Are entanglement correlations truly random?

[entropy1]

Suppose I walk down the street, and each time I look to my right, a red car is passing. If I don't look, I don't know which color the passing cars have.

So the correlation between me looking and a red car passing is 100%.

So I assume the moments I look are random (A) and the cars passing have FAPP random colors (B).

So, in this case, with the correlation manifesting, are (A) and (B) "truly" random?

Since we generally do not see correlations like this always and everywhere, it should be, however not impossible, improbable to see this. So, I cannot determine whether there is a red car convention in town or not, since I don't know the counterfactual measurements (looking). So, would a string of red cars passing me still be random? After all it would require a red car convention. And if there is NO red car convention, would the string of cars passing still be truly random if the correlation with my looking direction would be 100% red cars? (Or, for that matter, would my peeking be random?)

The problem I see, is that if (A) and (B) are truly random, the measurements should be typical for what is reality. For example, based on my perceptions, I might say that in this street probably only red cars are allowed, while the counterfactual data is in contradiction with that.

You could also see it the other way round: I see typical cars passing, while when I'm not looking only red cars pass which I wouldn't know of. My assessment of the data might lead me to faulty conclusions.

So I think "randomness" is required to accurately assess reality.

 

[stevendaryl]

Suppose I walk down the street, and each time I look to my right, a red car is passing. If I don't look, I don't know which color the passing cars have.

So the correlation between me looking and a red car passing is 100%.

So I assume the moments I look are random (A) and the cars passing have FAPP random colors (B).

So, in this case, with the correlation manifesting, are (A) and (B) "truly" random?

There was a different thread in the "Set Theory, Logic, Probability and Statistics" forum on this topic. Random is relative to a model or theory. You can't know whether something is "truly" random unless you know what theory is correct. Which, of course, you can never know.

According to QM, the results of certain types of measurements are random, in the sense that QM doesn't propose any means of determining the values ahead of time. According to a different theory (maybe Bohmian mechanics), the results may not be random.

The facts you describe above is consistent with multiple explanations:

1. All the cars are red.
2. There are cars of other colors, but for whatever reason, you only have an impulse to look at a car when the car is red.
3. There are cars of other colors, but just by coincidence, you happened to look at the moments a red car is passing.
4. Etc.

 

[Stephen Tashi]

I flip a coin and it lands heads. Does it still make sense to describe the probability of a heads for that flip as p=.5, ten minutes after the fact? Does probability even exist for events in the past?

Both of these thoughts goes to a time relationship of randomness... does the standard treatment not take time into account?

The standard mathematical treatment of probability (which uses measure theory) says nothing about events actually happening. It doesn't have any axioms that say you can take random samples. It does not have a model of time as that notion is used in physics. So the standard mathematical theory does not deal with questions about a probability "before" or "after" some time or a probability that changes with the "actual" occurrence of an event.

The standard techniques for applying probability theory to real life problems do assume that it is possible to take random samples and that events actually happen (or don't happen). In applications of probability theory the indexing set used in the abstract definition of "stochastic process" is often interpreted to be time in the physical sense.

The distinction between mathematical probability theory and interpretations that people make when applying it is blurred by the fact that only the most advanced texts on mathematical probability theory confine themselves to discussing that theory. The typical textbook on probability theory tries to be helpful by teaching both probability theory and its useful applications. For example, the "conditional probability" P(A|B) has a very abstract mathematical definition. However, typical textbooks present P(A}B) by interpreting it to mean "The probability of event A given that the event B has (actually) happened".

In mathematical probability theory, a specific sequence of numbers can be assigned a probability and it can be a member of a "sample space" on which a probability measure is defined. But there is no definition for a particular sequence of numbers being "random" or "not random". In mathematical probability theory, there is a definition for two random variables to be correlated However there is no definition for two specific sequences of numbers to be correlated. In this thread, there is the usual confusion involving numerical calculations done on specific sets of numbers to estimate mathematical correlation versus the mathematical definition of correlation.

Attempts have been made to create mathematical notions of randomness for specific sequences of numbers. These attempts are not "standard" mathematical probability theory.

When discussing physics, people are making their own interpretations of mathematical probability theory.