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#### Aufbauwerk 2045

Consider this a layman's question. I am not an expert on deeper aspects of probability. I simply rely on Kolmogorov's axioms and the calculation methods I learned as a student. To me it's just a bit of mathematics and it makes perfect sense as mathematics.

When it comes to actually understanding nature, I find this whole topic of probability and determinism quite mysterious. I ask the following question, and would love to know if someone has a good answer. Perhaps there is a good reference to an answer specifically to the following question? I do mean specific, not a general discourse on probability.

Consider the following thought experiment. I am presented with two black boxes. I am told that one contains some natural emitter of random numbers. I am told that this process is therefore "non-deterministic." The other contains a small computer that is running a random number generator. I am told that this process is therefore "deterministic." I understand what is meant by "deterministic" because I understand how a random number generator program works. But I do not understand "non-deterministic." What does it mean? Does it mean there is no so-called "causal relationship?" Of course this means we must define "causality." Another riddle.

Continuing with the thought experiment, the output of each box is a sequence of numbers. My job is to determine which box contains the natural process and which contains the computer.

I am only allowed to examine the output. I am not allowed to examine the boxes themselves in any way. Looking only at the output, and using only mathematical tests for randomness, how can I distinguish between the so-called "truly random" and the so-called "pseudo-random" processes?

My understanding is that if there is no such mathematical test, which can distinguish between the two outputs, then we would naturally fall back on Occam's Razor, namely "do not multiply entities without necessity." I know how random number generators work. Why should I believe that whatever is going on in nature's black boxes is something other than this? In other words, why do we introduce this idea of a "non-deterministic" black box in nature? Can we even define "non-deterministic?"

Is there a good explanation of this in the scientific literature? Please provide the reference if possible. Thanks!

P.S. I took several QM courses at university some years ago, and this question never came up. Maybe it's different these days. Maybe it's somewhere in a popular textbook? Or would it be considered a fringe question?

When it comes to actually understanding nature, I find this whole topic of probability and determinism quite mysterious. I ask the following question, and would love to know if someone has a good answer. Perhaps there is a good reference to an answer specifically to the following question? I do mean specific, not a general discourse on probability.

Consider the following thought experiment. I am presented with two black boxes. I am told that one contains some natural emitter of random numbers. I am told that this process is therefore "non-deterministic." The other contains a small computer that is running a random number generator. I am told that this process is therefore "deterministic." I understand what is meant by "deterministic" because I understand how a random number generator program works. But I do not understand "non-deterministic." What does it mean? Does it mean there is no so-called "causal relationship?" Of course this means we must define "causality." Another riddle.

Continuing with the thought experiment, the output of each box is a sequence of numbers. My job is to determine which box contains the natural process and which contains the computer.

I am only allowed to examine the output. I am not allowed to examine the boxes themselves in any way. Looking only at the output, and using only mathematical tests for randomness, how can I distinguish between the so-called "truly random" and the so-called "pseudo-random" processes?

My understanding is that if there is no such mathematical test, which can distinguish between the two outputs, then we would naturally fall back on Occam's Razor, namely "do not multiply entities without necessity." I know how random number generators work. Why should I believe that whatever is going on in nature's black boxes is something other than this? In other words, why do we introduce this idea of a "non-deterministic" black box in nature? Can we even define "non-deterministic?"

Is there a good explanation of this in the scientific literature? Please provide the reference if possible. Thanks!

P.S. I took several QM courses at university some years ago, and this question never came up. Maybe it's different these days. Maybe it's somewhere in a popular textbook? Or would it be considered a fringe question?

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