Quantum Physics for Dogs: Many Worlds, Many Treats?
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Transcript of Quantum Physics for Dogs: Many Worlds, Many Treats?
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Quantum Physics for Dogs
I like chees
e
Chad Orzel
Many Worlds, Many Treats?
http://scienceblogs.com/principles/
2x p
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“I’m Looking for Steak”
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“I Can Sniff Into Extra Dimensions”
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“Oh… That’s Fast.”
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And she’s off…
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Many Worlds?
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Quantum MechanicsCentral Principles of Quantum Mechanics:
1) Wavefunctions: Every object in the universe is described by a quantum wavefunction
2) Allowed States: A quantum object can only be observed in one of a limited number of allowed states
3) Probability: The wavefunction gives the probability of finding the object in eachof the allowed states
4) Measurement: Measuring the state of an object absolutely determines the state ofthat object
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What’s the Problem?1) Wavefunctions2) Allowed States3) Probability4) Measurement
ˆ( , ) ( , )i x t H x tt
Schrödinger Equation
Use Schrödinger Equation to find wavefunctionsdetermine allowed states
Dog states:
Awake Asleep
Problem: Can be in multiple states at once
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Superposition StatesMathematically, sum of two allowed states is also an allowed state
Not too surprising– use for convenience in classical physics
Awake Asleep
+ =
Quantum System only observed in one state
Awake Asleep
OR
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Measurement ProblemQuantum System exists in multiple states
When measured, find only one state
Problem: Why do we only see one state?
1) Wavefunctions2) Allowed States3) Probability4) Measurement
ˆ( , ) ( , )i x t H x tt
Schrödinger Equation
Nothing in mathematical apparatus of QM explains measurement
Interpretations: meta-theories explaining measurement
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Copenhagen InterpretationDeveloped by Niels Bohr in Denmark
Absolute division between scales
Microscopic: electrons, atoms, molecules
Obey quantum rulessuperposition states
Macroscopic: dogs, cats, physicists, steak
Obey classical rulesno superposition states
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Wavefunction CollapseMeasurement involves interaction
Macroscopic Apparatus
Microscopic System
Interaction causes “collapse” ofwavefunction
Physical change in probability distribution
Before: Many possible statesAfter: Only one state
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Problems with Copenhagen
2) No reason for scale separation
Why shouldn’t cats be quantum?
Major philosophical problems for interpretation
Lots of ad hoc solutions Look for something better
1) No mechanism for collapse
What counts as a measurement?
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Everett’s Many-Worlds Interpretation1957: Hugh Everett III, Princeton grad student
There Is No Collapse
Wavefunction always and everywhere evolves according toSchrödinger Equation
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Many-Worlds, Many MindsIf the wavefunction doesn’t collapse, why don’t we see superpositions?
Observers become entangled with system being observed
Different branches of wavefunction contain observers seeing different outcomes
| || dog dogasleep awake
| ||| |dog human dog humanasleep awasleep awakeake
Before measurement:
After measurement:
Different branches like different universes
Branches do not interact
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Pros and Cons of Many-Worlds
1) Gets rid of macroscopic/microscopic divisionAll quantum, all the time
2) Gets rid of mysterious “collapse”Mathematically consistent, elegant
Advantages:
Disadvantages:1) Extra universes all over the place
2) Why don’t branches interact with each other?
Aesthetic objection, not a real problem
Seems as arbitrary as Copenhagen
No obvious reason for separation
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DecoherenceWhat leads to split between “universes” in Many-Worlds?
“Decoherence”
Random, fluctuating interactions with environment
Cause shifts that obscure effects of other branches
Key idea:
Not that different branches don’t interact
Rather, the interaction is UNDETECTABLE
Different branches always interacting, but no way to tell
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Detecting Other “Universes”How do you detect presence of other branches of wavefunction?
Sadly, not as easy as SF wouldhave it…
Answer is INTERFERENCE
Wave-like behavior of particles
Interference effects are the signature of superposition states
Particles in two places at same timefollowing two different paths to same goal
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InterferometerDemonstration with photons
Split light, recombine
Classical particle:50% each detector
Classical wave:0-100% each depends on timing
+ =
+ =
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InterferometerDemonstration with photons
Split light, recombine
Quantum Particle:
0-100% each
Depends on timing
Repeat many times
Build up probability
Same probability every time
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Dog InterferometryWalk around block:
Which dog arrives first? Short walk, few distractions
Always same result
Red dog wins
Repeatable pattern depends on constant environment
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Dog Interferometry 2Look at much longer path:
Many more potential distractions
Distractions move from day to day
Winner becomes completely random
50% chance either dog wins
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InterferometerBack to photons
Longer path, more interactions with environment (air molecules, etc.)Interactions shift probabilitiesInteractions fluctuate randomly
Probability 50% for each detector
Looks just like classical particle
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Decoherence + Many-WorldsCombination fixes both problems with Copenhagen
2) No reason for scale separation
Why shouldn’t cats be quantum?
1) No mechanism for collapse
What counts as a measurement?
NO COLLAPSE superposition continues forever
Observer becomes entangled with observed
NO SEPARATION Everything obeys quantum rules
Decoherence hides quantum effects
Bigger objects look classical more interactionsfaster decoherence
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Many-Worlds in SFMost SF treatments get things wrong:
Not “real” parallel universes no extra mass
Not possible to move between “universes”
Can’t choose to be in universe where dogs eat steak
One universe, one (really big) wavefunction
(Can’t be invaded by evil alien squirrels, either)
Best treatment:
“Divided by Infinity” Robert Charles Wilson
(My opinion only)
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The End