In ordinary renormalization theory, we are allowed to reshuffle these divergences and use other gimmicks in order to eliminate them. In any gravity theory, however, this reshuffling is impossible, and each term in the series must be finite(be91)
In ordinary renormalization theory, we are allowed to reshuffle these divergences and use other gimmicks in order to eliminate them. In any gravity theory, however, this reshuffling is impossible, and each term in the series must be finite(be91)
In order for the problem of infinities to be solved in this way, it is necessary that the infinities occur in calculations in only certain very limited ways, which is the case only for a limited class of specially simple quantum field theories(dft114)
Infinities in the theory could be canceled by a redefinition of the masses and other quantities in the theory(dft119)
The problem with self-interaction is that in most reasonable models of the atom, when you calculate the self-interaction energy, it always turns out to be infinite(ftl86)
Renormalization bypassed the problem of mass, but did not solve it and so it remained behind as a quietly ticking time bomb to be activated by the Higgs boson(gp282)
The Yang-Mills field is not "renormalizable"; that is, it does not yield finite, meaningful quantities when applied to simple interactions(h119)
The energy of this photon activity surrounding an electron can be computed. The answer proves, unnervingly, to be infinite. The reason for this apparently absurd result is, however, readily understood. There is no limit to how short a journey a virtual photon may take, and so no limit to how energetic it may be(mm243)
Because we can never separate an electron from its attendant photons there is no way that this infinite energy can ever be isolated and observed. What we actually observe in the laboratory, and what any other particle in the universe "sees," is the combined energy the electron plus its retinue of photons, and this is certainly finite. The infinite self-energy of the electron, while an embarrassing feature of the theory, can, in fact, be side-stepped by deftly dividing both sides of the relevant equation by an infinite amount(mm244)
In the process of adding up his paths, Richard Feynman discovered that next to every wild path runs a parallel path with exactly opposite phase. Since two waves with equal amplitude and opposite phase totally cancel, complete destructive interference removes all wild paths. If electron paths couldn't interfere, the electron would be zipping all over the place(qr117)
Assume that a 'bare' electron (if such a thing could exist) would have infinite negative mass. With careful mathematical juggling, the two infinities can be made to cancel out, and to leave behind a mass corresponding to the mass we measure for an electron. The trick is called renormalization. It is unsatisfactory for two reasons. First, it involves dividing both sides of a mathematical equation by infinity. Secondly, even then it does not predict the 'correct' mass for the electron. Renormalization will give you a finite mass, but it could be any finite mass, and the physicists have to choose the right one and plug it in by hand. By putting in just one critical value by hand the equations then give the physicists very precise and accurate 'predictions' of the values of many other crucially important parameters - and that is why so many physicists have been happy to live with renormalization. If they could ever come up with a theory in which the infinities cancelled out by themselves, without the need for renormalization, then their joy would be unconfined(sss67)