Parmenides, Hegel, Heisenberg and Hawking

Singularities and the “One” — Modern Physics as the Mathematical Working Out of Hegel, Schelling and Holderlin’s “New Mythos”

Andrew Glynn

© 2020

Introduction

Parmenides, Hegel, Heisenberg and Hawking

Singularities and the “One” — Modern Physics as the Mathematical Working Out of Hegel, Schelling and Holderlin’s “New Mythos”

Andrew Glynn

© 2020

Introduction

Hegel, Schelling and Holderlin set out to create a “new” mythos of reality to replace the rationalist mythos decimated by Kant’s two great critiques of reason. The rationalist mythos itself originated in the foundation of the rational sciences — ratio, or accounting, and all the rational sciences attempt an accounting-for what is revealed in some other manner. Reality and our models of it of course are one such revealing, they have an ontological transparency that gives us a partial, if often skewed notion of the underlying “real” or “actuality”. Reality as such is one form of a type of revealing with which we are intimately familiar familiar, and modern science in particular attempts to account for what is revealed through more familiar forms of that revealing, the revealing we call technology. In doing so, it in fact accomplishes a mathematical working-out of the mythos most associated with Hegel.

Far from technology being applied rational science, modern science is an accounting-for patterns and correlations in data revealed by modern technology. Even in the mythos that supports the applied science construct, the pioneers of modern science such as Galileo remain dependent on new technologies of their time, such as the telescope, for the initial presentation of those patterns and correlations that are re-presented in their scientific theories and re-actualized in their repeatable experiments.

Reality is thus a technology, much as languages are technologies (including the various dialects of advanced mathematics). We tend to refer to things as ‘technological’ only when they are not yet familiar, so an iPhone is ‘technology’ while Alexander Bell’s telephone is no longer viewed as such by the common populace (though historians certainly continue to see it as a technology, and one that continues to affect and modify our models of reality). Note that I said an iPhone “is” technology, not “a” technology. This dropping of the difference between a specific technological artifact such as an iPhone and the essence of technology itself is an example of the ontological transparency of technology.

Singularities, or black holes to use the more common parlance, are as the name indicates another version of the “one”, the ultimately stable “real”, being itself, which Parmenides embarks on a journey towards at the very beginning of western philosophy. Parmenides is often seen as Heraclitus’ opposite in positing such a stable, unchanging basis to reality, whereas Heraclitus’ represents the view of reality as constantly in flux, constantly changing. However, this is a naïve distinction, and its naivety is demonstrated at the end of Parmenides journey, in which he finally arrives at the “place of the one” only to find it empty. That much of modern physics replaces the god of theism with a singularity that embodies all the necessary features of a creator being while dispensing with the uncomfortable features added in by various religions demonstrates that the underlying belief in an unchanging “one” that, at least at some point in the distant past, was all of Being, itself is the most unchanging aspect of our view of reality.

Virtual Black Holes

“a virtual black hole is a black hole that exists temporarily as a result of a quantum fluctuation of spacetime.[1] It is an example of quantum foam and is the gravitational analog of the virtual electron–positron pairs found in quantum electrodynamics. Theoretical arguments suggest that virtual black holes should have mass on the order of the Planck mass, lifetime around the Planck time, and occur with a number density of approximately one per Planck volume.[2]”

The emergence of virtual black holes at the Planck scale is a consequence of the uncertainty relation.”

“There is growing consensus, however, that quantum characteristics of the underlying gravitational theory might also be relevant to macroscopic, large scale phenomena. This is particularly important for the near horizon physics of astrophysical or supermassive black holes, including metric fluctuations [3], [4], [5], [6], exotic compact objects like boson or Planck stars [7], [8], and quantum structures that exist just outside the horizon [9], [10], [11]. It has been shown that such structures may even produce gravitational wave echoes in the ringdown phase of a compact binary merger [12]. In fact, it has been reported that such echoes have been observed with high statistical significance in the recent LIGO data [13], [14], [15], though these findings have been highly scrutinized [16].”

