What is the current understanding of time in modern physics?

[SanguineHorizon]

Can someone please explain to me the current theories of Time? I have an idea I want to put forward to you all, but need to get a little groundwork in first. Based purely on what I learned in school, time is currently veiwed as linear, if so, how is this even possible? Much appreciated, thanks.

 

[Antonio Lao]

The modern concept of linear time is probably the most popular one. It is practically being used in the formulation of a physical theory. But theories of relativity (special and general) both combined time with space to form spacetime. And in string theories, spacetime's dimension were increased only for the space part while the time dimension remains linear.

If time is linear, the logical thing is for it to have two directions. But according to the theory of thermodynamics, only one arrow of time is found, this is the direction of increasing entropy. The other arrows of time are implied in: electromagnetic radiation always emanates outward from a source never inward; the cosmological expansion of space (spacetime?); and, in psychology, we remember the past but not the future.

 

[The Bob]

The modern concept of linear time is probably the most popular one. It is practically being used in the formulation of a physical theory. But theories of relativity (special and general) both combined time with space to form spacetime. And in string theories, spacetime's dimension were increased only for the space part while the time dimension remains linear.

If time is linear, the logical thing is for it to have two directions. But according to the theory of thermodynamics, only one arrow of time is found, this is the direction of increasing entropy. The other arrows of time are implied in: electromagnetic radiation always emanates outward from a source never inward; the cosmological expansion of space (spacetime?); and, in psychology, we remember the past but not the future.

Time as a linear measurement? Intresting. I assume this is correct but (unless I am wrong) time must not only have direction but velocity. By that I mean it must travel in the direction of 3-D shapes and it must have its own factors. Although we have put a measurement on time it is still independed to everything else (I mean to say it works wih space independently).

Might be the greatest load of rubbish you have every heard but here it is anyway.

The Bob (2004 ©)

 

[Antonio Lao]

...time must not only have direction but velocity...

Time has a velocity component only in spacetime. While spacetime is the fabric of the cosmos; it is the background to everything else: space (stand alone), matter, and energy.

 

[The Bob]

...the fabric of the cosmos...

Therefore this means that time could be independent, like space can be, and so we have put a measurement on it and really it could change and we would be none the wiser.

The Bob (2004 ©)

 

[Antonio Lao]

...time could be independent...

Spacetime is independent of time iff spacetime is static. But spacetime is dynamic then the metric of spacetime will depend on the local motion of space and time.

 

[The Bob]

Spacetime is independent of time iff spacetime is static. But spacetime is dynamic then the metric of spacetime will depend on the local motion of space and time.

What I am asking is is it possible for Time to 'fold' like space? If so is it not, therefore, independent to everythin (in realtion to space)?

The Bob (2004 ©)

 

[sol2]

Spacetime is independent of time iff spacetime is static. But spacetime is dynamic then the metric of spacetime will depend on the local motion of space and time.

Up to Planck length, and then it is unobservable?

If such dimensions are compacted how would we ever know? http://wc0.worldcrossing.com/WebX?14@9.5Oq5cmTGeIL.7@.1ddf4a5f/11 and so would the actions of "spooky" at any distance?

We look ever deeper for the "interactive phases" that might represent solutions about that space? Everyone is saying no "hidden variables," yet we had not discerned relevance to Glast in geometrical considerations, so to all intensive purposes, this was hidden

 

[Antonio Lao]

...I am asking is is it possible for Time to 'fold' like space?

In spacetime, this folding is called the curvature of spacetime. But spacetime can still be curved while it can remain static. But in general relativity this is a tautology because of the existence of matter: matter dictates spacetime how to curve and the curvature of spacetime dictates matter how to move. This does not say anything if you want to find the origin of matter.

 

[Antonio Lao]

Up to Planck length, and then it is unobservable?

A theory can still be logical even though not observable.

If I put myself in the shoe of a zero dimensional spacetime point, and ask myself who are my nearest neighbors and how many are there? The logical answer is six. This answer is based on the assumption that the topology of an infinitesimal sphere is equivalent to that of an infinitesimal cube as the length of edge of the cube approaches zero.

 

[sol2]

A theory can still be logical even though not observable.

