- Absence of an Effective Horizon for Black Holes in Gravity's Rainbow

Ahmed Farag Ali, Mir Faizal, Barun Majumder

arXiv:1406.1980 [gr-qc]

Europhys.Lett. 109 (2015) 20001

The paper uses a modification of General Relativity known under the name of “rainbow gravity” which means that the metric and so the space-time background is energy-dependent. Dependent on which energy, you ask rightfully. I don’t know. Everyone who writes papers on this makes their own pick. Rainbow gravity is an ill-defined framework that has more problems than I can list here. In the paper the authors motivate it, amazingly enough, by string theory.

The argument goes somewhat like this: rainbow gravity has something to do with deformed special relativity (DSR), some versions of which have something to do with a minimal length, which has something to do with non-commutative geometry, which has something to do with string theory. (Check paper if you don’t believe this is what they write.) This argument has more gaps than the sentence has words.To begin with DSR was formulated in momentum space. Rainbow gravity is supposedly a formulation of DSR in position space, plus that it takes into account gravity. Except that it is known that the only ways to do DSR in position space in a mathematically consistent way either lead to violations of Lorentz-invariance (ruled out) or violations of locality (also ruled out).

This was once a nice idea that caused some excitement, but that was 15 years ago. For what I am concerned, papers on the topic shouldn’t be accepted for publication any more unless these problems are solved or at least attempted to be solved. At the very least the problems should be mentioned in an article on the topic. The paper in question doesn’t list any of these issues. Rainbow gravity isn’t only not new, it is also not a theory. It once may have been an idea from which a theory might have been developed, but this never happened. Now it’s a zombie idea that doesn’t die because journal editors think it must be okay if others have published papers on it too.

There is one way to make sense of rainbow gravity which is in the context of running coupling constants. Coupling constants, including Newton’s constant, aren’t actually constant, but depend on the energy scale that the physics is probed with. This is a well-known effect which can be measured for the interactions in the standard model and it is plausible that it should also exist for gravity. Since the curvature of spacetime depends on the strength of the gravitational coupling, the metric then becomes a function of the energy that it is probed with. This is to my knowledge also the only way to make sense of deformed special relativity. (I wrote a paper on this with Xavier and Roberto some years ago.) Alas, to see any effect from this you’d need to do measurements at Planckian energies (com), and the energy-dependent metric would only apply directly in the collision region.

In their paper the authors allude to some “measurement” that supposedly sets the energy in their metric. Unfortunately, there is never any observer doing any measurement, so one doesn’t know which energy it is. It’s just a word that they appeal to. What they do instead is making use of a known relation in some versions of DSR that prevents one from measuring distances below the Planck length. They then argue that if one cannot resolve structures below the Planck length then the horizon of a black hole cannot be strictly speaking defined. That quantum gravity effects should blur out the horizon to finite width is correct in principle.

Generally, all surfaces of zero width, like the horizon, are mathematical constructs. This is hardly a new insight, but it’s also not very meaningful. The “surface of the Earth” for example doesn’t strictly speaking exist either. You will still smash to pieces if you jump out of a window, you just can’t tell exactly where you will die. Similarly, that the exact location of the horizon cannot be measured doesn’t mean that the space-time does no longer have a causally disconnected region. You just can’t tell exactly when you enter it. The authors’ statement that:

“The absence of an effective horizon means there is nothing absolutely stopping information from going out of the black hole.”is therefore logically equivalent to the statement that there is nothing absolutely stopping you at the surface of the Earth when you jump out the window.

The paper also contains a calculation. The authors first point out that in the normal metric of the Schwarzschild black hole an infalling observer needs a finite time to cross the horizon, but for a faraway observer it looks like it takes an infinite time. This is correct. If one calculates the time in the faraway observer’s coordinates it diverges if the infalling observer approaches the horizon. The authors then find out that it takes only a finite time to reach a surface that is still a Planck length away from the horizon. This is also correct. It’s also a calculation that normally is assigned to undergrad students.