“These ideas suggest that black holes are fundamentally quantum objects, regardless of their size. Although the horizon is a prediction of General Relativity (GR), the physics governing it and the associated thermodynamics arise from quantum principles. This is perhaps most apparent from the black hole’s entropy, which is given by the well-known area-entropy law, and not the expected volumetric scaling for a classical object.”

While the existence of black holes beyond the microscopic and extremely short-lived “virtual” black holes is a prediction of General Relativity, the notion that they are fundamentally quantum objects comes as little surprise to those that view GR as a happenstantially close approximation to a complex mathematical model of reality, but one that tested to extreme limits invariably produces less accurate predictions than QM on both the micro and macroscopic scales, and moreover requires phenomena for which no explanation has even been proposed, much less demonstrated. The most obvious such phenomena is the absolute which the potential for motion demands being a relation between movement along two different dimensional axes, one in space and one of time. Speed is of course not a simple value but a correlation of movement in space to movement of time, and the different conjunctions involved results in the speed of light as the absolute encountering a fundamental problematic, one that has neither been solved nor even to my knowledge investigated with any success whatsoever, and one that breaks down at the ultimate microscopic and macroscopic extremes (What, for instance, could “speed of light” imply at the spatial and temporal level of Plank’s constant? Or, given the prediction and apparent observable demonstrability of an expanding universe, how would the constraint manifest at the ultimate horizon of such a universe, where the rate of expansion would suddenly hit a constraint that seemingly has no analogue, since it would have to constrain the same things in multiple directions at once. Put another way, at the edge of an expanding universe the paradox of something moving away from everything else creates the problem of that movement suddenly being constrained in every direction by another movement intrinsic to none of the involved objects along another dimension that in no way resembles the initial three is paradoxical both conceptually and within its mathematical expression. This form of an event horizon would resemble no other posited type of event horizon — not even that of a singularity, so positing reality itself as some type of black hole doesn’t help here, and distinguishing things from bodies is also of no help, since at this extreme they would be in fact the same — while being simultaneously implied by them).

Hawking, of course, famously stated that the nature of a black hole on a massive scale implies that it would “eventually” dissipate into absolutely nothing. I have often thought the sensation of a “grin” on Hawking’s face whenever he discussed that issue and the problems it causes with the conservation of mass and energy, a sensation present even after the effects of his illness prevented him from making the analogous facial movements, arose from both Heisenberg’s prediction of virtual “black holes” with sizes and lifetimes of one Plank constant, and the more commonly known GR prediction of massive and supermassive black holes, imply that within those event horizons time is an impossible axis of movement. Hawking’s “eventually”, which could in a general sense mean 10 seconds or 10 billion years, or any other arbitrary number, would in fact mean precisely one Plank constant of time, the shortest amount possible, which due to longer periods of time being necessary to form something larger than Plank’s constant eliminates the possibility of “real” black holes, leaving only Heisenberg’s “virtual” black holes.

Gravity and Energy

To go back to the quote describing a virtual black hole, namely:

[… they are] “an example of quantum foam and [are] the gravitational analog of the virtual electron–positron pairs found in quantum electrodynamics. Theoretical arguments suggest that virtual black holes should have mass on the order of the Planck mass, lifetime around the Planck time, and occur with a number density of approximately one per Planck volume.[2]”

We find two uses of the term ‘virtual’ without a commonly agreed meaning of the term within physics, and the introduction of ‘quantum gravitation’, a notion that is at least problematic with numerous different phenomena acquiring the name or at least being seen as part of the ‘problem’ of quantum gravitation. But perhaps we should go back to Heisenberg himself and his own statements on gravity in the Newtonian sense, which in most ways remains the sense in which it is used in GR.

“It’s more superstitious to believe that a massless, energyless force carries huge bodies in their orbits than it is to believe that angels do so.”

- Werner Heisenberg

The “massless, energyless force” is of course gravity itself. Is Heisenberg saying therefore that gravity itself is no more than a superstition? Famously he also stated that Plato was correct in that since the basest of the base particles of matter “have no mass” they are best understood purely as ideas. An idea for Plato is in fact the concept of a concept. While people had thought conceptually for eons, the notion of the concept itself lacked a conceptual framework on which it could be based. While it’s controversial as to whether the base particles do have the properties of charge and mass (the equations can be solved without them, and so their addition could be an unsupportable presumption), Heisenberg only worked with what he could measure — angular momentum. The problem Heisenberg is raising is that no aggregation of massless base particles could have any mass. Since the equations don’t require mass on the foundational level, we can work out analogous equations without mass on the macroscopic level — in that situation we are simply removing a divisor that was never used in the initial multiplier.

