Particles
Particles
As the quanta provide the smallest separation possible, particles transition between quanta in the direction of their points of contact. In a closely-packed random lattice of spheres, any one quantum sphere may contact a variable number of others. Therefore, the direction of movement of particles has a strong random component. Path lengths as small as crossing a proton involve over a billion trillion transitions between quanta. So that many deviations will have to be made to reach any particular destination.
As I assume the spacetime lattice is distorted by gravity alone, it does not rearrange its structure for particles in a moving composite body. Those particles are held in relative position by the nuclear and electromagnetic forces of the standard model. Particles in a moving assembly such as a spacecraft deviate in their relative position rather than disturb the spacetime lattice, except in so far as the matter and force particles have mass and exert a gravitational effect. The very large difference between the gravitational force and the electromagnetic force means that the gravitational effects in a composite object are very small compared with the electromagnetic force binding its component particles together. The particles making up the composite undergo small changes in their relative positions as they travel through the lattice but changes in the lattice itself are many orders of magnitude smaller. The huge spaces between particles compared to the random deviations at the Planck level means that these relative deviations are undetectable compared with engineering tolerances, provided they are prevented from aggregating into major deviations.
Wandering Light
However, single isolated particles may not be constrained by electromagnetic or nuclear forces, and therefore random deflections occur throughout their trajectories. The fact that light travels in straight lines needs explaining.
This property can be demonstrated when light is interrupted by a screen with a small hole, about a centimeter in diameter. A detector sensitive to light is placed a short distance behind the screen and parallel to it. This can be a photo detector coupled to a visual display that portrays the arrival of light at the screen. At normal intensity, we see a spot of light on the screen, opposite the hole and corresponding to the diameter of the hole. There may be some fuzziness at the edge of the spot, but nearly all of this beam of light appears to travel in a straight line.
A different conclusion is reached if the experiment is repeated with the hole narrowed to less than 0.1 mm and the intensity of the light is lowered until the steady patch of light disappears. Light now registers as individual events: single spots flash on the display, arriving at random positions at random times. These are the individual photons that make up a light beam. The photons are behaving like discrete particles. They all have the same energy, and they are not following each other in single file. The photons come out of the hole at random angles and hit different parts of the detector. The photons in a narrow, low-intensity beam of light do not travel in a straight line.
Now, an aperture of 0.1 mm has over a million trillion trillion spacetime pathways through it. The edges of the aperture are unlikely to be disturbing more than an extremely small fraction of these. I suggest that what we see instead is the randomization of direction that the spacetime lattice imposes on particles traveling through it. The fact that light travels in straight lines when the aperture is large suggests that with sufficient distance across the beam, and a suitable amount of time, some process shuffles deviant photons back into line. When the diameter of a light beam is squeezed below the distance across which correction occurs we see the unruliness of particles following random paths in the lattice before their average trajectory is corrected. This is perhaps what Feynman was referring to when he said that the idea that light travels in a straight line is a convenient approximation, and that light may speed faster or slower than the conventional speed, and that although this averages out over large distances, it has significant effects over short distances [9].
Effects of Random Paths
The averaging that takes place to overcome the randomness imposed by the spacetime lattice is an important clue as to how particles behave in the lattice. Photons are deflected from a straight path by the structure of the lattice. Some are subject to few deflections and so have a faster path through the lattice, others encounter many deflections and so are slower. There appears to be a correction process that takes the surplus energy-momentum from the faster particles and adds it to the slower particles. I suggest this could be achieved by a suitable waveform of potential energy without actual net expenditure of energy. The slower particles would be caught by peaks that push them forward, adding energy to them, while the faster particles would run into troughs that absorb energy and hold them back. Similarly, the process would detect increases or decreases of momentum away from the correct path of travel and subtract or add momentum to bring the particle back to the correct direction. The process is enforcing conservation of energy-momentum for photons within the lattice.
Matter particles also appear to travel in straight lines when not acted on by an external force, and they too have to pass through the randomized lattice. So their paths will need to be corrected in the way photon paths are. The suggested wave process could operate in the same way, assuming that in the absence of external forces energy and momentum are conserved. The smoothing process will provide conservation of energy-momentum for matter particles, independent of speed.
Repeating the experiment with electrons going through an even smaller hole would probably confirm this suggestion. (The experiment may be impossible to do, but an equivalent experiment can be carried out by examining the deflection of electrons by the regular array of atoms in a crystal.) Like photons, the electrons moving through a narrow hole at low intensities would arrive at random times and at random angles. For both photons and electrons, increasing the intensity of the beam increases the number of events, not the energy delivered by individual events. This adds further confirmation that both photons and electrons behave like changeless fundamental particles: individual photons and electrons do not grow or shrink when the intensity of the beam is changed.
For freely moving matter particles conservation of momentum requires that the average momentum is constant, otherwise there would be a net force to explain. And the same remark applies to photons – in the absence of a deflecting force, their average momentum should also be constant. Energy-momentum will be conserved.
As the experiment with light going through one sub-millimeter hole continues, the initial random spots turn into a smooth distribution as the number of particles reaching the film or display increases. The distribution looks similar to that expected from a scaled up version of the experiment, using solid bullets fired through a hole in a much larger screen. The normal distribution loks like that found if you plot the numbers of people of different heights in a single age group. The pattern on the screen shows that the maximum number of particles arrives at the part of the screen directly opposite the hole. Away from this point the number drops off smoothly. So, although most particles are clustered around a line that goes straight through the hole, many are coming out at random angles, some due to collisions with the edge of the hole but many, I would argue, due to the effect of randomness in the lattice. But the larger the angle of deflection the fewer the particles.
How these deflections might be corrected within the spacetime lattice is discussed in the next section;
12/19/2015