Uncertainty, quantum math, and A(Y)MS

This morning, one of my readers wrote me to say I should refrain from criticizing mainstream theory or – if I do – in friendlier or more constructive terms. He is right, of course: my blog on Feynman’s Lectures proves I suffer from Angry Young Man Syndrome (AYMS), which does not befit a 50-year old. It is also true I will probably not be able to convince those whom I have not convinced yet.

What to do? I should probably find easier metaphors and bridge apparent contradictions—and write friendlier posts and articles, of course! 🙂

In my last paper, for example, I make a rather harsh distinction between discrete physical states and continuous logical states in mainstream theory. We may illustrate this using Schrödinger’s thought experiment with the cat: we know the cat is either dead or alive—depending on whether or not the poison was released. However, as long as we do not check, we may describe it by some logical state that mixes the ideas of a dead and a live cat. This logical state is defined in probabilistic terms: as time goes by, the likelihood of the cat being dead increases. The actual physical state does not have such ambiguity: the cat is either dead or alive.

The point that I want to make here is that the uncertainty is not physical. It is in our mind only: we have no knowledge of the physical state because we cannot (or do not want to) measure it, or because measurement is not possible because it would interfere (or possibly even destroy) the system: we are usually probing the smallest of stuff with the smallest of stuff in these experiments—which is why Heisenberg himself originally referred to uncertainty as Ungenauigkeit instead of Unbestimmtheit.

So, yes, as long as we do not look inside of the box – by opening or, preferably, through some window on the side (the cat could scratch you or jump out when opening it) – we may think of Schrödinger’s cat-in-the-box experiment as a simple quantum-mechanical two-state system. However, it is a rather special one: the poison is likely to be released after some time only (it depend on a probabilistic process itself) and we should, therefore, model this time as a random variable which will be distributed – usually more or less normally – around some mean. The (cumulative) probability distribution function for the cat being dead will, therefore, resemble something like the curves below, whose shapes depend not only on the mean but also on the standard deviation from the mean.

1920px-Normal_Distribution_CDF

Schrödinger’s cat-in-the-box experiment involves a transition from an alive to a dead state: it is sure and irreversible. Most real-life quantum-mechanical two-state systems will look very different: they will not involve some dead-or-alive situation but two very different states—position states, or energy states, for example—and the probability of the system being in this or that physical state will, therefore, slosh back and forth between the two, as illustrated below.

Probabilities desmos

I took this illustration from the mentioned paper, which deals with amplitude math, so I should refer you there for an explanation of the rather particular cycle time (π) and measurement units (ħ/A). The important thing here – in the context of this blog post, that is – is not the nitty-gritty but the basic idea of a quantum-mechanical two-state system. That basic idea is needed because the point that I want to make here is this: thinking that some system can be in two (discrete) physical states only may often be a bit of an idealization too. The system or whatever is that we are trying to describe might be in-between two states while oscillating between the two states, for example—or we may, perhaps, not be able to define the position of whatever it is that we are tracking—say, an atom or a nucleus in a molecule—because the idea of an atom or a nucleus might itself be quite fuzzy.

To explain what fuzziness might be in the context of physics, I often use the metaphor below: the propeller of the little plane is always somewhere, obviously—but the question is: where exactly? When the frequency of going from one place to another becomes quite high, the concept of an exact position becomes quite fuzzy. The metaphor of a rapidly rotating propeller may also illustrate the fuzziness of the concept of mass or even energy: if we think of the propeller being pretty much everywhere, then it is also more useful to think in terms of some dynamically defined mass or energy density concept in the space it is, somehow, filling.

propeller This, then, should take some of the perceived harshness of my analyses away: I should not say the mainstream interpretation of quantum physics is all wrong and that states are either physical or logical: our models may inevitably have to mix a bit of the two! So, yes, I should be much more polite and say the mainstream interpretation prefers to leave things vague or unsaid, and that physicists should, therefore, be more precise and avoid hyping up stuff that can easily be explained in terms of common-sense physical interpretations.

Having said that, I think that only sounds slightly less polite, and I also continue to think some Nobel Prize awards did exactly that: they rewarded the invention of hyped-up concepts rather than true science, and so now we are stuck with these things. To be precise, I think the award of the 1933 Nobel Prize to Werner Heisenberg is a very significant example of this, and it was followed by others. I am not shy or ashamed when writing this because I know I am in rather good company thinking that. Unfortunately, not enough people dare to say what they really think, and that is that the Emperor may have no clothes.

That is sad, because there are effectively a lot of enthusiastic and rather smart people who try to understand physics but become disillusioned when they enroll in online or real physics courses: when asking too many questions, they are effectively told to just shut up and calculate. I also think John Baez’ Crackpot Index is, all too often, abused to defend mainstream mediocrity and Ivory Tower theorizing. At the same time, I promise my friendly critic I will think some more about my Angry 50-Year-Old Syndrome.