If the smallest of the base particles to which we consider ourselves to have any understanding have no mass, their signature remains the differential angular momentum of the three different types. Point particles cannot have spin in the sense that a volumetric thing has spin around its own axis, which means that it has to be thought as an intrinsic property, and it’s only in the difference between the three types that the most basic types of relations can form. It should be unsurprising that there are three signatures of angular momentum on this level — Heisenberg famously eliminated the “space” an electron would have to cross, and therefore the time involved, by eliminating the electron’s orbital momentum. This insight derives from Aristotle’s answer to Zeno’s paradox of movement, that “space” is simply unformed matter. The three signatures of intrinsic angular momentum are in fact the basis of the three dimensions of what we experience as space. This type of angular momentum cannot be an effect of spin, spin itself is only possible within a “space” already projected by the three different angular momentums of the foundational particles.

To go back, now, to the notion of a ‘virtual’ black hole, we put off defining the nature of the virtual itself. But the meaning of ‘virtual’ is not itself particularly difficult or complex, it’s something that in itself is not real, but has real effects. In our common experience of the virtual those effects can be accounted-for by the effect of the understood meaning of the specific virtual on an acting human being (such as the results of running software on the user). In QM the effects of the virtual are retroactively determined by the collapse of the wavefunction, which happens precisely when those effects are observed by the acting human being (as Wheeler demonstrated, although an ‘instrument’ may perform the initial observation, that only pushes the retroactivity further because at some point a human observation becomes necessary). A ‘virtual’ black hole can then be understood as Hegel’s ‘nothing negating itself’ on the level of Planck’s constant, it has both the size and lifespan of Planck’s constant because it negates itself in the shortest possible timespan.

A greatly misunderstood idea of Plato’s student Aristotle, that the heaviest items gravitate towards the center of any system, is the hidden basis for the belief that at least spiral galaxies are centered by supermassive black holes. The supposed evidence for them all presupposes Aristotle’s supposedly superseded idea. However, something gravitating in no way implies the concept of gravity. Gravity, conceptually, depends on the concept of mass, which we have already brought into doubt. In turn momentum is defined as the product of a thing’s mass and its velocity, while changes in velocity are a product of the application of energy. However, the whole edifice falls apart if angular momentum is an intrinsic property of the simplest particles, and thus requires no basis in either mass or velocity (velocity is a problematic requirement in any case since as a relative measure it cannot support an intrinsic quantity). This problematic edifice, though, provides the rather shaky foundation for utilizing another relative measure, speed (of light) as an intrinsic limit.

This latter term we use constantly, to the degree that physics is no longer thought as the science of movement, but as the science of mass and energy. Yet no essential determination of its meaning has been proffered, and it’s used as widely in the new age movement as in conventional physics, and unfortunately with as much (or little) justification. The definition current in physics, the potential for doing work, makes more sense in economics than it does in physics. That it can be synonymous with vitality, power and life itself demonstrates the problematic nature of the term. Yet its current usage is by no means traditional. It was first used in the manner physics uses it less than three hundred years ago. It was unknown as such as late as the Renaissance and the related Greek term has very different implications. So, what in fact does energy refer to?

Energeia, the Greek term from which it derives, meant nothing similar to its current usage. Within Aristotle’s thinking energeia is contrasted with dynamis and requires an Aristotelian understanding of causality for the contrast to be properly understood. The first usage of the term in anything like its modern sense is found in Leibniz, but it is Hegel’s understanding that concerns us more than that of the last great rationalist, great enough to understand he was the last, and therefore to anticipate in a certain manner what had to come after.

Energeia is usually translated as “actuality”, as what has already emerged and come to its stand as itself. In the most obvious sense, then, ‘energy’ should be more closely related to dynamis than to energeia, dynamis being the ability that underlies the movement bringing it to its rest as energeia.

