QUANTUM PHYSICS IS THE SIMPLEST ROOT OF CLASSICAL REALITY IMAGINABLE
Abstract: Quantum Mechanics is the simplest imaginable description of the world obtained by reducing all what is known from Classical Mechanics to its simplest parody. Simplest space, simplest math, simplest equations, etc. The organizing metaprinciple of QUANTUM PHYSICS IS Classical MECHANICS MADE AS SIMPLE AS POSSIBLE. We will focus on the simplest, two state systems.
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Simplicia: Physicists usually describe Quantum Mechanics as “weird”. You are the first one to claim Quantum Physics is NOT weird.
Tyranosopher : In his famous Lectures on Physics, Feynman describes Classical Mechanics as a “shadow” of Quantum Mechanics, or a mnemotechnical trick. Well, he was wrong, there is more to it than that. It took me many decades of deep study of the Quantum to find that in truth, arriving from the first approximation of Classical Mechanics, Quantum Physics is not philosophically weird, but the LOGICAL ROOT of Classical Mechanics. Let’s suppose you were God, and you wanted to devise the simplest barebone theory as a basis for Classical Mechanics… What would you find? Quantum Physics!
Simplicia: God is useful after all! What do you mean by barebone?
Tyranosopher: Logically barebone: the fewest and simplest axioms animated by the simplest logic. Take for example angular momentum. Classically, Angular Momentum can take any value in any direction: a classical massive object can rotate this way or the opposite, and more or less, along any axis, and can be measured again and again, ad vitam eternam: that’s a lot of freedom.
Simplicia: To make Angular Momentum barebone, if you were God, what would you do?
Tyranosopher: Instead of Angular Momentum having any value, you would decide, as God, that Angular Momentum could have JUST TWO VALUES: clockwise, or anti-clockwise. Then, instead of being able to point its axis in any direction, as God, you would decide ONE SINGLE direction is enough. And moreover, you measure it JUST ONCE. So barebone Angular Momentum takes only two values, and in only one direction, one time: and it turns out that this is the simplest version of Quantum Spin. When Quantum Spin is reduced to a two state system (automatically entangled).
And it is what the Stern Gerlach theorem reveals for silver atoms. Similarly for photons.
Simplicia: What do photons and silver atoms have in common?
Tyranosopher. Photon polarization and silver atoms are both two states’ systems. Apply the simplest mathematics to them, and you get the same mathematical, hence physical result. So they both exhibit nonlocality, entanglement, etc.
Simplicia: What are these “states”?
Tyranosopher: Quantum States are the outcomes of experiments with set-ups sensitive to Quantum effects. The presence of states is all very relative, or as Quantum Foundations theoreticians say, CONTEXTUAL. There is a theorem saying one cannot have non-contextuality.
Simplicia: Please elaborate.
Tyranosopher: Once again, suppose you are god, and you look at angular momentum or polarization. As I said, the simplest situation where something non-trivial happens is if you have built, or found, a device with two outcomes only: spin up, or spin down. Or polarization horizontal, or vertical. Each of these two distinct outcomes is called a state. Label these two distinct outcomes: I+> and I->. Then what’s the simplest non-trivial computational setup you can invent?
Simplicia: A vector space where I+> and I-> are the basis vectors?
Tyranosopher: Exactly. Let’s consider H, the complex vector space with basis I+> and I->.
Simplicia: Why complex?
Tyranosopher: Because you are God and you want to use the largest commutative field and that’s the complex numbers, called C. There all algebraic equations can be solved, with the help of the square root of (-1), called i. Turns out that this has all immediate deep physical meaning
Simplicia: Complex numbers, also called imaginary numbers, are natural?
Tyranosopher: Yes the number i corresponds to the rotation by pi/4, an angle of ninety degrees, around the origin in the plane.
Simplicia: What’s the connection of complex numbers and (i) with physics?
Tyranosopher: A photon is characterized by its momentum, which is a vector p which points in a direction, and has a frequency E. (hE, p) is the energy-momentum of the photon. It tells you where the photon is going and with how much energy. However, that does not characterize the photon fully. Experiments already conducted by the Vikings show that the photons have polarization.
Simplicia: The Vikings were physicists?
Tyranosopher: They navigated the North Atlantic, going from islands to islands, all the way to America. They needed to know where the sun was, say at noon, to know where the north was. The weather is often so cloud covered there, that one can’t say where the sun is, for weeks on end. Fortunately, the Vikings had stones which gave the direction of the sun. That’s because the atmosphere partially polarizes sunlight.
