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jeff

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Pathetically, some PF members for their own questionable reasons continue attempts to convince other members (they sure wouldn't be able to do so with physicists) that there's real parity between LQG and strings, but really, all of the good ideas are being generated by string research and none by LQG. The twistor program recently rehabilitated within string theory is just the most recent example of how all roads appear to lead to strings and that the best hope for LQG is that it will ultimately share the same fate.

Only a tiny, tiny fraction of papers on the subject of QG deal with LQG, and when compared to the thousands upon thousands of stringy papers submitted each year, are really of no consequence. All serious research in QG/TOE (not to mention a great deal of mathematical research) really is being driven by string theory and this will continue to be the case for a very, very long time to come.

It's often said that string theory makes no predictions, but as is well-known, this is untrue. It turns out that the only self-consistent string theories necessarily contain GR and in this sense, string theory predicts spacetime! In fact for reasons related to this, string theory is the only bonafide quantum gravity theory we've ever had. LQG appears not to contain GR and is therefore not a QGT or even a physics theory but rather just some pretty but in the end vacant mathematics. This is not just my personal view, it's the view of the overwhelming majority of researchers in this field, though they don't argue about it since they choose not to deal with the misguided hobbiests in forums like these.

One development likely to finally kill LQG off for good will be the generation in future accelerators of particles associated with the long predicted supersymmetries which have motivated so much important research in all aspects of physics (along with many aspects of mathematics as well) and required by strings for it's self-consistency.

So, if you enjoy spending lots and lots of energy trying to understand a theory which few outside forums like this one take seriously, then go straight ahead andworry about LQG. If on the other hand you want to know about whats

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Nereid

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... and/or the discovery of such particles in astronomical research (e.g. cosmic ray detectors, GLAST).jeff wrote:One development likely to finally kill LQG off for good will be the generation in future accelerators of particles associated with the long predicted supersymmetries which have motivated so much important research in all aspects of physics (along with many aspects of mathematics as well) and required by strings for it's self-consistency.

There are also a number of other astronomy projects that may provide solid support for - or refutations of - SST (SMT?) and/or LQG fairly soon, esp the neutrino telescopes and gravitational wave detectors.

jeff -> is string theory at the point where it can account for neutrino oscillations yet? how about predicting the mass of any neutrino mixtures (with non-zero mass)?

That's true, but isn't it a post-diction? What about predictions, in the sense of something specific and quantitative about things as yet undiscovered, such as the mass of the Higgs? How do SST/SMT and LQG compare in terms of their respective abilities to make specific, quantitative predictions (explicitly excluding post-dictions)?jeff wrote:It's often said that string theory makes no predictions, but as is well-known, this is untrue. It turns out that the only self-consistent string theories necessarily contain GR and in this sense, string theory predicts spacetime! In fact for reasons related to this, string theory is the only bonafide quantum gravity theory we've ever had.

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marcus

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It is sometimes said that string "requires" SUSY for its "consistency". So if LHC does not find SUSY that is certainly bad news for string (but it does not effect loop either way.)

And if, on the other hand, SUSY is found, this also does not effect loop either way. The spin networks just have to carry more fields, more quantum numbers.

Whether or not SUSY is found, string can still be wrong---supersymmetry is NOT in itself a final test of string theory.

Either one or the other or both of the two theories, Loop and String, can be wrong---gotta keep an open mind, the proof is in the empirical pudding

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jeff

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I very much appreciate that you responded marcus. Thankyou.

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marcus

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Originally posted by Nibles

hello Nibles, yeah I guess we might refrain from squabbles and get around to answering your question which basically was "what is Loop Gravity?" The way the term is used it includes several recently developed research lines---still small in terms of the number of people working them, but definitely experiencing an upswing, and getting results and gaining visibility.

The first hardcopy book on the subject will be published this year

or next---Rovelli's "Quantum Gravity", about 350 pages, Cambridge University Press.

Also hardcopy textbook by Thiemann "Lecture Notes on Quantum Gravity" or some such title will be published by Springer Verlag, Berlin.

Before this everything was online, or in scholarly journals. You did not have Loop

this year there are already more Loop conferences scheduled than last.

I listed some in the "Intuitive Loop---Rovelli's Program" thread

in the LQG String Brane Forum here at PF. I try to keep that

thread up to date on study resources and current events. So the

upcoming conference links should be near the end of the thread.

Also there was that Scientific American article by Lee Smolin, and the hardcopy magazine

The main names are Rovelli, Smolin, Bojowald, Thiemann, Freidel, Livine, Ashtekar, Corichi, Perez, Roche, Noui... I am leaving too many out. The main centers are Marseille, Berlin, Mexico City, Penn State, Waterloo, again it is hard to be complete.

Experimental tests of Loop Gravity are expected soon---especially with GLAST starting 2006----and "Quantum Gravity Phenomenology" has become a hot topic with collaboration going on between LQG people and leading phenomenologists like Kowalski-Glikman and Amelino-Camelia.

Phenomenology basically just means figuring out how to check theories against reality--how to get testable predictions from theory. Ted Jacobson, one of the founders of LQG with Smolin and Rovelli, is working primarily in phenomenology now---using astronomical data to narrow down and guide theory.

I have some discussion of developments in that area in recent posts in the "Intuitive LQG--Rovelli's program" thread.

So that is a birds-eye view of the research activity called Loop Gravity. There are links to plenty to read at that other thread.

Now I'll try to give a sketch of the various lines of theoretical development that come under this heading----quantizing General Relativity, spin networks, spin foams (the 4D version of spin networks), the hardcore principles that characterize all these approaches.

Actually Smolin's January 2004 SciAm article did that so well it is a shame to repeat it---I take it you read Smolin's article, which was the "cover story" of that SciAm issue.

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jeff

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Originally posted by Nereid

is string theory at the point where it can account for neutrino oscillations yet? how about predicting the mass of any neutrino mixtures (with non-zero mass)? What about predictions, in the sense of something specific and quantitative about things as yet undiscovered, such as the mass of the Higgs?

Since strings contain QFT, it can accomodate all of these ideas.

Originally posted by Nereid

That's true, but isn't it a post-diction?

The point is that strings must contain GR.

Originally posted by Nereid

How do SST/SMT and LQG compare in terms of their respective abilities to make specific, quantitative predictions (explicitly excluding post-dictions)?

The only way to get LQG to make any kind of conventional QFT prediction is to somehow put the requisite structure in by hand. On the other hand, string theory is unavoidably a theory of everything and so automatically contains all the requisite machinery. The problem for string theory is then how to break the symmetries needed to produce low energy phenomenology consistent with observation.

