What does a proton look like? The simple answer: Don’t ask. As with other subatomic particles, a proton is thought to be a complex of quantum wave functions—one for each of its quarks—distributed probabilistically through space. There is no “physical thing,” understood in realistic, everyday terms to which one could point and say, “There’s a proton!” At least that’s the theory.
Nevertheless, it would certainly be interesting, if only as a thought experiment, if we could build a simple, physical model of proton spin, using only standard Newtonian principles. To be convincing, it must generate a series of wavelengths analogous in its structure to hydrogen’s electromagnetic emission spectrum (Figure 1).
As it happens, such a model is possible and is surprisingly easy to explain. The dynamics involved are sufficiently straightforward and transparent that no rigorous methodology is required to illustrate the concept. A reasonably discerning non-scientist should be able to quickly grasp the basic ideas. The model is easy to visualize and simulate on a computer, and can be adjusted along a number parameters that will allow it, after some trial and error, to generate any of the various series of lines in hydrogen’s electromagnetic emission spectrum.
The primary component of this model is a dense spheroidal object composed of a smooth, cohesive gel, analogous in its properties to a firm but fluid variant of silicone. Flexibility is critical because this object spins in a very particular way. We start by drawing in a standard axis, but instead of setting the object spinning in the usual way, around the axis, this object is driven by a toroidal convection current that is rotated 360° about the axis (Figure 2). In effect, the object turns itself inside out as it circulates. For the purposes of this discussion, the cause of this convection is not important, only that it is very fast and energetic.
Assume further that this object is suspended, weightless, within an atmosphere composed of a gaseous version of the very same gel that, as a fluid, makes up the spheroid. And finally, we will assume that the entire system is located within a large, sealed chamber (with the walls well beyond the phenomenon itself) that maintains the gel-gas at a constant atmospheric pressure (Figure 3). For simplicity, we will refer to the point at which the surface is pulled into the spheroid as the north pole, and the opposite end, where the core of the spheroid emerges back onto the surface, as the south pole.
This simple system is all we need to generate the electromagnetic spectrum of hydrogen. Everything hinges on the fascinating properties that result from the convective circulation of the spheroid.
The vigorous spinning motion of a gyroscope yields a high angular momentum vector, perpendicular to its plane of rotation, stabilizing the object into which it is integrated (Figure 4). Because of their capacity to self-stabilize, gyroscopes are used in rockets and missiles to keep them upright and aimed in the right direction. The angular momentum vector is lined up with the long axis of the rocket, preventing it from rotating on a short axis and flying off course. At first glance, the vigorous convective motion of the spheroid would seem to have similar properties. But only at first glance.
To understand the angular momentum characteristics of this spheroid, we need to examine any one of an infinite number of possible sets of radially symmetrical cross sections (Figure 5(a)). Each cross section intersects two opposing convective cells. We can draw in the angular momentum vectors for each cell (Figure 5(b)), and then use simple vector addition to calculate the net value for the entire object. Incredibly, no matter what set of cross sections we select, the net angular momentum for the spheroid as a whole always has a value of exactly zero (Figure 5(c)).
This zero angular momentum value is fascinating because it means the whole object does not, like a gyroscope, resist any effort to push it out of a particular orientation. No matter how vigorous the convection, any applied force will cause the object to move or rotate just as if it were a solid, stationary ball. It also means that a tremendous amount of kinetic energy can be stored inside the spheroid without it having the slightest effect on anything outside of the object. And, correlatively, no matter how energetic the spheroid is internally, even the slightest external force can have an effect on it. In fact, the spheroid, because it possesses no net angular momentum, will only move in response to externally applied forces.
As the spheroid circulates, it draws the ambient gas into its north pole (Figure 6). At that location, gas particles are in contact with the surface of the object. And because they are composed of the same gel substance as the object, they have a tendency to stick to the surface. When that happens, the gas particles are pulled down into the object. Once inside, the gas is compressed as it is funneled down into the narrow channel that forms the spheroid’s core. It is also greatly accelerated by the vigorous movement of the gel through the core, along its major axis. When the gas emerges from the south pole it is propelled outward as a highly focused jet, into the ambient gas.
