Quantum Geometry-the Brian Greene quote

[marcus]

Quantum Geometry---the Brian Greene quote

This is a spin-off from the "Loop Gravity-Rovelli's program" thread
based on a post by Sol2.

We were talking about Rovelli's book Quantum Gravity---he recently redid his homepage---and Sol2 posted this, with a quote from Elegant Universe
and a reference to the notion of quantum geometry:

http://assets.cambridge.org/0521837332/cover/0521837332.jpg

Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

http://titles.cambridge.org/catalogue.asp?isbn=0521837332

It will be a must buy for myself as well.

But I wonder about the issue of quantum geometry. How will this be formulated into the LQG perspective, as it has in strings?

The Elegant Universe, by Brian Greene, pg 231 and Pg 232

"But now, almost a century after Einstein's tour-de-force, string theory gives us a quantum-mechanical discription of gravity that, by necessity, modifies general relativity when distances involved become as short as the Planck length. Since Reinmannian geometry is the mathetical core of general relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as Planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry."

I am seeing similarities arising not only from this perspective but from the current link Marcus supplied on the cosmological association (LQC ).

what I am hoping people will focus on in this thread is the Brian Greene quote that Sol2 copied in.

this quote raises a bunch of interesting issues

The "Rovelli program" thread, where we came from, is serving as a link-basket or surrogate sticky for LQG links. If there is a chance for lengthier discussions IMO we probably should start separate threads like this.

 

[sol2]

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 development 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

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

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?

 

[marcus]

Is this okay Marcus?

you betcha! I don't say I'm understanding everything but you put ideas together and I really thought it was good to bring together the Brian Greene quote, as you did, with the mention of the new book QG. I am hoping others can get in here and shed some light.

 

[marcus]

A propos of the topic "Quantum Geometry", the Cambridge
University Press published a book on it in 1997.
the title was Quantum Geometry
and it was by Jan Ambjorn and others

I haven't looked at the book.
the approach described in it only bore fruit this year
in the AJL paper that Baez was discussing recently in TWF
and on sci.physics.research

 

[sol2]

Just gathering information for consideration

Quantum gravity: progress from an unexpected direction

Over the last few of years, a new candidate theory of quantum gravity has been emerging: the so-called ``Lorentzian lattice quantum gravity'' championed by Jan Ambjorn [Niels Bohr Institute], Renate Loll [Utrecht], and co-workers [1]. It's not brane theory (string theory), it's not quantum geometry (new variables); and it's not traditional Euclidean lattice gravity. It has elements of both the quantum and the geometric approaches; and it is sufficiently different to irritate partisans of both camps.
Quantum gravity, the as yet unconsummated marriage between quantum physics and Einstein's general relativity, is widely (though perhaps not universally) regarded as the single most pressing problem facing theoretical physics at the turn of the millennium. The two main contenders, ``Brane theory/ String theory'' and ``Quantum geometry/ new variables'', have their genesis in different communities. They address different questions, using different strategies, and have different strengths (and weaknesses).

Brane theory/ string theory grew out of the high-energy particle physics community, and views quantum physics as paramount [2]. The consensus feeling in the brane community is that to achieve the quantization of gravity they would be willing to take quite drastic steps, to mutilate the geometrical foundations of general relativity and if necessary to force general relativity to fit into the brane framework. In contrast, the general relativity community views the geometrical nature of Einstein's gravity as sacrosanct, and would by and large be quite willing to do a little drastic surgery to the foundations of quantum physics if they felt it unavoidable [2]. ``Lorentzian lattice quantum gravity'' does a little of both: it adopts some aspects of each of these approaches, and violates other cherished notions of these two main candidate models.

http://www.phys.lsu.edu/mog/mog19/node12.html

 

[marcus]

Just gathering information for consideration

Sol2 that whole webpage is worth reading. By Matt Visser of Washington U., excellent essay! he seems to have spotted the potential in that approach comparatively early (2002)

 

[selfAdjoint]

And the extract shows what I found when I looked up "quantum geometry" in hep-th. Quantum Geometry means the Ashtekar - new variables - LQG project. Quantum Gravity is the name chosen by AJL for their approach. I've really got to internalize more of that AJL paper!

