| Why the laws of physics are just so |
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| The real problem | |
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The upshot of the previous article was that the formalism of non-relativistic quantum physics is a direct consequence of the existence of stable objects that (i) "occupy space" and (ii) are composed of finite numbers of objects that don't. There is more that can be deduced from the existence of such objects and, in fact, from the mere requirement that quantum theory be self-consistent.
Torus II by Eric J. Heller: A two dimensional plot of a three dimensional image of a four dimensional object. "When classical motion of particles is not chaotic, we say it is integrable; it can be confined to the surface of donut-shaped objects or 'tori' which live in four or more dimensions. We cannot accurately represent such objects on a two dimensional surface but we can try. The torus appears to intersect itself, but this is because we are pretending it exists in three dimensions. In the four-dimension space, it does not intersect. The surface of the torus was made partially transparent to reveal the structure within."
The validity of the special theory of relativity is a certainty, and together the two theories (special relativity and quantum mechanics) imply the theoretical framework of contemporary particle physics, relativistic quantum mechanics, which also goes by the misnomer "quantum field theory." The certainty of special relativity follows from the nature of space. If space is a set of relations, then there can be no such thing as absolute rest. The principle of relativity ("all inertial frames are created equal") therefore holds. This implies generalized Lorentz transformations, which contain a universal constant K with the dimension of an inverse velocity squared (sec2/meter2). Because units of measurement are human creations, Nature's options are limited to the following three possibilities: K>0, K=0, and K<0. The first is another possibility ruled out by the existence of stable material objects. This requires an objective difference between time and the spatial dimensions of spacetime, which does not exist if K>0. (Besides, in the absence of a temporal dimension one cannot even speak of such things as "motion", "inertial" frames, and quantum "mechanics.") Nature's second option — Galilean relativity — is viable only as an approximation to Nature's actual choice, K<0. More is implied by the quantum theory itself. Quantum mechanics presupposes the existence of measurement devices, and this arguably entails the validity (i) of the so-called standard model of fundamental particles and forces and (ii) of the general theory of relativity, at least as effective theories. (Details are available in this article.) This comes to saying that all of the well-established laws of physics may well be nothing but consequences of the existence of stable objects whose forms are sets of spatial relations between formless objects. |
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