Flowing with a Frozen River by Cristinel Stoica

Dear anonymous,

Thank you for reading my paper and for the interest you show.

"4 out of 5 sources in your essay are papers you wrote"

My first draft of this essay had 7500 words, and contained about 30 referenced to peer reviewed papers of various authors. I wanted to present as much as I can about my work related to the subject, but in the meanwhile I wanted to have under 5000 words. During the process of compression, the style become very laconic, some of the arguments were omitted, together with most of the references. Though, for these details I insisted to keep the references to my papers, where I provide details and the omitted references.

"Are the papers peer reviewed?"

Although I performed my research in many years, and I have many drafts, it is only this autumn when I started to write them as articles, and posted at an eprint archive. The oldest of them, "Smooth Quantum Mechanics", is presently under peer review at a review of Physics. I intend as soon as possible to submit to various reviews the other articles, but lately I was concerned most of the time with this essay.

"What is the thesis of your essay? Is it TOE?"

My essay is not about TOE (it is much more modest). One section, based on one of my papers, introduces the World Theory, which, as I wrote in the essay, is a framework for dealing with aspects related to time, space, physical laws and causality, until the TOE will be discovered. I try to make the least hypotheses, such that any current candidate theory to fit the definition of the mathematical structure which I named "world". I used this general picture to discuss more formal about time and causality, without knowing exactly the final form of the TOE. On the other hand, I used also more particular results from QM and Relativity to construct an image of time, of how we can understand the time flow in a block universe, and whether or not there is a place for free-will, and how can we test this experimentally.

Best regards,

Cristi Stoica

Dear Matt,

I appreciate your kind comments, thank you.

Best regards,

Cristi Stoica

Dear SW,

Thank you for being interest in my essay.

"Your essay does not show how the change is possible in the frozen block universe. You just assume it."

The frozen block contains time evolution, in the following way (which is not the point of my essay, it is a well-known picture which I assumed in the essay already understood). Consider it a 4-dimensional spacetime as in relativity. The history of an observer is represented by a timelike curve (I employ here the word "observer" in its meaning in relativity). We can determine a transversal spacelike surface at any point of the timelike curve. With care, we can make a proper choice of the spacelike hypersurfaces transversal to the observer's timelike curve. Let us for the moment allow us to use a meta-time in the description, just for explaining the ideas, then we will throw it away. If we move along the timelike curve in the spacetime, the restrictions of the fields at each spacelike hypersurface we constructed, will be different. Yet, they will not differ much between two spacelike hypersurfaces that are close one another. Like in a movie, when we replace one frame with another and obtain the illusion of change, we can do this in the spacetime. When we move along the timelike curve, we take successive 3-d slices, and the restrictions of the field will be different. We can interpret this as changes in the fields.

One step next is to understand that every physical quantity is such a field. The description of a field in space, changing in time, contains the same information as the 4-d description, without change. To the 4-d description we have to add the observer, because the changing picture depends on the observer. Any physical information contained in the 3d flowing view is equivalent to an information in the 4d+observer frozen view, and reciprocally. Given this equivalence, it follows that the change is also contained, if we view it as a "parametric change" - moving along the observer's timelike curve provides the illusion of change. Like when you move the pickup needle from one place of the disk to another, you enter a different time in the song.

Now, it is the time to drop the meta-time we used. I used it for explanatory purposes - only to show that the same information can be contained in the block spacetime view.

How can we drop the meta-time? Let us recall that the observer (as the one who perceives the flow of time) has a mind, which is manifested physically as a brain. For simplicity, we can think at a computer, not necessarily a brain. Each thought process is a succession of mind states, like each computation is a succession of the states of the computer. There is an equivalent representation as a succession of states. If we have on each spacelike slice a state of the brain, arranged properly, we have a 4d "movie of the thought". All the information concerning the thinking process can be represented in the frozen spacetime. From "outside" the spacetime there is no change. A changing observer can be viewed as a succession of instantaneous observers, one at each instant. Each instantaneous observer has a mind state which contains thoughts about the previous states, in a static way. There is no change, only that each instantaneous observer identifies himself as the flowing observer. We are made from a long line of instantaneous observers.

I think that this is the common image of the idea of block or frozen spacetime.

