How do you begin a qualitative description of the basic physics of a photon? Where would it go? Could it lead to a philosophical understanding of our reality? Could it help us understand the Cosmos? Could it actually found the quantitative sciences of physics and chemistry? Let’s see.
Last time our theme ended up being Photons in Space. Picking that back up, let’s consider the stresses induced on space by the presence of a photon. Considered as phenomena in their own right, some have called these stresses fields. Four orthogonal dimensions are involved. Three of these correspond to the dynamic and spatial aspects of a photon (and the three dimensions of space that we are familiar with). A stress in space along any of these dimensions is a kind of tension. The fourth kind of stress is a kind of density. It is orthogonal to the other three (in a mathematical sense).
The momentum vector of a photon points in the direction it is rippling through space. The ripple itself is transverse to this direction, an alternating motion of space from side to side. The tension this produces, as seen from the side, is an alternating electric charge that goes from some maximum negative amount to some maximum positive amount, and goes to zero in between. At right angles to the alternating sideways charge, there is an alternating magnetic field. The magnetic field reaches its maximum strength just as the transverse motion reaches its maximum speed, which is where it crosses zero.
Momentum is like the opposite of inertia. It has a direction and an amount. The momentum of a normal object (normal as opposed to a photon), is the mass of the object times its velocity. The momentum of a photon, on the other hand, is related to its wavelength. It still has a direction and an amount, however. A change in the path, or course, followed by a photon is accompanied by a change in its momentum.
All the principles of electricity can be derived from the simple alternating charge we find in a photon. A charge in motion causes a voltage. When a charge is accelerated it causes a magnetic field. The tension that originates in a positive charge is connected to a negative charge in such a way that the two are attracted to each other and cancel each other out. Two positive, or two negative, charges repel each other. Their charges add together. The tension between points of charge falls off by the inverse square of the distance that separates them.
In addition to its forward momentum and its sideways vibrations of tension, a photon contributes a slight overall increase to the density of the space around it. Thus, the density and tension at a point in space are the sum of the effects of all the photons in the vicinity.
There are two aspects to the changes in the density and tension of space. A photon carries with it the first aspect, and it encounters the second aspect in the space it propagates through. Because space is both infinitely elastic and infinitely strong, when space is pushed, it pushes back. It gives exactly as good as it gets. This guarantees the conservation of momentum and energy.
Although I won’t discuss it further, there is another very special kind of momentum called angular momentum. It occurs when objects rotate about some central point. A very peculiar type of inertia is associated with angular momentum. It produces the precession and other effects we observe with tops and gyroscopes. These effects become important when objects orbit one another.
Getting back to photons, the path of a photon curves in such a way as to increase density and decrease tension. When either density or tension increase, photons lose energy. They, or other photons, get the energy back when either density or tension decrease. As you can see, and as physicists have long observed, there are similarities between density and tension.
Consider density. When the relative distance between a bunch of photons decreases, density goes up. More photons in a given volume of space leads to a higher density. However, the effect is localized. Get far enough away, and the density is unchanged. A change in density is not propagated through space, but density does have an effect on the behavior of photons, and their propagation signals these effects.
Consider tension. Tension can seriously affect the path of a photon. Tension is a local displacement of space. It is the sum of all the wave effects of the photons in the region. Generally, tension is “relieved” in a small amount of space or time, but under the right circumstances the effects of tension can extend far into either space or time.
The path followed by a photon depends upon the photon’s characteristics and those of the space it travels through. The photon has a “shape” at any given point along its path, and space has a “curvature” at each point. The shape of the photon and the curvature of space contribute to “tell” the photon where to go. At the same time, the photon makes its own contribution to the local curvature of space. I use all the terms (curvature, displacement, tension, density, and any other that describes the elasticity and perturbation of space) somewhat loosely and metaphorically. I have no choice. No words for these concepts are in common usage, and I’m not sure that universally accepted definitions could be given if there were. The analogy of a wave on a surface, and a surface whose geodesics can become arbitrarily gnarly and choppy, is the closest analogy I’m able to construct.
One definition of a straight line is with respect to Euclidian space. Another definition is the geodesic path followed by a photon. The difference is easily seen when you compare a straight line drawn on the surface of a flat sheet of paper (a Euclidian line) to a line drawn on the curved surface of a basketball. If you stick to the surface of a sphere, for example, a “straight” line, or geodesic, is simply a line with the least curvature possible.
In Euclidian space parallel lines never meet. A straight line has no curvature. A Euclidian space of two dimensions is what we normally call a flat surface. The surface of a sphere is two dimensions curved within a third dimension. Our three dimensional space can be considered as a hyper surface curved within a fourth dimension. However, I want to make it clear that this type of curvature and folding is due to what I call density and tension.
The path of a photon deviates from the Euclidian definition of straight because it is constrained to follow a geodesic on the surface of space. When it does so, energy and momentum are transferred to or from the photon. Transfer is immediate and localized. It can occur in three ways. It can be into or out of another photon in the immediate vicinity. Another photon may be created or destroyed to account for the transfer. Or, it can be a change of the tension and density of space itself. Each transfer of energy causes a change in the wavelength of the photon. Each transfer of momentum causes a change in its direction.
If it sounds like these interactions are deterministic, it’s because they are in a sense. Determinism implies that every combination of initial conditions yields a unique result. The problem here is that the initial conditions cannot be known by any method of observation we have so far been able to imagine. Orthodox physics has solved this problem by concluding that these interactions are fundamentally not deterministic. Here we differ.
Clearly, photons are not point-like objects. The ripple in space we call a photon has a particular wavelength. A given wavelength is associated with a particular quantity of momentum and energy. The entire package is called a quantum. The shorter the wavelength the higher the energy and momentum of a quantum, and the greater the degree to which it deforms the space in its immediate vicinity.
Interactions, however, are point-like events. The entire theory of quantum mechanics is devoted to relating the large volumes of space that contain photons to the small volumes of space that contain events. It is a statistical theory because we can only get a vague idea of the initial conditions. The only way to observe a photon is to produce an interaction. We can only deduce some of the initial conditions from the resulting observation. The event we observe is point-like, but a repetition of the experiment will produce another point-like event that can vary quite widely from the first. The possible distribution of initial conditions is related by quantum mechanics to the statistical pattern of results that are observed.
We have already seen the notions of critical densities and black holes. These concepts are derived from Einstein’s general theory of relativity. We have also talked about the photon’s wave structure and photon interaction. These concepts belong to quantum mechanics. In the next installment we shall bring these two areas together and talk about particles of matter.