They try to conclude from this that the faraway observer sees a crossing of the horizon in finite time, which doesn’t make sense because they’ve previously argued that one cannot measure exactly where the horizon is, though they never say who is measuring what and how. What it really means is that the faraway observer cannot exactly tell when the horizon is crossed. This is correct too, but since it takes an infinite time anyway, the uncertainty is also infinite. The authors then argue: “Divergence in time is actually an signal of breakdown of spacetime description of quantum theory of gravity, which occurs because of specifying a point in spacetime beyond the Planck scale.” The authors, in short, conclude that if an observer cannot tell exactly when he reaches a certain distance, he can never cross it. Thus the position at which the asymptotic time diverges is never reached. And the observer is never causally connected.

In their paper, this reads as follows:

“Even though there is a Horizon, as we can never know when a string cross it, so effectively, it appears as if there is no Horizon.”Talking about strings here is just cosmetics, the relevant point is that they believe if you cannot tell exactly when you cross the horizon, you will never become causally disconnected, which just isn’t so.

The rest of the paper is devoted to trying to explain what this means, and the authors keep talking about some measurements which are never done by anybody. If you would indeed make a measurement that reaches the Planck energy (com) at the horizon, you could indeed locally induce a strong perturbation, thereby denting away the horizon a bit, temporarily. But this isn’t what the authors are after. They are trying to convince the reader that the impossibility of resolving distances arbitrarily well, though without actually making any measurement, bears some relevance for the causal structure of spacetime.

A polite way to summarize this finding is that the calculation doesn’t support the conclusion.

This paper is a nice example though to demonstrate what is going wrong in theoretical physics. It isn’t actually that the calculation is wrong, in the sense that the mathematical manipulations are most likely correct (I didn’t check in detail, but it looks good). The problem is that not only is the framework that they use ill-defined (in their version it is plainly lacking necessary definitions, notably the transformation behavior under a change of coordinate frame and the meaning of the energy scale that they use), but that they moreover misinterpret their results.

The authors do not only not mention the shortcomings of the framework that they use but also oversell it by trying to connect it to string theory. Even though they should know that the type of uncertainty that results from their framework is known to NOT be valid in string theory. And the author of the phys.org article totally bought into this. The tragedy is of course that for the authors their overselling has worked out just fine and they’ll most likely do it again. I’m writing this in the hope to prevent it, though on the risk that they’ll now hate me and never again cite any of my papers. This is how academia works these days, or rather, doesn’t work. Now I’m depressed. And this is all your fault for pointing out this article to me.

I can only hope that Lisa Zyga, who wrote the piece at phys.org, will learn from this that solely relying on the author’s own statements is never good journalistic practice. Anybody working on black hole physics could have told her that this isn’t a newsworthy paper.

## 47 comments:

Wrong things are soon forgotten.

If they write new papers still wrong, will be forgotten either.

Old not even wrong papers have a way of never to be forgotten. The question of sensational theories born anew in relation to an actual physics description of the universe meets our capacity to imagine new physics or potential pseudoscience at horizons or frontiers.

Yet it is thought that if our galaxy were the only one it would be enough as entropy to sustain arising life. But can the same be said for the deeper significance of our sentience?

Nemo:

This attitude of yours is exactly the reason why these things continue to live, people continue to get paid for it, and papers continue to get published on it. Don't you see that shrugging shoulders and trying to ignore it just doesn't work? There are more and more people building castles on air, because too many of their colleagues just look away thinking "oh, it will be forgotten". Yes, it will be forgotten, maybe in 10 years or 100 years. But until then it's eating up money that could be used on real research. Best,

B.

"The authors gratefully thank the anonymous referees

for enlightening comments and suggestions which sub-

stantially improved the quality of the paper."

Something, somewhere, is wrong.

Zeno would be proud.

Fair enough, but.... why pick on these poor bastards? They aren't alone. And there are people doing equally idiotic work and getting fame and fortune, or at least good jobs, out of it [ever hear of the amplituhedron? What about Susskind's stuff?]. They do *far* more harm. Why not clobber them instead?