Yet, we can use the same ideas to representing also classical mechanics, nonrelativistic quantum mechanics, etc. In relativity, there is also a geometric relation between space and time, and this provided a supplementary reason for employing the block universe image. Also, in deterministic theories, it is easier to accept the block universe than in the indeterministic, yet we can use the block view also for them, branching or not. Moreover, my solution to the discontinuity of the wavefunction collapse provides another view: a deterministic universe, in which the initial conditions are yet-to-be-determined. This is an alternative to indeterminism, which provides the same liberty for the free-will. Yet, neither indeterminism, nor delayed initial conditions don't guarantee the free-will. I argue in my essay that the free-will cannot be thought as following in a deterministic way from the past, nor as simple randomness. I propose a version of free-will, and an experiment to test it.

So yes, I don't give many arguments for the well-known picture presented above, since it was not the central point of my essay.

Best wishes,

Cristi Stoica

Christi Stoica,

You are eloquently and polite enough as to enough as to meet the public taste. I read your essay in order to check to what extent you are aware of possible mistakes at the very basics.

While an other leading candidate did not answer a seemingly

simple question of mine, you did not even mention a complex Ansatz. To accept or refute the main point of my essay would require serious and unbiased reasoning.

What about the word frozen in mathematics, you might know Fraenkel 1923.

I realized that you mentioned non-Hausdorff in connection. with smooth. So far, I did not exclude to be the almost only one who disdains Cantor's paradise.

If you need someone who supports your PhD program, I recommend John Baez. I doubt however he will appreciate your thought experiment instead of a little bit more mathematical background.

Good luck,

Eckard Blumschein

Dear anonymous who wrote "anonymously written on Dec. 6, 2008 @ 06:51 GMT",

You can check the submission date of the articles referenced in my essay at the eprint archive between 19-23 November 2008. Please acknowledge that there are two weeks since then, and not publishing them in such a short time does not mean that they are not publishable. I wrote them very recently, to backup my essay, because I knew that I cannot explain everything in 5000 words. Since it is allowed to have new and unpublished ideas at this contest, I took this opportunity to submit some of my ideas to this jury and contestants for peer reviewing.

One of them is a second version, the first one dating from the end of September, when I submitted it to a respectable physical journal. Following the suggestions of the reviewer, I obtained the second version, which is cited in the essay. Now I wait the reviewer's comments on the second version. The editor informed me that in the case of that journal it takes 3-6 months for a decision.

You are just rejecting on general basis my ideas, instead of pointing out where are the mistakes. I acknowledge that I may have some errors, and your help will be valuable. On the other hand, you cannot use the principle of peer-reviewing to reject new ideas, because any new idea is, initially, not peer reviewed.

Best regards,

Cristi Stoica

Dear Eckard Blumschein,

Thank you for pointing out a potential error. Fortunately, it was not an error, as you can find exemplified in some differential geometry books. Please refer to the following entries:

http://en.wikipedia.org/wiki/Non-Hausdorff http://www.dpmms.cam.ac.uk/~md384/examplesheet1.pdf

In your defense, I may say that perhaps the name Hausdorff made you thinking at fractal sets, hence the confusion.

I appreciate your effort,

Best regards,

Cristi Stoica

Comparison between a computer and a brain is the point. If you prove that the brain works as a computer, you prove that the Time does exist and that Algebraic Geometry or Empiricism method is Science.

But if the brain has nothing to do with the binary computation of informations, you are entirely wrong.

Dear F. Le Rouge,

You referred to the final part of my essay. I do not claim that the brain is entirely equivalent to a computer. What I said is that, assuming that someday in the future this equivalence will be proven, then this will rule out the free-will as is usually understood, by reducing all our decisions to either determinism, or randomness. But I say further that, even in these hard conditions, there exists a last possibility for the free-will, and I propose an experiment for verifying this hypothesis. I do not claim that free-will exists or not, nor that the brain is, or is not, a computer, since I don't know how to prove such claims. I just propose a hypothesis and an experiment.

Cristi Stoica

Dear Cristi Stoica,

You are formally correct. Perhaps you nonetheless did not get my point because of lacking time for reading my essay

"Let's benefit from special mathematics for elapsed time".

I am mainly pointing to improper interpretation of complex domains that possibly are to blame for serious mistakes.

