1. Quantum Nonlocality
Carlos R. Paiva
IST, June 2017

2. The following lecture is mainly based on two
non-technical accounts. On the one hand, I use
the line of thought put forward by Tim Maudlin.
On the other hand, I will use an abstract pictorial device developed by David Mermin.

3. References
Tim Maudlin, Quantum Non-Locality and Relativity, Third Edition.
Wiley-Blackwell, 2011 (Chapter 1).
N. David Mermin, Boojums All the Way Through.
Cambridge University Press, 1990 (pp. 81 – 94; pp. 110 – 176).

4. “It must have been around 1950
“It must have been around I was accompanying Einstein on a walk from The Institute for Advanced Study to his home, when he suddenly stopped, turned to me, and asked me if I really believed that the moon exists only if I look at it.”
Abraham Pais (1918 – 2000), Subtle is the Lord – The Science and the Life of Albert Einstein (p. 5).
New York: Oxford University Press, 1982 (reissued with a new foreword by Sir Roger Penrose, 2005)

5. “The questions with which Einstein attacked the quantum theory do have answers; but they are not the answers Einstein expected them to have. We now know that the moon is demonstrably not there when nobody looks.”
N. David Mermin (1935 –), Boojums All the Way Through (p. 81).
New York: Cambridge University Press, 1990

6. EPR experiment
A. Einstein, B. Podolsky, and N. Rosen,
“Can quantum mechanical description of reality
be considered complete?”
Physical Review, Vol. 47, pp. 777 – 780, 1935.

7. Malus’ law Input linearly polarized light Linear polarizer
Transmitted linearly
polarized light

8. Malus’ law

9. Malus’ law

10. Malus’ law

11. How come Malus’s law, something that is quite classical, is able to lead us from the world of classical field theory (namely, classical electrodynamics, governed by Maxwell equations) into the strange realm of quantum electrodynamics, i.e., into those mysterious and ellusive quanta of light called photons which, nevertheless, can be experimentally observed (e.g., using a photomultiplier tube, thereby exploiting the photoelectric effect)?
The photon, one should stress, is – as far as we can tell (at present) – a massless elementary and stable particle that has no electric charge and has two polarization states. Actually it is a gauge boson – the force carrier for the electromagnetic interaction.

12. Question
Maxwell theory – classical electrodynamics – predicts that the energy of a light wave depends on its intensity, not on its frequency. However, in the photoelectric effect (for example), the energy of the ejected photon (from the metal) is directly related to the incident light’s frequency, not to its intensity. After passing (if that is the case) a linear polarizer, each photon has the same energy has before. How can we explain, then, Malus’s law?
Answer
The only possibility is that fewer photons exit the polarizer than those going in. A photon either passes the polarizer or is blocked (i.e., absorbed) by it.

14. Three unconnected parts
Mermin’s device:
Three unconnected parts
Detector A
Source C
Detector B

15. Detector A

16. Mermin’s device

19. There are three linear polarizers at each detector;
we will call them «switches»

22. Mermin’s device: the three facts that
characterize the produced data – 1
Fact 1 When the switches have the same setting, the lights always flash the same color.
Fact 2 The same colors flash 75% of the time when
the switches differ by 30o.
Fact 3 The same colors flash 25% of the time when
the switches differ by 60o.

23. Mermin’s device: the three facts that
characterize the produced data – 2

33. Both particles must always choose the same strategy in complete ignorance of the questions (switches) they are to be asked.
The setting XY of both stwiches (at A and B) is determined by a random process that is perfectly independent of the adopted strategy.
The long-run results (i.e., the whole behavior) will depend only on the values (α, β, γ, δ) adopted by both particles.

42. Reinhold Anton Bertlmann (1945 –)
Bell has shown in a paper entitled
“Bertlmann’s socks and the nature of reality”
(Bell, pp. 139 – 158)
how his analysis is much more deep than the
following simple and naive observation:
«Dr. Bertlmann likes to wear two socks of different colors. Which color he will have on a given foot on a given day is quite unpredictable. But when you see that the first sock is pink you can be already sure that the second sock will not be pink.»