"To begin with DSR was formulated in momentum space. Rainbow gravity is supposedly a formulation of DSR in position space, plus that it takes into account gravity. Except that it is known that the only ways to do DSR in position space in a mathematically consistent way either lead to violations of Lorentz-invariance (ruled out) or violations of locality (also ruled out)." I'm not sure I properly understand what you say, but if you literally mean what you write, you're plainly wrong. DSR is not compatible with Lorentz violation, which is not ruled out anyway, and I do not not know of any reason why relative locality is to be ruled out.

http://www.amazon.com/Gravitys-Rainbow-Penguin-Classics-Edition/dp/0143039946

"Tyrone Slothrop, a GI in London in 1944, has a big problem. Whenever he gets an..."

http://www.npl.washington.edu/eotwash/sr

"

but depend on the energy scale that the physics is probed" Susurrus or neutron star binaries (Hulse-Taylor, PSR J0348+0432, etc.), Big G (GR) is solid. Spiral galaxies' Tully-Fisher relation is Wesley Crusher dark matter or bench top-testable Milgrom acceleration. Baryogenesis happened, but Sakharov conditions. Failure is a cornucopia, for more studies are needed.A black horse a quarter hand taller than a white horse is not about height. At least six

chemistryexperiments repair quantum gravitation and SUSY. Look to falsify not to validate.Arguments about black hole horizons using general relativity are akin to arguments on the high energy limits of hydrogen bonding using hydrodynamic equations. Such black hole arguments require a theory of quantum gravity.

Uncle AI

Today's climate of what are the ten leading questions for science in this century seem to me as intrinsically vague as all pointing to a single solution - that includes quantum gravity. But after difficult and often discouraging steps of doubts I understand that the underlying principles of such a step toward unity in relation to chemistry and organic code constructs have to address your experiment. An analogy if you will of what you said of fame after the discovery of bias in neutrino emission.

Posted to arXiv.org today is a paper (Larsson et al) that reports observing a long GRB jet launched from within about 2 x 10^7 cm of the central ultracompact (i.e., black hole).

RE: BICEP-2:

In a piece on the BICEP-2 issue in Physics World, Neil Turok is quoted as saying: "For the past 35 years, theoretical physics has been an extravaganza of model-building" [adding that theories have] "sort of run amok".

In my opinion, if we insist on retaining the dubious and untested assumptions of absolute scale and strict reductionism, then theoretical physics will continue to offer only ad hoc and unnatural model-building.

Just like the uncertainty at the horizon is greatly magnified for the external observer, if only there was a magnification of something measurable - - that would be gold for gravity research!

Alice,

If, when a group of improvising musicians can not pick up on a note played, then consensus will label that note (played) as wrong.

Improvisation are all the approaches taken towards QG.

There will eventually be an approach in which no note played will be or can be labeled (as) wrong.

That is music too.

Boobydoo Bob

Jerzy,

I am happy to elaborate on exactly what I mean. The thing is this: the vast majority of papers that I get to review on rainbow gravity, or modified commutation relations, generalized uncertainty principle, and so on never specify the transformation properties of the quantities involved - including this paper discussed here.

If one does not specify these transformations, one does not know whether one is dealing with a deformation or a violation of Lorentz-invariance.

Breaking Lorentz-invariance is a mathematically consistent way to realize the rainbow gravity/minimal length idea in position space. It's also in conflict with lots of data. Of course it isn't entirely ruled out, but "strongly disfavored by data."

The other way to do it is to deform the symmetries, which then leads to nonlocalities.

I didn't say anything about relative locality, as you might have noticed. You know that I think it's wrong because you're using physically meaningless coordinate systems, and somebody yet has to explain me how you avoid the problem I pointed out in my paper. (Oh, yes, I know that Giovanni has written a paper claiming that the problem isn't present. Unfortunately, the calculation in the paper merely shows that the relations I used are indeed fulfilled also in relative locality. I fail to see how that resolves the problem.)

Be that as it may, relative locality is clearly not the framework that the authors are using, and they're not even mentioning it, so it's somewhat besides the point going into this. What annoys me is simply that they're totally ignoring the problem altogether. They and dozens of other people whose papers I have to review in stacks.

See, those of you guys now working on relative locality are at least trying to address the relevant issue. I don't think you'll be getting anywhere, but maybe I'm wrong, and it's fine with me that you try. But I don't know what papers like the above are supposed to be good for. Best,

B.

Speaking of paper that make outlandish claims, I was wondering about this one:

http://arxiv.org/abs/1411.0977

The authors announce that they found the holy grail of spacetime quantization " ... a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics."

