/sci/ - Science & Math

[Anonymous No.9991632]

particles are modeled as wave-packets that represent a probability of finding the position of a single volume-less particle, but if the particle has no size and occupies no volume, wouldn't such a probability distribution have an infinite amount of particle superposition no matter what region of local space you're dealing in is if that space is nonzero? since an infinite amount of points could occupy it in theory? like if you say at coordinate (x,y,z) there is a probability of finding the particle there valued as P, then if you take infinitesimally larger or smaller values for x,y,z and measure the probabilities what happens? do they just smoothly distribute?

wouldn't this lead to probabilities approaching zero for every point if you wanted to preserve unitarity?

[Anonymous No.9991669]

The wave functiob is sinilar to a probability density function. A probability density function is a function that when integrated over a certain space gives you the probability of the particle (or whatever) being there.
In the case of the wave function it has amplitudes everywhere which you basically need to square first and then integrate.

[Anonymous No.9991674]

Consider a similar question: you throw a dark at a dartboard and it will land are equally distributed across the board. What is the probability that the dart hits the center? What are the odds the dart lands alongthe like dividing the board in half vertically? The answer to both is zero! However, we know that it is possible for the dart to hit the exact center. In stasticics we say the "almost surely" will not land at the center. There is nothing physically 'wrong' here, we're just looking at things with infinitely small area.

https://en.m.wikipedia.org/wiki/Almost_surely

The same applies to the particle. Usually people ask "what are the odds the particle is between a and b?" This gives the area a real size and results in nonzero probabilities.