Is Feasibility in Physics Limited by Fantasy Alone? by Cristian S. Calude and Karl Svozil

Lightspeed is negotiable via the Scharnhorst effect. Build a solid composed only of Casimir etalons, "Casimatter," with an alternating sector vacuum deposition rig. One sector continuously deposits 70 nm of aluminum (99% reflectance) onto a rotating ring, promptly covered by the next sector depositing 34 nm of 60:40 MgF2:LiF (thermal expansion mismatch of 0.1x10^(-6)/degree versus aluminum) transparent to 110 nm with refractive index 1.628. Round and round she goes. Cut out a section to obtain Casimatter, 37 wt-% zero point fluctuation-depleted fluoride alloy.

A paint can of finite volume and infinite surface area: sin(1/x) over (0,1] rotated about the x-axis. Filling is problematic absent paint originated in something infinitely smaller than atoms. Mathematics is not empirica, mathematics is not a science. Physics is limited by describing the observed universe. When mathematical hubris overwhelms empirical science, excrescences like string theory putrescently ooze into the world.

Mr. Calude,

Thank you for an interesting essay.

I'd like to point out, however, that Zeno's Achilles paradox is an artifact of a common misperception about the fundamental nature of time. I believe it can be successfully argued that what traditionally has been thought of and referred to as "the flow of time" is, in reality, nothing more and nothing less than the evolution of the physical universe. The race between Achilles and the turtle comprises but a small portion of that evolution. There simply is no "time" which is separate and distinct from the evolving configurations of the universe. Once this is recognized, the paradox vanishes. A fuller explanation and justification for this assertion may be found here. Some additional consequences of this idea may be found in the essay which I've submitted to this FQXi competition. I'd of course welcome your thoughts and comments on it.

Cristian,

I do not understand your statements:

"Of course, for the sake of principle, everybody is free to choose other "limiting speeds," thereby implicitly sacrificing the form invariant representation of the equations of motion in inertial frames dominated and stabilised by electromagnetic interactions. In this way it would also not be difficult to adopt special relativity to findings of higher signalling and travel speeds than the velocity of light in vacuum."

Do you mean to say that traveling at speeds higher than the speed of light is possible?

Cristian,

I like this thought provoking essay. Here is some more support for imagination and fantasy.

1. All our physical theories are based upon making measurements of the "universal" constants of nature. These include the gravitational constant G, Planck constant h, and the speed of light c.

2. These constants are only only known via measurement. We would like them to be true constants but they come with no guarantees about being constant. The best we can do is to continue making measurements to the best accuracy we can attain. [In my opinion the recent making the constant c a fixed number by definition is unfortunate. Now, it seems that we no longer need to measure this speed c because we know it by definition. This violates the spirit of science.]

3. The discovery and measurement of all the fundamental constants were made by "geniuses" who used imagination and fantasy as two of their tools. The constants we have today may not be as accurate as we think, and there are others that are yet to be undiscovered.

4. And thus what is possible is based upon imagination and fantasy.

Good Luck,

Don L.

Thank you all for your comments and questions. Here are some [partial] responses.

Uncle Al has referred to the Scharnhorst effect, which we mentioned by stating the possibility of a quantum field theoretic "index of refraction smaller than unity;" for a discussion about its feasibility, see also P. W. Milonni and K. Svozil, "Impossibility of measuring faster-than-light signaling by the Scharnhorst effect", Phys. Lett. B 248, 437-438 (1990), DOI:10.1016/0370-2693(90)90317-Y. This is only one conceivable possibility, among others, which might eventually push the speed of travel and communication beyond the speed of light barrier.

Florin Moldoveanu asked if we mean to say that traveling at speeds higher than the speed of light is possible. Here we mainly wanted to point out that Lorentz-type transformations follow from the assumption of the constancy of some "limiting speed;" be it light or another velocity. So far, there are no physical indications that we should assume limiting speeds greater than the velocity of light, but if these would be detected, relativity theory could be easily adopted to this new situation.

