About nine years ago, a movement trying to (largely or entirely) "replace" string theory research with would-be "competitors" culminated. Unproductive critics and third-class researchers disconnected from the last 30 years in physics were often marketed as peer of top string theorists – and sometimes as something better.

However, aside from the cheap anti-science populism, there has never been any substance in their claims, and one can't really run on "promises" indefinitely. For a while, the theory group at the Perimeter Institute operated as a fan club of Lee Smolin's of a sort – a warrior in the "string wars". Thankfully, "string wars" are over and the crackpots have lost. Unfortunately, they have been replaced by lots of other nonsense. Did this replacement make things better or worse? I don't know.

To return to the positive news, let me mention that after many decades, a person once working at the periphery of the loop quantum gravity community has understood a lethal problem with the Poincaré-invariant networks. Unfortunately, I can't link to the text.

The correct insight is that the Minkowski space can't really be represented by a network or graph that would fill it. The very same argument (with very similar pictures) has been written on this blog many times since 2004 – see e.g. the second myth, "a structure of links or surfaces filling a Minkowski space may be Lorentz-invariant, at least statistically", in the 2009 TRF blog post about myths about the minimal length.

I won't repeat it here but it's trivial to see that every quasi-uniform network drawn on a paper inevitably picks a preferred reference frame – the Lorentz boosts acting on the network inevitably make it look "skewed" and "different". So a theory representing the space by the network breaks the Lorentz symmetry – pretty much by 100 percent or so. Consequently, spin foams and all similar discrete theories of quantum gravity may be falsified (by pointing to the successful tests of the Lorentz invariance) within a few seconds, assuming that the falsifier is adequately competent and fast. Now, decades later, people like our life-long champion of "discrete physics of quantum gravity" started to get the point, too.

(Just to be sure, I don't claim to be the first one who invented the argument, although I hadn't heard it in the same clear form before.)

Second. The Perimeter Institute used to be a center of the "bogus research" of quantum gravity. Fortunately, real physics research was gradually strengthening over there in the last 10-15 years. So three days ago, Witten gave a PI lecture on superstring perturbation theory, a way to calculate the stringy S-matrix using the super world sheets (with Grassmannian coordinates).

It is a nice piece of technology but the talk is very technical so I won't recommend it to non-experts. However, I must mention that I liked his points about the vertex operators' being localized on divisors etc. because I have spent lots of time by thinking about the mysterious duality – and generalizations of string theory to 2+2-dimensional membranes – and the conclusion that the vertex operators should be associated with divisors seemed to be rather solid. I should write an update about these matters at some point.

**PR, ER=EPR, fuzzballs vs AMPS firewalls**

Meanwhile, a new controversy has erupted in quantum gravity – in the serious (at least before a split?) quantum gravity done by people who are familiar at least with the basic lessons from string/M-theory, and most of them are great string theorists. No, I don't mean the "gravity as the entropic force" nonsense that is hopefully dead by now as well (much like the spin foams above) – although the dying still took about 50 times longer time than it should have.

I mean the controversies about the "firewall" claims by Polchinski and collaborators, and positive insights that were made as part of the argumentation that the firewalls don't really exist.

The cover story of the April 2015 issue of Scientific American is hyping firewalls and Joe Polchinski himself wrote this embarrassing, self-glorifying yet completely wrong, article. I've written some critiques before. But I await a guest blog about the matters and fuzzballs by Samir Mathur – who is probably also rightfully upset that some of his decade-old claims are being attributed to Polchinski and pals.

