Question

How small an object has to be before it starts to show quantum mechanical affects?

Like if we keep hypothetically breaking down a macroscopic object smaller and smaller, in which size (negative power of metre) does it begin to show quantum mechanical affects? Like it being in 2 places unless we measure it's position.

Answer 1

Solution :

For objects in a macroscopic world, classical mechanics instructs how the laws of motion function while quantum mechanics predominates for particles in a microscopic world. Quantum Mechanics is generally thought of as the most fundamental concept and that classical mechanics is its limiting case. There have been numerous efforts in understanding and relating the quantum and classical descriptions of behavior of matter, indicating the possibilities of matter behaving classically in a quantum realm.

Classical mechanics, to be precise, describes the particle nature of the matter whereas, quantum mechanics describes the motion of the particle in terms of probability waves. To give an example, let there be a particle at rest ( in a quantum realm). This particle is described as a wave extending homogeneously throughout space. This results in a probability distribution that is same everywhere. Also, this happens to be constant throughout all space. Therefore, a particle at rest (quantum mechanically) is likely to be located anywhere in space.

There is no tool to understand how small an object should be to show quantum mechanical effects. But, to get an idea, consider the popular Heisenberg's uncertainity principle of position and momentum:

This gives

This gives the idea of how small or big the mass of an object must be for quantum mechanical measurements.

Also, if the dynamical action for a particle is calculated is large or approximately close to 1, then laws of classical mechanics thrive. Consequently, if the dynamical action for a particle is close to Planck's constant, then laws of quantum mechanics are applied.

Thus, individual atoms, molecules, etc require quantum mechanics to understand their behavior while the classes/groups of such atoms may require classical mechanics to account for their behavior.