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So as far as I am aware, there is currently no cause that explains how exactly two entangled particles remain correlated even when separated at a large distance. If there is a cause, it is presumed to be non local.

My question is: apart from this, is there any other example in physics (perhaps classical physics) where correlations between items separated at a large distance occur without either a common cause or a cause that involves communication between these objects?

Notice that I use the term common cause. This is because I can imagine a classical scenario where if I had two boxes, one containing a blue glove and one containing a green one, and I sent them out into different corners of space, and I opened one box and it had the green glove, I would immediately know that the other box contains a blue glove. Even though there is no communication, this is not an analogy to entanglement, since each box contains a definite state of being that glove, and the cause for this is the fact that at the origin point, I had boxes containing two gloves. Thus, this correlation still occurs because of a cause.

Is there any example in classical physics or really anywhere else where a consistent correlation between objects does occur without any cause?

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  1. Quantum entanglement is the only example of correlations breaking the Bell inequality for which there is strong experimental evidence.

  2. There are related phenomena in quantum mechanics regarding various measurements one can make on a quantum system (e.g. Leggett Garg inequality). These also having strong experimental evidence but do not involve spacelike-separated parts. The argument for these relies on plausible assumptions about the dynamics rather than on no faster-than-light communication.

  3. The terminology adopted in the question is not standard; you are using the term 'cause' in a non-standard way. But there is no universally agreed way to describe the Bell-inequality-violating observations. I think a good way is to say that a system consisting of an entangled pair of entities is in some respects a single system for which the attempt to describe it in terms of parts is not appropriate.

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    $\begingroup$ Point 3 is important and should always be kept in mind when working with quantum mechanics. We are so used to the reductionist approach of considering a system equal to a collection of its parts, but that just doesn't always work. $\endgroup$
    – Marius Ladegård Meyer
    Commented Apr 4 at 10:13