 

[Olias]

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?

Sakharov's induced gravity!

Great Sol, I have been an admirer of Matt Visser and his perspective papers for sometime. One has to have a arena in which to progress from, there are dimensional frame considerations?..for instance:

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

The first starting point in this sentence is portraying an allready 'EXISTING' frame of reference, this will lead to a constraining of the models predictions, 3+1 is allready in place!

Therefore the second part :Space tells matter how to move, will still be part of importance in the 'Geometrodynamics'.

Matter in its 'allready' existence has ALLREADY been told by SPACE how to move!

Much better is the fact that the definition 'Flat-Space' (I believe this is the 'Lattice' deemed to be the 'precurser-frame-background' in some new models) has to be assumed to have 'NEVER' told matter to move, because it is Flat, it is Flat as a consequence of it not encountering any curved-matter!

The Sakharov model has a very interesting dimensional angle on this(I'll dig out my PDFs showing this), now not to put any vague insights into your thread, I will say this only, Newtons-Bucket?

Now:Matter tells space how to curve, and space tells matter how to move,

for instance we can cross into some simplistic avenues for Newtonian Concepts?..watch/read closely

Space tells Matter how to un-curve, and Matter tells Space how to move during the encounter/interactions along a defined direction!

Get it?..Electro-Magnetic-Vacuum

Gravity in a pre-existing dimension is reduced to E-M-V force

I have produced some neat extensions to Newtonian Motions and General Relativity Energies, the Newtonian Bucket experiment I have been lead to re-formulate recently has the above consequence, and the total number of Dimensions go no more than 5!

A good interesting paper here:http://uk.arxiv.org/abs/gr-qc/0406044

 

[arivero]

About ten years ago, in 1995, Greene gave some lectures in Les Houches under this title, "quantum geometry". It was clear that there was a nomenclature problem, because by QG he was referring to a very specific topic of string theory.

 

[sol2]

I am tying to get a clear understanding of the basic perceptions of Quantum gravity. This will help greatly I think from what basis we might derive the issues of Quantum geometry?

What is Quantum Gravity?

Quantum gravity is the field devoted to finding the microstructure of spacetime. Is space continuous? Does spacetime geometry make sense near the initial singularity? Deep inside a black hole? These are the sort of questions a theory of quantum gravity is expected to answer. The root of our search for the theory is a exploration of the quantum foundations of spacetime. At the very least, quantum gravity ought to describe physics on the smallest possible scales - expected to be 10-35 meters. (Easy to find with dimensional analysis: Build a quantity with the dimensions of length using the speed of light, Planck's constant, and Newton's constant.) Whether quantum gravity will yield a revolutionary shift in quantum theory, general relativity, or both remains to be seen.

Quantum gravity is the field devoted to finding the microstructure of spacetime. Is space continuous? Does spacetime geometry make sense near the initial singularity? Deep inside a black hole? These are the sort of questions a theory of quantum gravity is expected to answer. The root of our search for the theory is a exploration of the quantum foundations of spacetime. At the very least, quantum gravity ought to describe physics on the smallest possible scales - expected to be 10-35 meters. (Easy to find with dimensional analysis: Build a quantity with the dimensions of length using the speed of light, Planck's constant, and Newton's constant.) Whether quantum gravity will yield a revolutionary shift in quantum theory, general relativity, or both remains to be seen.

http://academics.hamilton.edu/physics/smajor/quantgrav.html

Olias:Matter in its 'allready' existence has ALLREADY been told by SPACE how to move!

This would be a direct connection for sure, and from a dimensional perspective, the gravity field will have been deduced as weak, but there are stronger fields to consider, and why I raised the Heirarchy realtionship to dimensional values.

I do not understand Newton's bucket to only five dimensions? In context of the bose nova, the jets would say what?

