Relativistic Quantum Mechanics

It is more important to repair errors than to prevent them. This is the

quintessence of the philosophy of human cognition known as critical ratio-

nalism which is perhaps at its most dominant in modern natural sciences.

According to it insights are gained through a series of presumptions and

refutations, through preliminary solutions that are continuously, rigorously,

and thoroughly tested. Here it is of vital importance that insights are never

verifiable but, at most, falsifiable. In other words: a natural scientific theory

can at most be regarded as “not being demonstrably false” until it can be

proven wrong. By contrast, a sufficient criterion to prove its correctness does

not exist.

Newtonian mechanics, for example, could be regarded as “not being

demonstrably false” until experiments with the velocity of light were per-

formed at the end of the 19th century that were contradictory to the pre-

dictions of Newton’s theory. Since, so far, Albert Einstein’s theory of special

relativity does not contradict physical reality (and this theory being simple

in terms of its underlying assumptions), relativistic mechanics is nowadays

regarded as the legitimate successor of Newtonian mechanics. This does not

mean that Newton’s mechanics has to be abandoned. It has merely lost its

fundamental character as its range of validity is demonstrably restricted to

the domain of small velocities compared to that of light.

In the first decade of the 20th century the range of validity of Newtonian

mechanics was also restricted with regard to the size of the physical objects

being described. At this time, experiments were carried out showing that

the behavior of microscopic objects such as atoms and molecules is totally

different from the predictions of Newton’s theory. The theory more capable

of describing these new phenomena is nonrelativistic quantum mechanics and

was developed in the subsequent decade. However, already at the time of its

formulation, it was clear that the validity of this theory is also restricted as

it does not respect the principles of special relativity.

Today, about one hundred years after the advent of nonrelativistic quan-

tum mechanics, it is quantum field theories that are regarded as “not being

demonstrably false” for the description of microscopic natural phenomena