Naturally, this gas jet, as it exits the south pole, is at a much higher pressure than the ambient atmosphere. At the same time, the pressure near the opposite side of the spheroid is dramatically lowered by the vigorous suction exerted by the north pole. And because the spheroid has no net angular momentum, the force exerted on the object by the pushing and pulling of the poles causes it to move.
The propulsion generated by the south polar jet is far more significant than the suction generated by the north pole, so for the purposes of explaining the motion of the spheroid, we can ignore the north pole altogether. That is not to imply this force does not exist, only that the limited goal of this demonstration can be achieved without it. Indeed, if there is, in fact, a physical analog of this model, all forces, however subtle, are well worth investigating.
Because it has a zero net angular momentum value, this spheroid is not at all like a rocket equipped with a gyroscope. A propulsive force will tend to spin the object rather than send it flying off in a straight line, similar to a bottle rocket without the stick. We can start by examining the simplest component of this spinning (Figure 7). Now that the entire object is spinning in a more standard way—rather than exhibiting only its internal convection—we might expect to be confronted with a new candidate for angular momentum. But even this straightforward rotational motion does not confer angular momentum upon the object.
If we take a cross-section of a standard solid sphere, parallel to its rotation and perpendicular to its axis of rotation, we can examine the behavior of the physical material that, together with the matter in all similar cross-sections, lends the object its angular momentum. In a solid sphere all of these cross-sections are composed of matter that is spinning in parallel planes, and so we would expect the calculation of the net angular momentum to be a simple matter of adding up the contributions of all such cross-sections. But that is not what happens when we try to create similar cross-sections of our spinning convective spheroid. Though the entire object, abstracted from its internal dynamics, seems to behave much as a solid sphere, in fact none of the matter of which the spheroid is composed rotates in a plane parallel to the entire object’s rotational plane. If, then, we were to add up the contributions of each cross-section to determine the angular momentum of the entire object, we end up, once again, with an answer of zero.
This curious conclusion can be confirmed using a simple experiment. Hold a bicycle wheel by its axle and start it spinning. Any effort to twist the axle and move the wheel out of its rotational plane is resisted by the angular momentum of the wheel. And, more importantly for our purposes here, when the axle is twisted the applied force acts in opposition to the force of the wheel’s angular momentum, slowing or stopping the wheel. In an exactly analogous manner, the internal convection of the spheroid prevents the object as a whole from attaining any angular momentum, even while spinning. In effect, this object is incapable of possessing angular momentum.
With no angular momentum, the spheroid’s rotation is governed entirely by the action of the south polar jet. The jet, in turn, is governed both by the spheroid’s convective velocity and by the pressure of the ambient gas in the chamber. As mentioned above, we are assuming that the convective circulation of the spheroid is extremely energetic, sufficient to cause a spin velocity that is very high (a non-trivial fraction of the speed of light). If, then, we examine the system after one full rotation, we will find, surrounding the spheroid, a very dense ring of gas at a distance that marks the termination shock of the jet.
Termination shock occurs, in general, when the forced or fast flow of a substance succumbs to the steady or slow flow of that same substance. The most celebrated example of this phenomenon is the termination shock of the solar wind, way out at the inner edge of the solar system, located approximately 70-90 astronomical units from earth. In fact, due to sudden and pronounced changes in the prevalence of cosmic radiation at its current location, it is believed that the Voyager I spacecraft has recently passed through the termination shock. A far less grandiose but still instructive example of termination shock can be created in a kitchen sink (Figure 8).
Termination shock is interesting for many reasons, not least of which is its applicability to the solar wind, but our focus for now is on nothing more than the simple fact that it exists at all. In practice, there will no doubt be good cause to examine it in greater detail. What it means for the system we have been looking at here is that the energetic south polar jet will, at a well-defined distance from the spheroid, suddenly succumb to the slow flow of the gas, driving up the pressure of the gas at that radius. The gas pressure does not dissipate gradually, either smoothly or turbulently, off into the distance with no specific stopping point.
