A Matter of Relativity?
Copyright 2006/2007 James A. Tabb
Part 1: Introduction and Photons In Glass
Quantum Electrodynamics (QED) theory has developed to be the theory that defines almost all of the understanding of our physical universe. It is the most successful theory of our time to describe the way microscopic, and at least to some extent, macroscopic things work.
Yet there is experimental evidence that all is not right. Some weird things happen at the photon and atomic level that have yet to be explained. QED gives the right answers, but does not clear up the strange behavior – some things are simply left hanging on the marvelous words “Quantum Weirdness”. A few examples of quantum weirdness include the reflection of light from the surface of thick glass by single photons, dependent on the thickness of the glass; the apparent interference of single photons with themselves through two paths in double slit experiments; the reconstruction of a polarized photon in inverted calcite crystals, among others.
This paper introduces some ideas that may explain some of the weirdness.
Photons and Relativistic Effects:
I suggest that most of the difficulties we have in addressing the various weirdness phenomena at the particle level can be traced to relativistic effects. It all comes down to the two different simultaneous viewpoints: The one we can see and measure, and the one the photon experiences. Relativistic effects rule the photon world and our life experiences rule ours.
Consider that photons travel at the speed of light and thus experience relativistic effects. What are these effects? Einstein gave us some tools to work with to describe the various space-time relativistic changes as shown in Figure 1. There is a mass equation also, but the mass increase is not a factor here, since we know that the photon has no rest mass.
Figure 1. Relativistic Effects at c
The photon’s clock stops because the time between clock ticks becomes infinitely long at c. Similarly, the distance traveled becomes zero because the photon’s unit inch becomes infinitely long and stretches to the end of its journey in one bound. In other words, the entire path is foreshortened to zero length, and everything in its path is compressed to a dot.
We, on the other hand, see the photon from our experimental perspective. Photons move at speed c, take a nanosecond to go about a foot, take centuries to go from a nearby galaxy to earth, all of which we can measure or calculate with confidence and confirm with experiments.
The Photon’s Go-Splat World
The photon lives in a “go-splat” world. The clock of a photon completely stops the instant it is emitted and stays stopped throughout its journey. The distance traveled by a photon becomes zero as compared to the distance measured by the stationary observer. It may take a photon a billion years to cross from a distant galaxy to our telescope from our perspective, but for the photon, as soon as it is emitted, it arrives – splat; there is no time elapse in the photon world. In effect, the space and time between the photon’s emission and its destination are severely warped.
Therefore, the photon’s world is flat and stapled together, front-to-back, between its start point and its end point. In effect, the photon is touching its emitter on one end and our eye on the other with zero depth of field. Whatever phase it has at the time of emission, it has when it hits our telescope because it is all frozen in time. Physicists call the time experienced by the photon null time and the path the null time path.
It is this stapled together, zero time world that I believe explains much of the quantum weirdness we experience. Our life and experimental experiences are so strong that we can’t easily get our minds around the relativistic phenomena.
What the photon would know of the experimental setup, whatever it is, consists of wake-up calls at various edges or medium changes and eventually wherever it is absorbed in our screen or detector, all zero distance apart. This is vastly different from our perspective where everything is so carefully laid out, separated, calibrated with finite distances and photon flight times.
From our perspective, if it is going across a table, it moves about a foot every nanosecond. If it is going across the universe it takes years, even millions or billions of years to get from there to here. However we see it or calculate it, the time it takes for the photon’s lifetime is always zero. Go-Splat! As soon as it leaves on its journey, it arrives.
Quantum Weirdness in Glass
One of the weird aspects of photons involves reflection from glass of varying thickness. Send a laser pointer beam perpendicular to a pane of glass and about 4% of it will reflect back, on average, but, by carefully selecting glass of various thicknesses, the reflections vary from 0% to 16%. Glass a foot thick can be slightly adjusted in thickness to not reflect at all! All the light goes into the glass – perfect transmission. QED easily shows how this works for light beams. Rays from the back of the glass interfere with the rays coming in the front so as to cancel the reflection if the wavelength is a multiple of ½ wavelength.
However, the cancellation at ½ wavelength also works for individual photons for thick glass, and there seems to be no answer other than “quantum weirdness”. How does an individual photon know how thick the glass is the instant it hits the front surface when the back surface is thousands of wavelengths away? The reflected photon would be six feet away before a copy could make a round trip through a foot thick piece of glass. (Two feet round trip at 1/3 speed of light in air)
Quantum Weirdness and Relativity
Lets look closer at our foot thick piece of glass. The photon is moving at c and from a relativistic perspective our piece of glass has zero thickness (our entire experiment has zero thickness) as shown in Figure 2a.
Figure 2. Photon in Glass
Immediately after impact, a full half wave of the photon fits completely into the glass (2c), no matter how thick. The photon’s wavelength in glass is only 1/3 of its air wavelength. If the thickness of the glass is a multiple of a half-wave of the (shortened) photon, the photon will go right on through without reflection. Otherwise, depending on the thickness, some percentage (0 to 16%) of them will reflect. In effect, the glass collapses to zero thickness if it is an exact multiple of the half wavelength, and if not, there is an overhang on one of the collapsed thicknesses that determines the probability of reflection. Thus the photon does not have to “wiggle” its way to the far side and back to make its decision. If it is going to reflect, the decision is immediate due to the glass being foreshortened to fit the photon. It is, in fact, relativistic foreshortening of the glass.
Note, although the surfaces in the drawing above and those that follow are drawn with straight lines and flat, they are shown that way only for illustrative purposes. At c, all the points in the direction of travel are pulled to one point at the nose of the photon because they are zero distance apart to the photon, and surfaces near the path are severely bent.
It should also be noted that, once within the lattice of the atoms of glass, the atoms to each side of the photon resume their normal spacing and are no longer foreshortened. This is because they are perpendicular to the direction of travel. Those atoms in front continue to be shortened to meet the photon. Thus the photon length and the glass thickness exactly match, regardless of thickness, if the glass is an exact multiple of a half wavelength. In that case, the photon completely enters without reflection. If the thickness does not fit the wavelength of the photon exactly, there is a crisis due to a mismatch in which the glass is not quite zero thickness to the photon. The probability of reflection depends on the degree of mismatch, but the reflection decision is made while the photon is still at the front surface and just inside.
There are two effects going on simultaneously: The relativistic effects for the photon and the realistic effects for the observer. The photon fits within the entire experiment (zero thickness, no wiggle time due to no time elapse) while we, as the stationary observers, see the entire experiment where the photon is traveling at c and has to wiggle 130,000 times to get through the glass in a measurable time (about 3 nanoseconds for a foot of glass). One case of quantum weirdness explained by relativistic effects.
Next: Explaining Double Slit Weirdness