 465–471. doi:10.1093/oxfordjournals.molbev.a003825. PMID 11264397.Van Der Kuyl, A.C.; Dekker, J.T.; Goudsmit, J. (1999). "Discovery of a New Endogenous Type C Retrovirus (FcEV) in Cats: Evidence for RD-114 Being an FcEVGag-Pol/Baboon Endogenous Virus BaEVEnv Recombinant". Journal of Virology. 73 (10): 7994–8002. PMC 112814. PMID 10482547.Sverdlov, E.D. (February 2000). "Retroviruses and primate evolution". BioEssays. 22 (2): 161–71. doi:10.1002/(SICI)1521-1878(200002)22:2<161::AID-BIES7>3.0.CO;2-X. PMID 10655035.Belshaw, R.; Pereira, V.; Katzourakis, A.; et al. (April 2004). "Long-term reinfection of the human genome by endogenous retroviruses". Proceedings of the National Academy of Sciences of the United States of America. 101 (14): 4894–9. Bibcode:2004PNAS..101.4894B. doi:10.1073/pnas.0307800101. PMC 387345. PMID 15044706.Bonner, T.I.; O'Connell, C.; Cohen, M. (August 1982). "Cloned endogenous retroviral sequences from human DNA". Proceedings of the National Academy of Sciences of the United States of America. 79 (15): 4709–13. Bibcode:1982PNAS...79.4709B. doi:10.1073/pnas.79.15.4709. PMC 346746. PMID 6181510.Johnson, Welkin E.; Coffin, John M. (31 August 1999). "Constructing primate phylogenies from ancient retrovirus sequences". Proceedings of the National Academy of Sciences. 96 (18): 10254–10260. Bibcode:1999PNAS...9610254J. doi:10.1073/pnas.96.18.10254. ISSN 0027-8424. PMC 17875. PMID 10468595.Pallen, Mark (2009). Rough Guide to Evolution. Rough Guides. pp. 200–206. ISBN 978-1-85828-946-5.Tanaka, G.; Hou, X.; Ma, X.; Edgecombe, G.D.; Strausfeld, N.J. (October 2013). "Chelicerate neural ground pattern in a Cambrian great appendage arthropod". Nature. 502 (7471): 364–367. Bibcode:2013Natur.502..364T. doi:10.1038/nature12520. PMID 24132294.Andrews, Roy Chapman (3 June 1921). "A Remarkable Case of External Hind Limbs in a Humpback Whale" (PDF). American Museum Novitates.Hall, Brian K. (1995), "Atavisms and atavistic mutations", Nature Genetics, 10 (2): 126–127, doi:10.1038/ng0695-126, PMID 7663504hall, Brian K. (1984), "Developmental mechanisms underlying the atavisms", Biological Reviews, 59 (1): 89–124, doi:10.1111/j.1469-185x.1984.tb00402.x, PMID 6367843Lambert, Katie. (2007-10-29) HowStuffWorks "How Atavisms Work". Animals. Retrieved on 2011-12-06.Tomić, Nenad; et al. (2011), "Atavisms: Medical, Genetic, and Evolutionary Implications", Perspectives in Biology and Medicine, 54 (3): 332–353, doi:10.1353/pbm.2011.0034, PMID 21857125Raynaud, A. (1977), Somites and early morphogenesis in reptile limbs. In Vertebrate Limb and Somite Morphogenesis, Cambridge University Press, London, pp. 373–386Tabuchi, Hiroko (2006), Dolphin May Have 'Remains' of Legs, The Most Interesting Articles, Mysteries & DiscoveriesTyson, R.; Graham, J.P.; Colahan, P.T.; Berry, C.R. (2004). "Skeletal atavism in a miniature horse". Veterinary Radiology & Ultrasound. 45 (4): 315–7. doi:10.1111/j.1740-8261.2004.04060.x. PMID 15373256.Simpson, G. G. (1951), Horses: The story of the horse family in the modern world and through sixty million years of evolution, Oxford University PressDao, Anh H.; Netsky, Martin G. (1984), "Human tails and pseudotails", Human Pathology, 15 (5): 449–453, doi:10.1016/S0046-8177(84)80079-9, PMID 6373560Katja Domes; et al. (2007), "Reevolution of sexuality breaks Dollo's law", Proc. Natl. Acad. Sci. U.S.A., 104 (17): 7139–7144, Bibcode:2007PNAS..104.7139D, doi:10.1073/pnas.0700034104, PMC 1855408, PMID 17438282Harris, Matthew P.; et al. (2006), "The Development of Archosaurian First-Generation Teeth in a Chicken Mutant", Current Biology, 16 (4): 371–377, doi:10.1016/j.cub.2005.12.047, PMID 16488870Michael F. Whiting; et al. (2003), "Loss and recovery of wings in stick insects", Nature, 421 (6920): 264–267, Bibcode:2003Natur.421..264W, doi:10.1038/nature01313, PMID 12529642Robert J. Raikow; et al. (1979), "The evolutionary re-establishment of a lost ancestral muscle in the bowerbird assemblage", Condor, 81 (2): 203–206, doi:10.2307/1367290, JSTOR 1367290Robert J. Raikow (1975), "The evolutionary reappearance of ancestral muscles as developmental anomalies in two species of birds", Condor, 77 (4): 514–517, doi:10.2307/1366113, JSTOR 1366113E. Evansh (1959), "Hyoid muscle anomalies in the dog (Canis familiaris)", Anatomical Record, 133 (2): 145–162, doi:10.1002/ar.1091330204Castle, William E. (1906), The origin of a polydactylous race of guinea-pigs (49 ed.), Carnegie Institution of WashingtonHeld, Lewis I. (2010). "The Evo-Devo Puzzle of Human Hair Patterning". Evolutionary Biology. 