Friday, May 26, 2017

Can we probe the quantization of the black hole horizon with gravitational waves?

Tl;dr: Yes, but the testable cases aren’t the most plausible ones.

It’s the year 2017, but we still don’t know how space and time get along with quantum mechanics. The best clue so far comes from Stephen Hawking and Jacob Bekenstein. They made one of the most surprising finds that theoretical physics saw in the 20th century: Black holes have entropy.

It was a surprise because entropy is a measure for unresolved microscopic details, but in general relativity black holes don’t have details. They are almost featureless balls. That they nevertheless seem to have an entropy – and a gigantically large one in addition – indicates strongly that black holes can be understood only by taking into account quantum effects of gravity. The large entropy, so the idea, quantifies all the ways the quantum structure of black holes can differ.

The Bekenstein-Hawking entropy scales with the horizon area of the black hole and is usually interpreted as a measure for the number of elementary areas of size Planck-length squared. A Planck-length is a tiny 10-35 meters. This area-scaling is also the basis of the holographic principle which has dominated research in quantum gravity for some decades now. If anything is important in quantum gravity, this is.

It comes with the above interpretation that the area of the black hole horizon always has to be a multiple of the elementary Planck area. However, since the Planck area is so small compared to the size of astrophysical black holes – ranging from some kilometers to some billion kilometers – you’d never notice the quantization just by looking at a black hole. If you got to look at it to begin with. So it seems like a safely untestable idea.

A few months ago, however, I noticed an interesting short note on the arXiv in which the authors claim that one can probe the black hole quantization with gravitational waves emitted from a black hole, for example in the ringdown after a merger event like the one seen by LIGO:
    Testing Quantum Black Holes with Gravitational Waves
    Valentino F. Foit, Matthew Kleban
    arXiv:1611.07009 [hep-th]

The basic idea is simple. Assume it is correct that the black hole area is always a multiple of the Planck area and that gravity is quantized so that it has a particle – the graviton – associated with it. If the only way for a black hole to emit a graviton is to change its horizon area in multiples of the Planck area, then this dictates the energy that the black hole loses when the area shrinks because the black hole’s area depends on the black hole’s mass. The Planck-area quantization hence sets the frequency of the graviton that is emitted.

A gravitational wave is nothing but a large number of gravitons. According to the area quantization, the wavelengths of the emitted gravitons is of the order of the order of the black hole radius, which is what one expects to dominate the emission during the ringdown. However, so the authors’ argument, the spectrum of the gravitational wave should be much narrower in the quantum case.

Since the model that quantizes the black hole horizon in Planck-area chunks depends on a free parameter, it would take two measurements of black hole ringdowns to rule out the scenario: The first to fix the parameter, the second to check whether the same parameter works for all measurements.

It’s a simple idea but it may be too simple. The authors are careful to list the possible reasons for why their argument might not apply. I think it doesn’t apply for a reason that’s a combination of what is on their list.

A classical perturbation of the horizon leads to a simultaneous emission of a huge number of gravitons, and for those there is no good reason why every single one of them must fit the exact emission frequency that belongs to an increase of one Planck area as long as the total energy adds up properly.

I am not aware, however, of a good theoretical treatment of this classical limit from the area-quantization. It might indeed not work in some of the more audacious proposals we have recently seen, like Gia Dvali’s idea that black holes are condensates of gravitons. Scenarios such like Dvali’s might be testable indeed with the ringdown characteristics. I’m sure we will hear more about this in the coming years as LIGO accumulates data.

What this proposed test would do, therefore, is to probe the failure of reproducing general relativity for large oscillations of the black hole horizon. Clearly, it’s something that we should look for in the data. But I don’t think black holes will release their secrets quite as easily.

Friday, May 19, 2017

Can we use gravitational waves to rule out extra dimensions – and string theory with it?

Gravitational Waves,
Computer simulation.

Credits: Henze, NASA
Tl;dr: Probably not.

Last week I learned from New Scientist that “Gravitational waves could show hints of extra dimensions.” The article is about a paper which recently appeared on the arxiv:

The claim in this paper is nothing but stunning. Authors Andriot and Gómez argue that if our universe has additional dimensions, no matter how small, then we could find out using gravitational waves in the frequency regime accessible by LIGO.

While LIGO alone cannot do it because the measurement requires three independent detectors, soon upcoming experiments could either confirm or forever rule out extra dimensions – and kill string theory along the way. That, ladies and gentlemen, would be the discovery of the millennium. And, almost equally stunning, you heard it first from New Scientist.