Simplicia: So the complex numbers characterize polarization?
Tyranosopher: A photon is made of an electric field paired to a perpendicular magnetic field, both perpendicular to momentum p. It’s enough to know where the electric field points to know the polarization. A complex number gives you polarization.
Simplicia: Why can’t a single real number give you that, like, you know, the angle?
Tyranosopher: Complex numbers give you more information. Let’s backtrack. God is trying to build the most powerful yet most complex mechanics possible. By considering complex numbers, you augment the power, but also the simplicity, because all algebraic equations, the ones with powers, are solvable. So, in an important way, C, the complex plane, is simpler than the real line R. Physically speaking it also turns out that quantum waves multiply, to make quantum amplitudes, which are probability waves, and probabilities multiply, but only as complex waves.
Simplicia: So let’s recapitulate. You reduce angular momentum to simply + or -, plus or minus… instead of a continuum of numbers. You also reduce the direction of angular momentum to a single one, the one along which you measure it. You then build a vector space with I+> and I-> as base vectors, and you simplify maximally by choosing complex numbers instead of real numbers.
Tyranosopher: Absolutely. Isn’t it funny that complex numbers are actually both simpler and more powerful than real numbers? Complex numbers live in a plane and contain in their description light itself!
Simplicia: Are you identifying the complex plane with light?
Tyranosopher: Take a complex plane P, brandish it in space, and pick up a (complex) number N in it. That represents all the information we have on a photon.
The perpendicular to P through its origin gives you the direction of the photon, the norm c of N gives you the frequency and the angle a of c gives you the polarization. So the information (P, c(exp ia)) gives you the photon fully. You can’t do that with real numbers
Simplicia: Photons are points in flying complex planes?
Tyranosopher: Yes, but we are not finished.
We have this complex vector space H = C (I+>, I->)… that means it has two basis vectors. Consider a vector v in that space. It has coordinates in function of I+> and I->; the square of the norms of those coordinates are real numbers. They express the probability of v being in state I+> versus in state I->.
Once again the guiding meta-principle here is the same: make it the simplest for getting a non-trivial result, depicting reality which is what we know, namely that any experiment will give either I+> or I->.
Then we introduce another ingredient: that light and matter behave in a wave-like fashion. So make the coordinates of v into waves depending upon space and time. Also, at the simplest, when v is operated upon, it will give another vector w. To go simplest again from v to w, one should use a linear operator.
Simplicia: Is that the famous “matrix mechanics”?
Tyranosopher: Exactly.
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Simplicia: What of weird effects like tunneling, and Quantum Entanglement?
Tyranosopher: Tunneling comes from the wavy nature. It would require a bit more elaboration to explain as one needs to introduce energy and how it affects waves. Basically, not all of a sudden, hence (probability of presence) waves penetrate a bit, that’s tunneling.
Simplicia: And what about nonlocality?
Tyranosopher: The nonlocal nature of Quantum Entanglement is in plain sight. The simplest is two particles sharing the same two state spin system with total spin zero. :Choose an axis of measurement, call it Z. Then measuring gives the spin of the other particle along Z automatically even 4 lightyears away. But choosing Z was an act of will. So will acted 4 lightyears away.
Simplicia: Minds change the universe light years away?
Tyranosopher: Yes, indeed. Sub Quantum Physical Reality assumes that the propagation of that change is progressive.
Simplicia: What if the distances are too great?
Tyranosopher: Then entanglement fails, and, or Dark Matter and, or Dark Energy are created. That’s what I say.
Simplicia: Does spacetime make some sort of foam at the smallest scale?
Tyranosopher: It’s worse than that. It’s a topological foam, and it’s nonlocal. There again, as God, you would have been confronted with the following problem: how to describe the infinitesimally small?
Simplicia: By making the infinitesimally small ever smaller.
Tyranosopher: That was tried in biology. It was called the homunculus theory: a human being would start as a tiny reproduction of itself. In truth what happens is that bacteria divide, so they never get that small, and animals… more generally eukaryotes, start with molecular (DNA, RNA) and cellular formations which enter in a constructive dialogue with the environment (some of which is self-created). So basically sophisticated life doesn’t start as itself at all, but in a nonlocal way. Same thing for spacetime and particles.
Simplicia: Does Quantum Entanglement hold objects together?
