Flowing with a Frozen River by Cristinel Stoica

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Essay Abstract

For discussing foundational questions, like the nature of time, we need a framework. Ideally, this would be provided by a Theory of Everything. Until the discovery of TOE, I propose a mathematical structure that can be used to represent theories of Physics in a unitary framework, similarly to the way in which the group actions represent various geometries in the Erlangen program. This construction extracts essential aspects of various theories, concerning the space, time, physical law, and causality. I introduce a causal structure and apply it to models of time and time travel. I propose an argument, based on causality, for the initial singularity of the Universe, and for the physical reality of gauge potentials (all three related in an unexpected way). Then, I discuss a new version of Quantum Mechanics, that replaces the discontinuous wavefunction collapse with delayed initial conditions, and has significant implications on time and causality. After presenting the arrows of time as emergent phenomena, I discuss the mind and its perception of time as flowing, in the context of the block spacetime. Then, I apply the previous observations to analyze the possibility of free-will. I propose a hypothesis about the free-will, and a crucial experiment that can confirm or reject it.

Author Bio

Cristi Stoica has a master's degree in Differential Geometry with applications in Physics, and is enrolled in a doctoral program on the Fiber Bundle Geometry. He works as a computer programmer in the field of Computational Geometry. The present essay is based on the author's independent research.

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Hello Cristi,

Loved your essay!

Love your introduction which establishes the duality of time--"As our understanding of the Universe increases, the

time becomes more and more geometric. Initially be-

ing only a parameter in the equations of Mathematical

Physics, it proved to be more related to the space than we

expected, mixing together in the structure named space-

time. With the Theory of Relativity, these geometric

aspects started to suggest the image of a frozen time {

the block time { named frozen river" by Brian Greene.

On the other hand, we have the acute feeling that the

time is °owing, that we are subjects experiencing this

°ow, and that we are free to choose our experiences. If

the time is really frozen, then why do we perceive it as

°owing? Is the frozen time idea compatible with the

indeterminism? Is Physics compatible with the idea of

free-will? But what is this free-will? I will present some

thoughts about these questions, mainly based on my re-

search [1{4]."

This duality is resolved, along with all the other dualities, via Moving Dimensions Theory.

The block universe is a human construct, and the scene of the crime, where they froze the river of time, is where physicists glossed over the fact that time is not the fourth dimension, but rather x4=ict.

I take it you did not encounter MDT before writing your essay: http://fqxi.org/community/forum/topic/238 --Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken

"In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth dimension, but rather he wrote x4 = ict. The fourth dimension is not time, but ict. Despite this, prominent physicists have oft equated time and the fourth dimension, leading to un-resolvable paradoxes and confusion regarding time's physical nature, as physicists mistakenly projected properties of the three spatial dimensions onto a time dimension, resulting in curious concepts including frozen time and block universes in which the past and future are omni-present, thusly denying free will, while implying the possibility of time travel into the past, which visitors from the future have yet to verify. Beginning with the postulate that time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c, diverse phenomena from relativity, quantum mechanics, and statistical mechanics are accounted for. Time dilation, the equivalence of mass and energy, nonlocality, wave-particle duality, and entropy are shown to arise from a common, deeper physical reality expressed with dx4/dt=ic. This postulate and equation, from which Einstein's relativity is derived, presents a fundamental model accounting for the emergence of time, the constant velocity of light, the fact that the maximum velocity is c, and the fact that c is independent of the velocity of the source, as photons are but matter surfing a fourth expanding dimension. In general relativity, Einstein showed that the dimensions themselves could bend, curve, and move. The present theory extends this principle, postulating that the fourth dimension is moving independently of the three spatial dimensions, distributing locality and fathering time. This physical model underlies and accounts for time in quantum mechanics, relativity, and statistical mechanics, as well as entropy, the universe's expansion, and time's arrows and assyemtries."

