virtual information loss

Sabine Hossenfelder wrote a blog post about the information loss paradox, pretty much repeating standard arguments made in this debate. Among them the following:
"Physicists are using quantum field theory here on planet Earth to describe, for example, what happens in LHC collisions. [..] in principle black holes can be created and subsequently annihilated in any particle collision as virtual particles. This would mean then [..] we’d have no reason to even expect a unitary evolution."

As I said, this is a standard argument, but I have a problem with it:
In any experiment we can do, e.g. at the LHC, the energy of such a virtual black hole would be well below the Planck mass, i.e. far from the quasi-classical limit where the information loss problem is discussed.
In which sense can any particle fall into a microscopic b.h. with a radius much smaller than the Planck length, if its wavelength is much larger? So in which sense would a virtual b.h. pose an information loss problem?
We have to assume that the mass of an off-shell virtual b.h. could be arbitrarily large, but its contribution to any S-matrix element would be strongly suppressed (at least exponentially) for energies much larger than the collision energy, which is well below the Planck mass. Therefore its contribution would for all practical purposes be unmeasurable.


added later: Without a full theory of quantum gravity (and even string theory does not know how to handle black holes yet, see e.g. fuzzballs and firewalls vs. ER=EPR) we can only make some basic estimates.
There are estimates of proton decay due to virtual black holes and the expected lifetime is about 10⁴⁵ years - a factor 10¹¹ higher than what we could currently detect.
But I think even those estimates are too low if information loss requires a black hole of mass > m_Planck (if the surface area is indeed quantized black holes with a small mass m < m_Planck may not even exist). Wick rotation suggests that the contribution of a massive black hole m > m_Planck to any Feynman diagram would be suppressed by a factor exp(-k²) or exp(-(m/E)²) if E is the energy of the collision.
Btw the same exponential factor shows up in a different estimate, suppressing the production of black holes even for large collision energies E.

entanglement

About five years ago I sent this email to Erik Verlinde:

-----------------------------
1/24/10

Dear Professor Verlinde,

I read your preprint about gravity as 'entropic force' and have the following question/suggestion:
It seems that there are large classes of systems following an area law for entanglement entropy, see e.g. arxiv.org/abs/0808.3773
Should they all show 'entropic gravity' somehow?
If yes, the obvious next step would be to pick a simple model, e.g. arxiv.org/abs/quant-ph/0605112 and check if/how entropic gravity manifests itself.

Thank you,
Wolfgang
------------------------------

As it turns out this idea may not have been so stupid after all.

Of course, if entanglement stitches space-time together then the question remains: entanglement of what?
I still think the entangled qubits of a quantum computer are the most natural candidates; if we live inside one it would also solve the measurement problem.
But what would it be computing? We can only speculate.

no black holes?

Laura Mersini-Houghton and Harald Pfeiffer published a paper with numerical results suggesting that black holes may not really exist (see also this earlier result). As one would expect, several pop. sci. webpages have already picked this story up.

The paper is of course not a general proof, but describes a particular model using certain assumptions; it considers the spherically symmetric collapse of pressure-less dust and it makes simplifying assumptions about the Hawking radiation: The energy tensor for the Hawking radiation is taken from earlier calculations for (static) black holes, proportional to 1/R^2, and I don't think this is justified if one wants to prove that black holes do not exist. Further it is assumed that most of the radiation is generated by the collapsing body itself (*) and finally assumptions are made about the heat transfer function C which I cannot follow (yet).

The resulting differential equations are numerically integrated until a shell-crossing singularity appears, in other words a naked singularity (presumably an artifact of the model assumptions, i.e. perfect spherical symmetry, so it is only slightly embarrassing in a paper which wants to remove black hole singularities).
The behavior of the dust suggests a rebound near the horizon, but it is too bad the full evolution is unknown, because it raises interesting questions.
What happens to the pressure-less dust in the long run? Will it collapse again after the rebound, perhaps infinitely often?
What does the final state (including Hawking radiation and the "influx" of negative energy) actually look like?

I am sure this paper will generate several responses and eventually more realistic calculations will follow.
Until then I remain skeptical that this result will actually hold in general.