37 (2–3): 113–122. doi:10.1007/s11692-010-9085-4.Futuyma, Douglas J. (1998). Evolutionary Biology (3rd ed.). Sinauer Associates Inc. p. 122. ISBN 978-0-87893-189-7.29+ Evidences for Macroevolution: Part 1. Exploring the Creation/Evolution Controversy. Retrieved on 2011-12-06.Coyne, Jerry A. (2009). Why Evolution is True. Viking. pp. 8–11. ISBN 978-0-670-02053-9.Darwin, Charles (1859). On the Origin of Species. John Murray. p. 420.Tuomi, J. (1981). "Structure and dynamics of Darwinian evolutionary theory" (PDF). Syst. Zool. 30 (1): 22–31. doi:10.2307/2992299. JSTOR 2992299.Aravind, L.; Iyer, L.M.; Anantharaman, V. (2003). "The two faces of Alba: the evolutionary connection between proteins participating in chromatin structure and RNA metabolism". Genome Biology. 4 (10): R64. doi:10.1186/gb-2003-4-10-r64. PMC 328453. PMID 14519199.Brochu, C. A.; Wagner, J. R.; Jouve, S.; Sumrall, C. D.; Densmore, L. D. (2009). "A correction corrected:Consensus over the meaning of Crocodylia and why it matters" (PDF). Syst. Biol. 58 (5): 537–543. doi:10.1093/sysbio/syp053. PMID 20525607. Archived from the original (PDF) on 27 September 2013.Bock, W. J. (2007). "Explanations in evolutionary theory" (PDF). J Zool Syst Evol Res. 45 (2): 89–103. doi:10.1111/j.1439-0469.2007.00412.x. Archived from the original (PDF) on 12 May 2012.Kluge 1999Laurin 2000Fitzhugh 2006, p. 31Kluge 1999, p. 432Slifkin, Natan (2006). The Challenge of Creation…. Zoo Torah. pp. 258–9. ISBN 978-1-933143-15-6.Senter, Phil; et al. (2015), "Vestigial Biological Structures: A Classroom-Applicable Test of Creationist Hypotheses", The American Biology Teacher, 77 (2): 99–106, doi:10.1525/abt.2015.77.2.4Attila Regoes; et al. (2005), "Protein Import, Replication, and Inheritance of a Vestigial Mitochondrion", The Journal of Biological Chemistry, 280 (34): 30557–30563, doi:10.1074/jbc.M500787200, PMID 15985435Sekiguchi, Hiroshi; et al. (2002), "Vestigial chloroplasts in heterotrophic stramenopiles Pteridomonas danica and Ciliophrys infusionum (Dictyochophyceae)", Protist, 153 (2): 157–167, doi:10.1078/1434-4610-00094, PMID 12125757Paula J. Rudall; et al. (2002), "Floral Anatomy and Systematics of Alliaceae with Particular Reference to Gilliesia, A Presumed Insect Mimic with Strongly Zygomorphic Flowers", American Journal of Botany, 89 (12): 1867–1883, doi:10.3732/ajb.89.12.1867, PMID 21665616Strittmatter, Lara I.; et al. (2002), "Subdioecy in Consolea Spinosissima (Cactaceae): Breeding System and Embryological Studies", American Journal of Botany, 89 (9): 1373–1387, doi:10.3732/ajb.89.9.1373, PMID 21665739Ashman, Tia-Lynn (2003), "Constraints on the Evolution of Males and Sexual Dimorphism: Field Estimates of Genetic Architecture of Reproductive Traits in Three Populations of Gynodioecious Fragaria virginiana", Evolution, 57 (9): 2012–2025, doi:10.1554/02-493Golonka, Annette M.; et al. (2005), "Wind Pollination, Sexual Dimorphism, and Changes in Floral Traits of Schiedea (Caryophyllaceae)", American Journal of Botany, 92 (9): 1492–1502, doi:10.3732/ajb.92.9.1492, PMID 21646167Walker-Larsen, J.; Harder, L. D. (2001), "Vestigial organs as opportunities for functional innovation: the example of the Penstemon staminode", Evolution, 55 (3): 477–487, doi:10.1111/j.0014-3820.2001.tb00782.xGomez, Nadilla N.; Shaw, Ruth G. (2006), "Inbreeding Effect on Male and Female Fertility and Inheritance of Male Sterility in Nemophila menziesii (Hydrophyllaceae)", American Journal of Botany, 93 (5): 739–746, doi:10.3732/ajb.93.5.739, PMID 21642137Bejder, Lars; Hall, Brian K. (2002), "Limbs in Whales and Limblessness in Other Vertebrates: Mechanisms ofEvolutionary and Developmental Transformation and Loss", Evolution and Development, 4 (6): 445–458, doi:10.1046/j.1525-142x.2002.02033.x, PMID 12492145Coyne, Jerry A. (2009). Why Evolution Is True. Viking. pp. 60. ISBN 978-0-670-02053-9.West-Eberhard, Mary Jane (2003). Developmental plasticity and evolution. Oxford University Press. p. 232. ISBN 978-0-19-512234-3.P. C. Simões-Lopes; C. S. Gutstein (2004), "Notes on the anatomy, positioning and homology of the pelvic bones in small cetaceans (Cetacea, Delphinidae, Pontoporiidae)", LAJAM, 3 (2): 157–162, doi:10.5597/lajam00060"Example 1: Living whales and dolphins found with hindlimbs". Douglas Theobald. 