* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Slide presentation from lecture
Aharonov–Bohm effect wikipedia , lookup
Many-worlds interpretation wikipedia , lookup
Bell's theorem wikipedia , lookup
Wheeler's delayed choice experiment wikipedia , lookup
Quantum entanglement wikipedia , lookup
Ensemble interpretation wikipedia , lookup
Path integral formulation wikipedia , lookup
Measurement in quantum mechanics wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Canonical quantization wikipedia , lookup
Quantum state wikipedia , lookup
Quantum teleportation wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Elementary particle wikipedia , lookup
Probability amplitude wikipedia , lookup
Atomic theory wikipedia , lookup
Particle in a box wikipedia , lookup
Identical particles wikipedia , lookup
EPR paradox wikipedia , lookup
Hidden variable theory wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Wave function wikipedia , lookup
Double-slit experiment wikipedia , lookup
Wave–particle duality wikipedia , lookup
Matter wave wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Interpretations of Quantum Mechanics Scott Johnson Intel Mysteries of Quantum Mechanics Scott Johnson Intel Outline • Motivation: What the Bleep – What are the mysteries of quantum mechanics? • Mystery #1: Wave or particle? • Mystery #2: What is a measurement? • Mystery #3: Non-locality Dec 9, 2005 Johnson 3 Outline • Motivation: What the Bleep – What are the mysteries of quantum mechanics? • Mystery #1: Wave or particle? • Mystery #2: What is a measurement? • Mystery #3: Non-locality Dec 9, 2005 Johnson 4 “What the Bleep” Movie • A locally produced movie • Thought-provoking and entertaining – I liked it • Physics conclusions are speculative – Not a science documentary – Some good quotes • Good quantum measurement scene Dec 9, 2005 Johnson 5 “What the Bleep” Quantum Measurement When she does not look, there is a wave function. When she does look, it collapses to a single location. • Reasonable dramatization of Copenhagen interpretation – Except big object like basketball would have really small spread • How good of a description of quantum mechanics? Dec 9, 2005 Johnson 6 “What the Bleep” Clip • So, what are the mysteries of quantum mechanics? Dec 9, 2005 Johnson 7 Outline • Motivation: What the Bleep – What are the mysteries of quantum mechanics? • Mystery #1: Wave or particle? • Mystery #2: What is a measurement? • Mystery #3: Non-locality Dec 9, 2005 Johnson 8 Physics Is… • …using math to model the world • We don’t know why math is the best thing to use, but it works well Eugene Wigner Dec 9, 2005 Johnson 9 Classical Physics x cos2 k t • Mathematical model of the way things move Dec 9, 2005 Johnson 10 Classical Physics • Clear connection between the model and the real world Dec 9, 2005 Johnson 11 Quantum Physics Px cos 2 2 x • Also a mathematical model of the way things move • Very different form – probabilities! Dec 9, 2005 Johnson 12 Two-Slit Interference • Result is different from classical if we use elementary particles Dec 9, 2005 Johnson 13 Wave Mechanics Wolfgang Christian, Dickenson College • This is the same behavior we see from classical waves Dec 9, 2005 Johnson 14 Single Particle Interference • Not a wave of particles • Single particles interfere with themselves Dec 9, 2005 Johnson 15 Quantum Mechanics • Quantum mechanics is the mathematics of a wave function ψ – Wave function squared |ψ|2 gives the probability of finding the particle • Wave function has all the information we know about a particle Dec 9, 2005 Johnson 16 Quantum Mechanics • Wave packet travels, but still a probability Dec 9, 2005 Johnson 17 Quantum Measurement • How do we go from a probability to an actual event? • Standard answer: – Copenhagen interpretation – Wave function collapse Dec 9, 2005 Johnson 18 Quantum Measurement • Two-slit wave packet collapsing • Eventually builds up pattern Dec 9, 2005 Johnson 19 Wave or Particle? • Let’s ask a few questions that might help us to decide – Which path does particle follow through the 2 slits? – Does a particle in a ground state move? Dec 9, 2005 Johnson 20 Which Path? • A classical particle would follow some single path • Can we say a quantum particle does, too? • Can we measure it going through one slit or another? Dec 9, 2005 Johnson 21 Which Path? • Short answer: no, we can’t tell • Anything that blocks one slit washes out the interference pattern Dec 9, 2005 Johnson 22 Which Path? • The wave function is that of one slit Dec 9, 2005 Johnson 23 Which Path? Crystal with inelastic collision Movable wall; measure recoil Source Source No: Change in wavelength washes out pattern No: Movement of slit washes out pattern • Einstein proposed a few ways to measure which slit the particle went through without blocking it • Each time, Bohr showed how