That’s as far (in this particular case) as Leibniz can take us, but what of Hegel? Within the Hegelian dialectic as usually translated we find the initially impenetrable word “sublation” as the somehow both the “means” and the “goal” of the dialectic. But what is “sublation” and in what way can it lead to the disuse of dynamis (though Leibniz did reintroduce dynamis into physics, possibly the last productive application of rationalism).

Sublation is the translation, according to our best (completely inadequate) Wikipedia explanation, of “Aufheben or Aufhebung, a German word with several seemingly contradictory meanings, including “to lift up”, “to abolish”, “cancel” or “suspend”, or “to sublate”. The term has also been defined as “abolish”, “preserve”, and “transcend”.” Never mind that one of the meanings of sublation is listed as “to sublate”, (thanks, really), if the meanings are only “seemingly contradictory”, there must be a circumstance or set of circumstances in which the seeming contradictions are simultaneously necessary, and therefore not contradictory within that context.

A clue may lie in the even worse (in general) dictionary translation of energeia as the “ability to do work”. The Latin translation of energeia — industria — supports this notion. In some sense, then, the economic meaning is as important as the philosophical, perhaps far more so. Just as the basis of the rational sciences, ratio, is what we know as accounting, as “balancing the books”, the productive and even productionist sense of energeia (although as noted above, within our notion of simplistic cause and effect dynamis would seem more appropriate), it’s passing through the Latin word industria might be the clue to understanding how the Greeks understood energeia, and the sense of sublation within Hegel’s “new mythos”.

Aufheben/Aufhebung, and sublation as a translation of the Hegelian use of the word, is fundamentally an activity, not a thing. Energeia was also an activity, the highest activity in the Greek way of viewing reality, the activity of a thing that is done with its movement towards being what it is and can be at rest as what it is. The missing term here from a Greek perspective (missing precisely because the Greek perspective assumes it) is tension. What we refer to as “surface tension” of a liquid is more properly referred to in chemistry precisely as the liquid’s “sublation”.

A thing that has gone through the changes (movement) necessary to become what it was drawn towards becoming (what it gravitated towards, perhaps the fundamental meaning of gravitation) and is now at rest, is simultaneously at its highest point of tension, a point from which it can only “fall apart”. Going back to the notion of momentum, it includes mass and energy (as ability to achieve velocity in a specific direction) without differentiating them, but further includes a notion of time that’s completely foreign to GR and therefore the root cause of much of what relativity theorists find self-contradictory in QM, specifically time as we experience it — as moments that succeed one another without requiring a specific causal transition. Unlike the spatial determinations of time in GR there’s no necessary transition from one moment to another, it’s simply a different moment, just as there’s no transition from one electron state to another — the transitions we posit are done so retrospectively. The fractional times between moments that GR theorists are constantly trying to reintroduce were not thought in that manner either by the Greeks nor are they by QM. Thus the problem of quantum gravity is shown to be a pseudo-problem caused by an invalid separation of mass and velocity (a relative value in any case) from intrinsic angular momentum.

Horizons

The term “horizon” pops up in all the accounts of reality we have been considering, but in very different ways. Rather than simple, linear cause and effect, the Aristotelian notion of something coming to rest implies that it was drawn to its proper way of being itself, and this drawing-towards is a horizonal concept for the Greeks, specifically the erotic horizon. A thing becoming itself is not simply a matter of being worked on externally but even more primarily is a being-drawn-towards that is a fundamental part of itself, its telos. The most counterintuitive implications of QM are precisely those that involve retroactivity; the ideas in Hegel that cause the most problems for those first reading his works are those that involve retroactivity, often precisely because readers of Hegel try to replace retroactive reality with retrospective understanding, in much the same way as a large part of the physics community tries to subsume the retroactive nature of QM in some sort of consciously produced retrospectivity. Telos is commonly thought as the “end” or “goal”, and retrospectively it appears that way, but retroactively it is the beginning of the movement of something in terms of becoming itself. This retroactivity is therefore already very much a part of Aristotle’s thinking, and it’s not by accident that Heisenberg’s father was a professor of Aristotelian thinking.