But this deeply flawed pro-firewall propaganda makes it to many articles that are otherwise avoiding it, too. So the Quanta Magazine wrote the first article in a series about the ER-EPR correspondence

Wormholes Untangle a Black Hole ParadoxK.C. Cole wrote a pretty clear exposition of the proposed universal equivalence between the wormholes and the quantum entanglement. The article also contains an amusing historical anecdote about the birth of ER=EPR. How was it born? Well, on one sunny day, the master (Susskind's nickname for Juan Maldacena) wrote a cryptical e-mail to Susskind that said ER=EPR. Susskind read the e-mail and immediately saw where it was going, he decided it was correct, so he agreed to put his name on the preprint. Nice done, Gentlemen! ;-)

I must say that the origin of my much less well-known joint paper with Susskind was the same with one M-name replaced by another. :-)

There are some reactions to ER=EPR mentioned in Cole's article. Preskill tries to be characteristically neutral and talks about uncertain smells. Shenker is supportive of the "big new insight". On the other hand, Polchinski and Marolf, the main guys behind the AMPS firewall meme, do their best to kick into Maldacena's and Susskind's insight while looking like Gentlemen.

The two last paragraphs of Cole's article are dedicated to Marolf's criticism of ER=EPR which I find vague enough not to be "totally sharply and rigorously wrong" but which is still weird and at least morally wrong if you realize what he is saying in between the lines:

To be sure, ER = EPR does not yet apply to just any kind of space, or any kind of entanglement. It takes a special type of entanglement and a special type of wormhole. “Lenny and Juan are completely aware of this,” said Marolf, who recently co-authored a paper describing wormholes with more than two ends. ER = EPR works in very specific situations, he said, but AMPS argues that the firewall presents a much broader challenge.Please, Don!

Like Polchinski and others, Marolf worries that ER = EPR modifies standard quantum mechanics. “A lot of people are really interested in the ER = EPR conjecture,” said Marolf. “But there’s a sense that no one but Lenny and Juan really understand what it is.” Still, “it’s an interesting time to be in the field.”

First of all, it is complete nonsense that ER=EPR only applies to one special case "so far". ER=EPR is one of the insights that – assuming that they are right, and I think that the case is extremely strong – apply as generally as you can get. The degree of generality is similar to Joule's equivalence of heat and work – or, indeed, as Noether's theorem. The claim really is that

*any*entanglement is some kind of a wormhole; and any physically allowed wormhole may be equivalently described as a spacetime without a wormhole but with near-maximally entangled local degrees of freedom.

What could have Marolf meant by the wormhole's being very special? That it is an Einstein-Rosen bridge and not a traversable wormhole? It has to be so. This is a part of the insight. A traversable wormhole would imply massive non-locality (violation of special relativity) – and this is forbidden in both descriptions, one with the wormhole and one with the entanglement. So the choice of the non-traversable wormholes isn't a sign of any incompleteness of the proposal. It is a detail that is makes Maldacena's and Susskind's proposal much more specific and bold. Traversable wormholes are almost certainly prohibited by the laws of physics – and Maldacena and Susskind confirm this expectation while a new argument for the non-existence of traversable wormholes arises as a corollary of their work.

Otherwise, the insight works in many spacetimes where the wormholes have technically different shapes – and different number of dimensions, among other things. They also claim that a description for "excited" wormholes exists on both sides, too. Tiny amounts of entanglement don't allow the wormholes to be big and smooth. But that's not a defect of the proposal, either. It's another bold prediction that follows from the ER=EPR line of reasoning.

If wormholes with many throats etc. are allowed as well, there probably exists some very special kind of entanglement of the three systems that describes the object, too.

But it's really the comparison of the generality of ER=EPR and of AMPS that sounds crazy. Marolf claims that AMPS is much more general. Well, it's not. It's exactly the other way around. ER=EPR is supposed to be relevant and possible for

*any*black hole interior – it may be connected elsewhere without spoiling the overall outside appearance of the black hole. On the other hand, AMPS is as special as a physically wrong claim may be. It is extremely special because the firewall is only derived for theories where the black hole complementarity is forbidden as a strict assumption, where the exact locality holds, and where the field operators are state-independent. With these very strong assumptions, you end up with Polchinski-like contradictions. But the assumptions are not obeyed in string theory – in consistent theories of quantum gravity – which makes their range validity pretty much zero for all practical purposes.

