What does Quantum Mechanics Mean?

Patrice Ayme gave a long comment to my previous post that effectively asked me to explain in some detail the significance of some of my comments on my conference talk involving quantum mechanics. But before that, I should explain why there is even a problem, and I apologise if the following potted history seems a little turgid. Unfortuately, the background situation is important. 

First, we are familiar with classical mechanics, where, given all necessary conditions, exact values of the position and momentum of something can be calculated for any future time, and thanks to Newtom and Leibniz, we do this through differential equations involving familiar concepts such as force, time, position, etc. Thus suppose we shot an arrow into the air and ignored friction and we wanted to know where it was, when. Velocity is the differential of position with respect to time, so we take the velocity and integrate it. However, to get an answer, because there are two degrees of freedom (assuming we know which direction it was shot) we get two constants to the two integrations. In classical mechanics these are easily assigned: the horizontal constant depends on where it was fired from, and the other constant comes from the angle of elevation. 

Classical mechanics reached a mathematical peak through Lagrange and Hamilton. Lagrange introduced a term that is usually the difference between the potential and kinetic energy, and thus converted the problem from forces to one of energy. Hamilton and Jacobi converted the problem to one involving action, which is the time integral of the Lagrangian. The significance of this is that in one sense action summarises all that is involved in our particle going from A to B. All of these variations are equivalent, and merely reflect alternative ways of going about the problem, however the Hamilton Jacobi equation is of special significance because it can be mathematically transformed into a mathematical wave expression. When Hamilton did this, there were undoubtedly a lot of yawns. Only an abstract mathematician would want to represent a cannonball as a wave.

So what is a wave? While energy can be transmitted by particles moving (like a cannon ball) waves transmit energy without moving matter, apart from a small local oscillation. Thus if you place a cork on the sea far from land, the cork basically goes around in a circle, but on average stays in the same place. If there is an ocean current, that will be superimposed on the circular motion without affecting it. The wave has two terms required to describe it: an amplitude (how big is the oscillation?) and a phase (where on the circle is it?).

Then at the end of the 19th century, suddenly classical mechanics gave wrong answers for what was occurring at the atomic level. As a hot body cools, it should give radiation from all possible oscillators and it does not. To explain this, Planck assumed radiation was given off in discrete packets, and introduced the quantum of action h. Einstein, recognizing the Principle of Microscopic Reversibility should apply, argued that light should be absorbed in discrete packages as well, which solved the problem of the photoelectric effect. A big problem arose with atoms, which have positively charged nuclei and electrons moving around it. To move, electrons must accelerate, and hence should radiate energy and spiral into the nucleus. They don’t. Bohr “solved” this problem with the ad hoc assumption that angular momentum was quantised, nevertheless his circular orbits (like planetary orbits) are wrong. For example, if they occurred, hydrogen would be a powerful magnet and it isn’t. Oops. Undeterred, Sommerfeld recognised that angular momentum is dimensionally equivalent to action, and he explained the theory in terms of action integrals. So near, but so far.

The next step involved the French physicist de Broglie. With a little algebra and a bit more inspiration, he represented the motion in terms of momentum and a wavelength, linked by the quantum of action. At this point, it was noted that if you fired very few electrons through two slits at an appropriate distance apart and let them travel to a screen, each electron was registered as a point, but if you kept going, the points started to form a diffraction pattern, the characteristic of waves. The way to solve this was if you take Hamilton’s wave approach, do a couple of pages of algebra and quantise the period by making the phase complex and proportional to the action divided by (to be dimensionally correct bcause the phase must be a number), you arrive at the Schrödinger equation, which is a partial differential equation, and thus is fiendishly difficult to solve. About the same time, Heisenberg introduced what we call the Uncertainty Principle, which usually states that you cannot know the product of the position and the momentum to better than h/2π. Mathematicians then formulated the Schrödinger equation into what we call the state vector formalism, in part to ensure that there are no cunning tricks to get around the Uncertainty Principle.

