Is there a causal relationship between some physical thing or event being **possible** and a possibility actually happening?

[Gorgias]

Actually, in QM the probability of something occurring is meaningless in determining whether or not it will occur. If it can occur, it ALWAYS WILL OCCUR.

Actually, this implies a certain number of trials, and a particular probability of an occurrence that is outstripped by the number of trials, such that the sum of the probabilities of the trials approaches 1.

However, you would have to demonstrate that the sum of the product of the probabilities of the component events, which together result in “spontaneous house assembly”, approach 1. That’s a far higher bar to attain.

So if it’s possible for billions of atoms to spontaneously assemble themselves into a house, they will. Probability has nothing to do with it.

But, if we have n events, each of which has probability 0 < Pi << 1, and the probability of assembly is the product of all the Pi’s, then the probability – while non-zero – would have to be outstripped by the number of trials (not only of each individual event, but all together). You would have to demonstrate a sufficient number of trials such that the aggregate event was probable (that is, the aggregate had a probability > .5), let alone assured (i.e., probability = 1).

I think I’ve just repeated myself. Nevertheless, I’m not convinced you’ve met that standard.

 

[Gorgias]

But of course you’re perfectly free to reject QM

I’m just saying that I don’t think it’s applicable in this case.

(And yes… QM does bend the mind a bit. But, saying that “in a QM system, anything that can happen, will happen”, doesn’t mean that everything actually happens. Oh, wait… there’s a unicorn at my door – I’ll be right back! )

 

[Gorgias]

Whether you realize it or not, you’re suggesting that the answer to that question is…yes.

I would say that it’s the other way around. Another way of asking the OP’s question might be, “if there’s an event E with a non-zero probability (EP > 0), then does the fact that it’s non-zero cause the event to happen?” That seems backward. I think we would say that the establishment of the non-zero probability is derived from the observation that it’s not impossible. However, it doesn’t mean that it will happen, just because it’s not theoretically impossible.

That suggests that there actually is a causal relationship between the probability of something happening, and that event actually happening.

I think that’s looking at it backwards. If the probability is non-zero, then we’ve already established that it’s a possibility.

This leads to an interesting line of reasoning. Is there a threshold of probability beyond which an event can’t happen? Again the question is…why? Why would such a threshold exist?

Not that it can’t happen; just that it is so improbable that the expected value remains zero for any practicable number of trials. Let’s suppose that our probability of this event happening is 1/n, where n is some sufficiently large number. If we attempt m independent trials, m << n, (not because m is small, but because n is so large), then the probability of the event not occurring is (1 - 1⁄n)m, which, for sufficiently large values of n, is still nearly P=1.

We could ask the question “how many trials would it take before we get our first success?”, right? Now, let’s suppose that this meets the definition of a Bernoulli process. What we’re asking is a question about a geometric distribution. This is cool, since if it’s a well-behaved function, we’d expect that the event would eventually occur, and therefore, we’d get an answer that would tell us “well, after a certain number of trials, we’d expect it to have happened.”

Here’s the interesting thing: for sufficiently small probabilities (P=1⁄n , for large values of n), the number of trials (m) before we expect a success can get pretty large. Now, our probability of “house appearing spontaneously” isn’t a single value – it’s the product of a whole lot of very improbable events, all occurring at the same time. So, our P is rather small, and if the number of trials doesn’t outpace the product of the probabilities (n >> m, as it were), then the probability of our event happening, while it isn’t zero, is still effectively zero.

So: not non-zero, but close enough, over the life of our earth, that it’s still effectively nil. That’s all I’m saying.

 

[Gorgias]

When you flip a coin for example, the odds of it coming up heads or tails is pretty good, but the odds of it having that exact orientation, and in that exact position, are highly improbable. Yet these highly improbable outcomes actually happen…every time.

That’s not a very fair question. You’re comparing the probability of one particular outcome of n (relatively equally probable) outcomes occurring to the probability that any one of the n will occur. One is P=1⁄n and the other is (P=n⁄n) => P=1. In essence, you’re asking why, if the former is so unlikely, the latter is guaranteed.

(The answer is that you’ve covered the probability space, and therefore, regardless of the value of n, you’re assured of the event occurring. Not too surprising.)