Is the universe really not deterministic

Quantum Sense and Quantum Nonsense: What is Determinism?

Almost all applied sciences use dynamics with probability statements, which are of course far more sophisticated than those presented here, but are based on the same idea.

The results of non-deterministic processes are often called "random". In order to intuitively define a random sequence of results, let us consider the repeated tossing of a coin that has not been marked and register the results heads (K) and tails (Z). Such an experiment is typical of what we call random and so can be used to explain the term.

What do you expect when you toss a coin many times? As already mentioned, the first thing to assume is that K and Z occur half each. But one also expects that the pairs KK, KZ, ZK and ZZ each occur in a quarter. Each of the eight rows that result from three successive throws, i.e. ZZZ, ZZK, ZKZ etc., should each occur to an eighth. More generally: In a random sequence, the occurrence of any combination of K and Z depends only on the length of the series: the longer it is, the lower its frequency. Any finite series of length R. occurs in a random sequence of length n with a share of n/2R. on.

This notion of a random sequence becomes more plausible when one looks at examples of sequences that are "not" random. So is z. B. ZKZKZKZKZK… only the constant repetition of the pair ZK. Another example is the sequence ZZKKZKZZZKKZKZZZKKZKZ…, which is created by repeating ZZKKZKZ and is therefore not random. While in a random sequence of length n the series ZK n/22 = n/ Occurs 4 times, it occurs in the non-random sequence mentioned here n/R. = n/ 2 times before. For the second example with R. = 7 applies accordingly n/27 = n/ 128 in the case of the random sequence, but in the case of the non-random sequence one obtains n/7.

For reasons that will be explained below, we want to call a sequence that "looks" random, that is, does not have a regular pattern, "apparently random".

Suppose we have such a seemingly random sequence. We can now ask a fundamental question: Is this sequence "really random" or, to put it another way, "real, objective" or "intrinsically random". These terms mean that one cannot give a convincing deterministic explanation for the occurrence of such random sequences. The definition "apparently random", which is linked to a statistical property of the sequence (two finite series of the same length have the same frequency), is opposed to the definition "really random" or "intrinsically random", although it is impossible to use a deterministic one Mechanism of generating a "really random" sequence.