that measurement would wash out the wave function Dec 9, 2005 Johnson 24 Which Path? Source • Now possible to measure which slit a particle went through without disturbing its momentum at all – Not quite two slits, and fairly difficult to do • And the result … interference is still washed out! • Something more fundamental than disturbing momentum is at work here Dec 9, 2005 Johnson 25 Which Path? Path is measured at one or both slits: • Any which-path measurement destroys the interference pattern • We cannot determine which slit the particle goes through Dec 9, 2005 Johnson 26 Particle in Stationary State Move? • Waves and wave functions have ground states – The wave is stationary in time Dec 9, 2005 Johnson 27 Electron In Atom Move? Electron Proton Diagram of hydrogen atom More accurate picture of electron wave function • Example ground state is electron in an atom • Does the electron in the ground state move? – Quantum formalism says yes, but do we really know? Dec 9, 2005 Johnson 28 Electron In Atom Move? Electron Proton Proton Muon Muonic hydrogen “atom” Hydrogen atom • Great test: give the particle a clock and see if it runs slow – This is from relativity – fast clocks run slow • This test can actually be done – – – – Make atom with muon instead of electron Muon like a heavy electron Muons have short lifetimes, ~2.2μsec If their lifetimes increase, they are moving fast Dec 9, 2005 Johnson 29 Electron In Atom Move? Electron around proton (hydrogen) Muon around heavier nucleii Muon around proton (muonic hydrogen) • Muonic atoms made with heavier nucleii should be smaller and the muons should move faster • The result ... • Muons around heavier nucleii do live longer • The particle in a ground state is really moving! – ...at least according to Einstein’s special relativity Dec 9, 2005 Johnson 30 Wave or Particle? • So, from these last two experiments... – A particle is indeed moving, but – We can’t tell what path it follows • Could it follow a path but we just can’t see it? – Well, maybe. Here’s what such a path might look like: This path gives the correct position and momentum probability distribution for the ground state of the harmonic oscillator Dec 9, 2005 Johnson 31 Wave or Particle? • So, which is it, wave or particle? – Best answer is probably “neither” – It is something else that we don’t fully understand yet • Another way of asking that: – Is the wave function a real thing that collapses? – Or is it a statement about our knowledge of the particle? Dec 9, 2005 Johnson 32 Philosophy Positivism Realism Sense perceptions are the only admissible basis of human knowledge and precise thought. Physical objects continue to exist when not perceived. Niels Bohr Dec 9, 2005 Albert Einstein Johnson 33 Outline • Motivation: What the Bleep – What are the mysteries of quantum mechanics? • Mystery #1: Wave or particle? • Mystery #2: What is a measurement? • Mystery #3: Non-locality Dec 9, 2005 Johnson 34 Photomultiplier Tube photon 200V 400V 600V 800V electrons 100V 300V 500V 700V • Measurement requires interaction with other particles Dec 9, 2005 Johnson 35 What is a Measurement? • How do we differentiate between a measurement and a quantum interaction? • Measurement devices, including our eyes, are all quantum mechanical • Is a consciousness required for measurement? – Is a human required? A chimp? A cockroach? – You may be a physicist if: • … • You’re afraid that if you look at something, you’ll collapse its wave function • … Dec 9, 2005 Johnson 36 Schrödinger's Cat Paradox Paradox: A seemingly contradictory statement that may nonetheless be true Detector 1 releases poison Detector 2 prevents its release From John Gribbon In Search of Schrödinger's Cat • Why don’t we see superpositions of objects like cats? Dec 9, 2005 Johnson 37 Schrödinger's Cat Paradox • Note that a superposition is quite different than a pure probability, but both are still weird Dec 9, 2005 Johnson 38 Multi-Particle Wave Function • To investigate measurement, we need a new tool – Multi-particle wave function – Single wave function that describes multiple particles Dec 9, 2005 Johnson 39 Quantum Multi-Particle One 1D particle requires One 1D wave function One 2D particle requires One 2D wave function Two 1D particles require Two 1D wave functions? Dec 9, 2005 NO! Johnson 40 Classical Multi-Particle • Two 1D particles can be tracked with a single point on a 2D plane Dec 9, 2005 Johnson 41 Classical Multi-Particle • Another example Dec 9, 2005 Johnson 42 Classical Multi-Particle • Another example Dec 9, 2005 Johnson 43 Classical Multi-Particle • Another example Dec 9, 2005 Johnson 44 Classical Multi-Particle • Another example Dec 9, 2005 Johnson 45 Quantum Multi-Particle P2 Particle 2 Note: this is drawn, not calculated Particle 1 with fixed particle 2 P1 Erwin Schrödinger Particle 1 • 2 