T
We ended off at the point in which a greater emphasis was being placed on using complex numbers as a means to further capture and record the behaviour of quantum particles. It’s interesting to take note of these events, because, not only did they play such imperative roles in influencing our understanding and practises in science, mathematics and philosophy, but, have also catapulted us into a very interesting paradigm in the world, whereby, many environmental, social and governance factors now seem to be at teething point of disbandment for the individual. And what’s really fascinating is that a lot of the current emerging trends seem to point to a theme of us going back to our roots; there is good reason for it too, I believe, but we’ll get there.
Complex numbers proved to be very useful in physics and engineering because these numbers/equations have both a real and an imaginary component. When plotted on a graph, a complex number provides a single value that represents a point in two dimensions. As long as the imaginary parts cancel out before coming up with a real-world prediction, they proved a great tool.
Scientists, de Broglie, Heisenberg, Schrodinger and Dirac played a pivotal role in pushing forward quantum probability theory. Heisenberg developed a purely mathematical method called, ‘Matrix Mechanics,’ which was then challenged by Edward Schrodinger, a man who favoured more visual and practical theological examples. Schrodinger would go on to propose an original interpretation of the physical meaning of the wave function – developing the basis of ‘Wave Mechanics’ and the paradoxical ‘Schrodinger’s Cat’ thought experiment. However, he was further challenged by Max Born and Paul Dirac who held the view that if his approaches were truly representative of the behaviour of particles they would show that quantum particles gradually spread out over time, becoming immense. What Born and Dirac found was that Schrodinger’s equations did not actually say how a particle behaved by showing (its) location, but rather the probability of a particle being in a particular location.
There is a faulty conclusion that many scientists come to when trying to decipher this madness, and it’s that the photon is in two places at once – implying it goes through both slits and interferes with itself. Tempting but faulty, as Brian Clegg explains:
“It would be more accurate to say that a photon in Thomas Young’s Double-Slit Experiment isn’t anywhere until it hits the screen and is registered. Up to that point, all that exists is a series of probabilities for its location, described by the (Square of the) Wave Equation. If the experimenter puts a detector in one of the slits that lets a photon through but detects its passing, the interference pattern disappears. We have forced the photon to have a location and there is no opportunity for the probability waves to interfere.”
It was this fundamental role for probability that irritated Einstein so much and to which he exclaimed: “God did not play dice!”
It was from the central role of probability that Heisenberg would deduce the famous ‘Uncertainty Principle.’ He showed that quantum particles have pairs of properties – Location and Momentum/Time and Energy – that are intimately related by probability. He found that the more accurately you discover one of these pairs of values, the less accurately it is possible to know the other.
Source: Brian Clegg, Quantum Age Book
