Quantum Geometry-the Brian Greene quote

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  • #26
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There was a question on sci Physics string about the size of the string.

I wanted to add one more quote of Greene's here so that the undertsanding of the string not only froma cosmological standpoint are undertsood, but also from the very nature of the matters.

it turns out that within string theory ... there is actually an identification, we believe, between the very tiny and the very huge. So it turns out that if you, for instance, take a dimension - imagine its in a circle, imagine its really huge - and then you make it smaller and smaller and smaller, the equations tell us that if you make it smaller than a certain length (its about 10-33 centimeters, the so called 'Planck Length') ... its exactly identical, from the point of view of physical properties, as making the circle larger. So you're trying to squeeze it smaller, but actually in reality your efforts are being turned around by the theory and you're actually making the dimension larger. So in some sense, if you try to squeeze it all the way down to zero size, it would be the same as making it infinitely big.

Without this model comprehension it would be difficult to understand the transformatiom http://universe.gsfc.nasa.gov/images/lifecycles/cycles.jpg [Broken] in the cosmos?

The missions of Beyond Einstein can address some of the goals of the Cycles of Matter and Energy program. But to unravel the interlinked cycles, future missions with additional capabilities are needed.

To decipher the flows of gas and energy in the first galaxies: a cryogenic, large aperture infrared observatory.

To uncover how supernovae and other stellar explosions work to create the elements: an advanced Compton telescope and a hard-X-ray spectroscopic imager.

To map the "invisible" Universe of dark matter and gas expelled during the birth of galaxies: a large-aperture telescope for imaging and spectroscopy of optical and ultraviolet light.

To measure the motions of the hottest and coldest gas around black holes: a radio interferometer in space.

To see the birth of the first black holes and their effect on the formation of galaxies, and to probe the behavior of matter in extreme environments: a very large aperture arc-second X-ray imaging telescope.

To determine the nature and origin of the most energetic particles in the Universe today: a mission to track them through their collisions with the Earth.

http://universe.gsfc.nasa.gov/lifecycles.html [Broken]
I hope this sparks some new paradigmal views? :smile:
 
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  • #27
jeff
Science Advisor
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Hi sol/sol2 :smile:,

Thanks for all the comprehensions and perspectives? Your understandings and consistencies are good developments? In fact, the development of the question mark key off your keyboard would also be a good development?
 
  • #28
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jeff said:
Hi sol/sol2 :smile:,

Thanks for all the comprehensions and perspectives? Your understandings and consistencies are good developments? In fact, the development of the question mark key off your keyboard would also be a good development?
How can we say anything with absolute certainty( I have been reminded often) when we have all this theoretical developement going on?

You could jump in anytime, correct or add your perspective. I know I am always on shaky ground amongst those who are better educated then myself. I could use exclamation points, then it always seem like a surprize and that, would be misleading?

Or it could always end as a statement, as if I knew what I was talking about all the time. As we both know, I have a lot to learn :smile:

The smilies represent my humour, and happiness, with actually understanding something? So don't ask me about that. :biggrin:

I just wish all the posts were as simple as yours :rofl:
 
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  • #29
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I thought I better conclude this thread with one more quote from Greene to help point out the the central point for consideration and balance between, and imagine at what point the klien bottle could describe the Life cycle of energy and matter in the cosmo?


The familiar extended dimensions, therefore, may very well also be in the shape of circles and hence subject to the R and 1/R physical identification of string theory. To put some rough numbers in, if the familiar dimensions are circular then their radii must be about as large as 15 billion light-years, which is about ten trillion trillion trillion trillion trillion (R= 1061) times the Planck length, and growing as the universe explands. If string theory is right, this is physically identical to the familiar dimensions being circular with incredibly tiny radii of about 1/R=1/1061=10-61 times the Planck length! There are our well-known familiar dimensions in an alternate description provided by string theory. [Greene's emphasis]. In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249)
The End? :smile:
 
  • #30
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Sol, take something of profound interest in your many dimensional quests, here:http://physicsweb.org/objects/world/13/11/9/pw1311091.gif

and go ask a string theorist what are the paramiters of 'Distance' and 'Length', how does one define a distance of a single string(from its nearest neigbour), with one of its own individual total length (compared to any other string)?
 
  • #31
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Olias said:
Sol, take something of profound interest in your many dimensional quests, here:http://physicsweb.org/objects/world/13/11/9/pw1311091.gif

and go ask a string theorist what are the paramiters of 'Distance' and 'Length', how does one define a distance of a single string(from its nearest neigbour), with one of its own individual total length (compared to any other string)?
In such a compactified state how would we coordinate anything? :smile:

Given the dearth of knowledge about gravity in the subcentimeter range, the group is looking for any kind of deviation from expectations, not just extradimensional effects, he says. Nonetheless, the excitement about extra dimensions helps spur the group on, Price says.

