What Cosmologist Wants From String theory

The most surprising difference for the quantum case is the so-called zero-point vibration" of the n=0 ground state. This implies that molecules are not completely at rest, even at absolute zero temperature.

When I looked at the issues strings presented of itself, the very idea of changing the way we percieve the basis of reality came into question. If strings were to exist where did they come from? This assumption, on my part asked me to consider then, that the very basis of this reality was drive by a quantum harmonic oscillator, and that there was never really any zero point in which to consider? Was this a logical assumption about how we would percieve the basis, from some emergent property that had to always exist?



This kind of thinking then forces you to consider what if this universe had always existed? How could it have ever come into being? Could such a realization have been embued into the string cosmology understanding, of the way this universe is operating?

So on a cosmological scale, we have this synopsis of events, as they have been shown in this following Picture taken from Beyond Einstein. Imagine then, how you might encapsulate this whole picture into a simple explanatory feature that trends this quantum beginning to cosmological end, in a cyclcial fashion worth speculating.



From this perspective ,it is with some consideration that we are directed again to Turok, Steinhardt in brane collisions. Or others like Gasperini and Venziano in, "The Pre-Big Bang Scenario in String Cosmology".

The Gravity For Instance Varies with Time

There was some reference made in regards to Lubos and the post Santos quoted from, Superstrings, a Theory of Everything? by P.C.W Davies and J. Brown. The idea of the quote about ole men and how things change, seemed to have been caught in perspective by Santos? That becuase I had this book handy, I went and looked to the reference page that he suggested of 193.

Well, one has to go over the post in question and find the link provided by Peter Woit to understand the context in which this quote is being used. To see that Lubos makes light of his own position, where holding dogmatic to a certain position might be as relevant to where ole men do not accept the new reality easily. It was a innocent enough comment that has certain connatations to it, that moved me through the article santos quotes and brought forth different information for consideration.




For instance before quoting Feynman myself, lets read what Gabriele Veneziano has to say.

String theory suggests that the big bang was not the origin of the universe but simply the outcome of a preexisting state

Now considering the publishing date on this book, "Superstrings, A Theory of Everything," which was 1988, you have to wonder about the progression and way in which we determine dimenisons. I have detailed it in the previous post entitled, "Spheres and their Generalizations in Higher Dimensions." If such a view was to remain consistent then the statement of Richard Feynman to follow, answers today, what he speculated then.

Now it's possible that those kinds of laws in physics may be incomplete. It might be that the laws change absolutely with time; that grvaity for instance varies with time and that this inverse square law has a strength which depends on how long it is since the beginning of time. In other words, it's possible that in the future we'll have more understanding of everything and physics may be completed by some kind of statement of how things started which are external tothe laws of physics.

Pg 206 and 207, of Superstrings, A Theory of Everything, by P.C.W.Davies and J. Brown



So you see, perspective changes because of theoretical positions, concepts form and new insights develope. Because of a personal interest of Feynman's, about his perception of the physics of approach, did you think at first he had a cohesive picture of the toy models he produced? Do you think Andrew Wiles would have ever solved the Fermat Equation?

Such context of the Poincare Conjecture, answers a question we have about how quantum grvaity portrays itself, by the ole soccer ball( my solid), or by how we see conceptual changes allow us to think about the higher dimensional values in regards to gravity? Of tying geometry and topological understandings together.

Do you think Feynman toy models haven't been included?

A Merry Christmas to Everyone, and a Happy New Year.

Andrew Wiles and Fermat

In context of previous post on mathematical problems, it was interesting to carry on, and look at other math issues here. So these links help provide a interesting commentaries, on other math problems, that are interesting and thought provoking.

 

Fermat was a 17th-century mathematician who wrote a note in the margin of his book stating a particular proposition and claiming to have proved it. His proposition was about an equation which is closely related to Pythagoras' equation. Pythagoras' equation gives you:
x² + y² = z²

Update


See Also:

Andrew Wiles: 60th birthday

About Spheres and their Generalizations of Higher Dimensional Spaces

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

— Nikolai Lobachevsky

If a math man were to be left alone, and devoid of the physics, would he understand what the physics world could impart if he were not tied to it in some way?:)

Poincaré Conjecture

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

Now it is of course with some understanding, that few would recognize what this conjecture to mean, and having just read Andre' Weil's last word I do not think it to shabby to say that in this case, the Poincare conjecture has been recognized as a valid conjecture, that has taken some time in it being resolved.




