Impossible probability between theoretical possibility and reality

[Kinker]

TL;DR

Even if it is theoretically possible, does the physical probability of such an event in reality become 0 because there is a lower limit to the possibility of such an impossible event in reality?

Boltzmann's brain, entropy reduction, Poincaré's recursion theorem, the probability of oxygen molecules in a room gathering in one place, the probability of quantum tunneling of macroscopic objects, etc. are theoretically possible. But the probability of these events is very low. Additionally, physical interactions with the environment, emergent properties, and other factors make it even more difficult. Is there a difference between theoretical possibility and real possibility? Even if the time of the universe is infinite, are the above events only theoretically possible and will never happen in reality?

 

[.Scott]

As best that is known, if the probability is theoretically tiny but non-zero, that it what should be expected from experiments. But it's always open to more precise verification.

 

[phinds]

As soon as we have observed for an infinite amount of time, we'll let you know.

 

[Kinker]

As soon as we have observed for an infinite amount of time, we'll let you know.

You must do it. It's a promise

 

[Demystifier]

Even if the time of the universe is infinite, are the above events only theoretically possible and will never happen in reality?

If the time is infinite, these things will not only happen, but happen infinitely many times.

 

[Kinker]

If the time is infinite, these things will not only happen, but happen infinitely many times.

Isn't the probability of an event a measure of possibility, not certainty? Is the infinite monkey theorem valid in the reality of a universe with infinite time?

 

[Demystifier]

Isn't the probability of an event a measure of possibility, not certainty? Is the infinite monkey theorem valid in the reality of a universe with infinite time?

Yes. So?

 

[Kinker]

Yes. So?

Infinity cannot exist in reality, right? Therefore, I do not believe that the infinite monkey theorem is completely valid in reality. In reality and physics, I think an error occurs if you substitute infinity.

 

[Demystifier]

Infinity cannot exist in reality, right? Therefore, I do not believe that the infinite monkey theorem is completely valid in reality. In reality and physics, I think an error occurs if you substitute infinity.

You are making a category mistake. Infinity theorems, or any mathematical theorems for that matter, do not depend on physical reality.

 

[Kinker]

You are making a category mistake. Infinity theorems, or any mathematical theorems for that matter, do not depend on physical reality.

Probability does not indicate the certainty of an event, so wouldn't an event with an extremely low probability never occur even in a universe with infinite time?

 

[Demystifier]

Probability does not indicate the certainty of an event, so wouldn't an event with an extremely low probability never occur even in a universe with infinite time?

No, your reasoning is wrong.

 

[Kinker]

No, your reasoning is wrong.

Why? what is the reason?

 

[Demystifier]

Why? what is the reason?

Because for any arbitrary small ${\cal P}>0$ there is a sufficiently large $T<\infty$ such that ${\cal P}T=1$.

 

[.Scott]

Infinity cannot exist in reality, right? Therefore, I do not believe that the infinite monkey theorem is completely valid in reality. In reality and physics, I think an error occurs if you substitute infinity.

Be patient, none of these events require an infinite amount of time.
For example, in the monkey experiment, it may only take a billion billion years for a billion monkeys to outdo Shakespeare.
You just need to keep them fed and their typewriters in good working order for that amount of time.
I'm not saying things could not go wrong. In that amount of time those monkeys could evolve - and perhaps decide to test your narrative skills.

 

[hutchphd]

Isn't the probability of an event a measure of possibility, not certainty? Is the infinite monkey theorem valid in the reality of a universe with infinite time?

Methinks you miss the point. It is possible that the monkeys would produce Merchant of Venice overnight (with lotsa coffee)
I feel it necessary to reference a favorite comedy bit on the subject

 

[PeroK]

Be patient, none of these events require an infinite amount of time.
For example, in the monkey experiment, it may only take a billion billion years for a billion monkeys to outdo Shakespeare.
You just need to keep them fed and their typewriters in good working order for that amount of time.
I'm not saying things could not go wrong. In that amount of time those monkeys could evolve - and perhaps decide to test your narrative skills.

They tried this with some real monkeys. The monkeys soon got bored and one defecated on its typewriter.

 

[Kinker]

Because for any arbitrary small ${\cal P}>0$ there is a sufficiently large $T<\infty$ such that ${\cal P}T=1$.

In reality, there is no infinity, right? Isn't that moment finite, no matter how old it is? I think it is a paradox to make predictions by substituting infinity in reality.

 

[Frabjous]

In reality, there is no infinity, right? Isn't that moment finite, no matter how old it is? I think it is a paradox to make predictions by substituting infinity in reality.

Take the longest moment of time that you care about. Multiply it by the largest number you can think of. An infinite universe will exist longer than that.

 

[Demystifier]

Isn't that moment finite, no matter how old it is?

Didn't I write $T<\infty$?

 

[Nugatory]

See also https://www.physicsforums.com/threa...ects-undergo-quantum-tunneling.1055304/page-2 and https://www.physicsforums.com/threa...of-quantum-tunneling-of-macro-object.1055166/

 

[Kinker]

Didn't I write $T<\infty$?

So, are the events presented above inevitable?

 

[Demystifier]

So, are the events presented above inevitable?

Is the event with probability 99.999% inevitable?

 

[Kinker]

Is the event with probability 99.999% inevitable?

Yes, I think so. But my head hurts.

 

[Nugatory]

Yes, I think so. But my head hurts.

That’s because you’re trying to make a distinction between “can’t happen” and “could happen but won’t”. You can avoid the pain by not using ill-defined terms like “inevitable” or “infinite” and instead thinking in terms of the probability of something happening as a function of time.