So on a comsological level the curvaure parameters of the friedman eqaution? Dirac's matrices on a quantum level? Omega and critical density? So the nature of the curvature has to been understood as dynamical in nature. K=O, K>0, K<0, ds2 > 0, ds2 < 0, ds2 = 0.

G = k T

So how would this all change if we did not consider the energy value in the hierarchy Scenario, and relate dimension to gravity. I don't know if this made sense:)

General relativity becomes a theory of three constraints: Gauss, vector, and Hamiltonian. The metric is no longer a basic variable but a derived quantity; the electric field is a "square root" of the metric.

http://academics.hamilton.edu/physics/smajor/quantgrav.html

 

[Olias]

Sol from above:Does spacetime geometry make sense near the initial singularity? Deep inside a black hole?

It does if one links a singularity to the host Galaxy Blackhole? and not a Universal 'Singularity', every Galaxy has a '0', as every Galaxy has a 'Birth-date'.

 

[sol2]

Sol from above:Does spacetime geometry make sense near the initial singularity? Deep inside a black hole?

It does if one links a singularity to the host Galaxy Blackhole? and not a Universal 'Singularity', every Galaxy has a '0', as every Galaxy has a 'Birth-date'.

I think we have talked about this before, about the births and deaths of galaxies. Fusion and fission:)

So through it, there is a geometrical consistancy, like turning something inside out. Do you remember this? Heisenberg's collapsing sphere?

We are describining diferent "stages" of a consistent view, in regards to those galaxies, in the births and deaths? Why singularities are very difficult if you assume a harmonic vibration, as the basis of this existence?

You see how this is compatible with the Ekroptic scenario?

 

[sol2]

Undering the heading of Quantum Gravity I came across some information that I think speaks to the understanding of how we might look at measuring the information released from Gamma Ray Bursts.

Now what is interesting here is the relationship we had once talked about between Smolin and http://deseretnews.com/photos/1440359.jpg . I know that Joao has received some very hard criticisms because of the principals of VSL, but what is interesting I will point out shortly.

I assume He will show the mathematics

His patron is/was Lee Smolin, which is why anyone took him seriously in the first place

http://superstringtheory.com/forum/relboard/messages20/54.html

So now to the issue here of Quantum Gravity.

One of the foundation prinicpals that I found in regards to dimension, was a way in which to interpret features in regards to this idea. So we have this graviton as a representative, and what effects do we look for? So the question is, can a graviton slow a passing photon?


Of course at this point the question about classical discriptions affecting Quantum orientations come to light, and the insistence I have made along these lines of spin orientation. As a laymen then I have to wonder how such a classical discription of General Relativity, can ask us to look in this direction?

So what is postulated, and it becomes somewhat of a shocker.

Why the introduction of VSL approaches as an affront as it might seem to respecting physicist's, in relation too, constancy of speed of light, can how we can take this subject seriously?

Well to set it straight, the idea of photon discription is taken seriously and we will know in the near future of 2006, whether Glast will performs it job?

Now my interest here is how we might apply some model of quantum geometry to a truly predictable avenue of exploration, and we have seen such experiments spoken to in the nature of LIGO, derived from ideas of the supernova and Kip thorne about those distances? Does anyone see a relationship?

So in LQG is there a testable hypothesis in regards to what is discrete and in strings, what is continous? I think this question is raised here in the Glast experiment?

Although I am having difficulting understanding how, if the graviton is raised from the effects of GR, how the heck did Witten made this advance?

So the insight here in regards to the ideas of continuity and discreteness all of a sudden raise questions about how photon can move over those great distances and not "slight" speed of light constancies?

More on this as I look at it, and I hope some will respond here. Three Sol responses in a row and I think this thread has run it's course?

 

[marcus]

...
Although I am having difficulting understanding how, if the graviton is raised from the effects of GR, how the heck did Witten made this advance?

So the insight here in regards to the ideas of continuity and discreteness all of a sudden raise questions about how photon can move over those great distances and not "slight" speed of light constancies?