To the detriment of strings and LQG there defintiely has to be some consistancy

If I put myself in the shoe of a zero dimensional spacetime point, and ask myself who are my nearest neighbors and how many are there? The logical answer is six

How did you arrive at that? It becomes a little more difficult then this in term of defining the coordinates references for sure, but then the move to topological consideration overtakes this issue when we continue to think of the Reinmann and the spherical considerations. How did you get there?

Matter considerations can become very fluid and along side of this, gravitational considerations as well. So how well would we define such points without considering the space of considerations without understanding even in the gaussian world there was issues to contend with, that move along side of GR into the dynamical world of QM?

 

[Antonio Lao]

How did you arrive at that?

Please find my reply to your question in the edit of previous post.

 

[The Bob]

In spacetime, this folding is called the curvature of spacetime. But spacetime can still be curved while it can remain static. But in general relativity this is a tautology because of the existence of matter: matter dictates spacetime how to curve and the curvature of spacetime dictates matter how to move. This does not say anything if you want to find the origin of matter.

Therefore is it possible for time to pull away from space (if only for a small period of time) and change speed and then merge back in?

The Bob (2004 ©)

 

[sol2]

Please find my reply to your question in the edit of previous post.

And to yours, in mine

 

[Antonio Lao]

...when we continue to think of the Reinmann and the spherical considerations. How did you get there?

Riemannian geometry is static. But if the geometry is dynamic, i.e. introducing a force into the geometry, then the sphere can never be a closed surface. There at the least should have one hole in the form of a point. But the projection of this point into the sphere is an infinitely extended plane and for the infinite points of spacetime there should exist infinite numbers of orthogonal planes and three of these planes intersect at the said point at (0,0,0). These planes also formed a lattice structure separated by a constant distance which experimental limit is the Planck length.

 

[sol2]

Riemannian geometry is static. But if the geometry is dynamic, i.e. introducing a force into the geometry, then the sphere can never be a closed surface. There at the least should have one hole in the form of a point. But the projection of this point into the sphere is an infinitely extended plane and for the infinite points of spacetime there should exist infinite numbers of orthogonal planes and three of these planes intersect at the said point at (0,0,0). These planes also formed a lattice structure separated by a constant distance which experimental limit is the Planck length.

How would you then explain the topology of a sphere as a Genus Figure?

 

[Antonio Lao]

How would you then explain the topology of a sphere as a Genus Figure?

My research goal is to verify the genus of spacetime. At present, I don't think is that of a sphere. I am more incline to say that the topology of spacetime has genus equals 1 similar to that of a doubly twisted Moebius strip.

A sphere, in reality, separate spacetime into an inside and an outside with no connection between points inside and outside except through points on the boundaring spherical closed surface. Once a point is picked on the surface, it is the same thing as creating a hole, literally speaking.

 

[sol2]

My research goal is to verify the genus of spacetime. At present, I don't think is that of a sphere.

http://ccins.camosun.bc.ca/~jbritton/animcup.gif

http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/donut-coffeecup.gif

Topology is the branch of mathematics concerned with the ramifications of continuity. Topologist emphasize the properties of shapes that remain unchanged no matter how much the shapes are bent twisted or otherwise manipulated.

http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/wormhole.jpg

A wormhole is a genus 1 topological defect in space.

http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/Properties-of-Space.htm



I think I should have better asked the question on deviation from discrete to continuity and how this would have been defined mathematically.

In coordinate frames, as have been pointed out in various posts, none have really dealt with the issue of dimension other then within those confines.

Continuity has to explain dimension, and leads from classical discriptions now faced with, higher recognition of four dimensions of space(cube to hypercube), within the issues of topology and recognition of curvature?

The consistancy in geometrical expression has to be define through the different phases of that geometry(gravity has been defined up to this point)

U(1) is a point, also a circle, it's length as a one dimensional string defined in the brane:)

A sphere, in reality, separate spacetime into an inside and an outside with no connection between points inside and outside except through points on the boundaring spherical closed surface. Once a point is picked on the surface, it is the same thing as creating a hole, literally speaking.

The energy determination of the circle in U(1)is describing a means by which such consistancy might have been recognized? Immediately one wrap of the string, more energy more wraps, hence the length of that string? This movement is defining not only the length but is determining its twists and turns. Does this make sense?

 

[Antonio Lao]

I think I should have better asked the question on deviation from discrete to continuity and how this would have been defined mathematically.

