The 20th century has seen the most significant advances in science and physics, especially the birth of two great theories, General Relativity and Quantum Mechanics. The unification of these two is said to be the “theory of everything”, the holy grail of physics. While GR is a beautiful theory, Quantum theory, as we may have heard is often called “strange”,” un-understandable” or even “nonsensical”. Richard Feynman said, “I can safely say no one understands quantum mechanics”. What is it about quantum mechanics that prompts even physicists make such comments? It is known that Quantum mechanics has been very successful and explains almost all of chemistry as well. Therefore, it is remarkable that the apparent strangeness leads to no inconsistencies. How has physics made sense of this?
But why was quantum theory needed in the first place? Before discussing QM itself, we need to understand the ‘why’ of it.
Why Quantum Theory?
From the beginning of the 20th century, many observations were made which did not obey the then existing laws of physics. Planck’s law of radiation implied that the frequency of oscillators in a body is quantised. The photoelectric explanation by Einstein suggested that light is composed of particles, called photons. But light was already established to be a wave! How could something sometimes behave like a particle and sometimes, a wave? Atomic stability was a mystery. Bohr assumed discrete values of angular momentum of electrons in orbit and the Bohr model proved to be successful. However, the discrete values of angular momentum were against the classical view. The Stern-Gerlach experiment showed the electron has only two spin orientations.
So then, clearly, this impressive array of startling phenomena needed a new theory, probably just as surprising. Thus, came the need for quantum theory.
What is Quantum Theory, and why is it strange?
Quantum theory was gradually developed by several people and attained a final form at the late 1920s. Many ideas were put forth; however, it must be noted that all of QM follows from a small set of assumptions which themselves cannot be derived. Therefore, QM is based on axioms.
Looking at the wave-particle duality of light, in 1924 De-Broglie proposed that particles too could behave like waves. He put forward a relationship between the momentum of a particle and its wavelength, which could explain Bohr’s assumptions in his model of the atom. Thus, quantisation conditions came naturally from De-Broglie’s hypothesis.
The next big addition to QM is the Uncertainty principle/relation. The uncertainty principle is certainly one of the most notable aspects of quantum mechanics. It has often been regarded as the most distinctive feature in which quantum mechanics differs from classical theories. This was put forward by Heisenberg in 1927 using a theoretical ‘light microscope’, which took in Einstein’s formula for the energy of a photon. He showed that it was impossible to measure precisely the position and momentum of any particle. However, it must be noted that this is not due to lack of good measuring instruments but a fundamental restriction of nature itself. This led to a lot of doubt among many physicists, and as Einstein said, ‘God does not play dice with the Universe’. How could you proceed with physics if you could not measure properly in the first place?
Meanwhile, in 1925, Schrödinger expressed de Broglie’s hypothesis concerning the wave behaviour of matter in a mathematical form and arrived at the Schrodinger wave equation (SWE). This was wave mechanics, and it revolved around a quantity called the wave function. The wave function(psi) is the probability amplitude of finding a particle at some place. Thus, the concept of determinacy was reduced to probability. Therefore, the maximum anyone can know is the wave function! The modulus squared of psi was interpreted by Max Born as the probability. Thus, the probability of finding a particle anywhere, which was most that could be done, was governed by the SWE.
Another big change was the concept of measurement in QM. The Uncertainty principle implies that any quantum measurement has uncertainties. This means the outcome of an experiment cannot be predicted with certainty, like the roll of a die. Therefore, this led to a re-interpretation. The new view was that any state, before being measured, would be a superposition (writing a quantity as a sum of individual quantities, here the different states) of all possible states that can be measured. However, it must be noted that superposition doesn’t mean the system is at all of the states at the same time, as some people have interpreted. Representing a state as a superposition of eigenstates of the observable is a mathematical notation. The measurement of the state causes it to collapse into one of the eigenstates of the observable and yields an eigenvalue. This is called the Copenhagen interpretation. This was a radical change as opposed to the classical measurement, which was definite and had no concept of superposition. Thus, something as simple as measurement took an unknown face in QM.
However, physicists also made different interpretations. They said that the wave function did not actually collapse. Instead, it branched off into another reality on its own, where the measurement yielded another eigenstate. This means that all possible outcomes of an experiment are physically realised in some other ‘universe’! This is called the many worlds interpretation of QM.
The great physicist Richard Feynman devised a radical way to look at QM. He extended the concept of the double-slit experiment to infinite slits. He said that a particle going from A to B would take all possible paths (that’s right, all of them!) between A and B, each of which would contribute a number. From this picture, he formulated a mathematical quantity called the Path-Integral, which could again explain all of what traditional QM had done. This is an alternative way to do QM and not an interpretation and its called the Path-Integral formulation of QM.
Thus, the simple picture of classical mechanics now became a probabilistic picture. The outcome of a measurement cannot be predicted with certainty but by the probability of observing a particular state given by the SWE. This could imply the existence of different Universes where a particle takes infinitely many paths to go from A to B! Despite such a strange view and a ‘major setback’ to science in terms of measurement, Quantum Mechanics has been highly successful and can explain a large portion of Chemistry in itself, along with making new advances like Quantum computing. That’s the power of physics and maths (they must co-exist! lol), taking the strangest of observations and making a theory that describes nature. As the Universe surprises us with new concepts, physics follows with an explanation. But, as the quantum world has shown us,
Not only is the Universe stranger than we think, but it is also stranger than we can think.Werner Heisenberg