The Schrödinger equation expresses the energy in terms of a wave function ψ. That immediately raised the question, what does ψ mean? The square of a wave amplitude usually indicats the energy transmitted by the wave. Because ψ is complex, Born interpreted ψ.ψ* as indicating the probability that you would find the particle at the nominated point. The state vector formalism then proposed that ψ.ψ* indicates the probability that a state will have probabilities of certain properties at that point. There was an immediate problem that no experiment could detect the wave. Either there is a wave or there is not. De Broglie and Bohm assumed there was and developed what we call the pilot wave theory, but almost all physicists assume, because you cannot detect it, there is no actual wave.

What do we know happens? First, the particle is always detected as a point, and it is the sum of the points that gives the diffraction pattern characteristic of waves. You never see half a particle. This becomes significant because you can get this diffraction pattern using molecules made from 60 carbon atoms. In the two-slit experiment, what are called weak measurements have shown that the particle always goes through only one slit, and not only that, they do so with exactly the pattern predicted by David Bohm. That triumph appears to be ignored. Another odd feature is that while momentum and energy are part of uncertainty relationships, unlike random variation in something like Brownian motion, the uncertainty never grows

Now for the problems. The state vector formalism considers ψ to represent states. Further, because waves add linearly, the state may be a linear superposition of possibilities. If this merely meant that the probabilities merely represented what you do not know, then there would be no problem, but instead there is a near mystical assertion that all probabilities are present until the subject is observed, at which point the state collapses to what you see. Schrödinger could not tolerate this, not the least because the derivation of his equation is incompatible with this interpretation, and he presented his famous cat paradox, in which a cat is neither dead nor alive but in some sort of quantum superposition until observed. The result was the opposite of what he expected: this ridiculous outcome was asserted to be true, and we have the peculiar logic applied in that you cannot prove it is not true (because the state collapses if you try to observe the cat). Equally, you cannot prove it is true, but that does not deter the mystics. However, there is worse. Recall I noted when we integrate we have to assign necessary constants. When all positions are uncertain, and when we are merely dealing with probabilities in superposition, how do you do this? As John Pople stated in his Nobel lecture, for the chemical bonds of hydrocarbons, he assigned values to the constants by validating them with over two hundred reference compounds. But suppose there is something fundamentally wrong? You can always get the right answer if you have enough assignable constants.The same logic applies to the two-slit experiment. Because the particle could go through either slit and the wave must go through both to get the diffraction pattern, when you assume there is no wave it is argued that the particle goes through both slits as a superposition of the possibilities. This is asserted even though it has clearly been demonstrated that it does not. There is another problem. The assertion that the wave function collapses on observation, and all other probabilities are lost actually lies outside the theory. How does that actually happen? That is called the measurement problem, and as far as I am aware, nobody has an answer, although the obvious answer, the probabilities merely reflected possibilities and the system was always just one but we did not know it is always rejected. Confused? You should be. Next week I shall get around to some from my conference talk that caused stunned concern with the audience.

4 thoughts on “What does Quantum Mechanics Mean?

  1. In De Broglie Bohm (DBB) theory the particle stays a particle P, and it’s guided (there are actually two theoretical ways to do that, both launched by De Broglie).

    In SQPR, there is only a nonlinear wave W guided by its linear tail L. W, being nonlinear, is unstable: it tends to blow up, or spread out. Solitons happen when both effects are in balance. SQPR assumes blowing up, literally singularization, corresponds to particle formation, while spreading the linear wave corresponds to translation. Known real nonlinear waves blow up when amplitudes become more than linear (this is how rogue waves form at sea, the taller waves goes faster and catches up with the wave in front). So the blowing up (apparition of particles) will happen where amplitudes constructively interfere. All reasonings of wave mechanics as found in QMCI, which is linear, apply to the linear tail and forerunner, L.

    A claim is that “weak measurements” show that the DBB is right in the sense there is a particle P going through one slit, or the other.

    There may be a two lasers, one photon at a time, one laser per slit, THOUGHT experiment showing the same; one photon through one slit, or the other… yet still guidance from the other linear wave…

    Does that contradict SQPR? No. W = Non Linear Wave + expanding guiding Linear Wave = NL + L… But initially, NL has most of the energy, and L very little. This is why NL behaves like P when passing through the 2 slit.
    As time goes by, without Quantum interaction, NL loses energy, transferred to the linear forerunner L gains it. When a Quantum Interaction occurs, W blows up where L has high amplitude, while NL and L contracts at the absolute, global speed TAU, > 10^23 C. This is the famous Quantum Collapse. Thereof the nonlocal effects.

