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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:
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
•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
50%
A 50%
Detectors
B
50%
50%
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
A 0% •Always in detector B
100%
Interferometry requires that we
carefully position the mirrors
100% B 0%
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
C
25%
•Depending on which experiment you do,
photons sometimes act like particles and
sometimes act like waves
50%
B
25%
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
100%
B
•Faster than the speed of light
0%
•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
Called “Collapse of
the Wave Function”
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
The plan:
•Can we do both?
•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
pbefore
A 100%
pafter
B
0%
p
if upper path
0

 h  if lower 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
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
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