For me being presented with the cosmic string scenario might seem just as complex, when in considertaion of the brane. How our universe could be contained in it. Some might of laughed it off quite easily, being part of some revolution of strings to M-theory, that it could include 11 dimensions.How would you embed these dimensions with these shapes?

What fascinates me, is how we could have found such visualizations of these topological forms within the the brane world and how this may have been described?

So I am looking for traces of literature that would help me in this direction. For example, how a torus would be looked at in a 2 dimensional sheet. Would this be relevant to brane world happenings if we considered, the example of "sound" (make sure speakers are on) in higher dimensions, as viable means of expression of these curvatures of those same shapes?



Of course I know I have to explain myself here, and the intuitive jump I am making. Could be wrong?

Part of this struggle to comprehend what has happened with bringing GR and QM together in one consistent framework, was to undertand that you have altered the perceptions of what dimension will mean? To me, this says that in order now for us to percieve what the poincare conjecture might have implied, that we also understand the framework with which this will show itself, as we look at these forms.

The second panel I showed of the graph, and then the topological form beside it, made sense, in that this higher dimension shown in terms of brane world happenings would have revealled the torus as well in this mapping. This is of course speculation on my part and might fall in response to appropriate knowledge of our mathematical minds. This gives one a flavour of the idea of those extra dimensions.



Well part of this developement of thinking goes to what these three gentlemen have developed for us in our new conceptual frameworks of higher dimenions. If you ask what higher dimension might mean, then I am certain one would have to understand how this concept applies to our thinking world. Without it, these shapes of topological forms would not make sense. It seems this way for me anyway.:)



I hazard to think that John Baez and others, might think they have found the answer to this as well, in what they percieve of the mighty soccerball, and the fifth solid I espouse:)

Hodge Conjecture

Interplay between geometry and topology.

One of the things that I am having difficulty with is if I understood the idea of a cosmic string. The understanding would have to imply that the higher dimensions would reveal themselves within the spacetime curvatures of gravity. So I have been looking to understand how the quantum mechanical nature could have ever reduced itself from those higher dimensions in string theory, and revealed themselves within the context of the cosmos that we know works very well with Gravity.



Part of my attempts at comprehending the abtractness with which this geometry evolved, was raised diffrent times within this blog as to whether or not there was a royal road to geometry?

Throughout, I have shown the processes with which a smooth topological feature would have endowed movements like the donut into the coffee cup and wondered, about this idea of Genus figures and how they to become part of the fixtures of the terrain with which mathematicians like to enjoy themselves over coffee?:)



How would this information in regards to the strings, become a viable subject with regards to non-euclidean realms, to have understood where GR had taken us and where QM had difficult combining with GR(gravity).

Large extra dimensions are an exciting new development … They would imply that we live in a brane world, a four-dimensional surface or brane in a higher dimensional spacetime. Matter and nongravitational forces like the electric force would be confined to the brane … On the other hand, gravity in the form of curved space would permeate the whole bulk of the higher dimensional spacetime …. Because gravity would spread out in the extra dimensions, it would fall off more rapidly with distance than one would expect … If this more rapid falloff of the gravitational force extended to astronomical distances, we would have noticed its effect on the orbits of the planets … they would be unstable… However, this would not happen if the extra dimensions ended on another brane not that far away from the brane on which we live. Then for distances greater than the separation of the branes, gravity would not be able to spread out freely but would be confined to the brane, like the electrical forces, and fall off at the right rate for planetary orbits.

Stephen Hawking, Chapter seven

Mirror Symmetry and Chirality?

What is the mathematical reasoning, for reducing GR down to the quantum world? How would these application be considered in a supersymmetrical world?

Is the figure-eight knot the same knot as its mirror-image? The property of "being the same as your mirror-image" is called chirality by knot theorists. The image sequence below shows the figure-eight knot being transformed into its mirror image -- such knots are called achiral

You have to remember this is the year 2000, article was produced below.

