For millennia we’ve been walking the earth like two-dimensional Flatlanders, who are unaware – not even wanting to be aware – of the three-dimensional depth that would destroy all their theories and way of life and thought. In our world, this is exactly like the nature of true four-dimensionality which even Einstein was loath to accept.
As I write these words it was almost 100 years ago when H. Minkowski, Einstein’s mathematics professor, “restores the absolute to relativity” with an invariance on the space-time interval. This ‘invariance’ of size – and that’s exactly what it ultimately amounts to – was necessary to maintain the overwhelming, unshakable belief in finitism.
Einstein carried on with this absolute size in general relativity through the Riemannian geometry he used; so the four-dimensional cat he let out of the bag in special relativity got re-caged in general relativity. But it is in ironic confusion that we are left with a length invariance forever obscuring true four-dimensionality, since a length variable is precisely what the unsullied fourth dimension is all about!
However, incredulity is a formidable barrier to overcome. For it is exactly opposite from the static world of vision and memory, where all space and time seem to remain the same…day in and day out. We’ll speak more about this later when H. Weyl enters the scene.
But modern man, “the measurer”, simply refuses to even consider such a psychologically preposterous reality. And here’s why.
1. It exposes our sense of vision as deceptive and illusory. (Of course, mystics and philosophers such as Heraclitus and Plato have been telling us this for centuries.) And since we are so visually biased, the very idea is repugnant.
2. It makes measurement, the heart of the sciences, an ultimately meaningless endeavor; merely a local, “proximity effect” based on the current size of our solar system.
3. It renders all aspects of knowledge – even the meanings of our words – arbitrary, the result of majority opinion. Because:
4. It introduces infinity into all aspects of existence. Infinity, which simply means unlimited, is the ultimate freedom. It is also the ultimate taboo.
5. “Official Culture”, at least in its present form, may not be able to survive in its wake.
Science is the most believed and trusted; the most dominant and financially successful, and thus the most powerful belief system in our universe. It is the ultimate authority and brooks no other voice of discovery or truth. It has simply brushed aside religion, its initial inspiration while devouring its other parent, philosophy, “which languishes in a slow death”1.
But what if science, the champion of finitude and definition, discovered that the universe and everything in it was not finite and thus not ultimately definable; further, that the reality they have been trying to uncover for centuries is not “the true Jacob” at all, but merely an effect of it; thus, in and by effect, a secondary reality? What if they discovered that the world is a lot more ‘relative’ than even Einstein thought? And that Heisenberg’s principle of indeterminacy was only the tip of the iceberg called “uncertainty”? And that the powerful theory of the quantum they so worship had little to do with what we perceive, but instead was a discovery of how we perceive it? And that its purpose then would not only be flawed, but despite its usability, so incomplete as to be ultimately meaningless? And that its hold on the collective consciousness could slip away? That “billions and billions” of government and industrial dollars could slip away? Careers shattered? All publications deemed worthless? What would they do?
Sadly, one of the dominant themes of this work is that what they would do is pretty much what they did.
They could have won the game, peeked behind The Wizard’s curtain and discovered the truth, the great cosmic joke. They would have discovered that the Emperor really had no clothes at all! They really could have won the game. But they were so incredulous and so utterly thunderstruck by what they were discovering, that they balked. Then they talked. Then they argued (and still argue). Finally, they convinced, lobbied, formed a majority, improved their mathematics and Voila! They moved on to new and greater heights of mathematical abstraction.. But why didn’t they win the game?
Because to win the game is to end the game. Because they changed the game in order to continue the game. Either they could be the butt of the greatest joke in any universe, or become like a god, the new and improved Ultimate Authority.
And who can argue with them; especially in that incomprehensible language of the mathematical physicist?
The Cabal of the mathematician/physicist
Advanced esoteric mathematics and advanced esoteric physics – “the new physics” – grew up together in the twentieth century. You can hardly learn one without learning the other. Your field of endeavor seems to be either a physicist/mathematician or a mathematician/physicist.
The mathematician thinks mathematics is the master key; that, as Pythagoras said: “all things are numbers”. The physicist agrees then adds the particle as consisting ultimately of – what else – mathematics (statistical probabilities); mathematics that actually cause effects and construct a universe when observed: i.e., physical mathematics!