Originally posted by marcus

The observation of supersymmetry, or the failure to find it (should that happen) is not a test of Loop Gravity since the theory can take it or leave it. It is sometimes said that string "requires" SUSY for its "consistency". So if LHC does not find SUSY that is certainly bad news for string (but it does not effect loop either way.) And if, on the other hand, SUSY is found, this also does not effect loop either way. The spin networks just have to carry more fields, more quantum numbers. Whether or not SUSY is found, string can still be wrong---supersymmetry is NOT in itself a final test of string theory.

Suppose that while deciding between becoming a christian (string theory proponent) or a jew (LQG proponent) christ (supersymmetry) showed up. How persuasive would you find claims advanced by jews that this doesn't matter since they've no need of him and besides, it's possible that his 2nd coming could be incorporated into judiasm if necessary? My guess is not very.

Originally posted by marcus

Either one or the other or both of the two theories, Loop and String, can be wrong---gotta keep an open mind, the proof is in the empirical pudding

My basic point is that although this may be true, it's important to be honest and clear with PF members that only a handful of researchers have ever taken LQG seriously and that really strings dominate. It's not fair to take advantage of the lack of sophistication and knowledge of layman to coax them into spending enormous amounts of valuable energy learning ideas that have little bearing on what's currently driving high energy research.

Originally posted by marcus

... [LQG is] definitely...gaining visibility.

But not within the physics community.

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marcus

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I dont think this thread has any further purpose now that Nibles is satisfied that he doesnt have to know any more about Loop Gravity.

After all, it began with him asking about LQG---we never got around to saying anything very real about the subject but regardless of whatever curiosity he had is finished.

But I'll take the opportunity to give some of my own reasons (which others may share or not as they choose) why I am interested in Loop Gravity. I dont normally do this---I dont think anyone here should have to justify their physics interests. And I dont think I need to explain or justify liking to discuss LQG and report on recent papers etc.

Loop Gravity is interesting for me because it says something about the fundamental texture of space and time---even about their very existence---and because some strands of the theory are surprisingly close to being testable (contrary to what was expected a few years back)----and because as a research field it is still small, each person's contribution counts----and because it is just now "coming of age" with its first hardcopy books (having been mostly online till now)---and because the researchers themselves are obviously excited.

And because of a couple of notions that make Loop special.

----here's a footnote----

I take for granted you know that classical 1915 Relativity itself is BI and DI----no fixed background geometry, no absolute space, time and space coordinates have no physical meaning. No absolute time or any notion of an ideal clock: since relativistic mechanics is about relations between observables (not about evolution in time, though one of the possible observables can be a reading from some particular real-world material clock).

BI, background independence, says you have no prearranged background geometry---the shape of space is freely variable and dynamic.

DI, diffeo-invariance, says any smooth deformation of a solution is still a solution. If the shape of space and the distribution of energy in it are related according to the theory, and if you then re-map the shape and the energy, they stay in the right relation. Solutions--like silly-putty--can be stretched and squeezed and bent around at will.

BI and DI are the core principles of classical 1915 Relativity and they are what makes Loop Gravity different from stringy theories for example.

-------end of footnote---------

One suspicion I have about these things is that if GR is a large-scale limit of some more fundamental theory or class of theories, then those theories must also be BI AND DI.

A major stumbling block for string theory has been that by not being Background Independent it fails to really reproduce GR---only a kind of fake version that is not BI (sorry if the abbreviation bothers you because also used in the classified sex ads but it is needed here too).

A corollary of this is that string theory has not produced a candidate model of gravity that**has GR as a large-scale limit**. Since GR is BI and DI, you need some candidate which is itself also BI and DI, and because of string's basic limitations, such is not forthcoming.

Incidentally this central failure of string theory (Tom Banks mentioned it when he said the long hoped-for goal of Background Independence in string theory was a "chimera"---I think he meant an elusive will o' the wisp) is why evidence of supersymmetry wouldn't make me more interested in string theory. SUSY is a liability for string, not an asset----predicted in an earlier theoretical context but something the theory cannot do without.

------now to get to the heart of why I'm interested----

BTW remember YOU don't have to be interested in LQG. I dont care if you are or arent. I like to report on it and discuss it with others who share my interest. Some people may feel threatened by an open discussion of LQG but that's their problem.

What I see happening in recent physics is Relativity taking initiative and driving progress. A large fraction of current theoretical and observational developments is about extremely curved spacetime situations or those with dynamic geometry----quasars, gammaray bursts, neutron star mergers, black holes, inflation, big bang, singularity removal, ripples in the CMB, the integrated Sachs-Wolfe effect, dark energy, accelerated expansion, cosmological constant. All these things are born out of GR. The interesting things in the news (physics-wise) are increasingly turning out to be**General Relativity-type things.**

HEP physics is based on static geometry, it is built on fixed backgrounds which are NOT highly curved as a rule and not dynamic.

Minor perturbations of geometry can be considered, but the underlying space is not freely-evolving. A fixed space either can't even expand or at best does so in a rigid artificial fashion.

Fixed space theories can't cope gracefully what is increasingly of central interest. So HEP is out and GR is in---its that simple. What represents the leading edge of new understanding has started to be mainly in the precincts of Relativity (and I dont mean 1905 "special", which is not BI and DI and shouldnt even count as relativity).

What I am saying here is an observation about the history of science and in particular physics. The HEP (high energy physics) paradigm with its fixed absolute space was in charge for a while and did great things. And now the GR paradigm has taken the initiative and is calling the important shots.

People with a heavy investment in HEP-style thinking may sometimes feel envy or resentment---their sense of priority or privilege is somehow threatened---or they're in denial. Whatever. It does not concern me personally and it doesn't really have much to do with Loop Gravity.

Loop Gravity is just the most direct way to quantize classic 1915 BI and DI General Relativity. In the process of doing that it may come up with an explanation of the cosmological constant---there are hints of that in the Girelli/Livine paper (link in the other thread).

And it may come up with some non-commutative geometry or some quantum groups---like in the Noui/Roche paper (link in the same place).

Or with high-energy, planck scale modifications of GR, of which classic GR is the large-scale limit. Or a modification of Lorentz symmetry that makes both the speed of light the same for all observers and other planck quantities the same as well (like in DSR

and work by Kowalski-Glikman, Smolin and several others)

Links to all those papers are posted here

https://www.physicsforums.com/showthread.php?s=&postid=124320#post124320

in the "Rovelli's program" thread

In other words there are possibilities for interesting development stemming from insisting on really quantizing GR---preserving the core ideas of Background Indep and Diffeo-Invariance---and not giving up and falling back on some Absolute-Space-with-Gravitons substitute for GR.

So there are some reasons I'm interested.

Also I am not looking for something to believe in.

Physical theories arent religions. The idea of setting out to choose one to believe in---to decide whether to be a this-proponent or a that-proponent---seems ridiculous. I can happily contemplate the possibility that**all** theories in sight are wrong.