(*) I admit that I do not understand this passage in the earlier paper: "Hawking radiation is produced by the changing gravitational field of the collapsing star, i.e. prior to the black hole formation [..]. Otherwise the surface gravity of the black hole κ, and the temperature of Hawking radiation would increase with time..."
I thought the standard picture is that the "influx" is at the event horizon (not the collapsing body) and the temperature does indeed increase with time...


added later: Supposedly William Unruh was more direct and he thinks that the paper is nonsense.

any good answers to this one?

At the Strings 2014 conference, Piotr Bizon talked about the gravitational turbulent instability of AdS₅.
I became aware of this issue more than three years go and I have to admit that I still do not really understand what it means. As I see it, turbulence is one of the big unsolved problems in physics mostly due to the fact that it prevents us from neatly separating energy scales; the opposite of the clean separation which enables renormalization a la Wilson.
So what does it mean that this turbulence instability shows up on one side of the famous AdS/CFT correspondence?

the phase structure of CDT

In my previous post I criticized the description of the CDT phase diagram on a popular physics blog.
In this post I want to actually talk about the numerical CDT results.

The phase diagram depends on two coupling constants K and D (in the text they use kappa and delta). While K corresponds to the gravitational coupling, D measures the ratio of 'timelike' and 'spacelike' edges; I use quotes ' ' because the simulation is actually done in the Euclidean sector, but edges fall in different categories, depending on what kind of distances they would correspond to after Wick rotation. There is a third coupling parameter, which corresponds to a cosmological constant, but it is fixed for technical reasons.

As I already explained, one looks for a critical line in D,K corresponding to a 2nd order phase transition and the reason is that long-range fluctuations are associated with such a transition, so that the details of the discretization do not matter any more.
So this is what I find weird: The parameter D describes a detail of the discrete model and the hope is to fine tune D, as a function of K, in order to find a critical line where the details of the discretization no longer matter...

The authors notice that D has "no immediate interpretation in the Einstein-Hilbert action" and thus the critical value D(K) does not correspond to any feature of the continuum limit - unless the continuum limit is not Einstein-Hilbert but Horava-Lifshitz gravity. This is what the authors propose and discuss in section 4 of their paper: HL gravity breaks diffeomorphism invariance of EH gravity, just like CDT does, and the parameter D would have a 'physical' meaning in this case.

It seems that the authors hope that EH gravity will be restored somewhere along the critical D(K) line, however, it is unlikely imho that there is such a path from HL gravity to real gravitation.

backreaction

It seems that an internet tradition is emerging, whereby a blog remains dormant for a while, until something so outrageously wrong appears on the interwebs that one has no choice but to respond to it.

In my case, Sabine Hossenfelder wrote about the phase diagram of CDT on her popular physics blog and I just have to set a few things straight:

1) We read that "... most recently the simulations found that ... space-time has various different phases, much like water has different phases".
But, of course, the phase structure of various lattice gravity models has been studied (implicitly and explicitly) since the early days of lattice gravity simulations, i.e. the 1980s. If one wants to find a reasonable continuum limit for such a model, then one has to examine the phase structure of the lattice model; In general, if the model has one or more coupling parameters then it will (most likely) exhibit different phases, just like water.

2) The holy grail to a physically interesting continuum limit is the existence of a non-trivial fixpoint, which appears in the phase diagram as a 2nd order phase transition. IF such a transition exists for CDT, it will be located on (one of) the critical lines and perhaps at the tri-critical point. The continuum limit will not appear in the area C of the diagram; There you certainly cannot "share images of your lunch with people you don’t know on facebook".
As far as I know, the existence of such a 2nd order transition has not been demonstrated yet, although intriguing hints have appeared in other lattice models previously. Of course, even IF such a 2nd order transition could be demonstrated, one would still not know if the continuum limit has anything to do with gravitation as we know it.

3) This 2nd order phase transition is prerequisite to a consistent continuum model and all 4d geometries would be generated with the same critical parameter values. It is therefore misguided to imagine that this phase transition happened at or near the big bang.
Indeed, the coupling parameters depicted in the phase diagram are bare, i.e. un-renormalized, coupling parameters and while the diagram may indicate existence and location of a non-trivial fixed point, almost all of the phase diagram is actually non-physical.
Therefore one cannot expect that this phase transition may be an alternative and/or replacement for inflation (as Sabine discussed in the comments).

was Wolfram right after all?