Additional dimensions are today primarily associated with string theory, but the idea is much older. In the context of general relativity, it dates back to the work of Kaluza and Klein the 1920s. I came across their papers as an undergraduate and was fascinated. Kaluza and Klein showed that if you add a fourth space-like coordinate to our universe and curl it up to a tiny circle, you don’t get back general relativity – you get back general relativity plus electrodynamics.

In the presently most widely used variants of string theory one has not one, but six additional dimensions and they can be curled up – or ‘compactified,’ as they say – to complicated shapes. But a key feature of the original idea survives: Waves which extend into the extra dimension must have wavelengths in integer fractions of the extra dimension’s radius. This gives rise to an infinite number of higher harmonics – the “Kaluza-Klein tower” – that appear like massive excitations of any particle that can travel into the extra dimensions.

The mass of these excitations is inversely proportional to the radius (in natural units). This means if the radius is small, one needs a lot of energy to create an excitation, and this explains why he haven’t yet noticed the additional dimensions.

In the most commonly used model, one further assumes that the only particle that experiences the extra-dimensions is the graviton – the hypothetical quantum of the gravitational interaction. Since we have not measured the gravitational interaction on short distances as precisely as the other interactions, such gravity-only extra-dimensions allow for larger radii than all-particle extra-dimensions (known as “universal extra-dimensions”.) In the new paper, the authors deal with gravity-only extra-dimensions.

From the current lack of observation, one can then derive bounds on the size of the extra-dimension. These bounds depend on the number of extra-dimensions and on their intrinsic curvature. For the simplest case – the flat extra-dimensions used in the paper – the bounds range from a few micrometers (for two extra-dimensions) to a few inverse MeV for six extra dimensions (natural units again).

Such extra-dimensions do more, however, than giving rise to a tower of massive graviton excitations. Gravitational waves have spin two regardless of the number of spacelike dimensions, but the number of possible polarizations depends on the number of dimensions. More dimensions, more possible polarizations. And the number of polarizations, importantly, doesn’t depend on the size of the extra-dimensions at all.

In the new paper, the authors point out that the additional polarization of the graviton affects the propagation even of the non-excited gravitational waves, ie the ones that we can measure. The modified geometry of general relativity gives rise to a “breathing mode,” that is a gravitational wave which expands and contracts synchronously in the two (large) dimensions perpendicular to the direction of the wave. Such a breathing mode does not exist in normal general relativity, but it is not specific to extra-dimensions; other modifications of general relativity also have a breathing mode. Still, its non-observation would indicate no extra-dimensions.

But an old problem of Kaluza-Klein theories stands in the way of drawing this conclusion. The radii of the additional dimensions (also known as “moduli”) are unstable. You can assume that they have particular initial values, but there is no reason for the radii to stay at these values. If you shake an extra-dimension, its radius tends to run away. That’s a problem because then it becomes very difficult to explain why we haven’t yet noticed the extra-dimensions.

To deal with the unstable radius of an extra-dimension, theoretical physicists hence introduce a potential with a minimum at which the value of the radius is stuck. This isn’t optional – it’s necessary to prevent conflict with observation. One can debate how well-motivated that is, but it’s certainly possible, and it removes the stability problem.

Fixing the radius of an extra-dimension, however, will also make it more difficult to wiggle it – after all, that’s exactly what the potential was made to do. Unfortunately, in the above mentioned paper the authors don’t have stabilizing potentials.

I do not know for sure what stabilizing the extra-dimensions would do to their analysis. This would depend not only on the type and number of extra-dimension but also on the potential. Maybe there is a range in parameter-space where the effect they speak of survives. But from the analysis provided so far it’s not clear, and I am – as always – skeptical.

In summary: I don’t think we’ll rule out string theory any time soon.

[Updated to clarify breathing mode also appears in other modifications of general relativity.]

Tuesday, May 16, 2017

“Not a Toy” - New Video about Symmetry Breaking

Here is the third and last of the music videos I produced together with Apostolos Vasilidis and Timo Alho, sponsored by FQXi. The first two are here and here.

In this video, I am be-singing a virtual particle pair that tries to separate, and quite literally reflect on the inevitable imperfection of reality. The lyrics of this song went through an estimated ten thousand iterations until we finally settled on one. After this, none of us was in the mood to fight over a second verse, but I think the first has enough words already.