The question for me is where are the new concepts of space and time

coming from that will allow quantum mechanics to be put together

with general relativity. Rovelli discusses this in his book. From their birth early last century, QM and GR have had an incompatibility at the foundations level--they've been like oil and water.

Uniting them will cause a basic re-thinking of space and time. I guess I'd like to be on hand as more of nature gets to be understood and able to watch the deeper ideas as they emerge.

After all, it began with him asking about LQG---we never got around to saying anything very real about the subject but regardless of whatever curiosity he had is finished.

But I'll take the opportunity to give some of my own reasons (which others may share or not as they choose) why I am interested in Loop Gravity. I dont normally do this---I dont think anyone here should have to justify their physics interests. And I dont think I need to explain or justify liking to discuss LQG and report on recent papers etc.

Loop Gravity is interesting for me because it says something about the fundamental texture of space and time---even about their very existence---and because some strands of the theory are surprisingly close to being testable (contrary to what was expected a few years back)----and because as a research field it is still small, each person's contribution counts----and because it is just now "coming of age" with its first hardcopy books (having been mostly online till now)---and because the researchers themselves are obviously excited.

And because of a couple of notions that make Loop special.

----here's a footnote----

I take for granted you know that classical 1915 Relativity itself is BI and DI----no fixed background geometry, no absolute space, time and space coordinates have no physical meaning. No absolute time or any notion of an ideal clock: since relativistic mechanics is about relations between observables (not about evolution in time, though one of the possible observables can be a reading from some particular real-world material clock).

BI, background independence, says you have no prearranged background geometry---the shape of space is freely variable and dynamic.

DI, diffeo-invariance, says any smooth deformation of a solution is still a solution. If the shape of space and the distribution of energy in it are related according to the theory, and if you then re-map the shape and the energy, they stay in the right relation. Solutions--like silly-putty--can be stretched and squeezed and bent around at will.

BI and DI are the core principles of classical 1915 Relativity and they are what makes Loop Gravity different from stringy theories for example.

-------end of footnote---------

One suspicion I have about these things is that if GR is a large-scale limit of some more fundamental theory or class of theories, then those theories must also be BI AND DI.

A major stumbling block for string theory has been that by not being Background Independent it fails to really reproduce GR---only a kind of fake version that is not BI (sorry if the abbreviation bothers you because also used in the classified sex ads but it is needed here too).

A corollary of this is that string theory has not produced a candidate model of gravity that

Incidentally this central failure of string theory (Tom Banks mentioned it when he said the long hoped-for goal of Background Independence in string theory was a "chimera"---I think he meant an elusive will o' the wisp) is why evidence of supersymmetry wouldn't make me more interested in string theory. SUSY is a liability for string, not an asset----predicted in an earlier theoretical context but something the theory cannot do without.

------now to get to the heart of why I'm interested----

BTW remember YOU don't have to be interested in LQG. I dont care if you are or arent. I like to report on it and discuss it with others who share my interest. Some people may feel threatened by an open discussion of LQG but that's their problem.

What I see happening in recent physics is Relativity taking initiative and driving progress. A large fraction of current theoretical and observational developments is about extremely curved spacetime situations or those with dynamic geometry----quasars, gammaray bursts, neutron star mergers, black holes, inflation, big bang, singularity removal, ripples in the CMB, the integrated Sachs-Wolfe effect, dark energy, accelerated expansion, cosmological constant. All these things are born out of GR. The interesting things in the news (physics-wise) are increasingly turning out to be

HEP physics is based on static geometry, it is built on fixed backgrounds which are NOT highly curved as a rule and not dynamic.

Minor perturbations of geometry can be considered, but the underlying space is not freely-evolving. A fixed space either can't even expand or at best does so in a rigid artificial fashion.

Fixed space theories can't cope gracefully what is increasingly of central interest. So HEP is out and GR is in---its that simple. What represents the leading edge of new understanding has started to be mainly in the precincts of Relativity (and I dont mean 1905 "special", which is not BI and DI and shouldnt even count as relativity).

What I am saying here is an observation about the history of science and in particular physics. The HEP (high energy physics) paradigm with its fixed absolute space was in charge for a while and did great things. And now the GR paradigm has taken the initiative and is calling the important shots.

People with a heavy investment in HEP-style thinking may sometimes feel envy or resentment---their sense of priority or privilege is somehow threatened---or they're in denial. Whatever. It does not concern me personally and it doesn't really have much to do with Loop Gravity.

Loop Gravity is just the most direct way to quantize classic 1915 BI and DI General Relativity. In the process of doing that it may come up with an explanation of the cosmological constant---there are hints of that in the Girelli/Livine paper (link in the other thread).

And it may come up with some non-commutative geometry or some quantum groups---like in the Noui/Roche paper (link in the same place).

Or with high-energy, planck scale modifications of GR, of which classic GR is the large-scale limit. Or a modification of Lorentz symmetry that makes both the speed of light the same for all observers and other planck quantities the same as well (like in DSR

and work by Kowalski-Glikman, Smolin and several others)

Links to all those papers are posted here

https://www.physicsforums.com/showthread.php?s=&postid=124320#post124320

in the "Rovelli's program" thread

In other words there are possibilities for interesting development stemming from insisting on really quantizing GR---preserving the core ideas of Background Indep and Diffeo-Invariance---and not giving up and falling back on some Absolute-Space-with-Gravitons substitute for GR.

So there are some reasons I'm interested.

Also I am not looking for something to believe in.

Physical theories arent religions. The idea of setting out to choose one to believe in---to decide whether to be a this-proponent or a that-proponent---seems ridiculous. I can happily contemplate the possibility that

The question for me is where are the new concepts of space and time

coming from that will allow quantum mechanics to be put together

with general relativity. Rovelli discusses this in his book. From their birth early last century, QM and GR have had an incompatibility at the foundations level--they've been like oil and water.

Uniting them will cause a basic re-thinking of space and time. I guess I'd like to be on hand as more of nature gets to be understood and able to watch the deeper ideas as they emerge.

Last edited:

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Tsu

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Marcus,

I really enjoy reading your posts. Thanks.

I really enjoy reading your posts. Thanks.

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marcus

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Originally posted by Tsunami

Marcus,

I really enjoy reading your posts. Thanks.

I appreciate the compliment because I can return it,

I enjoy yours----largely because of the gift for one-liners,

the elements of humor and surprise.

the Joan Crawford's daughter inset caused some discomfort

but that may merely have been an idiosyncratic reaction

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marcus

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following the development of Loop Gravity means sharing

in a common conjecture that the planck scale (which is different

from the string scale) is fundamental and intrinsic to nature.

That means there is a fundamental length and a fundamental frequency in the universe.

The length is almost exactly (within half a percent) of

E-38 of a mile

the frequency is almost exactly (within a tenth of a percent or so) of E40 times middle D on a conventionally tuned piano.

So if you know what a mile is, imagine 10^{-38} of it and that is Planck length.