Together they represent a group of elite individuals that, according to them, they alone have the ability to understand the cardinal metaphors of space, time, mass, energy and number.
According to this cabal, the ‘key’, when it is found, will be an elegant mathematical formula that brings about the cause, or explanation (understanding) of the carefully contrived standard models of their previously published literature.
Again, who is going to argue with them? These are the most highly specialized ‘experts’ on the planet. They own the game! They own the field! They own the rules! They own the language! They are the only players allowed and are their own self-appointed referees! No competition.
So while the gods of fate have been playing their joke on science, the gods of Science have been passing the joke onto us. And we, the ultimate losers, drown our sorrows (of insignificance, existential loneliness, melancholia, depression, and despair) in the most fantastic self-serving belief systems imaginable using the data offered. It’s made somewhat palatable by the horn of plenty they’ve produced: “As it’s filled to the brim with its artifact lot/ To justify questions we pose”. (JOY the Rime).
But oh how easy it is to be blind-sided when you have tunnel-vision. And Tunnel-vision (in the virtual reality of appearance) rules. But the Achilles Heel of Science is huge and all pervasive. For alongside its exaggerated accomplishments lie its hushed failures. And the biggest of all begins and ends with the perennial mystery of weight.
“Next to nothing has been learned about this pervasive yet
mysterious force since Newton’s first description in 1665... As a force,
gravity is still puzzling scientists who can find no waves, rays, or
other signs of its transmission through space.” (James Trefil,
Space, Time and Infinity)
Question almost any scientist on the meaning of gravity and he will at once pull a long face, like a country parson asked to explain the doctrine of the trinity, and murmur something about its being the most mysterious force in the universe. Do not be deceived by his vagueness. Behind it lies the implacable determination to defend the sacred cow. (Alan McGlashen, Gravity and Levity)
According to Oxford’s celebrated mathematician/physicist, Roger Penrose, “…the local effects of gravity are equivalent to those of an accelerating reference frame…what Einstein referred to as the principle of equivalence” (pp. 204, The Emperor’s New Mind). Also, “No confirmed observations exist that contradict Einstein’s general relativity. For all its initial strangeness, Einstein’s theory is definitely with us!” (Ibid, Pp. 211,)
Now don’t be alarmed or confused by this cryptic message; Heinz Pagals says very plainly what it really implies:
On the earth it is not obvious that the effect of gravity we experience is equivalent to the ground accelerating up. But it is—gravity is precisely equivalent to non-uniform motion. (Cosmic Code, emphasis in bold added)
And there it is, THE GROUND ACCELERATING UP! Just what I thought when I was 6 or 7 years old. What nonsense: a simple, naïve, all encompassing answer that, of course, no scientist or philosopher can afford to even think about—except perhaps in jest. That which gives us the sensation of weight is “precisely equivalent to” THE GROUND ACCELERATING UP? We would all be on Einstein’s famous elevator constantly accelerating into space. What madness.
But wait a minute. In a vacuum with no air to hinder them, a feather and a hammer will fall at the same rate. And, they don’t just fall; they accelerate directly toward the center of the earth! To help explain this utterly flabbergasting phenomenon (called the falling bodies law discovered by Galileo and confirmed on one of our moon visitations), physicists long ago decided to give mass two separate realities. One was gravitational mass, which accounted for the “attraction” of gravity, and the other was inertial mass, a measure of the resistance to non-uniform or accelerated motion. The heavier body has more weight, the tendency to fall, but also has more inertia, a proportional tendency not to fall. One offset the other. Cosmic exuberance is held in check by cosmic laziness.
Enter Albert Einstein
At the heart of general relativity is the principle of equivalence, mentioned above. This states that both gravity and inertia are, somehow, one and the same thing! “Thus the concept of gravity as an independent force completely disappears from our reasoning…” (George Gamow). Or, as Roger Jones says: “…gravity hasn’t really been united with inertia, it’s been dispensed with altogether.”
No explanation for the falling bodies’ phenomenon has endured. It is still, like weight itself, a major physical mystery. The enormity of this failure cannot be overstated. Think about it. A physics based upon two monumental theories of gravitation (Newton/Einstein) has never been able to explain either the phenomenon of weight nor the falling bodies enigma. But what a coincidence; both are easily explained away by “THE GROUND ACCELERATING UP”!