More on this as I look at it, and I hope some will respond here. Three Sol responses in a row and I think this thread has run it's course?

whatever happens with this thread the topic of quantum geometry (and the B.G. quote) is a stubborn enduring topic. it hasnt run its course and it won't go away any time soon, I feel sure.

also you and Mike2 are both asking what i think are really good questions about gravitons (mike in the other thread)
simply because i don't answer doesn't mean I don't appreciate the depth of the questions (on the contrary maybe )

all I can say will sound very stupid: be patient

what should a quantum geometry look like?

(do you think I am going to answer? its a big question!)

there was that 1997 book "Quantum Geometry" in the Cambridge Monographs in Mathematical Science Series. I haven't looked at it. That should have addressed some of the fundamental questions.

Has a graviton ever been observed? (I think not, correct me if I'm wrong)

Do we have any reason to suppose that a satisfactory quantum theory of geometry would include gravitons?

(would it include "volume-ons" and "curve-ons" and "area-ons"
and "angle-ons"---that was said facetiously, don't give it a second thought---but the elements of geometry concern such things as area and angle and volume)

So far i only know of gravitons emerging as an approximation to behavior on a fixed background geometry
You decide on a rigid background geometry and you perturb it with a little ripple and call that a graviton.
thats because you can separate mentally between the background and the perturbation that twangs across it

but if there is no fixed background, where is the graviton?

In a background independent quantum geometry, would there be such things?

One would certainly expect is that observables corresponding to operators on the hilbertspace of a quantum theory of geometry corresponding to measurements of area, volume etc. would have discrete spectra

that is the usual thing that happens with quantum theories, there are
discrete eigenvalues corresponding to discrete outcomes of measurements e.g. discrete energylevels in an atom etc.

but having geometric observables with discrete spectra does not necessarily mean inventing and "discovering" particles, or does it?

I don't want to lean either way on this issue. maybe a background independent quantum geometry will have gravitons, maybe not. I personally cannot judge the odds. I am even still asking
what should a quantum geometry look like?


maybe i will get that Cambridge Monograph series book on quantum geometry and see what they say. from the library I mean
1997 is too old to buy.

 

[sol2]

Thank you Marcus.

I did see Mike2's response.

You know what's interesting is Arivero's response on fundamental particles, as to how such a standard model might arise from brane scenrios? U(1)*SU(2)*SU(3) and in the understanding of differiential structures, how would this appear in a model's like Greg Egans? It's good to see his animations:) Dirac's belt trick.

This view has to be consistent from a GR standpoint(geometrcial expression) as well as from a Quantum perspective. Rotations and http://oldsite.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html?

One would certainly expect is that observables corresponding to operators on the hilbertspace of a quantum theory of geometry corresponding to measurements of area, volume etc. would have discrete spectra

Moving to the KKtower this becomes a interesting summation to following Klein after Einsteins work. If we united Electromagnetism with gravity then how would spectra be involved?

To me then the issue of Calabi Yaus come into the picture because I think they have to complete this rotation mathematically. Someone would have to correct me here. But I think this would signal the unification? I am speculating here

 

[selfAdjoint]

Sol, the U(1) group is just the rotations of a circle (interpeted as the phase changes of EM). SU(2) is the cover of the rotations in three dimensional space, SU(3) transforms the "eightfold way" into itself. I am sure you can find pictures of Gell Mann's eightfold way if you google on it.

But the key thing about these groups is not what they do in space, but how they define particles. That gets into representations, and it's hard to picture.

 

[Olias]

Thank you Marcus.

I did see Mike2's response.

You know what's interesting is Arivero's response on fundamental particles, as to how such a standard model might arise from brane scenrios? U(1)*SU(2)*SU(3) and in the understanding of differiential structures, how would this appear in a model's like Greg Egans? It's good to see his animations:) Dirac's belt trick.

This view has to be consistent from a GR standpoint(geometrcial expression) as well as from a Quantum perspective. Rotations and http://oldsite.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html?



Moving to the KKtower this becomes a interesting summation to following Klein after Einsteins work. If we united Electromagnetism with gravity then how would spectra be involved?