And if you know what middle D sounds like, imagine a frequency which is imagine 10^{40} times higher and that is Planck frequency, the reciprocal of planck time, one event per planck time unit, one radian of phase or turn per planck unit, whatever.

The conjecture which is a semiconscious assumption in the minds of people involved with this kind of quantum gravity is that this frequency is "universe frequency" and this length also a universal---a threshold scale for new physics. Or a limit of some kind, the way the speed of light is a speed limit.

It is not yet clear HOW these new scales are built into nature but the suspicion is that they are built into her as deep proportions.

We think we understand fairly well how the speed of light is built in--thru all those special relativity formulas and thru the (lorentz) group of symmetries. But how, in what symmetries or formulas are these other scales present.

An early hint was when Rovelli and Smolin calculated the Loop Gravity area and volume operator's spectrum and found that all the possible eigenvalues (in a quantum theory, the outcomes of measuring some observable thing like a volume or area) were order-one multiples of the planck area and the planck volume.

Maybe they were wrong! The wheel is still turning.

But they may in fact be right and, in any case, even if the result eventually needs to be revised it seems likely that area and volume will still turn out to be a discrete set of order-one multiples of the planck units. That is these units of area and volume are basic to nature and to nature's space. It is a space that can only have areas and volumes chosen from that discrete set.

And then last year Girelli and Livine (part of a generation 20 or more years younger than Rovelli and Smolin) posted this exquisite 4-page paper that SPEED was quantized in little speed-steps too, in a way that incorporates the cosmological constant or vacuum energy density or "dark energy" density---something that can be incorporated as a small positive quantity rather easily in the theory, that "fits" in Loop Gravity without much trouble. Great that speed is quantized, but even better that determining the steps involves the density of dark energy.

So that is the suspicion, the conjecture----that the basic stuffs of geometry are quantized----that nature is constructed that way: dyed-in-the-wool so it wont wash out.

You can find the Girelli/Livine article link, if you want it,

in this post of useful Loop links:

https://www.physicsforums.com/showthread.php?s=&postid=124320#post124320

For links to the National Institute of Standards and Technology page that gives values for the planck length, timescale, temperature scale and such:

https://www.physicsforums.com/showthread.php?s=&postid=121318#post121318

in a common conjecture that the planck scale (which is different

from the string scale) is fundamental and intrinsic to nature.

That means there is a fundamental length and a fundamental frequency in the universe.

The length is almost exactly (within half a percent) of

E-38 of a mile

the frequency is almost exactly (within a tenth of a percent or so) of E40 times middle D on a conventionally tuned piano.

So if you know what a mile is, imagine 10

And if you know what middle D sounds like, imagine a frequency which is imagine 10

The conjecture which is a semiconscious assumption in the minds of people involved with this kind of quantum gravity is that this frequency is "universe frequency" and this length also a universal---a threshold scale for new physics. Or a limit of some kind, the way the speed of light is a speed limit.

It is not yet clear HOW these new scales are built into nature but the suspicion is that they are built into her as deep proportions.

We think we understand fairly well how the speed of light is built in--thru all those special relativity formulas and thru the (lorentz) group of symmetries. But how, in what symmetries or formulas are these other scales present.

An early hint was when Rovelli and Smolin calculated the Loop Gravity area and volume operator's spectrum and found that all the possible eigenvalues (in a quantum theory, the outcomes of measuring some observable thing like a volume or area) were order-one multiples of the planck area and the planck volume.

Maybe they were wrong! The wheel is still turning.

But they may in fact be right and, in any case, even if the result eventually needs to be revised it seems likely that area and volume will still turn out to be a discrete set of order-one multiples of the planck units. That is these units of area and volume are basic to nature and to nature's space. It is a space that can only have areas and volumes chosen from that discrete set.

And then last year Girelli and Livine (part of a generation 20 or more years younger than Rovelli and Smolin) posted this exquisite 4-page paper that SPEED was quantized in little speed-steps too, in a way that incorporates the cosmological constant or vacuum energy density or "dark energy" density---something that can be incorporated as a small positive quantity rather easily in the theory, that "fits" in Loop Gravity without much trouble. Great that speed is quantized, but even better that determining the steps involves the density of dark energy.

So that is the suspicion, the conjecture----that the basic stuffs of geometry are quantized----that nature is constructed that way: dyed-in-the-wool so it wont wash out.

You can find the Girelli/Livine article link, if you want it,

in this post of useful Loop links:

https://www.physicsforums.com/showthread.php?s=&postid=124320#post124320

For links to the National Institute of Standards and Technology page that gives values for the planck length, timescale, temperature scale and such:

https://www.physicsforums.com/showthread.php?s=&postid=121318#post121318

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- #13

Tsu

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Why, thank you very much!!Originally posted by marcus

I appreciate the compliment because I can return it,

I enjoy yours----largely because of the gift for one-liners,

the elements of humor and surprise.

Yes, I agree. That's why I posted it. I hate being alone in my discomfort zone.the Joan Crawford's daughter inset caused some discomfort

but that may merely have been an idiosyncratic reaction

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Tsu

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Totally fascinating stuff, but, being the non-nerd that I am, it certainly gives me the worst twisty-face!!! But keep it comin'!Originally posted by marcus

following the development of Loop Gravity means sharing

in a common conjecture that the planck scale (which is different

from the string scale) is fundamental and intrinsic to nature.

That means there is a fundamental length and a fundamental frequency in the universe...

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marcus

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Originally posted by Tsunami

...keep it comin'!

a distinctive thing about quantum gravity is that the planck scale of area and volume come out as a result---not something put in by hand.

starting from very general principles like background independence and diffeomorphism invariance (Einstein called it "general covariance") rovelli and smolin were able to derive the area and volume spectra and they turned out to be a discret set of multiples of the planck area and volume units---the natural units (at least up to order-one factors) of area and volume.

how to say this? It had been suspected on general theoretical grounds for more than half a century that a new picture of spacetime would emerge at planck scale. But when LQG came along it pointed like a compass-needle at that scale, without having been told by its inventors to do that. (smolin, rovelli 1995)

so if someone wants to follow the ongoing development of quantum gravity they would do well to get a comfortable familiarity with the planck units, hence this informal introduction.

down at the end of this post I will just directly define them in the immediate hard-ass algebraic way, as is usually done, without a serious attempt at motivation. So if you want to avoid the gradual step-by-step introduction, just scroll down and there will be the usual formulas.

-------gradualist treatment of planck units------

one way to get a handle on them is to take a fresh look at one of the most basic equations in science, the 1915 Einstein equation, the central equation in our model of how gravity works: General Relativity. this equation relates the density of energy in a region ("joules per cubic meter", "footpounds per cubic foot") to the curvature in that region. It says the two are proportional!

