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Nonlocal correlations and causation: conflict or peaceful coexistence? Lars-G¨ oran Johansson Uppsala University Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations day Arthur Bertie mon red green tues green red wed yellow blue thurs green red fri green red sat yellow blue sun red green mon blue yellow tues red green wed blue yellow Table : Tie colour each day for two persons living at different places Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations Observations: The sequence of colours of each person’s tie is random. No algorithm, shorter than the sequence, can produce the sequence. But Arthur and Bertie always choose complementary colours. Their tie colours are strictly correlated. How could this be? Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations Reichenbach’s principle : A true correlation between to types of events, A and B, can occur in three ways. A-events cause B-events, or B-events cause A-events, or A- and B-events have a common cause. Applied to this case: Arthur sends signals to Bertie Bertie sends signals to Arthur Arthur and Bertie have agreed in advance of following a common rule Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations Suppose that the sequence is unlimited. Since it is random it is not possible to have an algorithm for producing the sequence shorter than the sequence. But they cannot agree on an unlimited sequence. Suppose further that we can control that no signals go between Arthur and Bertie. If these conditions are fulfilled, the tie colour correlation is non-local . Is this situation possible? Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations My verdict is that this is an impossible situation. A correlation in an unlimited sequence of pairs of events without any mechanism would be a ’cosmic coincidence’. I don’t believe such things exist. But quantum theory predicts such correlations! Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations in quantum theory Arthur and Bertie are two electrons in a singlet state. It can be any distance between them. A two-electron state is a singlet state if the total spin, in any chosen direction, is zero. Tie colour is electron spin Blue/Yellow is spin up/spin down in, say x-direction. Red/Green is spin up/spin down in y-direction. Arthur and Bertie travel in opposite directions in the z-direction. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations in quantum theory Quantum theory says that a pair of electrons in a singlet state have, when measured , perfectly anti-correlated spins in a randomly chosen direction. Quantum theory also says that electrons can have a definite spin in only one direction at each point of time. Choose randomly a direction for a spin measurement of an electron: The result is either ’spin up’ or ’spin down’. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations in quantum theory Since the choice is random and a definite spin is possible in only one direction, the electrons cannot have the measured spin before the measurement. The electrons get definite spin values as a result of the interaction with the measurement device. The result of the measurement is random and unpredictable; The sequence cannot be produced by any algorithm shorter than the sequence. This is beyond doubt confirmed by experiment. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations in quantum theory One might guess that some kind of signal is sent between the two correlated electrons. According to relativity theory no signal can go faster than the speed of light. But the correlation is established within such a short time that no signal could have travelled from one to the other electron. This is well confirmed by Aspect’s and other’s experiments. But this is no violation of relativity! No signal is sent between the correlated electrons; no quantity of any conserved quantity is transmitted from the one to the other. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Nonlocal correlations in quantum theory The dilemma: On the one hand: I don’t accept that the colours of two men’s ties could be nonlocally correlated as described in the thought experiment; I accept Reichenbach’s principle. On the other, I accept that quantum theory predicts nonlocal correlations between pairs of particles in singlet states, and I accept that quantum theory is extremely well tested and confirmed on this point. So there must be a relevant difference between the thought experiment with the ties and the real case of nonlocal correlations between particles in singlet states. The crucial difference is that of being in a singlet state. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Particles and events in the quantum domain My conclusion: The events ’A gets spin up’ and ’B gets spin down’ are not two different events, if A and B are two particles in a singlet state. Question 1: What are the principles of individuation of particles and events? Question 2:What is a singlet state? Question 3: What is spin? Question 4: How does an electron look like? I’ll begin with spin. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Quantum spin-half objects z 1/ √ 2 1/2 √ 3/2 Figure : A model of spin-half Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Quantum spin-half objects Electrons can have well defined spins in only one direction at each moment of time; one can think of this as that the spin vector rotates around an axis. So the definite spin value cannot be had before measurement; the value must come into existence at the moment of measurement. Measuring spin is forcing the particle to perform an internal rotation around a well defined direction in space defined by an external magnetic field; it is not a determination of a preexisting value. This cannot be if the particle is a point object; internal rotation requires spatial extension. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Singlet states A singlet state of two electrons (or other fermions) is a state in which the total spin is zero, no matter how far from each other they are. Since an electron (or any other fermion) always show, upon measurement, a spin value equal to ± 1 / 2 (in units of h / 2 π ), this must mean that one of them has, when measured, spin + 1 / 2 and the other − 1 / 2. This is true no matter which direction we chose when performing the measurement. According to quantum mechanics, the alignment of spin values happens instantaneously, or at least faster than any signal between them. And experiments confirm the theory. Is it possible to explain? Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

How does an electron look like? We usually assume that electrons are very small particles having a diameter less than 10 − 14 m or so. This is certainly wrong! Interference experiments show convincingly that electrons sometimes can have macroscopic extension in space. This is so because interference pattern requires that each electron passes both slits. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Double slit experiment Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

Double slit experiment Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?

How does an electron look like? The interference pattern for light and for electrons are structurally similar. The only difference is that one need much narrower slit distance with electrons. The explanation in both cases is interference of coherent waves emerging from the two slits. The conclusion is that both light and electrons propagate as (more or less) extended waves. Further tests show convincingly that the interference pattern occurs even if only one electron is present at each point of time; so the interference is not the result of interaction between electrons. Lars-G¨ oran Johansson Uppsala University Nonlocal correlations and causation: conflict or peaceful coexistence?