The topology of spacetime is continuous. But spacetime has two distinct topologies merged together. This combination form a discrete dynamic "shape" (I am not going to use the word topology again so that there is a separate concept between discrete and continuous). This shape is analogous to the Hopf ring or doubly twisted Moebius strip when one the two dimensions is shrunk to zero.

The continuity of spacetime comes from its individual topology but the combination of these topologies creates a discrete shape for spacetime structure. This discrete shape is the square of energy and in vector notations: E^2 = \psi_E \times \phi_E \cdot \psi_B \times \phi_B where the \psi_i is the metric and \phi_i is the force but for time independent structure, it is the linear momentum and then the shape becomes a double actions or two interlinked angular momenta (square of Planck constant).

 

[Antonio Lao]

sol2,

Thanks for the beautiful pictures and the web links on topology and will visit them again and again.

 

[sol2]

sol2,

Thanks for the beautiful pictures and the web links on topology and will visit them again and again.

And thank you for your pateince.

I wanted to express this post here as what is revealled is really quite amazing to me. On the issue of quantum gravity there are two roads that we have ventured upon here in terms of LQG and Strings.

Not only is this fundamental difference important to recognize, but through the nature of harmonic realization(strings) and probability statistics(LQG in regards to the monte carlo process), the geometrical considerations have deviated from some point? You have been speaking to this.

What is revealing also, is the question in regards to algebraic means to quantum gravity determinations, that from such a theorectical discussion, how could we not implment what Smolin understood from the distilliation of the three roads, and solving a fundmental problem on the method to determnination? What arose from distilliation was a new math?

Really having come faced to face with such unifications in regards to Relativity and Quantum theory, how shall we measure this unique feature if we had not realized that there must be a method that supports such avenues to investigative tendencies of this theoretical movement?

Glast is a summation from a algebraic standpoint(?) and speaks to both. Smolin's signature new math is well evident to me here. Its sort of like reliving special relativity on the the road to Gr, but we have now institued this view in graviton interaction. How the heck did I get here:)

Geometrical consistancy is the baiss of any argument and its consistancy is written there? http://www.ensc.sfu.ca/people/grad/brassard/personal/THESIS/node21.html really helped to see this consistancy.

 

[Antonio Lao]

sol2,

Thanks for the links to John Baez's discussions.

I'm going to read Lee Smolin's book 'Three Roads to Quantum Gravity' again. Hoping to tie up some loose ends to my own research and also get rid of some loose ends.

 

[Antonio Lao]

sol2,

After reading the link on Klein's ordering of the geometries (and also thanks for this link as well) , I realized that I have been working on a Euclidean geometry without the notion of angles. But then another realization is that projective geometry, which I think I am also using, does not preserve distances. I have to assume that at the local infinitesimal domain of spacetime, the geometry of two linked topologies is elliptic which is the merging of two hyperbolic geometries.

 

[sol2]

sol2,

After reading the link on Klein's ordering of the geometries (and also thanks for this link as well) , I realized that I have been working on a Euclidean geometry without the notion of angles. But then another realization is that projective geometry, which I think I am also using, does not preserve distances. I have to assume that at the local infinitesimal domain of spacetime, the geometry of two linked topologies is elliptic which is the merging of two hyperbolic geometries.

Sometimes it is like asking if there are distinct lines in magnetic fields. Yet we know that the field exists. Some have even allowed us coordinates to consider (higher dimensions), like Gauss. This is a different kind of thinking, yet if I showed you soap bubbles, and then a soccer ball( its surface), how would your thinking change?

Look at this here

 

[Antonio Lao]

how would your thinking change?

Thanks for all these links to various discussions on topology.

When Dirac proposed the existence of magnetic monopole, his thinking was in term of closed surfaces similar to the supposed structures of charged particles or neutrally charged particles such as neutron and neutrinos. But as verified by experiments, all particles, charged or neutral, are point-particles and they all possesses magnetic dipole moments.

My proposal is that closed surfaces do not exist in nature. The genus of the topology that is behind magnetic field is possibly 2. It's like a sphere with two holes, one at the north pole and one at the south pole. And between these holes, some kind of torus topology can be described. And the limiting dynamic makes one topology shrunk to zero while the other approaches an infinitely extended line. The middle ground of these extreme topologies is a Hopf ring.

I am wondering is there a relationship between the genus of a topology and the concept of spin in quantum theory?

 

[sol2]

Thanks for all these links to various discussions on topology.