--http://fqxi.org/community/forum/topic/238

MDT allows the block universe (a human construct/tool) to coexist peacefully with time and all its arrows and assymetries, which are physically real.

Hope MDT helps you in your future research/contemplations!

You write, "The thermodynamic time arrow is an emergent law. It does not arise from the physical laws, rather from the highly improbable initial conditions of the Universe. The Universe evolves naturally to more probable states, and

entropy increases."

MDT is the mechanism that powers entropy.

Best,

Dr. E :)

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Hello Dr. E,

I am glad that you are interested in my research.

Thank you for your nice words. I look forward to read your essay.

Regards,

Cristi

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Dear Cristi,

Your entry was so late , with many alte comers, really didn't give time to old timers in the contest to view your contribution. In fact, came to your site after seeing your good last post on the essay of P.N. Tiwari.

Looking at your background, you have done a good job. But your view is restricted too like that of many in this competition, confined to computation and geometry, your field of interest and activity. The nature of Time is a very broad theme, encompassing the mysteries of nature, the working of human mind as a scientist and much more. As the competition closes, not much can be done to discuss your contribution in specific details. Any way, i commend your effort as one of the youngsters who have joined the competition. Best of luck.

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Dear Narendra,

Thank you for your kind thoughts. About entering late in the contest, I will do my best to read and appreciate all the essays, to learn from them, and from the comments I will receive.

Best wishes,

Cristi Stoica

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Dear Cristi,

Very best wishes to you. It certainly will be educative for you to go through the essays but also the posts on them. Yoour own essay and posts on other essays are the contributions i appreciate. Wish you all success in your future career!

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Dear Narendra,

You said "your view is restricted [...], confined to computation and geometry, your field of interest and activity".

But is there anything else but computation and geometry?

Surely I'm joking. Although I trained myself to let aside my ego, and to learn from critical comments, I have to answer to this observation, because it may hurt the way my work is perceived.

As a scientist, I try to formalize my ideas. Let me explain this in your reference frame (I saw that in your essay you quote Patanjali).

According to him, the knowledge comes from 1) experience, 2) authorized persons, and 3) logical deduction. Experience is a) subjective or b) objective. In constructing a theory, there are some steps. The first is the creation of the hypothesis, which is based mostly on 1) and 2). Then, the theory must be formalized, corresponding to step 3). We then submit it to peers, which try mostly to test our theory by applying 1 b) (objective experience), and 3) (logical deduction). This is according to Karl Popper; Thomas Kuhn on the other hand, suggests that 2) (which extend to authorized paradigms) still weights much in the acceptance of new theories.

The differential geometry and computation are not a limitation. I used them at purpose, to formalize my ideas. These ideas go beyond geometry and computation, and are not limited by them, exactly as Patanjali's ideas are not limited by the Sanskrit language.

Cristi Stoica

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- As your 'Geometry' is just computation or information (see Gunn Quznetsov on this forum) you could as well say 'Is there anything else than computation?' Cristi Stoica.

- I see you have a master in 'differential Geometry': God damn it! What is DIFFERENTIAL Geometry? This is Arithmetics! The problem of Geometry is: 'Where is the Unity of matter -sphera for instance- coming from?

The arrow of Time and the wave function are not 'emergent phenomena' as you say, they are just very very old ideas that are puting you under water.

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Dear F. Le Rouge,

Thanks for your observations.

I am not using the term "emergence" in a fundamentally reductionistic way. The reductionist "emergence" said that "this" occurred from "that" and it is caused by "that" only. The sense I use is that "this" is constructed over "that" by adding only additional rules, and no additional elementary objects. I wouldn't say that music can be reduced to musical notes, for instance.

If you want to be reductionist in this manner, you may say "God damn it! What is DIFFERENTIAL Geometry? This is Arithmetics!". But you are wrong. DG is arithmetic at most as we are a bunch of atoms.