The claim that "AMPS is more general than ER=EPR" is at least morally untrue. It is hard to decide how you define the "degree of generality" for two qualitatively different hypotheses that disagree with one another (which implies that at most one of them is actually right) and want to organize quantum gravity in different ways. But if I try to define the "degree of generality" in any sensible way, it's clear that ER=EPR is much more general.

Marolf's (and Polchinski's) assertion that "ER=EPR seems to violate the posulates of quantum mechanics" is preposterous, too. How could it violate the general rules of quantum mechanics? It's constructed within these rules from the very beginning. One has the quantum mechanical description of the microstates of two identical but separated black holes (pretty much a tensor product of two copies of the same Hilbert space of microstates). And one simply claims that some entangled basis vectors in this product Hilbert space may be given new labels, as "simple" microstates of an Einstein-Rosen bridge. How could it violate anything about quantum mechanics? It's really just a collection of new labels for some vectors in the Hilbert space. A way to define new observables – field operators in the wormhole's interior – that are complementary to (i.e. non-commuting with) the usual field operators in two black hole interiors. From the birth of quantum mechanics, its power to allow, encourage, or force us to use superpositions of states (e.g. the entangled states) – and see that many of them are eigenstates of rather natural operators – has been one of the most characteristic changes that quantum mechanics represented. Quantum mechanics is all about the non-commuting operators, stupid!

This ER-EPR correspondence is a non-vacuous hypothesis – there has to exist some Hamiltonian or evolution in both pictures that agrees with both descriptions (that share the idea about the evolution of the exterior of the black holes or the wormhole). But this test is a dynamical question, not one that could change anything about the fact that Maldacena and Susskind operate within the totally standard quantum mechanical framework at every moment of their research.

I think that by now, it should be clear that Raju and Papadodimas' insights about the unavoidable state dependence are the key – and it is the key that is misunderstood by Marolf, Polchinski, and others. Even in ER=EPR, I just said that what the field operators are depends on which "corner of the Hilbert space" you want to describe. For the non-entangled corners, you pick the field operators describing two interiors. For the maximally entangled corners, field operators within an ER bridge are a better description (in ER=EPR, the state dependence is "manifest" because the two regions of the Hilbert space invite you to use two

*inequivalent*sets of field operators because the spacetime topologies are different). The modest claim here is that the local field operators always have a "limited range of validity" on the Hilbert space. But that shouldn't be controversial. That's an aspect of the gravitational fields accompanying the masses created by the operators or the impossibility to describe quantum gravity in a manifestly local way.

Finally, Marolf claims that "no one but Juan and Lenny understand ER=EPR". Now, this is just a plain lie. Perhaps a cute lie – because it mimics the bizarre claims that general relativity was only understood by 12 people in the world. But it is a lie, anyway. I surely do claim to understand the content of the claim as well as Maldacena and Susskind, and so do numerous people who have written about it.

In less than 2 years, the ER=EPR paper has 150 citations and most of them seem to understand what Maldacena and Susskind say and why. 150 isn't astronomical but it's almost the same rate – 320 citations in 3 years – that the AMPS firewall paper has.

If Marolf was really talking about sociology, I think that if you look at the 320 followups of AMPS, there will be so many that cite it even though they disagree with the firewall claims that the total body of papers citing either AMPS or ER=EPR will have a majority thinking that the firewalls don't exist.

The truth isn't decided by polls, however. One may still see that Marolf's sociological claims painting Maldacena and Susskind as two lonely fenceposts is a complete fabrication – especially if you read this fabrication from someone who implicitly says that his "argument that firewalls exist" is understood and agreed with by almost everyone.

It always bothers me: Couldn't Erik Verlinde see that gravity as the entropic force has some lethal bugs he may have been (and we may have been) unaware of that kills the whole picture? Isn't Joe Polchinski, an extremely smart physicist, able to see that similar problems with their AMPS proof (and loopholes) have been found as well – along with some new, much more positive and specific insights – that make the beef of the firewall paper pretty much evaporate? And that make them ignore some nice developments just because they don't agree with some disproved faith of theirs?

