Heisenberg’s Uncertainty Principle

Heisenberg suggested that it is impossible to calculate or measure any object’s exact position and momentum. Heisenberg’s uncertainty principle is based on the dual nature of wave particles. However, it is ignored in macroscopic measurements as the particles have a tiny mass. This eventually results in a released accuracy of their position accompanied by an enhanced uncertainty in their velocities. Heisenberg’s uncertainty principle explains the inability to simultaneously calculate more than one quantum variable. 

What is Heisenberg’s Uncertainty Principle?

According to Heisenberg’s uncertainty principle, it is nearly impossible to accurately determine velocity and position for wave and particle nature. This principle is known after the famous German physicist Werner Heisenberg, who proposed this uncertainty principle in 1927. When Heisenberg built a quantum physics model, he formulated this principle and discovered various fundamental factors limiting our knowledge of specific quantities. 

All about Heisenberg’s Uncertainty Principle 

The wave-particle dual nature is the reason behind Heisenberg’s uncertainty principle, as every particle present is associated with a wave and it exhibits a wave-like behaviour. The undulations of the most intense or significant wave are the most favourable places where these particles can be found. The more intense the undulations become, the more poorly defined wavelength is received. It eventually determines the momentum of the associated particle. 

The uncertainty principle has an alternate expression in a particle’s position and momentum. 

Now that you have understood the basic concepts of Heisenberg’s uncertainty principle, let’s move on to the formulas and applications of the same.

Let us suppose, ∆x and ∆p are the errors in position measurements and momentum measurements of a particle, respectively, then 

∆x×∆p ≥ h/4π

We know that the momentum formula states that p = mv, so the formula for Heisenberg’s uncertainty principle can be rewritten in the form of

∆x × ∆mv ≥ h/4π

You can also express it as

∆x × ∆m × ∆v ≥ h/4π 

Where, 

∆v refers to the errors in velocity measurements and we also consider an assumption of constant mass in the whole experiment.

Then the equation can be rewritten like

∆x × ∆v ≥ h/4πm

If we apply Heisenberg’s uncertainty principle on a single electron in some atom’s orbit where h = 6.626×10-34 Joules second and m = 9.11×10-31 Kilograms.

On further solving with these quantities 

∆x × ∆v ≥ 10-4 m2s-1

What is Matter Waves?

Matter waves can be defined as a central unit of quantum mechanics theory that equips particle and wave nature. The concept of matter waves was brought to light by French physicist Louis de Broglie in 1924, which is why they are also referred to as de Broglie waves. These waves do not possess an electromagnetic nature and represent the distinct probability of finding a particle in space. 

Is Heisenberg’s Uncertainty Principle noticeable in all matter waves?

The answer to the question “Is Heisenberg’s uncertainty principle noticeable in all matter waves?” is yes, as Heisenberg’s uncertainty principle applies to all matter waves with some limitations. This principle helps determine the measurement error of different properties of a matter wave-like position and momentum or time and energy. However, there are limitations in terms of the mass of the matter-wave as the matter with a large mass does not satisfy the Heisenberg uncertainty principle; the error in its position and momentum measurements are comparatively minimal. They can be neglected for easy calculation. 

On the contrary, in terms of small masses like electrons, the errors in the calculation are noticeable and significant, as expressed by Heisenberg’s uncertainty principle. In a nutshell, it can be said that Heisenberg’s uncertainty principle is applicable for all matter waves, but it holds a significant value while dealing with small mass quantities.

Conclusion

The Heisenberg uncertainty principle is an important concept of matter science. It states that it is nearly impossible to calculate co-relative physical dimensions of a matter-wave simultaneously with no error or perfect accuracy. However, the Heisenberg uncertainty principle raises several questions, like “Is the Heisenberg uncertainty principle noticeable in all matter waves?”. The Heisenberg uncertainty principle is only applicable to matter waves with a very small mass, generating a large error possibility in calculating the core relative physical dimensions like momentum and velocity.