The reason for me to read Hausdorff's 1914 textbook "Grundzuege der Mengenlehre" was to find the reason for unresolved mathematical questions that relate to the notions point (something that does not have parts) and continuum (something every part of which has parts). An integral transform maps points on continua and vice versa.

I know that Hausdorff admittedly followed Cantor's naive set theory, and I guess having found the questionable point: The Peirce-continuous "real" line is ordered but not numerically metrizable.

Aren't Buridan's donkey and Schroedinger's cat both based on the same illusion? You certainly know that topology is unable to perform a symmetrical cut.

When I asked mathematicians how to deal with t=0 between past and future, I got as many mutually excluding suggestions as possible. I hate unfounded arbitrary definitions.

As a way out I am suggesting to understand the reals as useful hybrids but what I would like to call irreal numbers the non-Dedekind union of irrationals and non-canonically embedded rationals.

I am arguing that embedding into irrationals makes rationals likewise unapproachable "indiscrete" numbers being lumped together in indiscrete topology. Neither past not future time lacks the nil because points do not have an extension.

Eckard Blumschein

Dear reader,

In Dec. 2, 2008 @ 08:28 GMT I wrote several posts presenting very briefly the main points of my essay: a mathematical framework for foundational discussions (the World Theory), the Strong Causality Principle, the Smooth Quantum Mechanics and delayed initial conditions, minds flowing in the Frozen River, and a Free-Will Hypothesis.

In this essay, I intended to put together several ideas, because I think that, together, they propose an interesting view about the nature of time. The drawback was that I was compelled to present too briefly my ideas, as well as the connection between them, since I wanted to respect the 5000 words rule.

Because I don't know how will be the final theory, I tried to be as general as I could, when discussing the problems related to time, space, causality, and physical law. It is difficult to maintain generality when discuss alternative incompatible viewpoints, therefore I cooked up a mathematical structure named World, which is consistent, but general enough. In this structure, spacetime is a topological manifold, and the physical law is a sheaf (think of it as a collection of possible local solutions) over this spacetime. The matter field is a global section of the law sheaf. To determine the matter field, we need something like initial/boundary conditions. I abstract (in the cited article about World Theory) the conditions imposed both by the physical laws and the observations in such a manner that it become clear that the initial instant to which we apply an initial condition is not absolute.

On the other hand, trying to find an alternative to the discontinuity of the wavefunction collapse in Quantum Mechanics, I constructed a mechanism that uses this "relativity of the initial time" used in an initial condition. My explanation recover the unitary evolution at a higher level, while maintaining the appearance of the collapse, but replaces the discontinuous jump with a set of delayed initial conditions. This mechanism becomes clear when we account for the entanglement of the observed system with the preparation device.

As a consequence of the Smooth Quantum Mechanics, the matter field is determined gradually by each measurement, but we are not able to access the entire set of delayed initial conditions. We collect them in a "registry", which, being incomplete, can be employed only for probabilistic predictions. Therefore, even though the wavefunction evolves deterministically, it appears to us as collapsing, and as having a probabilistic behavior.

Returning to the mathematical structure named world, in the Smooth Quantum Mechanics we see that the matter field may be never determined, it is only a solution of the evolution equation and an incomplete registry of delayed initial conditions.

On the other hand, it seems that the observer, by making a choice of the observable, can impose a delayed initial condition, determining incompletely determined parts of the initial conditions in the past. The global solution don't preexist, only the set of possible solutions, which is gradually reduced by the observations, and the observer's choices of the observables.

This suggests the possibility that the free-will manifests in this deterministic world by the freedom to choose yet-to-be-determined initial conditions. This mechanism, if it exists, works also within the standard Quantum Mechanics, only that in the smooth version is more dramatic. In order to test this free-will hypothesis, I propose an experiment, which relies strongly on our progress in science and technology. Therefore, I suggest waiting until we can perform this experiment, or find another proof, before drawing a final conclusion about the free-will.

All the best,

Cristi Stoica

Congratulations on your essay, Cristi! What you wrote proves that this is your concern for a long time and this contest was only an opportunity to make your ideas more known than before. I am glad you were given this possibility and I congratulate you for your diplomacy and open spirit proven during discussions about your essay! All the best to you, too

Dear Cristi:

I have taken a look at your article; but unfortunately, I don't have the background vocabulary to follow your reasoning. Sorry about that. I hope that you are able to progress with good results, in the future.

Take care,

Ken.

