Bell s Theorem 1964 Local realism is in conflict with quantum mechanics

Transcription

1 Bell s Theorem 1964 Local realism is in conflict with quantum mechanics the most profound discovery in science in the last half of the twentieth century. For a technical presentation search Youtube.com Alain Aspect. From Bell's Inequalities to Entangled Qubits: A New Quantum Age? John Bell Presented to North York Physics Meetup 2011 by Victor P.

2 Background Classical vs. Quantum Classical Newtonian: An object stays in its state, until directly affected by another object. Objects exist independent of observation (Reality) Full determinism - no free will Classical Relativity: Information/interactions between objects cannot be exchanged faster than the speed of light (a contact force is required). Causality is c-speed localized (Separability). No action-at-a-distance spooky stuff Quantum: Observation creates real things (No reality) Objects do not exist separate from each other (No Separability) Non-locality permits THE POSSIBILITY OF free will! Probabilistic/random God [or we] rolls the dice

3 Even shooting one photon at a time, an interference pattern appears.

4 The Double Slit Experiment Enigma How can a particle act like a wave? The wave function allows a particle (a photon, electron, atom, virus,...) to tryout all available paths and also interfere with itself. The particle didn t exist at any particular place. This is the superposition aspect of the wave function. The double slit experiment is not the only demonstration of superposition: The wavefunction of a several thousand atom Bose-Einstein condensate is spread over several millimeters (3600 atoms in two places at once). An observer decoheres a particle s wave function. When decohered to the point of collapse of the wavefunction, the particle is made real. No interference pattern The particle s past/path is defined at the point of collapse (observation). Do we cause its past backward in time? John Wheeler: Somewhere something incredible is waiting to happen.

5 If we were superpositioned photons

6 Unreal particles In the experiments about atomic events we have to do with things and facts, the phenomena that are just as real as any phenomena in daily life. But the atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts. Werner Heisenberg atomic-scale objects exist only in some abstract realm, not in the physical world.

7 hc λ = E Measurement Dilemma h p= λ A smaller λ is needed to probe smaller (more localized) particles (increased position resolution) A smaller λ has greater energy, which affects the observable more (decreased momentum resolution) Conversely, measuring with a large λ photon gives high momentum but poor spatial resolution. The Heisenberg microscope Heisenberg easily calculated that photons with short enough wavelength would kick atoms hard enough to smear any interference pattern. Thus, if you saw each atom come from a single box, you could not also see an interference pattern showing that each atom had been in both boxes. Heisenberg uncertainty principle : The more accurately you measure an object s position, the more uncertain you will be about its momentum (velocity, mass or both).

8 Complete states needed by classical physics for full predictive/deterministic calculations... The idea that if an all-seeing eye knew the position and velocity of every object in the universe at one moment, the entire future could be predicted with certainty. We cannot know two conjugate variables to arbitrary precision at the same time. There must be an uncertainty in our measurement. h x p i.e. 2 Complementarity is the idea that classical concepts such as space-time location and energy-momentum, which in classical physics were always combined into a single picture, cannot be so combined in quantum mechanics.

9 Extending the wave function into the macroscopic world: The cat in the box Geiger counter is also neither fired nor unfired Observation, opening the box a week later not only collapses but also creates the week s history of the alive or dead cat! Erwin Schrodinger "no phenomenon is a phenomenon until it is an observed phenomenon" Niels Bohr.

10 When I hear about Schrödinger s cat, I reach for my gun. - Stephen Hawking

11 Schrodinger s Cat

12 I think that a particle must have a separate reality independent of the measurements. That is, an electron has spin, location and so forth even when it is not being measured. I like to think the moon is there even if I am not looking at it. Albert Einstein

13 Quantum Entanglement between two particles Entangled particles wave-functions cannot be separated Measurement of one particle affects the state of the other No classical model of this behavior There is a universal connectedness. Any objects that have ever interacted continue to instantaneously influence each other. FYI: More than two can be entangled (recently 4). Ultrafast Quantum Computer Closer: Ten Billion Bits of Entanglement Achieved in Silicon Twin entangled photons are emitted from an atom

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15 How it all started Einstein s 1927 challenge to Bohr Bohr was able to show that this uncertainty would be large enough to foil Einstein s demonstration.. But 3 years later Einstein tried again, but failed again too. 4 years later in 1935 Atoms fired one at a time through a movable two-slit barrier

16 1935 EPR In 1935 Einstein, Nathan Podolsky,Nathan Rosen presented the famous EPR paradox which wanted to show that [quantum entanglement was not observer-created, instant communication between twin photons, but observer independent hidden variables.] Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? (Einstein, Podolsky, and Rosen, 1935) Criterion of Completeness: Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory. There must be hidden variables missing from the quantum description... an incomplete theory. Criterion of Reality: If, without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of reality corresponding to this quantity. If you can predict something about a system without disturbing or interacting with the system in any way, then that something must be real.

