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

Half-mirrors and photons:

•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

•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

Let’s send photons through a half-mirror

Detectors

A

B

50%

50%

50%

50%

Interferometry

•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

Now use two mirrors and two half-mirrors•We can reconstruct the original waves

A

B

100%

0%

•The “phase difference” lets it remember which way it was going•Always in detector B

0%

100%

Interferometry requires that we carefully position the mirrors

Non-InterferometryHow does the photon remember which way it was going?•Replace one mirror with a detector

A

B

25%

25%

•The “memory” of which way it was going is in both halves

C

50%

•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

•Depending on which experiment you do, photons sometimes act like particles and sometimes act like waves

The Copenhagen InterpretationPretend you are a photon approaching the first mirror•Should you act like a particle or a wave?

B

100%

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

A

0%

100%

0%

Called “Collapse of the Wave Function”

Can you have your cake and eat it too?

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

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

•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?

A

B

100%beforep

afterp

0 if upper path

if lower pathp

h

0%

Assessing Quantum MechanicsThe 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

Interpretations of Quantum MechanicsAll 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