Now say for a moment that the ground actually is “accelerating up”. What in the world would cause such an action? And how can we picture such a thing?
Enter Erwin Schrödinger.
At the heart of the occult science of quantum mechanics is something called the Schrödinger wave equation. This remarkable formula plots the evolution of any quantum entity over time. This evolution – called “the wave function” – evokes a result that looks something like this: E0<E<E1…2 What this means is that each energy state increases over time. And to the consternation of everyone, it was realized that through Einstein’s formula E = MC2, mass-energy actually spreads out, or “gets fatter” in space over time!
Schrödinger proposed that the particle concept be entirely discarded and his concept of wave function be given all the physical reality, which meant that the electron was to be pictured as spread out continuously throughout space. (Atomic Scientists, Boorse, Motz, Weaver)
This Nobel Prize-winning equation and its bizarre ‘action’ were confirmed by G.P. Thomson’s Nobel Prize-winning electron refraction experiments, and voila: “It seems as though the whole conception of size is a mistaken one…”
Galileo’s idea of the particle acted on by no force which goes on forever in a straight line must be abandoned. It is not that the particle would stop but it would spread…But how can a particle spread? (G.P. Thomson)
(“How can it not spread”? would be the better question. For if it didn’t spread it would explode: “The electron should explode”3 “…there is nothing holding the electron together: like charges repel and it is all one like charge – it should explode”4 “Why doesn’t the electrical charge of an electron repel itself and fly apart?”5
We’ll come back to this point later. For what’s good for the goose is good for the gander: the proton should explode also. Or spread, which of course, it does.)
So Irwin Schrödinger’s spreading ‘fractional density’ quickly became Max Born’s spreading probability density: physical, causal mathematics! And for over 80 years now, Thomson’s experiments lack any acceptable interpretation. For obvious reasons: “…if the matter of our world consisted of a number of [spreading] disturbed areas it would by now have spread indefinitely” (Sullivan). That is, if all matter consisted of these constantly spreading entities – electrons, neutrons, and protons – which it does (including the eyes of man), then a causal explanation emerges for the utterly fantastic invisible action of THE GROUND ACCELERATING UP!
...the length of a meter stick expands, the atom expands? Then how can it make any sense to speak of expansion at all? Expansion relative to what? Expansion relative to nonsense. (Wheeler, Taylor, Thorne, Gravitation)
“Nonsense”, however, is no more a criterion of a falsehood than “common sense” is a criterion of truth. And it was Niels Bohr, the Copenhagen patriarch who said: “Only nonsense stands some chance of being the truth.” Of course, he was referring to his own brand of non-sense called Complimentarity.
It is this spreading of the wave packet that promotes incessant jokes about quantum weirdness among the connoisseurs. Amit Goswami, The Self-Aware Universe
For instance, Fred Alan Wolfe said:
Because it is so tiny, it takes only one billionth part of a billionth part of a second for the atom to spread out into fuzziness [read "uncertainty"]. And it continues to spread out until you come along and observe it. At that instant, depending on which experiment you perform, the atom is reduced to size. Just think, without you all atoms would spread out into the universe at an alarming rate. (Space-Time and Beyond, 1982, the ‘updated version’, with Bob Toben pp 127)
Enter the fourth dimension.
Physicists can 'experience' the four-dimensional space-time world through the abstract mathematical formalism of their theories, but their visual imagination-like everybody else's is limited to the three-dimensional world of the senses. (Fritjof Capra, The Tao of Physics, pp.150)
For nearly a century, physicists and philosophers have been in a state of confusion and even denial about the fourth dimension. They find it very difficult to believe that a fourth spatial dimension exists. Usually, in the modern expositions, the fourth dimension is said to be ‘time’. But this is only a half-truth. The fourth dimension “…is not exactly time, but time multiplied by the square root of –1” (“The Big View”— internet). The square root of –1 leads straight to the complex or imaginary state (i):
The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and not being. (Gottfried Wilhelm von Leibniz)
Now why is i used so much? Because i is the state that flutters, is the oscillation. This has been totally overlooked in mathematics [not to mention science and philosophy], that i is an oscillatory state. (G. Spencer-Brown)6
Is this just a coincidence? For the wave function, designated Ψ, the psi oscillation, is also an imaginary, or complex state. In fact all the major metaphors of physics – space-time, mass-energy, there can be nothing else – are infected with this imaginary coefficient. This is why it is said so often that they “can only be understood mathematically”. But if they are imaginary then they can be imagined. And, so can the fourth dimension.
