What does Quantum Mechanics tell us about the universe?

Transcription

1 Fedora GNU/Linux; L A TEX 2ǫ; xfig What does Quantum Mechanics tell us about the universe? Mark Alford Washington University Saint Louis, USA More properly: What do experiments tell us about the universe? 1

2 What the experts say I think it is safe to say that no one understands quantum mechanics. (Richard Feynman) Anyone who is not shocked by quantum theory has not understood a single word. (Niels Bohr) 2

3 Dr. A. Einstein on Quantum Mechanics God is subtle, but he is not malicious. (1921) God does not play dice. (1926) This theory reminds me a little of the system of delusions of an exceedingly intelligent paranoiac, concocted of incoherent elements of thoughts. (1952) 3

4 Suggested Reading: The Infamous Boundary (David Wick) Is the moon there when nobody looks? (David Mermin, Physics Today April 1985). 4

5 What does quantum mechanics allow us to understand? Everything that happens at small distances. Structure and behavior of atoms Chemistry Stability of matter Behavior of light (interference, photons...) Behavior of matter (conductivity, superconductivity, heat capacity...) Electronics Subatomic constituents of matter (particle physics) Radioactivity Antimatter So what s the problem? 5

6 What s weird about quantum mechanics? Classical physics Newton : Universe described by deterministic laws of physics. Deterministic means the results of all possible measurements are (in principle) predictable and encoded in the state of the system. Probabilistic statements are only necessary when we don t know everything about a system. Quantum mechanics now : quantum mechanics is highly successful, but gives predictions only in terms of probabilities. Executive Summary The universe seems to be inherently probabilistic. There cannot be a deeper deterministic theory. Nature doesn t know what result you ll get until you do the measurement. (unless you allow faster-than-light travel in the deeper theory). 6

7 Schrödinger s Cat In QM, the state of a radioactive atom is a mixture ( superposition ) of being intact and having decayed. Over time, the intact part shrinks to zero and the decayed part rises to 100%. This may be OK for atoms, but we can put the atom near a Geiger counter, and when it detects the decay it sets off a poison spray, which kills a cat. After 10 mins, suppose the atom is in a 50/50 state of being intact/decayed. So if we open the box, there is a 50/50 chance the cat will be alive/dead. But before we open the box? QM says the cat is in a 50/50 mixture...!? 7

8 Precursors to quantum mechanics : Planck and Einstein: Quantization of energy of electromagnetic field (photons) to explain thermal radiation and the photoelectric effect. 1913: Bohr: Bohr atom ; like a little solar system, but with quantization of energy levels. Explains simple atomic spectra. 8

9 The early stages : Bohr atom cannot explain quantized spin of electron, spectra of large atoms, response to magnetic fields, etc. 1923: Heisenberg and Born : Matrix mechanics. Heisenberg: It is my genuine conviction that an interpretation... in terms of circular and elliptical orbits of classical geometry has not the least physical meaning. : Grandfather of Olivia Newton-John 9

10 Invention of quantum mechanics 1926: Schrödinger and Born: Wave mechanics. The wavefunction tells you the probability of finding the electron in different places. Schrödinger s equation tells you how the wavefunction evolves in time. Mathematically equivalent to Heisenberg s Matrix Mechanics. 10

11 Schrödinger: life of a physicist 1887 born in Vienna married Annemarie ( Anny ) Bertel became professor at Univ of Zurich, became close friend of Weyl formulated quantum mechanics (aged 38!) during Christmas vacation at an Alpine resort with an old girlfriend from Vienna, while Anny stayed home in Zurich became professor in Berlin sought a position at Oxford for himself and a colleague, Arthur March. Schrödinger had had several affairs and was now in love with Arthur March s wife Hilde. Anny had already taken Schrödinger s friend Weyl as her lover for many years moved to Oxford, accompanied by Anny, Arthur and Hilde. Received Nobel Prize Hilde gives birth in Oxford to Schrödinger s child offered permanent position at Princeton, but offer fell through because he wanted to live at Princeton with Anny and Hilde both sharing the upbringing of his daughter moved to Graz, Austria after the Anschluss, dismissed from his post by the Nazis moved to Dublin. Had two more daughters while in Dublin, by two different Irish women returned to Vienna died of tuberculosis. 11

