physics 256: lecturephysics 256: lecture q8 lecture · · 2016-12-06question richard feynman...

Physics 256: LecturePhysics 256: LectureQ8 Lecture

State of Quantum Mechanics EPR Paradox Bell’s Thm

Physics 201: Lecture 1, Pg 1

Question

Richard Feynman said, “[the double-slit experiment] has in it the heart of quantum mechanics; in reality it contains the only mystery ” Can you tell what mysterycontains the only mystery. Can you tell what mystery Feynman is talking about?


Quantum Mechanics

Even physicists who accept QM disagree Even physicists who accept QM disagree about how to interpret the rules


Quantum Indeterminacy

Even if we know all there is to know (wavefunction) we cannot predict the result of a simple experiment to measure position

Question: Suppose I measure the position of a particle to be atQuestion: Suppose I measure the position of a particle to be at position xi. Where was it prior to the measurement?

A. Realist: It was really at xi (QM is incomplete)B. Orthodox (Copenhagen Interpretation): The particle wasn’t

anywhere. The act of measurement forced the particle to “take a stand.”


Einstein and Objective RealityEinstein was never comfortable with quantum mechanics Einstein was never comfortable with quantum mechanics

He felt that properties of physical objects have an objective reality independent of measurement

In the orthodox interpretation, we cannot say a quantonmeasured to be spin up had that property before themeasured to be spin up had that property before the measurement

In fact, we can only know one spin component of the particle, because measurement of one component disturbs knowledge of the othersof the others

Therefore Einstein thought QM was an incomplete description


g p pof reality

Two Views of Quantum Mechanics Realist: Quantum mechanics must be

incomplete There is such a thing as objectiveincomplete. There is such a thing as objective reality.

Orthodox/Copenhagen: There is nothingOrthodox/Copenhagen: There is nothing wrong with quantum mechanics. Objective reality does not exist.


Localityy

Locality (rough version): Only things close to me can affect meclose to me can affect me

Locality: No influence may travel faster than the speed of lightthan the speed of light


EPR Paradox (1935) Source of Spin 0 decays into an electron and positron To conserve spin one must have spin up one must p p p

have spin down (quantons are entangled) The state vector is some linear combination of

BAzz

BAzz

BA BA


Einstein-Podolsky-Rosen Paradox If you measure spin up at A you are determined to

have spin down at B Locality: A cannot affect B (at least not faster than

light) The particle at B must have been spin down all along,

it must be an element of realityAnd QM is just not good enough to predict this And QM is just not good enough to predict this (incomplete)


EPR Paradox

Einstein: Since we cannot have a non-local influence, the outcomes must be pre-determined by

bj ti l l ti (hidd i bl ) th tobjectively real properties (hidden variables) that each electron carries with itEinstein: Since quantum mechanics does not Einstein: Since quantum mechanics does not describe these properties it must be incomplete

Problem: The results of the EPR paradox are the Problem: The results of the EPR paradox are the same regardless of your interpretation


Bell’s Theorem

Provided a way to differentiate between a local hidden variable theory (LHVT) and QMhidden variable theory (LHVT) and QM

Bell’s Theorem: No physical theory of local hidden variables can ever reproduce all of the predictionsvariables can ever reproduce all of the predictions of quantum mechanics.

There are specific measurements that can beThere are specific measurements that can be made to distinguish between QM and LHVT

Experiments can now show whether QM is wrong, or if the world is inherently non-local


Bell’s Theorem

Bell’s Theorem: No physical theory of local hidden variables (LHVT) can ever reproduce all of thevariables (LHVT) can ever reproduce all of the predictions of quantum mechanics.

There are specific measurements that can be made to distinguish between QM and LHVTmade to distinguish between QM and LHVT

Experiments can now show whether QM is incomplete, or if the world is inherently non-local


Experiment Source of Spin 0 decays into an electron and positronSource of Spin 0 decays into an electron and positron Now experimenters measure the spin along one of three

axis at random (a, b or c: 120 degrees apart) Each measurement will return red (R) or green light (G) We will look at the combination of measurements The Same: RR or GG Different: RG or GR

1

23

R GR


G R

Instruction SetsFor the local hidden variable theories (LHVT) the results of the o e oca dde a ab e eo es ( ) e esu s o e

experiments are already known when the particles leave the source. There are eight ways this could be.