To me then the issue of Calabi Yaus come into the picture because I think they have to complete this rotation mathematically. Someone would have to correct me here. But I think this would signal the unification? I am speculating here

Sol you quite rightly point out the dirac belt trick?..if I may?

The existence of the a Graviton is akin to a 720 degree rotational curve, it is interesting that when one reduces the domain, what is a spin 2 particle (graviton) has a different configuration in a 2-D plane (remember Quark-table-confinement?) it turns into a 'double-rotational' static solution

Spin can only exist due to '3-D freedom', spin translates to rotation in say an E-M-V.

A 3-D anything that 'spins' or has a 'Spin', cannot execute the same dynamics when confined to the 2-D, there it is Rotation.

So for instance a particle that some are trying to 'seek' in some models, say the Higgs Particle, will have a static rotational value, because it does not exist in a 3-D domain, in a way it is a 'fixed' reference point, not only that, I would extend this further by stating that its direction of Rotation has two paramiters, when it Rotates one way the solutions are in expansion, and when it Rotates the opposite direction it is collapsing!

Now for a a 3-D particle that has a actual spin value of say +1, it can be encompassed by a lower dimensional 'particle' that has a Rotational value of 'Expansion', thus the 2-D Rotation will allways surround the 3-D spin.

My model is correct up to a certain value

If one has a spinning top with two strands wrapped around it in opposite directions, one can pull both strings away from the top to reveal the direction of which way it spins.

So let me ask you to think about this, which way does a top spin if so?..hint think Parity Conservation

 

[sol2]

Sol you quite rightly point out the dirac belt trick?..if I may?

The existence of the a Graviton is akin to a 720 degree rotational curve, it is interesting that when one reduces the domain, what is a spin 2 particle (graviton) has a different configuration in a 2-D plane (remember Quark-table-confinement?) it turns into a 'double-rotational' static solution

Spin can only exist due to '3-D freedom', spin translates to rotation in say an E-M-V.

A 3-D anything that 'spins' or has a 'Spin', cannot execute the same dynamics when confined to the 2-D, there it is Rotation.

So for instance a particle that some are trying to 'seek' in some models, say the Higgs Particle, will have a static rotational value, because it does not exist in a 3-D domain, in a way it is a 'fixed' reference point, not only that, I would extend this further by stating that its direction of Rotation has two paramiters, when it Rotates one way the solutions are in expansion, and when it Rotates the opposite direction it is collapsing!

Now for a a 3-D particle that has a actual spin value of say +1, it can be encompassed by a lower dimensional 'particle' that has a Rotational value of 'Expansion', thus the 2-D Rotation will allways surround the 3-D spin.

My model is correct up to a certain value

If one has a spinning top with two strands wrapped around it in opposite directions, one can pull both strings away from the top to reveal the direction of which way it spins.

So let me ask you to think about this, which way does a top spin if so?..hint think Parity Conservation

http://physicsweb.org/objects/world/13/11/9/pw1311091.gif
I will use this picture for reference.

A string can only vibrate in one direction in a dimensional sense. It can compress and stretch, and in this consideration, what is the photon as a wave,that the photon has been reconfigured, and considered as a longitudal wave?

Now if the string includes this longitudal wave capability, what is two dimensional that we now consider, the traverse application of gravitational waves? So we have now set up our thinking, not only geometrically, and I leave out the direct connections[geometrical correlations] in life of what others might see intuitively, and what they I hope wil share in the vision share of.

When these two waves are joined in the three dimensional world the tranverse waves can now rotate( what are our neutron stars doing). In a higher dimensional understanding we have seen where this correlation had followed the strick logic and consequences, to have understood not only the pendulum, but also the neutron stars orbit, to have come to a culmination of what is seen with the help of kaluza in that the model up top is now given forward for interpretation.

The Geometrical Considerations, Lead Us Here?

I do not consider the point particles, as nothing more then what is revealled in the consideration of its energy(what is zero-point energy?).