Except for a factor of [tex]8\pi[/tex] which is no big deal, and the fact that they use special symbols for curvature and energy density, this equation is customarily laid out this way:

[tex]curvature = \frac{G}{c^4}energy density[/tex]

Curvature in this context is measured in units of reciprocal area ("per square meter", "per square foot").

Now just suppose that we deviate a tiny bit from the customary layout and write the Einstein equation this way:

[tex]\frac{c^4}{G}curvature = energy density[/tex]

This quantity c^4/G is the planck unit of force, that is, the force unit which belongs to a system of units that Max Plack discovered in 1899 and presented to his contemporaries as a natural (rather than artificial or man-made) system of units.

So in 1915 Einstein discovered that nature knows about the force

c^4/G. It is the force that connects the amount of curvature in a region to the energy density there.

For dimensional reasons a force is the only type of quantity that can do that. Multiplying a curvature ("per sq. foot") by a force ("pounds") gives a pressure ("pounds per square foot") and that is dimensionally the same type of quantity as an energy density

("footpounds per cubic foot"). Or say the same thing substituting metric newtons for pounds and meters for feet. Newtons per sq. meter is the same as joules per cubic meter. The longandshort is that if you multiply a curvature by a force you get an energy density and the only thing you CAN multiply a curvature by to get an energy density is a force. Einstein found that the force that works in this context

is the unit force c^4/G in planck's 1899 system of units

----------------

we can get all the planck units from this force, and stuff you already know like the speed of light

People COULD have realized that planck units were basic as early as 1915, but they did not and it was still a bit surprising in 1995 when the area and volume spectra were found to be multiples of planck area and volume units. Our species is not quick to catch on, sometimes.

-----------

To summarize

around 1900 Planck discovered that nature knows about a certain ratio of energy to frequency called hbar. (when using hbar you need to express frequency in angular format, radians per unit time, but that is a technicality involving a factor of 2pi and I wont belabor it)

in 1905 Einstein reminded everybody that nature knows about c the speed of light, in fact you could almost say nature is

in 1915 Einstein showed that nature knows about a certain force

c^4/G which is the force unit belonging to Planck's system of natural units. It turns up as the central constant in General Relativity: the thing that relates the lefthand side to the righthand side in the main GR equation. If you have a book where you can look up the metric values of G and c, or if you just know them, then you can easily calculate what the planck force unit is---just follow the formula c^4/G. You will get the answer in terms of the metric force unit, the so-called "newton" which is about a tenth the weight of a kilogram in normal gravity.

----------------

all the other planck quantities come from these three that were already immanent and obvious in 1900, 1905, 1915.

in any system of units the unit power is always equal to the unit force multiplied by the unit speed (in our case c^4/G multiplied by c)

If you work out c^5/G with a calculator you get planck power unit is

3.6E52 watts. Lots of watts.

In the planck system, hbar is the ratio of unit energy to unit frequency. So unit power divided by hbar gives the square of unit frequency, namely c^5/hbarG

[tex]unit frequency = \omega = \sqrt{\frac{c^5}{Ghbar}}[/tex]

this is a frequency expressed in angular format, so the convention is to use the symbol omega for it, instead of the letter f.

Anybody who wants can immediately find out what the planck unit energy is at this point because it is [tex]hbar\omega[/tex]

-----------

in a consistent system of units the unit length is equal to the unit speed divided by the unit frequency

so in our case

[tex]unit length = \frac{c}{\omega} = \sqrt{\frac{Ghbar}{c^3}}[/tex]

-------

that's about it for the definitions, now we have unit force, power, frequency, time (the reciprocal of frequency), and length----the rest derive in familiar ways from these. the mass unit, for instance, is equal to the energy unit divided by the square of the unit speed (the square of the speed of light) and so on like that.

-----------

now the question is: what sizes are these units. Of course now you have the formulas for many of them so you could calculate them out in metric terms. But to save you the bother, the best way I know is just look them up at the NIST website.

BTW the NIST "fundamental constants" website has the planck temperature unit too---which is the planck energy unit divided by boltzmann's constant.

Beyond just always looking them up, there are some facts about them that are not too hard to remember. Like 2E-30 planck temp is a reasonably good reference temperature to remember---it's about 10 Celsius or 50 Fahrenheit. And E38 planck length is a mile.

-----direct no-nonsense definitions----

[tex]unit time = t_P = \sqrt{\frac{Ghbar}{c^5}}[/tex]

[tex]unit length = l_P = \sqrt{\frac{Ghbar}{c^3}}[/tex]

[tex]unit energy = E_P = \sqrt{\frac{c^5hbar}{G}}[/tex]

[tex]unit temperature = T_P = \frac{\sqrt{\frac{c^5hbar}{G}}}{k}[/tex]

-------direct no-nonsense explanation---------

the only way that it is possible to cook up a quantity with the dimension of time using the quantities G, hbar, c is this definition written here and simple constant multiples of it, but why bother to scale the thing by an extra number?

since c is going to be unit speed in the system, it must be unit length divided by unit time

so to get unit length simply multiply t

since hbar is the product of energy with time, and since it is going to be a unit quantity in the system, it must be equal to the unit energy multiplied by the unit time

so to get the unit energy simply divide hbar by the unit time

the boltzmann k is a ratio of energy to temperature and it is a unitary ratio (like c and hbar) in the system

so to get the unit temperature, divide the unit energy by k

I'm trying to remember how to spell the original titles of the two basic references. Planck's 1899 paper is little-known but lays out the system and gives essentially the same values for the basic natural units that we use today

Planck (1899). "Ueber irreversible Strahlungsvorgaenge. Fuenfte Mitteilung." Koeniglich Preussische Akademie der Wissenschaften (Berlin). Sitzungsberichte: 440-480.

Einstein (1916) "Grundlage der allgemeinen Relativitaetstheorie"

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Ivan Seeking

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marcus

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Originally posted by Ivan Seeking

LOL!

well Ivan you know I never have a sure notion of who, if anyone,

reads these posts. Or for whom, and at what level, to write

Did you ever read from the 3 article series "Scaling Mount Planck"

in Physics Today, by Frank Wilczek.

Wilczek is one of todays great (senior) theoretical physicists, at least in my view, and he gave one of best explanations Ive seen for why one ought to try to understand Planck scale and think about things from Planck scale perspective.

It is hard tho because the natural units are so extreme, many of them.

But they seem more and more to be a part of nature.

Tell Tsunami to smile enigmatically (as if she were nature) instead of looking puzzled

the calm enigmatic smile is the other side of the twistyface and much easier on the eyes

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Originally posted by marcus

Did you ever read from the 3 article series "Scaling Mount Planck"

in Physics Today, by Frank Wilczek.

If not I will...I don't recall reading the series.

Tell Tsunami to smile enigmatically (as if she were nature) instead of looking puzzled.

the calm enigmatic smile is the other side of the twistyface and much easier on the eyes

Really don't worry. She has looked twisted and pain ridden since the day we got married.