If the strength of gravity takes a sharp turn upward at around 1 TeV, as the Stanford-Trieste scenario implies, an opportunity opens for testing this theory also in accelerators. Collisions at such energies could produce gravitons in large numbers, and some of these particles would immediately vanish into the extra dimensions, carrying energy with them. Experimenters would look for an unusual pattern of so-called missing energy events.

This and more subtle effects of extra dimensions could show up at existing accelerators, such as LEP and the Tevatron at Fermilab, only if the dimensions have scales nearly as big as a millimeter. The powerful LHC will greatly improve the chances for detecting missing energy events and other prominent extradimension effects.

http://www.sciencenews.org/articles/20000219/bob1.asp
(bold emphasis my own)


Sometimes it seems incomprehensible how such thoughts could have ever gotten where they are and when one speaks, of what "realm(dimension)" are they speaking? :smile:

On what journey could any photon take and its interaction not make one wonder? Had it gone somewhere and re-appeared? Would it have been as simpe as looking at the tracks and knowing that some event had taken place and there is a gap?

http://www-egs.slac.stanford.edu/cgi-bin/egsdemo/newshower.html

What kind of Quantum "geometry" is going to explain Quantum Gravity?


'There comes a time when the mind takes a higher plane of knowledge but can never prove how it got there. All great discoveries have involved such a leap. The important thing is not to stop questioning.'

Albert Einstein
(1879- 1955)
 
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  • #32
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A Possible Origin of Dark Energy

sol2 said:
Since there were so few papers on this I wonder if many will have a perspective on this issue? I hope so. GR has to lead into QM?

There is a historical developement here that many do not need to be reminded about, but for a laymen, it was very important to undertand this developement in concert with current technolgical realites. This is a GR generalization and next I hope to demonstrate the other extreme of the Heirarchy problem in terms of Geometrodynamics.

Membrane Realization?

http://new.math.uiuc.edu/optiverse/img/rs11-107.jpeg [Broken]

Bubble eversions


An Introduction to Geometrodynamics

The existence of gravitational waves is a prediction of the General Theory of Relativity which is Einstein's explanation of the gravitational interaction (1915). The basic idea is:

Gravity is no force but an aspect of the geometry of spacetime.

Space is not an absolute invariant entity, but is influenced by the distribution of mass and energy in the Universe. The basic principle is:

Matter tells space how to curve, and space tells matter how to move.

Large masses introduce a strong curvature in spacetime. Light and matter are forced to move according to this metric. Since all the matter is in motion, the geometry of space is constantly changing. Hence Geometrodynamics is a better name for Einstein's theory of gravitation. In order to derive the basic field equation, one has to relate the curvature of space to the mass/energy density:


G = k T

http://www.physics.gla.ac.uk/gwg/geodynamics.html [Broken]

This will not answer the direct comparsion just yet Marcus, but I hope to demonstrate where I think it will lead too. I will back off now and hopefully we can will see a direction (quantum geometry) this forum takes, as well as sci.Physics.strings or even Peter Woit:)

Is this okay Marcus?
So we look at the universe in a different way? I mean the whole time we are talking about this quantum process we look at what's happening around it cosmologically. It does not discard what would happen with those galaxies as either in terms of the http://universe.gsfc.nasa.gov/images/lifecycles/cycles.jpg [Broken] as it would be a very dynamical universe.



T. D. Lee
We discuss the possibility that the existence of dark energy may be due to the presence of a spin zero field $\phi(x)$, either elementary or composite. In the presence of other matter field, the transformation $\phi(x)\to \phi(x) +$ constant can generate a negative pressure, like the cosmological constant. In this picture, our universe can be thought as a very large bag, similar to the much smaller MIT bag model for a single nucleon.
http://uk.arxiv.org/abs/astro-ph/0404601
Thanks Olias for link of earlier time
 
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  • #33
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What is David Gross and John Schwarz asking us to believe about those hidden dimensions? How did we get there?

http://www.hyper-mind.com/hypermind/universe/content/gsst09/anim100.GIF [Broken]

http://www.hyper-mind.com/hypermind/universe/content/gsst09/ima4.GIF [Broken]

So there is a easy assumption about gravtonic conisderations, that asks us to believe in the "bulk" and what can go there.

Do you see ? Do you really http://wc0.worldcrossing.com/WebX?14@240.ZqQwclGxAtV.1@.1ddf4a5f/104 [Broken] ? :smile:
 
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  • #35
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Arivero's thread and the ideas of compaction are being held in mind, and I am gathering my thoughts in his directions.

