Whats the deal with String Theory?

[Mentat]

So...uh...why'd you copy his post? I was kind of expecting a response to it .

 

[Ramanujan12]

Mentat.

The collage there is an unarranged string of mathematical (QST [inter] holographic theory) crunched together. With lack of a uniform language and higher-order symmetry (hypersymmetry) configured yet. To many notes not enough spaces [null]. More forthcomming...

 

[Ramanujan12]

BRST and World-Sheets.

The world is not written on a sheet.

Actually no wait...it is!. It's the language that's written on the sheet we haven't translated it into mathematics yet.

the Word-Sheet and the World-Sheet; we have not a Worldperfect spread for this darn sheet.

 

[jeff]

Originally posted by Mentat
So...uh...why'd you copy his post? I was kind of expecting a response to it .

Congratulations, you've asked the $64,000 question.

 

[jeff]

Originally posted by Mentat
Well, according to M-Theory, the Universe is not expanding or contracting, it's doing both. This is a result of the t duality, which I've brought up on numerous threads before.

Let me explain the aspect of T-duality that causes this misconception - including in me (but only for a couple of hours ) when I'd first heard about it as an undergrad. Like particles, strings can carry momentum. But strings also carry winding number, and in particular, they can wind around compact dimensions. Consider just one compact dimension, a circle, say with radius R. T-duality says that there's a mathematically different but physically equivalent description of this system in which the circle has radius ∝ 1/R so that a small circle in the original description becomes a big circle in the new but physically identical description. Thus T-duality is a symmetry relating string theories compactified on small and large tori (tori are higher dimensional generalizations of the circle. For example, the circle is a 1-torus, and the 2-torus is the surface of a donut). From this it should be clear how easy it is to goof if T-duality isn't explained properly when you first hear about it.

 

[marcus]

Originally posted by Mentat
So...uh...why'd you copy his post? I was kind of expecting a response to it .

hello Mentat, I copied Jeff's post because in the past when I've found some statements in one of his posts interesting I've often been unable to find them the next day or later thereafter because of editing. The personal story business does not square with my experience---I've never PM'd Jeff (that I can remember) and never gotten any useful PM from him that I know of-----I have found him acrimonious rather than informative as a rule: don't always read PM's written in what I suspect is ill will.

I think he greatly exaggerates what he thinks is his contribution to the discussion of quantum gravity and what he has told people about that they didnt already know.

I think he has given me one link that I didnt already have---a link to an article by two chinese (that I'm afraid didnt point in any useful direction-----gr-qc/0309018)----and has not raised new issues for me, tho he clearly believes he has!

I think right now he is mainly talking about a certain Lubos Motl tirade on Usenet spr, which drew some dubious conclusions from an excellent paper by Lobos and Neitzke

http://arxiv.org/hep-th/0301173

Assymptotic black hole quasinormal frequencies

Jeff does not paraphrase the paper particularly well or draw conclusions from it in a reliable fashion, perhaps he is repeating what he thinks Lobos said on spr based on the paper.

In any case it is an excellent paper and also points to work by Corichi and one of several possible resolutions of ambiguity about a numerical parameter in quantum gravity.

The Motl Neitzke paper is a followup of one by Motl that I introduced and discussed at PF:

"An analytic computation of asymptotic Schwarzschild quasinormal frequencies"
http://arxiv.org/gr-qc/0212096.

Thing about Lubos Motl is he does really good work for peer review publication but gets excited and goes over the top on Usenet.

I like him but you have to take some of his spr posts with a grain of salt.

He did a nice thing to me recently BTW. Lubos included a link in one of his spr posts that brought up a post of mine here at PF (down in archive) He said "this is the gist and if you want to know more, go to [link]" and if you clicked on the link you got my post. He may have guessed that it would make somebody feel good to be cited in that informal way.

