What does this matrix mean? It reveals quantum properties of matter! The question is: does it differ from the matrix of 2 spin-1/2 particles? In order to answer this question, one has to understand what these colors mean. So they are related to probability that the particle has spin UP or DOWN (explanation below). In general, the shown data present average value of spin, therefore they fluctuate about 0.5.
If color is getting blue, it corresponds to probability below 0.5. On the other hand, the more yellow color, the higher probability (above 0.5). And green is equal to 0.5.
This matrix was calculated for 100k particles! Btw it consumed about 20mins to generate it. In comparison to the previous matrix (2 particles), one can notice more green squares. It’s because of the fact that we consider relatively extensive set where statistics plays a crucial role. Probabilities converge to 0.5 so in such system one may receive the same number of particles with spin UP or DOWN. I repeated the process 400 times, which is shown as 20 x 20 matrix.
The extended explanation below:
I prepared N spin-1/2 particles. In the quantum world we are not certain of anything until it’s checked/ measured. Before the act of observation, a quantum system is described by a probability density function. One can notice that the system is in a specific state with a specific probability only. @kanyewestt_official would say “you never know homie”. So I prepared these particles with uncertain spin (let’s assume that spin describes whether a particle rotates left or right). In a quantum universe, phenomena and space and time are affected by the observer. The probability density functions of my particles had collapsed because of my act of observation. I obtained the certain information: for each of particles I knew how they rotate (I knew their spins). Then I calculated the average value of spins for these N particles. a^2 iterations were performed and voilà - we see the *a by a* matrix. Each square in the matrix corresponds to the average spin of N particles.
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