Best wishes,

Cristi Stoica

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Dear Cristi,

I have enjoyed going through your essay. When i used the term 'restricted', it was not a criticism of your approach.It is just that one needs to keep the broadest vision while contemplating about a problem. his helps one get to know the dominating or most significant factors that are playing the role in a process we wish to understand. Variables are to be kept minimum but at the same time we need to forget not any variable that may be significant. To me Time is an important concept , as the entire Physics is all about motion of one or the other kind. The change of position with time just can't be replaced with any other alternative. However, my queries arisere. its linearity and scaling! What may happen if the 'c' is not a constant'. The realtion x4 = ict then assumes special significance. Similarly, E = mc^2 faces questions re. the concept of Energy. In my essay, i have discussed the early universe and the consequence of marked shift of the value of 'c' to be on higher side for the light coming from source 12 billion years away! How would your attempt take care of such possibilities?

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Dear Narendra,

Thank you for reading my essay, and for clarifying your position. I will post on your discussion thread my answer to the interesting question you raise about the speed of light, since it is not related to my essay, but rather to your inquiries.

Best wishes,

Cristi Stoica

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This is about Music indeed. Symmetry, Infinity and Differential are coming from music and sound phenomenon.

Music as well as the Looney Tunes gives the illusion of Time and the binary structure of Algebraic Geometry is included. If I was not afraid by your irony I would tell you that Riemann's non-Euclidian 'Geometry' as he says makes me think about a saxophone.

The opposition between Geometry and Algebraic Geometry was still there in Greek Science six centuries B.-C. and may be before. And when Algebraic Geometry triumphated in History on Geometry, it was always linked with the triumph of Music. European XVIIth is a good recent example of that.

Although he is living in a musical epoch, P. Picasso after the event can be seen as a materialist and a geometrician against subtle poetry of some impressionist painters before him.

About 'free-will' idea at least that you seem to estimate as much as I do: what do you think about G. Vico ('New Science' - 1725) opinion? As History is made by people contrary to Nature that is made by God, Vico is suggesting to study Science History to avoid misunderstandings. I personally think that this immersed idea is not that bad.

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Dear Cristinel,

I think that mathematics is an increasingly crucial tool in the human aim of understands the universe. This is much truer because other more physical methods such as observation and experimentation are more difficult to perform each time; men are reaching its limits in these aspects. This is one of the arguments I take in my essay to argue on the convenience of a machine such as "simuverses" for calculating places, times and events not reachable by other means. Then, to have a deep knowledge of physic phenomena and to have the appropriated mathematical tool will be both invaluable and unavoidable.

Yours seems to be an in deep effort to manage an ideal tool. I am not able to criticize it more technically.

Congrats,

Venerando.

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Dear Venerando,

Thanks for your beautiful comments. Mathematics is, in a way, similar to your passion, Science-Fiction. In both, the author takes several ideas, and then develops them to the extreme, constructing, in the imagination, an entire world, with its own logic. Only that Science-Fiction has the difficult task to express important and difficult problems to the reader, to ask deep questions, under an entertaining form. Both Science-Fiction and mathematics can construct worlds that someday will become real, or that may remain forever a dream.

Best regards,

Cristi Stoica

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Noroc, Cristi! Felicitari pt. eseu, l-am citit cu mare interes.

"The thermodynamic time arrow is an emergent law. It doesn not arise from the physical laws, rather from the highlt improbable initial conditions of the Universe. The Universe evolves naturally to more probable states, and entropy increases.

The thermodynamic arrow is at the origin of the psychological time arrow: remembering the past is a thermodynamically irreversible process."

Excellent passage. Indeed, evolution as we understand it, is nothing but the direction towards probable states. It's either that or "nothing".

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Dear Bogdan,

Thank you for your interest in reading my essay, and for the appreciation. I look forward to read yours too.

