Congruent Solutions to Zeno's Paradoxes

[Copyright Steaphen Pirie 2009]

Overview:

This article (and the "Zeno's Paradoxes" section of this website) details the fundamental and irrevocable failure of standard scientific solutions to the paradox of movement. A new world-view is needed to account for the facts. The old Newtonian, Darwinian models of biological development are no longer tenable in the face of this new evidence.

Background:

Around 2,400 years ago a Greek philosopher (Zeno of Elea) questioned how anything or anyone moves around. Theoretically, for anyone to lift a finger, bat an eyelid, or even to fall down requires we move through a seamless but endless (never-ending) progression of ever-so-small little movements. He highlighted how there appeared to be a mismatch between our theories about life and our simple, everyday practical experiences.

The content in the following two sections was originally posted on the Wikipedia website under "Zeno's Paradoxes" in the Proposed Solutions section. However, after many objections from various Wikipedia commentators, the material was removed.

A great chasm has developed in the understanding and thinking of the great majority. Other articles in this section at this website go into greater detail as to the nature and cause of that blindspot in the pysche of people. Ironically1 it is scientists who are now failing to apply the scientific method in response to the evidence of quantum physics.

The resistance to asking questions and constructing new theories that explain experimental evidence, particularly anomalous phenomena, is a common human experience, and can be understood to be, in part, the practical expediency of "getting on with life" – in practical terms, if we had to question every move, or belief we held, most would get very little done.

As will be covered in other articles at this site, (e.g. "The Evolution of the Human Psyche") ignoring or avoiding gaps in our belief-systems is one means by which we form limits and frameworks for effective living.

[ Note, the following paragraph beginning "Another solution to some of the paradoxes ..." was existing content prior to the additional material by Steaphen Pirie]

Are space and time infinitely divisible?*

Another solution to some of the paradoxes is to consider that space and time are not infinitely divisible. Just because our number system enables us to give a number between any two numbers, it does not necessarily follow that there is a point in space between any two different points in space, and the same goes for time..

If space-time is not infinitely divisible (and thus not perfectly continuous), it is "discrete" (composed of “lumps” and “jumps” as is experimentally observed in the field of quantum physics (e.g. electrons jumping from one level to another) and affirmed theoretically (as physicist David Bohm emphasised, "according to the quantum theory, movement is not fundamentally continuous.")2. Ipso facto the "gaps" between the “lumps” (quantum excitations or perturbations) that comprise space-time will remain immeasurable and intangible (in accord with the Uncertainty Principle).

In fact, if movement of physical things was perfectly continuous, according to physicist Richard Morris, Maxwell's equations predict "that electrons circling an atomic nucleus would radiate energy so rapidly that atoms should quickly collapse."3

As British physicist Paul Davies has pointed out, "the energy released under such circumstances should have been infinite."4 As Morris goes on to explain, "If both Rutherford's theory and classical physics were correct, there should be no atoms, no matter as we know it, and, of course, no physicists."5

Some scientists and engineers (e.g. Norman Friedman) have likened space-time as being "projected" (actualised) like a motion-picture film, that "...our reality is more like a motion picture, but with the individual frames going by extremely fast—at the undetectable interval of the Plank time,6 and that, by some estimates, "our universe is flickering on and off every 5.3 x 10^-44 seconds".7 (i.e. it is continually regenerating (pulsing, unfolding/enfolding) at a rate of around 19 billion trillion trillion (10³³) gigahertz - (the inverse of the Planck time)).

As physicist Fred Alan Wolf explained: "At the smallest level of space-time-matter, space-time is continually fluctuating— creating momentary bubbles of matter, which just as quickly vanish into nothingness again."8

Other physicists have since suggested much the same. Using slightly different terminology, two Australian physicists Reginald Cahill and Christopher Klinger have suggested that "space and time and all the objects around us are no more than the froth on a deep sea of randomness."9

More directly, Cahill noted that:

"Far from being merely associated with quantum measurements, this randomness is at the very heart of reality ... randomness generates everything, it even creates the sensation of the 'present.' Randomness is more fundamental than physical objects."10

Within this conceptual framework — that our space-time is flickering on and off — perfectly smooth movement is, like a motion-picture film, an illusion, as Zeno originally posited. As physicist Fred Alan Wolf wrote "Werner Heisenberg was ... awarded the Nobel prize in physics for his realization that Zeno was correct after all."11

If space-time is discrete, then our space-time flickering requires instant nonlocal (super-luminal) interconnections (as speed-of-light connections will not be quick enough to orchestrate the in-phase flickering that gives rise to the order and solidity that we readily experience).

