interpretations of quantum mechanics scott johnson intel
TRANSCRIPT
Interpretations ofQuantum Mechanics
Scott Johnson
Intel
Mysteries ofQuantum Mechanics
Scott Johnson
Intel
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
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 5
“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 6
“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, 2005 Johnson 7
“What the Bleep” Clip
• So, what are the mysteries of quantum mechanics?
Dec 9, 2005 Johnson 8
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 9
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 10
Classical Physics
• Mathematical model of the way things move
tkx 2cos
Dec 9, 2005 Johnson 11
Classical Physics
• Clear connection between the model and the real world
Dec 9, 2005 Johnson 12
Quantum Physics
• Also a mathematical model of the way things move
• Very different form – probabilities!
xxP 2cos2
Dec 9, 2005 Johnson 13
Two-Slit Interference
• Result is different from classical if we use elementary particles
Dec 9, 2005 Johnson 14
Wave Mechanics
• This is the same behavior we see from classical waves
Wolfg
an
g Ch
ristian
, Dicke
nso
n C
olleg
e
Dec 9, 2005 Johnson 15
Single Particle Interference
• Not a wave of particles• Single particles interfere with themselves
Dec 9, 2005 Johnson 16
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 17
Quantum Mechanics
• Wave packet travels, but still a probability
Dec 9, 2005 Johnson 18
Quantum Measurement
• How do we go from a probability to an actual event?
• Standard answer:– Copenhagen interpretation– Wave function collapse
Dec 9, 2005 Johnson 19
Quantum Measurement
• Two-slit wave packet collapsing• Eventually builds up pattern
Dec 9, 2005 Johnson 20
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 21
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 22
Which Path?
• Short answer: no, we can’t tell• Anything that blocks one slit washes out the
interference pattern
Dec 9, 2005 Johnson 23
Which Path?
• The wave function is that of one slit
Dec 9, 2005 Johnson 24
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, 2005 Johnson 25
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, 2005 Johnson 26
• 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, 2005 Johnson 27
Particle in Stationary State Move?
• Waves and wave functions have ground states– The wave is stationary in time
Dec 9, 2005 Johnson 28
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 pictureof electron wave function
Proton
Electron
Diagram of hydrogen atom
Dec 9, 2005 Johnson 29
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
ProtonElectron
Hydrogen atom
Proton Muon
Muonic hydrogen “atom”
Dec 9, 2005 Johnson 30
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, 2005 Johnson 31
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 32
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 33
Philosophy
Niels Bohr Albert 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, 2005 Johnson 34
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 35
Photomultiplier Tube
• Measurement requires interaction with other particles
100V 300V 500V 700V
200V 400V 600V 800Vphoton
electrons
Dec 9, 2005 Johnson 36
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 37
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 GribbonIn Search of Schrödinger's Cat
Detector 1 releases poison
Detector 2 prevents its release
Dec 9, 2005 Johnson 38
Schrödinger's Cat Paradox
• Note that a superposition is quite different than a pure probability, but both are still weird
Dec 9, 2005 Johnson 39
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 40
Quantum Multi-ParticleOne 1D particle requires One 1D wave function
One 2D particle requires One 2D wave function
Two 1D particles require Two 1D wave functions?NO!
Dec 9, 2005 Johnson 41
Classical Multi-Particle
• Two 1D particles can be tracked with a single point on a 2D plane
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
Classical Multi-Particle
• Another example
Dec 9, 2005 Johnson 46
Quantum Multi-Particle
• 2 particles in 1D requires a 2D wave function!• This was a disappointment to Schrödinger
Par
ticle
2
Particle 1
Particle 1with fixedparticle 2
Note: this is draw
n, not calculated
Erwin Schrödinger
P2
P1
Dec 9, 2005 Johnson 47
Many-Particle Wave Functions
• These are not spatial dimensions!– Purely mathematical “wave function space”
dimensions
Space Wave function# particles dimensions dimensions 1 particle 1D 1D wave function2 particles 1D 2D wave function1 particle 3D 3D wave function2 particles 3D 6D wave function10 particles 3D 30D wave function1023 particles 3D 3x1023D wave function
Dec 9, 2005 Johnson 48
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 49
Quantum Multi-Particle
• Sometimes the 2D function separates neatly into two 1D wave functions…
Dec 9, 2005 Johnson 50
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 51
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 52
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 53
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 54
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 55
Decoherence
• Note the difference between these two graphs• Can a superposition become a mixed state?