There is, of course, another horizon, the technological horizon. It is the technological horizon that shows most clearly the ontological transparency that demarks something as a technology.

It’s in terms of the technological horizon, thought by Hegel from out of praxis (energeia/industria) more than poiesis (phusis), that the apparent contradictions of sublation resolve themselves, and do so through the notion of tension.

In what pragmatic context can abolish, cancel, lift up, transform, preserve and transcend co-exist in a manner in which each is necessary to the other, whether seemingly contradictory or not? In production, specifically in production as modern industrial manufacturing. The tension analyzed in the master/slave dialectic finds its rest in manufacture, but that rest is thought in a Greek manner, not as the temporal finish and release of tension but as its highest point — “The still point of a turning world.” To put it in Eliot’s phrasing. Dynamis as the ability to do work is merely a less developed form of energeia and drops to the side.

Momentum

But energeia, for its part, remains embedded in change as movement, in momentum. No wonder that for Heisenberg gravity was a superstition, and mass a fiction. Momentum creates tension. The real produces itself via a type of self-manufacture, in the simplest case the negation of nothing by itself on the Planck scale.

But is that all there is to Hegel’s new mythos? Is it merely a restatement of Aristotle in slightly clearer terms, more adapted to the realities of the 19th Century, the factory, automation (which Hegel foresaw clearly not only in itself but in the social issues that would inevitably arise)? Aristotle assumed retroactivity to a point yet couldn’t account for it and his notion of time fails as a result.

Technology has a certain ontological transparency by definition, but at a point an increase in quantity becomes a change in quality. Arising as it did from production and accounting our western thinking has since been an uncomfortable admixture of meta-physics and accounting-for. Production in terms of the self-production of plants and animals, the proper movement of phusis, combined with techne as handicraft, is not equivalent to biotechnology, cybernetics, ubiquitous automation and the rest of the changes Hegel foresaw clearly that have since been actualized.

The continuation of the futile attempts to resurrect a model of reality such as GR based on complex and probably unprovable mathematics shows only the common-sense side of most physicists, who almost immediately shy away from the counter-intuitive predictions of QM, predictions which to a one have been demonstrated to actually occur as predicted, wherever technology has advanced sufficiently to actualize what were originally thought-experiments, although the actual experiments were specifically designed to prove that QM must be wrong.

Heisenberg’s original equations and notes for QM are an oddity in physics — there’s no advanced mathematics involved. By taking Plank’s constant as 1 Heisenberg was able to use only the integer number set, with divisors only allowed if they had previously been used as multipliers. The result is that the only thing QM in fact depends on is the human ability to count, which isn’t really in question at this point. The old argument as to whether zero exists (now turned around by restrictive set theory into an argument as to whether one exists) is a simple misunderstanding, where something is counted the answer is one, where it is not, the answer is zero. Neither are numbers in the same sense as any of the other numbers in the integer set, they are the twin axioms that the validity of the integer number set itself rests on.

For this reason alone, QM is always and will always be more accurate at extremes than GR, because GR is a complex, close, but not precise approximation, and one based on assumptions that when looked at from outside the blinders of complex mathematics are naïve and, in some cases, absurd. If for no other reason than the basic rounding errors introduced by computers that run on base 16 floating point when the rest of the world runs on base 10, a QM that uses Planck’s constant as one never needs floating point calculations, and thus will never suffer rounding errors. The mere existence of the ‘theory’ of fragmented energy, aside from being a fundamentally meaningless phrase, which comes close to approximating the results of GR in specific contexts but fails to account for the demonstrated predictions of QM, simply shows that many average physicists would rather stick their heads in the sand than actually think through the implications of QM.

The sole benefit of the belief that engineering is “merely” applied science is that the fools that believe it don’t try to build things capable of killing anyone, because any engineer that thinks mathematics is more than a close approximation to reality will never actually get anything to work.

Perhaps nothing, though, shows the way that human beings are than the fact that at the same time as the world standardized to metric, a base 10 system, the same world was being automated on machines standardized to hexadecimal, base 16, and the two systems do not translate to each other without introducing errors.

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