    The advantage of both DBB and SQPR over Quantum Mechanics Copenhagen Interpretation (QMCI) is that, in DBB and SQPR the Quantum Wave is not a probability wave anymore.

    What is the advantage of SQPR over DBB?
    First SQPR do away with having a particle P “guided” by a Pilot Wave, or a Bohmian Potential. There is only one concept: the Quantum Wave W, which behaves a bit like a superluminal tsunami which would contract in just one point (where it exchanges energy).

    Second, SQPR readily explains nonlocal effects such as the original 1935 EPR (I don’t see how keeping particles localized can do so)… Or the Bohm spin variant of the EPR.

    Third, the Quantum Wave W in SQPR is really “real” (a bit of a play on words as it is a complex wave in configuration space). What does that mean? The two entangled components of W, NL and L, carry energy at all times. In some cases, some of L will be so spread out that it will not be able to make it back at speed TAU back to NL blossoming back into W. That’s the Dark Matter Energy phenomenon.

    Fourth, thus, SQPR predicts effects QMCI and DBB don’t, such as Dark Matter and possibly Dark Energy (if true, SQPR should also enable the snail pace construction of superluminal communication networks, say to close-by stars, at least as a thought experiment).

    • First, one example of the weak measurements that shows that one photon goes through only one slit: Kocsis, S. and 6 others. 2011. Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer Science 332: 1170 – 1173.

      My counter is that within one quantum of action, I see no examples of where proper logical analysis of data demonstrates ANY non-local effects. All such experiments that I know of have the wave comply with the Malus law, which is a classical expression for the law of conservation of energy in a system that has polarised waves, and the work-up that claims such deviations from Bell’s inequalities do not logically comply with energy or probability conservation, and they have too few real variables, as opposed to assumed variables. For example, they require a fixed background, which contradicts relativity. Also, non-compliance. I have explained this in relation to the Aspect experiment in my ebook “Guidance Waves”.

      • I have EPR position just out on my site…

        Why do you say a “fixed background” contradicts relativity?
        The essence of the EPR spin is that spin S can be either up or down in a direction D.
        1) We have two particles (P1, P2) separated but entangled, with total spin zero.
        2) Let separation T between P1 and P2 be more than light can travel within a unit of time.
        3) Chose a direction D, measure Spin of P1.
        4) Within T, measure spin of P2. In direction d.
        5) Find out that the Spin of P2 in direction d is only compatible with what was found with Spin of P1 in direction D.
        ***
        No whistles, inequalities and Bells required.
        One can give the signal for measuring Spin P1 then P2 from a distant cosmic event.
        ***
        One can also check a posteriori that measuring Spin P1 along D influenced Spin P2 (that has been done with photons by Aspect, Zellinger, they got the Prize).
        ***
        The result is to be expected because of conservation of angular momentum. Spin may not be angular momentum (we don’t know), but it behaves as if, and conservation happens.

  2. A fixed background denies relativity because relativity argues that everything is measured in a frame of reference defined by the measurer. Take the general rotating polariser experiment (Aspect experiment). The first polariser samples half the photons, but there is nothing special about that half because if you rotate the first polariser, you always get the same rate count, and defines a subset relevant to this measurement of all photons emitted during the time; the second samples the entangled partners of that subset that have a component on this second axis. Assume the first is vertical according to the local gravitational field plus a displacement of β, and the second horizontal plus a displacement φ. With Aspect, A+B- was β = 0, φ = 22.5. Then B+ C- was β =22.5, φ = 45. (numbers degrees)., i.e. B+ C- was the apparatus of A+ B- rotated through 22.5 degrees. How can that give you two new measurements? All you have done is make the same sample from a different angle. Further, suppose you start with a polarised source. Now rotating the apparatus does create new values because the source defines the reference frame, whereas before the first detector defines the reference frame.

    Nobody denies the EPR statement, and I do not deny the conservation of angular momentum. The EPR result is not a problem if the spins are set at creation of the particles/photons. Einstein’s concern was that Copenhagen asserted the spin is determined at measurement because they assert that the photon is a superposition of the spins. It is only because Copenhagen asserts that the spin of photon b is instantaneously determined by the measurement of photon A that we have a problem with signals, etc.

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