A Connectivity Theory of Space and Time by Honda Shing

Hi,

A very nice essay. Thanks for sharing it. Your approach to non-locality makes plenty of sense to me. Have you given any thought to what kind of dynamics would allow the kind of spatial structure you're describing to emerge? If so, I'd be very interested to hear about it.

Alex

PS: Hoorah for having another Berkeley person in the contest.

Dear Honda

I enjoyed your essay. In my essay I took a different approach but in some way could be closely related with yours. For example I explained how a Quantum many world can arise from a simple structure (a partial order or a topological space) , what you call zero-distance connection in my context is the fact that the each point in the order determine a universe which structure depends on his relation with other points in the order and the structure of their respective universes. What you call weight is just the structure of the order in my context and your word line order in my context are just the different paths in the order. We don't need to developed a new mathematical model to describe such things the model already exists and is based on the semantics of a non-intuitionist logic this is the more interesting part. I invited you to read my essay I would like to Know your opinions.

J.Benavides

Hi Alex,

Thanks for the encouragement. The paper presents the space-time structure as a proposal to the fundamental reality. Since it is "fundamental", the hope is to derive known physical phenomena and dynamics from it, rather than the other way around. I assume the highly connected structure to be intrinsic for the space-time, while its effect is hindered only in macroscopic view. We see 1D space as a geomatrical line, 2D space as a geomatrical plane, etc. only because of our macroscopic view point. Nonlocal quantum phenomena allow us to suspect that it may not be the case microscopically -- a line is not a line, a plane is not a plane etc. fundamentally.

It is great to know Berkeley folks in the contest. Wish you the best!

Honda

Dear John,

Thanks for sharing the thoughts! I haven't had time to read your essay yet. It sounds very interesting. I promise I will spend time on it and let you know what I think.

Honda

Dear Dr. Shing,

I enjoyed reading your essay, as it has something in common with my own.

Whereas you postulate: "The extra connectivity of space-time also has an ironic implication - the apparent discreteness of particle trajectories." In my essay I demonstrate the discreteness od particle trajectories by deriving a generalisation of the energy of a photon ('the Light'). Further, 'the Light' implies space-time. The question is, then, does 'the Light' imply "The extra connectivity of space-time"?

All the best,

Robert

Dear Honda Shing,

your essay is nicely readable.

1) You mention that

"...this theory, instead of seeking non-locality for particles or waves, embeds any nonlocal factor completely in the space-time structure."

This refers to your idea of having links, with probabilistic weights, connecting any spacetime event with any other spacetime event: high weights for short links, and low weights for long links. And you count on the long links for justifying non local effects, or actions at distance.

I think you can find this idea also in Wolfram, in his NKS book (p. 544, the 'thread' idea). Maybe some comparison between the two is fruitful.

2) You write:

Postulate 2 (Causality): A causal relationship is defined by 'world line order', rather than time order.

I notice that you still draw worldlines (as sets of points) embedded in a manifold, with dimensions x and t, as usual. But I suppose you do not want to inherit from that manifold the Lorentz metric, inducing causality and associated light cones (which would be violated by, say event subsequence 4-5 in Figure 6). What type of overall structure do you envisage, then, for a huge (and realistic) collection of world lines? How do you put them all together?

You seem to take world lines as a primitive concept: they are the thing that define causality. I personally find the idea of causal sets (discrete models of space-time) as more attractive. Causality among events is defined by the links of a causal set - as big as you want. Then you can focus on the various paths in it, that correspond to your world lines: the latter derive from the causal set structure, rather than being taken as primitive, and you do not have to put them together yourself. Also, in a causal set you immediately see the potential interactions among world lines, since nodes may well have more than one incoming and outgoing causal links.

In conclusion, I suspect that you might like the Causal Set idea, as investigated by Bombelli, Sorkin, Rideout, Reid, Henson and others. If so, you may also like my essay! Cheers

Tommaso

Honda,

I tend to grab the quote: "Particles propagate as waves but are detected as particles."

With my limited understanding of higher math, I tend to see models as imperfectly representing reality. Overall, I see an "Endless Universe" by Paul Steinhardt, and see the Planck-size world as a reality we try to simulate and ascribe characteristics of our models to but cannot truly know it, only grabbing views that fit our prejudices.

None of us can prove our views but you have a good approach.

Jim Hoover

Thank you for the essay Honda . I LOVE the graphs! Your written style and voice is so fluid, it was easy for me to follow your premises and conclusion.

May I suggest something? Since the universe is composed of:

Dark energy = 70%

Dark matter = 25%

Matter = 5%

In order to create a system that is both discrete and infinite, you would need to RECYCLE matter into dark matter, like a biosphere, or in science speak, a mirror reflection or intrinsic parity [link:en.wikipedia.org/wiki/Parity_(physics)]. Hence, in order to understand dark energy and dark matter, our FUNDAMENTAL understanding of the universe must be changed. For example, in math, we consider the square root of a negative number to be an "imaginary" number. (see link: http://en.wikipedia.org/wiki/Imaginary_number) Our problem is that the natural world actually exists in "imaginary" numbers.

