The Marriage of QM and Relativity
The title of this post will somehow sound strange but there are no concerns for the trouble. It is not a thing of present but we will talk about but the thinking of the past, when Paul Dirac made an astounding effort to join the two great theories of quantum mechanics and the special relativity. The theoretical discovery of the antiparticles in1920s in his equations when he predicted the negative energy regime for each particle that existed in the states of the positive energy led to some of the major consequences and opening of the new fields in areas of particle physics and quantum mechanics.
The term wedding for these two fields of physics was used by John Taylor in1986 in memory of describing the brilliance of Dirac. In his forewords on the book “ELEMENTARY PARTICLES AND LAWS OF PHYSICS” written by Feynman and Weinberg, Taylor describes Dirac as one who was able to guess the physical formulas in his mind. The book which is contributed to the works of Dirac describes the basis of the physical law and one of the interesting topic it explains is “ The Reason for Antiparticles.”
The famously called the Dirac equation was formulated by Dirac to explain the movement of the electrons in a quantum field relativistically. This famous equation ends with a prediction that a particle with similar mass to electron and negative spin would exist and thus the energy regime of the particle would be negative. This means an antiparticle of an electron does exist which was called the positron and it was confirmed by the observational experimental results in 1932.
Following this, Pauli proved that the Dirac equations can be applied to any particles with half integer spin. This led to predict that for every particle that exists there have to be an anti-particle associated with it.
The enigma to the existence of the antiparticles was beautifully explained by Feynman in the above mentioned book. Here he explains that the discovery of particles with negative energy is the lead in joining quantum mechanics and relativity. And it is there where he explains why are the antiparticles necessary in physics.
In the book he explains that the requirement of the shift in frames of reference for the positive energy of the particles would allow one to observe one of the particles in a process or annihilation or destruction to travel back in time which thus when viewed from the right frame of reference would appear as particle of negative energy. Since the process of annihilation and destruction do occur between two particles, this must be true that one must be the opposite pair of the other particle. Infact the frame dependence of the sequence of events require one’s observed virtual particle to be another’s virtual antiparticle.
The importance of the Dirac equations in quantum mechanics were seen as important as the work of Newton, Maxwell and Einstein in their respective fields. This was the first equation in the field of quantum mechanics and hence called the first quantum field theory. The theory was also in perfect agreement with the quantum mechanics as well as special theory of relativity. The appearance of the negative energy states in electron was somewhat paradoxical and thus to solve it Dirac developed a theory called the Hole Theory . He proposed that the vacuum is a many body quantum state where an electron occupies a quantum state of negative energy. Any eigenstate which is unoccupied is called a hole and represents a positively charged virtual mass.
Also there are many others important works of Dirac in the field of Quantum mechanics, theoretical physics and mathematical physics like the Dirac Delta function. But the discovery of the positive electron must have been the most important work of Dirac. The intermingle of the two theories still are seeding today and the union of the theories brought the field of quantum mechanics to another start. This theory modified the quantum mechanics from the one that Bohr initiated and led to new discoveries which broadened the scope of the quantum mechanics and making it the leading theory in the field of physics. Thus the marriage of the Quantum theory and Relativity can be said as to one of the Cornerstones of the theoretical physics of the 20th Century.
