quantum-mechanics

Compton Scattering

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Introduction

My work in physics relies heavily on the Compton Wavelength, which as far as I know, was introduced solely to explain Compton Scattering. Wikipedia introduces the Compton Wavelength as a “Quantum Mechanical” property of particles, which is nonsense. Compton Scattering instead plainly demonstrates the particle nature of both light and electrons, since the related experiment literally pings an electron with an X-ray, causing both particles to scatter, just like billiard balls. I obviously have all kinds of issues with Quantum Mechanics, which I no longer think is physically real, but that’s not the point of this note.

Instead, the point of the note, is the implications of a more generalized form of the equation that governs Compton Scattering. Specifically, Arthur Compton proposed the following formula to describe the phenomena he observed when causing X-rays (i.e., photons) to collide with electrons.

\lambda' - \lambda = \frac{h}{m_ec} (1 - \cos(\theta)),

where \lambda' is the wavelength of the photon after scattering, \lambda is the wavelength of the photon before scattering, h is Planck’s constant, m_e is the mass of an electron, c is the velocity of light, and \theta is the scattering angle of the photon. Note that \frac{h}{m_ec}, which is the Compton Wavelength, is a constant in this case, but we will treat it as a variable below.

For intuition, if the inbound photon literally bounces straight back at \theta = 180\textdegree, then (1 - \cos(\theta)) evaluates to 2, maximizing the function at \lambda' - \lambda = 2 \frac{h}{m_ec}. Note that \lambda' - \lambda is the difference between the wavelength of the photon, before and after collision, and so in the case of a 180\textdegree bounce back, the photon loses the most energy possible (i.e., the wavelength becomes maximally longer after collision, decreasing energy, see Planck’s equation for more). In contrast, if the photon scatters in a straight line, effectively passing through the electron at an angle of \theta = 0\textdegree, then (1 - \cos(\theta)) = 0, implying that \lambda' - \lambda = 0. That is, the photon loses no energy at all in this case. This all makes intuitive sense, in that in the former case, the photon presumably interacts to the maximum possible extent with the electron, losing the maximum energy possible, causing it to recoil at a 180\textdegree angle, like a ball thrown straight at a wall. In contrast, if the photon effectively misses the electron, then it loses no energy at all, and simply continues onward in a straight line (i.e., a 0\textdegree angle).

All of this makes sense, and as you can see, it has nothing to do with Quantum Mechanics, which again, I think is basically fake at this point.

Treating Mass as a Variable

In the previous section, we treated the Compton Wavelength \frac{h}{m_ec} as a constant, since we were concerned only with photons colliding with electrons. But we can consider the equation as a specific instance of a more general equation, that is a function of some variable mass m. Now this obviously has some unstated practical limits, since you probably won’t get the same results bouncing a photon off of a macroscopic object, but we can consider e.g., heavier leptons like the Tau particle. This allows us to meaningfully question the equation, and if it holds generally as a function of mass, it could provide an insight into why this specific equation works. Most importantly for me, I have an explanation, that is consistent with the notion of a “horizontal particle” that I developed in my paper, A Computational Model of Time Dilation [1].

So let’s assume that the more general following form of equation holds as a function of mass:

\Delta = \lambda' - \lambda = \frac{h}{mc} (1 - \cos(\theta)).

Clearly, as we increase the mass m, we will decrease \Delta for any value of \theta. So let’s fix \theta = 180\textdegree to simplify matters, implying that the photon bounces right back to its source.

The fundamental question is, why would the photon lose less energy, as a function of the mass with which it interacts? I think I have an explanation, that actually translates well macroscopically. Imagine a wall of a fixed size, reasonably large enough so that it can be reliably struck by a ball traveling towards it. Let’s posit a mass so low (again, nonetheless of a fixed size) that the impact of the ball actually causes the wall to be displaced. If the wall rotates somewhat like a pinwheel, then it could strike the ball multiple times, and each interaction could independently reduce the energy of the ball.

This example clearly does not work for point particles, though it could work for waves, and it certainly does work for horizontal particles, for which the energy or mass (depending upon whether it is a photon or a massive particle) is spread about a line. You can visualize this as a set of sequential “beads” of energy / mass. This would give massive particles a literal wavelength, and cause a massive particle to occupy a volume over time when randomly rotating, increasing the probability of multiple interactions. For intuition, imagine randomly rotating a string of beads in 3-space.

Astonishingly, I show in [1], that the resultant wavelength of a horizontal massive particle is actually the Compton Wavelength. I also show that this concept implies the correct equations for time-dilation, momentum, electrostatic forces, magnetic forces, inertia, centrifugal forces, and more generally, present a totally unified theory of physics, in a much larger paper that includes [1], entitled A Combinatorial Model of Physics [2].