17 Bohr Rejected EPR s assumption of separability. What happened to one object could indeed influence the behavior of the other instantaneously, even though no physical force connected them. The are no hidden variables, the observer influence can act at a distance because both particles are one system. The act of measuring one and then predicting the other is a measurement, not a prediction (not an independent real prediction without measurement). There are complementarity of 2 attributes of two electrons in one entangled system. If I measure the spin of one (A) electron, the other (B) of the entangled pair will always have the opposite spin (=TSZ). It seems that I indirectly measured B, but I did directly measure it because A and B are connected. If I could predict B without any measurement of A then EPR is right not the case. Both cannot be predicted independently. Bohr: the opposite of a great truth may be another great truth.. Einstein: NO spooky interactions please

18 The Game Begins hidden variables, Classical Realityno spooks? David Bohm test Quantum with hidden variables? EPR 1935 Quantum Theory is incomplete Bohr John Bell 1964 Who is right? Inequality Experiments 1981, 1982 Alain Aspect s experiments Prove Quantum Reality

19 EPR Alice and Bob receive the same photons from a twin-photon source. They each use a calcite crystal to measure the degree of vertical (D1) or horizontal (D2) polarization of each photon. The source is not measured/observed. Both Einstein and Bohr claimed a victory! Einstein: they are separate but have hidden variables (similar pilots that will guide the twin photon in a similar way when they hit the calcite crystal). No observer influence. Bohr: They are entangled, not separate, communicating instantaneously. If observer changes one twin the other changes too, even when the observer does not know the polarity or the result. The randomness is the same.

20 How to prove Quantum interpretation is true and the Classical Reality / Separateness is Wrong! Bell s Inequality Assumes the minimal correlation between pairs of outcomes, given that the outcomes depend only on the assumed hidden variables. (any higher correlation implies quantum entanglement no hidden variables) The violation of Bell s theorem, shows that one cannot explain all results of QM with hidden variables. In other words, EPR s if quantum mechanics is correct, then either nature is not locally deterministic (entaglement, no separability), or there is no observer independent reality, or both. EPR What was wrong was their insistence on local reality --- that the total, mixed wave function could not extend across large regions of space (no entanglements). There is entanglement, by quantum probability is a result of not knowing all variables (so there are hidden/unknown variables), and all variables are locally determined (no spooks from far away). Thus, Bell viewed two alternatives: (1) Quantum theory is right, or (2) local realistic models are right. But both cannot be right. Bell starts with believing EPR and tests it. TSZ> total spin zero Bell produced a mathematical theorem containing certain inequalities. He suggested that if his EPR inequalities could be violated by experimental tests, it would provide evidence in favor of orthodox (Copenhagen) quantum theory. He basically shows that the level of errors is changed for A by the remote measurement of B. So he proposed the following experiments.

21 twin photons with identical polarization, identical stick angles affected the same way. Alice and Bob each have their polarizer axes aligned vertically. They record a 1 every time their Path 1 detector records a photon and a 2 every time their Path 2 detector records a photon. They each end up with a long string of random 1s and 2s that perfectly match.

22 1. She deliberately rotates small Θ angle to cause an error rate of five percent (see below). 2. She goes back to vertical, and Bob rotes the same amount this time and gets the same error rate of 5 percent, as expected.

23 The error rate when both polarizers are rotated by Θ (in opposite directions) is equal to, or less than (i.e. <= but NOT >), twice the error rate for the rotation by Θ of a single polarizer (<=10%). No greater because they are independent actions. Less if errors not recorded correctly. Their actions are independent. Bell s <= inequality theorem! If true then there is not action at a distance (quantum entanglements) only pilot, hidden variables. But results where greater than twice the error rate Alice affected Bob s and vice versa.

24 Nick Herbert site (

25 Zero angle = 100% Match. Right angle = 0% Match. Angle between Zero and Right angle = Cosine Squared (Angle) Match In fact the mismatch should be less than 50% because if the two errors happen to occur on the same photon, a mismatch is converted to a match. However both theory and experiment show that the mismatch at 60 degrees is 75%. The code mismatch is 25% greater than can be accounted for by independent error generation in each detector. non-local observer influenced reality

26 In Alain Aspect s experiments

27 YOUTUBE lecture Alain Aspect Part 1 - From Bell's Inequalities to Entangled Qubits: A New Quantum Age? Local hidden variable theory

28 Entanglement Benefits Cbit is a classical binary bit as used in computers Qubit is an unmeasured quantum particle state having superposition values Ebit is an entangled particle/photon Qubit Quantum teleportation

29 Marge SIMPSON: [eight years in the future, praising technology] It's greeat! We can do *anything* now that Science has invented Magic. In this photo montage of actual quantum images, two laser beams coming from the bright glare in the distance transmit images of a cat-like face at two slightly different frequencies (represented by the orange and the purple colors). The twisted lines indicate that the seemingly random changes or fluctuations that occur over time in any part of the orange image are strongly interconnected or "entangled" with the fluctuations of the corresponding part in the purple image. Though false color has been added to the cats' faces, they are otherwise actual images obtained in the experiment. Credit: Vincent Boyer/JQI, 2008