1

23 23

R GR


G R

Clicker Question 1:Here are the eight possible combinations of spins that could e e a e e e g poss b e co b a o s o sp s a cou d

result from our decay (if there are hidden variables). What should the three highlighted boxes read?

(a) SSS(b) DSS(b) DSS(c) SDS(d) SDD(e) DDS


Clicker Question 2:Here are the eight possible combinations of spins that could

result from our decay (if there are hidden variables). If we run the experiment with a large number of electrons what is the “hidden variable” probability of getting Same?

(a) Pr(S) = 1(b) Pr(S) = 5/9(b) Pr(S) = 5/9(c) Pr(S) 5/9(d) Pr(S) 5/9( ) P (S) 5/9(e) Pr(S) 5/9


LHVT: Probabilities

Bell inequalities No matter how one adjusts the populations the j p p

results will be consistent with these inequalities

94Pr D9

5 95Pr S


Quantum Mechanics

Now we can calculate the probabilities according to QM

Two possibilities: The two axis are the same. The two axis are 120 degrees off of each other


Clicker Question 3:If the two axis are the same what results will we have?

Th S(a) The Same(b) Different(c) It Depends(c) It Depends

A = 0 B = 0

R GR


G R

Clicker Question 4:The detector at A is in the z-direction and the detector at B is

120 degrees off from this suppose you measure spin up at120 degrees off from this, suppose you measure spin up at A right before the measurement at B is made. What is the spin state vector at B before a measurement is made?

2

2

sincos

)(

a

2

2

cossin

)(

b zˆ 2 2

1

)(c

0

)(d

0

)(

1

)(

A = 0 B = 120

x

R GR

A 0 B 120


G R

Clicker Question 5:If the two axis are 120 degrees off of each other what is theIf the two axis are 120 degrees off of each other, what is the

probability you will get a Different result?

120120 1201202

120cos2

120sin)(a2

120cos2

120sin)(b

2

2

sincos

2120sin)( 2d

2120cos)( 2c

2

2sin

A = 0 B = 120

2cos

R GR

A 0 B 120


G R

QM: Probabilities The angle between measurements will be 0 1/3 of The angle between measurements will be 0 1/3 of

the time and 120 2/3 of the time Therefore QM makes the following predictionsTherefore QM makes the following predictions

1120i2P 2D 21

2120sin

32Pr 2 D

112021 21

2120cos

32

31Pr 2 S

These predictions are inconsistent with those of the LHVT


LHVT It is now an experimental question

Results These type of experiments have been carried out

and consistently agree with the predictions of t h i d th t l tquantum mechanics and thus seem to rule out a

local hidden variable theoryQuantum mechanics is inherently non local Quantum mechanics is inherently non-local

This non-localities that are at the foundations of quantum information and quantum computingquantum information and quantum computing

How can measuring A collapse the wave function at B? Doesn’t this violate relativity?y No. Because no information can be transmitted via this collapse


Clicker Question 6:

Experiments have been carried out and consistently agree withExperiments have been carried out and consistently agree with the predictions of quantum mechanics and thus seem to rule out a local hidden variable theory. Does this mean the Copenhagen interpretation is correct?Copenhagen interpretation is correct?

A. YesA. YesB. No


Schrodinger’s Cat


The Collapse Problem

Ordinary: Wave function evolves in a Ordinary: Wave function evolves in a leisurely fashion according to the S.E. TISE leads to the time-evolution ruleS eads o e e e o u o u e

Measurement: Wave function suddenly collapses around one point.p p


PCQ:Which do you personally think is the weirdest part of QM and

why?

(a) It does not support objectively real quanton properties(b) It requires possibly superluminal connections(b) It requires possibly superluminal connections(c) It has two incompatible time evolution rules(d) There seems to be some kind of unexplained disconnect

between microscopic and macroscopic physics


And Still Some Loose Ends


physics 256: lecturephysics 256: lecture q8 lecture · · 2016-12-06question richard feynman...

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