A Functional Virtual Reality by Efthimios Harokopos

Efthimios,

SR was an imaginative and elegant solution to the ether 'problem' However if it is assumed that all matter and the vacuum is electrical as Hertz theorized, that allows for an absolute space and time with variable speed of light. And it greatly simplifies GR (which is now dependent on SR) to a question of local density or potential of space. Such space refracts geodesics like a mirage would.

In my original Beautiful Universe Theory (reference 48 in my present fqxi paper) I have proposed an experiment to test the ordered texture of the universe. It is based on a standing wave of strong electromagnetic radiation in vacuum. A second wave is shone normal to it. If it acts like a diffraction grating it means the vacuum has this crystal-like structure. Two parallel standing waves can produce a moire pattern, I suppose.

The iphone example is just to show how an instrument can be used to distort reality. You have a specific idea - maybe a sketch will help explain it further. I feel your sensor may be like a filter moving to intercept elements of the digital world - like a baleen whale swimming through a school of tiny fish? Cheers

Vladimir

Dear Sir,

You begin with the premise that relativity deals with analog and quantum theory deals with digital descriptions of the Universe. In our essay, we begin with the premise that there is no consistency between the various interpretations of quantum theory and that there is no unanimity about what constitutes reality. Each branch of quantum theory comes with its own interpretations, which sometimes contradict the other interpretations. Thus, when you talk about quantum theory, you must specify which interpretation you are referring to. Elsewhere in this contest, we have elaborately discussed relativity in our posts to show that it is a wrong description of facts and that Einstein's mathematics is wrong. In one of the posts under Mr. Castel's essay, we have quoted verbatim from Einstein's 30-06-1905 paper and refuted it beyond doubt. Having said this, we examine your essay:

The simplest answer to Zeno's paradox is that velocity is related to the mass of the body that is moving, the energy used (force applied) to move it and the total density of and the totality of the energy operating on the field. These are all mobile units against the back drop of the field that is static with reference to these. Middle of the distance is related to the frame of reference, which is relatively static with reference to the other mobile aspects. Thus, it is like comparing position and momentum. They do not commute. Hence there is no paradox, which is borne out of experience. While the middle of the distance is gradually reduced, the velocity is not reduced by the same proportion.

While Descartes analyzed the problem correctly, his conclusion was not as correct. Once a force is applied in a certain direction, it disturbs the medium. The elasticity of the medium (which we call the inertia of restoration, as it is generated after the application of a force and its magnitude is equal to the force - till the applied force overcomes it - but in the opposite direction), generates the opposite force. The effect of these forces appears as stress and strain. This is one of the factors responsible for motion. The other factor is related to density, which is related to the strength of local confinement. Confinement is not related to quarks only, but it has a macro equivalent that confines every particle. The only difference between these is that while at micro level, this property leads two particles to create of a third product as in a compound, in the macro world they couple like a mixture. Thus, it is comparatively easier to isolate and separate them. Descartes was right that "an active cause is required that must be in direct contact with the body in motion and that cause should not be in motion itself". After the application of initial force (active cause), the force ceases to operate and the body moves on inertia. We have explained all motion and evolution of all forces and particles based only on inertia without bringing in God. Regarding nature of time and the views of Leibnitz, kindly read our essay and the posts below the essays of Mr. Biermans, Mr. Perez and Mr. Castel.

In our essay we had given a different interpretation about Uncertainty relation and Superposition of states. We do not use any hypothesis that cannot be derived from fundamental principles. In our post below the essays of Mr. Castel, Mr. Perez and Mr. Klingman we have discussed about entanglement and its macro equivalent. Locality is the extent of confinement. It may or may not be physical. What is often overlooked is the fact that the so-called entanglement of photons does not extend infinitely, but collapses maximum within a few kilometers. The movement of light in different media shows that its velocity is not constant. Since density of space is the least from other observable localities, the velocity of light is greatest in observable space. Since space is not homogeneous, it is not a constant in space either.

Kindly do not consider this post as the denunciation of your thoughts or our bravado. We are deeply pained by how the scientific community is making merry at public expenses in chasing mirages in the name of scientific research, while technologists are toiling without the benefit of theory guiding them. Thus, we are flooded with many comforts of life that slowly poison the whole world and leading it towards disaster. Thus, kindly excuse us if our post appears to hurt your sentiments.

Regards,

basudeba

Dear Sir,

We have refuted the experimental basis of of relativity in our post below the essay of Mr. Castel. Since it is very long, we are not reproducing it here. You may refer to that and refute if you wish.

