Quantum mechanics. Part 1.
Inconsistency of classical physics
Quantum mechanics has radically changed the world of science.
As a result, all of the theories in physics can now be divided into two groups: classical and quantum.
Quantum physics forms the basis for all the modern theories concerning elementary particles and their interactions.
The examples are:
- Quantum electrodynamics which describes electromagnetic interactions,
e.g. the behaviour of electrons in an atom.
- Quantum chromodynamics which studies the interaction between quarks building up protons, neutrons and a lot of other types of particles.
Promising theories like string theory are also based on quantum mechanics.
A lot of other models and theories use the fundamentals of quantum mechanics.
There is no alternative for quantum mechanics at the moment.
Its predictions are tested with unprecedented accuracy.
For now not a single observation has been made which would contradict the quantum theory.
But what made the scientists search for another theory at the beginning of the 20th century?
Almost all observed phenomena could be explained with Newtonian mechanics and classical electrodynamics of Maxwell, which had already been known for that time.
But unlike today, there were contradictions between the predictions of the theory and real observations.
The issue of atomic stability is an example of such a contradiction.
From a range of experiments by the beginning of the 20th century the scientists knew that atoms consisted of the positively charged  particles (protons) and negatively charged particles (electrons).
The most popular idea was the atomic planetary model presuming the electrons go around the nucleus just like the planets go around the Sun.
But the calculations showed that such a system would not be stable.
According to the Maxwell’s equations of classical electrodynamics a charged particle moving in a circle should produce electromagnetic waves.
But as far as the waves carry energy, according to the law of conservation of energy it should originate from the kinetic energy of the electron.
So the electron should gradually lose its speed and finally fall down on the nucleus.
According to calculations that would happen within a tiny part of a second.
If that was true, the world as we know it would end in a flash.
The problem of atomic spectrum
By heating up a substance and letting the light go first through it and then through the prism one can see its emission spectrum.
This kind of experiments were popular in the 19th century and showed that atoms can emit and absorb electromagnetic waves only of particular frequencies.
For example, an atom of a given substance can emit a photon of frequency v1, v2 or v3, but it can not be something in between like greater than v1 and less than v2.
The emission spectrum of each substance is unique just like fingerprints.
This is how we know the composition of stars distant from us for billions of light-years.
The light contains all the information.
It was empirically established that it is possible to build a so-called energy level diagram for every atom.
The frequencies of emitted and absorbed photons can then be found as a difference of energies of any two levels.
However the origin of  these discrete energy levels (“quantization levels” as they are called today) remained a mystery and the available theories did not allow to calculate their numerical values.
Another discrepancy between the theory and the results of observations is known as the ultraviolet catastrophe.
The vibration of atoms in the crystal lattice causes the emission of electromagnetic waves called ‘thermal radiation’.
At room temperature the radiation occurs in the infrared range, which is invisible to the human eye, but can be registered by  thermographic cameras and night vision devices.
By plotting the dependence of the intensity of this radiation on the frequency, we obtain a function having a definite maximum.
The type of the graph depends on the temperature.
If a metal plate is heated to high temperatures, then the radiation will be mostly in the visible red range ("red-hot").
By increased temperatures the maximum of the function is shifted to the region of higher frequencies.
By further increasing it will move to the ultraviolet region of the spectrum ("glowing with heat").
Classical physics predicts that the radiation intensity should keep increasing together with frequency forever.
It is clear that such a prediction contradicts observations.
It shows all the inconsistency of classical physics, which is reflected in the name of the paradox - "the ultraviolet catastrophe."
Historically the moment of solving this problem is seen as the birth of so-called 'old quantum mechanics'.
It was Max Planck who succeeded in deriving an equation correctly describing thermal radiation.
He assumed that that energy is radiated only by discrete portions - quanta.
The quantum of the electromagnetic field was called a photon.
The photon energy is proportional to its frequency.
The Planck constant serves as the coefficient of proportionality.
Now it belongs to the list of fundamental constants of nature, just like the speed of light.
