Solved? Problems My God, He Plays Dice! My Plays He God, 364 Chapter 45 Problems Solved? changes (quantum jumps) internal levels, between are energy radiation, e.g., emission of aphoton during collision, the or to reconcile macroscopic entropy with microscopic reversibility. reversing would time the it decrease again.. Thusthe puzzle, how random collisions could increase macroscopic the entropy, but deterministic, classical world. Ludwig Boltzmann showed that entropy, nor more importantly information, can increase ina are reversible, time entropy conserving and information. Neither Microscopic Irreversibility characteristics normally associated with quantum. the we hope that you find most themvisualizable of and intuitive, not of confusion and mystery surrounding quantum mechanics, but reality,” might to lead plausible solutions. analysis of Einstein’s of his idea an especially “ thinking, Solution: Problem proposedOur solutions are radical 13. 12. 11. 10. 9. 8. 7. 6. 5. 4. 3. 2. 1. In problems preface the thirteen we posed for adeep which Is universe the deterministic or indeterministic? between relativityConflict and quantum mechanics? “ No Schrödinger’s Cat and -dead Entanglement and “spooky” action-at-a-distance (1935) The role of a“ measurementThe problem (1930) “oneThe mystery” of two-slit the experiment Nonlocality and “action-at-a-distance” (1927) The metaphysical question of ontological chance (1916) Wave and “duality” particle (1909) Nonlocality, firstseen by Einstein in1905 The 19th-century problem of microscopic irreversibility : In classical mechanics, microscopic collisions particle hidden variables,” but hiddenconstants (1952) Reversibility fails any when matter interacts with conscious (1930) observer” alive? (1936) , ifonly compared to decades Problems Solved? objective 365

Chapter 45 reversibility reversibility recurrence objection is also is objection recurrence Josef Loschmid t’sJosef of change in spatially separated places. Nothing Nothing places. separated in spatially change of As Einstein noted in 1909, emission processes are are processes emission in 1909, noted Einstein As : the Schrödinger to solutions are : Probabilities : When a light wave, possibly carrying energy, spreads spreads carrying possibly energy, wave, a light : When : It took Einstein some years to see that the light wave wave the light see to that years some Einstein took : It ontological chance as discovered by Einstein in 1916. in Einstein by discovered as chance ontological appearance My God, He Plays Dice! My Plays He God, Problem Solution Comment Comment Wave-Particle Duality Wave-Particle Nonlocality not “invertible.” There are outgoing spherical waves, but incoming incoming but spherical waves, outgoing are There “invertible.” not seen. never are waves spherical energy be collected that suddenly can how in all directions, out in the photoelectric ejectto electron an point one at together the of “collapse” this instantaneous feared Einstein 1909 effect? In special his of theory relativity? of a violation was wave light quanta light his finding of the probability abstract just really is find- of the think probability particles. can One of material or as actually found is it where than other a particle somewhere ing a “collapse.” of the appearance which gives zero, to going suddenly is information abstract even or energy, case matter, no any In only is Nonlocality somewhere. when a particle found is moving the the of the boundary determined by conditions equation, particles. Probabilities incoming of the wavelength and experiment particle is when one change particles in the space do not other for 23. 6, 9, and Seedetected. chapters taken into account. Any quantum process with such transitions transitions such with process quantum Any account. taken into involves in the energy changes random introduces light with Interaction all both particle particles. motions If or either of momentum and energy the same with a photon of the absorption becould reversed, impossible, not is moment the correct at direction in the opposite very occur. statistically to unlikely but moving. is real objectively Ernst Zermelo Ernst ’s removed. is paradox states entropy low original, of because the recurrence eliminated is environment The the universe. of the expansion by prevented is 12. 11 and See chapters different. always 366 Chapter 45 accord with causal laws.