Anyway the real meaning of this little thread of technical papers about BH entropy in LQG is far from what Jeff suggests in my opinion. He says "Loop Quantum Gravity is dead!" but IMO it has gotten increasingly interesting over the course of the past year in part because of crunching into real numbers like the "Immirzi parameter" with the help of papers like Lubos Motl's and others of the same thread-----Corichi's for example (which I also brought up here at PF) and John Swain's (which I also posted on)---and partly due to work by Bojowald and others concerning big bang and inflation in LQ cosmology. I see a growing number of people beginning to publish as the field gets more interesting. Just the impression I get from checking Arxiv every so often and reading a paper by somebody new.

Jeff or anybody who wants is welcome to think that the ongoing efforts of people to quantize GR is "dead" or not interesting. People have their different viewpoints.

 

[marcus]

Lubos Motl
"An analytic computation of asymptotic Schwarzschild quasinormal frequencies"
http://arxiv.org/gr-qc/0212096.

Motl and Neitzke
"Assymptotic black hole quasinormal frequencies"
http://arxiv.org/hep-th/0301173
[/B]

discussing BH vibration modes and the BH entropy formula in LQG is a bit "off topic" for this thread, and also a mite technical!

So I will start a new thread on it---more fun than continuing
this which has gotten a bit acrimonious and personal.
Have to go, but I will be back later

Yeah, I started a quantum gravity and string BH entropy thread
a few minutes ago

 

[Avron]

Originally posted by marcus
Avron this is a cheering comment although you could be more specific---or you might illustrate what you mean and what you'd like to see more of.

I didnt see the "old forum on yahoo" you mention. Was that a Doctor Kaku board or a Greg board?

I was delighted by the term "hair-braned" to describe a category of bunk. It has definite possibilities.

### What can I say, I'm happy with it all; if someone has a question, there are always good answers somewhere along the line. Lot's of great posts with the math...which if I remember correctly I NEVER saw any math on the old board.

The board on Yahoo was a Kaku board, I don't remember if Greg had anything to to with it or not. It's been a couple of years.

And yes, "braned" was intentional, lol...Avron

 

[jeff]

Originally posted by marcus
hello Mentat, I copied Jeff's post because in the past when I've found some statements in one of his posts interesting I've often been unable to find them the next day or later thereafter because of editing.

If you like, you can stop being such a knob and just pm me and ask.

Originally posted by marcus
The personal story business does not square with my experience---I've never PM'd Jeff

I didn't say you pm'd me, you in fact posted it.

Originally posted by marcus
I think he greatly exaggerates what he thinks is his contribution to the discussion of quantum gravity and what he has told people about that they didnt already know.

What do you mean exaggerate? Where did I claim to make great contributions to anything on this site? I'll admit that I'm not the prolific poster that you are, but I don't start my own threads to lecture. I answer only those questions on which I think I can make useful points that others aren't so likely to. Also, I don't have an agenda. In particular, I don't push string theory. There have been a handful of questions about string theory since I've been here, and I've answered them, but I've never gone beyond that. My problem with you isn't that I want people studying strings rather than LQG, it's that you're claims about LQG and strings are just plain wrong and your attempts to steer everyone towards materials about QG that by design concentrate on ST's problems and LQG's strengths is just unfair. Given your influence on the people here, you should be qualifying your suggestions in this regard. I mean, I've read those papers too, and they're worth reading, but I think you have to look at mainstream publications to learn about and gain perspective on what's actually going on in QG research today, and it's simply not LQG, it's strings. I'm sorry, but that's the plain and simple truth.

Originally posted by marcus
I think right now he is mainly talking about a certain Lubos Motl tirade on Usenet spr, which drew some dubious conclusions from an excellent paper by Lobos and Neitzke

http://arxiv.org/hep-th/0301173

Assymptotic black hole quasinormal frequencies

Jeff does not paraphrase the paper particularly well or draw conclusions from it in a reliable fashion, perhaps he is repeating what he thinks Lobos said on spr based on the paper.

