• Choose a category
• All
• Classic-Fiction

By Root 639 0

light are much larger than an electron and therefore could not be used to determine its exact position as they washed over it like waves over a pebble. What was required was a microscope that used gamma rays, 'light' of extremely short wavelength and high frequency, to pinpoint its position. Arthur Compton, in 1923, had investigated X-rays striking electrons and found conclusive evidence for the existence of Einstein's light-quanta. Heisenberg imagined that, like two billiard balls colliding, when a gamma ray photon hits the electron, it is scattered into the microscope as the electron recoils.

There is, however, a discontinuous shove rather than a smooth transition in the electron's momentum due to the impact of the gamma ray photon. Since the momentum that an object possesses is its mass multiplied by its velocity, any change in its velocity causes a corresponding change in its momentum.35 When the photon hits the electron it jolts its velocity. The only way to minimise the discontinuous change in the electron's momentum is by reducing the energy of the photon, thereby lessening the impact of the collision. To do so entails using light of a longer wavelength and lower frequency. However, such a switch in wavelength means that it is no longer possible to pin down the exact position of the electron. The more precisely the electron's position is measured, the more uncertain or imprecise any measurement of its momentum and vice versa.36

Heisenberg showed that if p and q (where is the Greek letter delta) are the 'imprecision' or 'uncertainty' with which the momentum and the position are known, then p multiplied by q is always greater than or equal to h/2: pqh/2, where h is Planck's constant.37 This was the mathematical form of the uncertainty principle or the 'imprecision in knowledge of simultaneous measurements' of position and momentum. Heisenberg also discovered another 'uncertainty relation' involving a different pair of so-called conjugate variables, energy and time. If E and t are the uncertainties with which the energy E of a system can be determined and the time t at which E is observed, then Eth/2.

At first there were some who thought that the uncertainty principle was the result of the technological shortcomings of the equipment used in an experiment. If the equipment could be improved, they believed, then the uncertainty would disappear. This misunderstanding arose because of Heisenberg's use of thought experiments to draw out the significance of the uncertainty principle. However, thought experiments are imaginary experiments employing perfect equipment under ideal conditions. The uncertainty discovered by Heisenberg is an intrinsic feature of reality. There could be no improvement, he argued, on the limits set by the size of Planck's constant and enforced by the uncertainty relations on the precision of what is observable in the atomic world. Rather than 'uncertain' or 'indeterminate', 'unknowable' may have been a more apt description of his remarkable discovery.

Heisenberg believed it was the act of measuring the position of the electron that made the precise determination of its momentum at the same time impossible. The reason appeared, as far as he was concerned, to be straightforward. The electron is disturbed unpredictably when struck by the photon used to 'see it' in order to locate its position. It was this unavoidable disturbance during the act of measurement that Heisenberg identified as the origin of uncertainty.38

It was an explanation that he believed was supported by the fundamental equation of quantum mechanics: pq–qp=–ih/2, where p and q are the momentum and position of a particle. It was the inherent uncertainty of nature that lay behind non-commutativity – the fact that p×q does not equal q×p. If an experiment to locate an electron were followed by one measuring its velocity (and therefore its momentum) they would give two precise values. Multiplying the two values together yields an answer A. However, repeating the experiments in reverse order, measuring the velocity first and then the position,