When Dirac proposed the existence of magnetic monopole, his thinking was in term of closed surfaces similar to the supposed structures of charged particles or neutrally charged particles such as neutron and neutrinos. But as verified by experiments, all particles, charged or neutral, are point-particles and they all possesses magnetic dipole moments.

My proposal is that closed surfaces do not exist in nature. The genus of the topology that is behind magnetic field is possibly 2. It's like a sphere with two holes, one at the north pole and one at the south pole. And between these holes, some kind of torus topology can be described. And the limiting dynamic makes one topology shrunk to zero while the other approaches an infinitely extended line. The middle ground of these extreme topologies is a Hopf ring.

I am wondering is there a relationship between the genus of a topology and the concept of spin in quantum theory?

This last point in bold is a really interesting question for me because if you take all that we have discussed and geometrically apply some consistancy what would this look like? We don't know if we have a way of measuring it. The visualization you have, how will you verify it?

I make this issue deeper when the ideas of Optiverse is given, because now we have answered something about the nature of this geometry from a whole new perspective

If we now engage the universe and the dynamics that are going on, how shall we see this brane world when focus on the brane? Remember the topology place in winnipeg?

From this perspective we were given some ideas here on the dynamcial nature and interwoven aspects revealled by a pelastrian notion of elasticity( maybe he will share some of his diagrams and perspective here as it is a really good exercise in looking at the question and nature of this elasticity). How would we ever conceptualize this?

With powerful parallel computers networked to virtual environments, we can explore previously inaccessible problems in geometry, especially where a complex object evolves so as to optimize its shape. For instance, an unknotted loop of string, no matter how tangled, can be persuaded to move (automatically and without breaking) into a round circle. In 4-dimensions, a surface (like a topological sphere) may be knotted. When it is merely tangled we evolve it to its familiar round shape to show it was unknotted. We guide surfaces towards optimality by minimizing mathematical abstractions of physical energies like the Coulomb potential or the bending energy of bilipid membranes. Mathematical surfaces in 3-dimensions (like shadows from 4-dimensions) generally self-intersect, but the Willmore bending energy can still be used to optimize their shape. A sphere can be turned inside out, keeping the surface smooth, but allowing complex self-intersections; we demonstrate this by presenting for the first time a geometrically optimal and computationally automatic http://new.math.uiuc.edu/laterna/minimax/ .

http://new.math.uiuc.edu/laterna/

http://new.math.uiuc.edu/optiverse/img/rs43-196.jpeg

The question in bold is directly answered by Glast and imagine the Gamma ray feature of this universe? But there is more to it that has been spoken to before on your very point in bold. Gravity Probe B?


So now all of a sudden we have this view of the cosmos and the dynamcis that are going on. Olias new thread today, is speaking to this. It is a exercise in what we have been talking about After you read his post go look for the Bose Nova and tell me what you see? To join electromagnetism with Gravity there is a direct resulting view that must be adopted? Should we now speak again to your bold statement?

 

[Antonio Lao]

sol2,

Doing some investigations. Will reply as soon as possible.

 

[Antonio Lao]

sol2,

From reading the introduction section of these two papers

http://xxx.lanl.gov/PS_cache/math/pdf/0203/0203224.pdf

http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9508/9508018.pdf

I am leaning toward the realization that I am on the right track but I need more knowledge of advanced math to completely understand these papers.

As for the theory of elasticity of spacetime, I am making a few assumptions: (1) There is a minimum length (geodesic) between two spacetime points; (2) each spacetime point is associated with a constant force (in one dimension); (3) in two dimensions, this force is inversely proportional to the geodesic; (4) in three dimensions, this force is inversely proportional to the square of the geodesic. The result is Newton's law of universal gravitation but with the added bonus that the mass can be explained by the two distinct topologies of spacetime.

Carl Wieman's "bose nova" implies that repulsive forces arise when all the force vectors are pointing away from a spacetime point and attractive forces arise when all the vectors are pointing into the point.

One more assumption is that each spacetime point can only interact with 6 forces of 6 nearest points without disrupting the cubic lattice structure. But for a tetrahedronic structure, the geometry is less dynamic and hence more stable but highly curved approaching maximum curvature of spacetime.

The conserved quantity from all these interactions between geodesics and forces is the square of energy and there are two distinct forms (E^2 and -E^2).

