The misunderstood Uncertainty principle

Heisenberg introduced his famous relations in an article of 1927, entitled “Ueber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik”. A (partial) translation of this title is: “On the anschaulich content of quantum theoretical kinematics and mechanics”.

The Heisenberg uncertainty principle is often misunderstood with The observer’s effect which states that measurements of certain systems cannot be made without affecting the system, that is, without changing something in a system. We always hear the same story:

To accurately measure the position of an electron, a light of very short wavelength should be shone on the electron since we can only see particles as small as the wavelength of light used. By shining the light of such short wavelength, the high energy photon will knock off the electron producing uncertainty in the velocity

This explanation only describes The observer’s effect. The Heisenberg uncertainty principle, on the other hand, is something totally different.

The uncertainty principle arises from the wave-particle duality. Subatomic particles have dual nature i.e Particle and wave. Wave’s wavelength is related to momentum by De Broglie relations:

p=h/λ

The momentum can be calculated by knowing the wavelength of a wave but the wave stretches out in space making it impossible to measure the exact position.

On the other hand, To know its exact position, the wavefunction will needed to be changed from an infinite sine wave to something localized(wave packet). To achieve this feat, it will be needed to add wavefunction of the particles of which the momentum is known but position is not, making a cumulative wavefunction (Fourier transform). The wavelengths can vary slightly. Now the momentum cannot be measured since its wavelength has totally been altered.

Making the wave packet smaller will increase the certainty of exact position but it will also decrease the certainty of exact momentum and making the wave packet larger will decrease the certainty of exact momentum but it will increase the uncertainty in exact position.

Localized particle(wave packet)

To measure both position and momentum with minimum uncertainty, Enough wavefunctions are to be added by which both Position and momentum can be measured with some uncertainty.

The more you focus on the position the broader range of wavelength is needed and the more you restrict wavelength the less information you have about the position

This uncertainty doesn’t exist because of some limitations of equipment or anything related to altering the parameters of subatomic particles while observing. It exists because of wave-particle duality. This is no coincidence, these uncertainties are connected. Reducing one will increase other. The uncertainty is:

Where Δx is uncertainty in position and Δp is uncertainty in momentum.