Randomness of quantum mechanics and Pi

[kolleamm]

Just a thought I had one day, but the general idea I've heard is that quantum mechanics has a random property to it. The number Pi is apparently a number without any sort of apparent pattern to it either, seemingly random?

Could these two things somehow be related?
For example somehow representing the quantum randomness with some sort of pi formula?

 

[DennisN]

For example somehow representing the quantum randomness with some sort of pi formula?

The randomness in quantum physics means we can not/it is impossible* to predict the exact outcome of a measurement in certain experiments. What is successfully predicted is instead the probabilities of getting various outcomes, see e.g. Wavefunction postulate.

* To the best of our current knowledge.

 

[fresh_42]

Just a thought I had one day, but the general idea I've heard is that quantum mechanics has a random property to it. The number Pi is apparently a number without any sort of apparent pattern to it either, seemingly random?

Could these two things somehow be related?
For example somehow representing the quantum randomness with some sort of pi formula?

##\pi ## is deeply woven into the fabric of our world. It appears at places one wouldn't expect it. And by simulating the world by wave functions has again ##\pi## as periodicity in it. But whether all these circumstances are due to a deeper truth or just a consequence of the many radial objects, motions and symmetries in the world, cannot be said at this stage. So as of today, it is more an incident than a relation. E.g. we could as well write ##\pi## by ##1's## and ##0's## and then it's not so apparent, that its representation has randomness in it. Another point is, that ##\pi## can be written by closed formulas, e.g. here: https://www.physicsforums.com/threads/your-most-interesting-fact-about-pi.942054/#post-5958529, and all of a sudden it's far less asymmetrical and randomly. Also its definition as a ratio isn't randomly at all, only the decimal digits are to some extend.

 

[f95toli]

"What is random" is actually a very difficult question even from a purely "technical point" of view; i.e. if one re-formulates the question as "how does one show that a random number generator is really random", this is (obviously) an important practical questions since there are lots of applications of good random number generators.
There are all sorts of tests that can be used to test RNGs; but they are (usually) adapted to work well for pseudo-random generators, i.e. generators that use an algorithm to create a series of numbers; i.e. not dissimilar to how we calculate decimals of pi.
How one would show that a hardware random number generator does what it says on the tin(i.e how to validate it) is -as far as I know- an open problem and is an area of active research (I've sat through a few talks on the subject at various conferences). Hence, I don't think there is a known definite answer to your question.

Note that that you can actually buy quantum random number generators (see e.g. https://www.idquantique.com/random-number-generation/overview/)

 

[ZapperZ]

Just a thought I had one day, but the general idea I've heard is that quantum mechanics has a random property to it. The number Pi is apparently a number without any sort of apparent pattern to it either, seemingly random?

Could these two things somehow be related?
For example somehow representing the quantum randomness with some sort of pi formula?

What does it mean to be "related" in this context? Does the fact that pi appears in the mathematics of QM is enough to claim that they are "related"?

Furthermore, QM appears to NOT be random when we deal with huge numbers. After all, it makes uncannily accurate predictions, so much so that your electronics do not have random behavior, do they? Would you place your life under the actions of something that's unpredictably random? So do you see this similar property in calculating the next number for pi?

Zz.

 

[Rive]

Could these two things somehow be related?

Both seems to be random. That's already a kind of relation.
But anything more concrete would require scientific evidence, and that's lacking right now

 

[gmax137]

I don't see how you can say the digits of Pi are random, we can calculate them and there's no surprise when the next digit comes up, is there?

Does this just mean if I calculate Pi to 10,000 digits, I will see about 1000 zeroes, and about 1000 ones, and so on? The digits are equally present in a large sample?

 

[fresh_42]

I don't see how you can say the digits of Pi are random, we can calculate them and there's no surprise when the next digit comes up, is there?

Does this just mean if I calculate Pi to 10,000 digits, I will see about 1000 zeroes, and about 1000 ones, and so on? The digits are equally present in a large sample?

Someone has done the job: https://arxiv.org/ftp/arxiv/papers/1612/1612.00489.pdf

 

[russ_watters]

I don't see how you can say the digits of Pi are random, we can calculate them and there's no surprise when the next digit comes up, is there?

Agreed. The digits of Pi are most certainly *not* random.

 

[cosmik debris]

Agreed. The digits of Pi are most certainly *not* random.

The digits of Pi are not random but if you don't know it is a sequence of digits from Pi is the sequence random?

Cheers

 

[Vanadium 50]

"Random" is an ill-defined word.

A better - more technical - word for the "randomness" of digits is "normal". A number is normal if in every base b, a sufficiently long string of digits will have each digit represented 1/b times, each pair 1/b² times, each triplet 1/b³ times and so on. It is known that most numbers are normal, so there is nothing special about the sequence of digits in pi, and pi is not known to be normal, although pretty much everyone thinks it is.

So, given that,

Could these two things somehow be related?

No.