Discussion of the infinite distribution of electrons in the theory of the positron

1934 ◽  
Vol 30 (2) ◽  
pp. 150-163 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Quantum Theory ◽  
Kinetic Energy ◽  
Negative Energy ◽  
The Other ◽  
Exclusion Principle ◽  
Negative Energy States ◽  
The World ◽  
Energy States

The quantum theory of the electron allows states of negative kinetic energy as well as the usual states of positive kinetic energy and also allows transitions from one kind of state to the other. Now particles in states of negative kinetic energy are never observed in practice. We can get over this discrepancy between theory and observation by assuming that, in the world as we know it, nearly all the states of negative kinetic energy are occupied, with one electron in each state in accordance with Pauli's exclusion principle, and that the distribution of negative-energy electrons is unobservable to us on account of its uniformity. Any unoccupied negative-energy states would be observable to us, as holes in the distribution of negative-energy electrons, but these holes would appear as particles with positive kinetic energy and thus not as things foreign to all our experience. It seems reasonable and in agreement with all the facts known at present to identify these holes with the recently discovered positrons and thus to obtain a theory of the positron.

On the Annihilation of Electrons and Protons

1930 ◽  
Vol 26 (3) ◽  
pp. 361-375 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Quantum Theory ◽  
Kinetic Energy ◽  
Energy Distribution ◽  
Physical Meaning ◽  
Negative Energy ◽  
The Other ◽  
Exclusion Principle ◽  
Positive Energy ◽  
Frequency Of Occurrence ◽  
Negative Energy States

An electron, according to relativity quantum theory, has two different kinds of states of motion, those for which the kinetic energy is positive and those for which it is negative. Only the former, of course, can correspond to actual electrons as observed in the laboratory. The latter, however, must also have a physical meaning, since the theory predicts that transitions will take place from one kind to the other. It has recently been proposed that one should assume that nearly all the possible states of negative energy are occupied, with just one electron in each state in accordance with Pauli's exclusion principle, and that the unoccupied states or ‘holes’ in the negative-energy distribution should be regarded as protons. According to these ideas, when an electron of positive energy makes a transition into one of the unoccupied negative-energy states, we have an electron and proton disappearing simultaneously, their energy being emitted in the form of electromagnetic radiation. The object of the present paper is to calculate the frequency of occurrence of these processes of annihilation of electrons and protons.

scholarly journals The vacuum in Dirac's theory of the positive electron

1934 ◽  
Vol 146 (857) ◽  
pp. 420-441 ◽  
Keyword(s):  
Kinetic Energy ◽  
Infinite Number ◽  
Strong Support ◽  
Negative Energy ◽  
Positive Energy ◽  
Quantum Mechanical ◽  
Normal Density ◽  
Physical Picture ◽  
Negative Energy States ◽  
Energy States

According to a theory proposed by Dirac one has to picture the vacuum as filled with an infinite number of electrons of negative kinetic energy, the electric density of which is, however, unobservable. One can observe only deviations from this "normal" density which either consist of an addition of electrons in states of positive energy or absence of electrons from some of the negative energy states (positive electrons). The discovery of the positive electron and the observed magnitude of the processes involving it give strong support to this view. This theory, as it stands, however, is not complete because it makes use of infinite quantities which are inadmissible in physical equations. It therefore must be understood (and was meant so by Dirac) to be a physical picture showing a way in which the quantum mechanical equations can probably be modified in order to give account of the positive electron and to solve the difficulty connected with the states of negative energy.

scholarly journals Negative energy states in the Reissner–Nordström metric

2021 ◽  
pp. 2150120
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Turning Point ◽  
High Energy ◽  
Negative Energy ◽  
Infinite Chain ◽  
White Hole ◽  
Negative Energy States ◽  
Energy Formula ◽  
High Energy Collisions ◽  
Energy States

We consider electrogeodesics on which the energy [Formula: see text] in the Reissner–Nordström metric. It is shown that outside the horizon there is exactly one turning point inside the ergoregion for such particles. This entails that such a particle passes through an infinite chain of black–white hole regions or terminates in the singularity. These properties are relevant for two scenarios of high energy collisions in which the presence of white holes is essential.

scholarly journals A contribution to modern ideas on the quantum theory

1927 ◽  
Vol 115 (770) ◽  
pp. 208-214
Keyword(s):  
Quantum Theory ◽  
Kinetic Energy ◽  
Line Element ◽  
Natural Extension ◽  
Space Time ◽  
Relativity Theory ◽  
Unit Mass ◽  
The World ◽  
Free Particles ◽  
Theory Of Gravitation

The relativity theory of gravitation indicates that space-time is a four dimensional continuum in which the line element is measured by the equation ( ds ) 2 = g mn dx m dx n , (1) the notation being that generally adopted. The world-lines or natural tracks of free particles in this space are geodesics. From (1) we have g mn dx m /ds . dx n /ds = 1, (2) the quantity on the left being an expression corresponding to the kinetic energy of ordinary dynamics for a particle of unit mass. This correspondence is readily appreciated if it be noted that dx m /ds is the natural extension of the velocity, dx m /dt .

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