“Acausal” means not having a cause. In classical physics all events are believed to have a cause; none are acausal. In quantum physics, some interpretations of quantum theory allow for events to occur without a cause, that is, they are acausal.
The usual way to say this is that in quantum physics, there is “true randomness.” In true randomness, we don’t know the cause and also there is none. In classical physics, nothing happens randomly. If a billiard ball is picking up speed to the right, it’s because some force is pushing it in that direction. If we don’t know the nature of the force, it might seem like it’s random motion. But be assured, there is a causal force.
Another way of talking about this same issue is to say that classical physics is deterministic—every action is determined by prior actions. However, some behaviors of objects in quantum physics are undetermined, that is, not determined by anything.
In quantum physics, the timing of radioactive decay, for example, is random (“undetermined,” “acausal”). There is no cause that triggers the nucleus of a radioactive atom such as uranium 235 to split apart and release energy in radioactive decay. If we were triggering the atom to split by shooting particles at it, that would be one thing. The shooting particles would be the cause. But natural radioactive decay of a particular atom occurs at random times, acausally.
It’s true that the half-life of a group of atoms, the time at which approximately half the nuclei will split, can be predicted. But the moment that the nucleus of any specific atom will split cannot be predicted. Physicists do understand much about the sequence of causes once the nucleus begins the process of decay. But it’s as if the nucleus contains a random number generator, and it will begin to decay when its number is up.
It’s not only natural radioactive decay that occurs as if particles each have a random number generator within them; the position in which a particle is detected, its momentum, the direction of its spin, and several other properties appear to be acausal.
Acausality as a feature of quantum physics interpretations. The idea of acausality, true randomness, is a feature of many interpretations of quantum physics, including the so-called “orthodox” one, the Copenhagen Interpretation developed by the founders of quantum physics. This interpretation was developed by Niels Bohr, Werner Heisenberg, Erwin Schrodinger, and several other key physicists in the 1920’s and 1930’s.
At the time, Albert Einstein, also a founder of quantum physics, strenuously objected to the notion of acausality in the theory. He famously argued that “God does not play dice.” Einstein felt that if something in the universe appears to act randomly, it’s only because our understanding of it is not deep enough. He felt that there is always a cause.
Other, later, interpretations are completely causal or, at least, claim to be. This includes the Many Worlds Interpretation and the deBroglie-Bohm Interpretation. [Source: https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics]. In these interpretations, it may appear that quantum behavior is random; but this is an illusion. There is no true randomness. It should be noted that almost all the various interpretations of quantum physics rely on the same mathematical equations and create the same mathematical predictions. Their differences lie only in how they understand the physical reality that the equations describe.