The fourth dimension is all about freedom, real freedom. It puts all the other three dimensions in eternal motion. It is formally called (by some) “the fourth degree of freedom of motion”. In physics, this freedom of motion is action: “Density multiplied by volume in space gives us mass, or what appears to be the same thing, energy. But from our space-time point of view, a far more important thing is density multiplied by a four-dimensional volume of space and time; this is action.” (Sir Arthur Eddington)
The most common model of the fourth dimension is the easily constructed tesseract, or hypercube. Here is the one from Carl Sagan’s famous book, Cosmos:
About this cube nested within another cube, Sagan says “But for a real tesseract, in four dimensions, all the lines would be of equal length and all the angles would be right angles.”
Secondly, in the tesseract below, we have armed it with measuring rods. We have placed a measuring rod on the bottom front line of each cube. Each line, in fact, could be considered a measuring rod. If our world is four-dimensional then everything in it must be four dimensional including measuring rods and clocks. And the two cubes are a representation of one cube that has evolved via the interval in four-dimensional space-time. Therefore, the measuring rod must evolve proportionally and thus the lines are “of equal length.”
From the point of view from true four-dimensionality, P.D. Ouspensky tells us that
The idea of the fourth dimension ought to have arisen from observation of a series of progressively growing or diminishing spheres or cubes. One of the clearest and most comprehensive forms of motion in the fourth dimension in this sense is growth, the principle of which lies in expansion.
Although it “ought to have arisen”, it surely didn't. The idea that the fourth dimension is simply growth (or decrease) in size, the most natural process and long awaited mechanism that can never be observed, measured and categorized, is an abomination to the scientist – especially to a physicist, who dwells exclusively in “the science of measurement”.
Enter Hermann Weyl
When Einstein introduced his special theory of relativity in 1905, he likewise introduced the fourth dimension. And it wasn’t long before someone discovered its profound implications. It was Hermann Minkowski, Einstein’s former mathematics teacher, who realized in 1909 that “…space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”7
But Minkowski wasn’t just making profundities: the Encyclopaedia Britannica says:
Minkowski restores the absolute to relativity in the form of the invariant four-dimensional object, and the invariance (under all mathematical transformations) of the space-time interval and of certain fundamental physical quantities such as action (which has the dimensions of energy times time, even though neither energy nor time is separately invariant).
Process philosophers charge the Minkowski universe with being a static one.
Now this brings up an interesting question: If energy (thus, mass) is variable and time is variable (see above) and space is certainly variable, then how in anyone’s world can four-dimensional objects in curved space-time be invariant? Because this means that the fourth degree of freedom of motion has no motion!
This contradiction seems to be Hermann Weyl’s reasoning why “general relativity needed a variable for length variation!” (Hoffmann) So he revised the geometry of Riemann with its “…residual element of finite geometry – without any substantial reason, as far as I can see” (Weyl). This element is the preservation of lengths. If direction is not preserved, and neither time nor energy are preserved, then why the assumption that lengths should be preserved?
Such an assumption being recognized as false, a geometry comes into being, which, when applied to the world, explains in a surprising manner not only the phenomena of gravitation, but also those of the electromagnetic field. According to the theory which now takes shape, both classes of phenomena spring from the same source, and in fact we cannot in general make any arbitrary separation of electricity from gravitation. In this theory all physical quantities have a meaning in world geometry. (See note #7)
Hoffmann says this “sort of change of size” was “so natural and ingenious that it deserved a better fate than the one that befell it”. Einstein called it “an exceedingly ingenious attempt…a grandiose achievement of the mind”.8 But he couldn’t accept the reality it suggested.
Einstein's initial argument against the theory was that “...the lengths of objects would depend on their pasts”, in apparent disagreement with spectral analysis. Now this quote brings about two interesting scenarios. The first is a disjointed series of quotes from Lord Russell:
“Each particle being extended in time, must be regarded as composed of what we may call ‘event particles’: The whole series of the events makes up the whole history of the particle, and the particle is regarded as being its history [i.e., they would “depend on their pasts”]… For aught we know an atom may consist entirely of the radiation that comes out of it…Modern physics therefore, reduces matter to a set of events which proceed outward from a center. If there is something further in the center itself, we cannot know about it, and it is irrelevant to physics”9
I will address this mysterious conclusion in the last sentence later. What is relevant here is what is emphasized in bold and how it trivializes Einstein’s objection.
