ohn Gould, Studied mathematical logic as part of Computer Science
Question answered : If the world is truly causal, how can randomness exist?
Well that would depend entirely on what we mean by the term causal.
Causality, as usually understood, is a word that describes a mechanism, whereby some set of events, called the causes, necessitate another, called the effect. How this mechanism is to work, how it necessitates the consequences are not relevant here, merely that it does. It is the concept of necessitation that is relevant here. Otherwise causality would be indistinguishable from exact correlation. The idea here is that the causes are actually in some sense responsible for the effect, rather than the connection being merely coincidental.
Now, with that understanding of causality, the mere occurrence of the causing events, makes necessary the occurrence of the effect event, so that, on the face of it randomness cannot exist.
But there is a somewhat looser concept of causality where an event might consist of a random selection from some set of options, some set of possible outcomes, a choice event if you will, where the choice is not made deterministically. Such an event might intuitively be understood as the throw of a die or the spinning of a bottle.
With that understanding, randomness as manifested by random choice is of course not eliminated at all by the existence of causality, but form a component of it.
Given the question as it is written, I will ignore the second understanding of causality and focus on the first.
Now, I was somewhat puzzled by the certainty with which the other answers here claim that, since randomness is a real phenomenon, it therefore cannot be the case that the world is truly causal.
But, I would ask, how do we know that true randomness is a real phenomenon. The explanations I read, suggest that randomness finds its source in quantum events, which are claimed to be fundamentally probabilistic in nature.
But such a claim is not warranted, it relies on an interpretation of quantum mechanics which features something called wave collapse. Wave collapse is said to happen whenever a classical observer observes a quantum mechanical system. This wave collapse would result in making the observed system ‘definite’ rather than just a probability distribution. This is then claimed as the source of randomness.
However, it is very important to realise that wave collapse is not a part of quantum mechanics. There are other interpretations of quantum mechanics that do not have this feature, and yet yield exactly the same results, provably so.
This implies that wave collapse is not necessarily a physical phenomenon at all. The relative state interpretation is such an interpretation. It is arguably the simplest possible interpretation, and here it is assumed that the wave represented by the wave function is a physical object, objectively real. That is, take the Schrödinger equation at its face value. Such an interpretation is trivially compatible with quantum mechanics, because it adds nothing to the basic equations at all.
It is also the case that the time evolution of this wave function is actually completely deterministic. This interpretation takes seriously the idea that classical systems do not exist, they are merely approximations of quantum mechanical systems. There are no ‘classical’ observers, only quantum mechanical ones.
A consequence of this is that measurement or observation does not result in wave collapse (a non existent concept) but instead in the establishment of entanglement between the two systems. So there is never any randomness at all, only a lack of knowledge of the observer of the other states that are a part of the superposition.
So contrary to what the other answers write, I would claim that the world is not random at all. And given this, it clearly does not follow that the world is not causal.
It is, given the latest knowledge and best theories we have, entirely possible that the world simply is deterministic and therefore that randomness does not exist.
On that view, what we call randomness, is nothing more than a manifestation of the lack of knowledge we have as to precisely which branch of the global deterministic superposition we are on. In physics, randomness is to be viewed as the consequence of a lack of knowledge, not as true randomness of the underlying physical reality.
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