Don Limuti mentions that fixing the velocity of light c might be unfortunate. Indeed, as Asher Peres in Nature 312, 10 (1984) doi:10.1038/312010b0 pointed out, this leaves us with the issue of a possible frame (in)variance of the meter, and of length scales in general. As for now, there appears to be no problem with this issue; but as Petley & W.R.C. Rowley in Nature 312, 490 (1984) doi:10.1038/312490a0 point out, one could pragmatically change the definition of length, for example, should anisotropies of the velocity of light be detected experimentally.

Uncle Al,

While I did not manage to find your words excrescences and putrescently in my English Learner's Dictionary, I perhaps nonetheless correctly understood that you do not like mathematical hubris. Do you nonetheless accept mathematics as rigorously founded? If so, why? Are the votes for ultimate realism in physics given here not possibly correct?

Eckard Blumschein

Dear Professor Calude and Professor Svozil,

I like your essay, which is novel and creative, and on topic. I consider Professor's Calude book on constructive mathematics very good. I have some comments and questions about your essay.

The speed of light-based Lorentz invariance seems to be more than simply a convention suggested by Maxwell's equations. It is also related to the proper time of particles, and the experiments confirmed this. But I do not reject the possibility of superluminal speeds. Even a continuously accelerated penetration of light barrier may be possible, if the particles have somehow variable proper mass, going towards zero as the speed approaches that of light.

Assume that we have an accelerated Zeno-Turing machine, asymptotically approaching a time T.

- If the algorithm just switches a bool variable at each step, what value will the variable have after T?

It seems to me that, in order to have a result, either the Turing machine has to halt after a finite, although large, number of steps, or to converge to a definite limit, although the latter may require infinite storage capacity.

> "such a mechanism may compute incomputable functions, for example, the characteristic function of the halting problem"

This may be true. The characteristic function of the halting problem requires infinite storage, and browsing through the output allows us to access only a finite number of them in finite time.

To read an infinite output in a finite time will require an infinite mind. Having this capacity already makes us equivalent to an accelerated Zeno-Turing machine.

- Do you think we could use such a machine to provide a finite length derivation of the axiom of choice, and of the continuum hypothesis, from Zermelo-Frankel's axioms?

I agree that if Quantum Mechanics is indeterministic, or even if it is deterministic, but subject to delayed initial conditions (I give some details in my essay, and I will be honored if you would be interested to reading it), we may obtain unbiased randomness. Unbiased randomness seems indeed to be impossible to obtain from deterministic Turing machines. This may be used in constructing non-deterministic Turing machines, but these are known to be equivalent with the deterministic ones.

Congratulations for your essay, and success with this contest,

Cristi Stoica

Dear Mr Stoica,

Thank you for your comments and questions.

- If the algorithm just switches a bool variable at each step, what value will the variable have after T?

No, you cannot do this because of paradoxes like Thomson's lamp. We have two procedures describing what is the function computed by an accelerated Turing machine. See C.S.Calude and L. Staiger, A Note on Accelerated Turing Machines, CDMTCS Research Report 350, www.cs.auckland.ac.nz/CDMTCS/researchreports/350cris.pdf .

- Do you think we could use such a machine to provide a finite length derivation of the axiom of choice, and of the continuum hypothesis, from Zermelo-Frankel's axioms?

No, because both these axioms have been proved to be independent of ZF (by Goedel and Cohen).

Good luck for your essay!

Dear Professor Calude and Professor Svozil,

Thank you for your answers. I made a typo in my previous comment, which makes my question silly, and now I see it. It was my purpose to ask

"Do you think we could use such a machine to provide an infinite length derivation of the axiom of choice, and of the continuum hypothesis, from Zermelo-Frankel's axioms?" (or, of course, of their negations)

Of course I am aware of Godel's and Cohen's results, but I was thinking about infinite length proofs. We can choose one element of each set, in an infinite number of steps, at least for the case when we have a countable number of sets. The Zeno-Turing machine expands the possibilities related to the axiom of choice.