"At Cambridge University, mathematician Noah Linden and physicist Sandu Popescu have found that in the typical quantum state occupied by any group of particles the links between the particles are mostly of a nonlocal character. Quantum theory isn’t just a tiny bit nonlocal. It’s overwhelmingly nonlocal. Nonlocality is the rule for our Universe."12

As physicist Nick Herbert explained "without faster-than-light connections, an ordinary object model of reality simply cannot explain the facts."13

A discrete space-time model supports the theoretical and experimental proof of spatial and temporal nonlocality (Bell’s Theorem). (See also John Archibald Wheeler's Delayed Choice Experiments)

As physicist Nick Herbert emphasized

"any correct model of reality has to incorporate explicit non-local connections. No local reality can explain the type of world we live in. Furthermore, since Bell's result is based on experimental facts, it is independent of whether quantum theory is correct or not."14

The idea that our physical system is flickering on and off carries with it many implications. For example, it might provide a framework by which to expect that any out-of-phase flickering will (constructively or destructively) interfere with our in-phase physicality, thus accounting for the experimentally observed results in the single-photon double-slit experiments.

As Oxford University physicist David Deutsch explained "single-particle interference phenomena unequivocally rule out the possibility that the tangible universe around is all that exists."15

According to physicist David Bohm, the nonlocal "common ground" from which all physical entities are continually unfolding is an implicate order which is everywhere and every-when interconnected, at-once. According to Bohm a nonlocal, implicate order together with our everyday physical reality (what Bohm called an explicate order) constituted a "single undivided whole, in which analysis into separately and independently existent parts has no fundamental status."16 (see also Bohm's Holomovement).

Similarly, according to physicist and astronomer Victor Mansfield we exist

"in a radically interconnected and interdependent world, one so essentially connected at a deep level that the interconnections are more fundamental, more real that the independent existence of the parts."17

A perception of wholeness was also voiced by one of the pioneers of quantum physics Erwin Schrödinger who wrote:

"There is obviously only one alternative, namely the unification of minds or consciousness. Their multiplicity is only apparent, in truth there is only one mind."18

and

"Inconceivable as it seems to ordinary reason, you—and all other conscious beings as such—are all in all. Hence this life of yours which you are living is not merely a piece of the entire universe, but is, in a certain sense, the whole."19

The idea of "wholeness" has parallels with those espoused by Zeno's teacher Parmenides -- that "the reality of the world is 'One Being': an unchanging, ungenerated, indestructible whole".

This perception of "undivided wholeness” or "Oneness" is echoed in various spiritual and (typically Eastern) religious traditions, such as ...

Hinduism "By understanding the Self, all this universe is known" (Upanishads);
Brahman-Atman Yoga in which "Brahman" (God) and "Atman" (Individual souls) are considered one;
Islam, "He who knows himself knows his lord," (Muhammad);
Confucianism, "Heaven, earth and human are of one body";
Zen Buddhism, "Look within, you are the Buddha";
Christianity, "The Kingdom of God is within you";
Jewish Kabbalah, "if one contemplates things in mystical meditation, everything is revealed as one."20

[the following material was also deleted by Wikipedians, but originally included by Steaphen Pirie]

Status of the paradoxes today

... with the discovery of quantum mechanics, those mathematical (infinite-series) solutions have now been shown to be incongruent with deeper physical (quantum) processes (see above section Are space and time infinitely divisible?). This is quite clearly demonstrated with the failure of calculus (and mathematics generally, as of late 2006) to accurately and reliably describe or predict the transition of quantum possibilities (as mapped by a wavefunction) to observed physical reality - what is generally known as the wave-function collapse.

In other words, as has been experimentally verifed (see above section Are space and time infinitely divisible?) as of late 2006, there is no known rule, description, equation or principle which can accurately and fully predict the movement of physical objects at small intervals or scales.

Furthermore, the proposed mathematical solutions using geometric series and calculus (see above) are reliant on the assumption of perfect (infinite) divisibility of space-time, an assumption that has (as of late 2006) not be experimentally or theoretically verified or proven.

In the quantum realm, Zeno's Paradoxes not only remain unresolved, but form the very foundations of science's "most successful physical theory in history"21 as is reflected in Heisenberg's Uncertainty Principle and Bohr's Principle of Complementarity).

These quantum paradoxes (along with Zeno's) have led some physicists to assert that they are a fundamental, irreducible feature of life, including the operation of intelligence. As Physicist David Bohm, Einstein's protégé explained:

The actual operation of intelligence is thus beyond the possibility of being determined or conditioned by factors that can be included in any knowable law ... Intelligence is thus not deducible or explainable on the basis of any branch of knowledge (e.g. physics or biology). Its origin is deeper and more inward than any knowable order that could describe it"22

Notes: * The foregoing sections "Are space and time infinitely divisble?" and "Status of the paradoxes today" are verbatim transcripts of content that was removed from the Wikipedian entry on Zeno's Paradoxes after many objections from various Wikipedian commentators.

