Quantum Philosophy

1. Quantum Philosophy EPR and Bell's Inequalities By Bill Kavanagh M.Sc Candidate MUN Physics, Cosmology www.physics.mun.ca/~wkavanag

2. Introduction • Philosophy of Science • Causality and SR/GR • What is Quantum? • EPR (The clash with Relativity and Quantum and Einstein's problem etc.) • Bell's Inequality • Back to Realism & Objective reality???

3. Philosophy of Physics (or Science) • Physics ultimately tries to explain • What are the constituents of the world? • Entities (electrons, atoms) • First principles (causality) • This actually represents the two fields of • Relativity • Quantum

4. Classical Physics • Before physics was broken into Quantum and Relativity there was just Classical physics • It describes macroscopic objects. • Astronomy • Mechanics (Galileo) • Newton Laws of Motion • The birth of electromagnetism; the study of light sparked a change in thinking. • This lead to a “fracture” of physics and philosophy[Omnes].

5. Relativity • It was Einstein who discovered light didn't need a medium in which to propagate • This lead to the postulate of relativity; • No object can move faster than the speed of light. • Incredibly this leads to the fact that measurements of time and distance are relative to the observer and her velocity.(Essence of Relativity) • This postulate also leads to Causality or Locality

7. Quantum • Quantum physics describes the world of the small. • Introduced by Planck to describe the energy in light (radiation) as being made up of quanta or photons. • Such quantum particles can only be described by their probabilities since their motions are random. • Wave function describes the state of a particle (or system of particles). It gives the probability of a particle to be in a given state. (i.e. position and time)

8. Fundamentals of Quantum • A particle can be in a Superposition of states. • Heisenberg's Uncertainty Principle • We can not determine exactly both the position and momentum of a particle.(Heisneberg's Microscope) • Particles like photons and electrons exhibit wave-particle duality as seen in the Double Slit Experiment

9. Double Slit Experiment

10. Formulation of Quantum Mechanics • Related to the uncertainty principle is the fact that... • one can not describe light as being a particle and a wave at the same time as illustrated by the Principle of Complementarity.[Omnes] • The Copenhagen Interpretation distinguishes between what is observed and what is not observed. • There is a distinction between the superposition of states that exist before a detection is made. • Collapse of the wave function is a term that represents detection in the Copenhagen Interpretation

11. Quantum Clash with Relativity • This clash was apparent through some experiments that seemed to violate causality like the double slit experiment. • Einstein didn't consider this clash. He was of the belief that Quantum mechanics was in some way incomplete. • On probabilities - “God does not play dice” • On non-locality - “Spooky action at a distance” • Einstein wrote a paper to prove Quantum's incompleteness

12. EPREinstein, Podolsky, and Rosen • Reality- as “If, without in any way disturbing a system, we can predict with certainty (100% probability) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.” • EPR started with the premise that operators corresponding to two physical quantities (say A and B) don't commute leads to a problem. • A and B represent momentum and position respectively (uncertainty principle) this means knowing the momentum of the particle means its coordinate has no physical reality.

13. EPREinstein, Podolsky, and Rosen • Two Possibilities • (I) Quantum mechanics is incomplete. • (II) When operators corresponding to two physical quantities do not commute the two quantities have simultaneous reality. • EPR then proceeds on the assumption that a wave function does contain a complete description of physical reality. • The physics of the thought experiment then involves two particles (called systems) which interact and then separate

14. EPREinstein, Podolsky, and Rosen • The result using relatively simple quantum mechanics is “it is possible to assign two different wave functions to the same reality” • Without getting into the QM, this can be reasoned. • Imagine two particles that decay from a single particle and go off in opposite directions with equal and opposite momenta p1=p2

15. EPR ConclusionEinstein, Podolsky, and Rosen • The negation of (I) leads to the negation of (II), which is the only alternative. • Thus premise (I) must be true. • A summary of the logic is as follows either (I) or (II) If not-(I) then not-(II) (I) • EPR concludes that the quantum-mechanical description of physical reality given by wave functions is not complete.

16. Bell's Inequality • Bell recognized that EPR were actually correct. • However, one of the assumptions Einstein made (a reasonable assumption at the time) distorted the conclusion. • Using the assumption of causality actually meant that the true conclusion of EPR was that Quantum Mechanics is incomplete or locality is violated.

