## The Relationship between Voltage and Energy

Energy is proportional to voltage squared. If we make the assumption that a variable voltage is being fed to a constant load-resistor, then with voltage, current would increase, and current would get multiplied by voltage again, to result in energy.

Sound energy is proportional to sound pressure squared. With increasing sound pressure, minute displacement / compression of air results, which causes displacement to rise, and displacement times pressure is again – energy.

The decibel scale is in energy units, not pressure units. Therefore, if a voltage increases by the square root of two, and if that voltage is fed to a constant load, then energy doubles, which is loosely expressed as a 3db relationship. A doubling of voltages would result in a quadrupling of energy units, which is loosely described as a 6db relationship.

Something similar happens to digitally sampled sound. The amplitudes of the samples correspond roughly to the Statistical concept of Standard Deviation, while the Statistical concept of Variance, corresponds to signal-energy. Variance equals Standard Deviation squared…

Dirk

I should add that this applies to small-signal processing, but not to industrial power-transmission. In the latter case, the load resistances are intentionally made to scale with voltages, because the efficiency-gains that stem from voltage-increases, only stem from keeping current-levels under control. Thus, in the latter case, higher amounts of power are transmitted, but without involving higher levels of current. And so here, voltages tend to relate to power units more-or-less linearly.

## Quantum Mechanics is Falsifiable.

One concept which exists in Science, is that certain theories are Falsifiable. This means that a given hypothesis will predict some sort of experimental outcome, which other theories would not predict, and then an experiment can be performed to test whether this outcome is according to the theory. If it is not, then this test will break the theory, and will thus falsify it.

Quantum Mechanics is often Falsifiable. If the reader thinks it is not, then maybe the reader is confusing Quantum Mechanics with String Theory, which is supposedly not falsifiable? And thinking that String Theory is just the same thing as Quantum-Mechanics, is a bit like thinking that Cosmology is just the same thing as Astronomy.

(Edit 02/03/2018 :

There is an aspect to a theory being Falsifiable, which I did not spell out above, assuming that the reader could infer it. But certain conversations I’ve had with people I personally know, suggest that those people do not understand this concept.

The result of a physical experiment can easily be, that the outcome is according to the theory. Just as much as the inverse situation would falsify the theory, such an outcome can eventually confirm the theory, and without confirming the theory, there is no real way in which Scientists can know, whether a new theory is in fact valid.

There is no specific imperative to prove a theory wrong, in the theory being Falsifiable. )

(Edit 02/15/2018 :

One aspect to how this posting should be read, which some readers might infer, but which other readers might not infer, is that it begins by stating a hypothesis. At first, I declared this hypothesis as distinct from several other theoretical explanations of light.

But it would break the flow of a blog-posting, if every paragraph which I wrote after that, began with a redeclaration, stating that the truth of the paragraph depends on the initial hypothesis.

This dependency should be assumed, and belongs to my intended meaning. )

According to Quantum Mechanics, light can be polarized, just as it can according to the classical, wave-based theory of light. Only, because according to Quantum-Mechanics light is driven by particles – by photons – its explanation of polarization is quite different from polarized light, according to the classical, electrodynamic explanation.

According to wave-based light, plane-polarized light is the primary phenomenon, and circular-polarized light is secondary. Circular-polarized light would follow, when waves of light are polarized in two planes at right-angles to each other, but when these waves also have a 90⁰ phase-shift.

(Edit 02/20/2018: A Hypothesis which I’ve just disproved, but which this whole posting’s validity depends on.) According to Quantum-Mechanics, the photon is in itself a circular-polarized quantum of light, of which there can trivially be left- and right-handed examples. According to Quantum-Mechanics, plane-polarized light forms, when left- and right-handed photons pair up, so that their electrostatic components form constructive interference in one plane, while canceling at right-angles to that plane.

From a thermodynamic point of view, there is little reason to doubt that photons could do this, since the particles which make up matter are always agitated, and since the photons in an original light-source also have some random basis. So a conventional plane-polarizing filter, of the kind that we used to attach to our film-cameras, would not be so hard to explain. It would just need to phase-shift the present left-handed photons in one way, while phase-shifting the present right-handed ones oppositely, until they line up.

But there exists one area in which the predictions of Quantum-Mechanics do not match those of classical wave-mechanics. If we are given a digital camera that accepts lens-attachments, we will want to attach circular polarizing filters, instead of plane-polarizing filters. And the classical explanation of what a circular polarizer does, is first to act as a plane-polarizer, which thereby selects a plane of polarization which we want our camera to be sensitive to, but the output of which is next circularly-polarized, so that light reaches the autofocus mechanism of the camera, which is still not plane-polarized. Apparently, fully plane-polarized light will cause the autofocus to fail.

This behavior of a polarizer is easily explained according to Quantum-Mechanics. The plane-polarized light which is at first admitted by our filter, already possesses left- and right-handed photons. After that, we could visualize sorting out the photons that are circular-polarized in the wrong direction.

But the opposite behavior of a filter would not be predicted by Quantum-Mechanics. According to that, if we first pass randomly-polarized light through a circular polarizer, and if we then pass the resulting beam into a plane-polarizer, we should not be able to obtain plane-polarized output from the last polarizer.

According to the classical explanation of light, this should still be an easy thing to do. Our circularly-polarized light is supposed to have two components at right-angles, and our plane-polarizer should only allow vibration in one plane. But according to Quantum-Mechanics, if the incident beam is already circularly-polarized, it should only consist of either left-handed or right-handed photons, and then a simple filter should not be able to conjure photons that are not present in the original beam. And so our circularly-polarized light should not be convertible into plane-polarized light.