# Lowest probability for physical possibility

• I
• Brian1952
In summary, there is no lowest possible probability for something to physically occur on a cosmic basis. Zero probability events do occur, but they are rare.

#### Brian1952

My question is whether there is a lowest possible probability for something to possibly (physically) occur on a cosmic basis? That is, is there a threshold 'lowest' probability below which something cannot occur? I'm not referring to 'zero' as the lowest probability. That's obvious. Rather, a finite value above zero that is the threshold.

Not only need there be no lowest probability, but we can imagine models in which events with zero probability occur. Consider a multiverse containing an infinite number of spacetimes, in only one of which a particular event E occurs. Then the probability of E occurring in a randomly selected spacetime is zero, even though it does occur in one spacetime. Very informally, that is because the probability can be thought of as like ##1/\infty = 0##. That statement is not mathematically valid, but it can be replaced by as longer, more complicated one that has the same essential effect, and is valid.

There is every reason to believe zero probability events occur all the time. What we would not expect is for particular zero probability events to occur. It is a common fallacy that low probability events are uncommon. They are not, but they are hard to predict. As far as predicting unusual things how many trials will you preform?
For example the probability of rolling ten cubic dice and having them all match is about 10^-7 it probably won't happen on your first try, but if you take several million attempts it might and after a billion attempts it will may have happened several times.

Brian1952 said:
My question is whether there is a lowest possible probability for something to possibly (physically) occur on a cosmic basis? That is, is there a threshold 'lowest' probability below which something cannot occur? I'm not referring to 'zero' as the lowest probability. That's obvious. Rather, a finite value above zero that is the threshold.

The mathematical theory of probability assumes a contiguous set of probablities from ##0## to ##1##. There is no way to test whether this applies to the physical universe or whether probablities associated with physical processes are discrete in some way. Although, it's difficult to see why they would be discrete.

Unlike the other posters above, I would dispute that events with zero probability occur in real physical processes. This is a potential misapplication of probablity theory to physical processes.

For example, the simple mathematical statement: Let ##f(x) = \sin x##, defines a function infinite in extent. But, you can never physically have such an infinite sine function in reality. Likewise, "Let ##X## be a random variable uniformly distributed on ##[0, 1]## defines a mathematical object ##X##. But, such an ##X## cannot be conjured so easily in the real universe.

Likewise, "let E be an event with zero probability" seems to me a mathematical statement, conjuring a mathematical object, but cannot (necessarily) be shown to conjure a physical event.

My thanks to all for the responses. My original question had more to do with probability in physical events (chemistry, biology, geology, etc.) within the limits of our observable portion of whatever 'multiverse' might exist in reality. Thanks again.

Brian1952 said:
My original question had more to do with probability in physical events (chemistry, biology, geology, etc.) within the limits of our observable portion of whatever 'multiverse' might exist in reality.

There is no fixed relation between the probability of an event and the actual frequency with which the event happens. A fixed relation would contradict the concept of probability. For example, if you pick a number p and declare that an event with probability p cannot actually happen, then the probability of the event not happening is 1, but that probability must also be 1-p.