Henning:

I only looked at this briefly. Too much outside my area too make a qualified statement about it. It vaguely looks like a spin-off of Connes' non-com geometry, or maybe it's just a reincarnation. I haven't seen any comment on it either, I'd be interested to hear. Best,

B.

Sabine,

"the vast majority of papers that I get to review on rainbow gravity, or modified commutation relations, generalized uncertainty principle, and so on never specify the transformation properties of the quantities involved - including this paper discussed here." Agreed. As for rainbow gravity, I do not really understand the idea, and besides, every solution of Einstein equation with nonzero e-m tensor is "rainbow".

Breaking Lorentz-invariance [...] conflict with lots of data. I disagree. You do not know what is the value of the parameter of deformation, so no conflict.

As for the relative locality, indeed, it would be good to discuss. I think it is perfectly healthy, albeit not fully understood. The argument is simple. Since RL can be obtained in 2+1 D from a perfectly physical gravity + particles model, it must be physical. So if we are puzzled by some aspects of it, it just reflects our lack of understanding, not the sickness of the model.

Hi Jerzy,

As so often, I find myself mostly agreeing with you.

Regarding rainbow gravity. The metric in GR is a function of the energy DENSITY, not of the energy, which is an integrated quantity. The integrated quantities appear in some metrics, yes, but the point is that the actual source for the curvature is local. This isn't the case in rainbow gravity. (This is also, essentially, what causes the problems with locality.)

I don't know what you mean with there not being any conflict of LIV with data. Right, one doesn't know the value of the parameter of deformation (how convenient, if you excuse the cynicism) but the game always goes the same: if that parameter is much smaller than one, then it looks very implausible. You can read off the LIV corrections from the modified dispersion relation, 3rd order corrections in the dispersion relation (corresponding to order 5 operators) need to have parameters smaller than 10^-13 if I recall the most recent bounds correctly. In my book that counts as "ruled out".

I don't know what's physical about 2+1 dimensional gravity.

Sure, we can discuss this at some point if you want - thought I've tried to stay out of this because I feel like I've wasted enough time on it. Best,

Sabine

"Posted to arXiv.org today is a paper (Larsson et al) that reports observing a long GRB jet launched from within about 2 x 10^7 cm of the central ultracompact (i.e., black hole)."And the relevance to Sabine's post is?

Phillip,

The more we observe nature in depth the more she writes extravagant papers.

Robert has fundamental points predicting that science will ultimately deal with scale issues if our predictions correspond to what can be observed or measured in nature.

Some papers are part of an explosion that are at best beyond the discussion of the physical and worse do not say anything about what might be metaphysical as natural. Our equations at best read to me as descriptive rather than exact compact solutions save for partial comprehensive unity of a bigger picture.

Consequently, the number of these papers exceed those of the exploding yet vague at least intuitive poetic nature.

The microtone group on Facebook are dealing with waves and music and outside their area such questions of mathematics as discrete nature. So maybe it is just my frame of mind but try what I do my guitar music comes out too sweet and harmonic.

Right Bob?

So we are lucky not to live close to rare energetic bursts and interaction with say dark matter is rare but if Bee is overwhelmed by such clever but laughable papers in retrospect that will not help us to review and understand our marvelous new explosion of hard data.

Bee - Breaking Lorentz invariance must not contradict prior observation, but can occur in new observations. Physics contains deformed symmetries as curve fittings, below. Only "

nicht einmal falsch" experiments falsify. Math is rigorous either way.Matter's elegant models fail: parity violations, symmetry breakings, chiral anomalies, baryogenesis, dark matter, SUSY failure, Chern-Simons repair of Einstein-Hilbert action. Load existing equipment with

nicht einmal falschfills: Eötvös experiment opposing enantiomorphic single crystal alpha-quartz test masses. Microwave rotation temperature(s) of racemic 4-oxa-D_3-trishomocubane. Look. Demonstrate theoretical violations are instead empirical diagnostics.Newton was wrong. The cycle continues.

http://arxiv.org/abs/1501.06468

Physics desperately seeks eldritch complexity. Instead observe eldritch simplicity.

One thing is almost guaranteed.