17. Bell's Inequality First Assume: Num(A, not B, C) + Num(not A, B, not C)  0 Adding Num(A, not B, not C) + Num(A, B, not C) LHS: Num(A, not B, C) + Num(A, not B, not C) + Num(not A, B, not C) + Num(A, B, not C) LHS: Number(A, not B) + Number(B, not C) RHS: 0 + Num(A, not B, not C) + Num(A, B, not C) RHS: Num(A, not C)  Num(A, not B) + Num(B, not C)  Num(A, not C)

18. Testing Bell's Inequality • In order to test Bell's Theorem we need an experiment that mimics quantum particles. • A Gedanken (thought) experiment can be used that is free of quantum complexity. • One such experiment consists of two detectors, A and B, and a source C. (Mermin) • The mechanics of how the setup works will come later. • Each detector has a switch with three positions. • Depending on the setting of the switch an “event” will result in a Green (G) or Red (R) light coming on.

19. The Experiment • There are no connections between detectors • There is a randomness in the setting of the switches • The procedure mimics a quantum world.

20. Procedure • Switches are randomly selected • Button is pushed on source (...to release particles. Note: ignore for now... the details will follow). • Consequently each detector flashes red or green. • Data: pair of colors and switch settings i.e. “32RG”

21. Features of Data • Feature 1: • Looking at runs where switches have the same setting results in the lights on respective detectors are always the same • Feature 2: • Looking at all runs; flashing of lights is entirely random. • The lights flash the same ½ of the time • Lights are different ½ of the time

22. How does it Work? • The flashing of the lights is linked to pressing the button. • How can each light know to flash the same color in the event that the switches have the same setting? • Detectors can't be preprogrammed to flash the same color because ½ the time they are different. • The answer is in the particles. • The detectors can have targets in side.

23. First Feature • The first feature of the data is accounted for if the particles produced at the source are of the same variety. “Fearture 1: • Looking at runs where switches have the same setting results in the lights on respective detectors are always the same”

24. Information Sets • For this explanation of the experiment to work the particle should carry with it a set of instructions for how it is to flash on each setting. • 1.Instructions for each of 3 settings is required • For the case of flashing the same color particles will not know if the setting's are 11, 22, 33. • 2.The absence of communication means instruction sets must be carried in every trial. • Even when switches aren't at the same setting the particles always have to be ready for that case

25. Impossible Experiment • We will see: This experiment, nor any other, can satisfy the second feature of the data. “Feature 2: • Looking at all runs; flashing of lights is entirely random. • The lights flash the same ½ of the time • Lights are different ½ of the time”

26. Information Sets in this Experiment • If instruction sets exist then consider the event of instruction set RRG same color flashes: 11, 22, 33, 12, 21 different color flashes: 13, 31, 23, 32 • Each of these possibilities is equal in probability because the settings are random. • Chances of same color flashes is 5/9, as well as for other similar sets. • RRR and GGG result in same color all the time.

27. Bell's Inequality Violated! • If instruction sets exist the same colors will flash at least 5/9 times. (Bell's Inequality) • The actual gedanken experiment results in, as already illustrated, the same colors flashing in ½ the trials. • Also there can be no instruction sets. • This experiment represents quantum mechanisms that display the same violation of Bell's Inequality.

28. Quantum Spin

29. Stern-Gerlach Experiment • Putting all the magnets in a box makes a spin filter. • The orientation defines the direction up or down for the spin.

30. Application of Bell’s Inequality A: electrons are "spin-up" for zero degrees. B: electrons are "spin-up" for 45 degrees. C: electrons are "spin-up" for 90 degrees. Num( 0°, not  45°) + Num( 45°, not  90°)  Number( 0°, not  90°) • Experiment was done in 1969. • Inequality was violated!

31. Meaning? • We can look at the example of a particle in our experiment by forcing a particle to arrive at A before B. • If we detect it's 3-color(color when switch is 3) at B we know the other particle will have the same color at A. • Did the particle at A have its 3-color prior to the measurement at B? • NO. Prior to the measurement at B the detector can still decide to detect the 1 or 2-color.

32. Meaning? • Thus, if the 3-color already existed then so must 1- and 2-colors. • But we have already illustrated that there are no information sets. • Is the particle at A 3-colored after the measurement at B. • Yes. It is a particle that will cause A to flash the same color. • This suggest that something may transmitted between the two; non-locally

33. Conclusions • The failure of Bell's Inequality means that Einstein's insistence on the realism and locality was not right. • In the quantum world we have seen that things don't have a value unless we detect them.

34. Is the Moon There When Nobody Looks? • No

35. Bibliography • Omnes, Roland Quantum Philosophy. Princeton University Press, Princeton, New Jersey, 1999. • Aczel, A. D. Entanglement The Greatest Mystery in Physics. John Wiley and Sons Ltd, 2002 • Harrison, David M.., Physics Virtual Bookshelf Upscale, 2000, http://www.upscale.utoronto.ca/GeneralInterest/QM.html