Any theroem therefore must recognize imaginary numbers because 95% of the universe is composed of imaginary numbers.

Hence, any wavefunctions of certain types of particles have to be multiplied by −1, in addition to being mirror-reverse. What this means is that those particles must have negative or odd parity (P = −1, or alternatively P = -).

Thank you for the feedback. I will think about the comments and the question you stated.

Thank you for the comments and for the information. I am not familiar enough with the concept of causal set at this time. I will explore more of it and also the papers by the authors you mentioned.

Unlike the causal set concept, the theory I propose is based on a continuous model. It does not throw away the 4+1 space-time manifold with Lorentz metric. It merely defines new connectivity over the manifold such that world lines take a brand new form, i.e. all routes are possible, even discrete ones.

Thanks for your comments. Indeed, whatever theories and equations we can derive, are just models to describe the reality. While we may have our subjective preferences and prejudices about a certain model, it is also possible to come up with objective experiments or new observations to prove or disprove its correctness. Hopefully, in the process, models can be refined to come closer to the reality, and so will our understanding about the universe.

Honda

Thanks for the encouragement and for the suggestion! As you suggested, it is important to address dark matter and dark energy for any theories that try to describe the reality. After all, they do represent the major part of the universe. They are something for me to think about in further development of the theory.

Honda

Dear Honda,

Interesting essay, but I am afraid it contains a fatal flow: your model can develop closed causal loops. Causal Set theory is in the same kind of vein as your approach, but they specifically exclude closed causal loops in their starting axioms. I think that if you would refine your approach with minimal changes to answer physical objections, in the end you would recover the causal set theory.

Thanks for the comment. The model does implies the existance of causal loops (time loops), as indicated in Section 2.2 of the essay. However, the last two paragraphs of the same section also explains why this is not a problem, although I could not put in more details due to the page limitation.

As explained in the essay, in order to statisfy the requirement of a STATIC global spave-time diagram, only casaully consistent loops can exist. This means that inconsistent loops, such as grandfather paradox or Polchinski's paradox, cannot exist. One reference about this is the Novikov self-consistency principle.

Although there are arguments against Novikov's principle, they don't seem to apply in our case. First, the spacelike causal relationships are the result of the defined space-time structure, rather than the curvatures caused by GR effects. Second, spacelike connections are in planck scale, general QM rules may not directly apply.

Honda

Dear Honda,

I like your essay because it is very readable and it tackles the hard problems with quantum mechanics: the dual slit and entanglement.

You may be interest in the essays:

1. Continuous and Discrete Aspects of Nature by Vesselin Petkov

2. Making Waves by Don Limuti

because they go after the same target with some different starting points.

Best of luck,

Don Limuti

Thank you very much for your encouragement and for the information! I will take a look at the essays you mentioned.

Honda

Dear Sir,

Quantum theory is like Pioneer Anomaly. It started with a small anomaly between the postulated and actual position of Pioneer 11 that has grown to more than 400,000 kilometers now challenging the existing theories of gravitation and giving rise to alternate theories like MOND, none of which are successful in giving a complete explanation of the phenomenon. The different interpretations of quantum theory, which are really different theories with their own sets of postulates often contradicting each other, has made the dream of a cohesive theory almost impossible. The task has been made more difficult by the blind followers of different branches. The present essay is an example of such posturing.

We fail to understand how: "the infinite connectivity of space-time implies its hyper-continuity", "introduces discreteness into particle trajectories." A "zero-distance connection with every other position in space-time" implies an all embracing spreadsheet without any intervening space. Thus the question of discreteness or dimensions for connectivity does not arise.

The Kaluza-Klein compactification and other "theories" relating to extra-dimensions are only figments of imagination. The term dimension is applied to solids that have fixed spread in a given direction based on their internal arrangement independent of external factors. For perception of the spread of the object, the electromagnetic radiation emitted by the object must interact with that of our eyes. Since electric and magnetic fields move perpendicular to each other and both are perpendicular to the direction of motion, we can perceive the spread only in these three directions. Measuring the spread is essentially measuring the space occupied by it. This measurement can be done only with reference to some external frame of reference. For the above reason, we use axes that are perpendicular to each other and term these as x-y-z coordinates (length-breadth-height). These are not absolute terms, but are related to the order of placement of the object in the coordinate system of the field in which the object is placed. Thus, they remain invariant under mutual transformation. If we rotate the object so that x-axis changes to y-axis or z-axis, there is no effect on the structure (spread) of the object. Based on the positive and negative (spreading out and contracting in) directions from the origin, these describe six unique positions (x,0,0), (-x,0,0), (0,y,0), (0,-y,0), (0,0,z), (0,0,-z), that remain invariant under mutual transformation. Besides these, there are four more unique positions, namely (x, y), (-x, y), (-x, -y) and (x, -y) where x = y for any value of x and y, which also remain invariant under mutual transformation. These are the ten dimensions and not the so-called mathematical structures. These are described elaborately in our book.

