In this article, we will discuss Heisenberg’s Uncertainty Principle (Introduction). So, let’s get started.
Heisenberg’s Uncertainty Principle states that there is inherent uncertainty in the act of measuring a variable of a particle. Commonly applied to the position and momentum of a particle, the principle states that the more precisely the position is known the more uncertain the momentum is and vice versa. This is contrary to classical Newtonian physics which holds all variables of particles to be measurable to an arbitrary uncertainty given good enough equipment. The Heisenberg Uncertainty Principle is a fundamental theory in quantum mechanics that defines why a scientist cannot measure multiple quantum variables simultaneously. Until the dawn of quantum mechanics, it was held as a fact that all variables of an object could be known to exact precision simultaneously for a given moment. Newtonian physics placed no limits on how better procedures and techniques could reduce measurement uncertainty so that it was conceivable that with proper care and accuracy all information could be defined.
Heisenberg made the bold proposition that there is a lower limit to this precision making our knowledge of a particle inherently uncertain. More specifically, if one knows the precise momentum of the particle, it is impossible to know the precise position, and vice versa. This relationship also applies to energy and time, in that one cannot measure the precise energy of a system in a finite amount of time. Uncertainties in the products of “conjugate pairs” (momentum/position) and (energy/time) were defined by Heisenberg as having a minimum value corresponding to Planck’s constant divided by 4π. More clearly:
Where Δ refers to the uncertainty in that variable and h is Planck’s constant.
Aside from the mathematical definitions, one can make sense of this by imagining that the more carefully one tries to measure position, the more disruption there is to the system, resulting in changes in momentum. For example compare the effect that measuring the position has on the momentum of an electron versus a tennis ball. Let’s say to measure these objects, light is required in the form of photon particles. These photon particles have a measurable mass and velocity, and come into contact with the electron and tennis ball in order to achieve a value in their position. As two objects collide with their respective momenta (p=m*v), they impart theses momenta onto each other. When the photon contacts the electron, a portion of its momentum is transferred and the electron will now move relative to this value depending on the ratio of their mass. The larger tennis ball when measured will have a transfer of momentum from the photons as well, but the effect will be lessened because its mass is several orders of magnitude larger than the photon. To give a more practical description, picture a tank and a bicycle colliding with one another, the tank portraying the tennis ball and the bicycle that of the photon. The sheer mass of the tank although it may be traveling at a much slower speed will increase its momentum much higher than that of the bicycle in effect forcing the bicycle in the opposite direction. The final result of measuring an object’s position leads to a change in its momentum and vice versa.
All Quantum behavior follows this principle and it is important in determining spectral line widths, as the uncertainty in energy of a system corresponds to a line width seen in regions of the light spectrum explored in Spectroscopy.