Dumb Question: Is there a Planck length for probability

[Fiziqs]

I was listening to people in another forum discuss the idea of Quantum Immortality, and the thought occurred to me, is there a point where the odds of something occurring become so small, that they aren't just extremely, extremely remote, they are in fact, zero?

For example, if we took a bucket of Nitrogen-13, which I believe has a half-life of ten minutes, and we waited for 100 years, the odds of not one atom of Nitrogen-13 decaying would seem to be extremely remote. But although the odds may get smaller and smaller, mathematically, they would never actually reach zero. We could wait a billion years, and it would still be possible that not one atom of Nitrogen-13 would have decayed.

It seems like there is a Planck scale for everything else, but is there a Planck scale for probability? Or is this a ridiculous idea? If so, what am I missing?

 

[phinds]

Since probabilities are mathematical models, not reality itself, I see no reason why there should be any lower limit to a probability.

 

[Fiziqs]

Since probabilities are mathematical models, not reality itself, I see no reason why there should be any lower limit to a probability.

I would agree with you if I was referring to a purely mathematical model. But I believe that in the real world there are restrictions that do not apply in a purely mathematical model. I am thinking of course about the Planck constants.

For example, if we take the double slit experiment and we cover one slit, leaving only one slit open, we should then see the majority of the detections occurring in a strip directly behind the open slit, with a diminishing number of detections the further me move to either side. Just using a purely mathematical model, the odds of detecting a particle diminish the further we move away from the center, but it will never actually drop to zero. Even a million miles away from the center, the odds would not be zero.

But what I'm wondering is, whether or not the other Planck constants put some limitations on the potential outcomes. One thing that I don't know, is whether the particle's energy in the double slit experiment, (In this case a single slit) diminishes, the further the particle gets away from the center. If the energy does diminish the further the particle gets away from the center, then there should come a point, when due to the limitations of the Planck constants the particle can no longer be detected. If this is true, then there may be limitations on the "real world" probabilities, that do not exist in a purely mathematical model. If beyond a certain point the particle would be undetectable, then the probability model would need to be modified to exclude anything outside of a parameter defined by the other Planck constants

I hope that I have explained this clearly enough. This is why I ask whether the Planck constants can in some way put a limitation on the probabilities, and whether there could be a Planck constant for probability.

 

[Matterwave]

I am assuming by "planck constants" you mean the Planck units of e.g. the Planck mass, Planck Length, etc., and not just the Planck constant h itself. From a purely pragmatic point of view, as the Planck units all have units (which is why they are units!), how do you propose to use them to set a limit on something unitless like probability?

 

[mfb]

The Planck constants are just a way to make units dimensionless. They are not "smallest quantities" or anything similar. They define regions where gravity becomes important and our current model of physics cannot be used to calculate the systems any more.

Probability already is a dimensionless quantity.

There are some ideas about extensions to quantum physics, which could set really small probabilities to exactly 0 and modify some other probability values, too (like mangled worlds). However, they are just speculations at the moment.

 

[FrY-Yau]

It probably would be meauserd the same manor you measure light, and since probability is a manifestation of light and consciousness you would have to measure it as it was happening in it's partial function.

If you could measure the wave function of probability's and if they exist in some fashion a form of future probability in their wave function then maybe you would win some poker games.

 

[Fiziqs]

Excuse me for bumping this thread back to the top, but I'm still wondering if there could possibly be a Planck type constant for probability. Not in a mathematical sense, as probability can get infinitely small in a purely mathematical model, but in a real world sense there must come a point where probability drops from non-zero to zero.

If we have a light source that is far enough away from us, and the universe is expanding fast enough, then the odds that light from that source will ever reach us is zero. But the point where the probability changes from being simply very, very small, to being actually zero, must occur somewhere. Logically, if the probability of an event occurring changes from being non-zero to being zero, it shouldn't occur randomly, but rather at a definable point, but what is that point?

I realize that there probably is no known answer to this question, but does anyone agree that there should be an answer to this question?

Thanks

 

[mfb]

but in a real world sense there must come a point where probability drops from non-zero to zero.

Why?

If we have a light source that is far enough away from us, and the universe is expanding fast enough, then the odds that light from that source will ever reach us is zero. But the point where the probability changes from being simply very, very small, to being actually zero, must occur somewhere.

It happens exactly at the event horizon of our expanding universe.

 

[bhobba]

Excuse me for bumping this thread back to the top, but I'm still wondering if there could possibly be a Planck type constant for probability. Not in a mathematical sense, as probability can get infinitely small in a purely mathematical model, but in a real world sense there must come a point where probability drops from non-zero to zero.

Why?

Probability, in the modern view, is simply an axiomatic system like say natural numbers. Its proven useful in modelling and is part of the toolkit of any physicist or applied mathematician. Your question would be like asking, in the real world, there should come a point where a real number drops from non-zero to zero. As such it doesn't really make any sense.

Thanks
Bill

 

[Jano L.]

It is strange but there seem to be some support for this kind of idea:

Cournot’s principle says that an event of small or zero probability singled out
in advance will not happen. From the turn of the twentieth century through
the 1950s, many mathematicians, including Chuprov, Borel, Fréchet, Lévy, and
Kolmogorov, saw this principle as fundamental to the application and meaning
of probability. In their view, a probability model gains empirical content only
when it rules out an event by assigning it small or zero probability.

http://www.probabilityandfinance.com/articles/15.pdf

Does anybody know more about this? Some application where this helps?

 

[bhobba]

Does anybody know more about this? Some application where this helps?

Well in applying the Kolmogorov axioms you can remove an event of zero probability and the axioms still apply. Consistency would seem to imply the assumption that an event of zero probability can't occur and people likely assume it without even realizing it.

Thanks
Bill