msumm21 said:
This is the assumption of free will. It is a free decision what measurement one wants to perform. In the experiment on the entangled pair of photons, Alice and Bob are free to choose the position of the switch that determines which measurement is performed on their respective particles. It was a basic assumption in our discussion that that choice is not determined from the outside. This fundamental assumption is essential to doing science.
I find this quote not as free of ambiguity as it is intended to be. There are several plausible interpretations, particularly: what does it means for both Alice and Bob to exercise
free will in choosing the position of their respective spin determining apparatus. The following is my attempt at describing several examples of what the quote might intend.
Each of a series of experiments has a series of trials. Each trial involves determining each of the spins of the pair of entangled photons. I am assuming that when a pair of entangled photons are created, and they move in opposite directions, their paths may not take them from the creation apparatus to the spin determining apparatus. That means that randomly only some of the created pairs of photons get measured for spin by the apparatus. As the spin of a photon is determined, the time of the occurrence of the measurement is recorded along with whether the spin is "up" or "down". The distance between the entangled photon pair creating apparatus and each spin determining apparatus is the same. Also the two clocks which record the time of spin determination are synced. That means that for every recorded spin and time at Alice's apparatus will have a corresponding recorded spin and time as Bob's apparatus, and the two recorded times will be identical, and vice versa.
The distances between the apparatus which creates the photon pairs and the two measuring setups are identical. Assuming the size of the measuring setup is fixed, say for example a circle of diameter 20 m, the farther apart this distance is, the fewer photons will be measured. If Alice and Bob's setups are 100 m apart, then only 1% of the created pairs of photons will be measured.
The spin determining apparatus has two possible settings.
(1) Vertical. Normally this means the direction is relative to the direction of Earth's gravity. This implies that the two apparatus setups will not have the vertical settings exactly parallel. However, assuming the 100 m separation, this should not matter significantly.
(2) Horizontal. This is perpendicular to the direction of the separation, and perpendicular to the local vertical direction. The two horizontal settings will be parallel.
For each experiment, the principal scientist, Jessie, who is in charge of the research will calculate
p the fraction of times Alice's apparatus and Bob's apparatus agree on "up"/"down". It is of course expected that the
p value will either be close to zero or close to some value I am not sure about, but I think it is either 50%, or 70.7%, or 29.3%.
For each of the a first series of experiments Alice and Bob will set the orientation of the spin direction detector according to the Jesse's instructions. The following are the options. Some of these are (a) consistent with "Alice and Bob
are free to choose the position of the switch", and some are (b) not consistent. I think different readers here might disagree which the of the options are consistent and which not.
(1) Both are instructed to choose vertical.
(2) Both are instructed to choose horizontal.
(3) Alice is instructed to choose vertical and Bob is instructed to choose horizontal.
(4) Alice is instructed to choose horizontal and Bob is instructed to choose vertical .
(5) Both Alice and Bob are instructed to flip a coin, and if heads, choose vertical, and if tails choose horizontal.
The following options give instructions Jesse will use for a second series of experiments. For each of these options Alice and Bob will use identical copies of a pseudo random number generator (PRNG). Each use of a PRNG involves entering (a) a key multi-digit number which controls the sequence of pseudo random numbers generated, and (b) an integer that determines the number of pseudo random numbers to be generated and printed out. The specific random numbers generated with be a "1" or a "2".
(6) Jessie gives Alice and Bob different key numbers to use. If a "1" is the next Pseudo random number to use, use horizontal on the apparatus. If a "2" is the next Pseudo random number to use, use vertical on the apparatus.
(7) Same as (6) except Alice and Bob independently choose whether "1" is for horizontal and "2" is for vertical, or vice versa.
(8) Same as (7) except both Alice and Bob choose the key number they will use with no consulting with each other. Some examples might be (a) a date of birth for someone she/he knows personally , (b) a telephone number of someone she/he knows personally, or (c) other choices the reader might think of.
Which of these 8 options (if any) involve free will choices by Alice and Bob in the sense intended by the quote? I suspect that different responders will give different answers.
Regards,
Buzz