particles in 1D requires a 2D wave function! • This was a disappointment to Schrödinger Dec 9, 2005 Johnson 46 Many-Particle Wave Functions Space # particles dimensions 1 particle 1D 2 particles 1D 1 particle 3D 2 particles 3D 10 particles 3D 1023 particles 3D Wave function dimensions 1D wave function 2D wave function 3D wave function 6D wave function 30D wave function 3x1023D wave function • These are not spatial dimensions! – Purely mathematical “wave function space” dimensions Dec 9, 2005 Johnson 47 Quantum Multi-Particle • These 2 particles are described by one 2D wave function • Projecting (integrating) the 2D function onto each axis gives 1D wave functions Dec 9, 2005 Johnson 48 Quantum Multi-Particle • Sometimes the 2D function separates neatly into two 1D wave functions… Dec 9, 2005 Johnson 49 Quantum Multi-Particle • But not in general • These two particles are correlated or entangled – The 1D probability densities don’t have complete info Dec 9, 2005 Johnson 50 Quantum Multi-Particle • This “classical state” is very useful because it keeps its shape as it oscillates – Only available for a harmonic oscillator Dec 9, 2005 Johnson 51 Quantum Multi-Particle • Particles can stay separable – Don’t need 2D function (two 1D functions are good enough), but can plot one anyway Dec 9, 2005 Johnson 52 Quantum Multi-Particle • Particles usually don’t stay separable – They usually become entangled with other particles – They always become entangled when being measured Dec 9, 2005 Johnson 53 Decoherence • Schrödinger's cat is a good problem because it is specific and physical – Why don’t we see superpositions of macroscopic objects like cats? • The answer has recently (last 10-15 years) been appreciated as decoherence Dec 9, 2005 Johnson 54 Decoherence Superposition Mixed State • Note the difference between these two graphs • Can a superposition become a mixed state? Dec 9, 2005 Johnson 55 Decoherence • Yes! Decoherence turns a superposition into a mixed state Dec 9, 2005 Johnson 56 Decoherence • We can look at the second particle, too Dec 9, 2005 Johnson 57 Decoherence for 2-Slit A particle in here flips states Source • 2-slit is a 2D system • Need a 3rd dimension for the “environment” particle Dec 9, 2005 Johnson 58 Decoherence for 2-Slit Slices of 3D total function shown here in blue P1 y 2D particle going through slits shown on this face in red P1 x Dec 9, 2005 Johnson P2 Measurement particle shown along this axis 59 2-Slit Decoherence Measurement No measurement P1 y P1 y P1 x P2 P1 x Wave function stays in one region in that 3rd dimension Dec 9, 2005 P2 Measurement moves wave function in 3rd dimension – no longer overlap Johnson 60 Effect of Measurement Measurement No measurement P1 y P1 y P1 x P2 P1 x P2 • Measurement shifts the wave function so it no longer overlaps Dec 9, 2005 Johnson 61 Effect of Measurement Measurement No measurement P1 y P1 y P1 x P2 P1 x P2 • Origin not as clear away from slits Dec 9, 2005 Johnson 62 2-Slit With Partial Measurement P1 y P1 x P2 • Partial transfer of wave function • Interference pattern is washed out but still there Dec 9, 2005 Johnson 63 Decoherence… • …is fast – A molecule interacting with heat photons in a lab vacuum will decohere in ~10-17 seconds • Faster than any possible measurement we can make • Possibly the most efficient process known • … Solves Schrödinger's Cat – Any macroscopic object will decohere long before we can see a macroscopic superposition • People are trying to get superpositions of fairly macroscopic objects – work in progress • …is holding up practical quantum computers Dec 9, 2005 Johnson 64 Quantum Computing Quantum computer Classical computer 1 0 0 1 0 1 1 0 All 8-bit numbers at once! (superposition) • Much faster than a regular computer for some problems • Use superpositions to represent all numbers at once • Catch is, only get one random output at a time • Shor showed how to use this to factor big numbers very quickly Dec 9, 2005 Johnson P x 65 Measurement Still Has a Mystery • Decoherence leaves us with two (or more) outcomes as proper probabilities – Probabilities are less mysterious than superpositions • It does not say how nature chooses among these probabilities • I also does not say when the choice is made Dec 9, 2005 Johnson 66 Outline • Motivation: What the Bleep – What are the mysteries of quantum mechanics? • Mystery #1: Wave or particle? • Mystery #2: What is a measurement? • Mystery #3: Non-locality Dec 9, 2005 Johnson 67 Wave Function Collapse detector A detector B • If A detects particle, wave function collapses instantaneously so B cannot detect it • If collapse is instantaneous, this violates causality • Explanation is from relativity Dec 9, 2005 Johnson 68 Relativity of Simultaneity t A B x • In one reference frame, A and B take place at the same time – No problem yet for A