Interpretations of Quantum Mechanics Scott Johnson Intel

Mysteries of Quantum Mechanics Scott Johnson Intel

Dec 9, 2005Johnson3 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, 2005Johnson4 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, 2005Johnson5 “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, 2005Johnson6 “What the Bleep” Quantum Measurement Reasonable dramatization of Copenhagen interpretation –Except big object like basketball would have really small spread How good of a description of quantum mechanics? When she does not look, there is a wave function. When she does look, it collapses to a single location.

Dec 9, 2005Johnson7 “What the Bleep” Clip So, what are the mysteries of quantum mechanics?

Dec 9, 2005Johnson8 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, 2005Johnson9 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, 2005Johnson10 Classical Physics Mathematical model of the way things move

Dec 9, 2005Johnson11 Classical Physics Clear connection between the model and the real world

Dec 9, 2005Johnson12 Quantum Physics Also a mathematical model of the way things move Very different form – probabilities!

Dec 9, 2005Johnson13 Two-Slit Interference Result is different from classical if we use elementary particles

Dec 9, 2005Johnson14 Wave Mechanics This is the same behavior we see from classical waves Wolfgang Christian, Dickenson College

Dec 9, 2005Johnson15 Single Particle Interference Not a wave of particles Single particles interfere with themselves

Dec 9, 2005Johnson16 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, 2005Johnson17 Quantum Mechanics Wave packet travels, but still a probability

Dec 9, 2005Johnson18 Quantum Measurement How do we go from a probability to an actual event? Standard answer: –Copenhagen interpretation –Wave function collapse

Dec 9, 2005Johnson19 Quantum Measurement Two-slit wave packet collapsing Eventually builds up pattern

Dec 9, 2005Johnson20 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, 2005Johnson21 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, 2005Johnson22 Which Path? Short answer: no, we can’t tell Anything that blocks one slit washes out the interference pattern

Dec 9, 2005Johnson23 Which Path? The wave function is that of one slit

Dec 9, 2005Johnson24 Which Path? 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 Movable wall; measure recoil Source Crystal with inelastic collision Source No: Movement of slit washes out pattern No: Change in wavelength washes out pattern

Dec 9, 2005Johnson25 Which Path? 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 Source

Dec 9, 2005Johnson26 Any which-path measurement destroys the interference pattern We cannot determine which slit the particle goes through Path is measured at one or both slits: Which Path?

Dec 9, 2005Johnson27 Particle in Stationary State Move? Waves and wave functions have ground states –The wave is stationary in time

Dec 9, 2005Johnson28 Electron In Atom Move? 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? More accurate picture of electron wave function Proton Electron Diagram of hydrogen atom

Dec 9, 2005Johnson29 Electron In Atom Move? 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 Proton Electron Hydrogen atom Proton Muon Muonic hydrogen “atom”

Dec 9, 2005Johnson30 Electron In Atom Move? 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 Muon around proton (muonic hydrogen) Electron around proton (hydrogen) Muon around heavier nucleii

Dec 9, 2005Johnson31 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, 2005Johnson32 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, 2005Johnson33 Philosophy Niels BohrAlbert Einstein Positivism Sense perceptions are the only admissible basis of human knowledge and precise thought. Realism Physical objects continue to exist when not perceived.

Dec 9, 2005Johnson34 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, 2005Johnson35 Photomultiplier Tube Measurement requires interaction with other particles 100V300V500V700V 200V400V600V800V photon electrons

Dec 9, 2005Johnson36 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, 2005Johnson37 Schrödinger's Cat Paradox Why don’t we see superpositions of objects like cats? Paradox: A seemingly contradictory statement that may nonetheless be true From John Gribbon In Search of Schrödinger's Cat Detector 1 releases poison Detector 2 prevents its release

Dec 9, 2005Johnson38 Schrödinger's Cat Paradox Note that a superposition is quite different than a pure probability, but both are still weird

Dec 9, 2005Johnson39 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, 2005Johnson40 Quantum Multi-Particle One 1D particle requiresOne 1D wave function One 2D particle requiresOne 2D wave function Two 1D particles requireTwo 1D wave functions? NO!

Dec 9, 2005Johnson41 Classical Multi-Particle Two 1D particles can be tracked with a single point on a 2D plane

Dec 9, 2005Johnson42 Classical Multi-Particle Another example

Dec 9, 2005Johnson43 Classical Multi-Particle Another example

Dec 9, 2005Johnson44 Classical Multi-Particle Another example

Dec 9, 2005Johnson45 Classical Multi-Particle Another example

Dec 9, 2005Johnson46 Quantum Multi-Particle 2 particles in 1D requires a 2D wave function! This was a disappointment to Schrödinger Particle 2 Particle 1 with fixed particle 2 Note: this is drawn, not calculated Erwin Schrödinger P2P2 P1P1

Dec 9, 2005Johnson47 Many-Particle Wave Functions These are not spatial dimensions! –Purely mathematical “wave function space” dimensions Space Wave function # particles dimensions dimensions 1 particle1D 1D wave function 2 particles1D 2D wave function 1 particle3D 3D wave function 2 particles3D 6D wave function 10 particles3D 30D wave function particles3D 3x10 23 D wave function