Secondly, with apparent difficulty, Hoffmann tries to translate (from the original German) Einstein's response to Weyl. Alluding to the Hoffmann quote above, he begins with a note of suspicion: “Such was Einstein's official argument against Weyl's theory...But it leaves something hidden. Here is an excerpt from a letter to Weyl in 1918 that shows a deeper Einstein objection”:
Could one really accuse the Lord God of being inconsistent if he passed up the opportunity discovered by you to harmonize the physical world? I think not. If he had made the world according to your plan [I would have said] to him reproachfully: "Dear God, if it did not lie within Thy power to give an objective meaning to the [equality of sizes of separated rigid bodies] why has Thou, Oh Incomprehensible One, not disdained ... to [preserve their shapes]?"10 Sic (all brackets in Hoffmann’s original)
Once Einstein pointed out the deadly implications for ‘the finite realm’, Weyl dropped it like a hot potato. It wasn’t so much disproved as disowned. For Weyl was a ‘finitist’; he didn’t even believe in mathematical infinities, much less, real ones.
In fact the theory has never been disproved, other than a bunch of excuses why it could never be true – all based upon incredulity or a desperate attempt to "save the appearances".
But if Max Born’s probabilities, Heisenberg’s uncertainties and the Plank/Einstein discontinuities are only applicable to the reality of appearances – i.e., the observation, the measurement or “collapse” – as Roger Penrose clearly points out (see GQCU Ch. 3, Reprise); and if Weyl’s “length variable” replaces the Riemann/Einstein ‘invariance’ in the geometry of general relativity to let true four-dimensionality develop, then all bets are off. The unification of electricity and gravitation becomes a done deal. Because once you figure out true four-dimensionality, the entire picture starts to come together like a finely crafted jigsaw puzzle, where all the pieces fit snugly and perfectly.
Said another way, quantum theory, slightly altered in the interpretation, gives us understanding about the world of appearances. Relativity, slightly altered in the application, gives us understanding about the world of substance. And the bridge that unites is science’s Holy Grail itself. Because the alteration of both is one and the same: the fourth dimension, the within to without – and vice versa – of Growth, Gravity and the Gateway to the Gods.
If a fourth dimensional creature existed it could, in our three dimensional universe, appear and dematerialize at will, change shape remarkably, pluck us out of locked rooms and make us appear from nowhere. It could also turn us inside out. (Cosmos)
These impossible scenarios by Sagan exist because an interval in space-time is impossible11 with a static length invariant. A length variable is never spoken of. It’s an unmentionable because, like Schrödinger’s spreading ψ function, if it’s considered as a real thing, it gives birth to infinite notions. You cannot imagine a fourth dimension only because our own incredulity forbids. They have made it completely impossible with this invariance because a length variable is precisely what the fourth dimension is!
Again, P.D. Ouspensky answers from the point of view of true four-dimensionality:
...if there are three dimensions, a real body of two dimensions cannot exist... In the same way...if there are four dimensions, a real body of three dimensions cannot exist... If the fourth dimension exists while we possess only three, it means that we have no real existence, that we exist only in somebody's imagination... If we do not want to agree with this we must recognize our-selves as beings of four dimensions.
The discovery of the fourth dimension came in the wrong century. We simply weren’t ready to absorb this truth: that the third dimension is a great cosmic hoax! That the models of reality we’ve been constructing and using for millennia are so heavily influenced by the process of observation. And that nothing can even exist in the third dimension, the world of appearance, the very world we see with the eyes. And, being visually biased, it is not easily sacrificed.
We have gleaned from relativity that space and time are not permanent, as Newton and his followers assumed. But the understanding of the above – that size and duration (in effect, the same thing as space and time) are not permanent – is a bitter pill to swallow. And so science avoids it like the plague. For it leads hand in hand to the notion of “THE GROUND ACCELERATING UP”!
1. Roger S. Jones, Physics as Metaphor