Here I am remaining consistent to the ideas of geomertical consideration, in a point line plane, and sayng, that any point is a circle and its radius is figured by that energy. The point(where it all begins) cylinder, brane world is all connected, but is not supported.:) Yet it follows the euclidean perspectives, and is raised to the level of non euclidean considerations?

Energy allows us to do that, and its beginning is, its endAs bosons, the graviton and photon are well considered, and following GR, can leave the brane world

http://www.superstringtheory.com/forum/geomboard/messages3/154.html

What I recognize is how we must find a consistent method on these degrees of freedom. I have another link I wanted to place here in these consideration and to speak to the way you are thinking.

So let me ask you to think about this, which way does a top spin if so?..hint think Parity Conservation

http://www.sciencenews.org/articles/20000909/a3744_3415.JPG

A mirror universe" is predicted to exist if parity and/or time reversal are unbroken symmetries of nature [1,2]. The idea is that for each ordinary particle, such as the photon, electron, proton and neutron, there is a corresponding mirror particle, of exactly the same mass as the ordinary particle. The parity symmetry interchanges the ordinary particles with the mirror particles so that the properties of the mirror particles completely mirror those of the ordinary particles. For example the mirror proton and mirror electron are stable and interact with the mirror photon in the same way in which the ordinary proton and electron interacts with the ordinary photons. The mirror particles are not produced in Laboratory experiments just because they couple very weakly to the ordinary particles.

In the modern language of gauge theories, the mirror particles are all singlets under the standard G _ SU(3) SU(2)L U(1)Y gauge interactions. Instead the mirror particles interact with a set of mirror gauge particles, so that the gauge symmetry of the theory is doubled, i.e. G G (the ordinary particles are, of course, singlets under the mirror gauge symmetry) [2]. Parity is conserved because the mirror particles experience V +A (i.e. right handed) mirror weak interactions while the ordinary particles experience the usual V _ A (i.e. left-handed) weak interactions. Ordinary and mirror particles interact with each other predominately by gravity only. At the present time there is some experimental evidence that mirror matter exists coming from cosmology [3] as well as from the neutrino physics anomalies [4].

It was realized some time ago by Glashow [5] that the orthopositronium system provides one sensitive way to search for the mirror universe. The idea is that small kinetic mixing of the ordinary and mirror photons may exist which would mix ordinary and mirror ortho positronium, leading to maximal ortho positronium - mirror orthopositronium oscillations.

http://arxiv.org/PS_cache/hep-ph/pdf/0003/0003278.pdf

To get to the graviton we had to move through GR and its consistancy, and then enter the quantum realm for consideration.

One of the foundation prinicpals that I found in regards to dimension, was a way in which to interpret features in regards to this idea. So we have this graviton as a representative, and what effects do we look for? So the question is, can a graviton slow a passing photon?


Of course at this point the question about classical discriptions affecting Quantum orientations come to light, and the insistence I have made along these lines of spin orientation. As a laymen then I have to wonder how such a classical discription of General Relativity, can ask us to look in this direction?

 

[selfAdjoint]

A string can only vibrate in one direction in a dimensional sense. It can compress and stretch, and in this consideration, what is the photon as a wave,that the photon has been reconfigured, and considered as a longitudal wave?

This is not physically correct. A string can vibrate in the transverse directions, that's 24 for bosonic strings and 8 for superstrings (subtracting the dimension along the string and the time dimension).

 

[sol2]

This is not physically correct. A string can vibrate in the transverse directions, that's 24 for bosonic strings and 8 for superstrings (subtracting the dimension along the string and the time dimension).

Woud it have been better to say the string is a one dimenisonal entity?

http://physicsweb.org/objects/world/13/11/9/pw1311091.gif

The correlation to U(1) charcteristics as a circle (boson considerations)

"Point and line," are entangled here? I am trying to remain geometrically consistsent. IN a flat world, eucildean. Yet the energy determinations move to hyperdimensional realities?

There is a metric field to consider in any quark to quark measure? This energy determination depends on the string's length?

sol2
I think of the Quark to Quark measure and the metric. Consider the energy value

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."

