With the formulation of Planck’s constant, our limits of observation were set. Beyond this limit, our observation lacked any meaning. The confidence of what we saw beyond this was imaginary and superstition. Try as we might to define the route that an electron took to reach the other side of the neutron, it was a mere conjecture.
The postulation was a crushing mandate on not only classical physics but classical human philosophy – Path had no meaning beyond a point. We may keep yearning for it and try charting it or forcing it upon ourselves but that was merely to humor ourselves. How could something so dynamic and infinite at the same time lend itself to a static path?
To reinforce this idea further, he used matrices to find the difference between observing the momentum first or the location and found that even that was equal to the same constant. He however added an imaginary number to the result to convey the message – a very significant one.
In 1925, following pioneering work with Hendrik Kramers, Heisenberg developed matrix mechanics, which replaced the ad-hoc old quantum theory with modern quantum mechanics. The central assumption was that the classical motion was not precise at the quantum level, and electrons in an atom did not travel on sharply defined orbits. Rather, the motion was smeared out in a strange way: the time Fourier transform only involving those frequencies which could be seen in quantum jumps.
Heisenberg’s paper did not admit any unobservable quantities, like the exact position of the electron in an orbit at any time, he only allowed the theorist to talk about the Fourier components of the motion. Since the Fourier components were not defined at the classical frequencies, they could not be used to construct an exact trajectory, so that the formalism could not answer certain overly precise questions about where the electron was or how fast it was going.
The most striking property of Heisenberg’s infinite matrices for the position and momentum is that they do not commute. His central result was the canonical commutation relation:
and this result does not have a clear physical interpretation.
What he wanted to say was not that such a constant did not exist but that it did not do complete justice to the infinity of possible differences.
de Broglie had showed that not only what we hitherto thought as wave was like matter, but even the reverse was true! All matter also had wave like qualities!
Schrödinger on the other hand, approached the de Broglie hypothesis from the other side of looking at electron as a wave. Both, he and Heisenberg came to the same answers.
Path and certainty is relevant only in Newtonian world of the gross and matter. The moment you move to finer reality of the creation, uncertainty exposes the weakness of that physical world. The uncertainty does not obviate the truth of Newtons phyical laws. They exist and work. The wonder is HOW can they despie all the attempts of nature at the finer level to completely discredit them!
The uncertainty and dynamism of the sub-atomic world is not the mystery – rather the mystery is that it can lend itself to definite reality of look and feel creation.
Ever since Planck showed that light was emitted as quanta and Einstein followed him up to show that it was even absorbed as quanta all the while between those points it seemed like a wave; science has had three camps – One, who revel in the Infinite world only; Second, who cannot leave the material reality; and Third, who have learned to live with these two contradictions.
While the first two can get offended by the other, the third set remains oblivious to the conflict. For in living with that conflict is the key to Truth.