Is the probability of a quantum outcome ever zero such as with....

[CosmicVoyager]

TL;DR

Is the probability of a quantum outcome ever zero such as with the location of an electron around atom or with radioactive decay?

Greetings,

Given an infinite universe or an infinite number of universes?

- Regarding the location of an electron around an atom, is there a tiny volume in which finding the electron 100%? Or is there a possibility, no matter how remote, it might be found a meter away or a kilometer away?

- Regarding radioactive decay, must the half-life rule always occur? Is there any possibility that all the radioactive atoms in a billion atom sample will decay at once?

Are such outcomes prevented by matter, energy, space, and time being quantized? By Planck units? Does that cause probabilities to become zero?

Thanks

 

[EmilD]

There are zero or one probabilities in quantum mechanics.
For example there are transitions in atoms (best example is hydrogen) which can't occur. So called forbidden transitions.
Also electrons are fermions and thus can't occupy the same quantum numbers. I.e. if you have a wave function $\psi(x_1, x_2)$ this will become zero for $x_1 \to x_2$. And if the wavefunction is zero then the probability (density) $|\psi(x, x)|^2$ is also zero.

Regarding your second question: This is effectively a statistical property. So in theory.. yes. However I reckon the probability of a billion atoms all decaying at the same time is effectively zero. So in theory yes, in practice not really.

 

[PeroK]

- Regarding the location of an electron around an atom, is there a tiny volume in which finding the electron 100%? Or is there a possibility, no matter how remote, it might be found a meter away or a kilometer away?

Basic QM is non relativistic and there is a non-zero probability of a particle being found outside its future light cone. That's one reason that ultimately you need QFT to describe elementary particles.

Moreover, in order to test something you need a realistic probability in order to confirm the theory with experiment. If the probability of something is vanishingly small, then it's experimentally indistinguishable from the impossible.

 

[CosmicVoyager]

So in theory yes, in practice not really.

If the probability of something is vanishingly small, then it's experimentally indistinguishable from the impossible.

Thanks for your very helpful replies. So, though the odds of us observing such events is practically zero, in an infinite universe or in an infinite number of universes, these events would occur. And would actually occur an infinite number of times, correct?

 

[PeroK]

Thanks for your very helpful replies. So, though the odds of us observing such events is practically zero, in an infinite universe or in an infinite number of universes, these events would occur. And would actually occur an infinite number of times, correct?

I'm not sure that's a well-defined question. In QM generally you can only talk about the measurements you do make.