We are going to continue to spin our wheels fruitlessly until someone comes along with a testable theory of principle, instead of all this Ptolemaic model-building, which as Maxwell put it, leaves us with "an unnatural and self-contradictory mass of rubbish."

Does Helbig advocate dumpster-diving?

Perhaps we should start with the concept of n-dimensional spheres in a flat space having intrinsic chiral spin. We can also imagine Tori of progressive genus having a different and even sub orbits of distinct chiarilities. Between the two a circle of progressive chain codes over limited or unlimited projective space may form a minimum quantization (discrete grounding for continuous volume enclosing baseball curve) where each point has orientation. These can be aleigned to derive a third direction time arrow vector usually negative in value relatively but in a unified space is more deeply mirrored that this has wider possibilities as to how we quasifinitely resolve dimensional representative measure.

My approach would be a bit different.

I would ask for an explanation of the blatant hierarchical organization of nature.

Then I would ask for an explanation for the obvious fact that the nature's hierarchy is highly stratified.

Then I would ask why self-similarity is such a ubiquitous and fundamental property of nature.

I would expect that the answers might be found in transitioning to some form of conformal geometry that is broken to agree with the stratification.

Unfortunately this is far too radical. It would mean overturning hardened and well-defended models. It would completely change the way we think about nature - its organization and fundamental principles.

But it is fun to think about how nature achieves unification and the cosmic "harmony" you implied.

Robert, Otto:

I will delete all further off-topic comments. This is not the place to discuss your personal solution-for-everything. Thanks,

B.

/* relying on the author’s own statements is never good journalistic practice */

The same applies to this blog also. Author of this study didn't say, that the black hole will not exist - so that such an interpretation has no place in title. He just says, that under situation when the event horizon will be fuzzy due to variable speed of gravity, then it will leak the light. In AWT I'm explaining the total reflection mechanism: the strong gradient of space-time curvature behaves like the water surface mirror for light waves coming from inside of it. Once this gradient will be scratched, then the light can pass into outside from black hole.

/* In the paper the authors motivate it, amazingly enough, by string theory. */

The fuzzy black hole concept exist long time in realm of string theory ("fuzzball") as a consequence of quantum effects or extradimensions of space-time.

Zephir:

As usual, you're not making any sense. First, you are saying I shouldn't rely on the author's statements (which I didn't even ask them for) and then complain that I summarized the paper. The title refers to the title of the phys.org piece. And please stop boring us to death with your theory of something. Can't you see that nobody is interested hearing about it? Best,

B.

I do not understand how one can reject the SR at a certain scale since the SR is verified experimentally at any scale. In addition, the rejection of the SR imply to reject the constancy of the speed of light in vacuum or the Pythagorean theorem. To reject the constancy of the speed of light, we must reject the constancy of the vacuum permittivity and permeability vacuum or the reasoning of the Maxwell electro-magnetic induction which perfectly explains the speed of light. No, really, any deformation of the Lorenz transformation other than the assumption of the existence of a privileged reference frame (existence of space-time at rest) is really doubtful.

I highly congratulate Dr. Hossenfelder for this blog that allows amateurs of physics like me to enjoy his thoughts openly and which allows to develop our reflection on the world. I also thank her for his great patience, this should not be easy every day, I dont have such patience.

Bee - different topic - what is the status of gravitational wave detection with LIGO? I remember visiting the LIGO lab at Caltech some 25 years ago. Seems like a long time for a lot of nothing.

Arun: I think they're still upgrading, no? There's always this dance that every time somebody upgrades their detector, the better version is supposed to just find whatever they are looking for...

Because regardless of the theory of gravitation used (modification of GR) some gravitational waves are generated if the speed of the gravity is c then it would more sure to rely on this measure for now.

http://link.springer.com/article/10.1007%2Fs11434-012-5603-3

Arun, you can look at

Figure 1 of http://arxiv.org/abs/1304.0670

It is supposed to restart this year with sensitivity of

40-80 Mpc

I think this article is based on a total misunderstanding of what the paper is trying to say. The paper is trying to say that the problems/ paradoxes with black holes occur because people try to investigate phenomena at scales at which the spacetime breaks down due to quantum gravitational effects. If one limits the scales at which one ask questions, then one obtains the correct answers.

