Wringing%20John%20Bell

1
Wringing John Bell

• vocabulary
• the EPR paradox
• Bells theorem
• Bells assumptions
• what does it mean?

Guy Blaylock Williams College 4/17/15
2
Characteristics of a Garden Variety Classical
Scientific Theory
locality 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.
3
Characteristics of Orthodox QM
Orthodox QM obeys none of these characteristics

• When a wave function collapses, it collapses
  everywhere at once. (nonlocal)
• When a physical system is in a state of
  superposition, it is not in a single well-defined
  state. (indefinite)
• When a system collapses to a single final state
  among multiple possibilities of a superposition,
  it does so randomly. (indeterminate)

4
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 (in QM this is thetwin
state).
There are several sources that do this
1. atoms2. downconverters3. subatomic
decays/annihilation
5
Quantum Twin State
QM explains the EPR experiment using the quantum
twin state

• Prior to measurement, the two-photon system is
  not in one definite state its in a
  superposition of V1V2 and H1H2.
• When a measurement is made, both photon
  polarizations collapse, nonlocally.
• The final choice, V1V2 or H1H2, is determined
  randomly.

6
EPR logic

• 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.

• If one can determine certain parameters (such as
  polarizations in Bohms EPR) without interfering
  with the system, those parameters must bereal.
• If a theory is to be considered complete, it
  should predict all real parameters, including the
  polarizations in Bohms EPR experiment.
• QM does not predict the polarizations.
• QM is not complete!

7
EPR caveat
Original statement of EPR
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
No reasonable definition of reality could be
expected to permit this.
8
newspapers
Why cant the photons just be generated with some
definite polarization, like two newspapers sent
to different places?
9
Bells Theorem
1964 - John S. Bell publishesON THE EINSTEIN
PODOLSKY ROSEN PARADOXPhysics 1 (1964)
p.195-200.Reprinted in Speakable and Unspeakable
in QM
Exploring 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!
10
QM prediction
What should we expect from Quantum Mechanics?
What is the probability of getting the same
measurement (i.e. both transmitted or both
absorbed)? Prob( M1(?1) M2(?2) ) cos2(?2 -
?1)
?1
?2
down conversion crystal
11
Amplitude filtering
?????
For 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 (??????.
12
Common Sense
What should we expect from Common Sense?
This is where Bell comes in.
13
Arbitrary angle
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 T T A A T A T A T T T A T A A A A T A T T A T
Prob( M1(?) M2(?????) ) 0 coincidence For
?????between 0 and 90o, the coincidence is
between 100 and 0 In particular, let ? be some
angle such that Prob( M1(?) M2(???) ) 75
coincidence mismatch 25
14
Common Sense Prediction
Apply this common sense to several different
cases
??????????????? avg mismatch 25 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 T T T A T A T A A T A A T T A T A T A T T T T
???????????????? avg mismatch 25? F? ??? F?
???
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 A A T A T A T T T A T A A A A T A T T A T
Bells Inequality
???????????????? avg mismatch ? 50 F? ??? F?
???
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
15
QM for 30/60o
QM disagrees!
For ?? 30o, coincidence is 75, mismatch
25 (Remember cos2(30o) 0.75)
For ??????????????????? QM says the coincidence
should be cos2(30o 30o) cos2(60o)
25 mismatch 75, certainly not less than 50
16
Experiment vindicates QM
1972 -- 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.
17
Why is Bells inequality violated?
Why is Bells inequality violated?
??????????????? avg mismatch 25 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 T T T A T A T A A T A A T T A T A T A T T T T
???????????????? avg mismatch 25? F? ??? F?
???
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 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!
???????????????? avg mismatch ? 50 F? ??? F?
???
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
18
the other assumption

• The two photons always yield the same
  polarization.
• easily verified by experiment
• There exists an angle ?, such that mismatch
  25.
• easily verified by experiment
• The mismatch for ?????????????? is the same as
  for ???????????????? (i.e. rotational symmetry)
• easily verified by experiment
• The mismatch rate between ???????and ????? is
  still 25 even when we dont make the measurement
  for ??????Counterfactual definiteness (CFD).

QM says there is more than one possibility for
each measurement. The ????? sequence that
disagrees with ????? by 25 is not the same as
the ????? sequence that disagrees with ?????? by
25.
19
Common Sense Prediction
??????????????? avg mismatch 25 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 T T T A T A T A A T A A T T A T A T A T T T T
???????????????? avg mismatch 25? F? ??? F?
???
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 A A T A T A T T T A T A A A A T A T T A T
In QM the two sequences for ???????and ??????
dont need to be the same!
20
Conclusions

• The universe is nonlocal or non-CFD, or both.
• There are interpretations of QM that follow each.

• Whatever you decide, the world is

Weird
21
underlying realities
Orthodox/Copenhagen - (Bohr, Heisenberg)
non-CFD, non-deterministic non-local Bohms
interpretation - (Bell, Bohm, deBroglie)
definite, deterministic non-localPilot waves
direct the particles non-locally. Many Worlds -
(DeWitt, Everett) local, deterministic
indefiniteNo collapse every possibility exists
as a part of the superposition.
Agnostic - (many contemporary scientists)Who
knows, who cares. Makes no sense to ask what is
going on outside of observation.
22
More on Definiteness

• CFD might seem to implyrealism. This is
  probably what EPR were trying to say with their
  elements of reality.
• The reverse is not true. Realism does not imply
  CFD. If one considered a photon wave function
  (which may be a superposition) to be real, it
  still would not imply a definite polarization.
• Definiteness does not imply determinism. The
  definite characteristic could evolve randomly.
• BTW, if a theory is local it must also be
  deterministic. (deduce from EPR expt.)

23
(No Transcript)
24
History of the Worlds
1957 Hugh Everett writes a thesis on the
relative state interpretation of QM Hugh
Everett III, Relative State Formulation of
Quantum Mechanics, Rev. Mod. Phys. 29, 454-462
(1957)
Bryce DeWitt popularizes, embellishes and
somewhat misrepresents the concept in the many
worlds interpretation Bryce S. DeWitt ,
Quantum mechanics and Reality, Physics Today
23, 30-35. (1970)
The essence of Everetts many worlds
interpretation is the same as orthodox QM except
that collapse does not happen. Superpositions
persist.
every quantum transition taking place on every
star, in every galaxy, in every remote corner of
the universe is splitting our local world on
earth in myriads of copies of itself.
25
polarizing filters
A wave that moves only in a plane is called
plane-polarized or linearly polarized.
A vertical filter allows a vertically polarized
wave to pass,
and lets the vertical part of a 45o wave through.
but blocks a horizontally polarized wave,
vertically polarized
26
polarized photons
For light waves, the plane of oscillation defines
the polarization. A photons polarization is
determined by whether it does or does not pass
through a polarizing filter.
A photon that passes through a vertical filter is
vertically polarized.
but it will not make it through a horizontal
filter.
It will pass through any number of other vertical
filters.
Think of photon polarization as a binary
quantity. A polarizer provides a way of measuring
it.
27
(No Transcript)