Werner Karl Heisenberg (1901–1976)
Heisenberg, a German physicist, was awarded the Nobel Prize for physics in 1932, for his work on a matrix
theory of quantum mechanics. It was a dualistic theory, meaning that phenomena could be described either in terms of waves or in
terms of the new quanta (particles). In 1927, Heisenberg stated his uncertainty principle that a particle's both momentum
and position cannot be determined. This means that subatomic events have to be predicted using probabilities.
In classical physics, studying the behavior of a physical system is often a simple task due to the fact that several physical qualities can be measured simultaneously. However, this possibility is absent in the quantum world. In 1927 the German physicist Werner Heisenberg described such limitations as the Heisenberg Uncertainty Principle, or simply the Uncertainty Principle, stating that it is not possible to measure both the momentum and position of a particle simultaneously.
In order to understand the conceptual background of the Heisenberg Uncertainty Principle it is important to understand how physical values are measured. In almost any measurement that is made, light is reflected off the object that is being measured and processed. The shorter the wavelength of light used, or the higher its frequency and energy, the more accurate the results.
For example, when attempting to measure the speed of a tennis ball as it is dropped off of a ledge, photons (measurement of light) are shot off the tennis ball, reflected, and then processed by certain equipment. Because the tennis ball is so large compared to the photons, it is unaffected by the efforts of the observer to measure its physical quantities. However, if a photon is shot at an electron, the minuscule size of the electron and its unique wave–particle duality introduces consequences that can be ignored when taking measurements of macroscopic objects.
However, the collision between such high energy photons of light with the extremely small electron causes the momentum of the electron to be disturbed.
Atom
Illustration of the atom according to Heisenberg and Born: The atom is made up of a cloud of electrons which
can only be visualized through mathematical calculations.
Heisenberg concluded in his famous 1927 paper on the topic, “At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position. At the instant at which the position of the electron is known, its momentum therefore can be known only up to magnitudes which correspond to that discontinuous change; thus, the more precisely the position is determined, the less precisely the momentum is known...”
Heisenberg realized that since both light and particle energy are quantized, or can only exist in discrete energy units, there are limits as to how small, or insignificant, such an uncertainty can be. As proved later in this text, that bound ends up being expressed by Planck's Constant, h = 6.626×10−34 J.s.
It is important to mention that The Heisenberg Principle should not be confused with the observer effect. The observer effect is generally accepted to mean that the act of observing a system will influence that which is being observed. While this is important in understanding the Heisenberg Uncertainty Principle, the two are not interchangeable. The error in such thinking can be explained using the wave–particle duality of electromagnetic waves, an idea first proposed by Louis de Broglie. Wave–particle duality asserts that any energy exhibits both particle–like and wave–like behavior.
Random universe
The above picture represents the fundamental uncertainty of the universe, as seen in quantum theory
(Heisenberg's Uncertainty Principle) and in probability theory. Even seemingly random events can be studied using chaos
theory. This image can also represent the idea that the universe began as a chance quantum event. Even though scientific theories
(such as statistical mechanics) often use probabilities, quantum uncertainty is a much more difficult concept. Einstein expressed
his lack of satisfaction with such interpretations of quantum theory by saying: “God does not play dice”.
Heisenberg's Uncertainty Principle:It is mathematically possible to express the uncertainty that, Heisenberg concluded, always exists if one attempts to measure the momentum and position of particles.First, we must define the variable “x” as the position of the particle, and define “p” as the momentum of the particle. The momentum of a photon of light is known to simply be its frequency, expressed by the ratio h/λ, where h represents Planck's constant and λ represents the wavelength of the photon. The position of a photon of light is simply its wavelength, λ. In order to represent finite change in quantities, the Greek uppercase letter delta, or Δ, is placed in front of the quantity. Therefore,
Δp=h/λ Δx=λ By substituting Δx for λ in the first equation, we derive
Δp=h/Δx
or,
ΔpΔx=h
Note, we can derive the same formula by assuming the particle of interest is behaving as a particle, and not as a wave. Simply let Δp=mu, and Δx=h/mu (from De Broglie's expression for the wavelength of a particle). Substituting in Δp for mu in the second equation leads to the very same equation derived above-ΔpΔx=h. This equation was refined by Heisenberg and his colleague Niels Bohr, and was eventually rewritten as ΔpΔx = h/4π.
What this equation reveals is that the more accurately a particle's position is known, or the smaller Δx is, the less accurately the momentum of the particle Δp is known. Mathematically, this occurs because the smaller Δx becomes, the larger Δp must become in order to satisfy the inequality. However, the more accurately momentum is known the less accurately position is known.