“ lawsthe of probability, but probability the itself propagates in states indeterministically. deterministically. Particles are discrete might found. particle the be Continuous motionthe of particle. It the is only estimate best the of where quantumspecific state. provide probabilities for inagiven finding particles place and ina Schrödinger equation, with continuous ferent quantum statistics! - fermions and bosons. Twenty years later, he discovered dif- their twothe families of “standard inthe elementary particles model” matter and particles hypothesized light prototypes the particles, of or energy. It was Einstein proved in 1905who existence the of onethe mystery deep of quantum mechanics. waves have astatistical power over location the of that particles is that allow us to calculate probabilities for finding particles. These as imaginary, mathematical fictions, “ghostly” and “guiding” fields, orparticles, perhaps at both same the time? quantumdescribe as objects sometimes waves and sometimes ticles. Einstein’s light quanta (photons) are mediating the par material are particles mediated by exchange the of par energy therethen is only one possible future. togetherparticles with natural the force laws of classical physics, controlled completely by distribution the and motions of other all Ontological Chance See chapterSee 9. Particles are physics. Waves, and fields, are metaphysics. As Waves, or wave functions, are mathematical solutions to the Particles are discrete Solution Problem: Solution Problem: collision material If between is particles every Comment Max Born Max : Particles are real Einstein objects. was first wavessee to : In physics, modern interactions all between Popular interpretations of quantum mechanics : The evolution time of wave the is function not described it “The motion it “The of follows particle described the discontinuous quanta localized of matter and change quantum their values in all space, values which inall wave functions evolve Problems Solved? - - 367

Chapter 45 free creations of the of freecreations . objective reality,” without any interactions interactions any without reality,” objective magnetic radiation. In 1916, Einstein showed that that showed Einstein 1916, In radiation. magnetic from the start of the experiment as what we called we what as the experiment the start of from : The emergence of classical laws and apparent apparent and laws classical of emergence : The : There was no “action” by either particle on the other the other particle on either by “action” no was : There : Einstein’s 1927 presentation at the fifth Solvay conference conference the fifthSolvay at 1927 presentation : Einstein’s : Einstein’s blackboard drawing shows us that the that us shows drawing blackboard : Einstein’s free choice” of the experimenter, and “ and the experimenter, of freechoice” locally quantum-to-classical transition” occurs when the mass of occurs of when the mass transition” quantum-to-classical My God, He Plays Dice! My Plays He God, Comment “ The Comment Solution “ idea of Einstein’s Using Problem correspondence principle” claims classicality also occurs classicality when claims principle” correspondence human mind.” mind.” human large. are numbers quantum h, so the constant Planck’s to compared very object m is an large 11. 1 and very Δv Δx ≥ h / m is uncertainty small. See chapters deterministic causality occurs whenever the number of particles of occurs the whenever number causality deterministic Bohr’s over. becan averaged randomness so quantum large grows “ Two-Slit Experiment Two-Slit in this case, so we call it “knowledge-at-a-distance.” See chapters 9, See chapters thisin case, “knowledge-at-a-distance.” call so we it 23. 17, 18, and “hidden constants” of the motion. of “hidden constants” electron’s wave function propagates in all directions, but when the but in all directions, function propagates wave electron’s point. a single at found is it all of particle appears, traveled have the particle must the momentum, change could that The found. is it where the point the to origin from line in a straight have in 1927 could Einstein by the particle considered of properties evolved Nonlocality and Action-at-a-Distance was his first public description of an issue that had bothered him had bothered that issue an of description public first his was in a spacelike places two at events saw he thought 1905. He since special theory His relativity of simultaneously. happening separation the impossibility of show simultaneity to claims ticles for electro for ticles these energy particle exchanges always involve chance. Quantum Quantum chance. involve always these energyparticle exchanges free needed for the possibilities opening statistical, is mechanics will,the “ 368 Chapter 45 the non-unitary,the discontinuous deterministic evolution time of Schrödinger the equation versus distinct (indeed, opposing) processes, unitary, the continuous Measurement Problem chapteropen. See 33. one slit reacting to probabilities that are on two based slits being remaining mystery inquantum mechanics. abstract probabilities particles’ influencethe motions is one the wave said canto function be “know” holes which are open. How minimum for least action, thus resulting the probability amplitude “sum space(the all over paths”) determine variational the as they mechanics suggests same the solution. His particles” “virtual explore are different two when slits are open, explaining interference. through only one slit. Probability amplitudes of wave the function “objective reality,’ its all properties conserves particle and the goes wavelength -are different for of case the one slit open. In Einstein’s for