Of course, there are more brutal examples of this. Couldn't Gerard 't Hooft, a more than well-deserved Nobel prize winner, have seen that his claims about hydrodynamical models behind quantum mechanics have turned to a complete self-evident failure after those 20 years? Why do all these men keep on defending something that has become completely indefensible for so many years? Have they really lost the ability to think rationally, or are they afraid to admit that they were wrong and they know that to defend an arbitrarily silly proposition will always be OK in the broader public because most people don't have a clue, anyway?

In the late 1990s, when 't Hooft began with his hydrodynamic things that could have been shown to be wrong, he was ignored, despite his immense aura. But I am worried that similar, demonstrably wrong "research directions" are eating an increasing portion of the researchers, that a majority of the body of researchers is losing their competence. Are we entering a period in which people will defend AMPS-like paradoxes and entropic gravities for centuries even though it should take at most minutes for a competent physicist to understand why they're not right? Are we returning to the Middle Ages?

## snail feedback (38) :

Recently Alain Connes et al. have joined the quantum gravity community, e.g.:

http://arxiv.org/abs/1411.0977

https://www.youtube.com/watch?v=t_4hRuNvDmU

They claim in the paper:

"... these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model

emerge from Quantum Mechanics."

Any opinions ?

Thanks for this nice and important article Lumo, there is probably not more one can do against obviously wrong ideas becoming popular not only among the lay audience, than pointing out the errors again and again as you do so nicely ...

What may also contribute to the fact that wrong ideas seem to die harder these days, is the insane notion of "political correctnes" that has taken over in "western" societies. There seems to be an increasing notion that even wrong things have to be tolerated and supported, calling out mistakes and errors clearly is considered to be rude, etc ...

Hi Dilaton!

'Let's pray' that Lubos becomes EU's minister for Science and the Media - and from there goes on to amasses enough extra power through becoming chief of NATO and INTERPOL, etcetera, so that his attitudes and ideas can be implemented as long as he promises to take and follow advice and vetoes from you and me. ;-)

I have never found any opinion about a double pressure solution for Q Gravity, see my own proposal Q Gravity as the statistical result of opposing pressure vectors created by the Higgs field opposing the garviton field, around a fermion ( image below). Why not?

"t Hooft does not deal with "hydrodynamical models behind quantum mechanics."

http://physics.stackexchange.com/questions/34165/in-t-hooft-beable-models-do-measurements-keep-states-classical

Dear Lubos,

some questions:

1) the argument given against discrete structures underlying spacetime relies in an essential way on the fact that the Lorentz group is of infinite volume. Is there a way to exclude the possibility to have a "discrete theory" of Euclidean quantum gravity (as the ordinary orthogonal group is compact, it is obviously possible to have a rotationally invariant statistical distribution of networks or whatever) and then to define a true theory of quantum gravity by analytic continuation from Euclidean to Lorentzian signature?

2) At some point, you mention the mysterious duality, which I guess is the one between M-theory on tori and del Pezzo surfaces. Do you know the current status of this question ? Is there a satisfactory explanation of this relation or is it still an open problem? Also what is the relation you are alluding to with the Witten's talk and the fact that vertex operators are associated to divisors?

Dear monster,

1) naively, it may look like an OK possibility. The Euclideanized spacetime is invariant under a compact group that may emerge as a symmetry group in the limit. Indeed, one may define many similar theories on Euclidean spacetimes as limits of discrete structures, and their amplitudes may have some Minkowski continuation, too.

However, what's impossible is that before taking the limit, the Euclideanized discrete structure at t=i*tau=0 gives you a discrete structure at the t=0 of the Minkowski spacetime. The reason is simple. If the t=0 slice of the discrete structure could be interpreted in this way, the time-translational symmetry implies that the other slices in the Minkowski space would have to have the same interpretation, and one would be back to the disproven structure in the Minkowski space.