Physicists Finally Find a Way to Test Superstring Theory

As the unification quest has forged ahead, physicists have found it necessary to expand superstring theory to include vibrating membranes -- called branes for short. These are not just two-dimensional surfaces, like the skin of a drum or the world of the Flatlanders. Hard as it may be to picture, there can be branes with three, four, five or more dimensions. These "surfaces" can be tiny like the strings but they can also span across light-years.

by George Johnson

I know this may seem a little slow but if the cosmic string was considered in context of the Fresnel lens and I apologize for my ignorance, how would reverse imaging account for gravitational lensing?

The gravitational lensing has to reveal the warp field as such a possibility? Yet, in that distant time, such alteration of the shapes, amongst it event, would have show two points, but would also have indication that one was the reverse of the other. What signatures would we see of this?



So in keeping with the direction we were given by Lubos in his article, I a am trying to comprehend.

This page is the beginning of a demonstration of strong gravitational lensing about a pseudo-isothermal elliptical mass distribution (PID). You can look at a simple animation or read about the mathematics behind the PID lensing.

Dilation and the Cosmic String

One such field, called the dilaton, is the master key to string theory; it determines the overall strength of all interactions. The dilaton fascinates string theorists because its value can be reinterpreted as the size of an extra dimension of space, giving a grand total of 11 spacetime dimensions

According to T-duality, universes with small scale factors are equivalent to ones with large scale factors. No such symmetry is present in Einstein's equations; it emerges from the unification that string theory embodies, with the dilaton playing a central role.

Gabriele Veneziano


According to Einstein's theory of general relativity, the sun's gravity causes starlight to bend, shifting the apparent position of stars in the sky.

Time will also pass more slowly in a strong gravitational field than in a weak one? So what effect would this have if we consider the gravitational lensing, that had been talked about in previous post?:)

On the Effects of External Sensory Input on Time DilationA. Einstein, Institute for Advanced Study, Princeton, N.J.

Abstract: When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute and it's longer than any hour. That's relativity.

As the observer's reference frame is crucial to the observer's perception of the flow of time, the state of mind of the observer may be an additional factor in that perception. I therefore endeavored to study the apparent flow of time under two distinct sets of mental states.



Where spacetime is flat, there is no gravity, hence light will travel unabated. If we move this consideration in contrast to the non-euclidean realms, what have we learnt of gravity? What have we learnt of dimensions?



Mass, Photons, Gravity Dr. Lev Okun, ITEP, Russia

Warped Field Creates Lensing

The statement of this post, is distilled from the collaboration of some of the images to follow.



In cosmic string developement there are these three points to consider.

1. Cosmological expansion

2. Intercommuting and Loop Production

3. Radiation

I am always looking for this imagery that helps define further what gravitational lensing might have signified in our perception of these distances in space. How the cosmic string might have exemplified itself in some determination, as we find Lubos has done in the calculation of the mass and size of this early event. This image to follow explains all three developemental points.



Bashing Branes by Gabriele Veneziano
String theory suggests that the big bang was not the origin of the universe but simply the outcome of a preexisting state

The pre–big bang and ekpyrotic scenarios share some common features. Both begin with a large, cold, nearly empty universe, and both share the difficult (and unresolved) problem of making the transition between the pre- and the post-bang phase. Mathematically, the main difference between the scenarios is the behavior of the dilaton field. In the pre–big bang, the dilaton begins with a low value--so that the forces of nature are weak--and steadily gains strength. The opposite is true for the ekpyrotic scenario, in which the collision occurs when forces are at their weakest.

The developers of the ekpyrotic theory initially hoped that the weakness of the forces would allow the bounce to be analyzed more easily, but they were still confronted with a difficult high-curvature situation, so the jury is out on whether the scenario truly avoids a singularity. Also, the ekpyrotic scenario must entail very special conditions to solve the usual cosmological puzzles. For instance, the about-to-collide branes must have been almost exactly parallel to one another, or else the collision could not have given rise to a sufficiently homogeneous bang. The cyclic version may be able to take care of this problem, because successive collisions would allow the branes to straighten themselves.

The most strongest image that brought this together for me was in understanding what Neil Turok and Paul Steinhardt developed for us. It was watching the animation of the colliding branes that I saw the issue clarify itself. But before this image deeply helped, I saw the issue clearly in another way as well.

The processes of intercommuting and loop production.

It was very important from a matter distinction, to understand the clumping mechanism that reveals itself, after this resulting images of the galaxy formation recedes in the colliding brane scenrio viewing. If such clumping is to take place, we needed a way in which to interpret this.