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What is time and what defines it? Can time and light be considered alike?

You ask such common questions….That was a joke. What defines time is any which way we choose to measure it. Like a volume of whiskey in a shot, you can measure it by fingers, grams, cubic centimeters, cubic miles, %alcohol it will raise your blood level (but has not yet done so), how much thermal radiation it will absorb (again, in the future), how much thermal radiation it did absorb (in the past), how many fleas you can drown in it….or have drowned in it…As for what it is, all we can say it is a shot of whiskey, which is a volume of distilled spirits. However, the whiskey has finer components, and is a mixture. The finer we try and refine the individual components, we get down to the quarks and gluons that hypothetically hold the nuclei together (Internal Strong Force), at which point our story ends.Time is also a mixture, a mixture of dimensions, a mixture of information, the information lies on a surface, and the surface; in a turnaround (called a fractal) can be measured in time intervals.The number of bits of information is given by: (Verlinde; Erik Verlinde, On the Origin of Gravity and the Laws of Newton; arXiv:1001.0785v1 [hep-th] 6 Jan 2010)Verlinde wrote the equation 3.10 asWhich rearranges to:After correcting for Beckenstein information entropy. [1]Where c=1Lp/1tp (tp being the Planck interval of time), Lp and tp are interchangeable. As in Minkowski Space, space-time; indifferentiable. We say that the speed of lght, ‘c’ is a ‘natural unit,’ and set it equal to 1. In which case 1Lp = 1tp.Where A-omega is the surface area of the region being measured; we call that the ‘world-sheet’. And 1 bit of information, by rearranging the Beckestein-Verlinde relationship; then is given by:That is, in an attempt to determine what the hitherto ‘bit’ of information is (which oddly, no one has defined to date) we use dimensional analysis to derive what a ‘bit’ of information in the Bekenstein-Hawking ‘information paradox’ would be. Keep in mind Bekenstein was one of Wheeler’s students. In any case, the argument that raged on for four decades never had ‘information’ defined. With the exception of the derivation above, that remains true today.What is 4Lp^2? Well, you can envision it as a trigonal pyramid:But you have to keep in mind that because the pyramid has a hypotenuse that is not an integer value of Lp, this, or any other shape on a Planck Scale is impossible. a circle for instance has pi diameters making the circumference, also not an integer value of Lp. Only integers of Lp can exist, as this is the finest slice you can take in normal space-time. The Planck Scale is a shapeless, formless, domain.So as not to fail to contradict myself (the Kaufman Paradox - why do you feel embarrassed when the performer sucks?) we takeand it oddly becomes an analog ofThe reason I say this is odd is because it has the same characteristic as a Black Hole, it has no interior, meaning that surface shown bisecting the two halves is impossible. Remember that a Black Hole has no interior. All force and time dilation, etc is directed toward the Schwarzschil radius, which I refer to as the Schwarzschild surface. Nothing happens below this surface because space-time does not exist below this surface. In fact, time itself ceases to exist at the surface.The fact that time ceases to exist at the Schwarzschild surface is why we can say in Holographic Theory (which is actually a hypothesis, not a theory) that the Schwarzschld surface is 2-dimensional, and time is not a valid dimension there. It is static, frozen, time has been infinitely dilated, according to the Schwarzschild transformation:Most people are accustomed to seeing it written asHowever, this is non-intuitive, as it shows time shrinking away to nothing, not intuitively ‘dilation.’ Remember, in Special Relativity we define time dilation as expanding toward infinity. So as to remain consistent with Special Relativity, in General Relativity (which this is actually not) I flip the equation so as to intuitively represent ‘dilation toward infinity.’ That is, the temporal distance at the Schwarzschild surface between any two events is infinite. That’s why I flip the equation.The term, 4Lp^2 is supposed to be a surface area, which defines the 1 bit as a trigonal equilateral pyramid. However, no regular shapes are possible on a Planck scale. For instance, the height of the pyramid is not in integer values of Lp, and therefore not possible. Spheres and circles require piLp, don’t work, and so on to all shapes. The trigonal equilateral pyramid is imaginary.So, time is a trigonal equilateral pyramid that represents 1 bit of information; 1 bit of information being the smallest amount of information needed to describe exactly 1 unit of entropy and/or Ordiny. (Ordiny is the opposite of entropy).As for force, distance, time, emergent gravitation, thus the emergent geometry of space-time (quantum gravitation) can be summarized as: when the number of possible superpositions increases, that is entropy, and when the number of possible superpositions decreases, that is Ordiny. I can then use this simple model as the driving mechanism of all of the forces of nature.The natural state of a ‘thing’ is as a wave function. The Heisenberg Uncertainty Principle, the most misquoted and incorrectly explained equation of all time does not have anything whatsoever to do with particles. The HUP states that the wave function has a distribution of possible superpositions, and therefore a distribution of velocities (that give it momentum) that got it to each of those superpositions.The very first YOU DO NOT DO is divide the indivisible h by the irrational number, 4 pi, rendering a numeric value that cannot exist in this universe 1) because h is the smallest value in normal space-time, 2) pi is not a rational number. So, the instant you see someone ‘divide’ h by 4 pi, change the channel.The 4 pi means ‘two wavelengths.’ The distribution of possible superpositions for x and the superpostions of velocity that got x to each of those probable superpositions is greater than or equal to the smallest unit of time dependent energy, h spread over exactly two wavelengths. Why 2 wavelengths as the minimum? Because, if you are in quantized space-time, and you can either be walking somewhere along the current wavelength, but to be considered in another position (you cannot overlap in quantized space-time) you must therefore be exactly 2 wavelengths to be considered 2 positions. That is the HUP, not the ‘particle’ nonsense.Once the wave function is detected, it is no longer a wave function, it is a particle. At that exact instant, the HUP is non-sequitur. The HUP has nothing to do with ‘particles.’In the mythos, the claim is I cannot know the exact location and exact momentum of say, an electron. OK. So we set up a detector to measure the electron’s momentum out to a zillion decimal places. It is essentially a tiny catcher’s mit. When an electron hits the mit, it will measure the exact momentum out to a zillion decimal places.So we wait…. Caught one! We now know the exact momentum of the electron (via its velocity and mass) with mind blowing precision. Where is the electron at that instant? According to myth we haven’t any idea, at least with respect to the electron’s Compton wavelength. It is exactly in the catcher’s mit. Where is the lack of certainty in this picture?Once the electron is detected, it has no Compton wavelength, it is a ‘particle,’ e.g., tiny cannon ball. If you could not know