Perhaps I should take a break from quantum mechanics and study, say, chaos theory, or fluid dynamics—something else, some new math. I should probably also train to go up Mont Blanc again this year: I gained a fair amount of physical weight while doing all this mental exercise over the past few years, and I do intend to climb again—50-year-old or not. Let’s just call it AMS. 🙂 And, yes, I should also focus on my day job, of course! 🙂

However, I probably won’t get rid of the quantum physics virus any time soon. In fact, I just started exploring the QCD sector, and I am documenting this new journey in a new blog: Reading Einstein. Go have a look. 🙂

Post scriptum: The probability distribution for the cat’s death sentence is, technically, speaking a Poisson distribution (the name is easy to remember because it does not differ too much from the poison that is used). However, because we are modeling probabilities here, its parameters k and λ should be thought of as being very large. It, therefore, approaches a normal distribution. Quantum-mechanical amplitude math implicitly assumes we can use normal distributions to model state transitions (see my paper on Feynman’s Time Machine).

Dismantling myths

I just published a paper in which I show we do not need the machinery of state vectors and probability amplitudes to describe quantum-mechanical systems (think of a laser here, for example). We can describe these systems just as well in terms of a classical oscillation: the Planck-Einstein relation determines frequencies, which can then be used to determine the probabilities of the system being in this or that state.

The paper was quite an effort. The subject-matter is very abstract and the ruse and deceit in the quantum-mechanical argument (that basically assumes we do need all that humbug) is very subtle. It is, therefore, difficult to pinpoint exactly where the argument goes wrong. We managed to find and highlight the main deus ex machina moment, however, which is the substitution of real-valued coefficients by complex-valued functions.

That substitution is not innocent: it smuggles the Planck-Einstein relation in – through the backdoor, so to speak – and makes sure the amplitudes come out alright! The whole argument is, therefore, typical of other mainstream arguments in modern quantum mechanics: one only gets out what was already implicit or explicit in the assumptions, and those are rather random. In other contexts, this would be referred to as garbage in, garbage out.

The paper complements earlier logical deconstructions of some of these arguments, most notably those on the anomalous magnetic moment, the Lamb shift, 720-degree symmetries, the boson-fermion dichotomy and others (for an overview, see the full list of my papers). In fact, we have done so many now that we think we should stop: this last paper should conclude our classical or realist interpretation of quantum mechanics!

It has all been rather exhausting because we feel we had to cover pretty much everything from scratch. We did—and convincingly so, I think. Still, critics – I am quoting from one of the messages I got on ResearchGate here – still tell me that I should continue to “strengthen my arguments/proofs” so to “convince readers.” To those, I usually reply that I will never be able to convince them: if 60+ papers (with thousands of downloads) and a blog on physics (which also gets thousands of hits every month) is not sufficient, then what is? I should probably also refer them to a public comment on one of my papers—written by someone with (a lot) more credentials than me:

“The paper presents sound and solid reasoning. It is sobering and refreshing. The author is not only providing insight into central conceptual problems of modern physics but also recognizing the troubles that indoctrination causes in digesting this insight.”

Let us see how it all goes. I know I am an outsider and, therefore, totally insignificant. I should just stop writing and wait a bit now. This mysterious hyped-up Copenhagen interpretation should become irrelevant by itself: people will realize it is just hocus-pocus or, worse, A Bright Shining Lie.

That may take a long time, however, and I may not last long enough to see it happen. Mainstream physicists will soon be celebrating 100 years of what Paul Ehrenfest referred to as the ‘unendlicher Heisenberg-Born-Dirac-Schrödinger Wurstmachinen-Physik-Betrieb.

On the other hand, it is not because the indoctrination has, obviously, been very successful, that we should give up. An engineer, alumnus of the University of California, also encouraged me by sending me this quote:

“Few people are capable of expressing with equanimity opinions
which differ from the prejudices of their social environment. Most
people are even incapable of forming such opinions.” (Einstein: A Portrait, Pomegranate Artbooks, Petaluma, CA, 1984, p. 102).

That is as good as it gets, I guess. And if you read these words, it probably means you are part of that group of few people. We will not celebrate 100 years of metaphysical nonsense. We will keep thinking things through for ourselves and, thereby, find truth—even if only for ourselves.

That is enough as a reward for me. 🙂

Planck’s quantum of action

I find it most amazing that – with few physical laws and geometry formulas – we are able to understand reality.

These laws – Maxwell’s equations, Einstein’s mass-energy equivalence relation, and the Planck-Einstein relation – are not easy. The geometry formulas – Euler’s formula, basically – are not easy either. But once you get them, all falls into place—like Enlightenment (or kensho, satorinirvana, etc. if you’d happen to like Buddhist philosophy). 🙂

All has a resonant frequency: photons, electrons, protons, neutrons, atoms, molecules, complex systems—all that is stable. Unstable particles and systems do not obey the Planck-Einstein relation: ω = E/ħ. They die out: they are short-lived transients or even shorter-lived resonances. We should not refer to them as particles or particle-systems, and we need non-equilibrium math to analyze them.

It is all most beautiful. I will, therefore, not say anything more about it here. I’ve written about the nitty-gritty elsewhere.