The String's Length (http://www.superstringtheory.com/forum/extraboard/messages12/493.html )

It does not logically make sense to me that a string's length cannot remain consistent geometrically, if you do not transfer the thinking to a energy value? Why the Radius of U(1) becomes a determination of a point?

But then let's look at a point on the brane? In supersymmetry how shall we express this point?

---------.---------http://wc0.worldcrossing.com/WebX?14@72.ABPtcShRb6u.2@.1dde5d80/4

What will a Gamma ray blast tell us? Can some photons act short and long?

 

[selfAdjoint]

Think of a violin string. It stays the same length (as long as it's not stopped), but it vibrates - transversely.

Here's a thought I had long ago, about the separation of variables in the wave equation. Suppose you had a stretched string like that, one end fixed at x=0 and the other at x=L, some length. Set it vibrating (assume a pure tone).

Now first, fix a little light somewhere (anywhere) along the string and film it going up and down. After you collect this TIME-ORIENTED data, plot its vertical coordinate against time, and you will see it follows a sine curve.

Next get a strobe camera and photograph the string at some moment (any moment) while it's vibrating. When you develop the picture, you will see that in this SPACE-ORIENTED picture, the string itself forms a sine curve.

This motivates the fact that the wave equation for the string, which is a partial differential equation in the two variables x and t, can be factored into two ordinary differential equations, one in x alone and the other in t alone. The variables can be separated.

 

[sol2]

Think of a violin string. It stays the same length (as long as it's not stopped), but it vibrates - transversely.

Here's a thought I had long ago, about the separation of variables in the wave equation. Suppose you had a stretched string like that, one end fixed at x=0 and the other at x=L, some length. Set it vibrating (assume a pure tone).

Now first, fix a little light somewhere (anywhere) along the string and film it going up and down. After you collect this TIME-ORIENTED data, plot its vertical coordinate against time, and you will see it follows a sine curve.

Next get a strobe camera and photograph the string at some moment (any moment) while it's vibrating. When you develop the picture, you will see that in this SPACE-ORIENTED picture, the string itself forms a sine curve.

This motivates the fact that the wave equation for the string, which is a partial differential equation in the two variables x and t, can be factored into two ordinary differential equations, one in x alone and the other in t alone. The variables can be separated.

You set my mind alight:) Consider Einstein's Bovine Dream. Joao highlighted this for us as well. From differents perspectives. But I will put that comparison aside for there is great resistance here in respect of constancy of speed of light.

Just so it is undertsood, I can look at the aquarium in one, of two ways. From the side, or from its end.

For two people, we see different perspectives of the same thing.

Einstein understood this, from the perspective of a dream, he had coming down the mountain, and viewing the cows in the field. What he saw, and what the farmer saw, as electricity traveled down the wire, and made the cows jump, was a difference in that perspective.

To Einstein, they all jumped, but to the farmer, they jumped one at a time:)

http://superstringtheory.com/forum/extraboard/messages12/660.html

But if you think about the significance in terms of the long(weak gravitational fields) and the short( stronger gravitational fields), what happens then if we are faced with the gamma ray blast and such interference with the graviton, holds the greatest energy and the evidence for the universe now?

You must see what the gravitons "represent" in terms of its dimensional relationship?

I am thinking of something from the experiment of Glast. I'll put it here when I find it. It deals directly with the issue about these photons. Windows on the Universe is really a popular phrase

I won't say much more for now.

 

[sol2]

http://www-glast.sonoma.edu/resources/cubeimages/glastallskysm.jpg

We have been given different perspectives on how we can view the comsos, and this latest method is the most revealing I think in terms experimental possibilties.

If the graviton understanding is opened up for consideration, then how would we discuss such issues in terms of these photons not speaking to a legitimate process that looks deeply into the nature about that universe, not only on a classical level, but from a quantum one as well.

Looking at Olia's current link to Lee Smolin and Fotini, how would we not consider the issues of "teleportation or quantum cryptography" in concert with the issues of photon application with that graviton?

