All you need to know about cosmology…

I just did a short paper with, yes, all you need to know about cosmology. It recapitulates my theory of dark matter (antimatter), how we might imagine the Big Bang (not a single one, probably!), the possibility of an oscillating Universe, possible extraterrestrial life, interstellar communication, and, yes, life itself. It also tries to offer a more intuitive explanation of SRT/GRT based on an analysis of the argument of the quantum-mechanical wavefunction – although it may not come across as being very ‘intuitive’ (my math is, without any doubt, much more intuitive to me than to you – if only because it is a ‘language’ I developed over years!).

I introduced the paper with a rather long comment on one of the ResearchGate discussion threads: Is QM consistent?. I copy it here for the convenience of my readers. 🙂

The concept of ‘dimension’ may well be the single most misunderstood concept in physics. The bare minimum rule to get out of the mess and have fruitful exchanges with other (re)searchers is to clearly distinguish between mathematical and physical dimensions. Physical dimensions are covered by the 2019 revision of SI units, which may well be the most significant consolidation of theory which science has seen over the past hundred years or so (since Einstein’s SRT/GRT theories, in fact). Its definitions (e.g. the definition of the fine-structure constant) – combined with the CODATA values for commonly repeated measurements – sum up all of physics.

A few months before his untimely demise, H.A. Lorentz delivered his last contributions to quantum physics (Solvay Conference, 1927, General Discussion). He did not challenge the new physics, but did remark it failed to prove a true understanding of what was actually going on by not providing a consistent interpretation of the equations (which he did not doubt were true, in the sense of representing scientifically established facts and repeated measurements) in other words. Among various other remarks, he made this one: “We are trying to represent phenomena. We try to form an image of them in our mind. Till now, we always tried to do using the ordinary notions of space and time. These notions may be innate; they result, in any case, from our personal experience, from our daily observations. To me, these notions are clear, and I admit I am not able to have any idea about physics without those notions. The image I want to have when thinking physical phenomena has to be clear and well defined, and it seems to me that cannot be done without these notions of a system defined in space and in time.”

Systems of equations may be reduced or expanded to include more or less mathematical (and physical) dimensions, but one has to be able to reduce them to the basic laws of physics (the mass-energy equivalence relation, the relativistically correct expression of Newton’s force law, the Planck-Einstein relation, etcetera), whose dimensions are physical. The real and imaginary part of the wavefunction represents kinetic and potential energy sloshing back and forth in a system, always adding up to the total energy of the system. The sum of squares of the real and imaginary part adding up to give us the energy density (non-normalized wavefunction) at each point in space or, after normalization, a probability P(r) to find the electron as a function of the position vector r. The argument of the wavefunction itself is invariant and, therefore, is consistent with both SRT as well as GRT (see Annex I and II of The Finite Universe).

The quantum-mechanical wavefunction is, therefore, the pendant to both the Planck-Einstein relation and the mass-energy equivalence relation. Indeed, all comes out of the E = h·f = p·λ and E = mc2 equations (or their reduced forms) combined with Maxwell’s equations written in terms of the scalar and vector potential. The indeterminacy in regard to the position is statistical only: it arises because of the high velocity of the pointlike charge, which makes it impossible to accurately determine its position at any point in time. In other words, the problem is that we are not able to determine the initial condition of the system. If we would be able to do so, we would be able to substitute the indefinite integrals used to derive and define the quantum-mechanical operators to definite integrals, and so we would have a completely defined system. [See: The Meaning of Uncertainty and the Geometry of the Wavefunction.]

Quarks make sense as mathematical form factors only: they reduce the complexity of the scattering matrix, but they are no equivalent to a full and consistent application to the conservation and symmetry laws (conservation of energy, linear and angular momentum, physical action, and elementary charge). The quark hypothesis suffers from the same defect or weakness as the one that H.A. Lorentz noted in regard to the Uncertainty Principle, or in regard to 19th century aether theories. I paraphrase: “The conditions of an experiment are such that, from a practical point of view, we would have indeterminism, but there is no need to elevate indeterminism to a philosophical principle.” Likewise, the elevation of quarks – the belief that these mathematical form factors have some kind of ontological status – may satisfy some kind of deeper religious thirst for knowledge, but that is all there is to it.