Recently, Gerard 't Hooft published his own version of superstring theory.

"Ideas presented in two earlier papers are applied to string theory. ... We now also show that a cellular automaton in 1+1 dimensions that processes only ones and zeros, can be mapped onto a fermionic quantum field theory in a similar way. The natural system to apply all of this to is superstring theory ..." (*)



The earlier papers he refers to describe a duality between a deterministic cellular automaton and a bosonic quantum field theory in 1+1 dimensions and argue that Born's rule strongly points towards determinism underlying quantum mechanics (x).



All this is far from the mainstream, but 't Hooft is a physicist not a crackpot and so he points out problems of his proposal(s) in his papers, e.g. he notes that some of his models have an unbounded Hamiltonian and he does discuss the apparent contradiction with Bell's inequality.




(*) It is known for a long time that the Ising model is equivalent to a fermionic field in 2 dimensions (see e.g. this paper for references).



(x) Quantum theory without the Copenhagen 'collapse' is a deterministic theory, so it is not too surprising if one finds such a duality. But it is unusual that Born's rule 'strongly points towards' determinism.

still asking the same question(s)

I write this post mostly to show that this blog is still alive ... and still asking the same question(s).



Recently, I read this paper about a numerical study in lattice gravity, trying to distinguish 1st and 2nd order phase transitions. They use and refer to the methods I am familiar with, but I do wonder if this is really the best one can do nowadays.



If one does e.g. fit the location of the critical coupling as a function of lattice size, one has to deal with two big problems: First, the location of the critical coupling is not so well defined (e.g. due to the metastable states associated with 1st order transitions) for a given lattice size; there are limits on computation time and resources (*).

Second, how can one be sure if the lattice is big enough to be in the 'scaling region', i.e. big enough that small size corrections can be neglected (if the typical size of the 'bubbles', which come with a 1st order transition, is n and the lattice size N is smaller than n one has a problem).



So what is the current state-of-the-art and where are the professional statisticians and their Bayesian stochastic network thingy-ma-jiggies when we need them (x)? Please let me know if you know something.






(*) A related question for the practitioner: Is it better to spend the available computation power on a small number of iterations on a large lattice or is it better to do many iterations on a small lattice?



(x) Speaking of Bayesian thingy-ma-jiggies ...

follow up on quantum gravity

A year ago I mentioned a numerical study which indicates that AdS is unstable against small perturbations.

Meanwhile, Horowitz et al. "find strong support for this idea". They also mention that "any field theory with a gravity dual must exhibit the same turbulent instability, and transfer energy from large to small scales", but it is unclear (to me) what this means for the AdS/CFT correspondence. But notice that they study AdS₄, although the assumption seems to be that AdS₅ contains the same instability.



Two years ago I wrote about higher order gravity models. Recently, Leonardo Modesto considered "higher derivative gravity involving an infinite number of derivative terms".
This new model "is instead ghost-free" and "finite from two loops upwards: the theory is then super-renormalizable".



Last , but not least, Daniel Coumbe and Jack Laiho have published version 2 of their paper "exploring the phase diagram of lattice quantum gravity"; a while ago I mentioned the talk about it at the Lattice 2011 conference.





added later: In a new paper Ashoke Sen calculates logarithmic corrections to the entropy of black holes which "disagree with the existing result in loop quantum gravity".

harmonic universe

Yet another attempt to reduce the physics of our universe to the harmonic oscillator; An interesting paper and a pleasure to read. But there is a problem with this approach near the end imho. I do not feel that the proposed boundary conditions psi(0) = 0 and psi(infty) = 0 are natural and honestly I have no intuition what would be natural in this context.

I think that this is a general problem whenever one tries to calculate the 'wavefunction of the universe'. While we have a good intuition for boundary conditions in conventional quantum theory, this intuition is lost for quantum cosmology. But of course those boundary conditions determine everything...

Eppley and Hannah

Every now and then somebody asks if it is really necessary to find a quantum theory of gravitation. After all, it is most likely not possible to detect single gravitons, following an argument of Freeman Dyson (because one would need a detector of planetary size for it).

