One of the core principles of all of quantum mechanics is the Heisenberg’s Uncertainty principle. Introduced in 1927 by Werner Heisenberg, the principle limits our ability to measure two physical quantities to a 100% accuracy at the same time. More specifically, it limits our ability to measure two complementary properties of an object simultaneously. Complementary properties are pairs of physical properties that cannot be measured simultaneously. Of all the complementary properties, the most common are Momentum and Position. The Uncertainty Principle is given as- ΔpΔx≥ℏ/2
in the equation above, ℏ is the Reduced Planck’s constant, Δp and Δx are uncertainty in momentum and position respectively. The more accurately we measure the position of a quantum particle, the less precise is our measure of its momentum and vice versa, but why does this happen? To understand this, we must answer how we measure these physical quantities of quantum particles.
An Experiment to Understand Uncertainty
To measure position and momentum of quantum particles we bounce waves off of them, for example waves of light. Now, there is something called wavelength which is the distance between two consecutive peaks or valleys. The wavelength poses a margin of error. The shorter is the wavelength, the lower is the error. To understand this, imagine that you wish to measure the length book. Let’s assume its length to be 10.125 cm. If you are given a centimetre scale to measure the length of the book, you will be able to measure the length of the book to an accuracy of just 1 cm. in this case you find the length of the book to be 10cm. the error is 0.125 cm. now we use a more accurate scale, a millimetre scale. This time you are able to measure the book length to be 10.1 cm. The error is 0.025cm. The smaller are the units in the scale, the more accurate is our answer.
In case of quantum mechanics things aren’t so simple. If the wavelength of light is reduced, its frequency increases and therefore its energy. By doing this, the high energy photons of light will knock the quantum particle in unpredictable ways. Meaning that if you try to measure the position of a quantum particle to a higher accuracy, you change its momentum. But similarly if we use light of shorter wavelength, we know the position less precisely and the momentum more accurately.
Does this principle work in the macroscopic word?
Yes, the principle is true for the macroscopic world as well but the uncertainty is just too small to measure.