Summary Visualization of Bell Experiments
The Mechanism Behind
Author: Gerard van der Ham
Animations: Maurice Hickendorff
In Bell experiments spin directions of pairs of particles are measured at certain relative settings of detectors.
Pairs of particles are being produced in a source S.
A1The particles move in opposite directions along a line of motion.
A2This line of motion is the reference frame.
The pairs of particles have pairwise opposite spin in random directions, making a spherical vector space.
A detector is defined by its setting. A setting is a line with a direction.
A4The settings start from the line of motion, being the reference frame.
A5The detectors (settings) are being placed perpendicular on the line of motion, in a random direction, chosen by Alice and Bob.
The angle between the settings is ⱷ.
A7Detector A detects one particle of a pair. In order to be able to detect the other particle, B rotates 180° around A, keeping the angle at ⱷ.This rotation cuts double cone halves out of the vector sphere.
The opposite rotation cuts symmetric double cone halves out of the vector sphere.
Together the halves make a double cone.
This double cone has A as its axis.
This double cone is being rotated 90°, inversely to A’s rotation of 90°, making its axis coincide with the line of motion.
This double cone contains the spin directions of the pairs that show combinations of equal outcomes.
A12These pairs, counted as part of the total number of pairs, show QM’s correlation. The correlation depends on ⱷ. The shape of the double cone also depends on ⱷ. From one viewpoint only one cone is observed.
That cone, represented at ⱷ, varying from 0° to 360°, looks like this:
representation of vector spaces in a sphere containing spin directions of pairs that yield combinations of equal outcomes (blue), and vector spaces containing spin directions of pairs that yield combinations of opposite outcomes (yellow), in side view (b) and front view (c), depending on ⱷ (a), and corresponding correlations (d).
| a | b | c | d |
|---|---|---|---|
| angle ⱷ between the settings of A and B | View perpendicular onto the line of motion | View along the line of motion | Correlation C = -cos ⱷ |
| A14 A | A14 B | A14 C | A14 D |
Blue is: vector space containing vectors of pairs that show combinations of equal outcomes. Yellow is: vector space containing vectors of pairs that show combinations of opposite outcomes. Green is: blue space surrounded by yellow space or yellow space surrounded by blue space.
Bell’s inequalities, on the other hand, describe the vector spaces between the centre perpendicular planes of the detectors. They are also governed by ⱷ but they differ from QM’s cones. For ⱷ varying from 0° to 360° they look like this (from one viewpoint):
representation of vector spaces in a sphere, as described by Bell’s probabilities, containing spin directions of pairs that yield combinations of equal outcomes (blue), and vector spaces containing spin directions of pairs that yield combinations of opposite outcomes (yellow), in side view (b) and front view (c), depending on ⱷ, and corresponding correlations (d).
| a | b | c | d |
|---|---|---|---|
| angle ⱷ between the settings of A and B | View perpendicular onto the line of motion | View along the line of motion | Correlation C = (2ⱷ ̶ π) / π |
| A15 A | A15 B | A15 C | A15 D |
Explanation
An object can be observed by one observer from only one direction. Always. When two detectors detect one object, their detections are not equivalent: one detector cannot know, and neither can it calculate, what the other detector detects. In that case the Principle of Perspective has to be applied. This means that all movements of the detectors in respect of the reference frame of the object (the line of motion) have to be taken into account.
The objects (particle pairs) determine the reference frame. To detect their spin directions (vectors) as they are, they must move along with the detectors in respect to the reference frame. Since in reality spin directions don’t move along, they must inversely be moved back, including the vector spaces defined by the detectors. So, when the rotations of the detectors are being applied to the spin directions (vectors) and then inversely being applied to the vectors and the vector spaces, the correct detections are obtained. The outcomes of the detections correspond to QM calculations.
If this explanation is incomprehensible then only realize that someone else cannot, in any way, see your face as it is for you.