Can particles appear and disappear "with" a cause?

The first thing we need for this is to define what a particle is...
It is an object that has specific intrinsic properties and is described by a wave sign

How to measure it?

This is done by the interaction of the particle to be measured with the measurement system. When measuring, the wave function collapses and the quantum beam that represents the particle collapses into one specific state that reflects the observed value.

Now let's imagine a particle called A and a particle called B.

Its description is:

Ψ> = a|A>|B>+b|Ā>|B̅>

In the form of B and the body A, there are individual body states and they are A> and |B>

Their opposite states are: Ā> and |B̅>

Their Linear combination =a/b

When we measure particle A the wave function of the entire system collapses

So it becomes |Ψ>→|A>|B>

Thus particle "b" changes. If body A is not measured, the state of the system remains in the superposition and is considered to not exist in the first place.

if the body is not measured, it is considered non-existent, and when measured, the wave function collapses to a specific state, The collapsed state is the reason for its appearance and disappearance, and it is not unknown in the quantum world. On the contrary, Werner heisenberg in his theory proved this.

So that leaves us on a single thing...does this mean particles can appear and disappear "with" a cause? Or a main reason? Because tge collapsed state by itself is the reason for its appearance and disappearance?

zaramahdi said:

All the time in quantum we hear that particles can appear and disappear "without" a cause

Where do "we hear" this? Please give a specific reference. Your post looks confused, and I suspect you are either using an unreliable pop science source or you are misinterpreting what your source is saying.