the exact velocity and position of an electron, an old fashioned CRT television couldn’t work. The CRT worked by ‘painting’ the image one dot (electron hitting a flourescent screen) at a time, requiring exacting precision in position and velocity to draw the Beverly Hillbillies.However, there is a dual going on, as information entropy is measured by:There is no way to get S=+1 without using imaginary numbers, complex conjugates.It gets weirder…Among Nicolini’s first statements: “Conventionally, entropy is defined as a measure of the loss of information about the microscopic degrees of freedom of a physical system, when describing it in terms of macroscopic variables.” [16] That is, as Leonard Susskind put it, ‘Entropy is a measure of ignorance. In a maximally entangled state, we are at maximal entropy.’ We can ween out of that, the ‘microscopic degrees of freedom’ have to take into account that any system is to some degree entangled with some other system. That is, they either share information, and/or the state of system B (Bob) may depend on system A (Alice), such is in the classic EPR entanglement of simple spin up-spin down particle-antiparticle pair production. For instance, if system A is spin up, then system B is spin down; and this is not a time dependent phenomenon.I believe the first mistake people make when approaching entangled systems is to think of space and/or time as figuring into the equation somehow. But the reason EPR could not get around the idea of superluminal signaling is that they couldn’t get around a phenomenon which existed in a world that ‘we are weird to.’ That is, a wave function is happy as such, that is its native form. It is only when we try and drag the thing into our human frame of reference that we think it is weird.Albeit visible in normal space-time,’the paradox’ had no correlation to space-time with respect to the state of either system. That is, there is information regarding either system that has no relationship or interdependency with space or time. I, for one, do not understand why people cannot get around that issue. Bob’s state of being, the information describing Bob’s degrees of freedom have no relationship with when and where he is. The only thing that defines Bob’s state is the state of Alice, and no other thing, property, particle, force, distance, time, etc. matters whatsoever.‘the paradox’ is the result of trying to predict behavior, the outcome, when it is obvious the answer is that there is no such property until detection occurs.If we do not measure or detect the state of Alice, we know nothing about either system. There is a matrix of possible things she could be, if only considering her spin, the matrix (disregarding system B) has only 2 elements. It isn’t until Alice is measured that we know her state. So, state A is always in hand, since we have to take the measurement.However, system B (Bob) has at the moment of Alice’s measured value, no degrees of freedom, he is slave to Alice. Since Bob has zero degrees of freedom, entropy is always zero (or infinity if you’re doing the Product from a different approach). Since the entropy is zero, N, the number of bits to describe Bob is zero; we know Bob’s state even if he is billions of light-years away once we measure Alice. Using Verlinde’s approach: I corrected the more modern 1/4That equation states that Bob, being slave to Alice, has no unique information describing him. Whatever Bob is, is completely a result of Alice. The world-sheet a-omega, falls to zero.This means that the surface Area of omega is zero, and as a result, all distances are zero. This is the root and key to Quantum Entanglement, those past 4 paragraphs.In which case for Bob, who can only have 1 state and no possible alternative once Alice is measured, Log Pi = 0, and the entire equation becomes S=0. That is what I mean by zero entropy (for Bob). In an attempt to directly correlate S and N, the number of bits of information, we look at the value Lp2.Even 19th century gas law entropy beinghas a result of zero, because time has ceased to progress.At the fundamental length, Lp, a