Published on February 16, 2009
Quantum Physics for Dogs I like cheese Chad Orzel Many Worlds, Many Treats? http://scienceblogs.com/principles/
“ I’m Looking for Steak”
“ I Can Sniff Into Extra Dimensions”
“ Oh… That’s Fast.”
And she’s off…
Quantum Mechanics Central 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 each of the allowed states 4) Measurement: Measuring the state of an object absolutely determines the state of that object
What’s the Problem? 1) Wavefunctions 2) Allowed States 3) Probability 4) Measurement Schrödinger Equation Use Schrödinger Equation to find wavefunctions determine allowed states Dog states: Problem: Can be in multiple states at once Awake Asleep
Superposition States Mathematically, sum of two allowed states is also an allowed state Not too surprising– use for convenience in classical physics + = Quantum System only observed in one state OR Awake Asleep Awake Asleep
Measurement Problem Quantum System exists in multiple states When measured, find only one state Problem: Why do we only see one state? 1) Wavefunctions 2) Allowed States 3) Probability 4) Measurement Schrödinger Equation Nothing in mathematical apparatus of QM explains measurement Interpretations: meta-theories explaining measurement
Copenhagen Interpretation Developed by Niels Bohr in Denmark Absolute division between scales Microscopic: electrons, atoms, molecules Obey quantum rules superposition states Macroscopic: dogs, cats, physicists, steak Obey classical rules no superposition states
Wavefunction Collapse Measurement involves interaction Macroscopic Apparatus Microscopic System Interaction causes “collapse” of wavefunction Physical change in probability distribution Before: Many possible states After: 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 Interpretation 1957: Hugh Everett III, Princeton grad student There Is No Collapse Wavefunction always and everywhere evolves according to Schrödinger Equation
Many-Worlds, Many Minds If 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 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 division All 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
Decoherence What 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 would have it… Answer is INTERFERENCE Wave-like behavior of particles Interference effects are the signature of superposition states Particles in two places at same time following two different paths to same goal
Interferometer Demonstration with photons Split light, recombine Classical particle: 50% each detector Classical wave: 0-100% each depends on timing + = + =
Interferometer Demonstration with photons Split light, recombine Quantum Particle: 0-100% each Depends on timing Repeat many times Build up probability Same probability every time
Dog Interferometry Walk around block: Which dog arrives first? Short walk, few distractions Always same result Red dog wins Repeatable pattern depends on constant environment
Dog Interferometry 2 Look at much longer path: Many more potential distractions Distractions move from day to day Winner becomes completely random 50% chance either dog wins
Interferometer Back to photons Longer path, more interactions with environment (air molecules, etc.) Interactions shift probabilities Interactions fluctuate randomly Probability 50% for each detector Looks just like classical particle
Decoherence + Many-Worlds Combination 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 interactions faster decoherence
Many-Worlds in SF Most 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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