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Everything out of focus?

In the world of quantum mechanics, it is impossible to accurately measure certain pairs of a particle's physical quantities simultaneously, even with the best measuring instruments. Examples of such pairs include position and momentum, or time and energy. In the language of physics, two complementary properties of a quantum system cannot have clearly defined values at the same time. Examples of such pairs include the position and momentum of the same particle, as well as energy and time. Mathematically, the uncertainty principle states that there is a universal lower limit to the product of position uncertainty (Δx) and momentum uncertainty (Δp) (or other pairs), given by Planck's constant, ħ:
Δx·Δp≥2ħ/2 (ħ = 1.05×10−3) J s).

This means that measuring the momentum of a particle inevitably perturbs its position, and vice versa. This demonstrates that, at the atomic scale, classical concepts such as "exact position and speed" are no longer applicable.

 

Uncertainty principle - an example

The uncertainty principle always applies, but its effects can only be observed at very small dimensions, such as the size of an atom (10⁻¹⁰ meters). If the position of an electron is determined with 10⁻¹⁰-meter accuracy, then the momentum measurement accuracy is 10⁻²⁴ kg m/s. This means the electron's speed can only be measured with 1,000,000-meter-per-second or 3,600,000-kilometer-per-hour accuracy, which is roughly the speed at which an electron moves around the nucleus of an atom. Therefore, the uncertainty of the speed is almost as great as the speed itself, making it difficult to determine the speed effectively.

However, if you apply the same example to a ping-pong ball with a diameter of 2 cm and a mass of 2.7 g, determining its position with the accuracy of an atomic nucleus (10⁻¹⁵ meters), its speed can be determined with an accuracy of 10⁻¹⁷ meters per second. A typical ping-pong ball moves at about one meter per second. This means it would be possible to measure the ball's speed to 17 decimal places while determining its position with the same accuracy.

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The more precisely a particle's speed is determined, the more its location becomes blurred. According to Heisenberg's uncertainty principle, it is impossible to measure both precisely at the same time.
Picture: Ruth Bründler, UZH

 

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