The fundamental constant ℏ, which is pronounced ‘aitch-bar’, is called the quantum of action, or alternatively Planck’s constant. Planck discovered the quantum principle when studying the properties of incandescent light, i.e., of light emanating from hot bodies.
All attempts to observe physical action values smaller than this fail. In other words, in nature – as in a good cinema film – there is always some action. The existence of a smallest action value is the so-called quantum principle.
When Planck saw that the quantum of action allowed defining all units in nature, he was as happy as a child; he knew straight away that he had made a fundamental discovery, even though (in 1899) quantum theory did not yet exist. He even told his seven-year-old son Erwin about it, while walking with him through the woods around Berlin. Planck explained to his son that he had made a discovery as important as universal gravity. Indeed, Planck knew that he had found the key to understanding many of the effects that were then unexplained.
Quantum effects surround us on all sides. However, since the quantum of action is so small, its effects on motion appear mostly, but not exclusively, in microscopic systems. Quantum theory is the description of microscopic motion. Quantum theory is necessary whenever a process produces an action value of the order of the quantum of action.
Therefore, a smallest action implies that there is a smallest change value in nature. If we compare two observations, there will always be change between them.
Any system whose indeterminacy is of the order of ℏ is a quantum system; if the indeterminacy product is much larger, the system is classical, and then classical physics is sufficient for its description. So even though classical physics assumes that there are no measurement indeterminacies in nature, a system is classical only if its indeterminacies are large compared to the minimum possible ones !
In other terms, quantum theory is necessary whenever we try to measure some quantity as precisely as possible. In fact, every measurement is itself a quantum process. And the indeterminacy relation implies that measurement precision is limited. In other words, the microscopic world is fuzzy
Randomness – a consequence of the quantum of action
What happens if we try to measure a change smaller than the quantum of action? Nature has a simple answer: we get random results. If we build an experiment that tries to produce a change or action of the size of a quarter of the quantum of action, the experiment will produce, for example, a change of one quantum of action in a quarter of the cases, and no change in three quarters of the cases,* thus giving an average of one quarter of ℏ.
⊳ Attempts to measure actions below ℏ lead to random results.
If you want to condense quantum physics in one key statement, this is it.
The quantum of action leads to randomness at microscopic level. This connection can be seen also in the following way. Because of the indeterminacy relations, it is im-possible to obtain definite values for both the momentum and the position of a particle.
Obviously, definite values are also impossible for the individual components of an experimental set-up or an observer. Therefore, initial conditions – both for a system and for an experimental set-up – cannot be exactly duplicated. The quantum of action thus implies that whenever an experiment on a microscopic system is performed twice, the outcomes will (usually) be different. The outcomes could only be the same if both the system and the observer were in exactly the same configuration each time. However, because of the second principle of thermodynamics, and because of the quantum of action, reproducing a configuration is impossible
Obviously, there will be some average outcome; but in all cases, microscopic observations are probabilistic. Many find this conclusion of quantum theory the most difficult to swallow. But fact is: the quantum of action implies that the behaviour of quantum systems is strikingly different from that of classical systems. The conclusion is unavoidable:
⊳ Nature behaves randomly