So even if there were some Euclideanized discrete graph-like picture of the spacetime, it must look very different in the Minkowski space, even at individual slices.

2) I am not aware of anyone who is really working on that - at least as much as I do.

The idea for the divisors is that in a certain limit, a theory on the 2+2D space - which is now Euclideanized to the 2 complex dimensional del Pezzo - reduces to the world sheets in perturbative string theory. If that's so, you have some choices what the vertex operators from the world sheet are "upgraded to" on the del Pezzo, and I think that the only viable picture is that they're not pointlike operators but operators associated with 1-complex-dimensional submanifolds of the del Pezzo, divisors, and there's some story about the moduli spaces etc. that makes a partial sense.

Lubos, started reading your blog a few months ago but first time commenting. I am a non-physicist but interested in these topics as an amateur- that said, do you have a post laying out your reasons for dismissing non-string theory alternatives that a layman could understand? Or a summary of the supporting arguments for string theory and your thoughts on likely frontiers for progress that would strengthen those arguments? I know such a thing is not always possible but it would be extremely valuable. I have been trying to glean the info from your archives but don't feel like I am making progress.

Highly enjoying the blog, thank you for writing!

Hi Ben,

the archive is full of such explanations by Lubos. While these are reduced to the absolute essential, a certain knowledge of physics is required. E.g., do you have a good understanding of special relativity?

"Good" being relative but yes I feel like I understand them. Is there a post you can link to that you think is particularly thorough?

It has really taken Sabine a long time to "see the light", hasn't it? She could have read your 2009 blog post on myths to generate the same arxiv paper she posted. Now we need Carlo Rovelli to realise that his theories violate Lorentz-invariance which he vehemently denied to me a few years ago on physicsstackexch.

Even very good physicists, like I think Polchinski is, seem to have mental lacunae with bizarre thoughts---Penrose with his quantum computer brain theory, Eddington and Dirac with their drift into numerology, t'Hooft, Schwinger with cold fusion...(Sean with his "explanation" of low entropy and time's arrow---but then, I said "good", didn't I? :) )

I went through the archive and decided that she already "began" to understand this point about discrete theories a year ago:

http://motls.blogspot.com/2014/06/sabine-began-to-understand.html?m=1

IMHO, the triangulation of the Torus seems a major step to create form changing by rotation of the torus over discrete hinges and use the subquantum forms to make compound particles see below:

I like this one for instance:

http://motls.blogspot.com/2009/09/myths-about-minimal-length.html

Also some obviously right ideas continue to be fought. The anti-quantum zealots being an obvious example.

For your last paragraph, I think you are wrong here. I don't know what firewall is about but quantum mechanics had been understood for much longer and there are very clear arguments like GHZM. The thing that people understood t'hooft is wrong doesn't say much.

Also I think they believe what they say, if they wouldn't even if they wouldn't acknowledge that they were wrong, they would shut up and work on something else.

This other one also meets your expectations, it makes some deep arguments on the topic, and that is why it is in my favorites:

http://motls.blogspot.com/2013/05/richard-dawid-string-theory-and.html

Dear Lubos, I have a question. In a paper by Raamsdonk the first reference is a paper by Banks about Matrix theory(yours also), so in what sense Matrix theory is connected to Raamsdonk paper.Thanks.

Building up spacetime with quantum entanglement

http://arxiv.org/pdf/1005.3035v1.pdf

Hi Qsa, Mark cites Matrix theory along with AdS/CFT as nonperturbative descriptions of quantum gravity - string theory.

Things like connecting space from pieces are bound to be nonperturbative - far from expansions around fixed backgrounds - too. So one could expect more direct connections between Matrix theory and Raamsdonk's stuff, etc.

I am not aware of papers in literature about it but I have some partial results how to see things like ER-EPR within Matrix theory, and what it means. Some of the clearest things deal with membranes and BPS black holes which are different by their causal diagrams than the ER bridge discussed in ER=EPR, but ER=EPR has to have implications in the extremal limit, too.

