Thursday, 05 May 2011 21:17

Hyperspherical time

Ah, how refreshing to excercise one's democratic rights, whilst voting seems less fun than rioting, it seems much more fun than all out civil war, so I dragged my womenfolk down to the polling booth to vote NO to AV with a high expectation of success. Unfortunately no illiberal dimocrat canvassers were present for me to bait with insults and rhetoric.

anyway, now to something a bit more lighthearted for a change..........

The Geometry and Topology of Hyperspherical Time.

This essay arises in response to frequent questions about TIME that have arisen from the VHC, Vorticitating Hypersphere Cosmology hypothesis advanced in our recent books The Apophenion and The Octavo, which concentrated mainly on the spatial aspects of a hyperspherical universe.

By popular request we omit most of the supporting mathematics and attempt to express this in prose. Heck, mathematics only means measuring and counting really, this doesn’t hurt much once you get used to it, although some do seem to have an inexplicable terror of it, which perhaps derives from having only ten fingers.

The big bang theory does not supply an explanation for the existence of the universe; it merely purports to explain how it got into its presently observed condition from a highly improbable previous condition of extreme density or singularity, into which it may yet collapse again. It cannot explain the origin of the supposed big bang or what came before it, although it can perhaps sidestep the question of what came before it by pronouncing that time itself began with the big bang, and may end in another singularity at a big crunch.

Conditions before a big bang or after a big crunch cannot in principle submit to any kind of rational investigation because at a singularity all physical laws become meaningless. The speculation that singularities explode into new universes ‘elsewhere’ in some sort of a multiverse does not solve the question of the existence of the universe, it merely makes it into a much bigger question.

Either way, any version of big bang theory appears as a species of Creatio ex Nihilo, ‘creation from nothing’. This theory began to take shape amongst second century Christian theologians keen to replace previous pagan ideas about the universe and the gods themselves evolving from Chaos with a vision of an uncreated single god that created the entire universe with a beginning and an end. The big bang theory seems to have devolved from a similar linear view of time and has attracted the attention of monotheists as a possible supporting argument for such a Creatio ex Nihilo.

Despite that we never observe anything created out of nothing, and that instead we observe all things as recycled out of other things, many people seem to regard nothingness as somehow more fundamental than something-ness, but for no discernable reason.

Now from the HD8 perspective, only the moment of observation or interaction has a particle like existence, the past and the future consist of a quantum wavelike (or ‘astral’)  reality that we cannot directly perceive, and the past and future wave reality spreads out like two cones from the point of the present.

Whilst most people can readily accept that the future contains many possible states represented by the ever expanding forward cone, the idea of multiple possible pasts seems more challenging to common sense. Nevertheless we have to remember that the present moment, including all records and memories present in it, could have arisen from ANY past that could have given rise to it, and indeed we cannot explain the behaviour of fundamental particles or even many chemical compounds without accepting that they behave as if they had had more than one previous state before observation or before interacting with one another.

For most recently recorded or remembered events this makes little difference, the coincidence of my birth with other events occurring 7.5 hours before sunrise some 58.3 revolutions of the earth about the sun ago remains on paper, but if the paper ceased to exist an anatomical examination of me could not achieve an accuracy now of better than plus or minus 3 or so years. The further back we seek to date events the greater the uncertainty. Indeterminacies in planetary motions mount up over hundreds of thousands of years, whilst we can calculate full moon dates for the past several centuries we cannot calculate such things with any confidence over millions of years.

Given sufficient time, the uncertainties surrounding any past event mount up to make it objectively indeterminate in the sense that increasingly vast numbers of possible states may have applied. For atomic particles, sufficient time may correspond to mere fractions of a second, for astronomical events, sufficient time may correspond to millions or billions of years.

Now in a universe with a finite and unbounded spacetime geometry and topology, time exists as a closed ‘loop’ as does space, and gravity achieves this closure by curving both. Thus the very deep past of any event or moment of observation also corresponds to its very deep future. We can visualise this as the expanding cones of past and future probabilities bending round in a circle and eventually meeting at the temporal antipode about 11 billion years away. The vast disc like surface where they theoretically meet would represent all possible pasts and futures of the moment of observation.

