©Fernando Caracena 2014
Quantum mechanics governs the motion of “particles” on the subatomic level, and in it, there there are really no objects that can be followed along trajectories the way we follow ordinary projectiles. The word “particle”, used in quantum theory, may suggest a very small object, but it is really a name for a field quantum, which is a discrete bundle of energy, momentum, angular momentum and other properties such as charge that characterize those quanta. In quantum theory, a “particle” moving from some point A to another B is not described as moving along a curvilinear trajectory, but rather, as along a wave front, and perhaps within a wave packet, or wave train.
The detection of a particle usually happens as a flash or equivalent, at some point B, i. e., as a point-like event. Because the discrete properties that it carries are delivered to the small area of impact, and it came from a point-like source, our mind jumps at an image of a very small particle traveling along a well defined trajectory between point A and point B, not as the wave that quantum mechanics employs. This is the origin of the idea of a wave-particle duality. But, discreteness of of the properties of each quantum is all that quantum physics specifies. Between the source of the quantum and its point of impact, quantum physics does not assign a position to the particle. The quantum is spread out over the entire landscape. Where it will likely be detected is described by the amplitude of an expanding wave train that progresses at a speed consistent with causality: the quantum cannot be detected as progressing much faster or slower than its initial speed, which is also not absolutely defined, but with a precision limited by Heisenberg's Uncertainty principle.
Although we can think of field quanta as spreading out as a wave, the moment it is detected, that wave collapses to a point. This known as the collapse of the wave function, which is a paradox because it brings in motion that is faster than the speed of light. Quantum mechanics itself contains strange non-local effects, what Einstein called spooky action at a distance.
Localization and the Matter Matrix
The question of what produces localization, is interesting philosophically in connection with quantum physics. It is obvious that empty space cannot localize a field quantum because the space does not contain anything that the quantum can interact with, except the zero point fluctuations that form the basic fabric of space and are not localizable except as modifying the properties of the field quanta themselves. So what is it that makes a particle local?
Only the material medium can receive a field quantum, which it does so as as a localized event. The matter matrix is made up of quanta trapped in stationary states, which constitute the atoms and molecules that make up the matter matrix. Quanta are emitted by processes on atomic and subatomic scales by well defined transitions from excited states, and they are absorbed by the reverse of the same processes. A fundamental principle of quantum physics is that energy is emitted and absorbed in whole units, or quanta. If there is no way that a field quantum can deliver its properties exactly over a large area of a medium, because there is no resonant process there to absorb it, then the quantum is not absorbed, but continues as a wave that interacts with the distribution of matter as a wave.
Absorption of quanta corresponds to the inelastic scattering of "particles" and the interference effects of waves, to the elastic scattering of "particles".
The most likely way that a field quantum is absorbed is by the reverse of the process that created it, that is, in an atom, if emitted from an atom; and the atoms are held somewhat fixed within a material matrix. Thus a quantum comes into existence at some very localized volume of a material medium and subsequently delivers its full load of properties to another localized volume of the material medium.
The conclusion is that the large scale structure of the material medium forms the basis for localizing both the emission and absorption of field quanta.
There are many subtleties surrounding the above question, the complete discussion of which could easily expand to become the dominant theme here that would dwarf that part devoted to our main theme of localization of quantum event, but I will not raise these technical points here, reserving any such discussion for the future.
A lot of our discussion (below) is reserved for low energy field quanta that are commonly encountered in college laboratory experiments on quantum mechanics.
Localization of field quanta can be demonstrated from experience, as follows: A ball that is painted white can reflect any color of visible light. Shine an intense beam of light into empty space, and you will see nothing; but let the ball cross the path of that light, and light will be reflected brilliantly by the ball. The ball furnishes the material matrix that localizes the scattering of photons in the beam of light. The eye, of course, is the detector that further localizes the photons by resonant absorption.
An important property of the material matrix that makes it apt for localization is that it has mass or mass density and is embedded in a medium that satisfies Newtonian Mechanics to a high degree of approximation. The portion of a material medium, which responds to a quantum event can be tracked in time and space. This serves to anchor the event in the space-time framework. In this context, we can view quantum theory as a mapping of discrete non-localizable discrete excitations spread out in space between materially defined space-time points of emission and absorption of those quanta. The medium that defines the space-time points is subject to the laws of inertia, and is characterized by elementary components that have non-zero rest masses.
Conclusion--the Emergence of Space and Matter
At present, physicists are trying to understand how the visible universe happened. The universe is expanding away from us in all directions at a rate proportional to the distance that we look out to. This is called the Hubble expansion. Running the expansion back ward in time puts everything on top of everything else as a point, which suggests that the visible universe emerged from a singularity about 13.7 billion years ago in an event called the Big Bang. The physics for handling the Big Bang is not yet complete, although the outline of what happened looks like Wu Wu physics.
From the early processes, space was filled with electromagnetic radiation in a spectrum of frequencies and of intensity very uniformly distributed in space. At that time, there was still no there there, because every place was identical to every other place. This symmetry very soon broke down, as internal symmetries broke down. The break down of internal symmetries, manifested themselves as the differentiation of a universal force, into the four fundamental forces that we observe now in physics.
The breakdown of internal symmetries opened up channels of interactions that allowed photons to turn into particle and antiparticle pairs. An asymmetry in the decay of each of the particle types somehow allowed antiparticles to disappear faster than particles and ordinary matter emerged. Very slight perturbations on the otherwise initial distribution of the energy of the Big Bang led to the formation of the galaxies and galactic clusters that we now see. Thus, the matter matrix emerged, which made the localization of events possible, and that made it possible for humanity to develop the science of physics.