blaylock - clark university 2/17/10 wringing john bell vocabulary the epr paradox bell’s theorem...

Blaylock - Clark University 2/17/10

Wringing John Bell

vocabulary the EPR paradox Bell’s theorem Bell’s assumptions what does it mean?

Guy Blaylock Clark University 2/17/10


Characteristics of a Garden Variety Classical

Scientific Theorylocality – actions at one location do not immediately have any effect at a separate location.

(counter)factual definiteness – any measurable quality of a physical system has a single well-defined value when it is measured (factual) or before it is measured (counterfactual).

determinism – complete knowledge of the current state of a physical system is sufficient to determine the future state of the system.


EPR à la Bohm (almost)Consider a pair of photons produced with the same polarization.

Measure the polarization of one. The polarization of the other must always turn out to be the same (“twin state”).1. atoms

2. downconverters3. subatomic decays/annihilation

There are several sources that do this:

down conversion crystal

polaroid filter

€

ψtwin =1

2VV +HH( )

QM describes this as:


EPR logic

• If one can determine certain parameters (such as polarizations in Bohm’s EPR) without interfering with the system, those parameters must be ‘real’.

• If a theory is to be considered complete, it should predict all real parameters, including the polarizations in Bohm’s EPR experiment.

• QM does not predict the polarizations.

QM is not complete!

• One could determine the polarization of photon 2 simply by looking at photon 1, without disturbing photon 2. Similarly, one could determine the polarization of photon 1 without disturbing it.


EPR caveat Original statement of EPR

“No reasonable definition of reality could be

expected to permit this.”

“…one would not arrive at our conclusion if … [the values of the second system] depend upon the process of measurement carried out on the first system”


newspapersWhy can’t the photons just be generated with some definite polarization, like two newspapers sent to different places?


Bell’s Theorem

1964 - John S. Bell publishes“ON THE EINSTEIN PODOLSKY ROSEN PARADOX”Physics 1 (1964) p.195-200.Reprinted in Speakable and Unspeakable in QMExploring the correlations between different measurements leads to new constraints based on common sense (Bell inequalities).

e.g. What if we measured polarizations at arbitrary angles 1, 2?

QM makes predictions about the correlations of polarizations that are different from the predictions of ‘common sense’ theories!


QM prediction

What is the probability of getting the same measurement (i.e. both transmitted or both absorbed)?

Prob( M1(1) = M2(2) ) = cos2(2 - 1)

What should we expect from Quantum Mechanics?

down conversion crystal

1

2


Amplitude filteringFor a wave impinging on a filter at an arbitrary angle…

Acos( A

…the amplitude that passes through is Acos ( The probability that a photon passes through is cos2 (.


Common Sense

What should we expect from Common Sense?

This is where Bell comes in.


Arbitrary angle

Prob( M1() = M2() ) = 0% coincidence

For between 0 and 90o, the coincidence is between 100% and 0%

In particular, let be some angle such thatProb( M1() = M2() ) = 75% coincidence; mismatch 25%

Prob( M1() = M2() ) is 100% coincidence

A series of photon pairs will show a sequence of both being absorbed, or both transmitted, never one absorbed and one transmitted.

F :

F :

A T T A A T A T A T T T A T A A A A T A T T A T



A A A A A T A T T T T T A T A T T A T A T A T T

A T T T A T A T A A T A A T T A T A T A T T T T

Common Sense Prediction

avg mismatch 25%F :

F :

avg mismatch 25% F :

F :

avg mismatch 50%F :

F :

Apply this “common sense” to several different cases:

Bell’s Inequality






QM for 30/60o

For

QM says the coincidence should be:

cos2(30o + 30o) = cos2(60o) = 25%

mismatch = 75%, certainly not less than 50%

QM disagrees!For = 30o, coincidence is 75%, mismatch 25%

(Remember cos2(30o) = 0.75)


Experiment vindicates QM1972 -- John Clauser (Berkeley) performs a Bell measurement using mercury vapor atoms that produce twin state photons. QM wins but the experiment does not rule out slower than light speed interactions.

1982 -- Alain Aspect performs an experiment with extremely fast acousto-optical switches to demonstrate faster-than-light effects.

1997 -- Nicolas Gisin uses Swiss telecom network optical fiber and a downconverter to demonstrate quantum effects over a distance of 7 miles.

…and many more.




Why is Bell’s inequality violated?

avg mismatch 25%F :

F :

avg mismatch 25% F :

F :

avg mismatch 50%F :

F :

Why is Bell’s inequality violated?A T T A A T A T A T T T A T A A A A T A T T A T




Assume that rotating F2 from to does not affect what happens at F1.

locality!


…the other assumption

1. The two photons always yield the same polarization.

easily verified by experiment

2. There exists an angle , such that mismatch = 25%.

easily verified by experiment

2. The mismatch for is the same as for (i.e. rotational symmetry)

3. easily verified by experiment

3. The mismatch rate between and is still 25% even when we don’t make the measurement for Counterfactual definiteness (CFD).


Conclusions

•The universe is nonlocal or non-CFD, or both.

•There are interpretations of QM that follow each.•BTW, if a theory is local

it must also be deterministic. (deduce from EPR expt.)

•Whatever you decide, the world is

blaylock - clark university 2/17/10 wringing john bell vocabulary the epr paradox bell’s theorem...

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