[AntonioLao]

How many handles would be sufficient to describe the structure of space-time completely? If space-time is a sphere then its number of handle is zero. If space-time is a donut then its handle is unity. Two holes pretzel would be a two handles bundle, 3 holes – 3 handles, 4 holes – 4 handles. The progressive pattern is clearly self-explanatory.

A zero no handle spherical universe would have to be separated into 3 distinctive regions: inner, outer, and the 2D surface of the sphere. Both Einstein’s general relativity of gravity (GR) and quantum mechanics (QM) of elementary particles seem to conform to this genus zero structure of space-time. For QM there are the point-like elementary particles with their inner space-time completely hidden. For the cosmos there is the unreachable boundary of the visible universe. The inner space-time represents time past. The outer space-time represents time future. The now is represented by the edgeless surface where Euclid’s 5th postulate could be replaced by two axioms of non-Euclidean geometries. (1) The no parallel lines axiom and (2) the infinite parallel lines axiom. The 1st is called Riemannian geometry. The 2nd is called hyperbolic geometries invented independently by Gauss, Lobatchevsky, and Bolyai.

The 2nd were discovered first but the first is used for all the mathematical underpinnings of GR and QM. Nevertheless, they are based on a genus zero of a sphere without a hole or a handle to hold on to. Furthermore, not even a single handle space-time structure is sufficient for its description. Therefore, a conjecture can be made such that two holes topology with genus 2 is sufficient for a complete description of microscopic and macroscopic space-time structures. Any physical theory formulated using a double-handle fiber bundle could surpass the hurdle of the space-time riddle.

[Profpat]

An interesting post Antonio, but as usual I'm a little confused.

You mention the spherical model as having time past in inner space, time future as outer space.

My question is what makes up the space in those areas? Is the inner space dimensionless point particles of past events? Is the outer space void waiting for the surface area to touch it and create it into present time?

I view space/time as being a continuum and therefor both a description of time and space would be necessary.

Motion should also be addressed. The surface expanding or propagating. Any inner movement? Any outer movement?

Your thoughts and conjectures sir would be most welcome.

Best to you,

Pat

[bottomlander]

Originally Posted by AntonioLao The thread tittle is double-handle bundle hurdle riddle.

Dear AntonioLao,

I think you delineated all words in the tittle be ended with ...le, a smart word game!

I also noticed that some galaxies have bright spiral arms/handles.

Best Regards. Bottomlander

[mkirkpatrick]

Prehaps the answer to the riddle lies in one bundle?



regards michael.

[bottomlander]

Dear AntonioLao,

Your tittle double-handle bundle hurdle riddle also has all its words appear in the end of your message: " ... a double-handle fiber bundle could surpass the hurdle of the space-time riddle".


Only now, I notice further that all words in that tittle are ended with ...ble/dle, not just ...le.


I also remember you once asked what is the use to learn Chinese. One of the use is to be more sensitive to possible word games! Many Chinese characters have styled prefixes/ends nice for word games.

Also the Chinese classics you once learned is in 3 characters throughout the contexts. Another classic is all in 4 characters per sentence. The classic poems are in either 5 or 7 characters each line. Is that true?


Best Regards. Bottomlander

[Profpat]

The traditional haiku consisted of a pattern of 5, 7, and 5 on.

AntonioLao,
Did ask how many handles,
But how many pots?

[AntonioLao]

Originally Posted by Profpat what makes up the space in those areas

I'm afraid I have no answers or no proofs for the inner space but for the outer space I used to look thru telescopes and one was the refractor at the Naval Observatory in Washington D.C., and I can say that the wonders of the outer space is beyond my comprehension. The ring of Saturn, the giant red spot in Jupiter, the star clusters, the double-star systems, the craters on the Moon, etc.
But my guess for the inner space is that it is composed of squares of energy. The universe started as uniform squares of energy then its symmetry was broken creating matter and energy. Now that matter and energy can change back to squares of energy.

Originally Posted by mkirkpatrick the answer to the riddle lies in one bundle

A bundle of squares of energy.

Originally Posted by bottomlander Many Chinese characters have styled prefixes/ends nice for word games.

Now I realized should have paid more attentions in the Chinese classrooms.

[mkirkpatrick]

Too many squares of energy needs rounding off?



regards michael.

[Profpat]

Thanks for your thoughts Antonio.

Why squares or cubes of energy, why not circles or spheres?

[mkirkpatrick]

Originally Posted by Profpat Thanks for your thoughts Antonio. Why squares or cubes of energy, why not circles or spheres?

My very thoughts too Pat,your not reading my mind are you?



regards michael.