Quantum Mechanics is Weird

1. Quantum Mechanics is Weird It’s all done with Mirrors • Many of the predictions of quantum mechanics are verified with ordinary matter particles (like electrons), but these experiments are hard • The calculations are harder, but the results are similar when you use photons • And we are very good at manipulating light! • Ordinary mirrors reflect light with nearly 100% effectiveness • If you make the reflecting layer thin enough, you can get it to reflect only half the light mirror half-mirror

2. Half-mirrors and photons: Let’s send photons through a half-mirror • The photon gets split into two equal pieces • Each detector sees 50% of the original photons • Even if we send photons in one at a time • Never in both detectors 50% A 50% • If you send in a wave the other way, the same thing happens • There’s a “phase difference”, but since we square the amplitude, the probabilities are the same • 50% in each detector Detectors B 50% 50%

3. Interferometry • Now use two mirrors and two half-mirrors • We can reconstruct the original waves • The photon gets split into two equal pieces • The two halves of the photons are recombined by the second half-mirror • Always goes to detector A • Even one photon at a time • If you send in a wave the other way, the photon is still split in half • The “phase difference” lets it remember which way it was going • Always in detector B 0% A 100% Interferometry requires that we carefully position the mirrors 100% B 0%

4. Non-Interferometry • How does the photon remember which way it was going? • Replace one mirror with a detector • The photon gets split into two equal pieces • Half of them go to detector C • The other half gets split in half again • Detectors A and B each see 25% • Even if you do it one photon at a time • The “memory” of which way it was going is in both halves A 25% C • Depending on which experiment you do, photons sometimes act like particles and sometimes act like waves 50% B 25%

5. The Copenhagen Interpretation • Pretend you are a photon approaching the first mirror • Should you act like a particle or a wave? 100% 0% A • The Copenhagen interpretation • The photon gets split into two equal pieces • When it reaches one of the detectors, it either: • Suddenly is all there, and not at all the other place (50%), or • Suddenly is all the other place, and not there (50%) • This change occurs instantly • Faster than the speed of light • There is no way to use this to communicate faster than light, however • This process is probabilistic, you can’t predict which of these two outcomes will occur 100% B 0% Called “Collapse of the Wave Function”

6. Can you have your cake and eat it too? • When you do interference, you can tell the photon went both ways • For other experiments, you can measure which way it went • Can we do both? • The plan: • Do experiment in space (no friction, etc.) • Carefully measure momentum of mirror before you send one photon in • Check photon goes to detector A • Remeasure momentum and determine the path A 100% • The problem • If you measure the mirror’s initial momentum accurately, you have small p, and big x • Poor positioning of mirror ruins the interference B 0%

7. Assessing Quantum Mechanics • The Good: • Schrödinger’s Equation can be used to calculate lots of things: • Energy, Dynamics, Probability of outcomes • The Bad: • When you perform a measurement, something complicated happens • Probabilistic, Non-local • What it means is under dispute • The term “measurement” isn’t defined • The Ugly: • In the Copenhagen Interpretation, 80% of the rules describe how you do measurements • But 90% of calculations deal only with Schrödinger’s equation

8. Interpretations of Quantum Mechanics • All of the following are taken seriously by some people • Copenhagen interpretation • Collapse of the wave function happens as soon as you measure • Probabilistic, instantaneous quantum transmission of information • Bohm Pilot wave theory • The “wave function” guides the “particle”, which has an actual place • Instantaneous transmission of information • Not clear if it can be generalized to all QM • Advanced Wave • At measurement, information gets transmitted backwards in time • Weird, but it works • Quantum Mechanics as Statistical Mechanics • Quantum mechanics only describes probabilities – infinitely repeated experiments • Not clear what this has to do with the real world • Many Worlds • Wave functions, instruments, and people never collapse waves • Defies common sense – “Meet your Maker” game show