The general perfect entanglement between distant objects may arguably be described by a crisp wave function of the matrix degrees of freedom in Matrix theory. In practice, I think that it's like embedding a smaller block U(N) to the U(2N) theory via a special form of the wave functions etc.

Much more work was focused on AdS/CFT and its interpretation of Raamsdonk and ER-EPR things etc.

I think that Raamsdonk didn't try to do anything of the sort with Matrix theory. He just listed vaguely related papers that try to solve deep conceptual nonperturbative questions in quantum gravity.

Dear Lubos, I have two questions:

(1) "A traversable wormhole [TWH] would imply massive non-locality (violation of special relativity)" – Why do you think so? I guess TWH would at least respect special relativity locally, right ?

(2) "Traversable wormholes are almost certainly prohibited by the laws of physics" – could you give us a general argument who justifies this belief ?

Thanks in advance!

Dear NumCracker, I think that your two questions are exactly the same.

Traversable wormholes may look like "obeying special relativity locally", at very short distance scales, but it only obeys a part of the conditions implies by special relativity.

To keep a traversable wormhole, you need a negative energy density, and it violates some of the energy conditions, see e.g.

http://www.quora.com/What-is-the-relation-between-violations-of-energy-conditions-in-quantum-field-theory-and-in-the-concept-of-a-warp-drive

for a similar discussion in the context of the "warp drive" which is prohibited for similar reasons. A negative energy density is largely equivalent to a condensate of tachyons that move faster than light, and they violate causality according to special relativity.

Also, the "local" preservation of special relativity isn't the only sense in which special relativity has to hold. Special relativity and its laws of causality have to be obeyed at very long distance scales as well - whenever the spacetime at these distance scales may be approximate by a nearly empty Minkowski space with some localized perturbations or objects in it.

The throats of the TWH would be such objects, and they would allow you to send objects superluminally from one place to another. This is prohibited because of special relativity and the fact that the "microscopic structure" of the wormhole requires general relativity to be described can't allow an exception to this violation.

In the nearly empty space, one may still consider how various experiments look from the viewpoint of different inertial systems. An object that travels from A to be through a TWH superluminally looks like an object moving backwards in time from another inertial frame - which must be as allowed as the original one because the space is still mostly empty. If it were possible to send objects backwards in time, one could ultimately castrate your grandfather at a moment when he met your grandmother, making your existence both necessary and excluded, a logical contradiction of the usual closed timelike curves.

It is one of the deep and rudimentary myths - discussed in many previous blog posts - that is especially widespread in the non-stringy "quantum gravity" pseudoscience community that general relativity allows us to "forget" or "circumvent" special relativity. Nothing of the sort holds. Special relativity is as strong as before - general relativity is really a description how theories with spin-2 fields or particles have to work to be compatible with special relativity. It's special relativity, and not general relativity, that is the source of the primary principles, and GR is a derived consequence in special situations (for theories with a certain field content etc.).

On the other hand, is there similar constraints if the TWH had its throats connecting parallel branes in a braneworld ?

Hi, two parallel D-branes connected with a "tube" of the same D-brane stuff that looks like a wormhole may be the usual visualization of a wormhole, but it is *not* a wormhole because there's still the surrounding space.

Wormholes are only objects that change the geometry of the *whole spacetime*, not just some branes in it.

The D-branes connected by a tube don't have to violate any energy conditions. They wouldn't allow any superluminal transfer of signals, either.

Thanks Lubos!

A final question: has "c" to be numerically the same constant in different (parallel) branes (i.e. "4d-worlds") embedded in the 5d bulk ?

It depends on your units. In all sensible ones, Yes, tautologically. The question is physically inconsequential.

Adult physicists use units where c=1 everywhere. SI has one meter chosen so that numerically c=299792458 m/s, always. So yes.You may choose different units - depending on your position along the transverse direction to the branes - so that c won't be the same, too.

At any rate, if relativity holds in your Universe, and it should if that Universe is supposed to be similar to what we observe, then it is possible to set c=1 because it's a universal and essential constant.

