Introduction

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 4π4π. More clearly:

Where ΔΔ 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.

What does it mean?

It is hard to imagine not being able to know exactly where a particle is at a given moment. It seems intuitive that if a particle exists in space, then we can point to where it is; however, the Heisenberg Uncertainty Principle clearly shows otherwise. This is because of the wave-like nature of a particle. A particle is spread out over space so that there simply is not a precise location that it occupies, but instead occupies a range of positions. Similarly, the momentum cannot be precisely known since a particle consists of a packet of waves, each of which have their own momentum so that at best it can be said that a particle has a range of momentum.

Let’s consider if quantum variables could be measured exactly. A wave that has a perfectly measurable position is collapsed onto a single point with an indefinite wavelength and therefore indefinite momentum according to de Broglie’s equation. Similarly, a wave with a perfectly measurable momentum has a wavelength that oscillates over all space infinitely and therefore has an indefinite position.

You could do the same thought experiment with energy and time. To precisely measure a wave’s energy would take an infinite amount of time while measuring a wave’s exact instance in space would require to be collapsed onto a single moment which would have indefinite energy.

The Heisenberg Principle has large bearing on practiced science and how experiments are designed. Consider measuring the momentum or position of a particle. To create a measurement, an interaction with the particle must occur that will alter it’s other variables. For example, in order to measure the position of an electron there must be a collision between the electron and another particle such as a photon. This will impart some of the second particle’s momentum onto the electron being measured and thereby altering it. A more accurate measurement of the electron’s position would require a particle with a smaller wavelength, and therefore be more energetic, but then this would alter the momentum even more during collision. An experiment designed to determine momentum would have a similar effect on position. Consequently, experiments can only gather information about a single variable at a time with any amount of accuracy.