 

[Antonio Lao]

sol2,

In response to the bold statement, I used Euler characteristic to see a very strong indication that spin is related to genus of its associated topology.

For graviton, topology is a double torus, genus is 2, spin is 2. For spin zero particles, the topology is a sphere, genus is zero. For spin 1 particles, the topology is a torus or Klein bottle or Moebius strip, genus is 1. For spin half particles, the topology is a projective plane, genus is 1/2. For spin 3/2, the topology is three-projective planes, genus is 1/2 + 1/2 + 1/2.

 

[sol2]

sol2,

In response to the bold statement, I used Euler characteristic to see a very strong indication that spin is related to genus of its associated topology.

For graviton, topology is a double torus, genus is 2, spin is 2. For spin zero particles, the topology is a sphere, genus is zero. For spin 1 particles, the topology is a torus or Klein bottle or Moebius strip, genus is 1. For spin half particles, the topology is a projective plane, genus is 1/2. For spin 3/2, the topology is three-projective planes, genus is 1/2 + 1/2 + 1/2.

Can you show correspondance of the graviton, as a double torus genus two?

I am just referring back to a post that I left before for you.


Hyperspace, by Michio Kaku Page 84 and 85,

"To see higher dimensions simplify the laws of nature, we recall that any object has length, width and depth. Since we have the freedom to rotate an object by 90 degrees, we can turn its length into width, and its width into depth. By a simple rotation, we can interchange any of the three spatial dimensions. Now if time is the fourth dimension then it is possible to make "rotations" that convert space into time, and vice versa. These four-dimensional "rotations" are precisely the distortions of space and time demanded by special relativity. In other words, space and time have mixed in a essential way, governed by relativity. The meaning of time as being the fourth dimension is that time and space can rotate into each other in a mathematical precise way. From now on, they must be treated as two aspects of the same quantity: space-time. Thus adding a higher dimension helped to unify the laws of nature."

Antonio said:Space is basically three dimensional. Can subtracting dimension (say from 3 to 2, 2 to 1, 1 to 0) also helped more to unify the laws of nature?

http://www.physics.ucsb.edu/~strings/superstrings/unify.gif

http://www.physics.ucsb.edu/~strings/superstrings/standard.gif

When we move to brane considerations how is it we could see genus types figures here in topology, and not consider the relevance on the issues of fermion and bosons. That fundamental principals arise, in regards to the brane that is not unlike a relationship that restricts photons to the brane, while gravitons are free to roam?

What consistancy geometrically define would allow us to speak to the dimensions and at the same time realize such functions of topology are relevant here in brane considerations as to the "standard model" rising from these views?

Orbitals in terms of topological features? If such manner can be describe in the issues of the bose nova then what relavance could such orbitals play here? Is there a connection in how we are view the higher aspects of geometry in regard to probabiilty determinations?

Lets look at the http://wc0.worldcrossing.com/WebX?14@7.uKihc5VZfze.0@.1ddf4ac3/2 in the cosmos?

The four-year set of observations reveals new clues about how a stellar black hole converts matter into streams of energy, unleashed in a powerful flash, and how these jets interact with interstellar space. Studies stemming from the data suggest how the process might be similar to events a far grander scale, over longer time periods, around the colossal supermassive black holes that anchor some galaxies

http://www.space.com/scienceastronomy/black_hole_011003.html

We needed some way in which to marry concepts of GR with Quantum Theory, and how would we do this with any geometrical consistancy?

 

[Antonio Lao]

sol2,

Will reply as soon as possible.

 

[Antonio Lao]

sol2,

My complete reply will be broken into several posts. Please bear with me.

A double torus is the same as a sphere with two holes. But it is still a surface. If we contract one dimension to zero, what will the one dimensional double torus looks like. The image I am visualizing is that of two linked loops just like a Hopf ring.There should be two distinct topologies. Let's denote them as H^{+} and H^{-}.

 

[Antonio Lao]

sol2,

furthermore, the H's can interact with each other. There are two types of operation. (1) \bigotimes and (2) \bigoplus. And the following algebra can be applied:

H^{+} \bigoplus H^{-} = 0
H^{+} \bigoplus H^{+} = a H^{+}
H^{-} \bigoplus H^{-} = b H^{-}

H^{-} \bigotimes H^{-} = c H^{+}
H^{+} \bigotimes H^{-} = d H^{-}
H^{+} \bigotimes H^{+} = e H^{+}

a and b give the values of the electric charge and c,d,e give the value of the mass.

