In a double-slit experiment, a particle (such as a photon) emitted from a source
The particle emitted from
Let us see what happens if we instead follow the two “quantum rules”: first we add the amplitudes, then we square the absolute value of the sum to get the probability.
Thus, the particle will reach the detector with probability
The algebra is simple; our focus is on the physical interpretation.
Firstly, note that the important quantity here is the relative phase
Secondly, what has happened to the additivity axiom in probability theory? What was wrong with it? One problem is the assumption that the processes of taking the upper or the lower slit are mutually exclusive; in reality, as we have just mentioned, the two transitions both occur, simultaneously. However, we cannot learn this from probability theory, nor from any other a priori mathematical construct — we can only observe this by repeated scientific experiments in our physical world.26
There is no fundamental reason why Nature should conform to the additivity axiom.
We find out how nature works by making “intelligent” guesses, running experiments, checking what happens and formulating physical theories. If our guess disagrees with experiments then it is wrong, so we try another intelligent guess, and another, etc. Right now, quantum theory is the best guess we have: it offers good explanations and predictions that have not been falsified by any of the existing experiments. This said, rest assured that one day quantum theory will be falsified, and then we will have to start guessing all over again.
That is, if one happens then the other one cannot. For example, “heads” and “tails” are mutually exclusive outcomes of flipping a coin, but “heads” and “6” are not mutually exclusive outcomes of simultaneously flipping a coin and rolling a dice.↩︎
According to the philosopher Karl Popper (1902–1994) a theory is genuinely scientific only if it is possible, in principle, to establish that it is false. Genuinely scientific theories are never finally confirmed because, no matter how many confirming observations have been made, observations that are inconsistent with the empirical predictions of the theory are always possible.↩︎