Branes Reform Big Bang By Atalie Young

Catch a Wave From Space

Imagine the journey it took for us to have come to the developement of the methods to discern the nature of the Universe, and what Einstein has done for us in terms of General Relativity. A statement, about Gravity.




Imagine these great distances in space, and no way in which to speak about them other then in what LIGO will translate? That any extention of this prevailing thought could not have found relevance in the connection, from that event to now, and we have found ourselves limited in this view, with bold statements in regards to Redshifting perspectives?



Without a conceptual framework in which to look at the gravitational differences within the cosmo, how the heck would any of this variation make sense, if you did not have some model in which to regulate distances traversed, in the space that must be travelled?

Albert Einstein discovered long ago that we are adrift in a universe filled with waves from space. Colliding black holes, collapsing stars, and spinning pulsars create ripples in the fabric of space and time that subtly distort the world around us. These gravitational waves have eluded scientists for nearly a century. Exciting new experiments will let them catch the waves in action and open a whole new window on the universe - but they need your help to do it!

Cosmic strings are associated with models in which the set of minima are not simply-connected, that is, the vacuum manifold has `holes' in it. The minimum energy states on the left form a circle and the string corresponds to a non-trivial winding around this.

3 Sphere

What would mathemaics be without artistic expression, trying out it's hand at how such geometrical visions continue to form? Did Escher Gauss and Reimann, see above 3 sphere?

An expression of Salvador Dali perhaps in some religious context, who then redeems himself, as a man and author of artistic expression?

A sphere is, roughly speaking, a ball-shaped object. In mathematics, a sphere comprises only the surface of the ball, and is therefore hollow. In non-mathematical usage a sphere is often considered to be solid (which mathematicians call ball).

More precisely, a sphere is the set of points in 3-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. The fixed point is called the center or centre, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.



Spheres can be generalized to higher dimensions. For any natural number n, an n-sphere is the set of points in (n+1)-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is, as before, a positive real number. Here, the choice of number reflects the dimension of the sphere as a manifold.

a 0-sphere is a pair of points
a 1-sphere is a circle
a 2-sphere is an ordinary sphere
a 3-sphere is a sphere in 4-dimensional Euclidean space

Spheres for n ¡Ý 3 are sometimes called hyperspheres. The n-sphere of unit radius centred at the origin is denoted Sn and is often referred to as "the" n-sphere. The notation Sn is also often used to denote any set with a given structure (topological space, topological manifold, smooth manifold, etc.) identical (homeomorphic, diffeomorphic, etc.) to the structure of Sn above.

An n-sphere is an example of a compact n-manifold.

So in looking for this mathematical expression what does Gabriele Veneziano allude too in our understanding of what could have come before now and after, in the expression of this universe, that it is no longer a puzzle of what mathematics likes express of itself, now a conceptual value that has encapsulated this math.



Cycle of Birth, Life, and Death-Origin, Indentity, and Destiny by Gabriele Veneziano


In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. A regular sphere, or 2-sphere, consists of all points equidistant from a single point in ordinary 3-dimensional Euclidean space, R3. A 3-sphere consists of all points equidistant from a single point in R4. Whereas a 2-sphere is a smooth 2-dimensional surface, a 3-sphere is an object with three dimensions, also known as 3-manifold.

In an entirely analogous manner one can define higher-dimensional spheres called hyperspheres or n-spheres. Such objects are n-dimensional manifolds.

Some people refer to a 3-sphere as a glome from the Latin word glomus meaning ball.

So as if beginning from some other euclidean systemic pathway of expression, how in spherical considerations could topolgical formation consider Genus figures, if it did not identify the smooth continue reference to cosmoogical events? Where would you test this mathematics if it cannot be used and applicable to larger forms of expression, that might also help to identfy microstates?

The initial process of particle acceleration is presumed to occur in the vicinity of a super-massive black hole at the center of the blazar; however, we know very little about the origin of the jet. Yet it is precisely the region where the most important physics occurs: the formation of a collimated jet of charged particles, the flow of these particle in a narrow cone, and the acceleration of the flow to relativistic velocities.


So in looking at these spheres and their devlopement, one might have missed the inference to it's origination, it's continued expression, and the nice and neat gravitational collpase that signals the new birth of a process? Can it be so simple?

Would it be so simple in the colliders looking for those same blackholes?