I like to do thought experiments. Many of them lead to dead ends, but I write most of them down anyway because I’ve found that very often I will go down another thought path and end up crossing an earlier one. Then things get interesting. The one below includes a thought experiment that dates to Fri, 25 Sep 1998, and I’ve updated it a little to my more recent thoughts. If you have an idea, keep it around as it may become useful someday. This one is mostly useful to describe how thought experiments work for me.
Right now I’m still spending some time with the speed of light and with electromagnetic waves, such as from a radio, since both propagate at the speed we call c. It is easy to visualize a radio wave as a wave because we have always called it that: radio wave. Duh…, and something radiating in all directions from an antenna is more of a reminder of waves in a pond after we toss a rock in. But if photons are discrete and quantized (but sometimes seem to act as waves), how do you visualize a radio wave as a quantizable entity?
Photons at Radio Frequencies
If light and radio are both in the same electromagnetic spectrum, just when do you stop quantizing and start waving? Stop photoning and start rippling? Can you just get rid of the waving altogether and talk about photons at any frequency? The object of this thought experiment is to start with a simple radio wave and see if it can be described as a photon eventually. In other words, find out if all electromagnetic waves are photons and maybe even decide how big they are. After all, if they can be shown to be photons always, then the quantum weirdness could explain lots of things, including light diffraction and interference at radio and lower frequencies in a different way than as a wave – particles even. The object is to take a whack at this duality thing physicists are hung up on.
I am visualizing first a rather coherent radio signal (such as from a radio transmitter generating its carrier frequency) from a typical antenna as it expands in a sphere or bubble front. I’m thinking of the very first cycle after the carrier is turned on, but it could apply to any peak in the signal as it propagates outward. The leading edge of the bubble (or any individual peak) as I see it, is an equal-strength signal that covers the surface. I am visualizing on that bubble (on the surface) countless whorls of small fields rotating in opposite directions and in close proximity to each other. (I’ve just made them up for thought purposes, hoping that they can become photons later.)
For example, pick one of the circular whorls and it is rotating clockwise and all around it on every side are other whorls/fields rotating counterclockwise, all the same size whatever that is. Adjacent to any of those you pick are small fields rotating clockwise, the pattern being like a polka-dotted balloon with the black dots rotating one way and the white dots rotating the other. Between these whorls, the fields are moving in the same direction on all sides. For example, the one on the left is spinning clockwise and the one next to it on the right is spinning counter clockwise. In between the whorls, the fields are both moving down – same direction. The same thing applies for the fields above and below, adjacent fields moving in the same direction. So far, so good. These whorls are helping each other out as they move along.
Now, I look at the small rotating field and realize that since the bubble is moving at the speed of light, the rotating field, if it had a crayon, cannot draw a line on the bubble at all, or it would be doing so at faster than the speed of light. Therefore, as each point of the rotating field is drawn on the surface of the bubble, it immediately falls behind the bubble and describes a spiral arc in space that, when looked at in profile, from the top and from the side, could be the sinusoidal magnetic field and its companion electric field that we detect as the field passes us. Any following energy such as for a continuous signal would fall into step with the leading bubble, describing subsequent bubbles behind the first one, but in sync. For now, I am still looking at a single cycle and things are looking better for photons.
Thus, I see countless rotating fields dragging behind the bubble, the bubble that represents the front of the beginning of the radio signal. I visualize that the size of the rotating fields do not change, but are related to the frequency of the carrier, such that the higher the frequency, the faster they rotate and the smaller they are. The energy is related to the frequency by Planck’s constant as e = hf. This means the faster they rotate, the greater the energy. (Whatever energy these whorls have, it is exceedingly small, but there are lots of them.)
Now, we need to do a little head scratching. Can we speculate as to the size of the whorls? I think we can establish the maximum size of each whorl by assuming that if these are actually photons, then the energy contained in each photon is located in a flattened disk due to relativistic effects as in my drawing in “Speed of Light Regulated“. If it is rotating around the whorl as in our thought experiment, then no part of the rotating photon can exceed the speed of light. Therefore, the trip around the circumference of the whorl cannot be faster than the speed of light.
We also have decided to go down a particular path of our thought experiment by assuming that the whorl rotates at the same rate as the frequency of the carrier and so makes a single turn in one wavelength, λ. We know that λ=c/f and also that the circumference = Πd = λ. or d = λ/Π. The diameter of the whorl can’t be more than the wavelength divided by pi. For a blue photon which has a wavelength of 450nm, the diameter would be d= 143 nm which is quite small, about 1/3 of the wavelength. For a radio wave of 105 mhz the photon can’t be larger than 0.9 meters, about 1 yard, still about 1/3 of the wavelength, but about 630,000 times larger than for a blue photon.
There is nothing to say that there can’t be billions upon billions of these photons overlapping each other at every point of the bubble. In fact, there has to be. Energy is being poured into the antenna and the output is billions upon billions of photons in ever expanding bubbles. A photon has energy that we can calculate as e = hf, but h is very small, 6.26×10^-34 joules sec. For a blue photon this is e = 4.2×10^-14 joules and for a 105mhz photon, e = 6.3 x 10^-28 joules, which is much much smaller. To put this into perspective it would take 5400 x 10^27 photons (105mh photons) to make one watt-hour of energy. That’s 5400 billion billion billion photons (roughly) for each watt hour!
As our bubble expands, the surface “stretches,” and it is that stretching, as the surface field in dynamically expanding, that causes the field to eventually separate into individual photons as the signal strength falls over huge distances and the wave identity is forever lost – all we have left is photons to try to detect. The whorls represent in my visualization, the photon/particle aspect of the wave, as the wave is separated into compact quantum induced by the need to tightly spin along the bubble front, each whorl being my visualization of the photon.
As the field further expands, the various quantum (whorls) begin to separate and the interaction with its neighbors becomes less distinct. Each quantum continues to have the same energy but its neighbors contribute less and less to its effect when exposed to a detector, unless lenses or antennas are used.
If we look at the field as it arrives at a detector (say an antenna), we detect the arrival of the photons as energy buildup on the antenna from one of the peaks involving billions of photons of the carrier followed by a decrease in signal and then a rise to the next peak. The photon, being on the same order of magnitude as the detecting antenna (by design of the antenna based on electromagnetic theory, not photon theory) is easily captured, but billions upon billions need to arrive in order to make a good signal. Maybe this dualality of wave / particle can be moved to quantum only – particles.
Enough is enough. The thought experiment has run its course and it is time to have someone else pick it apart or perhaps add to it. Well…. after all, it is just a thought experiment, but it’s mine and I’ve now written it down for others to consider or pick at – which should be an easy task.