Good luck,

Cristi Stoica

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Dear reader,

I decided to add several observations about the ideas in my essay on this forum. I was motivated by the impression that on these posts is preferred a particular subject, which is not the main idea of my article, being just a more or less known part of my larger argumentation. I will not blame the reader for missing my main points, because I am fully aware that it is my responsibility to make them clear. I tried in this essay to concentrate some of my ideas in less than 5000 words, which was a difficult task. Although this contest is a good opportunity to propose them, I don't consider appropriate to spread my ideas on other contestant's threads. These threads should be for discussing other contestants' ideas. My purpose is to submit these ideas to the critical review of other researchers, and this is a good opportunity for doing so.

I will use my own thread to present them.

Cristi Stoica

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1. A mathematical framework for foundational discussions

Discussing about foundational things like time, space, physical law, causality, requires a framework, for example a theory of everything. In waiting for such a ToE, I propose a mathematical structure which I consider general enough to support such discussions and reasoning, without assuming the final form of the ToE. We can discuss at an abstract level, but in concrete terms, which, in my attempt, are mathematical. I consider this a feature, because anyway physicists are trying to move the discussions on mathematical realm.

To understand my approach, think at the geometries of the XVIII century. Klein managed, at the Erlangen program, to put all of them in the form of a set, endowed with transformations. The properties studied by each geometry are in fact defined as the invariants of the corresponding transformation (symmetry) group. My idea is much larger than that, generalizing the geometry such that it contains in a nontrivial way each theory of Physics. In http://philsci-archive.pitt.edu/archive/00004355/ I present largely this World Theory, and show that it can be particularized on the currently available theories.

One important issue is that of causality, and I tried to define it in a general way, in the framework of the World Theory I proposed. I generalized it to local causality, in order to provide a basis for discussing branching and cyclic times, and to provide a mathematical framework for discussing the time travel and what appear to be paradoxes related to it.

Cristi Stoica

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2. The Strong Causality Principle

I propose a principle requiring the initial data to be independent in each point on the data at other points. This SCP is not respected by an important class of PDE in Mathematical Physics. I showed that this principle can be respected if:

A. The Universe started with a particular type of singularity. This argument is an alternative to the Singularity Theorems discovered by Penrose and Hawking. I believe that my approach is based on fewer hypotheses, and it arises naturally as a consequence of the SCP.

B. An alternative solution is to consider the Maxwell and Yang-Mills potentials as having physical reality, rather than the corresponding fields, as it was believed before Aharanov and Bohm proposed their celebrated experiment.

Cristi Stoica

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3. The Smooth Quantum Mechanics

Although it is not stated in my essay, in the World Theory I introduced a way to select the matter field, which generalizes the standard PDE initial/boundary conditions approach. My way also emphasizes the idea that the initial conditions should be made invariant on the initial hypersurface and the particular values of the fields, when restricted to that hypersurface.

Starting with this idea, I realized that the discontinuous collapse in Quantum Mechanics can be eliminated, if we replace it with appropriate initial conditions for the evolution equations. In order for this mechanism to work, we cannot limit ourselves to the observed system. But, if the apparatus used in the previous measurement is taken into consideration, it can supply the free parameters required for the next measurement.

Because the initial conditions used in this solution converged towards the eigenstates of the observable, I decide to name them "delayed initial conditions" (as a reference to the well-known idea of delayed-choice experiment).

Consequently, the Smooth Quantum Mechanics allows new measurements of the same system, without requiring to discontinuous jumps. It is a deterministic theory, but doesn't contradict the free-will, as it is usually believed in other deterministic theories. Moreover, not only SQM is compatible with a deterministic Many Worlds Interpretation, but also suggests such a possibility, if we remember that the solution is selected from a sheaf representing the physical law, and that in Quantum Mechanics this selection is not established by an initial condition, but by the measurements. The observer cannot make use of this hidden determinism, but he/she has access only to a limited set of measurements (therefore, of delayed initial conditions). Consequently, although my version of MWI des not allow the world to split, the data collected by the observer (the "registry") can be completed in many incompatible ways, providing splitting of this registry.

Cristi Stoica