However because of the 3 dimensional nature of time the present moment of time also has a similar sized disc surrounding it in the orthogonal time plane and this represents all possible pasts and futures of some arbitrarily designated moment of observation at the temporal antipode.

Indeed, all moments of the present would have a disc of orthogonal time surrounding them, so if we string together all the hypothetical moments of the present to form a circle then the whole structure looks like a torus (a doughnut) with a ring representing the series of hypothetical moments of observation running hidden in the middle of the torus.

Now the past and the future of any moment of observation do not actually exist in particle form because time consists of nothing other than a succession of particle arrangements, it consists of movement. Thus time travel remains a nonsensical concept that would require the recreation of an entire previous arrangement of the particles of the whole universe or the sudden creation of a future arrangement that somehow bypassed all the usual intermediate states.

The pasts and futures of any moment of observation exist only as probabilistic wavefunctions, or what esotericists have sometimes called the ‘astral’, they don’t consist of the same sort of particle like manifestations that compose the moment of the present, and remain somehow hidden. Nevertheless as experiments in both physics and magic confirm, such wavefunctions do have real effects on the observed particle reality of the moment of observation, and from this we infer their reality, although we cannot perceive or detect them directly.

Now the toroidal model of time remains useful only in the context of an imagined sequence of moments of the present that did happen or will actually happen, represented by a line running like a ring through the middle of the body of the torus. Yet no certain past or future actually exists very far from the moment of the present and the wavefunctions of the pasts and futures of the present spread out in closed finite and unbounded 3 dimensional time to form a temporal hypersphere that actually has no preferred direction, although as Hawking observes, ‘entropy increases with time because we choose to measure time in the direction in which entropy increases’, and local events usually tend to move in the direction of more probable rather than less probable states.

Thus time has the same hyperspherical geometry and topology as space. Every moment of the present has a temporal antipode about 11 billion years ago which represents both its deep past and its deep future, however, and here comes the really strange bit, from the position of an observer at any moment of the present, the temporal antipode of that observer does not exist as a single definite state, but rather, like the spatial antipode it seems spread around the entire spherical surface of the temporal horizon.

Here we approach the central schism between classical-relativistic and the quantum interpretations of reality. In classical terms reality must have a singular origin, in quantum terms reality can have multiple probabilistic origins.

Using the quantum perspective presented in The Octavo, we can see that an application of the Boltzmann -Gibbs entropy principle and the Shannon theory of information via the Beckenstein-Hawking conjecture of Black Hole Entropy applied to a gravitationally closed hyperspherical universe suggests that it will have roughly about Temporal Horizon time squared over the Planck time squared, as the number of its possible past and future states.

This number comes out at as an impressive ten to the power of one hundred and twenty, suggesting that from the point of view of any observer at any moment of the present that this universe has a staggering number of possible past and future states, which all contribute in some sense to the observed conditions of now, rather than just one, as classical physics and magic and religion might suggest.

So what does this mean?

Well it strongly suggests that the moment of now, of the present, of the moment of observation of particle reality, consists of an interference pattern from some vastly greater probabilistic waveform reality that we could call Chaos.

Partum in Chaos, rather than Creatio ex Nihilo?

This Chaos at the antipodal past and future of the moment of now presumably permits the universe to exist as a result of random vacuum fluctuations, an improbable big bang, or perhaps as a result of some sort of closed loop of cosmic panpsychism, which we could call god, although that clarifies very little; or perhaps via some form of observer created reality which permits the universe to exist simply because it can.

Either which way, or multitude of ways, we cannot from within the fishbowl of hyperspherical spacetime itself, currently derive an answer to the question of how it comes to exist at all.

Perhaps we should rephrase the question, which itself implies the dubious proposition of the existence of a state of non-existence; with the question of could the universe exist in any other than the form in which we observe it? It does after all exhibit a remarkable self consistency based on a small handful of laws or rules or conventions or whatever you want to call them. Do these form the only self-consistent set possible?   

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