Quantum Theory, Gravity, and the Standard Model of Particle Physics
- Using the hints of today to build the nal theory of tomorrow -
When a mountaineer is ascending one of the great peaks of the Himalayas she knows that an entirely new vista awaits her at the top, whose rami cations will be known only after she gets there. Her immediate goal though, is to tackle the obstacles on the way up, and reach the peak. In a similar vein, one of the immediate goals of contemporary theoretical physics is to build a quantum, uni ed description of general relativity and the standard model of particle physics. Once that peak has been reached, a new (yet unknown) vista will open up. In this essay I propose a novel approach towards this goal. One must address and resolve a fundamental unsolved problem in the presently known formulation of quantum theory : the unsatisfactory presence of an external classical time in the formulation. Solving this problem takes us to the very edge of theoretical physics as we know it today!
Modern physics can be said to have begun with the work of Kepler, Galileo and Newton, when the classical laws of motion of bodies were laid down, and the law of gravitation was discovered. The next major development in theoretical physics was Maxwell's theory for the electromagnetic eld, and the realization that light is an electromagnetic wave, which travels through vacuum at a universal speed. The inconsistency of this latter result with Newton's mechanics led to the special theory of relativity, and in turn, the incompatibility of special relativity and Newtonian gravitation saw the arrival of the general theory of relativity. Side by side, the failure of classical physics to explain observed phenomena such as the black-body spectrum of electromagnetic radiation, the photo-electric e ect, and the spectra of atoms, heralded the discovery of the laws of quantum mechanics. Over the last century or so, quantum theory has been extremely successful in explainning the microscopic structure of matter, and has given us the very precisely tested theories of quantum electrodynamics, electroweak interactions, and strong interactions. To date, the theory has passed every experimental test that has been performed to verify it.
Can we be sure then, that quantum theory is exact, and not an approximation to a deeper underlying theory of mechanics? The answer is no. On the contrary, as will be demonstrated below, one can be sure that the linear quantum theory as we know it, is an approximation to a nonlinear theory, with the non-linearity becoming signi cant only near the Planck mass/energy scale! Before we do so, we make two observations. The rst is that, contrary to popular perception, quantum theory has not been experimentally tested in all parts of the parameter space quanti ed by the number of degrees of freedom. The theory is found to work extremely well for atomic systems, say for aggregates having up to a thousand atoms. Also, as we know, it works very well for classical systems, which are aggregates of say 1018 atoms, or more. In between these two limits, there are some fteen orders of magnitude (the mesoscopic domain) where quantum theory has not been experimentally tested, simply because the experiments are very di cult to perform. The di culty lies in isolating the system from the environment; interaction with the environment decoheres the system, and renders it classical. Performing decoherence free tests on mesoscopic quantum systems is a frontline experimental area, and one could be con dent that in the next few decades such tests will become possible. As of today, we should be wary of presuming that these experiments will necessarily nd that mesoscopic systems do not violate quantum mechanics; in the same spirit that it was wrong to assume that Newtonian mechanics holds for moving objects even if their speed is close to the speed of...