Of course there are many good reasons why one would like to find a way to quantize gravity like all other fields [1, 2, 3]. But I was never worried about this sort of debate, because I knew that there was a thought experiment, published in the '70s or '80s, which settled this issue once and for all: Consistency requires that gravitation must be quantized. I remember that I read the argument and that I found it convincing at the time.



Recently, I was asked about this whole issue and I mentioned the thought experiment and that paper. Finally I promised that I would dig out the reference and I actually did.

K. Eppley and E. Hannah, Found. Phys. 7, 51 (1977)



The reason it was relatively easy to find the reference was that almost thirty years later somebody checked the argument and found that it was flawed. The problem is that the thought experiment asks for a detector so large and heavy that it cannot be built, somehow closing the circle back to Dyson's argument.

asymptotic safety

Georg v. Hippel blogs about the Lattice 2011 conference and he mentioned a talk by Jack Laiho on Asymptotic Safety and Quantum Gravity.

There is already a paper about that on the arXiv. The main idea is that three coupling parameters are needed in the lattice model and they consider dynamical triangulation in the Euclidean sector with an additional measure term, which comes with the third coupling parameter. The hope is to find a tri-critical point (with 2nd order phase transition) as a candidate for the continuum limit in the asymptotic safety scenario.

modified gravity?

Lubos suggests an explanation (or actually a replacement) for MOND, which sounds like entropic gravity to me (*). Did he not recently explain to us why such explanations have to be wrong?

The purpose of his proposal is to explain observations which suggest that gravity changes at low accelerations a < a₀ = 1.2x 10^-10 m/s² and it is based on the idea that a₀ could be the inverse size of the visible universe (times c).



(*) I should make it clear that Lubos never mentions 'entropic gravity' in his post, but how would a sentence like "The existence of this center on the hologram may be needed for the usual Kepler scaling laws to emerge." make any sense otherwise? See e.g. this paper on how MOND was derived previously from 'entropic gravity' using "a holographic principle".



added later: When I asked explicitly in a comment, he insisted that his proposal has nothing to do with "the crackpottery called entropic gravity". Alright, I will admit then that I do not understand what he is talking about and leave it to others to sort it out. Feel free to leave a comment to enlighten me. I will leave this post up as it is, because the links could be useful to others.

Perhaps I should make it clear that I am (still) not convinced 'entropic gravity and/or MOND make any sense.



added even later: While Lubos focuses directly on the quantity a₀ = c/T, with T being the age of the (visible) universe, I think it would be more natural to consider the energy E = h/T. The associated temperature is E/k, which is on the order of 10^-28 kelvin and comparable to the critical temperature used to derive MOND in the paper linked above; In fact plugging hk^-1/T into equ. (12) gives a₀ = c/T !



added several hours later: Obviously, there is a straightforward way to test this type of proposal. If one looks into the night sky one sees galaxies at different age T of the universe and the deviation from Newtonian dynamics should be stronger the further back in time one looks.
Perhaps there is already enough statistics of galaxy rotation curves to check this.



added much much later: As a counter point to all this speculation a paper [pdf] about an experiment which "finds good agreement with Newton’s second law at accelerations as small as 5 x 10^-14 m s^-2.

lattice gravity

You may have noticed the link to quantum gravity on the left hand side of this blog, below the picture of the plastic bag; It leads to several blog posts about "lattice gravity" as well as posts about quantum gravity in general.



If you want to know more what "lattice gravity" is all about, you can browse some of the references provided here; Another good starting point would be Renate Loll's review (in particular sect. 3) and for even more motivation I recommend this paper.



One warning: It is very much possible, and actually quite likely, that these models have nothing to do with real (quantum) gravity. In fact there are several good arguments why a lattice approach can never work. In other words, it is very much possible that this will turn out to be a waste of time.

Just another reason it makes for a good topic on this blog...

is AdS unstable?

"We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) spacetime by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS spacetime is unstable under arbitrarily small generic perturbations."

Piotr Bizoń, Andrzej Rostworowski



Notice that this study was done in 3+1 dimensional AdS₄, but the authors claim (in the conclusion) that they observed "qualitatively the same behavior" for the 4+1 dimensional AdS₅.