Post-WWII developments saw a confluence of (Cold War) politics and scientific dogma – which is not at all unusual in the history of thought, but which has been documented now sufficiently well to get over it (see: Oliver Consa, February 2020, Something is rotten in the state of QED). Of course, there was also a more innocent driver here, which Feynman writes about rather explicitly: students were no longer electing physics as a study because everything was supposed to be solved in that field, and all that was left was engineering. Hence, Feynman and many others probably did try to re-establish an original sense of mystery and wonder to attract the brightest. As Feynman’s writes in the epilogue to his Lectures: “The main purpose of my teaching has not been to prepare you for some examination—it was not even to prepare you to serve industry or the military. I [just] wanted most to give you some appreciation of the wonderful world and the physicist’s way of looking at it, which, I believe, is a major part of the true culture of modern times.”

In any case, I think Caltech’s ambitious project to develop an entirely new way of presenting the subject was very successful. I see very few remaining fundamental questions, except – perhaps – the questions related to the nature of electric charge (fractal?), but all other questions mentioned as ‘unsolved problems’ on Wikipedia’s list for physics and cosmology (see: https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics), such as the question of dark matter (antimatter), the arrow of time, one-photon Mach-Zehnder interference, the anomaly in the magnetic moment of an electron, etcetera, come across as comprehensible and, therefore, ‘solved’ to me. As such, I repeat what I think of as a logical truth: quantum physics is fully consistent. ‘Numerical’ interpretations of quantum physics (such as SO(4), for example) may not be wrong, but they do not provide me with the kind of understanding I was looking for, and finally – after many years of deep questioning myself and others – have found.

Feynman is right that the Great Law of Nature may be summarized as U = 0 (Lectures, II-25-6) but also notes this: “This simple notation just hides the complexity in the definitions of symbols: it is just a trick.” It is like talking of “the night in which all cows are equally black” (Hegel, Phänomenologie des Geistes, Vorrede, 1807). Hence, the U = 0 equation needs to be separated out. I note a great majority of people on this forum try to do that in a very sensible way, i.e. they are aware that science differs from religion in that it seeks to experimentally verify its propositions: it measures rather than believes, and these measurements are cross-checked by a global community and, thereby, establish a non-subjective reality, of which I feel part. A limited number of searchers may believe their version of truth is more true than mainstream views, but I would suggest they do some more reading before trying to re-invent the wheel.

For the rest, we should heed Wittgenstein’s final philosophical thesis on this forum, I think: “Wovon man nicht sprechen kann, darĂĽber muĂź man schweigen.” Again, this applies to scientific discourse only, of course. We are all free to publish whatever nonsense we want on other forums. Chances are more people would read me there, but as the scope for some kind of consensus decreases accordingly, I try to refrain from doing so.

PS: To understand relativity theory, one must agree on the notion of ‘synchronized clocks’. Synchronization in the context of SRT does not correspond to the everyday usage of the concept. It is not a matter of making them ‘tick’ the same: we must simply assume that the clock that is used to measure the distance from A to B does not move relative to the clock that is used to measure the distance from B to A: clocks that are moving relative to each other cannot be made to tick the same. An observer in the inertial reference frame can only agree to a t = t’ = 0 point (or, as we are talking time, a t = t’ = 0 instant, we should say). From an ontological perspective, this entails both observers can agree on the notion of an infinitesimally small point in space and an infinitesimally small instant of time. Again, these notions are mathematical concepts and do not correspond to the physical concept of quantization of energy, which is given by the Planck-Einstein relation. But the mathematical or philosophical notion does not come across as problematic to me. Likewise, the idea of instantaneous or momentaneous momentum may or may not correspond to a physical reality, but I do not think of it as problematic. When everything is said and done, we do need math to describe physical reality. Feynman’s U = 0 (un)worldliness equation is, effectively, like a very black cow in a very dark night: I just cannot ‘see’ it. 🙂 The notion of infinitesimally small time and distance scales is just like reading the e-i*pi = -1 identity, the ei0 = e0 = 1 or i2 = -1 relations for me. Interpreting i as a rotation by 90 degrees along the circumference of a circle ensures these notions come across as obvious logical (or mathematical/philosophical) truths. 🙂 What is amazing is that complex numbers describe Nature so well, but then mankind took a long time to find that out! [Remember: Euler was an 18th century mathematician, and Louis de Broglie a 20th century physicist so, yes, they are separated by two full centuries!]

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