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What are the smallest "non-switching" or "non-boolean" properties of quanta, which can we measure?

This is perhaps something of an abstract question but I'm interested in understanding better the role of "switching" in quantum phenomena. Clearly "switching" properties such as a collision or the conversion of an electron into a photon etc. are more easily amplified up to human scale than non-switching properties such as some tiny deviation in the amplitude of a wave.

A switching property is something which has a binary value; yes or no. What I understand less about, is what might constitute a non-switching property of a quanta - perhaps these are velocity and position, or perhaps there is no such thing which we can measure; I don't know -that's what I'm hoping to learn.

The motivation behind this question is the conjecture that it is the ability to construct a "switch" out of some wave activity, which governs the existence and properties of what we call a quanta. But that is just a bit of background. If it helps to understand the motivation behind the question, this reminds me of the process by which a human comes to observe some individual quantum event.

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  • $\begingroup$ The continuous properties would be those that depend on the reference frame: position, speed/momentum, energy. In contrast, the "binary" properties or quantum numbers do not depend on the frame: charge, spin, etc. would you consider the particle mass to be a continuous property? (I would since mass is the intrinsic energy.) Would you also consider the probability of detecting the particle (based on its wavefunction) to be a property? $\endgroup$
    – safesphere
    Commented Sep 6, 2017 at 17:00
  • $\begingroup$ @safesphere I'm not so sure about mass and energy as Boolean as we can't add or remove it except in chunks. I think the principle is sound but I'm unsure how to map it to observation. $\endgroup$ Commented Sep 6, 2017 at 19:31
  • $\begingroup$ I didn't get your comment: "'I'm not so sure about mass and energy as Boolean". I didn't say "Boolean"; I said energy was continuous and mass was a type of energy and therefore also not Boolean. Surely you can increase or reduce energy continuously, e.g. in a red shift or simply by moving your own frame. In turn, mass is the energy of interactions. It is specific for each particle and is a consequence of quantum numbers, but is not a Boolean quantum number in itself. For example, take a neutrino, give it a quantum number of the electric charge, and it becomes an electron 10^7 times heavier. $\endgroup$
    – safesphere
    Commented Sep 6, 2017 at 20:30
  • $\begingroup$ @safesphere yes I see what you mean now. I would say the process e.g. red shifting is a continuous reduction in energy but this is perhaps not fundamental to energy since e.g. an electron can drop an energy level and this would appear to be a switching process. $\endgroup$ Commented Sep 7, 2017 at 2:29
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    $\begingroup$ The energy levels are the result, but not the cause of quantization. For example, you can slightly shange the energy levels by applying a magnetic field. However, if the electron charge is 1, it is always 1 no matter what you do. In other words, quantum numbers are just whole numbers that represent the presence or absence of a certain property. However, energy is not a whole number. Think of playing in a sandbox with buckets. The fact that your buckets take only a quantized amount of sand is not a reflection of the sand coming only in buckets. This is a secondary level effect. $\endgroup$
    – safesphere
    Commented Sep 7, 2017 at 4:21

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