In any case it is an excellent paper and also points to work by Corichi and one of several possible resolutions of ambiguity about a numerical parameter in quantum gravity.

The Motl Neitzke paper is a followup of one by Motl that I introduced and discussed at PF:

"An analytic computation of asymptotic Schwarzschild quasinormal frequencies"
http://arxiv.org/gr-qc/0212096.

Thing about Lubos Motl is he does really good work for peer review publication but gets excited and goes over the top on Usenet.

I like him but you have to take some of his spr posts with a grain of salt.

Anyway the real meaning of this little thread of technical papers about BH entropy in LQG is far from what Jeff suggests in my opinion. He says "Loop Quantum Gravity is dead!" but IMO it has gotten increasingly interesting over the course of the past year in part because of crunching into real numbers like the "Immirzi parameter" with the help of papers like Lubos Motl's and others of the same thread-----Corichi's for example (which I also brought up here at PF) and John Swain's (which I also posted on)---and partly due to work by Bojowald and others concerning big bang and inflation in LQ cosmology. I see a growing number of people beginning to publish as the field gets more interesting. Just the impression I get from checking Arxiv every so often and reading a paper by somebody new.

This is misdirection and bull. It's the following paper I was talking about.

http://arxiv.org/abs/hep-th/0307013

Originally posted by marcus
Jeff or anybody who wants is welcome to think that the ongoing efforts of people to quantize GR is "dead" or not interesting. People have their different viewpoints.

Sounding a bit equivocal there. Are you saying that in your view, ours is simply an innocent difference of opinion? Because if you are, it's your acrimony that needs explaining. I've extended the olive branch to you many times, I really don't know what else I can do. But I do know that there's no rule here that says I have to let you mislead everyone here, intentionally or not.

Anyway I didn't say LQG was uninteresting. Even though it's wrong, one can still enjoy learning about LQG because it's quite a cool little construct, as I've said many times.

 

[marcus]

Jeff said:
-------------------
This is misdirection and bull. It's the following paper I was talking about.

http://arxiv.org/abs/hep-th/0307013
-------------------

Why didnt you say so? I printed that paper out a while back and was just reading it earlier this afternoon!

the paper you mention (Berti, Cardoso et al) is a natural followup to the two I mentioned and they refer back to those two, it is hard to see the relevance of that one without the context of
Motl and Neitzke. So I'd say my guess was right on target rather than "misdirection".

I suggest you start a thread and explain what is going on in Berti/Cardoso, since you cited it and claimed to be discussing it.
This thread is about string theory though you have diverted it into discussing the supposed impossibility of quantizing general relativity-----the paper you just cited is not a string theory paper or related to any string/brane line of research. Let's get back onto the topic "What's the deal with string theory?" that the original poster of the thread started.

Although it does not have much bearing on string/branery, the paper you cited does mention LQG and provides semiclassical results which have an clear bearing on future LQG development. This will give quantum gravity theorists some numbers to work with analogous to experimental results, which would be the most helpful of all, but are still scarce!

As I told you back when you called yourself "steinitz" I don't have time for adversarial stuff---so I will have to resume ignoring your posts soon. Best wishes, however, have a good time doing whatever it is you do.

 

[jeff]

Originally posted by marcus
Why didnt you say so? I printed that paper out a while back and was just reading it earlier this afternoon!

I assumed you'd know about that paper and it's implications, and like any normal person here, if you didn't, you'd let me know.

Originally posted by marcus
the paper you mention (Berti, Cardoso et al) is a natural followup to the two I mentioned and they refer back to those two, it is hard to see the relevance of that one without the context of
Motl and Neitzke. So I'd say my guess was right on target rather than "misdirection".

This is utter nonsense. It's, dreyer's hypothesis that this paper undermines since it would've done so with or without lubos's paper, which was simply a mathematical verification that the value of the term to which hod's conjecture applied and on which dreyer's hypothesis rested was in fact exact, thus supporting the idea that this was not mere conincidence (Of course we now know this was coincidence, just of a different sort then was suspected initially).