Best regards,

Cristi

Drs. Calude and Svozil,

You are by any standard two of the most interesting and useful active scientists around, up there along with Brukner and Zeilinger, Chaitin, Gisin, Suarez. I became hooked on Svozil years ago when I first read "Undecidability Everywhere?" in the Casti and Karlqvist collection, and it has only gotten better. Dr. Calude has not merely, among much else, computed 64 digits of an Omega and afforded the world a glimpse of randomness, but, with the excellent Mike Stay, also given us (nearly most recently) "From Heisenberg to Gödel via Chaitin". This is the cutting edge.

But for me this paper is a disappointment. I can almost see you guys (figuratively) sitting down at the kitchen table with a six pack and saying, "Okay, let's win this contest. What do you think they want?" and then giving it to them.

Dear Cristian and Karl,

I much enjoyed your essay in particular modeling using Turing state machines.

In my FQXi essay I suggest a computer model of the universe with atomic systems being bimodal Turing machines which alternate between modes. One mode conducts classical computation and the other mode quantum computation as a network. Have you or to your knowledge anyone else thought along those lines?

Sincerely,

George Schoenfelder

Thanks for your new comments.

Cristinel Stoica: Unfortunately we don't know the answer to your interesting question. ATMs can be useful for mathematics: with an ATM having no more than 5000 bits one can solve the Riemann Hypothesis or prove the Four Colour Theorem.

Nick Mann: Thank you for your nice (hardly deserved) comments about us and please accept our apology for disappointing you. Can you elaborate?

You have been almost right in your guess: we have started thinking about this essay at a table, not in a kitchen, but in a small restaurant in Vienna woods. We assume that anybody submitting an essay wishes to win, but this is hardly the point: it's more important to take this opportunity to share some ideas with an interested community.

George Schoenfelder: We haven't seen any elaboration of the ideas in your essay, but, of course, our knowledge is quite limited.

CC and KS,

Thanks for your thanks. But don't be modest. Your output is abnormally interesting. Dr. Svozil's obvious cultural reach helps a lot in his case. Quantum Artaud. White noise, Nature-Beauty and garden gnomes. One sits up, pays attention.

My kitchen table image may have been influenced by the story of GC, KS and AZ inventing the Quantum Omega in a coffee shop and I believe I toyed momentarily with that more elegant setting before my innate vulgarity took over.

What bothered me about this paper was the gee whiz tenor of (paraphrasing here) "This may (could, might) actually happen!" to which my automatic response was, "No, it actually may not." I know that KS has played around, fascinatingly, with similar material before (in the computational worlds paper, for example) but done so with, well, more restraint. Okay, to avoid getting into the highly technical issue of computational oracles -- which I don't claim I'm especially qualified to do anyway -- here's a collateral example.

You start right out with: "Nuclear science has made true the ancient alchemic dream of producing gold from other elements such as mercury through nuclear reactions." Putting aside the somewhat operatic quality of this, one has to say, well, yes and no. Actually the ancient alchemic dream, although of course they didn't realize it back then, was to become rich by getting around what today we're familiar with as the Second Law of Thermodynamics. I've never seen the monthly electric bill for a collider, but I'm willing to bet modern transmutation is a seriously unprofitable and entropy-producing enterprise and will always be unprofitable and seriously entropy-producing even if Dan Nocera and his MIT team succeed -- pray that they do -- in making comparatively cheap energy available via artificial photosynthesis. Just saw this:

"This historic anecdotal evidence suggests that what is considered tractable, operational and feasible depends on time. One could even extend speculations to the point where everything that is imaginable is also feasible."

Sure you can. In one of its forms it's called science fiction. You strap on your antigravitation pack and float off to work. But limits, gentlemen, limits. Even turning undecidability against itself in a cool judo move must discover a limit. Boundaries, barriers. As for re-programming the universe ...

Nick Mann: thanks for your explanation.

