| Relativity also leads to another crucial and striking consequence: for every particle, there must exist an anti-particle which has exactly the same rest mass and spin but with opposite charge of the original particle. To see this, we recollect how to excite a field and create particles. A field is excited if an adequate amount of energy is added into it. A particle is created somewhere and sometime in spacetime. Quantum mechanics tells us that we have uncertainty to specify precisely ‘somewhere and sometime’. This means we do not know exactly where and when the new particle is created. In quantum mechanics, we want to compute the ‘evolution’ of a wavefunction and that can done by calculating the Schroedinger equation, the equivalent of Newton’s law in classical mechanics. In particular, we need to compute, given the value of the wavefunction at some initial time t0, what is the wavefunction at some later time t. This is an exactly the same procedure in classical physics where we are normally asked to compute the position of an object at time t given the position at x0 at time t0. In classical physics, we have trajectories, the history of the positions. In quantum mechanics, we do not have trajectories and we only have probabilities. Therefore, in quantum mechanics, the ‘evolution’ or ‘prediction’ problem changes into “finding the wavefunction at time t.” That is equivalent to “finding the correlation of wavefunction at any time t and that at an initial time t0.” Correlation function (of wavefunctions) is not only easier to compute in many cases, but also can be directly extended to quantum field theories. Actually, the same strategy can also be employed in classical physics to increase computing efficiency and in many circumstances offer invaluable insights. (It is categorically called Green function method.) In quantum field theories, therefore, the primary goal is to find the correlation functions of the creation/annihilation operators. All calculations in quantum field theories boil down to computing these correlation functions. In quantum mechanics, the correlation function may show space-like characteristic, i.e., faster-than-light propagation (‘spooky action at distance’ as Einstein bitterly called it) is allowed in quantum mechanics because quantum mechanics, as we mentioned earlier, is supposed to be non-relativistic and does not observe the constraint of relativity. Quantum field theories, however, are born to be relativistic and must not permit such space-like correlations. Since particles are created or destroyed at random positions and instants, space-like correlations are intrinsically and inevitably present in quantum field theories. On the other hand, relativity theory is by no means violable. Therefore, the ball is in the court of the quantum field theory. An acceptable quantum field theory has to get rid of this ‘spooky action at distance’to marry with relativity. This, it turns out, is not an irrational demand, but a fortuitous blessing. After some struggle, physicists came to a perfect, or ’more perfect than perfect’, solution to this conundrum. If for every particle, an anti-particle, with exactly the same mass, spin but with opposite charge, is introduced, then the annoying ‘spooky action at distance’ disappears. The space-like correlations caused by the wanton hide-n-seek games played by the particles are exactly cancelled out by the same tricks played by their respective antiparticles. Don’t you think this is a one-stone-for-two-birds solution? This kind of elegant combo show of the human’s intelligence and Nature’s beauty is rare in the history of science and is never overpraised. |
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