Superposition Mixed State
Dec 9, 2005 Johnson 56
Decoherence
• Yes! Decoherence turns a superposition into a mixed state
Dec 9, 2005 Johnson 57
Decoherence
• We can look at the second particle, too
Dec 9, 2005 Johnson 58
Decoherence for 2-Slit
• 2-slit is a 2D system• Need a 3rd dimension for the “environment”
particle
Source
A particle in here flips states
Dec 9, 2005 Johnson 59
Decoherence for 2-Slit
P1 x
P1 y
P2
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, 2005 Johnson 60
2-Slit Decoherence
P1 x
P1 y
P2 P1 x
P1 y
P2
No measurement Measurement
Measurement moves wave function in 3rd dimension – no longer overlap
Wave function stays in one region in that 3rd dimension
Dec 9, 2005 Johnson 61
Effect of Measurement
• Measurement shifts the wave function so it no longer overlaps
No measurement Measurement
P1 x
P1 y
P2 P1 x
P1 y
P2
Dec 9, 2005 Johnson 62
Effect of Measurement
• Origin not as clear away from slits
No measurement Measurement
P1 x
P1 y
P2 P1 x
P1 y
P2
Dec 9, 2005 Johnson 63
2-Slit With Partial Measurement
• Partial transfer of wave function• Interference pattern is washed out but still there
P1 x
P1 y
P2
Dec 9, 2005 Johnson 64
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 65
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
1 0 0 1 0 1 1 0
Classical computer Quantum computer
All 8-bit numbers at once!(superposition)
x
P
Dec 9, 2005 Johnson 66
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 67
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 68
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, 2005 Johnson 69
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, 2005 Johnson 70
Relativity of Simultaneity
• In another reference frame, A happens first– Still no problem, A can stop B
x
t
A
B
Dec 9, 2005 Johnson 71
Relativity of Simultaneity
• In this reference frame, though, B happens first!– How can A stop B if B happens first?– Violates causality
x
t
AB
Dec 9, 2005 Johnson 72
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, 2005 Johnson 73
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, 2005 Johnson 74
Small Source
• Back-to-back 2-slit with correlated particles• With small source, separate interference patterns
Source
Particle 2
Par
ticle
2
Par
ticle
1
Par
ticle
1
Dec 9, 2005 Johnson 75
Large Source
• Same back-to-back 2-slit w/ correlated particles• With large source, correlated interference pattern
Source
Particle 2
Par
ticle
2
Par
ticle
1
Par
ticle
1
Dec 9, 2005 Johnson 76
Small Source
• Change slit width 1, only pattern 1 changes
Particle 2
Par
ticle
1
Particle 2
Par
ticle
1
Change particle 1’s slit
Dec 9, 2005 Johnson 77
Large Source
• Change slit width 1, correlated pattern changes
Particle 2
Par
ticle
1
Particle 2
Par
ticle
1
Change particle 1’s slit
Dec 9, 2005 Johnson 78
Correlated Pairs
• We could (in principle) change the slit width after the particles were launched!
• This is a non-local correlation
Particle 2P
artic
le 1
Particle 2
Par
ticle
1… … … … … … … … … …Say thatparticle 1lands here
Possibilitiesfor particle 2 depend on particle 1’s slit!
Dec 9, 2005 Johnson 79
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 80
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, 2005 Johnson 81
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 82
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 83
Q&A
Dec 9, 2005 Johnson 84
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 85
Shor’s Algorithm• 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
Peter Shor, 1994