I am goint to say diffeomorphism invariance a lot for awhile just to annoy her. By the way, she wanted to know if this - diffeomorphism invariance - has anything to do with Michael Jackson?

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marcus

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Originally posted by Ivan Seeking

If not I will...I don't recall reading the series.

In case you want to look at them online

Earlier articles (June, Novemember 2001, August 2002)

http://www.physicstoday.org/pt/vol-54/iss-6/p12.html [Broken]

http://www.physicstoday.org/pt/vol-54/iss-11/p12.html [Broken]

http://www.if.ufrgs.br/~jgallas/wilczek.html [Broken]

Much in them is too technical for me or general readers but

I believe there is an understandable perspective that comes thru

despite this. See what you think.

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he starts by considering the question of why gravity is so weak

compared to other forces, and defines a number N as a measure or indicator of its weakiness, and about halfway thru the first paper he says:

"...Thus hbar and c appear directly as primary units of measurement in the basic laws of these two great theories. Finally, in general relativity theory, spacetime curvature is proportional to the density of energy--and G (actually c^4/G) is the conversion factor.

If we accept that G is a primary quantity, together with hbar and c, then the enigma of N's smallness looks quite different. We see that the question it poses is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in natural (Planck) units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number sqrt N.

That's a provocative and fruitful way to invert the question, because..."

The tiny number sqrt N that he is talking about is one over the rather large number 13.01 quintillion. It is one of a small bunch of mysterious numbers that are really fundamental constants, like 137 or 1/137. It is easiest to remember it as 13E18 or 13 quintillion.

What Wilczek says is that our theory is being challenged to explain this number 13 quintillion, and (surprisingly enough) according to him it is making some progress towards explaining it!

Remember Feynmann saying something like this about the number 137, that in his opinion every physicist worth his salt should have that number pasted up on the wall to remind him to try to figure out why it was that----why it was 137 instead of something else.

(I dont always distinguish between numbers and their reciprocals as you see )

- #21

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well its the same as asking why Planck energy is so large

because the time unit is only as small as the frequency unit is high, and hbar times that frequency is the unit energy

so brief time corresponds to high energy (as we know so well!)

energy being more or less the same scale as mass, the question comes down to

"why is the planck mass 13 quintillion times the proton mass?"

So he boils the problem of understanding planck scale (and the weakness of gravity) by reinterpreting it this way

"what causes the proton mass to be 1/(13E18) of the natural mass unit"

now the problem is with the proton

the natural unit of mass is just the natural unit and we challenge our theory to come up with the small number which is the reciprocal

of 13 quintillion.

It seems so simple, I can even feel comfortable with it. Maybe you and/or Tsunami can too! All we need to do is trust that the people we pay to be theoreticalphysicists have all stuck the number 13 quintillion up on the study wall or over the shaving mirror and that

eventually some one of them will come up with a reasonable explanation of why it is what it is.

I guess I trust them to that extent. so I can feel comfortable about the sizes of the Planck units.

and this is the scale that appears to be emerging in (for instance the area and volume spectra of) loop gravity.

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erm......gonna need a little absorption time, here.....

- #23

marcus

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Originally posted by Tsunami

erm......gonna need a little absorption time, here.....

Hello Tsunami, I am embarrassed to say that

while you have been friendly and encouraging I have not

written any posts specifically for you---too busy talking to myself

and possibly to Ivan and others.

So I have not reciprocated. Which, come to think of it,

is rude. So I would like to make amends for this, if

possible. Maybe by responding to some question or idea of yours

in a comprehensible way.

Have you met Nereid and selfAdjoint here, by the way. They

tend to be nice and answer people's questions in a way so that

the person understands and is left feeling good about

having asked. By contrast, I often fly off on tangents.

It was probably a mistake, for example, for me to get started

talking about Planck units----though they truly have something

to do with quantum gravity, quite a lot actually.

Maybe we can get this thread back on track and make it have

more genenral interest. Any ideas or suggestions?

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Tsu

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And I'M embarrassed to say that here I thought that ALL OF THESE POSTS IN THIS WHOLE FORUM were written JUST FOR ME!! Imagine my surprise to find out that this is not so! I'm actually very relieved to know I won't be held responsible to know the contents of your last post!Originally posted by marcus

Hello Tsunami, I am embarrassed to say that

while you have been friendly and encouraging I have not

written any posts specifically for you---too busy talking to myself

and possibly to Ivan and others.

Not to worry. I'm thinking there's probably not a rude bone in your body. But I do have an idea forming...So I have not reciprocated. Which, come to think of it,

is rude. So I would like to make amends for this, if

possible. Maybe by responding to some question or idea of yours

in a comprehensible way.

Yes, I've 'met' Nereid and selfAdjoint. I like both of thier posts very much. Wolram is another whose posts I enjoy. Don't worry about your tangents...I'm pretty 'tangential' myself. Planck units are good, especially with all these special relationships they seem to have with everything else.Have you met Nereid and selfAdjoint here, by the way. They

tend to be nice and answer people's questions in a way so that

the person understands and is left feeling good about

having asked. By contrast, I often fly off on tangents.

It was probably a mistake, for example, for me to get started

talking about Planck units----though they truly have something

to do with quantum gravity, quite a lot actually.

Here's my idea. Let's let this thread continue on in it's own little nerdy fashion , and I'll start a thread or two of my own later today. I need to get more than one explanation to all my questions so I can pull it all into a better understanding of the more important aspects and theories in today's physics. Hope to see you in MY threads!Maybe we can get this thread back on track and make it have

more genenral interest. Any ideas or suggestions?

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marcus

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I'm happy with that.

This thread has a lot that is just my personal views of Loop Gravity and continuing (with that reminder) here is the gist of LQG or its main interest for me.

It reinforces a historical change in the view of space and time that was already in General Relativity. GR already has freedom from background geometry and it already has what A.E. called "general covariance" which deprives the spacetime continuum of physical existence and leaves the fields of energy and spatial relationship the only things with invariant meaning. Contemporaries call these two feature of General Relativity by the names BI and DI (Background Independence and Diffeomorphism Invariance) and Smolin did a good job explaining them for wide audience in his SciAm article.

But these are not specifically LQG things. They are aleady in 1915 GR and LQG merely confirms them by confirming GR and making it harder to ignore. A lot of people are in denial about the 1915 message because it does away with absolute Minkowski space (beloved of Particle guys) and absolute Newtonian space which is the mothers milk imbibed the Freshman year by all physicsmajors. So the 1915 message is disturbing and there has always been this resentful dream floating around of throwing out what we learned from GR and replacing it with some imagined "more fundamental" theory that wouldnt have BI and DI and would still have the beloved spacetime continuum.

What LQG does that is new---the essential thing I believe---is lend credence to a burgeoning thicket of new theories called Double Special Relativity which say that there is something else besides the speed of light that is the same to all observers.

