Quantum Physics for Dogs

I like chees

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Chad Orzel

Many Worlds, Many Treats?

http://scienceblogs.com/principles/

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“I’m Looking for Steak”

“I Can Sniff Into Extra Dimensions”

“Oh… That’s Fast.”

And she’s off…

Many Worlds?

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

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

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

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

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

Wavefunction CollapseMeasurement involves interaction

Macroscopic Apparatus

Microscopic System

Interaction causes “collapse” ofwavefunction

Physical change in probability distribution

Before: Many possible statesAfter: Only one state

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?

Everett’s Many-Worlds Interpretation1957: Hugh Everett III, Princeton grad student

There Is No Collapse

Wavefunction always and everywhere evolves according toSchrödinger Equation

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

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

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

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

InterferometerDemonstration with photons

Split light, recombine

Classical particle:50% each detector

Classical wave:0-100% each depends on timing

+ =

+ =

InterferometerDemonstration with photons

Split light, recombine

Quantum Particle:

0-100% each

Depends on timing

Repeat many times

Build up probability

Same probability every time

Dog InterferometryWalk around block:

Which dog arrives first? Short walk, few distractions

Always same result

Red dog wins

Repeatable pattern depends on constant environment

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

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

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

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)

The End