 

[Antonio Lao]

sol2,

For an electron, it is composed of 7 H{-} and 1 H{+}.
For an photon, it is composed of 4 H{-} and 4 H{+}.
For an neutrino, it is composed of 1 H{-} and 1 H{+}.
For an up quark, it is composed of 1 H{-} and 5 H{+}.
For an down quark, it is composed of 3 H{-} and 1 H{+}.

Since there is level of existence (LOE) for the H's, the 2nd and 3rd and maybe more generations can also be provided with each mass values with no change in the charge values.

 

[Antonio Lao]

sol2,

From the interactions, they seem to indicate two kinds of mass. H^{+}represents kinetic mass and H^{-} represents potential mass which is another name for inertial mass and gravitational mass. Therefore, the graviton is made of H^{-} exclusively. But H^{-} can also be derived from the interaction between an H^{-} and an H^{+}. In this case, it's a higher excitation state of the graviton. Basically, all fermions are higher excitation states of the fundamental unit graviton H^{-}. And all bosons are higher excitation states of the fundamental unit H^{+}. Both H's are the square of energy E^2 = \psi_E \times \phi_E \cdot \psi_B \times \phi_B.

 

[Antonio Lao]

Can you show correspondance of the graviton, as a double torus genus two?

It seems that i can show this only in a one dimensional topological structure of the Hopf ring.

 

[Antonio Lao]

sol2,

With regard to dimension, I going the opposite of what Michio Kaku suggested. He suggested going to higher dimension for unification. I am working on a theory that can only make sense in one dimension of space.

 

[Antonio Lao]

sol2,

The unification of U(1), SU(2), SU(3), and gravity maybe beyond the Planck scale seems to indicate to me that the resultant force derived from all fundamental orthogonal forces of nature in a small region of spacetime is tremendous because they are the vector sum of the infinite numbers of spacetime point each is associated with a contant magnitude force but its direction can vary. But to think that there must be a reason why the gravitational force is very weak is because gravity is the difference between two great orthogonal forces that are not equal in their numerical values.

F_G = F_E - F_B

and that antigravity is given by

F_G = F_B - F_E

Both gravity and antigravity are the difference of the projected forces in an arbitrary axis.

 

[Antonio Lao]

sol2,

For p-branes, the topologies are the p numbers of projected plane. So branes topology are good for particles with 1/2 integer spin.

 

[Antonio Lao]

Is there a connection in how we are view the higher aspects of geometry in regard to probabiilty determinations?

The random quantum fluctuations of the vacuum are good indications that spacetime points are quantized with their six orthogonal forces. The random orientations of their directions give rise to two distinct topologies. The probability arises from this fundamental random fluctuations of the directions. In some case, H-plus is dominant, in other case H-minus is dominant. When a lot of H-minus combined together, the inertial mass is increase creating black holes and to balance the forces, the H-pluses expand as noted by the universal expansion. There seems to be a 2 to 1 ratio between the formation of H-plus and H-minus.

 

[sol2]

I just got the opportunity to go over your posts now. I will need some time to think over what you are saying and will try to respond appropriately. I'll be doing that tomorrow.

Antonio:The unification of U(1), SU(2), SU(3), and gravity maybe beyond the Planck scale seems to indicate to me that the resultant force derived from all fundamental orthogonal forces of nature in a small region of spacetime is tremendous because they are the vector sum of the infinite numbers of spacetime point each is associated with a contant magnitude force but its direction can vary. But to think that there must be a reason why the gravitational force is very weak is because gravity is the difference between two great orthogonal forces that are not equal in their numerical values.

One of the puzzles for me in consideration of supersymmetry at a early time in the universe formation, requires such consistancy.

Antonio:From the interactions, they seem to indicate two kinds of mass. represents kinetic mass and represents potential mass which is another name for inertial mass and gravitational mass. Therefore, the graviton is made of exclusively. But can also be derived from the interaction between an and an . In this case, it's a higher excitation state of the graviton. Basically, all fermions are higher excitation states of the fundamental unit graviton . And all bosons are higher excitation states of the fundamental unit . Both H's are the square of energy .

