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Transcript
Does the Everyday World Really Obey Quantum Mechanics? Anthony J. Leggett University of Illinois at UrbanaChampaign 2 3 Account given by quantum mechanics: B E A C Each possible process is represented by a probability amplitude A which can be positive or negative • Total amplitude to go from A to E sum of amplitudes for possible paths, i.e. ABE and/or ACE • Probability to go from A to E = square of total amplitude 4 1. If C shut off: Atot = AB P PB = A 2B 2. If B shut off: Atot = AC 2 A P PC = C 3. If both paths open: Atot = AB + AC “SUPERPOSITION” 2 2 2 2 A A + A P PB or C = tot = (AB + AC) = B C + 2 AB AC PB or C = PB + PC + 2ABAC “interference” term TO GET INTERFERENCE, AB AND AC MUST SIMULTANEOUSLY “EXIST” FOR EACH ATOM 5 PB or C = PB + PC + 2ABAC Suppose AC = ±AB, at random. Then average of PB or C is av. of AB AC PB or C = PB + PC + 2ABAC but ABAC = av. of +A2B and -A2B = 0 so PB or C =PB + PC “COMMON SENSE” RESULT, i.e.“as if” each system chose path B or path C WHEN AB AND AC SIMULTANEOUSLY “EXIST”, NEITHER B NOR C “SELECTED”. 6 Figure 1 Erwin Schrödinger (left) and Niels Bohr. Bohr claimed that a momentum kick, imparted by any measurement of particle position, could explain the disappearance of quantum interference in ‘two-slit’ experiments. A new experiment1 shows that this effect is too small, and the disappearance must instead be explained using Schrödinger’s ‘entanglement’ between quantum states. 7 In quantum mechanics, if state 1 state 1' and state 2 2' , then superposition of 1and 2 superposition of 1' and 2'. Here, B cat alive C cat dead Superposition of B and C superposition of “alive and “dead”! i.e. ampl. (cat alive) 0 ampl. (cat dead) 0 8 9 10 Is quantum mechanics the whole truth? How do we tell? If all “everyday-scale” bodies have the property that the interference term is randomized (“decoherence”), always get “common sense” result, i.e. all experimental results will be “as if” one path or the other were followed. cannot tell. So: must find “everyday-scale” object where decoherence is not effective. Does any such exist? Essential: difference of two states is at “everyday” level nevertheless, relevant energies at “atomic” level extreme degree of isolation from outside world very low intrinsic dissipation QM CALCULATIONS HARD! BASE ON: a) A PRIORI “MICROSCOPIC” DESCRIPTION b) EXPTL. BEHAVIOR IN “CLASSICAL” LIMIT 11 12 13 Pairing of electons: “di-electronic molecules” Cooper Pairs In simplest (“BCS”) theory, Cooper pairs, once formed, must automatically undergo Bose condensation! must all do exactly the same thing at the same time (also in nonequilibrium situation) 14 15 16 17 18 Possible outcomes of SQUID experiment. a)Experiment doesn’t work (i.e., too much “noise” quantum-mechanical prediction for K is < 2). b)K > 2 macrorealism refuted c) K < 2 quantum mechanics refuted at everyday level. 19