Dear Ken,

Thank you for being interested in reading my essay, and for your wishes.

Best regards,

Cristi Stoica

Dear Florina,

Thank you for your appreciation, and good luck with your research and explorations.

Best wishes,

Cristi Stoica

Dear Cristi Stoica,

One of many questions in the essay "Flowing with a Frozen River": is time discrete, or continuous? Or in other words: whether time has the quantum nature? In the essay "The Theory of Time, Space and Gravitation" the time is created by the motion, and properties of the motion define properties of time. Therefore, discrete character of the motion in principle can form discrete time. But, all it is not so simple. The continuous motion forms the causal effect, which we observe, and the inertial mass here plays a large role. The causal effect in turn forms the arrow of time. In case of the discrete motion the causal effect is not obvious. The moving material point actually disappears in one spatial cell and afresh appears in the next cell. In this case all Universe periodically disappears and again is born in a somewhat changed form. Each material point should be in the separate cell of space some minimal time. Here we observe the second problem: it is impossible to find a physical meaning to minimal time, when any motion, i.e. any change of a state of the material system is absent. The third problem consists in necessity of renunciation of laws of conservation of energy and momentum because of the contradiction with the discrete time and discrete motion. Acceptance of the minimal space and minimal time can be caused by necessity to exclude infinitely large and infinitesimal values, for example, the infinitesimal sizes of the electron and infinitely large potential energy of the electromagnetic field of the electron. But, for this purpose there are other solutions (see essay http://www.fqxi.org/community/forum/topic/331). Thus, contrary to the general tendency to quantize all, we accept the continuous space, continuous time and continuous motion because of absence of any contradictions.

Yours faithfully

Robert Sadykov

Dear Cristi,

Your essay is very well written. Given your interpretation of block time (the standard one), however, I don't think your argument relating to frozen time flowing makes sense. Saying that time merely seems to flow (or if one doesn't believe in time, that motion and change merely seem to happen) because we also think in frozen instants, doesn't add up, because it doesn't explain how such thoughts (or "states") are able to progress from one frozen instant to the next. That is, based on such an interpretation of gr and block time, all motion and change - including neural processes or continuous algorithms running on a computer - would not be possible.

I think the problem lays in your and the standard interpretation's assumption of the physical existence of instants, spatial points, and space-time points (and as such, time, space, and space-time). Although I believe that we do think within the context of frozen instants, such things have no foundation in Nature. As soon as one recognizes this, motion and change (including neural processes) suddenly become possible, and can be seen to be completely compatible with gr and the block view, with all times (those shown by a clock) sharing equal footing.

Best wishes

Peter

Dear Robert,

Thank you for reading my essay, and for the comment. Your essay contains interesting viewpoint, and arguments for the continuity of spacetime. In my essay, I introduced a general framework in which I tried to avoid the assumption regarding continuity or discreteness, because I wanted to deal on the same footing with a large class of theories, including the continuous and discrete ones.

Respectfully,

Cristi Stoica

Dear Peter,

I appreciate that you read and comment my essay. I observe that the most discussed aspect on my thread is the one of block spacetime, which is not one of the central points of my essay. You may have read my two posts detailing the standard view, and you may have observed that in my essay I introduced more general ideas of block world. Anyway, returning to your remark about the standard block spacetime, I want to mention that the "frozen instants" are related by the topology and the equations, which provide the processes required. However, if we insist to consider that the "frozen instants" contain (referring to point-like particles) only the positions of the particle, we cannot, indeed, link the successive states. But, as soon as we remember to include also the velocities or the momenta, everything becomes obvious. Perhaps in your essay, considering its name, you provide more arguments for your affirmations, and I look forward to read it.

Best regards,

Cristi Stoica

In response to questions regarding Essay Contest voting:

Thanks for giving some thought to some general voting issues in this Essay Contest, which as you can imagine are tricky. In answer to the issues raised, which concern ALL ESSAYS, we would advise all entrants that the provenance of all votes is being recorded. These records for potential essay contest winners will, after voting closes, be carefully examined for consistency with the stated rules that (a) one should not vote for oneself, (b) members or authors can vote for three essays as a restricted voter, and (c) a given author can only submit one essay. Non-adherence to these rules may be grounds for disqualifying votes and/or essays from consideration.

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K Rajanna

FQXi