Explain the limitation to classical mechanics that gave rise to quantum mechanics?

Answer 1

1) Classical mechanics does not account for the fact that energy can only be exchanged by tiny packets of a given minimal energy. Therefore in classical mechanics the energy of a system can increase or decrease continuously, while in quantum mechanics it can only decrease and increase by tiny steps.

2) Classical mechanics does not account for the fact that particles behave like waves in some circumstances. Equivalently, one can talk about the introduction of the uncertainty principle that basiquely tells: "the more precisely you will measure a particle position, the less precisely you will measure its speed" and vice et versa. This is not seen as an observational limit due to the weakness of the instruments used or of the human operator, but as a fundamental one: nature seems to be built like that.

Both points are usually not visible at our scale, where the tiny energy packets are infinitesimal for us, and the uncertainty principle seems to vanish under the influence of the many waves interfering with each others.

Quantum mechanics experimentally emerges from point 1). By studying what is called "black bodies", that is to say bodies that (almost) perfectly absorb light (like charcoal for instance), scientists observed a discrepancy between their observations and the predictions of classical mechanics. Such bodies are them selves emitting a faint light, only due to the thermal agitation of their own particles. At high temperature, the light emission measurements was not predicted correctly by classical mechanics. Planck proposed a theoretical solution that seemed to succeed in predicting the observations, but he presented it in a quite shy manner because it was a strange hypothesis at that time: energy is exchanged by small quantities, not continuously. Einstein was inspired by this idea and took it a step further by postulating that light was composed of energy particles for explaining the photoelectric affect (Nobel prize for this).

Concerning point 2), it might be even more adapted to say that sometimes waves are behaving like particles... Modern experiments are confirming one after the another the strangeness of uncertainties and de-localization of particles in the quantum world (that is to say: very tiny).