Transcript ppt

Quantum Philosophy
EPR and Bell's Inequalities
By Bill Kavanagh
M.Sc Candidate MUN Physics, Cosmology
www.physics.mun.ca/~wkavanag
Introduction
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Philosophy of Science
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Causality and SR/GR
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What is Quantum?
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EPR (The clash with Relativity and Quantum and
Einstein's problem etc.)
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Bell's Inequality
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Back to Realism & Objective reality???
Philosophy of Physics (or Science)
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Physics ultimately tries to explain
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What are the constituents of the world?
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Entities (electrons, atoms)
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First principles (causality)
This actually represents the two fields of
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Relativity
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Quantum
Classical Physics
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Before physics was broken into Quantum and
Relativity there was just Classical physics
It describes macroscopic objects.
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Astronomy
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Mechanics (Galileo)
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Newton Laws of Motion
The birth of electromagnetism; the study of light
sparked a change in thinking.
This lead to a “fracture” of physics and
philosophy[Omnes].
Relativity
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It was Einstein who discovered light didn't need a
medium in which to propagate
This lead to the postulate of relativity;
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No object can move faster than the speed of light.
Incredibly this leads to the fact that measurements
of time and distance are relative to the observer
and her velocity.(Essence of Relativity)
This postulate also leads to Causality or Locality
Quantum
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Quantum physics describes the world of the small.
Introduced by Planck to describe the energy in light
(radiation) as being made up of quanta or photons.
Such quantum particles can only be described by
their probabilities since their motions are random.
Wave function describes the state of a particle (or
system of particles). It gives the probability of a
particle to be in a given state. (i.e. position and time)
Fundamentals of Quantum
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A particle can be in a Superposition of states.
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Heisenberg's Uncertainty Principle
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We can not determine exactly both the position and
momentum of a particle.(Heisneberg's Microscope)
Particles like photons and electrons exhibit waveparticle duality as seen in the Double Slit
Experiment
Double Slit Experiment
Formulation of Quantum Mechanics
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Related to the uncertainty principle is the fact that...
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one can not describe light as being a particle and a
wave at the same time as illustrated by the Principle
of Complementarity.[Omnes]
The Copenhagen Interpretation distinguishes between
what is observed and what is not observed.
There is a distinction between the superposition of states
that exist before a detection is made.
Collapse of the wave function is a term that represents
detection in the Copenhagen Interpretation
Quantum Clash with Relativity
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This clash was apparent through some
experiments that seemed to violate causality like
the double slit experiment.
Einstein didn't consider this clash. He was of the
belief that Quantum mechanics was in some way
incomplete.
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On probabilities - “God does not play dice”
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On non-locality - “Spooky action at a distance”
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Einstein wrote a paper to prove Quantum's
incompleteness
EPR
Einstein, Podolsky, and Rosen
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Reality- as “If, without in any way disturbing a
system, we can predict with certainty (100%
probability) the value of a physical quantity, then
there exists an element of physical reality
corresponding to this physical quantity.”
EPR started with the premise that operators
corresponding to two physical quantities (say A
and B) don't commute leads to a problem.
A and B represent momentum and position
respectively (uncertainty principle) this means
knowing the momentum of the particle means its
coordinate has no physical reality.
EPR
Einstein, Podolsky, and Rosen
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Two Possibilities
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(I) Quantum mechanics is incomplete.
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(II) When operators corresponding to two physical
quantities do not commute the two quantities have
simultaneous reality.
EPR then proceeds on the assumption that a wave
function does contain a complete description of
physical reality.
The physics of the thought experiment then
involves two particles (called systems) which
interact and then separate
EPR
Einstein, Podolsky, and Rosen
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The result using relatively simple quantum
mechanics is “it is possible to assign two different
wave functions to the same reality”
Without getting into the QM, this can be
reasoned.
Imagine two particles that decay from a single
particle and go off in opposite directions with
equal and opposite momenta
p1=p2
EPR Conclusion
Einstein, Podolsky, and Rosen
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The negation of (I) leads to the negation of (II),
which is the only alternative.
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Thus premise (I) must be true.
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A summary of the logic is as follows
either (I) or (II)
If not-(I) then not-(II)
(I)
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EPR concludes that the quantum-mechanical
description of physical reality given by wave
functions is not complete.
Bell's Inequality
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Bell recognized that EPR were actually correct.
However, one of the assumptions Einstein made
(a reasonable assumption at the time) distorted
the conclusion.
Using the assumption of causality actually meant
that the true conclusion of EPR was that Quantum
Mechanics is incomplete or locality is violated.