Dec 9, 2005Johnson48 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, 2005Johnson49 Quantum Multi-Particle Sometimes the 2D function separates neatly into two 1D wave functions…

Dec 9, 2005Johnson50 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, 2005Johnson51 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, 2005Johnson52 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, 2005Johnson53 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, 2005Johnson54 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 years) been appreciated as decoherence

Dec 9, 2005Johnson55 Decoherence Note the difference between these two graphs Can a superposition become a mixed state? SuperpositionMixed State

Dec 9, 2005Johnson56 Decoherence Yes! Decoherence turns a superposition into a mixed state

Dec 9, 2005Johnson57 Decoherence We can look at the second particle, too

Dec 9, 2005Johnson58 Decoherence for 2-Slit 2-slit is a 2D system Need a 3 rd dimension for the “environment” particle Source A particle in here flips states

Dec 9, 2005Johnson59 Decoherence for 2-Slit P1 xP1 x P1 yP1 y P2P2 2D particle going through slits shown on this face in red Slices of 3D total function shown here in blue Measurement particle shown along this axis

Dec 9, 2005Johnson60 2-Slit Decoherence P1 xP1 x P1 yP1 y P2P2 P1 xP1 x P1 yP1 y P2P2 No measurement Measurement Measurement moves wave function in 3 rd dimension – no longer overlap Wave function stays in one region in that 3rd dimension

Dec 9, 2005Johnson61 Effect of Measurement Measurement shifts the wave function so it no longer overlaps No measurement Measurement P1 xP1 x P1 yP1 y P2P2 P1 xP1 x P1 yP1 y P2P2

Dec 9, 2005Johnson62 Effect of Measurement Origin not as clear away from slits No measurement Measurement P1 xP1 x P1 yP1 y P2P2 P1 xP1 x P1 yP1 y P2P2

Dec 9, 2005Johnson63 2-Slit With Partial Measurement Partial transfer of wave function Interference pattern is washed out but still there P1 xP1 x P1 yP1 y P2P2

Dec 9, 2005Johnson64 Decoherence… …is fast –A molecule interacting with heat photons in a lab vacuum will decohere in ~ 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, 2005Johnson65 Quantum Computing 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 Classical computer Quantum computer All 8-bit numbers at once! (superposition) x P

Dec 9, 2005Johnson66 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, 2005Johnson67 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, 2005Johnson68 Wave Function Collapse If A detects particle, wave function collapses instantaneously so B cannot detect it If collapse is instantaneous, this violates causality Explanation is from relativity detector A detector B

Dec 9, 2005Johnson69 Relativity of Simultaneity In one reference frame, A and B take place at the same time –No problem yet for A instantaneously stopping B from detecting particle x t A B

Dec 9, 2005Johnson70 Relativity of Simultaneity In another reference frame, A happens first –Still no problem, A can stop B x t A B

Dec 9, 2005Johnson71 Relativity of Simultaneity In this reference frame, though, B happens first! –How can A stop B if B happens first? –Violates causality x t A B

Dec 9, 2005Johnson72 Fate? Violating causality might imply fate Not so bad – classical physics had fate –“Determinism” –Can predict every particle’s location location time particles colliding

Dec 9, 2005Johnson73 Bell’s Theorem OK, maybe wave functions don’t collapse instantaneously So, is quantum mechanics local? John Bell devised a way to test for non- locality (Bell’s theorem) –Compares “local hidden variables” to QM Some of these experiments have been carried out The verdict … Quantum mechanics is non-local! John Bell

Dec 9, 2005Johnson74 Small Source Back-to-back 2-slit with correlated particles With small source, separate interference patterns Source Particle 2 Particle 1

Dec 9, 2005Johnson75 Large Source Same back-to-back 2-slit w/ correlated particles With large source, correlated interference pattern Source Particle 2 Particle 1

Dec 9, 2005Johnson76 Small Source Change slit width 1, only pattern 1 changes Particle 2 Particle 1 Particle 2 Particle 1 Change particle 1’s slit

Dec 9, 2005Johnson77 Large Source Change slit width 1, correlated pattern changes Particle 2 Particle 1 Particle 2 Particle 1 Change particle 1’s slit

Dec 9, 2005Johnson78 Correlated Pairs We could (in principle) change the slit width after the particles were launched! This is a non-local correlation Particle 2 Particle 1 Particle 2 Particle 1 … … … … … Say that particle 1 lands here Possibilities for particle 2 depend on particle 1’s slit!

Dec 9, 2005Johnson79 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, 2005Johnson80 What Does Non-Locality Mean? 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 location time particles colliding

Dec 9, 2005Johnson81 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, 2005Johnson82 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, 2005Johnson83 Q&A

Dec 9, 2005Johnson84 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, 2005Johnson85 Shor’s Algorithm Picture a 250-bit number; with a quantum computer, make that a superposition of every 250-bit number, all of them at once! –Call each of these numbers by variable name a Now say we have some function f(a)=k a mod N with a really long repeat period, like –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 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 Peter Shor, 1994