The Kaluza-Klein compactification of strings can be done on more than one dimension at once. When n dimensions are compactified into circles, then this is called toroidal compactification, because the product of n copies of a circle is an n-torus, or Tn for short.


The effect of adding an extra compact dimension is more subtle than that. It causes the effective gravitational constant to change by a factor of the volume 2pR of the compact dimension. If R is very small, then gravity is going to be stronger in the lower dimensional compactified theory than in the full higher-dimensional theory.
http://superstringtheory.com/experm/exper5a.html


I would like to illustrate further from Hypermind and David Gross here, to define how we see these dimensions. Clarity, in how this is seen.

"String theory tells you that this must be the structure of the world. There must be three of these big dimensions that we know about. And six of these small dimensions that we can't see. And the reason we can't see them is that their size has the same characteristic very small length. "
http://www.hyper-mind.com/hypermind//universe/content/gsst.htm [Broken]


http://www.hyper-mind.com/hypermind//universe/content/gsst09/ima4.GIF [Broken]

1 dimension of time + 9 dimensions of space
=
10 dimensions

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

If we take the radius of the circle to be very large (the dimension is de-compactifying) then the allowed values of the momentum become very closely spaced and begin to form a continuum. These Kaluza-Klein momentum states will show up in the mass spectrum of the uncompactifed world. In particular, a massless state in the higher dimensional theory will show up in the lower dimensional theory as a tower of equally spaced massive states just as in the picture shown above. A particle accelerator would then observe a set of particles with masses equally spaced from each other. Unfortunately, we'd need a very high energy accelerator to see even the lightest massive particle.

Strings have a fascinating extra property when compactified: they can wind around a compact dimension which leads to winding modes in the mass spectrum. A closed string can wind around a periodic dimension an integral number of times. Similar to the Kaluza-Klein case they contribute a momentum which goes as p = w R (w=0,1,2,...). The crucial difference here is that this goes the other way with respect to the radius of the compact dimension, R. So now as the compact dimension becomes very small these winding modes are becoming very light!
http://www.physics.ucsb.edu/~strings/superstrings/extradim.htm

One of the important features I had been trying to drive home is how the cosmos, not only holds our eye to the vastness of what GR tells us, but with the string persperctive, we also have a eye on the very nature of the reality strings provides. So how would such models materialize into observable views of matter orientated states?

Further reading helps in regards to the links, but the real essence of the light switch has not been totally understood.

The advancement I see in superstringtheory comes from a understanding of a perception that that brings th every small and the very large together within a comprehensive view and to me signals a advance within the consciousness and a new route that reveals the depth of the reality around us.

Of course some will say that this post might have been a disservice to science and the fundamentals of theoretcial developement, but the true beauty to me, is in the recognizition of the igniting neurons that can take place rapidly when above and below are joined :smile:


How can a speck of a universe be physically identical to the great expanse we view in the heavens above?
(Greene, The Elegant Universe, pages 248-249)

Liminocentric Structures



M theory, is Eleven.
 
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  • #36
selfAdjoint
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Sol, I don't want to hassle you, and I have thought long and hard about whether to post this, but I think you will apopreciate the facts, rather than a pacifier.

The happy string talk you quoted from that UCSB site is obsolete. I think it was Witten who first pointed out that the standard model isn't just "generations of particles". it has some specific, rather complex, machinery under the hood. Chiral properties, if you want a buzzword. And the simple models like the one you link to just don't cope with the chiral properties.

Furthermore, when you build string models that do respect the chiral facts of life, those models don't look like the pretty models that were originally fed to the public. Now we have strings with their endpoints fixed to branes - different branes for each end, and the branes intersect, so you get kind of a mesh of branes and strings running every which way, and all this machinery is needed to faithfully represent that machinery which is under the hood of the standard model.

It is a long dream of humanity to find a SIMPLE explanation for the variety of our perceived world. For a while, it looked like string physics coud do that. And maybe they will eventually get back to a simple explanation. But right now their attempts to model what the accelerators see is looking uncomfortably like Ptolemy's epicycles.
 