Originally posted by marcus
tI suggest you start a thread and explain what is going on in Berti/Cardoso, since you cited it and claimed to be discussing it.

If your unable to understand how this paper explodes dreyer's hypothesis, start a thread with an appropriate question.

Originally posted by marcus
This thread is about string theory though you have diverted it into discussing the supposed impossibility of quantizing general relativity

.

You were the one who diverted the subject on the opening page of this thread! You posted:

Originally posted by marcus
at the most fundamental level what makes it difficult to quantize classical 1915 General Relativity is that the classical theory is "background independent"

ordinary quantum theories, quantum field theories, are constructed on some pre-established space+time geometry----which could be like normal 3D Euclidean space with a time line, or like the plain vanilla uncurved unexpanding 4D space of SPECIAL relativity, or
whatever----the flaw (from a GR standpoint) is pre-committment to any set geometry whatever.

to just begin defining the gear: waves, particles, strings, some fixed framework or geometric background has to be established---
but GR is different

in GR the shape of the spatial background is totally variable and dynamic, determined by the basic Einstein equation relating curvature to the distribution of matter and other energy---as the energy flows the curvature changes and as the curvature changes it guides the flow of matter and energy

the problem is not discrepancy of scale (as some posters suggest) although applicability at various scales is always an issue----the problem is that

GR lives on a completely free dynamic evolving geometry which emerges from the GR equations-----to precommit, even if you change it or perturb it later, trashes GR at its foundations.

String theory does not attempt to quantize GR. It is an attempt to arrive at an alternative explanatory model for gravity which will approximate the results of GR in certain situations at certain scales. There is a plethora of variant string theories and they are background dependent. I have not seen much evidence of numbers being predicted by this proliferating batch of stringy theories----numbers that could be checked against observation and experiment so as to help kill off some of the variants and select lines of development to pursue.

But probably it does not matter because people are proceeding outside of the stringy context---there is a clear established way to quantize classical theories, called "canonical" quantization. We don't need an alternative explanation of gravity if we are satisfied with GR and can succeed in quantizing GR. All along since before 1950 there has been an ongoing effort to quantize GR while conserving background independence! People have been gradually working out a way to quantize GR in a way that preserves the essence of the theory
(which is the most precisely predictive model of gravity we have so far, and not lightly to be discarded).

This is finally getting done and the theory is beginning to make predictions, which as they are checked by observation or experiment will help refine and guide further development. This quantizing of classical 1915 GR, only just now happening, has nothing to do with stringy business but is a different kind of quantum gravity often called LQG (something of a misnomer since the loops attribute is not the essential element, what is essential is a straightforward quantization of the 1986 new variables version of GR with minimum additional structure, and this is done in various but interrelated ways, not always using loops).

So your question "what makes it hard" really applies most appropriately to direct quantizing GR (by LQG) and is an interesting, even historical, question. Why has it taken so long?
GR was born in 1915 and ordinary quantum mechanics in 1929 and people have known for 70 years what they had to do----quantize background independent GR---and people have struggled with it for that long and only in the 1990s began to make real progress.

Originally posted by marcus
I don't have time for adversarial stuff

You could ameliorate the adversarial nature of our relationship by making clear that your enthusiasm about LQG is shared by few QG researchers so that the people you influence who decide to invest serious time in studying LQG do so with a clear-eyed view of what's actually going on in QG and why. I really don't think that's asking too much from the guy who just won PF's signature award.

 

[selfAdjoint]

In other words, Jeff, you will stop being adversarial when he knuckles under. Some collegiality!

Baez responded to Motl's spr sally, and his response goes to the paper you cite as well. Both this paper and the Motl's ones show that a speculation about the role of these modes is false. But the speculation was never at the core of LQG work, even though it attracted a lot of attention. LQG is in the same place it was before the speculation was first made. It has some puzzles and is still moving forward. It is not dead.