L.E. Otto,

Alice and Bob are momentarily untangled.

I am their unqualified spokesperson for this comment.

"So maybe it is just my frame of mind but try what I do my guitar music comes out too sweet and harmonic. Right Bob? - Otto"

No theorist is expected to perform what they compose (theorize).

That is for a hapless lot of low life forms labeled experimentalists. (Do not take literally - Susskind is a plumber)

Imagine the stacks on Bee's desk as scores of music. Pretend further Bee has a Doctor in music, not physics.

And last, but not least, imagine all those who submitted and contributed to the stacks on Bee's deck exclaim:

We, nor anyone, can perform what we compose or write or improvise (in our heads)!

Well, in that universe of Bee's alternative Professorship there are no stacks. The prerequisite to perform the theory is never met.

Just a pretty little tale where the physics in theories and the theories in physics are supposed to live together... happily together ...forever.

Alice and Bob are back together again...time for me to go.

Sabine, l enjoy reading your blog. l think that it's amazing, love reading your views and analysis.Also, l am writing a paper on a thermodynamic origin for the Newton force. There are superficial analogues to Verlinde's work. I have sent 3 pages to your Nordita email. l hope l am not wasting your time. Many thanks.

Islam:

I know that this is what the paper *wants* to say. But this isn't how science works. I don't care what the authors *want* to be true, I care what claim their argument actually supports. And their calculation shows nothing of that type. Best,

B.

Thanks, Shantanu, following forward from there, I've reached July 2014:

http://www.nature.com/news/physics-wave-of-the-future-1.15561

"Physics: Wave of the future

After two decades and more than half a billion dollars, LIGO, the world's largest gravitational-wave observatory, is on the verge of a detection. Maybe."

Haven't found anything more recent.

From the above

Even as project leaders try to get Advanced LIGO up and running, they are also pushing to place a third detector in India, where it would allow astronomers to pinpoint the source of gravitational waves even more accurately. LIGO engineers have already built a set of components, and are storing them at Hanford. They are waiting for India's new government to select a site and approve funding, but depending on when that happens, LIGO India could be operational by 2022 for a total cost of roughly $350 million.Arun: For more up to date info you can watch the the elogs of both the detectors which are public to see progress on a daily basis. Of course the postings on these are technical

https://alog.ligo-la.caltech.edu/aLOG/

and

https://alog.ligo-wa.caltech.edu/aLOG/

Alice,

Narrowing our chances to be anything*

*Besides reality.

http://arxiv.org/pdf/1412.6213v2.pdf

...on the reality of the wave function.

Boding Bob

Risk of off topic deletion accepted.

If the ambition of the quantum theory to describe the reality turns out true, the wave function is necessarily real. If this comment exists in a world where it is deleted and in another world where it is not then the wave function is not real.

Henning,

Alain Connes gave an absolutely amazing talk on this work:

Geometry and the quantum

Best

""I can only hope that Lisa Zyga, who wrote the piece at phys.org, will learn from this that solely relying on the author’s own statements is never good journalistic practice.""

There is another post from Ahmed and Lisa:

http://phys.org/news/2015-02-big-quantum-equation-universe.html

@nicolas

A description. True.

You see more than that?

@hush

Quantum computing is a practical use of the wave function, if the calculation is actually performed, so this calculation is real and the wave function is real.

"If the wavefunction is a state of knowledge, seemingly inconvenient quantum phenomena

such as wavefunction collapse can be explained elegantly:

if the wavefunction represents knowledge, a measurement

only collapses our ignorance about the real state of af-

fairs, without necessarily changing reality; there is thus

no physical collapse in the epistemic picture, but rather a

reassignment of a more appropriate wavefunction."

Your stance and your quantum computer want physical collapse.

Not required.

Quantum computing will reduce ignorance. Yours, mine and the computers'.

If that makes you feel 'closer' to reality, then all the better.

The measurement shows that the calculation has actually taken place and therefore that the information has existed and therefore the space has stored the information. This experience demonstrates the existence of an objective genuine computational process, it would be absurd to claim that because we can only measure the result of the calculation that it is not an objective phenomenon that actually occurred.

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