conditions given the boundary -two open slits, screen, particle move through slits both inorder to “interfere with itself.” patterns slits both when are open, suggesting that must aparticle screen at atime, large numbers of experiments show interference irreversible makes ameasurement. Measurement requires recording the of appears bothers (which time particle critics), the the somewhere. to time-dependent the Schrödinger equation. Then, at an unknown system evolves as aprobability amplitude wave according function involving two processes, these but one after other. the First, the alone.function There are say. they no particles, Schrödinger agreed. convinced that quantum mechanics on should wave the based be wavethe function.” Decoherence theorists and many-worlders are Problem mechanicsBohmian defends also that aparticle through goes Comment Solution Problem The oftime collapse may simply moment the be an experimenter Solution : Solutions to time-independent the Schrödinger equation : We of can evolution time think the of asystem as : : In experiments where travels a single particle to the information about location the of particle, as the von John : Feynman’s path integral formulation of quantum von Neumann saw alogical , and indeterministic “ Problems Solved? problem with two collapse of , and 369

Chapter 45 ) Schnitt before any any before cut” ( appears in David in David appears from their original values their original values from . See chapter 25. . See chapter : We might say that information becomes known known becomes information that say might : We : This problem shows why we need to get “beyond logic” logic” “beyond get need to we why shows problem : This : In his 1935 EPR paper, Einstein discussed particles two Einstein paper, 1935 EPR his : In Copenhagen Interpretation and many of its its of many and Copenhagen Interpretation : The : Information must be recorded irreversibly be recorded must : Information by state its in stays one each apart, travel the electrons As : My God, He Plays Dice! My Plays He God, Problem Solution Comment Solution Problem Comment Entanglement and “Spooky” Action-at-a-Distance “Spooky” and Entanglement to used principles conservation He the center. from away traveling the other about information particle gives one measuring that show particles’ the two shown have We directly. it measuring without locally evolved have could properties between the experiment and the mind? the mind? between and the experiment recorded Data a measurement. of observer the results know can new information creates instrument measuring a by (ontologically) structure information newly created so does any But in the universe. to reality objective wanted Einstein observer. an without in nature a are that measurements are there observers, of but be independent reality. a new part of creating the experimenter, of choice” “free as long as apart, the particles are far how matter no the center at and theirvalues altered has the environment with interaction no a true nonlocality But their “coherence.” destroyed spin in which electron experiment, the EPR 1952 version Bohm’s momenta. linear of instead measured are components conserved. are momenta linear and spins Their laws. conservation total p. The is other -p. The say is particle electron left-moving The (epistemological) when it is recorded in the world and then seen by then seen and by in the world recorded is whenit (epistemological) ontological, is created new information most But observer. a human observing is the universe itself Eugene Eugene Neumann, von John Heisenberg, Werner e.g., supporters, reaches it until complete not a measurement considered Wigner, the “ is where They asked the observer. of the mind in the philosophy of science. of in the philosophy ObserverConscious conscious a conscious beto of in the mind have does not It knew. Neumann observer. 370 Chapter 45 which endswhich up with either alive or cat. dead statistics alive. The predicted probabilities mechanics gives us are only and alive. What superposition the of possible states inquantum probabilities. There is never an individual probabilities for asystem indifferent to be states have violated. been would have happened. and conservation Symmetry laws would correlated directions. But not, had they something evenworse of two-particle wave the anywhere, function come out inperfectly how spatial the directions of two the spins, created by ameasurement opposite value. measuresthen at same the angle, correlated he gets perfectly the by her measurement into spin components, say z+and z-.If Bob from origin. The the directionless tion. Thenow particles appear in a spacelike separation equidistant surement decoheres and disentangles two-particle wave the - func waswhich not present at entanglement. original the Alice’s- mea spinthe (or polarization) component, she information adds new definite spatial direction. process of entanglement has not electron the left spins with a electron is spin other ℏ/2,the opposite. is exactly But original the linear