Latest experimental developments supporting the granular nature of space-time (February 2009):

"According to Craig Hogan, a physicist at the Fermilab particle physics lab in Batavia, Illinois, GEO600 has stumbled upon the fundamental limit of space-time - the point where space-time stops behaving like the smooth continuum Einstein described and instead dissolves into "grains", just as a newspaper photograph dissolves into dots as you zoom in."

Experimental evidence and theoretical developments that invalidate Newtonian 'clockwork universe' models.

"Most working scientists hold fast to the concept of 'realism' - a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affect by actions in spacelike separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned."23

Additional developments revealing the deeper superpositioning of whole systems:

Quantum Physics Leaps Into The Visible World

"the structure they created still behaved in a quantum way — a structure you can see with the naked eye."

Quantum wonders: The Hamlet effect

"tests with larger and larger objects - including, recently, a resonating metal strip big enough to be seen under a microscope - seem to show that they really can be induced to adopt two states at once (Nature, vol 464, p 697)."

Quantum Mechanics at Work in Photosynthesis

"This and other recent discoveries have captured the attention of researchers for several reasons," says Scholes. "First, it means that quantum mechanical probability laws can prevail over the classical laws of kinetics in this complex biological system, even at normal temperatures. The energy can thereby flow efficiently by -- counter intuitively -- traversing several alternative paths through the antenna proteins simultaneously."

Untangling the Quantum Entanglement Behind Photosynthesis

"This is the first study to show that entanglement, perhaps the most distinctive property of quantum mechanical systems, is present across an entire light harvesting complex," says Mohan Sarovar, a post-doctoral researcher under UC Berkeley chemistry professor Birgitta Whaley at the Berkeley Center for Quantum Information and Computation. "While there have been prior investigations of entanglement in toy systems that were motivated by biology, this is the first instance in which entanglement has been examined and quantified in a real biological system."

1. It is ironic that modern scientists are failing to include the evidence of quantum physics in their world-views, as scientists generally view the Galilean era as having epitomised that failure to observe evidence, and accomodate those observations within a new world-view.
2. David Bohm, Wholeness and the Implicate Order, Routledge, London 1995, page 202
3. Richard Morris, Achilles in the quantum universe: the definitive history of infinity, Souvenir Press, London 1998, page 79. (Morris labelled the dilemma of the predicted annihilation of the universe, based on classical theory, "The Atomic Catastrophe").
4. Morris, page 80.
5. Morris, page 80.
6. Norman Friedman, The Hidden Domain: Home of the Quantum Wave Function, Nature’s Creative Source, The Woodbridge Group, Eugene OR 1997, page 165.
7. Friedman, page 164.6
8. Fred Alan Wolf, Parallel Universes, Paladin, London 1991, page 188.
9. Marcus Chown, “Random Reality,” New Scientist, 26 February, 2000, reporting on the theoretical work of physicists Reginald Cahill and Christopher Klinger.
10. Chown, New Scientist, 26 February, 2000.
11. Fred Alan Wolf, Taking the Quantum Leap, Harper & Row New York 1989, page 21.
12. New Scientist, Reed Business Information, Sydney, August 22, 1998.
13. Nick Herbert, Quantum Reality, Anchor Press/Doubleday, New York, 1985, page 51.
14. Nick Herbert, Quantum Reality, Anchor Press/Doubleday, New York, 1985, page 245.
15. David Deutsch, The Fabric of Reality, Penguin Books, London 1998, page 47.
16. David Bohm, Wholeness and the Implicate Order, Routledge, London 1995, page 174
17. Victor Mansfield, Synchronicity, science and soul-making, Chicago, 1995, Open Court, page 226
18. Erwin Schrödinger, What is Life? and Mind and Matter, Cambridge University Press, London, 1969, page 139
19. Deepak Chopra, Unconditional Life: Mastering the Forces That Shape Personal Reality, Bantam Books, New York, 1991, page 78 {quoting physicist Erwin Schrödinger}.
20. Prof. Amit Goswami, The Self-Aware Universe, G.P.Putnum's Sons, New York, 1995, p. 50
21. Paul Davies, J.R. Brown, The Ghost in the Atom, Cambridge University Press, Cambridge 1995, page 84. (Quoting Oxford University physicist, Dr David Deutsch)
22. David Bohm, Wholeness and the Implicate Order, Routledge, London 1995, page 52
23. Simon Gröblacher, Tomasz Paterek, Rainer Kaltenbaek, Caslav Brukneret, Marek Zukowski, Markus Aspelmeyer, Anton Zeilinger. An experimental test of non-local realism