I was trying to think of how I might have seen your points in terms of H^{-}
and H^{+} in dynamcal movement, consistant from that early universe. This presents interesting comparisons to energy conversation to matter states. As you pointed out it would be quite strong in this supersymmetrical state, yet in terms of expansitory relevance, we are defining this action to end in a weak field manifestation? The gravitons are already in the bulk. You might want to correct my thinking here.

A topological space is described as being simply connected if every loop it contains can be shrunk to a single point; a loop with this property is called contractible. For example, ordinary Euclidean space is simply connected, and so is the surface of a sphere, but the surface of a doughnut isn't. The group of rotations in three dimensions, SO(3), is not simply connected, because the set of rotations around any fixed direction by angles ranging from – to forms a loop that is not contractible. This becomes clear if you picture SO(3) as a solid sphere of radius , with a rotation by the angle around an axis pointing in the direction of a unit vector u being represented by the vector u. Antipodal points on the surface of the sphere correspond to identical rotations, so any continuous path that crosses the surface must re-appear on the opposite side of the sphere. Having formed a loop from any diameter of the sphere, the two endpoints of the diameter will necessarily remain on opposite sides. Gathering up portions of the loop and poking them through the surface won't make the loop contractible, because doing this to any segment that lies between two points on the surface breaks the original segment in three, and only pairs of such segments could be contracted down to points.

http://gregegan.customer.netspace.net.au/APPLETS/21/DiracNotes.html

http://gregegan.customer.netspace.net.au/APPLETS/21/21.html

 

[Antonio Lao]

Sol2,

The theory of H-plus and H-minus, as you might have already noticed, is time independent because its variables are metrics and orthogonal forces.

But the topological structure and because of its dynamic, can also represent a chronon (quantum of time).

If we needed time incorporated into the theory, then the forces must be expressed in the time rate of change of linear momenta. When these are done, we get a generalized double actions integral which is numerically equal or greater than the square of Planck's constant.

\int_{0}^{\infty} \int_{\infty}^{0}\left[E^2\right]\,dt_1\,dt_2 \geq h^2

 

[Michael F. Dmitriyev]

Riemannian geometry is static. But if the geometry is dynamic, i.e. introducing a force into the geometry, then the sphere can never be a closed surface.

Certainly the geometry of space-time is dynamic. Each dimension is a force unwrapping the space in a direction perpendicular to all previous.
The fourth too. Therefore the cube in the fourth dimension is transformed to sphere.

 

[Antonio Lao]

Therefore the cube in the fourth dimension is transformed to sphere.

Then in the fifth, the 4-sphere is transformed back to a cube? Could you write down the transform matrix for me?

 

[Michael F. Dmitriyev]

Then in the fifth, the 4-sphere is transformed back to a cube? Could you write down the transform matrix for me?

Cube and corresponding matrixes it is the STATICS. Rotation of a cube concerning all three coordinates forms a sphere. The fifth and the following dimensions are sphere too because any rotation of sphere gives a sphere in the result.
We can observe spheres in the nature. Such form have atoms, planets, stars and the universe itself. But where you saw a cube in the nature? Crystal lattice this three-dimensional internal structure of four-dimensional object.

Michael.

 

[sol2]

If we entertain the sphere these are interesting ideas.


How would they compare to the Klein bottle back to back, or compare to the mobius band?

 

[Michael F. Dmitriyev]

If we entertain the sphere these are interesting ideas.


How would they compare to the Klein bottle back to back, or compare to the mobius band?

The sphere is not a simple figure. Its surface does not contain direct lines.
The sphere can be received through rotation of a cube only.
It satisfies to the requirement of a principle of perpendicularity to all previous dimensions.
Except of that, we lIve in the dynamic space which was valid named as "SPACETIME".

 

[sol2]

The sphere is not a simple figure. Its surface does not contain direct lines.
The sphere can be received through rotation of a cube only.
It satisfies to the requirement of a principle of perpendicularity to all previous dimensions.
Except of that, we lIve in the dynamic space which was valid named as "SPACETIME".

I understood your example to Antonio the first time

To reduce topological movement to a coordinate system?

We still focus on GR, but I think we tend to forget that people were seeing the higher geometries even while Einstein was looking at Reinmann and his graduation speech. We have to thank Gauss:)(rephrase his name if you will:) for his developements and the success of his teachings?

Also the success of leaving Euclid's postulates to a fifth, and how could we not have accepted non-euclidean coordinates?