To this point, we have an extremely energetic convective spheroid that possesses zero net angular momentum, even once it starts rotating, with a powerful jet that propels high-pressure gas from its south pole, and a termination shock at a stable radius from the spheroid. After one complete rotation, the system resembles Figure 9(a). Once the polar jet comes around for the second rotation, the termination shock from the first rotation will still be present (if slightly dissipated) and will push back against the jet. This high-pressure ring will push the jet off to one side, and because the spheroid has no angular momentum, it will not resist this slight reorientation. As a result, the second rotation will trace a new circumference and create a new termination shock (Figure 9(b)).
Extending this reasoning over several more rotations, and we begin to see a pattern emerge. The far end of the jet, the termination shock point, migrates into lower pressure regions, turning the spheroid accordingly. This new rotational axis is derived from the migration of the spheroid’s primary convective axis (its polar jet) over several rotations. Indeed, this derivative axis is easy to locate since it is defined by the two points through which the primary axis passes on each primary rotation (Figure 9(b)).
The most interesting property of the first derivative axis is that its poles possess a much higher pressure than any of the other points along the termination shock. Notice that the jet attempts to minimize the frequency with which it passes through any point on the termination shock—but it cannot avoid the poles of the first derivative axis, which it hits on every single rotation, raising the pressure at those points.
Recall, the spheroid has no angular momentum. Consequently, the increased pressure at the poles of the first derivative axis has the same effect as the south polar jet itself; it introduces yet another, independent rotational motion. And, like the south polar jet, the poles of this new axis migrate into lower pressure regions as they are resisted by the relatively high pressures at various points on the termination shock, ultimately giving rise to a second derivative axis.
We can extend this reasoning to create a series of derivative axes, each produced by rotating the poles of the previous one (Figure 10). With the addition of this series of axes, the system now has all of the properties needed to generate the basic behaviors of hydrogen’s electromagnetic spectrum, specifically, the wavelengths of its spectral lines.
With each rotation of the spheroid, the north polar jet creates a high-pressure ring on the termination shock. As the high pressure at this ring decompresses outside of the termination shock, it generates a wave in the ambient atmosphere (Figure 11). For the major axis only, the frequency of this wave will be directly related to the rotational velocity of the spheroid. Similarly, the rotation of the first derivative axis also creates high-pressure rings on the termination shock, and the decompression of those rings also creates waves in the ambient atmosphere.
Now, it is easy to see that there is an exponential relationship between the axes. If, for the sake of simplicity, we assume that each axis must rotate only twice in order to generate the next one, then the first derivative axis implies two rotations of the spheroid, the second derivative axis implies 2 x 2 or 4 rotations, the third, 2 x 2 x 2 or 8, etc., which generates a graph like Figure 12 over the first ten derivative axes.
Since this is simply a notional model, Figure 12 does not exactly replicate any of the series of lines in hydrogen’s EM spectrum. However, this is very obviously the type of phenomenon that could generate them. For the purposes of creating a computer simulation of this model, it would be useful to choose values for the various elements that closely mirror what we know of the hydrogen atom from empirical research.
Density and Size of the Spheroid: As nearly all the mass of an atom is found in the nucleus, the spheroid will be very small by comparison to the diameter of the termination shock, and its density should be extremely high.
Convective Velocity: This is a non-trivial fraction of the speed of light. This extreme value is necessary both because the density of the atmosphere (see below) is so low, and because the distance between the nucleus and the termination shock is so large.
Ambient Gas Density: The density and pressure of the gel gas in the sealed chamber should be very low, reflecting—to the extent possible—the extreme difference in density between solid matter and “empty” space (the vacuum pressure). This low density will ensure that the termination shock is far from the nucleus.
These values will create an “atom” that roughly approximates the relative sizes of the nucleus (spheroid) and electronic shell (termination shock) that experiment has observed.
As compelling as this simple model is, accepting it as anything more than an astonishing coincidence would involve a major reconsideration of existing physics. So, the bar is very high. With that in mind, let’s reconsider the evidence:
- The physics is very simple and well established—entirely Newtonian.
- The model works best when we choose values for the variables that reflect what we already know from experiment.
- In a real hydrogen atom, the south polar jet would manipulate space at the vacuum pressure to generate its electronic shell, a phenomenon that has a compelling analog at the termination shock at the edge of the solar system.
- The EM waves are generated by a spinning object, which is a very intuitive, trigonometric way to generate waves.