43. In our macroscopic world we are accustomed to believe that Dr
In our macroscopic world we are accustomed to believe that Dr. Bertlmann wears a well-defined sock in each foot. This means: although we might not know the color (before seeing it), we do know for sure that he has, in reality, only one definite sock in each foot.
However, if quantum mechanics is correct then we cannot say – in the quantum realm – that Dr. Bertlmann is wearing a well-defined sock in each foot. What we actually have is a quantum state which is a linear superposition of the two eigenstates (i.e., «pink» and «not pink») in each foot. Only when we see (measure) that one foot is wearing «pink» can we predict, with certainty, that the other foot is wearing «not pink». Furthermore, the two feet may be far from one another: spooky action at a distance, according to Einstein.
Somehow, by revealing the color from one foot, we have forced instantaneously a projection of the other foot from its obscure superposition of eigenstates (a murky combination of «pink» with «not pink») onto a well-defined eigenstate (either «pink» or «not pink»).
Experimental observations confirm the validity of quantum mechanics and disprove EPR.

44. “In particular [Ernst Pascual] Jordan [1902 – 1980] had been wrong in supposing that nothing was real or fixed in that world before observation. For after observing one particle the result of subsequently observing the other (possibly at a very remote place) is immediately predictable. Could it be that the first observation somehow fixes what was unfixed, or makes real what was unreal, not only for the near particle but also for the remote one? For EPR that would be an unthinkable ‘spooky action at a distance’. To avoid such action at a distance they have to atribute, to the space-time regions in question, real properties in advance of observation, correlated properties, which predetermine the outcomes of these particular observations.”
John Stewart Bell (1928 – 1990), Speakable and Unspeakable in Quantum Mechanics, Second Edition (p. 143).
Cambridge: Cambridge University Press, 2004 (with a new introduction by Alain Aspect)

45. “For instance, if we have a pair of identical twins we do not know what their blood type is before testing them, but if we determine the type of one, we know for sure that the other is the same type. We easily explain this by the fact they were born with, and still carry along, the same specific chromosomes that determine their blood type. What Bell’s paper shows us is that if we try to describe the correlations between the entangled particles in the way we understand the correlations between the twins, we will be making a serious error.”
Alain Aspect Bell (1947 –), Speakable and Unspeakable in Quantum Mechanics, Second Edition (pp. xxiii – xxiv).
Cambridge: Cambridge University Press, 2004 (with a new introduction by Alain Aspect)

46. Albert Einstein
(1879 – 1955)
Physics has shown that EPR locality is not observed. Experiments corroborate quantum entaglement and, in this sense, we must agree that there exists some sort of quantum nonlocality. However, Einstein’s characteristic scientific standard has helped to set the appropriate stage for this whole physical development, by rejecting discussions solely grounded on «language» or «philosophy» and insisting on clear physical and mathematical arguments.

47. Niels Bohr
(1885 – 1962)
Bohr was right and Einstein was wrong. But only in the sense that Bohr always adhered to the mainstream of quantum mechanics through a very contrived line of reasoning which could only be conveyed by suitable choices of «language» or «philosophy» rather than precise physical or mathematical formulations.

48. John Bell
(1928 – 1990)
Bell was always a physicist who, like Einstein, rejected the obscurantist worldview set up by Bohr to justify the strange results of quantum mechanics. He was the first physicist capable to put in clear mathematical form (Bell inequality, 1964) the dispute between EPR locality and quantum nonlocality. The stage was thus ripe for explicit experimental tests.

49. Alain Aspect
(1947 –)
Aspect was the first physicist leading a team that was able to conduct a set of experimental tests (in 1981 and 1982) which have clearly proven that quantum nonlocality is right and EPR locality is wrong, thereby showing that quantum mechanics does indeed violate Bell inequality. In this sense his work was «experimental metaphysics», not a vague construction of an appropriate language for a so-called «quantum logic».

50. Appendix:
Quantum entanglement

51. “Entanglement: you can know everything about a
system and know nothing about its parts.”
Leonard Susskind (1940 –)

52. Bloch sphere: geometric representation of 1 – qubits

63. “Nonlocality, an actual fact proven by experimental evidence that leaves no room for reasonable doubt, presents characteristics of such a peculiar kind as to keep it from being used to produce instantaneous effects between distant physical systems.”
Giancarlo Ghirardi (1935 –), Sneaking a Look at God’s Cards, Revised Edition (p. 291).
Princeton, New Jersey: Princeton University Press, 2005