There is currently a kind of uncontrolled growth of DSR theories and they all take seriously the possibility that there is something real about the planck scale. This would mean Minkowski space is the wrong space (even tho everything in Particle physics is built on it).

The reason that LQG lends credibility to DSR theories (which are growing wild and need to be pruned back by experiment) is that

when Rovelli and Smolin (1995) calculated the spectra of the area and volume operators----essentially the possible results of microscopic measurements of area and volume, beyond current technical capability---they found they were a bunch of fractional and rootly multiples of the planck unit area and planck unit volume.

Another thing LQG does is show you in concrete detail how to throw away the old Riemannian manifold and still keep the fields.

You can chuck out the spacetime continuum (which does not have physical existence in GR, being a mere "gauge" or mathematical convenience) and still describe quantum states of the gravitational field using networks or knots.

Or maybe I should say "abstract graphs". The kind of thing that is just a set of points with a list of which points are connected to which others. It does not have to live in a conventional Euclidean space or anywhere in particular because it is an abstract "combinatorial" being-----you write down a list of nodes and a list of links----or you draw a networklike thing on a piece of paper---but the thing itself does not have to be embedded in some oldfashioned absolute space in order to exist. It exists.

And all kinds of fields can be defined on this graph, or net, or knot, just by coloring its nodes and its links.

And a quantum superposition of enough such graphs will look and behave sufficiently like familiar space that it will fool most people.

the graph is pure relation, abstracted out of any spatial or temporatl continuum. the continuum can be thrown away and all the fields defined relationally, on the graph

one of the Loop people likes to call the quantum states of the gravitational field "polymers" because to him they seem like huge ball and stick molecular models---we are talking jillions of nodes.

the nodes supply volume to whatever physical region contains them and the links supply area to whatver surface they pass thru

What this is doing is REIFYING or thing-ifying a basic insight that Einstein already had and made fundamental to General Relativity. The continuum does not physically exist, what counts are the interrelationships, the intersections and meetings of worldlines. These have a physical meaning that does not go away when you morph the space.

If the paths of two particles cross, then they still cross after you morph all space and time. So that coincidence or intersection has meaning, although the coordinates on the map do not.

That was already there in 1915, but the 1990 loop business with its "spin networks" just gives a concrete representation of a purely relational quantum state. Something they could calculate with---and when they calculated area and volume spectrums they encountered the natural units. It think that's basically the story (in its briefest outline)

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marcus

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Originally posted by marcus

...And a quantum superposition of enough such graphs will look and behave sufficiently like familiar space that it will fool most people.

the graph is pure relation, abstracted out of any spatial or temporal continuum. the continuum can be thrown away and all the fields defined relationally, on the graph...

so the main thing the Loop approach does is finish (what Einstein began in 1915 namely) getting rid of the classical continuum.

by offering a blurred superposition, a quantum dogpile, of all the possible relationship graphs

graphs that describe proximity or contact between things, saying what neighbors on what

and a blurred heap of enough such graphs will act in a way that resembles the old familiar continuum (but not exactly, UV infinities go away in the quantum fields of particles, a cosmological singularity disappears, microscopic quantization of geometric features area and volume occur, new problems arise)

now string theory has always been done in the old-fashioned continuum---indeed mostly in the simplest and flattest space of all, Minkowski space---and in that context it would not work unless the space had an unrealistic number of dimensions like 26 or 10 depending on what particular variant of string theory one was considering.

But what would happen if you set up a string to vibrate in the new picture of space, this quantum heap of networks?

Thiemann says that some friends at the Albert Einstein Institute (AEI) at Berlin (like Hermann Nicolai, a string theorist) kept urging him to try this. He tried it and some problems that had bothered string theory went away.

the analysis no longer required 10 or 26 dimensions, you could do it in any number of dimensions including the number we see (the obvious 3+1)

no more ghosts, no more negative normed Hilbert spaces

no more tachyons (particles faster than light)

no dependence on supersymmetry, can adopt or not adopt, depending on

whether experiment shows the extra particles exist or not

-------------------------

It looks to me as if Berlin is going to be pretty strong in gravity.

Bojowald is already there

Thiemann is currently in Canada but will probably go back

in this new paper he is using results of Hanno Sahlmann and ones he got with Sahlmann. Sahlmann will probably go back.

The AEI is part of the Max Planck Institute for Gravitation Physics there---they held the October 2003 conference called "Loops meets Strings" and Hermann Nicolai was the co-host with Abhay Astekar.

The top people in DSR (doubly special relativity) are in Europe. Kowalski-Glikman is right down the road from Berlin, in Wrocz.

Carlo Rovelli has already moved to Marseille.

It looks like the center of gravity in 21st Century theoretical physics is shifting or has already shifted to Europe

---------------------

Thiemann's new paper just scratches the surface. Everything has to be checked and extended to more cases (he only does a boson string, he or somebody needs to do a fermion one)

there is a huge amount of open research territory in this direction

as Thiemann indicates (but you can gauge for yourself without that)

-----------------------

what was Edward Witten's last paper about? anybody remember?

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marcus

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this is a high-risk thread, I guess, so I'll open this here can of worms

a minority of comparative newcomers in Loop Gravity are proposing the possibility that the area spectrum is not what Rovelli/Smolin calculated in 1994 but instead (if expressed in units of the planck area, the natural unit of area)

consists of multiples of

[tex]4 ln 3[/tex]

here are three papers explaining that possibility, and why it might be true

Gilad Gour, V. Suneeta

"Comparison of area spectra in loop quantum gravity"

http://arxiv.org/abs/gr-qc/0401110

Alexios Polychronakos

"Area spectrum and quasinormal modes of black holes"

http://arxiv.org/hep-th/0304135 [Broken]

Alekseev, Polychronakos, Smedbaeck

"On the area and entropy of a black hole"

http://arxiv.org/hep-th/0004036 [Broken]

Interestingly enough, the last of these papers cites a 1992 paper of Edward Witten which gives an example of when "regularizing" a casimir element changes it from

[tex]j(j+1)[/tex]

to

[tex](j + 1/2)^2[/tex]

For the most part that is all this little fracas is really about.

You can see the two things are not really very different. They differ only by a quarter, one is

[tex]j^2 + j[/tex]

and the other is

[tex]j^2 + j + 1/4[/tex]

And there are times when "quantum corrections" require changing from the first to the second. The Edward Witten paper apparently affords one example of this:

Journal of Geometrical Physics 9 (1992) 303-368

and they give other instances as well.

