Question

In quantum mechanics, the probability, say, that a radioactive atom will decay is well defined. By the Born Rule, it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude. But if, say, these things were unpredictable and happening for no reason, why does the Born’s rule exist in the first place? Why is it the square of the amplitude and not 1/4 or 1/8? Secondly, why does the way this work stay constant? If for example, a radioactive atom’s decay point is truly happening for no reason, why doesn’t it just suddenly start decaying with different probabilities? It is easy to imagine this to happen, atleast in a logical sense. But because this does not happen, does it not still indicate some level of order? If there is order, where does this come from without determinism?

Answer 1

The Born Rule states that the probability of obtaining any possible measurement outcome in quantum mechanics is equal to the square of the corresponding amplitude. The use of the square ensures that the probability is a positive real number. The way quantum mechanics works is based on the uncertainty principle and the deterministic evolution of the wavefunction.

Step-by-step explanation:

In quantum mechanics, the square of the wavefunction represents the probability density of finding a particle at a specific location in space. This is known as the Born Rule. The square of the amplitude is used because it ensures that the probability is a positive real number. If it were 1/4 or 1/8, it would not accurately represent the probability.

The way quantum mechanics works is based on the uncertainty principle, which states that we cannot precisely determine the position of a particle. The probabilities of different outcomes are determined by the wavefunction and remain constant because the wavefunction evolves deterministically according to the Schrödinger equation. While the individual decay events may be unpredictable, the overall behavior is determined by the underlying wavefunction.