Thanks for the reply. I tried to find some links but only came up with some papers like this one

http://arxiv.org/abs/quant-ph/0407047

I have not gone through it and I am not sure of the relation between "Matrix theory" and "random matrix theory".

In fact, the question was: could "c" change from a 4d-braneworld to another 4d-braneworld ? And, in case the answer is "yes", what forbids the usage of two (aforementioned) "tubes" connecting that pair of braneworlds to "emulate" a wormhole ?

Dear NumCracker, are you talking about two different braneworlds - disconnected universes or two models - or do you use the word "braneworld" for the branes within one Universe?

If the former, it makes no sense to compare dimensionful constants in two different universes or models. And as I said, c=1 may be set at all times.

If you talk about 2 branes in 1 universe, then if this theory is viable, compatible enough with experiments, then it is still Lorentz-invariant under the 4D Lorentz symmetry that only acts on the dimensions that the branes share, and this may be interpreted as having the same "c" on both branes.

Whatever I can imagine under "two different c" - you didn't define how this seemingly contradictory situation could arise - almost certainly means either a serious inconsistency, or at least a conflict with the Lorentz invariance i.e. with some experiments.

Moreover, I have a problem with your suggestion that a wormhole is the same as a "different c" or "two different c's". A wormhole is a tube connecting two different places in the Universe. It may be used to get between them more quickly than through the normal big distances in between but that shouldn't be interpreted as changing the speeds or "c" in any region.

The flight through the wormhole is a one-time process that avoids the normal space in between, not a sped up motion through the normal space.

"a structure of links or surfaces filling a Minkowski space may be Lorentz-invariant, at least statistically",

The proofs seem to assume content dimension equal to 4, or at least look at the question of the fractality of the sample as unimportant. But time ago it was suggested that the networks emerging from this approach had content dimension equal 2.

Dear Alejandro, I think that you have made the term "content dimension" but assuming it's obvious what you mean, your loophole doesn't work because "content dimension" equal to 4 is needed for the macroscopic Poincare invariance, too.

Moreover, it isn't really a loophole because while my proof indeed did assume that lower "content dimension" - a fractal structure of the thing - doesn't arise, one can still generalize the proof so that it does apply even if the "content dimension" is different.

So this suggestion of yours that there is a loophole is just fog.

I made the term to avoid "Minkowsku dimension" which was confuse in this context. The full accepted name is "Minkowski box-counting dimension" but 20 years ago some translators used "containing dimension" or similar constructs in French and Spanish.

Indeed I do not thing it is exactly a loophole but something that is related to the problem: that when you try anyway to go further with the loop program, the mathematics rescues itself by lowering the fractal dimension of the object being asked to work with.

Dear Alejandro, with the fractal structure, you make the disagreement with the Poincare invariance worse, not better.

Moreover, fractal dimensions depend on the fractal character at arbitrarily short distances. This can't occur if one has anything like the minimum proper length which these models unavoidably have.

If you try to reduce the dimension by the behavior of the networks at very long length scales, you get the violation of the smoothness space and its symmetries at these long scales which is very bad.

Well now, the "entire muslim population" would be "terminated" if they all converted to some other creed, or atheism as you claim you did.

Would that offend you too?

By the way, what is the penalty for apostasy under your former creed? Do you find that offensive too and tell its followers so? Or do you just keep your mouth shut and your head down?

By the way, WTF is it about some types that they feel the need tell others that what they said offends them? I'm constantly being offended by what I see and hear around me, especially by apologists for pisslam, but I never feel the need to tell anyone. I never tell anyone I have a headache either, unless of course it's by way of an explanation that might be needed under the particular circumstances. I mean why the fuck should anyone care whether I have a headache or not and why the fuck should I think that they might? One of life's great mysteries, that.

Hey, I'll tell you what — I'll make an exception just for you:

I'm offended by people who say they take offence at what I say. It's as if the stupid bastards think it makes any difference to me. Well, it fucking doesn't.