Returning to the problem at hand, the more massive a particle is, the more inertia it has, and so the rotational and more general displacement of the particle due to collision with the photon will be lower as a function of the particle’s mass. Further, assuming momentum is conserved, if the photon rotates (which Compton Scattering demonstrates as a clear possibility), regardless of whether it loses energy, that change in momentum must be offset by the particle with which it collides. The larger the mass of the particle, the less that particle will have to rotate in order to offset the photon’s change in momentum, again decreasing the overall displacement of that particle, in turn decreasing the probability of more than one interaction, assuming the particle is either a wave or a horizontal particle.

Conclusion

Though I obviously have rather aggressive views on the topic, if we accept that Compton’s Scattering equation holds generally (and I’m not sure it does), then we have a perfectly fine, mechanical explanation for it, if we assume elementary particles are waves or horizontal particles. So assuming all of this holds up, point particles don’t really work, which I think is obvious from the fact that light has a wavelength in the first instance, and is therefore not a point in space, and must at least be a line.

Thought on the Double Slit Experiment

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I realized the other day that the equations I present in Section 3.3 of my paper, A Computational Model of Time-Dilation, might imply that wave behavior will occur with a single particle. I need to go through the math, but the basic idea is that each quantized chunk of mass energy in an elementary particle is actually independent, and has its own kinetic energy. This would allow a single elementary particle to effectively sublimate, behaving like a wave. The point of the section is that on average, it should still behave like a single particle, but I completely ignored the possibility that it doesn’t, at least at times, because I wanted single particle behavior, for other sections of the paper. I was reminded of this, because I saw an experiment, where a single neutron plainly travels two independent paths. If the math works out, we could completely ditch superposition, since there’s no magic to it, the particle actually moves like a wave, but generally behaves like a single particle. That said, I think we’re stuck with entanglement, which seams real, and I still don’t understand how it works, but nothing about entanglement contradicts my model of physics.

Spatial Uncertainty and Order

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I presented a measure of spatial uncertainty in my paper, Sorting, Information, and Recursion [1], specifically, equation (1). I proved a theorem in [1] that equation (1) is maximized when all of its arguments are equal. See, Theorem 3.2 of [1]. This is really interesting, because the same is true of the Shannon Entropy, which is maximized when all probabilities are equal. They are not the same equation, but they’re similar, and both are rooted in the logarithm. However, my equation takes real number lengths or vectors as inputs, whereas Shannon’s equations takes probabilities as inputs.

I just realized, that Theorem 3.2 in [1], implies the astonishing result, that the order of a set of observations, impacts the uncertainty associated with those observations. That is, we’re used to taking a set of observations, and ignoring the ordinal aspect of the data, unless it’s explicitly a time series. Instead, Theorem 3.2 implies that the order in which the data was generated is always relevant in terms of the uncertainty associated with the data.

This sounds crazy, but I’ve already shown empirically, that these types of results in information theory work out in the real world. See, Information, Knowledge, and Uncertainty [2]. The results in [2], allow us to take a set of classification predictions, and assign a confidence value to them, that are empirically correct, in the sense that accuracy increases as a function of confidence. The extension here, is that spatial uncertainty is also governed by an entropy-type equation, specially equation (1), which is order dependent. We could test this empirically, by simply measuring whether or not prediction error, is actually impacted by order, in an amount greater than chance. That is, we filter predictions, as a function of spatial uncertainty, and test whether or not prediction accuracy improves as we decrease uncertainty.

Perhaps most interesting, because equation (1) is order dependent, if we have an observed uncertainty for a dataset (e.g., implied from prediction error), and we for whatever reason do not know the order in which the observations were made, we can then set equation (1) equal to that observed uncertainty, and solve for potential orderings that produce values approximately equal to that observed uncertainty. This would allow us to take a set of observations, for which the order is unknown, and limit the space of possible orderings, given a known uncertainty, which can again be implied from known error. This could allow for implications regarding order that exceed a given sample rate. That is, if our sample rate is slower than the movement of the system we’re observing, we might be able to restrict the set of possible states of the system using equation (1), thereby effectively improving our sample rate in that regard. Said otherwise, equation (1) could allow us to know about the behavior of a system between the moments we’re able to observe it. Given that humanity already has sensors and cameras with very high sample rates, this could push things even further, giving us visibility into previously inaccessible fractions of time, perhaps illuminating the fundamental unit of time.