"But limits, gentlemen, limits. Even turning undecidability against itself in a cool judo move must discover a limit. Boundaries, barriers. As for re-programming the universe ... "

That's the point: limits are not forever.

It is indeed a joy to go through the freshness of your approach and a widening of landscape you have provided. I for one believe in an open approach, free from biases based on ' what we call established theories '. There is nothing in Physics yet that can be called the final truth. We simple work towards better and better relative truths. it is quite possible to have a sudden revision in our ideas.

i have already indicated in my own essay on this forum that there are questions about the so-called physical constants as well as about the constancy of the the strengths of the force fields from the start of the universe. It is my belief that things were so differnt at the the start and early universe that present day physical concepts can not hold true under those circumstances. Isolated measurements in cosmology have already indicated the velosity of light to be higher from cosmic objects as far back as 12 billion years back. Also. e/m ratios were measured to be differnt from spectroscopic studies in similarly placed cosmic objects. Physics worked out in the past few hundred years hold for more recent universe only. There is thus a great need to make cosmological measurements with greater accuracy and precision from objects placed way back in the early universe. If speed of light has varied our estimate for the age of the Universe will also get changed, as we assume c to be constant.

I believe in what Einstein said about Quantum Mechanics getting replaced some day by an alternate and better theory. A simple look at Cosmolgical facts observed thus far show that things may appear to be random in nature as our measuremental conclusions are based on large number of individual events only. There has been a clear indication of great depth of logic in the evolution of the Universe that 100 % randomness just can not be considered to be the truth about the physical universe. Then there are huge parts of the universe ruled by dark matter/energy that we hardly have understood. There is the question of primordial matter that must have given rise to both the dark & visible matter. We understand the small 4% part and then say that bark matter is non-baryonic in nature, preventing any study by us located in the visible part. Thus, there are some mysteries we need to resolve still before we can reach hurriedly about the holiness of the concepts evovled thus far and physics based on the same. I totally agree with your essay questioning such 'fact'. If the universe appears infinte we humans on this earth must have possibilities for space travel , with speeds far exceeding the the value of c. It is even possible, as conjectured by me, that if a space vehicle has means to distort the surrounding space, contracting ahead and expanding behind, such a inhomogeneity in space can permit velocities far higher than 'c'. But such technologies are apparently not on the scene yet, but surely can evolve in the times to come if we keep an open mind and freedom of thought,free from biases.Nothing should distract us from possibilities that open up when our minds are quiet, unbiased and permit freedom of thought! After all, the concepts evolve in the human mind, as all our physical, mental and consciousness sensers start to work with the full potential>

Sorry for the long comments that i have put on your nice essay. perhaps you find it hard to respond o/c shortage of time. Otherwise, i would love to have the wisdom of your responnse in view of your inspiring essay.

Dear Cristian S. Calude,

As quantum indeterminacy evolves from complementarity, the multi-field interactions of travelling wave in a spin matrix may have similarities with the phenomenology of neutrino oscillations. As the relative unit of refractive index is not absolute, there is probability of superluminal speed of travel in adaptations with neutrino oscillations.

In context with the causally of consequence of collision, I think all matters are conjugated cluster-matters with a coherent and an incoherent cluster-matters that are synchronized in rotations as gear wheels. When there is collision of such conjugated cluster-matters, there is disjunction and re-conjugation with different counter parts at the detectors that observer; in that the actions are representational by correlation variables in incidence geometry. In this case indeterminism from randomness is transformational by correlation probabilities, in that the quantum numbers and unitary transformations are valid. This case differ as it requires more sensor purity in that a domain of negative sensing neighbourhood is much importance for source sensing rather than correlating all observables for an event. If there are deterministic observables, then there is phenomenological probability describable for travel through wormholes, may be from sphere to sphere surfaces rather than from open to open surfaces.

With this, Turing is more appropriate rather than time travel, in that it defines functions for multiple interactions on travel as neutrino oscillations and this indeed, 'reprogramming to observe universe' rather than 'reprogramming of the universe'; it's good, thanking you ..

With best wishes,

Jayakar