When applied to objects, one dimension implies distance, two-dimension implies area and three-dimension implies volume. Since time does not fit in this description but implies duration of each cycle of events or part thereof, it is not a dimension. Thus the description of space-time continuum or world-points is also wrong description of facts.

"Temporal orders of world points are generally different when observed from different reference frames". They do not affect temporal evolution of objects, but only describes how they are perceived by different observers. Since observation that leads to perception does not affect temporal evolution of objects, temporal orders of observation are not relevant for time evolution. We have already shown that:

Consider an example: A B → C D.

Here a force acts on A and B to produce C and D. The same force doesn't act on C and D as they don't exist at that stage. If we change the direction of the force, B interacts with A. Here only the direction of force and not the interval between the states before and after application of force (time) will change and the equation will be:

B A → C D and not B A ← C D.

Hence it does not affect causality. There can be no negative direction for time or cause and effect.

The measurement problem of Quantum Mechanics is still being debated without a solution. Different interpretations of the theory describe the concept and mechanism of collapse differently. There is no unanimity in this regard. We have described this issue at different threads. Measurement is a process of comparison between similars. We have also explained YDS and Entanglement differently.

Entanglement is related to the intrinsic relationship of particles with their fields. As we have said earlier, particles are nothing but confined fields. Confinement implies a central point (nucleus or center of mass) around which the mass concentrates due to confinement (orbitals). Thus, there is a coupling between the two mediated by a force. Entanglement is related to this mediating force. Since energy does not have a nucleus or center of mass, it does not have a fixed structure. Hence it is always dynamic unless it is contained within some container. Here also, it interacts with the container at the surface while there is no such interaction at other places. This leads to a chain reaction leading to further destabilization. Thus, energy is always mobile. All measurements are done at "here-now", which is a fixed position in some frame of reference.

Just like a fluid flows or seeps through a porous container and not through a solid one, the energy associated with the quantum particles can flow (entanglement) or seep through (quantum tunneling) macro barriers. Since all objects display a three fold structure (nucleus, orbitals or confinement and the extra-nuclear field), any release of energy in one direction will be associated with the absorption of equivalent energy in the opposite direction, which will generate chain reactions in their surrounding fields. Since particles have parallel and anti-parallel spins, the release of energy by a pair with opposite spins will induce similar reactions in opposite directions. This is known as entanglement. However, till one particle's spin is measured, there is no way to know about the spin of either. Thus, there is nothing extraordinary about entanglement. We had given its macro examples in various threads. It has unnecessarily been sensationalized. Particles move in the field automatically (in the absence of any induced force) based on the property of the field to attain uniform density. Since the density of the medium through which the energy travels is different from the density of the released energy, it gradually tapers down after a few kilo meters. Alternatively, it loses its own identity and becomes indistinguishable from the field. In both ways, the result is the same.

Truth exists independent of personalities. Hence kindly forgive us for the language used. There is nothing personal.

Regards.

basudeba

Dear Honda,

Wisdom is more important than imagination is more important than knowledge for all the we know is just an imagination chosen wisely.

Please read Theory of everything at your convenience posted by me in this contest.

Who am I? I am virtual reality, I is absolute truth.

Love,

Sridattadev.

Dear Shing,

I was so happy to read your essay since it is very much related to my own theory:

http://www.qsa.netne.net

I think all the ideas of John Benavides , Tommaso Bolognesi ,D'Ariano, Zenil and few other are very much related. my website has not been updated, but here is the abstract of my upcoming paper.

In this letter I derive the laws of nature from the hypothesis that "Nature is made out of mathematics, literally". I present a method to design a universe using simple rules which turns out to have the properties similar to our reality. Particles are modeled as end of lines, one end is confined to a small region and the other goes to allover the universe. The Coulomb force (when lines cross) and gravity(when lines meet) appear naturally and they are two aspects of one process involving the interaction of these lines, and then by calculating the expectation values for positions. I am able to calculate what appears to be the Fine-structure constant. Gravity also appears with surprising results, it shows that gravity becomes repulsive when distance is great or when distance is very small. At this time I have only done 1D full simulation with interaction and 2D and 3D and indeed nD without interaction. I am working on 2D interaction now and already showing very surprising results. I can see a hint of the strong and the electroweak force. Time and space could be looked upon as derived quantities. I show that not only nature is discrete but also mathematics, since dx can only approach zero but it never is zero. In my model the ultimate irony is that our reality came about because there is only one way to design a dynamic universe and that only one allowed our existence. I guess you could say fortunately or unfortunately depending on how one's life unfolded.