variety of phenomenon occur. The Planck mass, actually as large as 10 nanograms, becomes a Black Hole of diameter equal to its Comptonwavelentgth/π, or a radius of Lp. It will radiate away as Hawking Radiation in roughly 1tp (5E-39 seconds). The wavelength of that radiation will be 1Lp (any other wavelength is not possible as its self-energy would again collapse into a black hole).The surface of the black hole cannot be regarded as a sphere, because it is so heavily pixelated at that size. For instance, since a curvature would not be possible on that scale, as this would require finely dividing the Planck length into shorter pieces, thus collapsing into self-energetic black holes, only a triangle can describe the circumference. Oddly, even a triangle becomes an impossible shape as the hypotenuse is not an integer of Lp, and so on.I will get to deriving that soon. For now, Bob has no information or degrees of freedom associated with him, being slave to Alice. Entropy, space, time, and so on have no relevance to Bob, when or where he is.Quantum Gravity takes this approach. For any closed region of space-time given by a volume representing N=1 as I showed above, a virtual particle may or may not exist in it. It is more correct to say that information may or may not be present in it.Two virtual particles cannot exist in N=1 volume of space-time, not even a boson, as more than 1 boson would require more than N=1 bits to describe.Virtual particles are created in particle-antiparticle pairs, and are entangled. 1 particle (Alice) has any number of degrees of freedom, but Bob’s state is slave to Alice, Bob has no degrees of freedom, either before or after Alice is measured. Since the virtual particle-antiparticle pairs are created entangled, as the distance between Alice and Bob grows larger, the likelihood that Bob will be created at all decreases. That is, at a distance of 1Lp the likelihood is high, at a distance of Andromeda, the likelihood that virtual Bob will be created out of the vacuum as an antiparticle entangled component of Alice is very low.Thus, the creation/annihilation of entangled virtual particle-antiparticle pairs is distance dependent (and so time dependent). This is beginning to look like gravitation. I would go through the derivation, but Nicolini [19] has already done so based on Verlinde’s work:After a complicated paper of derivation, we get back Newtonian mechanics, based on the number of bits of information, understanding that all distance is in reference across a Schwarzschild surface (like a Black Hole).The term on the left is clearly Newtonian, on the right is the entropy per surface area as defined by the number of bits of information.Thus, it is the QED vacuum itself that seems to provide the emergent gravitation, tied together by entanglement.In short, we take that trigonal pyramid (4Lp^2). It may or may not have information in it. If it does, it is because it is the result of a ‘quantum fluctuation.’ (another entire chapter). As such, that bit of information in our trigonal pyramid (Alice) is entangled with Bob, somewhere in space and time. 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Protons repel protons, and electrons repel electrons supposedly by the momentum of emitted photons. So how do photons attract, for example, protons to electrons?

I believe I already answered this exact question a few weeks ago. I hate to disagree with Dr Muller, but in this case, in my opinion, the uncertainty of the proton’s position is not an answer, sorry Dr Muller. Uncertainty is a black box that ‘in my opinion,’ is used to explain off too many phenomenon that no one wants to give thought to.The Heisenberg Uncertainty Principle gives us the minimum constraint on a wave function’s position, not how BIG it can be. That is, The HUP is given byThe 4 pi in the denominator is the result of usually seeing Planck’s constant written in ‘reduced form,’ represented by h-bar. There are a few things to know here. First, Planck’s constant, by definition is indivisible, as it represents the smallest slice of energy possible in normal space-time. You