The EPR Paper and Bells Theorem

Cushing, Chapter 22The EPR Paper and Bells TheoremMikey PilgerAlbert Einstein: Man or Ghost??

EPRAlbert Einstein (1879 1955)

Boris Podolsky (1896 1966)

Nathan Rosen (1909 1995)

Rosen died in our lifetimes perhaps the most contemporary of all the physicists weve studied.3Copenhagen Quantum Physics (CQP)A few tenets:The physical reality of a wave/particle system can be completely described by a wave function Uncertainty Relation Determining a definite measurement of one property of the system (e.g. momentum) limits our knowledge of other properties (e.g. position) to mere probabilitiesThe Copenhagen view was the prevailing understanding of quantum mechanics. The EPR paper was a response to the Copenhagen view.4Einstein on the Copenhagen ViewUncomfortable elements of CQP:No single, objective reality until we observe the system directlyThe observation renders merely probabilistic all information other than the element of the system directly observedTo Einstein, CQP seems more like a general statistical summary of the properties of systems than a complete theoryEPRs Plan of AttackThe EPR Paper is titled Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? (1935)EPR attempt to show that CQP is, if not illogical, then at least incompleteDescribing a Complete TheoryWhat is a complete theory?It must contain a formal element corresponding to every relevant phenomenon in the physical worldWhich criterion should we use to distinguish complete and incomplete theories?If an observer can use a theory to predict a physical quantity (e.g. momentum, position) without disturbing the system and without uncertainty, then he or she establishes the quantitys physical realityEPRs AssumptionsLocalityThere is no spooky action at a distanceRealismThe physical world really exists, and not just as a wave function, even when it is unobservedIntroductionImagine that a particle composed of two joined photons, at rest, decays into two physically separatde photons, A and B, which fly off in opposite directionsWave function can now describe the properties of both photons as members of a larger single systemFor example: the angular momenta of the photons must add up to zero, because they started from rest as one systemObserving the spin of photon A to be + instantly forces photon B to conform to a - spin Hidden VariablesEPR believe that rather than an instantaneous force working on particle B at a distance, there are hidden variables in the system which explain the particles behaviorThere was information latent in the particles before they separated, which later influences their behaviorHidden VariablesImagine a space traveler who takes one glove, out of a pair of gloves, with him on an interstellar voyage. He doesnt look at which glove he takes, and before he can check, he seals it in a box. He leaves the other (also unknown) glove with his brother. When he gets to Alpha Centauri, many light-years away, and opens the box to finally look at the glove for the first time, he suddenly knows whether he has taken the left or the right glove, and he knows that the glove he left with his brother is the opposite glove.The EPR Paradox: Thought ExperimentIf an element of reality exists, it has a definite valueWhen the two photons separate, observing the position of photon A gives a definite value to that part of wave function , and puts the system in eigenstate 1, which also determines a definite position for photon BSimultaneously, observe the momentum of photon B, and arrive at a definite value for the momenta of both photon A and BBut, the Heisenberg uncertainty relationship between position and momentum will not allow thisEither CQP is incomplete, or position and momentum cannot have simultaneous realityConclusions from EPRCQP is incomplete, because we will not sacrifice the definite reality of the properties of a system to save CQPInexplicable particle behavior is attributable to hidden variables(Locality is safe and it was never in trouble)Criticism of EPRDid EPR really understand the indeterminacy relationship between position and momentum?LocalityEPR strongly influenced the thinking of prominent physicists, though the paradox itself is wantingClassical notions of determinism and locality BOTH survive in the minds of some physicistsBells TheoremOn the Einstein, Rosen, Podolsky Paradox (1964)

Bells Theorem: SimplifiedFrom the work of N. David Mermin

The ParticlesThe central signal box sends one particle each to the detector boxesThis is intended to be the only transfer of information between the signal and detection boxesThe particles are equivalentE.g. two +1/2 spin particlesThe information conveyed is identicalAssume that the particles are programmed with instructions information that does not change between leaving the signal box and arriving at the detector boxSwitch SettingsBox A and Box B have three switches each (1, 2, and 3). For each round of the experiment, a switch on each box is randomly selected and engaged.