Since the various ontological commitments of the different interpretations of quantum theory are not fully integrable to a common approach, this aspects needs to be examined at length.

We do not want to know more about Zeno's paradox, we refute it. We have shown that the fundamental premise is false. Regarding velocity function, we cannot see how does it validate Zeno's paradox, but we have the answer, which we have discussed in our post below the essay of Mr. Perez and others.

Our only intention is to find out the truth and not score points. Kindly forgive us if any of our comments appear harsh. After all palatable benevolence is a rarity.

Regards,

basudeba.

My two favorite essays in this competition both have to do with virtual reality -- yours and Brian Whitworth's. Though the essays are only loosely related, because of differences in definition, the overarching idea that we cannot differentiate "reality" from "process" _in principle_ is one that deserves a lot more attention than it gets, IMO.

For myself, I long ago decided that metaphysical realism (Popper) is the correct substitute for "physical" notions. We can't know what's physical in any objective sense, yet we can know how to reconcile theory with result on something resembling Tarski's correspondence theory of truth, from which Popper drew much of his philosophy.

I think your proposed experiment may not be Popper falsifiable, however, because I don't see a way to show that the program potentially halts. To illustrate, consider how Popper demonstrated hypothesis testing by reformulating two number theory conjectures (still unproven) that are closely related: The Goldbach Conjecture and the Twin Primes Conjecture.*

Popper called the Goldbach Conjecture true if G: for every natural number x > 2, there exists at least one natural number y such that x y and (2 x) - y are both prime. The Twin Primes Conjecture is true if H: for every natural number x > 2, there exists at least one natural number y such that x y and (2 x) y are both prime.

Neither G nor H are verifiable, but G is falsifiable and H is not. Your proposal as I read it falls into the H category; i.e., I think at best you could only conclude that the quantum configuration space cannot be mapped onto the physical space (which in your case amounts to a universal Turing machine) without a nonlocal model. Bell's theorem already informs us of that. If Chaitin's number Omega is the halting probability of a universal Turing machine (and I think it is) then there is no possible falsfication. (G potentially halts when an iterated calculation hits a counterexample). If you want to read a more formalized treatment,my ICCS 2006 paper goes into it.

Thanks for a really thoughtful, well organized and well argued essay. (Though you might have found a spell checker would improve it.)

Tom

*K. Popper, 1983. _Realism and the Aim of Science_.

Efthimios,

The ingenuous Lieu and Hillman paper you cited proves that there is no evidence for Planck-scale fluctuations in time and space. So far so good, but then it uses that result to say the ether does not exist. This is a very weak conclusion hinging on the assumptions that probabilistic effects are an inherent property of nature and not merely the result of macroscopic measurements and theoretical interpretation of what may be a very different physical reality at the Planck-scale, presumably the ether granularity level. I have suggested in my my original 2005 Beautiful Universe paper on which I based the fqxi essay, how probability can emerge as diffusion within an exquisitely ordered ether. Such an ether may exist and not contradict Lieu's result.

Atomic interference has been demonstrated, even for molecules, (which incidentally I now conclude in my above paper may be the result of the interference of the gravitational fields surrounding the particles). But how would that give any data for or against a much finer supposed granularity of space? It will be interesting to read the Italian paper if you find it thanks. BTW here is an interesting demonstration of moire patterns it may inspire something!

Good luck. Vladimir

Dear Sir,

We are amused by your joke.

Millions of people have "seen" mirages. If we describe the truth about it, we are not wrong. The description of the desert, the water and the illusion that appears as water are all correct and real. It is only the misconception of those who believe that it is full of water, that is wrong. If someone wants to belief in the reality of mirage water, we can only advise him to go to that spot and find the truth for himself. We cannot help if someone regards superstition as more scientific than the results of physical experiments.

We hope you will enjoy this joke.

Regards,

basudeba.

Efthimios,

The point I was trying to make is that the halting probability of a program with choices among a continuous range of variable values is zero. That's the difference between the sign and the - sign in Popper's hypothesis testing criteria.