momentum is zero. Similarly total their spin is zero. If one consequence of Paul Dirac’s he was what criticizing, really ridiculing, he thought was an absurd macroscopic cat inasimilar superposition. When he suggested it, in asuperposition of decayed and undecayed state, leading to a of his equation could with start amicroscopic nucleus radioactive Schrödinger’s Cat Solution Comments: It of is mystery part deep of the quantum mechanics When her “ uses Alice Problem inlarge numbers of identical experiments, each one of : Schrödinger was just criticizing superposition and its : Erwin Schrödinger imagined that evolution time the : Erwin free choice”free of angle which to measure probabilities principle of superposition, superposition, of principle are empirically by confirmed the and opposite spins are projected for cat the dead being cat simultaneously dead Problems Solved? with its or or 371

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- by by from Hidden Constants aspect is that these spin components have have components these aspect spin that is of a decay or remaining undecayed. Once there there Once undecayed. remaining or a decay of spooky” action-at-a-distance. Our hidden constants Our hidden constants spooky” action-at-a-distance. suggested that “hidden variables” “hidden variables” Bohm that suggested David : The individual radioactive nucleus is never in a super never is radioactive nucleus individual : The : The two spin components, say z+ and z-, are Alice’s Alice’s z-, are z+ and say components, spin two : The : : In our adaptation of Einstein’s “objective reality,” the reality,” “objective Einstein’s of adaptation our : In projections of the opposing spins that traveled locally traveled that spins the opposing of projections My God, He Plays Dice! My Plays He God, Problem Solution can we be Bohmian not “hidden variables,” might there While Comment Comment locally travel that the electrons of spins if the opposing Of course position of decayed and not decayed. Quantum mechanics gives gives mechanics Quantum decayed. not and decayed of position the probabilitiesus is a decay, the evolution results in a dead cat. If no decay, then a decay, no If in a dead cat. results the evolution a decay, is not cats of superpositions do macroscopic only not Indeed, cat. live are There in a superposition. not is the radioactive nucleus exist, microscopic no are because there superpositions macroscopic no either. superpositions Hidden Variables,” but No “Hidden Variables,” between information communicate instantaneously could great at theirproperties perfectly particles to correlate entangled a of spins -1/2 electron +1/2 and specificallydistances, the opposite zero. spin total with system two-electron momenta, properties, individual with generated particles are they conserve and until these properties spins, momenta, angular “locally” carried with along are These properties measured. they are feared. Einstein as special relativity violate the particles, so do not of (“constants “hidden constants” call these conserved quantities the appearance They explain sight). hidden in plain the motion,” of Einstein’s “ Einstein’s of the explain they cannot but results, the original EPR explain can created which are components, spin electron of measurements measurement. Alice’s nonlocal the The origin. be to about they even though are directions perfectly opposing collapsed function has the wave two-particle once separated, greatly functions. single-particle wave two of the product into when perfectly anti-correlated remain the did not origin from nonlocal 372 Chapter 45 Is theUniverse orIndeterministic? Deterministic violation of conservation the laws. measured and projected into direction, that aspecific would a be have same the physical dimensions as angular momentum J. E =hν,we have of expressions ΔEΔt=ΔpΔxΔJΔφh. All these Heisenberg. no reference to measurements as “disturbances,” and embarrassing showed thatΔνΔt=1,thus deriving uncertainty the principle with ΔpΔx = h. In Bohr’s obscure Como lecture of 1927,he otherwise operator matrices, and in1927 his resulting uncertainty principle in 1925,it was non-commutation the of momentum and position number of wavelengths fits around an electron orbit. For Heisenberg 1924 it was that linear the momentum p=h/λand that an integer orbits,their as suggested by J.W.Nicholson. For Louis deBroglie in for existence the of discrete objects. What IsQuantized? nonlocal paid little attention to his concerns, had which turned entirely to the quantum mechanics by some around time 1930.But his colleagues chapters 30,31,32,and 34. “interpretations” of quantum mechanics are deterministic. See he insisted that “God not does play dice.” Many of alternative the physics, chance he called a“weakness theory.” inthe And many times theory. When in1916 he discovered randomness the inquantum for hoping quantum physics found could be adeterministic to be universe and Einstein’s “ Multiplying Multiplying For in1913,it was Bohr angular the momentum of electrons in “ The Solution: Problem Comment: quantum condition” underlying the reason deep describes aspects of quantum aspects mechanics. : Einstein was well inhis known, younger especially years, Einstein accepted had fully indeterministic the nature of Without indeterminism, we could not have acreative ΔνΔt =1by Max Planck’s constant h,and noting free creationsfree of human the mind.” Problems Solved? 373

