Pyramid of Probability – Probabilities and observations

Next, we drop a particle on an invisible path down to Level 3. In which of the four boxes is the ball now?
Prior to measuring the location, we only know the eight possible paths.

The sum of probabilities into all possible boxes is 1/8 + 3/8 + 3/8 + 1/8 = 1 = 100%.

Next, we open a box and thus perform a measurement – the ball has been located. The probability for that box becomes 100%. For all other boxes, the probabilities immediately drop to zero, independent of spacial distances.

Again, we open a box and thus perform a measurement – the box is empty. This measurement causes again all other probabilities to change immediately, since the probabilities needs to be normalized 100%.

Prior to measuring, the probability for this box was equal to 3/8; after measuring, it is zero, and, for the other boxes, accordingly 1/5 or 3/5. Thus, the probability of each individual path is now 1/5.

Wherever there are causal connections between probabilities, each measurement alters all the other probabilities, without any delay, irrespective of how far a box is away from the measurement. Thus, any given measurement brings about a non-local change in all probability distributions. However, the ball already dropped prior to taking the measurement. This means that the measurement does not affect the possible measurement results. It is only our awareness of the possible location of the ball that changes through the measurement.