therefore do not divide the indivisible h by 4 pi (I see this in doctoral level lectures, and it is the second most stupid thing I have ever seen; I’ll save the first most stupid for some other post). Second: pi is not even a rational number. Dividing the indivisible h by an irrational number that has no discrete value in itself is - absurd. Third, h-bar was written by Dirac because he recognized that since h only deals with wave functions, it must have a value fundamentally related to a wave cycle, which is 2-pi. This is why h-bar is h/2pi. Four: 4-pi represents two full wave cycles, the minimum number to describe a wave function as being in one of two possible positions. Thus, the 4-pi in the denominator purely represents the smallest amount of energy possible in normal space-time, spread over the minimum requirement for a wave cycle to be considered as being in more than one position.Five, sigma-x represents the distribution of possible locations of the wave function, sigma-p represents the distribution of velocities (and hence momenta) that got the wave function to those superpositions distributed over sigma-x. The equation ONLY STATES THAT THIS DISTRIBUTION MUST BE GREATER THAN THE MINIMUM SLICE OF ENERGY POSSIBLE IN NORMAL SPACE-TIME SPREAD OVER TWO WAVE CYCLES. THERE IS NO PROVISION FOR ALLOWING A PROTON TO INFLATE TO 10,000 TIMES ITS SIZE.SIX: I don’t know how many times I have had to repeat this, the HUP only refers to wave functions, not ‘particles.’ Once a wave function is detected, it is no longer a wave function, and the HUP is non-sequitur. The proton is not a wave function. According to the Standard Model (We’ll go with that for a moment) it is a composite of we don’t know what. It has taken ‘particle physicists’ half a century of smashing them with a giant hammer to figure out that they don’t know what it is made of by looking at the broken pieces. The pieces, so far, weigh 100 times more than the thing before they smashed it with a hammer. So, they invoke the HUP to (Uncertainty Principle) claim the excess mass comes from the Uncertainty Principle, with a certainty out to about 15 decimal places… The spin of these invoked contents account for 2% of the proton’s spin. (Referred to a the ‘spin catastrophe.’)Now, we have someone claiming this composite region inflates to 10,000 to a million times it size, consistently, to explain the position of the electron; as absurd as the answer is, doesn’t answer the question, ‘why do electromagnetic things attract?’If we use the spin angular momentum of the electron, and the proton or positron, whatever, and think of it as a boomerang, I use this analogy:In Feynman terms, imagine a man in one boat and a woman in another. They have no means of propelling their boats, but happen they are supplied with boomerangs. How can they get their boats together? By throwing a boomerang away from the man, the woman would experience a reaction force from the boomerang towards the man. The boomerang could then circle round and approach the man from behind, and on reaching him, could exert a force on him towards the woman.In this diagram, the woman throws the boomerang (virtual photon, spin 1), which has spin +1/2, producing force Fv, the momentum of the throw also producing force F1. The man catches the boomerang, producing force F2. In this instance, there is an ‘attractive’ force, likened to the man being an electron and the woman being a positron. But why does the ‘force’ obey the inverse square law?We can generalize the electromagnetic force in terms of any constant, represented by k, two charges, and distance:And again, Heisenberg’s uncertainty principle, purely in terms of delta-E:In this case, delta-t is purely mediated by r^2, the distance.That is as close to a Feynman explanation as one would get, perhaps.A virtual photon is not massless, but is off mass shell, that is, possess mass. This is where we come to chirality and helicity. Helicity is a spinning massive particle, we’ll say counter clockwise. Because it has mass, it cannot go as fast as light, meaning thqat you can get in front of it and see it