Anyway in 1994 Rovelli/Smolin calculated the area spectrum in LQG to consist of "squareroot casimir terms"

[tex]\sqrt{j(j+1)}[/tex]

And now these other people like Polychronakos say they should have considered making a quantum correction and putting in

[tex](j + 1/2)^2[/tex]

which, when it goes under the squareroot sign just comes out

a very simple

[tex](j + 1/2)[/tex]

So for them the area of a physical surface, like a tabletop or a beachball or a blackholeeventhorizon will consist of a sum of

terms like that

This is the "equidistant spectrum" version LQG area.

also called the "evenly spaced" spectrum.

Either way the abbreviation ES would do as a tag.

and as a consequence, in the ES version a certain so-far undetermined paramter in the theory which may still be adjusted would, according to these minority voices, equal the natural logarithm of 3, divided by 3 pi:

[tex]\frac{ln 3}{3\pi}[/tex]

this is the Immirzi parameter and its a wild-card in the Loop Gravity deck, which disturbs some people and not others. Theories under construction just have undetermined parameters. It is a blessing LQG has so few, I think, and I dont worry about this parameter and its eventual fate. Some Loop/Foam theories look like they may get rid of the parameter altogether but that hasnt happened conclusively. So if there is this parameter, well, maybe it will turn out to be the log of 3 divided by 3 pi (and maybe it wont) and if it does turn out to be that someone will doubtless find an ingenious explanation for why.

But that is something to look forward to, and not worry about at the moment.

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Originally posted by marcus

Theories under construction just have undetermined parameters. It is a blessing LQG has so few, I think, and I dont worry about this parameter and its eventual fate. Some Loop/Foam theories look like they may get rid of the parameter altogether but that hasnt happened conclusively. So if there is this parameter, well, maybe it will turn out to be the log of 3 divided by 3 pi (and maybe it wont) and if it does turn out to be that someone will doubtless find an ingenious explanation for why.

But that is something to look forward to, and not worry about at the moment.

My money is on a little exercise in Feynman 'Negative Probability', functions.

There is a root to the problem, and at the same time there is a definate answer, inner probability against outer probabilities! just a teaser to a great time to be alive!

- #29

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Hi ranyart! well I am not placing any bets for now.

I just want to see what it is these "equidistant spectrum" (ES)

people are saying

To a passerby it might seem a bit picky or obsessive-compulsive for people to be concerned with whether an area formula is this or that, when the numbers are so close. But that attention to little numerical nits comes with the territory and so lets be picky

We are talking about a physical surface, S, defined by some material object, and a quantum state of geometry called a spin network state.

Geometry is the same as the gravitational field. So the a spin network is also a concise description of the gravitational field.

Particles and/or other fields can be located on the network. Information about area and volume are contained in the network. Each node contributes a bit of volume to whatever region contains that node. Each link or edge of the network contribute a bit of area to whatever the edge passes thru.

Each edge is labeled with a number j (called a "spin" by Roger Penrose who first used these networks). If a particular surface is intersected by N edges, indexed n = 1,....,N, and edge #n is labeled by spin

[tex]j_n[/tex]

then in the evenly spaced (ES) version the area is

[tex]A_S = 8\pi l_P^2 \gamma \Sigma (j_n + 1/2)[/tex]

Here gamma is the famous Immirzi number and

[tex] l_P^2[/tex] is the planck unit of area, the square of the planck length

Now basically all these people seem to be saying, it seems to me, is that this formula is only a little bit different from the Rovelli/Smolin (let's abbreviate it RS) formula and that it works out better. They get that in the case of a Schwarzschild black hole the

area will change by increments of 4 ln 3. (In natural units) and

that seems to be nice and compatible with other findings, including the big one of Shahar Hod.

for comparison, I'll write down the RS version of the area. You will see it is not much different. Same spin network quantum state of the gravitational field (determining distances angles areas volumes etc) and same surface, intersecting the same N edges with the same N spin labels: In the not-evenly spaced (RS) version the area is

[tex]A_S = 8\pi l_P^2 \gamma \Sigma \sqrt{j(j+1)}[/tex]

I just want to see what it is these "equidistant spectrum" (ES)

people are saying

To a passerby it might seem a bit picky or obsessive-compulsive for people to be concerned with whether an area formula is this or that, when the numbers are so close. But that attention to little numerical nits comes with the territory and so lets be picky

We are talking about a physical surface, S, defined by some material object, and a quantum state of geometry called a spin network state.

Geometry is the same as the gravitational field. So the a spin network is also a concise description of the gravitational field.

Particles and/or other fields can be located on the network. Information about area and volume are contained in the network. Each node contributes a bit of volume to whatever region contains that node. Each link or edge of the network contribute a bit of area to whatever the edge passes thru.

Each edge is labeled with a number j (called a "spin" by Roger Penrose who first used these networks). If a particular surface is intersected by N edges, indexed n = 1,....,N, and edge #n is labeled by spin

[tex]j_n[/tex]

then in the evenly spaced (ES) version the area is

[tex]A_S = 8\pi l_P^2 \gamma \Sigma (j_n + 1/2)[/tex]

Here gamma is the famous Immirzi number and

[tex] l_P^2[/tex] is the planck unit of area, the square of the planck length

Now basically all these people seem to be saying, it seems to me, is that this formula is only a little bit different from the Rovelli/Smolin (let's abbreviate it RS) formula and that it works out better. They get that in the case of a Schwarzschild black hole the

area will change by increments of 4 ln 3. (In natural units) and

that seems to be nice and compatible with other findings, including the big one of Shahar Hod.

for comparison, I'll write down the RS version of the area. You will see it is not much different. Same spin network quantum state of the gravitational field (determining distances angles areas volumes etc) and same surface, intersecting the same N edges with the same N spin labels: In the not-evenly spaced (RS) version the area is

[tex]A_S = 8\pi l_P^2 \gamma \Sigma \sqrt{j(j+1)}[/tex]

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marcus

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Originally posted by marcus

...Then in the evenly spaced (ES) version the area is

[tex]A_S = 8\pi l_P^2 \gamma \Sigma (j_n + 1/2)[/tex]

...

[tex] l_P^2[/tex] is the planck unit of area, the square of the planck length

and in the evenly spaced (ES) version the area is

[tex]A_S = 8\pi l_P^2 \gamma \Sigma \sqrt{j(j+1)}[/tex]

...

In physical models parameters accumulate like barnacles on the bottom of a ship, depending on history and who discovered what when.

So what happens if we just put in the value for gamma that they want.

namely ln3/3pi. If Tsunami were to look at this and see the gamma she would not be pleased. Neatness and simplicity matter. So let us get rid of it. Make the formulas as clean as we can.

And if we take for granted the area is going to be measured in Planck units of area, then we dont have to include that in the formula either. So then the ES area formula is

[tex]A_S = (4 ln 3)\frac{2}{3} \Sigma (j_n + 1/2)[/tex]

the fraction 2/3 is what still needs discussion

It is getting clearer that in the case of a black hole event horizon the area could gain and lose in steps of (4 ln 3) because that is already appearing in the formula.

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