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pirillo
science forum beginner

Joined: 02 May 2005
Posts: 5

Posted: Thu May 12, 2005 5:46 am    Post subject: Re: Size of strings compared to size of elementary particles

 Quote: You want to average that over space _and_ time to get the rms size of the string. I seem to recall that this is discussed in the references that I provided.

Oh, so you do sort of a " average size for the whole history"
operator which say first computes the average distance from cm at each
time and then averages this over the whole history.

Hmmm?

I thought in curved backgrounds you did this at one instant
and found that the string became larger as time passed.
Or, were you saying more like there's an external parameter
which labels a family of spacetimes (the string lives in)
and as you vary this parameter, the quantity you described
above varies, although --if one changes the target space,
then one changes the states.
Urs Schreiber
science forum Guru Wannabe

Joined: 04 May 2005
Posts: 127

Posted: Thu May 12, 2005 6:33 am    Post subject: Re: Size of strings compared to size of elementary particles

"pirillo" <ultraman2002@hotmail.com> schrieb im Newsbeitrag
 Quote: You want to average that over space _and_ time to get the rms size of the string. I seem to recall that this is discussed in the references that I provided. Oh, so you do sort of a " average size for the whole history" operator which say first computes the average distance from cm at each time and then averages this over the whole history. Hmmm?

I am sorry, but I have a hard time understanding what you are confused

The idea we are talking about is not particular to string theory at
all but seems to be just a matter of common sense: You have some fluctuating
something and want to get an idea of its rough size. So you average the
distance of all its points from its center of mass and, since its
fluctuating, average these distances over some period of time. If that piece
of something is systematically growing or shrinking on larger time scales
you will want to take the time average over an interval which is large
enough compared to the fluctuations but small enough to be local in time
with respect to the long-term behaviour.

To be frank, I feel that the discussion of this point is getting a little
off-topic for sci.physics.strings.
pirillo
science forum beginner

Joined: 02 May 2005
Posts: 5

Posted: Tue May 17, 2005 6:11 am    Post subject: Re: Size of strings compared to size of elementary particles

 Quote: you will want to take the time average over an interval which is large enough compared to the fluctuations but small enough to be local in time with respect to the long-term behaviour.

Yeah, but you said integrate over the "whole" world sheet
not over a "short time band" on the worldsheet. So you're averaging
over the "whole" infinite history. I'm just saying what you seemed to
say --- not what you meant. Which I now think is to integrate over a small
time band.

 Quote: To be frank, I feel that the discussion of this point is getting a little off-topic for sci.physics.strings.

And questions about Gerbes, Calabi Yau manifolds and all these objects
which are purely mathematical are not! Ha
I think this "is" very stringy!
mihai cartoaje
science forum beginner

Joined: 29 May 2005
Posts: 10

Posted: Sun May 29, 2005 6:03 pm    Post subject: Re: Dirac operators on Lorentzian manifolds

i have written:

 Quote: j = Psi^h gamma^0 gamma^a Psi eta_ab w^b which has *d*j = 0.

This is not always true from the construction.
Actually,

j = Psi^h gamma^0 gamma^a Psi eta_ab w^b
= j^b w_b

has the divergence *d*j = j^b w^a(v_a, v_b).

FAIK, it might work to find a coordinate
system in which w = sqrt( eta g ) has the
property v_a . w^a = 0. At first order,
a solution exists iff R = 0 + O(h^2).
Puppet_Sock
science forum Guru Wannabe

Joined: 17 May 2005
Posts: 124

Posted: Mon Jun 06, 2005 9:41 pm    Post subject: Re: From Magnetic Monopole to Magnetic Strings

Golden Boar wrote:
 Quote: I made a huge mistake here, a positive magnetic monopole would annihilate with a negatice magnetic monopole, so no magnetic strings would be formed.

Not necessarily. Monopoles can have electric and topological
charge. There's a name for it objects with both, but I don't
recall it just off. Both values need to be coserved.

You should get a review article or two before you continue.
Socks
zitterbewegung@gmail.com1
science forum beginner