  • #37
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selfAdjoint said:
Sol, I don't want to hassle you, and I have thought long and hard about whether to post this, but I think you will apopreciate the facts, rather than a pacifier.
I have appreciated your posts over the years the most, and as a true mentor. Will it deter the direction I am going? :rofl:

selfAdjoint said:
The happy string talk you quoted from that UCSB site is obsolete. I think it was Witten who first pointed out that the standard model isn't just "generations of particles". it has some specific, rather complex, machinery under the hood. Chiral properties, if you want a buzzword. And the simple models like the one you link to just don't cope with the chiral properties.
It has been very important that this subject come forward in its perspective, and looking at the standard model still requires a framework from which to map it's features from the early universe to today. I do not think we will have argument here. We needed to go beyond the standard model would you agree?

selfAdjoint said:
Furthermore, when you build string models that do respect the chiral facts of life, those models don't look like the pretty models that were originally fed to the public. Now we have strings with their endpoints fixed to branes - different branes for each end, and the branes intersect, so you get kind of a mesh of branes and strings running every which way, and all this machinery is needed to faithfully represent that machinery which is under the hood of the standard model.
Yes getting to that point is a real challenge for some. :smile: It still requires a basic understanding of why graviton consideration are being used and how this was advanced. If this is not looked at, there is no way in which to move ahead here in a very abstract world the mathematics is building.

So yes in the sense I am going over old material and trailing the current perspectives, but the concepts are still there in general. This has not been removed from the explanation of higher dimensional applications, even though those dimensions are hidden. I still have to understand the frame work in which these branes are establish and working on the thread how branes came to be, is a continuing effort. My advancement will come from those who I can engage and those who are continuing to publish. My past history here and gathering of information will support that opinion.

selfAdjoint said:
It is a long dream of humanity to find a SIMPLE explanation for the variety of our perceived world. For a while, it looked like string physics coud do that. And maybe they will eventually get back to a simple explanation. But right now their attempts to model what the accelerators see is looking uncomfortably like Ptolemy's epicycles.
This is a good point. Before I finished this post below it was well evident to me where I would be going next to post and fortunately you responded in the very thread :smile:

What had to be realized is that all the time we have this model(string/Mtheory) trying to describe the very nature of our reality, granted it is a model of apprehension that has so many paintings that one could draw, the application still had to be recognized in the current structure experimental data is current confronting.

Here this means Glast, and LQG attempt at photon intersection. Theoretically this has to be taken a step further, yet there are limitations that we have come to face, which requires greater undertandings by me, but do not lack the trail I have followed to its conclusion for LQG. Why would I say this?

One had to have a model in mind the whole time we ask to falsify these methods we like to use. Looking at the information released in gamma
radiation we get this preview, of the dynamics being revealled over a vast amount of time.

The ideas of strings attached to branes became a complicated one to me when I look back to those events and find the fermions could be attached and then not? Yes very confusing, when you hold in mind that the em considerations are held to the brane. This would mean the length of that travel from the event has never really been separated, once we get this information here?

Holding this thought in mind, I had heard LUBOs and Urs make a comment sometime back about the nature of the photon if we had given it another spin? That sort of tweaked my ears and of course complicated the picture more :smile: Even Smolin, with information revealed by Marcus is speaking to this nature.

But that's not what I want to say :smile: What I want to say is that the method needs to be esatblished to describe the negative energy being ejected at the same time the grvaiational collpase is taking place and how much further string/M theory will establish a view , then what will be limited by LQG? This is important

The downfall as I have stated before will be if LQG is verified through this Glast process, and the issue then it will be how to describe that negative energy being ejected from the gravitational collapse. A I said before LQG is limited here, and we will have to look for a much more romantic process if strings are proved wrong. :smile:

But I am a optimist. I look at the gravitational understanding we have in place. Those boson's that arise from the point on the brane, and as gravitons, geometrically describe for us a the nature of quantum geometry, of quantum gravity.

The models that I am demonstrating, together, point to the understanding of the boson as a close string, that reveals information about the event. That I might have shown the boson as a ring that vibrates, would not have removed the thinking from this view, that we could not look back to the early universe and know, we are directly connected to all around us.

You understand this or we could not look at the information we hope to recieve in LIGO.Kip Thorne is very smart this way and has been a good father for a lot of us. :smile:

Thank you for the continued support you offer.
 
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  • #38
  • #39
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As you can see LQG is not alone in its attempt to define the parameters of quantum geometry to qubits in computation, to accurately describe the nature of the universe.
 
  • #40
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Degrees of Freedom

I had found some relation in how LQG could applied it geometrical structure in relation to John Baez's soccer ball, to look at the cubist art demonstated here and in the link supplied in following quote. You have to travel in this link to get to the picture.


http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/frontpicture.jpg [Broken]

We live in a space with three different degrees of freedom for movement. We can go to the left or to the right. We can go forward or backward. We can go up or we can go down. We are allowed no more options. Any movement we make must be some combination of these degrees of freedom.

Any point in our space can be reached by combining the three possible types of motion. Up / down motions are hard for humans. We are tied to the surface of the Earth by gravity. Hence it is not hard for us to walk along the surface anywhere not obstructed by objects, but we find it difficult to soar upwards and then downwards. Space is more 3-D for a bird or a fish than it is for us.
http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/dimensionality.htm [Broken]
 
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