A photon, or quantum, occupies a volume, not a point. The higher the energy of a photon, the less the volume it occupies. At some energy level, a single photon and the volume it occupies become critical. It can form its own black hole. Now what happens takes even more imagination to understand than anything we have had to visualize so far. In fact, what we have to do now is invent quantum relativity.
Let’s take this in stages: First, special relativity, then general relativity, and finally quantum relativity. We’ll only hit the high points. I’ll use as little math and geometry as I can get away with. The theory of special relativity is based on the observation that the speed of light remains a constant in all non-inertial frames of reference. Although we haven’t come to such highly derivative objects as “observers” or even particles of matter, we need to at least imagine them at this stage. These phenomena have one property that is very different from a photon: They can (and must) move through space at less than the speed of light. The speed of light is a speed limit that can never be observed to be broken.
What happens when two photons collide head on? If both are traveling at the speed of light, wouldn’t they collide at twice the speed of light? They would if the surface of space were flat at the point of impact, but it isn’t. As they get extremely close together, the density of space goes up. This affects the surface they are forced to travel over. As the density approaches a maximum, the surface develops a “peak” between the photons. Each photon is climbing that peak from the opposite side. The angle of the surface between them, when the density becomes critical, is exactly ninety degrees. Thus, each photon encounters the other at a right angle, and the collision is not head on after all.
However, this only occurs at the point of impact (and this crash doesn’t allow any witnesses). The main observation that led to the special theory of relativity was that in a moving frame of reference light can be shown to travel at exactly the same speed in every direction. If light propagates on the surface of space, a frame of reference moves through space, and space itself provides a reference, how is it possible that the speed of propagation appears to be constant in all directions? The answer is that space does not provide a reference.
The relative speed between two frames of reference (or between your frame and the fixed framework of space, the existence of which is denied by orthodox physics), can be anywhere from zero to the speed of light. Clearly, relative speed can’t be less than zero. The fact that it can’t be greater than the speed of light conforms to all the observations of science, and appears to be a basic phenomenon of our universe.
What happens in special relativity is that distances in the direction of the relative motion between two frames of reference appear to contract in the opposite frame of reference as the relative speed approaches the speed of light. Nothing appears to change in your local frame of reference—the contraction of length is only observed to occur in the opposite frame of reference. Likewise, all clock-like phenomena in the opposite frame of reference appear to slow down.
Both of these phenomena are in the same proportion as given by the Pythagorean Theorem, where one side of a right triangle is the relative speed between the frames, the hypotenuse is the fixed speed of light, and the third side of the right triangle represents the apparent distance or time. The ratio of the third side to the hypotenuse is the fraction of apparent distance or time with respect to “expected” distance or time.
The mathematics of this have been tested and retested in countless ways for over a hundred years. No exceptions have been found. However, there are a few paradoxes if you adopt the orthodox view that there is no absolute frame of reference. It’s true that such a frame is (nearly?) impossible to distinguish from any other frame, but the paradoxes go away if you relate all frames to one that is at absolute rest. The fact that distance and time are affected within moving frames isn’t too surprising when you consider that distance and time are derived from the speed of light in the first place.
All theories of relativity are called that because they relate different frames of reference. They show how differences between frames can affect what is observed from one frame to the other. Special relativity relates two frames of reference that are moving, but not accelerating, with respect to one another. In special relativity, the primary insight was that absolute speed cannot be distinguished, and that all speed is relative between two frames of reference. The orthodox view is that every frame has an equal claim on being the one at rest.
General relativity relates two frames of reference that are accelerating with respect to one another. In general relativity, the primary insight was that gravity and acceleration cannot be distinguished. The phenomena of acceleration and gravity are highly derivative. Both involve the transfer of momentum and energy. Both require ongoing interactions. There are differences between these phenomena working on photons and when they work on laboratory frameworks built out of particles. Suffice it to say that the description I present parallels the logic of the general theory of relativity, and the key concept in this regard is that of density. As the density goes up in a region of space, clocks slow down. Clocks actually stop at the critical density. Remember, we are speaking relatively. The observations I describe are made in one frame and appear to occur in the other. Distances appear to shrink in a highly dense region of space from the point of view of an outside observer. Thus, as density reaches the critical point, the apparent volume of a black hole becomes zero. I claim that the absolute characteristics of space are unchanged in relativity, only the observed characteristics change. An orthodox relativist would claim that there are no absolute characteristics. However, both of us would agree that the observed characteristics are “real.”
Quantum relativity begins with the following observation: for every quantum there is a particular critical volume. However, the smaller the quantum, the larger its wavelength, and therefore the larger the volume of space it can be stuffed into. The larger the quantum, the smaller its wavelength, and therefore the smaller the volume of space that contains it. At a certain energy level, a photon exists whose volume and density are exactly critical. It is capable of forming its own black hole. If it did, an observer would see its clock to be stopped and its size to be exactly zero. From the photon’s point of view, it would continue to travel over the surface of space as before. The only way both points of view could be satisfied is if the photon were traveling in some kind of circle.
What would happen if you could somehow hook the head of a photon to its tail? The properties of space (interference, if you like) don’t allow you to hook it anywhere else. It would then propagate in a circle exactly one wavelength in circumference. Visualize this in two dimensions. Imagine a photon on a plane surface such as a sheet of paper. It traces a straight path across the paper, wiggling from side to side. Now, make it go in a circle. Its sideways wiggling becomes inside-outside wiggling. From a point outside the circle, it has an alternating positive and negative charge. But from outside the circle, we are looking at a black hole! Its clock has stopped! What we actually see is a static charge, either positive or negative, but not both in an alternating sequence. There are only two points at which a photon’s clock can stop. These are the points of maximum positive or negative charge, because these are the only two points at which the charge is static. At every other degree of charge, the charge is in motion, generating a magnetic field. Think of stopping a pendulum. At the ends of its swing, all of its energy is potential and static. Anywhere else, and you have to deal with the energy of motion, and motion is not a property of a stopped clock.
Likewise, in our three dimensional space, the photon arranges itself in a black hole such that it presents either a positive or negative charge to the outside. In this case, however, “outside” refers to a sphere, not a circle. The path of the photon is a hypercircle whose outside edge is the outside surface of the sphere, and its inside edge is the inside of the sphere. We have just seen how the simplest particle is created.
Although the apparent size of a black hole is zero, the apparent energy (which is now observed as a mass) of the photon is unaffected. Various combinations of wavelength (mass/energy) and associated critical densities, together with viable orientations within one or more black holes, and involving one, or perhaps two or three photons, give us all the stable and unstable particles that we observe.
Electrons and positrons appear to involve a single photon. Unless they come together and annihilate each other, they would have to be perfectly stable (infinitely long lived), because their clocks are perfectly stopped. Neutrons don’t appear to be perfectly stable, but they become very nearly so with the addition of a positron, to form a proton. Such particles must be composed of several photons that depend upon one another to produce a mutually critical density. In another model, this is reminiscent of the interdependence of quarks. Try to remove one, and the whole structure breaks down.
Using this model, I imagine that the lore of data obtained from particle accelerators would allow someone familiar with it to work out the various arrangements and quanta involved. This model should also enable the various characteristics of each particle to be derived from first principles. Clearly, if this general framework is appropriate, there remains much yet to be done. The next installment will discuss some thinking points and conjectures based on this theory.