Tyranosopher: It has been difficult to find when, where and how an object switches from Quantum behavior to Classical behavior. It is imaginable that Quantum Entanglement holds objects together. After all the more massive an object, the higher the probability that an entangled state will collapse. Collapse is the glue.
Simplicia: How so?
Tyranosopher: De Broglie associated a matter wave to every single massive object.
Simplicia: Are photons massive?
Tyranosopher: Yes they are, in the sense of inertial mass. Poincaré published and taught in 1899 that a photon has inertial mass m = E/cc. That’s coming straight out of electromagnetism. Photons of course have no rest mass, because they are never at rest. But they contribute to gravity as E/cc, from the axiom: inertial mass = gravitational mass (Einstein called that the “Principle of Equivalence”).
Simplicia: Let’s go back to matter waves.
Tyranosopher: An object of mass M has wavelength L = h/M, where h is Planck’s constant. A deep question is how that L is generated. Clearly L should be equal to a sum, what is called an integral in mathematics: Sum(m(i)), where m(i) are the zillions of zillions of particles constituting M: all the gluons, quarks, photons, electrons inside. However, the sum should be extended to entanglement itself. I mean what’s called the “particles” are actually the states. Most of the time Quantum systems are actually delocalized Quantum fields.
Simplicia: Are Quantum Entanglement and Delocalization the same?
Tyranosopher: No. QE is an example of delocalization. Sometimes
Simplicia: What happens to mass during these delocalizations?
Tyranosopher: Good question! The experience has not been made. Einstein postulated, in 1905, as an axiom that a photon was localized always… and this may have led him to the EPR thirty years later, and introducing the doubt of “spooky action at a distance”… He was a bit arguing with himself.
From the introduction section of Einstein’s March 1905 quantum paper “On a heuristic viewpoint concerning the emission and transformation of light”, Einstein states:
“According to the assumption to be contemplated here, when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of “energy quanta” that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole.“
This statement has been called the most revolutionary sentence written by a physicist of the twentieth century. However, it’s probably not completely true, and I have called it “Einstein’s Error“. First, Quantum Field Theory, and even QED, its predecessor, which Einstein tried, but failed to learn, has replaced “particles” by (delocalized) Quantum Fields: no more localized particles at a point. Moreover, and worse, if one believes the Quantum amplitudes that one computes with have some physical reality, as SQPR, Sub Quantum Physical Reality, believes, Einstein is not completely correct, and the difference is Dark Matter, and Dark Energy. Indeed, in SQPR, Sub Quantum Physical Reality, some mass-energy is spread out. Experimentation will have to decide, although the existence of DM and DE is massive proof enough for me. But this is all speculative, whereas deducing Quantum from Classical, as the maximal non-trivial abstraction from Classical, the original subject of this essay, is not.
Simplicia: Feynman often put philosophy is a bad light.
Tyranosopher: Feynman, like, Mach, Boltzman, Planck, Einstein, De Broglie, and all great physicists, was a philosopher. Dirac deduced his equation for the electron field according to the principle of abstraction from Classical Mechanics and simplicity. Dirac looked for the simplest Partial Differential Equation the square of which would be the relativistic mass-energy-momentum formula for an electron. That’s the Dirac equation! It produced correct quantum electrodynamics, spin and anti-matter! It was deducted according to the general machinery I advocate! So in a way the method I exhibited here to deduce Quantum Physics had already been used, at least in particular cases.
Simplicia: Is your own SQPR deducted similarly?
Tyranosopher: Yes, from classical obvious to fully abstracted and still obvious. Newton said, in a private letter, that it was madness to suppose that the gravitational interaction was instantaneous. A century later, Laplace filled in the idea, making gravitation into a field, and thus predicting gravitational waves. SQPR assumes that Quantum Entanglement, like Delocalization in general, is a field with finite speed: present Quantum Mechanics assumes that QE and nonlocality propagate at infinite speed. This finite speed assumption produces Dark Matter and Dark Energy quasi-instantaneously.
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Conclusion: This is as it should be: after all, Classical Mechanics is the appearance, the first order approximation, and Quantum Physics what generates that appearance. One can deduce Quantum Physics from Classical Mechanics. One just has to expand the notion of “deduction” beyond what Feynman was familiar with. A love of wisdom helps with science, as it allows us to expand what logic means.
Patrice Ayme
Patrice Ayme's Thoughts 