1. Quantum Philosophy EPR and Bell's Inequalities By Bill Kavanagh
M.Sc Candidate MUN Physics, Cosmology

2. Introduction Philosophy of Science Causality and SR/GR
What is Quantum?
EPR (The clash with Relativity and Quantum and Einstein's problem etc.)
Bell's Inequality
Back to Realism & Objective reality???

3. Philosophy of Physics (or Science)
Physics ultimately tries to explain
What are the constituents of the world?
Entities (electrons, atoms)
First principles (causality)
This actually represents the two fields of
Relativity
Quantum
-you can probably replace the word physics with science in this case and other general philosophical points but I prefer physics. -

4. Classical Physics
Before physics was broken into Quantum and Relativity there was just Classical physics
It describes macroscopic objects.
Astronomy
Mechanics (Galileo)
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].
-(intro) classical physics was used on the premise that things were as we perceived them
-2-Newton's Laws:
-object stays in uniform motion
-Action = Reaction
-F=ma
-3-physicists tried to discover what light propagated in. Experiment showed that there was no propagation medium.
-4-The fracture is between our perception of the universe and the means by which we can investigate it.

5. Relativity
It was Einstein who discovered light didn't need a medium in which to propagate
This lead to the postulate of relativity;
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

7. Quantum 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)
-1- Quantum describes electrons and protons and atoms. They are hard to keep track of at such a small scale.

8. Fundamentals of Quantum
A particle can be in a Superposition of states.
Heisenberg's Uncertainty Principle
We can not determine exactly both the position and momentum of a particle.(Heisneberg's Microscope)
Particles like photons and electrons exhibit wave- particle duality as seen in the Double Slit Experiment

9. Double Slit Experiment

10. Formulation of Quantum Mechanics
Related to the uncertainty principle is the fact that...
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

11. Quantum Clash with Relativity
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.
On probabilities - “God does not play dice”
On non-locality - “Spooky action at a distance”
Einstein wrote a paper to prove Quantum's incompleteness

12. EPR Einstein, Podolsky, and Rosen
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.

13. EPR Einstein, Podolsky, and Rosen
Two Possibilities
(I) Quantum mechanics is incomplete.
(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

14. EPR Einstein, Podolsky, and Rosen
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
-3-Using the conservation of momentum we can determine the momentum of the other.

15. EPR Conclusion Einstein, Podolsky, and Rosen
The negation of (I) leads to the negation of (II), which is the only alternative.
Thus premise (I) must be true.
A summary of the logic is as follows
either (I) or (II)
If not-(I) then not-(II)
(I)
EPR concludes that the quantum-mechanical description of physical reality given by wave functions is not complete.
-1-Our initial assumption leads to the negation of (II).
-3- possibilities are for (I) &(2) are :[OR table]
true & true = true
false & true = true
false & false = false

16. Bell's Inequality 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.

17. 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) 
Num(A, not B) + Num(B, not C)  Num(A, not C)

18. Testing Bell's Inequality
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.

19. The Experiment There are no connections between detectors
There is a randomness in the setting of the switches
The procedure mimics a quantum world.

20. 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”
-2- Mechanisms that allows this to work will gradually be explained
-4- detector 1: switch = 3 color=Red
detecotr 2: switch = 3 color=Green

21. Features of Data Feature 1: Feature 2:
Looking at runs where switches have the same setting results in the lights on respective detectors are always the same
Feature 2:
Looking at all runs; flashing of lights is entirely random.
The lights flash the same ½ of the time
Lights are different ½ of the time

22. How does it Work?
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.
-5-each detector is wired so that if a particle lands in the GRG bin the detector flips into a mode in which the light flashes G if the switch is set to 1...
It makes sense now that on the detectors when on the same setting the flashes will be the same

23. 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:
Looking at runs where switches have the same setting results in the lights on respective detectors are always the same”

24. Information Sets
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
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.
Even when switches aren't at the same setting the particles always have to be ready for that case
-Instruction sets should meet the following requirements.

25. Impossible Experiment
We will see:
This experiment, nor any other, can satisfy the second feature of the data.
“Feature 2:
Looking at all runs; flashing of lights is entirely random.
The lights flash the same ½ of the time
Lights are different ½ of the time”

26. Information Sets in this Experiment
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
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.

27. Bell's Inequality Violated!
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.

28. Quantum Spin

29. Stern-Gerlach Experiment
Putting all the magnets in a box makes a spin filter.
The orientation defines the direction up or down for the spin.

30. 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!

31. Meaning?
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.

32. Meaning?
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

33. Conclusions
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.

34. Is the Moon There When Nobody Looks?

35. Bibliography
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,