Joined: 24 May 2006
Posts: 8

 Posted: Thu Jun 08, 2006 2:24 am    Post subject: Hybrid Manifold Abstract: [Moderator's note: no responsibility for content. LM] This is an attempt to define a bulk which corresponds to both a string cosmological and brane cosmological formalism which disallows other branes that exist outside this universe. Our bulk is homogenous manifold similar to a Joyce manifold but this then glued at every point to an AdS4 which forms a surface to the manifold . This manifold forms the background of everything that exists. Definition of the Hybrid Manifold We define our bulk as continuous map of all points on a AdS4 (which may or may be periodic) manifold and the Joyce manifold. We state that the observation of the propagation of point particles is actually a reflection of the current shape of the Joyce manifold. On our manifold when the Joyce manifold bends or is warped then the AdS4 manifold's characteristics change as a result of the continuous mapping. In other words the AdS4 manifold shows the shape of the underlying substructure of the Joyce manifold. The Joyce manifold is bound to a certain set of shapes and transformations which must follow the laws of physics in the AdS4. But now we must extend the hybrid manifold to have properties that reflect current physical observations. We must have a manifold that is both restricted to a subset of shapes that can exist on the manifold. Also we must deal with the fact that energy is quantized. A quantization of energy using hybrid manifolds As a string moves through the part of our manifold that consists of the G2 manifold it bends the manifold slightly so that we can detect the point particle on the AdS4 space. The surface of our new manifold is glued and because of this it can reflect properties of its bending The reason we can detect different messenger particles is because as a string moves through our hybrid manifold it is bound at certain parts of the hybrid manifold due to the structure of the manifold. There are only a specific set of path's that the string can move through and that determines how the surface is bent. Another property is that due to quantization the vibrations of the string follow an ascending or descending chain of vibrational patters as the strings gain or lose energy. Therefore each string follows a set of vibrations given a specific amount of energy that a string possesses. Disallowing Violations of the Laws of Physics Certain properties of physics can be disallowed by the Joyce Manifold being unable to transform to that state because it is impossible. Certain holes that may occur may require a great deal of energy which are prohibitive to accomplish because they require a great deal of mass , energy, or mass/energy density. Therefore they would be difficult or maybe even impossible to accomplish. Gravity Representation There are two ways to represent gravity using this hybrid space. One way is to give it a formal messenger particle and have a given energy value for it. Another method is to say that gravity is a result of the specific shape of the Joyce manifold and requires no messenger particle whatsoever. This representation will be chosen once we have direct evidence for either outcome and may remain independent of the theory. Conjectures An interesting conclusion that we can get from this formalism is that we don't need a set of interacting branes to start the process of the formation of the universe. Instead some event must create a difference inside of the space and make it form into a stable state. Therefore we can confine the universe formation to just this brane. Another conclusion we might be able to draw is that the underlieing substructure allows for the space to be improbablly flat and bypasses all horizons by being glued to a singular space that influences all spacetime. That it is merely a propery of the substructure and independant of an alternate form of matter.
zitterbewegung@gmail.com1
science forum beginner

Joined: 24 May 2006
Posts: 8

 Posted: Thu Jun 08, 2006 2:25 am    Post subject: Rewrite of my assumptions. Was: Mistakes (again) [Moderator's note: no responsibility for the content. LM] This is an attempt to define a bulk which corresponds to both a string cosmological and brane cosmological formalism which disallows other branes that exist outside this universe. Our bulk is homogenous manifold similar to a Joyce manifold but this then glued at every point to an AdS4 which forms a surface to the manifold . This manifold forms the background of everything that exists. This bulk exists Definition of the Hybrid Manifold We define our bulk as continuous map of all points on a AdS4 (which may or may be periodic) manifold and the Joyce manifold. We state that the observation of the propagation of point particles is actually a reflection of the current shape of the Joyce manifold. On our manifold when the Joyce manifold bends or is warped then the AdS4 manifold's characteristics change as a result of the continuous mapping. In other words the AdS4 manifold shows the shape of the underlying substructure of the Joyce manifold. The Joyce manifold is bound to a certain set of shapes and transformations which must follow the laws of physics in the AdS4. But now we must extend the hybrid manifold to have properties that reflect current physical observations. We must have a manifold that is both restricted to a subset of shapes that can exist on the manifold. Also we must deal with the fact that energy is quantized. A quantization of energy using hybrid manifolds As a string moves through the part of our manifold that consists of the G2 manifold it bends the manifold slightly so that we can detect the point particle on the AdS4 space. The surface of our new manifold is glued and because of this it can reflect properties of its bending The reason we can detect different messenger particles is because as a string moves through our hybrid manifold it is bound at certain parts of the hybrid manifold due to the structure of the manifold. There are only a specific set of path's that the string can move through and that determines how the surface is bent. Another property is that due to quantization the vibrations of the string follow an ascending or descending chain of vibrational patters as the strings gain or lose energy. Therefore each string follows a set of vibrations given a specific amount of energy that a string possesses. Disallowing Violations of the Laws of Physics Certain properties of physics can be disallowed by the Joyce Manifold being unable to transform to that state ; because to do so would change the topology of the space so greatly that the energy required would be enormous. Gravity Representation There are two ways to represent gravity using this hybrid space. One way is to give it a formal messenger particle and have a given energy value for it. Another method is to say that gravity is a result of the specific shape of the Joyce manifold and requires no messenger particle whatsoever. This representation will be chosen once we have direct evidence for either outcome and may remain independent of the theory.
zitterbewegung@gmail.com1
science forum beginner

Joined: 24 May 2006
Posts: 8

 Posted: Sat Jul 15, 2006 10:54 am    Post subject: PDF version of Idea Here is a pdf of the idea with minor modifications. http://1946875.tripod.com/brane-hybrid-manifold.pdf [Moderator's note: the newsgroup does not endorse this document. LM]

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