instantaneously stopping B from detecting particle Dec 9, 2005 Johnson 69 Relativity of Simultaneity t x B A • In another reference frame, A happens first – Still no problem, A can stop B Dec 9, 2005 Johnson 70 Relativity of Simultaneity t A B x • In this reference frame, though, B happens first! – How can A stop B if B happens first? – Violates causality Dec 9, 2005 Johnson 71 Fate? particles colliding time location • Violating causality might imply fate • Not so bad – classical physics had fate – “Determinism” – Can predict every particle’s location Dec 9, 2005 Johnson 72 Bell’s Theorem • OK, maybe wave functions don’t collapse instantaneously • So, is quantum mechanics local? • John Bell devised a way to test for nonlocality (Bell’s theorem) – Compares “local hidden variables” to QM • Some of these experiments have been carried out John Bell • The verdict … • Quantum mechanics is non-local! Dec 9, 2005 Johnson 73 Particle 1 Source Particle 1 Particle 2 Small Source Particle 2 • Back-to-back 2-slit with correlated particles • With small source, separate interference patterns Dec 9, 2005 Johnson 74 Particle 1 Particle 1 Particle 2 Large Source Source Particle 2 • Same back-to-back 2-slit w/ correlated particles • With large source, correlated interference pattern Dec 9, 2005 Johnson 75 Small Source Particle 1 Particle 1 Change particle 1’s slit Particle 2 Particle 2 • Change slit width 1, only pattern 1 changes Dec 9, 2005 Johnson 76 Large Source Particle 1 Particle 1 Change particle 1’s slit Particle 2 Particle 2 • Change slit width 1, correlated pattern changes Dec 9, 2005 Johnson 77 …………… Particle 2 Particle 1 Say that particle 1 lands here Particle 1 Correlated Pairs …………… Particle 2 Possibilities for particle 2 depend on particle 1’s slit! • We could (in principle) change the slit width after the particles were launched! • This is a non-local correlation Dec 9, 2005 Johnson 78 Another Quantum Mystery • Quantum mechanics non-locality cannot be used for faster-than-light communication – More subtle, but still non-local • One group has “teleported” a single particle – Again, not faster than light • What does this non-locality mean philosophically? Dec 9, 2005 Johnson 79 What Does Non-Locality Mean? particles colliding time location • Non-local “hidden variables”? – Just like classical physics, each angle is fixed – Value of fixed angle is not the same for each vertex with same input conditions – Although appealing to me, this idea is not popular • Transactional interpretation – The present transacts with the future much like with the past – Wave function from the future + wave function from the past Dec 9, 2005 Johnson 80 Status of Mysteries • Mystery #1: Wave or particle? – Unsolved; wave function gives probabilities only • Mystery #2: What is a measurement? – Solved; interactions with decoherence give pure probabilities • Mystery #3: Non-locality – Unsolved; universe is non-local; what does that mean? Dec 9, 2005 Johnson 81 Retrospect: What the Bleep • So, how good is What the Bleep’s picture of quantum measurement? • The good: – Striking and easy to understand – Captures the spirit of Bohr’s Copenhagen interpretation • The bad: – Implies that consciousness is needed to collapse wave function • Eyes closed, or even back of head, would have the same effect on the wave function – Vastly exaggerates size of spread for a basketball-sized object • Would be too small to see, even un-collapsed Dec 9, 2005 Johnson 82 Q&A Dec 9, 2005 Johnson 83 Outline • Motivation: What the Bleep – What are the mysteries of quantum mechanics? • Mystery #1: Wave or particle? – – – – 1-particle wave function Which way? Does an electron in an atom move? Does an atom really jump from state to state? • Mystery #2: What is a measurement? – Multi-particle wave function, entanglement – Schrödinger's cat – Decoherence • Mystery #3: Non-locality – Wave function collapse – Relativity of simultaneity – Bell’s theorem Dec 9, 2005 Johnson 84 Shor’s Algorithm Peter Shor, 1994 • Picture a 250-bit number; with a quantum computer, make that a superposition of every 250-bit number, all 2250 of them at once! – Call each of these 2250 numbers by variable name a • Now say we have some function f(a)=ka mod N with a really long repeat period, like 1040 – This long repeat period can be used to find the prime factorization of N • Act with this function on the superposition once and you have effectively done the calculation 2250 times, a phenomenal speed-up – The catch is you can only read out one randomly chosen answer at any one time • Do an FFT on the number (which is also the function) – Even multiples of the period will be large; other values small • Read out the value of all bits – This will be one possible answer • Repeat several times to get a approximation of the function Dec 9, 2005 Johnson 85