12 Schrödinger and Heisenberg: proud parents of quantum theory The wave function is easy to visualize, and evolves deterministically according to Schrödinger s equation. But when we make physical predictions, the wave function only tells us the relative probabilities of different outcomes (Heisenberg s uncertainty principle). Schrödinger: My theory was inspired by de Broglie and... Einstein. No genetic relationship whatever with Heisenberg is known to me. I knew of his theory, but felt discouraged, not to say repelled, by the methods... and by the lack of visualizability. Heisenberg: The more I reflect on the physical portion of Schrödinger s theory, the more disgusting I find it... What Schrödinger writes on the visualizability of his theory... I consider trash. 12

13 Accepting the weirdness: the Bohr-Einstein debates Einstein tries to show that even within quantum mechanics, sufficiently clever measurements can avoid the uncertainty principle. Bohr refutes every attempt. Conclusion: Within quantum mechanics, Heisenberg s uncertainty principle cannot be evaded. QM predictions are inherently probabilistic. But probabilities are usually just a sign that we don t know everything. Are the probabilities in QM predictions like that? Could there be a deeper deterministic theory that would tell us which outcome we will observe? ( hidden variables ). No. 13

14 The ultimate weirdness: no underlying determinism! How do we know the universe is fundamentally vague (probabilistic)? Why couldn t there be an underlying deterministic theory? (1) Einstein-Podolsky-Rosen/Bohm ( EPR ) thought-experiment: brings the probabilistic nature of QM to the surface. (2) Bell Inequality : Deterministic theories only allow a limited set of outcomes of EPR experiments: they obey Bell s inequality (3) Perform EPR experiments : results violate Bell s inequality and agree with QM s probabilistic predictions. Conclusion: No deterministic theory can reproduce QM. (unless the deterministic theory allows faster-than-light travel) Experimental results agree with QM: reality is probabilistic. 14

15 The EPR/Bohm experiment source 2 Source produces spin-zero pairs of particles, with opposite spins Each detector has a 3-way switch: red, green, blue. The detector sends the particle either to a + slit or a slit. We set detector 1 to ask, Is your spin pointing in the red direction?, particle says No ( ). We set detector 2 to ask, Is your spin pointing in the green direction?, particle says Yes (+). 15

16 How an EPR-type experiment would behave in a deterministic universe (Bell Inequality) States of the system 1 2 : Select a subset 1 2 : Bell Inequality: prob(subset) 1 p(1:,2: ) + p(1: + p(1: 1,2:,2: ) ) In QM, by contrast, the outcomes of the measurements are not already encoded in the state of the system: they aren t decided until the measurement occurs. 16

17 Quantum mechanics predicts violation of Bell Inequality Deterministic system p(1:,2: ) + p(1:,2: ) + p(1:,2: ) 1 Quantum mechanics p(1:,2: ) = 3/8 p(1:,2: ) = 3/8 p(1:,2: ) = 3/8 total: 9/8 = Conclusion: When you measure the particle spins in an EPR experiment, the answer you get cannot be encoded in the state of the system. Nature doesn t know what the result will be until you make the measurement. 17

18 Experimental observations agree with QM Nature 403, pp (03 Feb 2000) 18

19 Conclusions about quantum mechanics and the universe QM describes the world with fabulous accuracy. QM somehow manages to be both deterministic: the evolution of the wavefunction probabilistic: predictions of measurement results The probabilistic vagueness seems to be a feature of nature. We still don t have a clear picture of what a quantum-mechanical universe is like: is it one world with collapsing wavefunctions (Copenhagen) or Many Worlds, or something else? 19

20 Science and philosophy Science does not provide a suitable foundation for metaphysical speculation, i.e. deep eternal truths about the world. Experiments produce unexpected results. Theories change. 19th century: stable universe, obeying deterministic classical laws. 20th century: expanding universe of finite age, obeying probabilistic quantum-mechanical laws. Who knows what will come next? 20

21 The universe does not have to be understandable, let alone easily understandable. As we learn more, our theories become weirder... My own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. (J.B.S Haldane, 1927) 21