Upvote!

Lubos:

This may be a place to post a query which has bugged me for some time. It is probably a wildly naive question; so as an amateur, I am throwing myself on your famously tender mercies:

You are doubtless aware that some theorists, including Vafa, Ooguri and others, have speculated on the loose idea that black holes might generate baby universes. The papers

I’ve tried to parse involved extremal black holes, and they state that such baby universes would be “disjoint” from

our universe.

Do you know if there is anything in known physics which would absolutely forbid a real (non-extremal) black hole,

say Cygnus X-1, from generating a baby universe which would be able to propagate gravitation (presumably gravitons/gravitinos) back and forth with our universe.

Such graviton exchange would not be through the BH

event horizon, which is one-way, but through a bulk spacetime which separates both parent and baby (analogous to gravitation traveling between two or more D-brane-universes imbedded in a higher D bulk, while all open

strings remain stuck on their respective 'branes')? Thanks.

Dear Stargene, I actually remember when they - Cumrun, Robbert, Hiroši, and Rajesh

http://arxiv.org/abs/hep-th/0504221

were working on the paper while at Harvard, and I am among those thanked at the end. ;-)

I think that the key thing you must be careful is that the baby universes appear in the Euclidean spacetime - i.e.after the continuation to the imaginary time - not in the Minkowski signature. So you shouldn't better make the same conclusions about the astrophysical black holes.

So for me, this is a fancy mathematical transformation of the degrees of freedom of multi-center black holes whose horizons mix with each other in some way. If you have a particular black hole horizon, it should look like a black hole from outside, so what you get outside should be at most the Hawking radiation - if it is non-extremal. What happens inside is a different issue.

But in quantum mechanics, there are always many different complementarity descriptions. Moreover, there are many ways to analytically continue and choose contours, and I think that this paper - which I believe is fundamentally correct at the end - combines these two "freedoms" in a particular way. I think that none of these totally new ways to interpret what's going on will be interpreted as perceptions of an observer that is born on Earth and flies to these black holes in any "normal" way.

Hi Lubos,

Thanks for your response and it's great you've been involved in their discussions. If I understand what you’re saying (not likely, considering that these subjects are far over my head), but just in case…I’m guessing that whatever you guys discover about extremal BHs, being

special restricted cases, it can’t yet be safely applied to real 3+1 BHs in our universe. I’ll mention why I ask, in addition to pure curiosity:

Regardless of any specific parent-and-baby geometry/topology, and

still assuming only gravitational interaction, I am motivated by at least two corollary possibilities:

Assuming…

(1) Gravitational interaction between a parent universe (eg: us) and its large complement of baby universes suggests a possible source for the mysterious dark matter potential, whose origin still continues to elude particle physics.

Ie: One kind of DM potential source may lie effectively outside our universe.

(2) Since there seems no reason to expect that our universe might not be similarly derived as a baby universe, birthed by a black hole in a yet older universe, and that this proliferation sequence continues upward, so to speak, without bound, and considering that each universe may also be spinning in some sense with respect to its parent (reflecting the spin of its generator black hole?)… What might be the presumably stochastic effect of the totality of all gravitational interactions (i.e.:

potentials), generated by the infinite sequence of universes, at any point or particle in our universe?

Regarding (2):

Whether one initially posits universes which are locally classical (e.g.: classical strings), or which already have quantum mechanics imposed on them, I suspect that the instantaneous effect on micro-spacetime (perhaps ~planckian) scales might not be trivial.

FWIW.

Thanks again,

Gene

Dear stargene, I think that all these insights apply to unrealistic situations or are formal for a simple reason: the behavior of real-world black holes under real-world experiments has been understood by classical GR for 100 years, since 1915. It's unlikely that one finds something that macroscopically contradicts the predictions from GR at these everyday scales.

That's why I think that one has to go to a deeper description or experiments not performed in practice to get insights that go beyond this GR. But there are lots of extremely exciting ones.

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