With that, I have reached the end of what little funding I had. And unfortunately, the Germans haven’t yet figured out that social media benefits science communication. Last month I heard a seminar on public outreach that didn’t so much as mention the internet. I do not kid you. There are foundations here who’d rather spend 100k on an event that reaches 50 people than a tenth of that to reach 100 times as many people. In some regards, Germans are pretty backwards.

This means from here on you’re back to my crappy camcorder and the always same three synthesizers unless I can find other sponsors. So, in your own interest, share the hell out of this!

Also, please let us know which video was your favorite and why because among the three of us, we couldn’t agree.

As previously, the video has captions which you can turn on by clicking on CC in the YouTube bottom bar. For your convenience, here are the lyrics:

Not A Toy

We had the signs for taking off,
The two of us we were on top,
I had never any doubt,
That you’d be there when things got rough.

We had the stuff to do it right,
As long as you were by my side,
We were special, we were whole,
From the GUT down to the TOE.

But all the harmony was wearing off,
It was too much,
We were living in a fiction,
Without any imperfection.

Every symmetry
Has to be broken,
Every harmony
Has to decay.

Leave me alone, I’m
Tired of talking,
I’m not a toy,
I’m not a toy.

Leave alone now,
I’m not a token,
I’m not a toy,
I’m not a toy.

We had the signs for taking off
Harmony was wearing off
We had the signs for taking off
Tired of talking
Harmony was wearing off
I’m tired of talking.

[Repeat Bridge]
[Repeat Chorus]

Thursday, May 11, 2017

A Philosopher Tries to Understand the Black Hole Information Paradox

Is the black hole information loss paradox really a paradox? Tim Maudlin, a philosopher from NYU and occasional reader of this blog, doesn’t think so. Today, he has a paper on the arXiv in which he complains that the so-called paradox isn’t and physicists don’t understand what they are talking about.
So is the paradox a paradox? If you mean whether black holes break mathematics, then the answer is clearly no. The problem with black holes is that nobody knows how to combine them with quantum field theory. It should really better be called a problem than a paradox, but nomenclature rarely follows logical argumentation.

Here is the problem. The dynamics of quantum field theories is always reversible. It also preserves probabilities which, taken together (assuming linearity), means the time-evolution is unitary. That quantum field theories are unitary depends on certain assumptions about space-time, notably that space-like hypersurfaces – a generalized version of moments of ‘equal time’ – are complete. Space-like hypersurfaces after the entire evaporation of black holes violate this assumption. They are, as the terminology has it, not complete Cauchy surfaces. Hence, there is no reason for time-evolution to be unitary in a space-time that contains a black hole. What’s the paradox then, Maudlin asks.

First, let me point out that this is hardly news. As Maudlin himself notes, this is an old story, though I admit it’s often not spelled out very clearly in the literature. In particular the Susskind-Thorlacius paper that Maudlin picks on is wrong in more ways than I can possibly get into here. Everyone in the field who has their marbles together knows that time-evolution is unitary on “nice slices”– which are complete Cauchy-hypersurfaces – at all finite times. The non-unitarity comes from eventually cutting these slices. The slices that Maudlin uses aren’t quite as nice because they’re discontinuous, but they essentially tell the same story.

What Maudlin does not spell out however is that knowing where the non-unitarity comes from doesn’t help much to explain why we observe it to be respected. Physicists are using quantum field theory here on planet Earth to describe, for example, what happens in LHC collisions. For all these Earthlings know, there are lots of black holes throughout the universe and their current hypersurface hence isn’t complete. Worse still, in principle black holes can be created and subsequently annihilated in any particle collision as virtual particles. This would mean then, according to Maudlin’s argument, we’d have no reason to even expect a unitary evolution because the mathematical requirements for the necessary proof aren’t fulfilled. But we do.

So that’s what irks physicists: If black holes would violate unitarity all over the place how come we don’t notice? This issue is usually phrased in terms of the scattering-matrix which asks a concrete question: If I could create a black hole in a scattering process how come that we never see any violation of unitarity.

Maybe we do, you might say, or maybe it’s just too small an effect. Yes, people have tried that argument, which is the whole discussion about whether unitarity maybe just is violated etc. That’s the place where Hawking came from all these years ago. Does Maudlin want us to go back to the 1980s?

In his paper, he also points out correctly that – from a strictly logical point of view – there’s nothing to worry about because the information that fell into a black hole can be kept in the black hole forever without any contradictions. I am not sure why he doesn’t mention this isn’t a new insight either – it’s what goes in the literature as a remnant solution. Now, physicists normally assume that inside of remnants there is no singularity because nobody really believes the singularity is physical, whereas Maudlin keeps the singularity, but from the outside perspective that’s entirely irrelevant.