FTL in terms of constancy of light speed, again affronts the idea, yet within the framework of gravitational understanding, how would we define this relation when a graviton affects the photons discription of the nature of these fields, strong or weak?

VSL also affronts the nature of constancy of speed of Light? If we do not do our summation of the reasons for these terms, then the quest for representation of that quantum world becomes a very difficult issue to discuss. Joao took his chances, and how well did he fair?

How did Witten calculate the "graviton" from GR to string context?

What is a graviton? I am sure the mathematical discritption could be shown(?) with a generalization based on this?

Like the photon, as a representative of EM waves how would we encapsulate this move to unification of EM to Gravitational consideration?

There had to be some consistancy parameters to geometrical expression of this logic? Self adjoint the other day spoke on Feynmens toys models, as discriptors for us of the nature of photon interaction from "two directions." He can correct here:)

Any thoughts here?

 

[sol2]

I wanted to place this post here as well as it helps to elucidate some of the issues I have been talking about here. Does this information seem consistant and satisfactory to those better minds of focus?

sol2,

Is supersymmetry, according to Jim Gates, the answer to the resolution of spacetime?

What I think is that it is the answer if and only if spacetime is static. If spacetime is dynamic, then the outcome is two distinct topologies. One for fermions and the other for bosons.

My hunch is that the dynamic of spacetime of more than 3 dimensions is very difficult to analyze. But spacetime of 2 dimensions are representable by matrices.

On the first part I would say Jim Gates gives us a way in which to percieve the dynamcial relationship of these colliding branes.

A interesting development of this logic would have to ask, how would a photon define this relationship for us? You point out the matrices and to me Feynmenn used this and incorporated it into his discriptors for us. But there is a probelem if em considerations are held to the brane? The logic would say to me that this feature then even though travels great distances is still describing something from the origination of that brane? Gamma ray blast.

What becomes difficult for me is to undertanding the issue of supergravity in relations to suerpmetrical points derived from a gravitational metric point considerations. So you have this scale to consider, and we know full well the dynamcis at the early universe?

So discriteization is based on dynamcial relationships? How and what would you use to speak on this?

The turn about is, I am speaking from the current realization of the universe as it stands now. I have pointed you backward to the brane realizations of supersymmetry. This would be consistent with the understanding of a classical discritption moving to the quantum reality of this cosmo? This would be derived from the equations of metric point consideration to supermetric point consideration(gravity to supergravity).

Yet visualize in your mind plasmatic features and it's dynamics, and in hand, you have gained in realization of the issues on that brane although fluid, has raised quantum realities for us to talk about?

addition: we have not spoken on the issue of the supersymmetrical partners

https://www.physicsforums.com/showthread.php?goto=newpost&t=30929

https://www.physicsforums.com/showthread.php?goto=newpost&t=29382

 

[sol2]

I just wanted to place a http://wc0.worldcrossing.com/WebX?14@42.mjEWcUDugWt.11@.1ddf4a5f/21 here for consideration as to the evolving perspective Antonio has, in light of the mathematics he has been showing most of us .

The developemental concepts have been most rewarding in terms of his support that his statements now reflect to me a accurate theoretical development as "I see it," of a geometry that must be relevant to both the perspectives of LQG and M Theory. My perceptions could be wrong:)

Models we work On?

Window on the Universe

 

[sol2]

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 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

I hope this sparks some new paradigmal views?

 

[jeff]

Hi sol/sol2 ,

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?

 

[sol2]

Hi sol/sol2 ,

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 development 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

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

I just wish all the posts were as simple as yours

 

[sol2]

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?

 

[Olias]

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)?

 

[sol2]

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?

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?

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)

 

[sol2]

A Possible Origin of Dark Energy

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 development 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

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

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 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

 

[sol2]

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

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

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 ?

 

[sol2]

It is interesting to see Kip Thornes thought's manifesting in regards to strings?

http://online.itp.ucsb.edu/online/plecture/thorne/oh/24.html

 

[sol2]

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


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

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

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.