03
Jul

In a word, Yes, they are. And what they have in common is the *moving present moment*, or *now*. For after all, when collapse occurs, it does so *now*, instantaneously across the full extent of the wave function. And in the conscious being, the external world is experienced in a succession of such moments. As physics in 3 + 1 dimensions knows nothing of this dynamic side of time, little wonder that wave function collapse is standardly referred to as a paradox, and consciousness as a mystery. Clearly to have any hope of resolving these conundrums, we cannot rely on conventional physical theory. Instead, we turn to the Law of Laws, and look within its formalism for the presence of the now.

As noted in** Post 2**, in ordinary spacetime—Minkowski *M* ^{4 }— time *x *^{0} ( *= ct* ) is just another coordinate, on a par with the spatial three-vector **x **. Together these four coordinates locate events in a static representation of the physical world sometimes called a *block universe*. In the block universe there are world lines—continuous curves connecting the point-events of particles in motion—but no sign of a moving present moment. To explain time as it is actually experienced, we need to take account in our description of reality the infinite extra dimensions, *x *^{5 }and *x *^{6} . Specifically, we demand form-invariance of the 6-D Dirac equation under rotation *θ *in the *x *^{0 }–* x *^{5 }plane. The rotation is circular, not relativistic, because, although *x *^{5 }acts as an extra spatial dimension, both coordinates are metrically time-like. We find that, under rotation, the Dirac equation retains its form for two angles only, namely *θ* *= *± 90 º . The original frame *K* and rotated frame* K *_{D }, separated as they are by a finite rotation angle, represent two distinct realms of spacetime, each inaccessible one from the other. I call* K *_{D } the *dual* of frame *K* . The two frames superimposed I refer to as *dual spacetime*. In dual spacetime, each event in *K *is repeated as a dual event in *K *_{D . }

For definiteness, let us take *θ *=* − *90 º . Then time * x *^{0} in frame *K* transforms into * x ‘ *^{5} in *K *_{D }. The equation of rotation transformation is

*x ‘ *^{5 }*= x *^{0} *= ct *, (1)

which we readily recognize as an equation of motion. It describes, within *K *_{D }, a line of infinite extent (actually a 3-D hyperplane) oriented perpendicularly to the *x ‘ *^{5} axis and moving in a direction parallel to it at the speed of light. *This moving line is the moving present moment or now.* With respect to frame *K*, it is a moving line of simultaneity.

So, according to the Law of Laws, spacetime is not at all the simple 4-D monolith we thought it was. Instead, it consists (at a minimum) of a superposition of two disjoint frames, *K* and *K *_{D }, forming dual space time, with *K *_{D} containing as an objective element of nature the moving present moment.

Which at once resolves the paradox of collapse. For illustration, consider a spin-zero quantum system consisting of two correlated, circularly-polarized photons flying off in opposite directions from their common source. Undisturbed, the two photons are to be thought of as being at once right- and left-handed, with respective polarization-state probability amplitudes of 1 / √ 2 . When the polarization of one of the photons is measured, the wave function collapses and, because angular momentum is conserved, the polarization of the other photon is instantaneously determined, no matter how far it may be from the measured photon. How can this be? We now know the answer. In dual spacetime our quantum system is described twice: once in frame *K* in terms of the diverging world lines of the two photons; and again in frame* K *_{D }in terms of the *duals* of those world lines. In frame *K*, at the time of measurement, the interval between the two photons is spacelike, and no signal can pass from the measured photon telling the other photon what its polarization should be. But in frame *K *_{D}, at the time of measurement the two dual world lines are connected by the moving present moment, which is a line of simultaneity. Consequently, in *K *_{D }, at the time of measurement, the photons are in causal contact, resolving the paradox of collapse.

So much for wave function collapse. Now what about consciousness? Already in **Post 2** we noted that conscious experience takes place in a privileged frame of reference—the *first person perspective*—a clear violation of the Principle of Relativity. Dual spacetime, however, restores the natural order. For we have an obvious parallel between dual spacetime and the classic dualism of mind and brain. If brain occupies frame *K *, then frame * K *_{D }, inaccessible from frame *K* , offers the possibility of a first person perspective. And not only that, it provides as well the moving present moment. Thus *K *_{D} is the natural home of conscious experience, or could be, if someone is at home to have the experience. In the next post we shall look to the physics of the Self and its inner life.