Bell's Inequality
First Assume: Num(A, not B, C) + Num(not A, B, not C)  0
Adding Num(A, not B, not C) + Num(A, B, not C)
LHS: Num(A, not B, C) + Num(A, not B, not C) +
Num(not A, B, not C) + Num(A, B, not C)
LHS: Number(A, not B) + Number(B, not C)
RHS: 0 + Num(A, not B, not C) + Num(A, B, not C)
RHS: Num(A, not C)
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Num(A, not B) + Num(B, not C)  Num(A, not C)
Testing Bell's Inequality
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In order to test Bell's Theorem we need an experiment
that mimics quantum particles.
A Gedanken (thought) experiment can be used that is
free of quantum complexity.
One such experiment consists of two detectors, A and
B, and a source C. (Mermin)
The mechanics of how the setup works will come
later.
Each detector has a switch with three positions.
Depending on the setting of the switch an “event”
will result in a Green (G) or Red (R) light coming on.
The Experiment
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There are no connections between detectors
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There is a randomness in the setting of the
switches
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The procedure mimics a quantum world.
Procedure
Switches are randomly selected
● Button is pushed on source (...to release particles.
Note: ignore for now... the details will follow).
● Consequently each detector flashes red or green.
● Data: pair of colors and switch settings i.e. “32RG”
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Features of Data
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Feature 1:
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Looking at runs where switches have the same setting
results in the lights on respective detectors are always
the same
Feature 2:
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Looking at all runs; flashing of lights is entirely
random.
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The lights flash the same ½ of the time
Lights are different ½ of the time
How does it Work?
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The flashing of the lights is linked to pressing the
button.
How can each light know to
flash the same color in the event
that the switches have the same
setting?
●Detectors can't be
preprogrammed to flash the
same color because ½ the time
they are different.
●The answer is in the particles.
●The detectors can have targets
in side.
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First Feature
The first feature of the data is accounted for if the
particles produced at the source are of the same
variety.
“Fearture 1:
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Looking at runs where switches have the same setting
results in the lights on respective detectors are always
the same”
Information Sets
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For this explanation of the experiment to work
the particle should carry with it a set of
instructions for how it is to flash on each setting.
1.Instructions for each of 3 settings is required
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For the case of flashing the same color particles will
not know if the setting's are 11, 22, 33.
2.The absence of communication means
instruction sets must be carried in every trial.
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Even when switches aren't at the same setting the
particles always have to be ready for that case
Impossible Experiment
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We will see:
This experiment, nor any other, can satisfy the
second feature of the data.
“Feature 2:
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Looking at all runs; flashing of lights is entirely
random.
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The lights flash the same ½ of the time
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Lights are different ½ of the time”
Information Sets in this Experiment
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If instruction sets exist then consider the event of
instruction set RRG
same color flashes: 11, 22, 33, 12, 21
different color flashes: 13, 31, 23, 32
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Each of these possibilities is equal in probability
because the settings are random.
Chances of same color flashes is 5/9, as well as
for other similar sets.
RRR and GGG result in same color all the time.
Bell's Inequality Violated!
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If instruction sets exist the same colors will flash
at least 5/9 times. (Bell's Inequality)
The actual gedanken experiment results in, as
already illustrated, the same colors flashing in ½
the trials.
Also there can be no instruction sets.
This experiment represents quantum mechanisms
that display the same violation of Bell's
Inequality.
Quantum Spin
Stern-Gerlach Experiment
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Putting all the
magnets in a box
makes a spin filter.
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The orientation
defines the
direction up or
down for the spin.
Application of Bell’s Inequality
A: electrons are "spin-up" for zero degrees.
B: electrons are "spin-up" for 45 degrees.
C: electrons are "spin-up" for 90 degrees.
Num( 0°, not  45°) + Num( 45°, not  90°)
 Number( 0°, not  90°)
● Experiment was done in 1969.
● Inequality was violated!
Meaning?
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We can look at the example of a particle in our
experiment by forcing a particle to arrive at A
before B.
If we detect it's 3-color(color when switch is 3) at
B we know the other particle will have the same
color at A.
Did the particle at A have its 3-color prior to the
measurement at B?
NO. Prior to the measurement at B the detector
can still decide to detect the 1 or 2-color.
Meaning?
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Thus, if the 3-color already existed then so must
1- and 2-colors.
But we have already illustrated that there are no
information sets.
Is the particle at A 3-colored after the
measurement at B.
Yes. It is a particle that will cause A to flash the
same color.
This suggest that something may transmitted
between the two; non-locally
Conclusions
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The failure of Bell's Inequality means that
Einstein's insistence on the realism and locality
was not right.
In the quantum world we have seen that things
don't have a value unless we detect them.
Is the Moon There When Nobody
Looks?
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No
Bibliography
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Omnes, Roland Quantum Philosophy. Princeton
University Press, Princeton, New Jersey, 1999.
Aczel, A. D. Entanglement The Greatest Mystery
in Physics. John Wiley and Sons Ltd, 2002
Harrison, David M.., Physics Virtual Bookshelf
Upscale, 2000,
http://www.upscale.utoronto.ca/GeneralInterest/QM.html