But with all the activity about AdS/CFT, it is it hard to believe that nobody checked the stability of AdS in classical GR before.

shape up

"I figured you might be able to give me some pointers. I need to shape up."

Lester Burnham



Well, there is this paper which explains 'why decoherence has not solved the measurement problem'. (It is pretty much the argument I used here to state the 'interpretation problem'.)



Then there is this talk about the divergence of perturbation series in QFT.



And finally there is this paper about the strong coupling limit of the Wheeler-deWitt equation.

triangles

In a recent preprint Renate Loll et al. present numerical evidence that causal dynamical triangulation is eventually a discretization of Horava-Lifshitz gravity.

But is this really good news?

In an earlier paper by Christos Charmousis et al. an argument was given that "the original Horava model, and its 'phenomenologically viable' extensions do not have a perturbative General Relativity limit at any scale". Lubos wrote more about that at the time and there is also this paper with a more general argument.

I am neither an expert on CDT nor Horava-Lifshitz gravity and would welcome comments about this. (Of course, I always welcome comments!)

entropic gravity

Recently, Erik Verlinde proposed that gravity can be described as entropic force. I am not sure yet what to think about this, but Lubos explains why he is certain this can never work.

Meanwhile, Lee Smolin published a preprint using Verlinde's idea to derive Newton's law from loop quantum gravity. I am not convinced by his argument.

Verlinde considers the change in entropy dS for displacements dx assuming a holographic principle and in his calculation he implicitly assumes the geometry of a smooth and indeed flat geometry.

There is of course nothing wrong about that, but if Lee Smolin wants to use this argument, then he has to first show that there is a reasonable limit of loop quantum gravity which reproduces this smooth and (almost) flat spacetime and I don't see that.



added later:



More discussion Lubos vs. Erik (scroll down through the comments).



Lee Smolin responds to my comment here.



Robert Helling comments on entropic everything.

living with ghosts

" We conclude that quantum gravity with fourth order corrections can make sense,
despite apparently having negative energy solutions and ghosts. In doing this,
we seem to go against the convictions of the last 25 years ..."

Hawking and Hertog, 2001



It is well known that the perturbation theory of quantum gravity is not renormalizable, but one can 'fix' this problem by introducing higher order terms ( R² ) in the action.
Unfortunately, it is also well known that higher order derivative terms (appear to) come with
dangerous ghosts, threatening the S-matrix with states of negative probabilities.
However, in their (very clear and easy to read) paper Hawking and Hertog provide for a convincing argument that one should not be afraid of such ghosts.



In a related paper Bender and Mannheim, 2007 showed that "contrary to common belief .. theories whose field equations are higher than second order in derivatives need not be stricken with ghosts. In particular, the prototypical fourth-order derivative Pais-Uhlenbeck oscillator model is shown to be free of states of negative energy or negative norm."



Last but not least, Benedetti, Machado and Saueressig, 2009 "study the non-perturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques" and argue that "asymptotic safety also resolves the unitarity problem typically haunting higher-derivative gravity theories."



In other words, if (for whatever reason) you don't like string theory, you could try to get used to living with ghosts...

constraints

The field equations of general relativity can be separated into
hyperbolic evolution equations and elliptic constraints [ADM].
The evolution equations propagate an initial field configuration
'forward' in time, similar to other theories of classical fields.

However, due to the constraints one cannot choose the initial
configuration freely and this is very different from other classical
fields. In some sense the constraints 'connect' spacelike points and
thus one could call general relativity 'holistic' if this would
not be such an abused word.



We don't really know what the quantum theory of gravitation is,
but one would assume that the classical theory reflects the properties
of the underlying quantum theory and indeed the Wheeler-deWitt equation
is nothing but the operator version of one of the constraints.

I think one needs to keep this in mind when discussing thermodynamics
of general relativity, the information loss problem or the entropy of
black holes. E.g. if one specifies the metric near the horizon of a
(near spherically symmetric) black hole, the constraints already
determine the 3-geometry; Therefore I do not find it surprising that
counting microstates provides for a holographic result which differs
substantially from the naive expectation.

I would also think that an approach to the information
loss problem which emphasizes locality as 'conservative' is misguided.