There are nine possible AB switch combinations. If Box A is set to switch 2, and Box B is set to switch 3, this is represented as 23.Switch1B2B3B1A1112132A2122233A313233Color Outputs(Information conveyed by particles)There should be at least a one-third chance that the lights will flash the same color after receiving their respective signal particles

CaseS1S2S3Same Color?1RRR1.0002RRG0.3333RGR0.3334RGG0.3335GGG1.0006GGR0.3337GRG0.3338GRR0.333Will the Light Color Match?Expected Results:Switch SettingCasexxx1112132122233132331RRR2RRG3RGR4RGG5GGG6GGR7GRG8GRRExpected ResultsSwitch SettingCasexxx1213212331322RRG3RGR4RGG6GGR7GRG8GRRExcluding Cases 1 and 5, which will always yield matching light flashesThe Competing PredictionsCQP: 25%

Classical physics: >33%

The WinnerCQP is right: the lights match only 25% of the time

Above: me, reading about this stuffHow, CQP?First, a description of the experiment as Bell described itThe particles emerging from the box are equivalent spin particlesDetector magnets are arranged at perpendicular to the vertical, or 120 from perpendicular to the vertical in the path of the particleThe orientation of the magnet depends on one of three switch positionsIf the magnets A and B have the same switch position, then they have the same magnet orientationHow, CQP?The detector indicates the particles orientation with respect to the fields orientation, and activates a green or red light accordinglyGreen = particle spin is along the fieldRed = particle spin is against the fieldIt is a well-known elementary result that, when the orientations of the magnets differ by angle , then the probability of spin measurements on each particle yielding opposite values is cos2(/2). This probability is unity when = 0 and when = 120 (Mermin 408).R.I.P. LocalityThe two particles seem to interact instantaneously when one or the other is observedThough the detection system is, effectively, the cause of this change in the particles, it does not interfere with the particles as they leave the box, though it does measure the spin of each before reaching the magnetNo hidden variable can explain the behavior of the experimental particles without sacrificing locality

(E)PR?I was very pleased with your detailed letter, which speaks about the little essay. For reasons of language, this was written by Podolsky after many discussions. But still it has not come out as well as I really wanted; on the contrary, the main point was, so to speak, buried by the erudition (Howard 175).

- Einsteins letter to Schrdinger, 19 June 1935

Competing Scientific PurposesHesinberg said:Einstein agreed . . . That the mathematical formulation of quantum mechanics, developed in Gttingen and consolidated further in Cambridge and Copenhagen, correctly described the phenomena within the atom. He may also have been willing to admit, for the time being at least, that the statistical interpretation of Schrdingers wave function, as formulated by Born, would have to be accepted as a working hypothesis . . .Competing Scientific Purposes. . . But Einstein did not want to acknowledge that quantum mechanics represented a final, and even less a complete, description of these phenomena. The conclusion that the world could be completely divided into an objective and a subjective sphere, and the hypothesis that one should be able to make precise statements about the objective side of it, formed a part of his basic philosophical attitude. But quantum mechanics could not satisfy these claims, and it does not seem likely that science will ever find its way back to Einsteins postulates (Cushing 320).Einstein: Realist, or Instrumentalist?The engineer of an unparalleled upheaval in physics, now defending a realist interpretation of the world against quantum revolutionariesDiscussWhy did Einstein propose his theory of relativity, but resist CPQ? Was it a mathematical, or an emotional or moral question?

What was the role of the larger scientific community in establishing the dominance of quantum theory, despite the leading mind in the worlds adamant opposition?Works CitedMermin, N. David. "Quantum Mysteries for Anyone." The Journal of Philosophy 78.7 (1981): 397-408. 27 Feb. 2007. Web. 20 Apr. 2013.

Howard, Don. "EINSTEIN ON LOCALITY AND SEPARABILITY." Studies in History and Philosophy of Science 16.3 (1985): 171-201. Print