 

[Mentat]

Originally posted by jeff
Let me explain the aspect of T-duality that causes this misconception - including in me (but only for a couple of hours ) when I'd first heard about it as an undergrad. Like particles, strings can carry momentum. But strings also carry winding number, and in particular, they can wind around compact dimensions. Consider just one compact dimension, a circle, say with radius R. T-duality says that there's a mathematically different but physically equivalent description of this system in which the circle has radius ∝ 1/R so that a small circle in the original description becomes a big circle in the new but physically identical description. Thus T-duality is a symmetry relating string theories compactified on small and large tori (tori are higher dimensional generalizations of the circle. For example, the circle is a 1-torus, and the 2-torus is the surface of a donut). From this it should be clear how easy it is to goof if T-duality isn't explained properly when you first hear about it.

*Slaps self on forehead*, I'm startin' ta get it now .

So, basically, t-duality is just the duality that unifies some of the different string theories, by creating a symmetry between the physics of higher and lower tori...aren't those higher tori what "branes" are, or is that a different concept also?

Another question: What is the string explanation for the Big Bang? I had always thought that this t-duality was what was used to explain the postulated "bounce" effect, but now I see I was mistaken in that, so it leaves this question open again.

Any further help is appreciated.

 

[Mentat]

Originally posted by jeff
Anyway I didn't say LQG was uninteresting. Even though it's wrong, one can still enjoy learning about LQG because it's quite a cool little construct, as I've said many times.

BTW, just a small interjection...I've often wondered about something: if LQG makes interesting and noteworthy predictions, then when M-Theory emerges on top as the T.O.E. (sorry, just rootin' for home team ), doesn't it have to explain why LQG's approach worked on those particular occasions - or, at least, give an alternate approach that is just as good, or better?

 

[Mentat]

Originally posted by selfAdjoint
In other words, Jeff, you will stop being adversarial when he knuckles under. Some collegiality!

I don't think that's fair, selfAdjoint. Jeff may be going about it wrong, but he has a good intention - at least, that's the impression I'm getting from his posts - which is to help those of us who are not yet experts to go into the study of QG without false preconceptions.

Mind you, I don't mean to say that marcus is necessarily encouraging false preconceptions, but that jeff seems to believe marcus is making LQG look much better than it really is, thus causing certain students to spend their time on a theory that may die soon (in jeff's opinion).

All I'm saying is that, while jeff may be wrong, it doesn't mean this is some personal battle with marcus that he's trying to win. Rather, I think he is trying to look out for the "eager young minds" on the Forum (whether what he perceives as a threat really is or not).

 

[Mentat]

Originally posted by Mentat
*Slaps self on forehead*, I'm startin' ta get it now .

So, basically, t-duality is just the duality that unifies some of the different string theories, by creating a symmetry between the physics of higher and lower tori...aren't those higher tori what "branes" are, or is that a different concept also?

Another question: What is the string explanation for the Big Bang? I had always thought that this t-duality was what was used to explain the postulated "bounce" effect, but now I see I was mistaken in that, so it leaves this question open again.

Any further help is appreciated.

Another question (sorry if this flood of questions bothers any of you ): Why can nothing be smaller than the Plank's size, according to string theory, if there is no "bounce" effect caused by the simultaneous contraction and expansion of space (which I had thought was the result of differences in measurement of wound and vibrational strings...but, thankfully, jeff has put me right on that point)?

 

[selfAdjoint]

Mentat, you wrote

All I'm saying is that, while jeff may be wrong, it doesn't mean this is some personal battle with marcus that he's trying to win. Rather, I think he is trying to look out for the "eager young minds" on the Forum (whether what he perceives as a threat really is or not).

Jeff's knock on LQG, as far as I can see is first, the Immirzi parameter (that "fundamental ambiguity" in the black hole entropy calculation), and second, that the number of physicists doing it is much less than the number doing stringy physics of various kinds.