Chapter 45 on another another on , which first appeared in 1900, 1900, in appeared whichfirst h, Planck’s quantum of action action of quantum Planck’s , all take on continuous values. It is the angular the angular is It values. time continuous t, all take on E, and “one mystery” of quantum mechanics is how probability probability how is mechanics quantum of mystery” “one measurement problem is explained as when new information when as new information explained is problem measurement My God, He Plays Dice! My Plays He God, Particles are real physics. Waves are imaginary. Fields are are Fields imaginary. are Waves physics. real are Particles happens. ever nothing it, Without exists. chance Ontological actualized. is when a possibility “collapses” physically Nothing The The leaves soon as one separate Particles nonseparability. no is There no microscopic reversibility. microscopic no is There acting event one of in the form nonlocality no is There action, or angular angular or action, always is Erwin it As explained, Schrödinger one least at involves matter and radiation of interaction Any in a spacelike separation. There are simultaneous synchronized synchronized simultaneous are There separation. spacelike a in his violated feared which Einstein separation, in a spacelike events They do not. special theory relativity. of metaphysics. produce particlesto of motions thestatistical control waves effects. interference their perfect particles retain entangled two But cone. light the other’s until laws, the conservation by required as properties of correlation decoheres. and in the environment something with interacts one the particles still of begins the properties with A measurement The disentanglement. and decorrelation with ends It correlated. into function separates the wave two-particle of power mysterious also direction spin their new with single-particle spatial functions direction the component particular spin But perfectly correlated. be can viewed as the It origin. at known Alice not was by chosen entropy Local entropy apparatus. in the measurement recorded irreducibly is increases. Global entropy reduced. is The Bottom Line Bottom The though only as a heuristic mathematical device, not the radical device, not mathematical a heuristic as only though so like Einstein, seen was by first That new a physics. idea of core the before long saw he concepts mechanical the quantum of many methods. calculation their developed powerful quantum “founders” , position x, p, position . Momentum quantized is being that momentum, energy h. of multiples in integer comes J that spin or momentum of unit 374 Chapter 45 opens classical for withobjects large mass. And it is never inasuperposition, never intwo places at same the time. nuclearthe decay This has is justoccurred. as individual areobjects or energy matter. carrying had been mechanics, though there would have probability ifthe been waves “knowledge-at-a-distance.” lated. There is no “action” by one on particle other. the It is simply measured at separation and found to remain corre perfectly - communication or interaction entangled when are particles spacelike separation. informationnew appearing nonlocally, i.e. simultaneously ina in today’s “ hypothesis that comes light also indiscrete energy quanta hν. awarded Nobel the Prize, should taught be as revolutionary the hypothesis of atoms. of quanta. He thought he had proved Boltzmann’s controversial first proofthat matter is not continuous, but discrete. It consists toand teach especially teachers of quantum mechanics must change way the discuss they How to Restore Credit to Einstein his often colleagues, who the creditget that belongs to him. mysterious truly the seeing of quantum aspects physics well before quantum mechanics, much so of he which discovered or created. for Einstein’s “free creations of human the mind.” There is one world. It is aquantum world. The world appears Schrödinger’s cat always found will be as alive, dead,or dying if relativityThere special between is no conflict and quantum “Spooky action-at-a-distance” is just appearance the In two 1905papers, these Einsteinthe was first the elementssee to His paper explaining “ the His paper explaining Brownian motion should taught be as the To correct problem, this historians of physics and especially His many criticisms and objections didnot prevent himfrom Einstein’s “ alternative possibilities alternative standard model” of physics particle fermions -the objective reality” can explain world the with standard Einstein’s contributions to physics. for an open, free, and creative future, photoelectric effect,” forwhich he was indeterministic, which Problems Solved? of of