apparently spinning the opposite way, clockwise. Chirality refers to massless photons, which you cannot get in front of because you cannot exceed v=c to do so, so they only ‘spin’ in two polarization states, clockwise or counterclockwise.Because a virtual photon has mass, it is helic, not chiral, giving it 3 polarization states. The 3rd polarization state is observed by passing the slow moving virtual photon and watching it ‘spin’ apparently in the opposite direction.Its mass and 3rd polarization state account for the boomerang effect shown above. Note that in order for the boomerang argument to work, the arrow goes around and points the opposite way, as seen coming at you as opposed to the helic spin of when it was launched.I hope this over simplified explanation helps. As for the proton’s uncertain position as a wave function, you will note that the delta-t in the HUP equation above simply will not allow for a proton to extend as far as a valence electron. So, that is just wrong.In fact, as I look at this a few months later, I can tell you exactly how wrong it is. A virtual photon mediating a magnetic field can live exactly 3 wavelengths. That is a certainty; exactly three. This is referred to as a Near Field Effect. Radio antennas, for instance, produce a powerful magnetic field that does not drop off with the square of the distance. For instance, if your transmission is at 300 megahertz, then your wavelength is 1 meter. The magnetic field produced by the Near Field Photons is exactly uniform throughout a 3 meter domain from the antenna; then comes to a dead stop, like a brick wall.A proton has a diameter of 1 femtometer, 10^-15 meters. The first electron orbital is out at 10^-10 meters. That means Muller’s Uncertainty Principle explanation has to extend the proton diameter 5 orders of magnitude greater than it normal cross section. In order for that to happen, the delta-t has to decrease by 5 orders of magnitude, spontaneously. In this amount of time, if you do the algebra, you find that the massive virtual photon actually has to exceed the speed of light in order for there to be any prayer of that answer being in any way possible.The proton has a diameter of 10E-15 meters, a hydrogen atoms valence electron is 10E-10 meters, meaning the uncertainty principle would have to allow the photon to inflate to 10,000 times its diameter, for just the lowest ground state of hydrogen. When you take the virtual photon mass and spin angular momentum, that is impossible. The HUP will work no magic here. The argument via HUP might hold some, but very little, water if the virtual photon had no mass, but this is not the case.The uncertainty of the photon’s position is also equally outward as it is inward, that is, of what little uncertainty there is in a virtual photon’s position (because of its mass, reduces the uncertainty, such as the uncertainty of a battle ship’s position) it is not emitted unidirectionally away from the proton from the electron. This exacting vector must be exactly 180 degrees opposite the proton’s position to be true. Since it is the electron’s position that is uniquely uncertain, this requires the electron to have 1) a certain position and 2) foreknowledge of its vector toward the proton from where it will be when it emits the virtual photon, exactly 180 degrees away from the proton’s position and 3) a reason for emitting only photons 180 degrees away from the proton.Thinking inside the box and staying there because it feels safe when people agree with you is why we are living in the Holocene Extinction. If we thought for ourselves, the world would change; would already have done so.I’d like to thank Dmitry Popov for catching my typos, I was writing proton when I was thinking photon.I answered a similar question at When we say that spin-1/2 fermions must go through 720 degrees to equal the 360 degrees required by spin-1 bosons, what exactly is being measured?I found this in an old text I wrote some years ago:It is not possible to ignore the relativistic effect of velocity of recession. 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