On the first point, the Immirzi parameter is not understood and is a lively topic of interest within the LQG community. One speculation about its origin was shot down by Motl and others (that was the quote war between Jeff and Marcus), but that was just one angle on the parameter and research goes on.

On the second, I think it's unworthy of discussion. GR and its descendants have always attracted fewer physicists than particle theory and its descendents. But note Baez's snarky retort to Motl on todays spr - GR has been rigorously based, not so any form of quantum field theory.

I certainly have no problem with Jeff believing what he will. My problem is with his treatment of a professional part of physics as if it was some crank theory.

 

[Mentat]

Originally posted by selfAdjoint
I certainly have no problem with Jeff believing what he will. My problem is with his treatment of a professional part of physics as if it was some crank theory.

Understood.

 

[jeff]

Originally posted by Mentat
I don't think that's fair, selfAdjoint. Jeff may be going about it wrong, but he has a good intention - at least, that's the impression I'm getting from his posts - which is to help those of us who are not yet experts to go into the study of QG without false preconceptions.

Mind you, I don't mean to say that marcus is necessarily encouraging false preconceptions, but that jeff seems to believe marcus is making LQG look much better than it really is, thus causing certain students to spend their time on a theory that may die soon (in jeff's opinion).

All I'm saying is that, while jeff may be wrong, it doesn't mean this is some personal battle with marcus that he's trying to win. Rather, I think he is trying to look out for the "eager young minds" on the Forum (whether what he perceives as a threat really is or not).

Thankyou.

 

[jeff]

Originally posted by selfAdjoint
I certainly have no problem with Jeff believing what he will. My problem is with his treatment of a professional part of physics as if it was some crank theory.

Where did I say that LQG is a crank theory? I've never thought that.

 

[jeff]

Originally posted by Mentat
Another question: What is the string explanation for the Big Bang? I had always thought that this t-duality was what was used to explain the postulated "bounce" effect, but now I see I was mistaken in that, so it leaves this question open again.

It wasn't the relation between T-duality and the idea of a "bounce" I was addressing. I was correcting the idea that T-duality allows the possibility that the universe may in some sense be both contracting and expanding. I'll get to the relation between T-duality and the pre-big bang or "bounce" scenario below. Also, one can imagine that certain dimensions might expand while others do something else, but again, this has nothing to do with T-duality, and in fact can even be considered independently of SMT (String/M-theory).

Originally posted by Mentat
So, basically, t-duality is just the duality that unifies some of the different string theories, by creating a symmetry between the physics of higher and lower tori...aren't those higher tori what "branes" are, or is that a different concept also?

Firstly, T-duality (which as I've explained relates theories on large and small tori) is just one type of a web of dualities that relate different descriptions of the same physical systems in SMT.

We'll suppose that spacetime has p noncompact spatial dimensions and one compact dimension given as a circle of radius R. D-branes appear in connection with T-duality as it applies to open strings. The T-duality transformation

(1) R → R′ = α′/R

produces a different but physically equivalent description in which open string endpoints can't move in the compact direction, now of radius R′, but only in the spatial hyperplane extended in the p noncompact spatial directions. However the rest of the string can move in all p+1 spatial dimensions.

Such hyperplanes are actually autonomous objects in their own right, D-branes. Their definition is in fact as surfaces upon which open strings end. Their dynamics are described by the compact components of the massless excitations of open strings whose endpoints live on them. Thus these massless excitations of open strings are in the T-dual picture physically equivalent to fluctuations of the D-branes on which they end.

This picture is greatly enriched by charging open string endpoints with U(n) gauge degrees of freedom and introducing a corresponding flat gauge field background for them to interact with. In this case, the spacetime coordinates of D-branes become noncommuting quantities suggesting that spacetime itself is quantized, but it's true meaning is currently a mystery. It's really in the full supersymmetric theory that D-branes have been so important in identifying the different dualities by which the many nonperturbative results have been established.