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Compton exist and at all times at and exist of finding a discrete particle. Quantum mechanics mechanics Quantum particle. a discrete finding of ! My God, He Plays Dice! My Plays He God, His third paper in 1905, explaining relativity, should not not should relativity, explaining 1905, in paper third His of certain specificheat the anomalous explaining 1907 paper His be should duality wave-particle explaining 1909 paper Einstein’s His 1916 paper on transition probabilities between energy levels, probabilities transition on 1916 paper His the “ of 1923 explanation Compton’s Holly Arthur multiple at simultaneously appear or cease exist, to don’t Particles very simple Bose’s Nath based Satyendra 1925 papers on Einstein’s overshadow his quantization of matter and energy and his fourth fourth his energy and and matter of quantization his overshadow 2. - E = mc their interchangeability showing year, that paper and energy the discovery as in atoms levels of be taught should atoms quantum Bohr’s Niels before between them, six years the “jumps” energy in the atom. levels between postulated his jumps function giving ψ) the wave later (and wave the continuous as taught the probabilityus is statistical (matter) and the bosons (energy). For this work alone, Einstein Einstein alone, this work (energy). the bosons For and (matter) mechanics quantum be seen of should the true as founder which discovered the stimulated emission of radiation behind radiation of emission the stimulated whichdiscovered chance ontological the discovery as of be taught lasers, should today’s interactions The interact. radiation and matter whenever in nature action h. They introduce of quantum one least at involve always Heisenberg’s Werner indeterminacy a decade and before statistics principle. uncertainty of particles predictionthat 1916 Einstein’s confirmed which effect,” Einstein’s as be taught should energy, as well as momentum have light motions the so that principles, conservation in deepconfidence particles objectively quantum of paths and energy. and momentum for obeying those laws conservation are Niels invalidate to used had principles these fundamental Einstein in hypothesis quantum light Einstein’s to deny attempt final Bohr’s be should taught work This paper. 1924, in the Bohr-Kramers-Slater reality.” “objective belief in an Einstein’s the for basis as quantum of the Copenhagen Interpretation by claimed as places, does paths measure continuously can’t because we Just mechanics. observe we until them. exist particles do not that mean not as be taught in 1924, should law the Planck of derivation quantum 376 Chapter 45 discovery ofdiscovery nonseparability and entanglement. can acquire correlated perfectly properties instantaneously, his EPR paper, he when showed that twoagreat particles distance apart passing through aslit should taught be of as beginning the his 1935 conference of 1927showing nonlocal the “fermions”and unit-spin “bosons.” and consequent their strange and different statistics for half-spin Einstein’s of discovery indistinguishability the 1 “ether,”the the “pressing;” attempts failed the motion to the detect through of Earth Arthur cited I. Miller three problems he thought Poincaré felt were just one yeartranslated afterbeen book had his intoGerman. 1905 Einstein solved three great problems by Poincaré, described Henri Poincare’s Science La et l’Hypothèse. Mill, Ernst Mach, and Karl Pearson. weeks were Several spent on read great the and discussed works of David Hume, John Stuart evening of meal sausage,frugal honey, cheese, fruits, and tea,they and physics.themselves thecalled Olympia They Academy. After a metcolleagues who frequently inphilosophy ideas to new discuss was inspired by Henri Poincaré’s great Science book and Hypothesis. between readingbetween Poincaré in1904and his death fivelater. decades problems, these with all afew unsuccessfully but always creatively, “knowledge-at-a-distance.” realize that in quantum mechanics what Einstein discovered is only or of of relativity, but one-way the also increase of entropy with its problem moreseveral problems to Einstein, most importantly principle the of reading of Poincaré’s shows book that great suggested thinker Einstein’s misunderstood and ignored presentation at Solvay the Recently afew scholars have shown that inhis “miracle year” of Many of Einstein’s biographers have young the described Einstein’s Some historians of have science pointed out how much Einstein Poincaré andEinstein We hope to have shown that far-seeing the Einstein grappled irreversibility, indeterminism, and amazingly “ Miller, 2002, p.185. Rigden 2005,p.8, Holt, 2018,p.5 photoelectric effect, photoelectric effect, and Maxwell’s demon, question the of determinism action-at-a-distance.” We now behavior inasingle particle Brownian motion. of elementary particles Problems Solved? 1 A close A close 377

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