So even if your program is a finite state (Turing) machine with infinite processing capacity, there is no possibility that any finite state will return a discrete result from that continuous range of variable values in a bounded length of time even if the bound is infinity. In Popper's example, the reformulation of the twin primes conjecture, there is no possibility that at least one natural number, y, will not be prime given the terms x y and (2 x) y, because twin primes by definition are sums of successive primes, mod 2. Therefore, x y and (2 x) y are the same thing in this context -- there will always be a sum of successive odd primes, mod 2, whether the pairs are twins or not. We're not concerned with sorting twin primes from all other pairs, only with the characteristic that defines them, and we can't use that characteristic to prove that twin primes are infinite, because we already know by Euclid's proof that the prime sequence is infinite.

The potential proof of the Goldbach conjecture, on the other hand, is not bounded at infinity. We don't know beforehand (as we do with Euclid's proof) that an infinite number of prime pairs (P > 2) sum to an even integer -- that's what we're asked to prove. So why don't we use Goldbach to test our halting hypothesis? Problem is, as I showed in my ICCS 2006 paper, that even though the conjecture, as Popper established, is of the same kind as the twin primes conjecture, we have a pseudo-continuous range of variable values in the field of natural numbers R; i.e., R is of the same cardinality as the infinite prime sequence. The problem input is not bounded at infinity (it is algorithmically compressed), yet the output is. That's what makes the case mathematically interesting because the finite state maps to the infinite sequence, unlike the case of twin primes in which infinite sequence maps to infinite sequence (that is, both input and output are bounded at infinity in the sense that there is no sign change).

I presented (ICCS) an existence proof of a weakened Goldbach conjecture that removes the problem to a complex Hilbert space. The C* algebra is closed, giving us all the arithmetic functions we would use on R, plus the added dimension we need to establish a kind of congruence (mod 2) between complex numbers with zero imaginary part and the geometric nature of C as Euler described it. The proof could only be made constructive by quantum computing, because the domain would obviate the time dependence of purely classical computation, without sacrificing the continuous range of variable values.

See if you can get an expert in quantum computing to agree that a polynomial time solution is possible using this strategy and you might get the falsifiable experiment you seek. Obviously, I would be intersted in the outcome.

Good luck!

Tom

Dear Efthimios Harokopos,

I have just downloaded your essay. I will be looking for your support for:

"I will assume in this paper that reality is fundamentally digital and then based on a modern version of the old doctrine of Cartesian occasionalism I will sketch a model of the world that allows both uncertainty and autonomy within the limits of physical laws."

You begin with digital and sketch a model that allows for uncertainty. I assume that you mean that uncertainty frees us from a digital universe. I think that uncertainty does not free us from anything. If I have misunderstood your meaning, I will learn that from your essay. Thank you for participating.

James Putnam

Dear Efthymios (and all),

I wonder if you have a look to my essay. In it there is an idea of "granularity" of space and how virtuality fits in between or "reality" fits in between "granular" virtuality.

Giving the oportunity, I would like to make clear what I meant in my previous responce to your experiment proposed. Human brain as a huge local computer working with its trementous capacity and following the same rules usually gives various results although the inputs are the same. Because all these different results can not be the "expected" answer this is an indication that there is a limit in the local processing capability. Whether this is THE upper limit I think we will not in a position to ever know as we will never manifacture a machine better than our own brain for the simple reason that its results will be interpreted as faulties.

Regards, narsep (ioannis hadjidakis)

Very interesting article Mr Harkopos.

I was under the assumption that Zeno's paradoix was implicitly resolved with the advent of differential calculus and the idea of limits.

i.e. the sum of an infinite series may converge to a finite value, which in turn represents the limit of the series. The infinitesimal sum of dx(1/dx/dt) approaches a finite value over any abritrary interval on R, prodived dx/dt is continuos, smooth, and exists on the interval.

The erroneous assumption implicit in Zeno's paradox is that the sum of an infinite sries is always infinite.

Also, all of the variations of Zeno's Paradox also lack any self-consistency and self-referential integrity.

For example, the argument put forth that in order to travel an interval AD one must first travel half that interval AB, and so on, leads to obvious problems.

The lack of consistency arises when one states that once one reaches the first half-interval AB, another half-interval awaits and this progression continues indefinitely. One must therefore complete an infinite amount of actions and can never arrive at the end of the interval. The obvious problem here is, you managed to travel the first half-interval AB in a finite amount of actions without encountering infinity.That interval AB itself is arbitrary and contains an infinite number of half-intervals. Since the original intent is to show one can never reach the original interval AD in a finite umber of steps and actions, how is it you came to traverse the sub-interval AB? Based on the assumptions, an infinite number of actions would also have been required for that interval.

This should immediately tell one that the something is amiss with the idea of actions on intervals as they relate to the infinite.