The space of inequivalent theories under the T-duality transformation (1) are thus given by R ≥ α′^½ suggesting that the string scale α′^½ represents in string theory a minimum observable length i.e. an ultraviolet cutoff, and there's considerable circumstantial evidence that it is. In particular, space-time singularities are expected to be avoided (or at least reinterpreted) in any geometric model of gravity which is compatible with string theory. In other words, in quantum string theory, relativistic quantum mechanics should solve the singularity problems in much the same way as non-relativistic quantum mechanics solves the singularity problem of the hydrogen atom, by keeping the electron and the proton a finite distance apart.

As a result, string theory allows us to formulate scenarios in which the universe can be sensibly said to "smoothly" pass or "bounce" from a collapsing to an expanding phase. In this way, string theory gives us a rationale for asking what there was before the big bang, and in no other currently available framework can such a question be meaningfully asked.

If you'd like more detail on any of this stuff, don't hesitate to ask.

 

[Mentat]

Thanks a lot for that post, jeff.

I do have another question though. How does this postulate, that requires there to be a minimum possible size of spacetime, cause the "bounce" effect?

IOW, what is it exactly that causes the Universe to begin expanding again, once it reaches the minimum possible size?

 

[Loren Booda]

Mentat,

Per the "bounce." I think of it in part as a "quantum gravitational degeneracy," like the progression from parent star to supernova to white dwarf with nebula.

Picture the mass-energy of collapsing spacetime as it approaches the Planck density _[rho]* at horizon radius R-->L* (the Planck length). Its gaining density in real space, according to T-duality, corresponds to an decrease in the virtual energy density _[rho]' for R'=(L*)²/R.

When the two densities and radii reach each other in magnitude, it is equivalent to say that the virtual universe either exchanges, or bounces, with the actual universe at the Planck length. The virtual Mentat also sees what seem the same events occurring, and too cannot distinguish between elastic or transitional processes at L*. [zz)]

 

[Mentat]

Originally posted by Loren Booda
Mentat,

Per the "bounce." I think of it in part as a "quantum gravitational degeneracy," like the progression from parent star to supernova to white dwarf with nebula.

Picture the mass-energy of collapsing spacetime as it approaches the Planck density _[rho]* at horizon radius R-->L* (the Planck length). Its gaining density in real space, according to T-duality, corresponds to an decrease in the virtual energy density _[rho]' for R'=(L*)²/R.

When the two densities and radii reach each other in magnitude, it is equivalent to say that the virtual universe either exchanges, or bounces, with the actual universe at the Planck length. The virtual Mentat also sees what seem the same events occurring, and too cannot distinguish between elastic or transitional processes at L*. [zz)]

I think I understand. Could you perhaps elaborate on the concept of "virtual universe"?

 

[Loren Booda]

Mentat,

Imagine the Planck surface to be a mirror - that is, in the sense of the spacetime without being represented by the image "within." This "reflection" is actually the real spacetime being inverted, through a spherical symmetry of T-duality, to the virtual universe geometry below the radius L*. That virtual spacetime, existing at all points of the global spacetime, is defined by the Heisenberg uncertainty principle and the Schwartzschild metric. Their dynamics, relative to the Planck surface, are equivalent.

 

[Mentat]

Originally posted by Loren Booda
Mentat,

Imagine the Planck surface to be a mirror - that is, in the sense of the spacetime without being represented by the image "within." This "reflection" is actually the real spacetime being inverted, through a spherical symmetry of T-duality, to the virtual universe geometry below the radius L*. That virtual spacetime, existing at all points of the global spacetime, is defined by the Heisenberg uncertainty principle and the Schwartzschild metric. Their dynamics, relative to the Planck surface, are equivalent.

Ooooooo-tay! That makes perfect sense.

Thank you, Loren.