It is also correct, as Maudlin writes, that remnant solutions have been discarded on spurious grounds with the result that research on the black hole information loss problem has grown into a huge bubble of nonsense. The most commonly named objection to remnants – the pair production problem – has no justification because – as Maudlin writes – it presumes that the volume inside the remnant is small for which there is no reason. This too is hardly news. Lee and I pointed this out, for example, in our 2009 paper. You can find more details in a recent review by Chen et al.

The other objection against remnants is that this solution would imply that the Bekenstein-Hawking entropy doesn’t count microstates of the black hole. This idea is very unpopular with string theorists who believe that they have shown the Bekenstein-Hawking entropy counts microstates. (Fyi, I think it’s a circular argument because it assumes a bulk-boundary correspondence ab initio.)

Either way, none of this is really new. Maudlin’s paper is just reiterating all the options that physicists have been chewing on forever: Accept unitarity violation, store information in remnants, or finally get it out.

The real problem with black hole information is that nobody knows what happens with it. As time passes, you inevitably come into a regime where quantum effects of gravity are strong and nobody can calculate what happens then. The main argument we are seeing in the literature is whether quantum gravitational effects become noticeable before the black hole has shrunk to a tiny size.

So what’s new about Maudlin’s paper? The condescending tone by which he attempts public ridicule strikes me as bad news for the – already conflict-laden – relation between physicists and philosophers.

Saturday, May 06, 2017

Away Note

I'm in Munich next week, playing with the philosophers. Be good while I'm away, back soon. (Below, the girls, missing a few teeth.)

Thursday, May 04, 2017

In which I sing about Schrödinger’s cat

You have all been waiting for this. The first ever song about quantum entanglement, Boltzmann brains, and the multiverse:

This is the second music video produced in collaboration with Apostolos Vasilidis and Timo Alho, supported by FQXi. (The first is here.) I think these two young artists are awesomely talented! Just by sharing this video you can greatly support them.

In this video too, I’m the one to blame for the lyrics, and if you think this one’s heavy on the nerdism, wait for the next ;)

Here, I sing about entanglement and the ability of a quantum system to be in two different states at the same time. Quantum states don’t have to decide, so the story, but humans have to. I have some pessimistic and some optimistic future visions, contrast determinism with many worlds, and sum it up with a chorus that says: Whatever we do, we are all in this together. And since you ask, we are all connected, because ER=EPR.

The video has subtitles, click on the “CC” icon in the YouTube bottom bar to turn on.


(The cat is dead)

We will all come back
At the end of time
As a brain in a vat
Floating around
And purely mind.

I’m just back from the future and I'm here to report
We’ll be assimilated, we’ll all join the Borg
We’ll be collectively stupid, if you like that or not
Resistance is futile, we might as well get started now

I never asked to be part of your club
So shut up
And leave me alone

But we are all connected
We will never die
Like Schrödinger’s cat
We will all be dead
And still alive

[repeat Chorus]

We will never forget
And we will never lie
All our hope,
Our fear and doubt
Will be far behind.

But I’m not a computer and I'm not a machine
I am not any other, let me be me
If the only pill that you have left
Is the blue and not the red
It might not be so bad to be
Somebody’s pet

[repeat chorus 2x]

Since you ask, the cat is doing fine
Somewhere in the multiverse it’s still alive
Think that is bad? If you trust our math,
The future is as fixed, as is the past.
Since you ask. Since you ask.

[Repeat chorus 2x]

Monday, May 01, 2017

May-day Pope-hope

Pope Francis meets Stephen Hawking.
[Photo: Piximus.]
My husband is a Roman Catholic, so is his whole family. I’m a heathen. We’re both atheists, but dear husband has steadfastly refused to leave the church. That he throws out money with the annual “church tax” (imo a great failure of secularization) has been a recurring point of friction between us. But as of recently I’ve stopped bitching about it – because the current Pope is just so damn awesome.

Pope Francis, born in Argentina, is the 266th leader of the Catholic Church. The man’s 80 years old, but within only two years he has overhauled his religion. He accepts Darwinian evolution as well as the Big Bang theory. He addresses ecological problems – loss of biodiversity, climate change, pollution – and calls for action, while worrying that “international politics has [disregarded] well-founded scientific opinion about the state of our planet.” He also likes exoplanets:
“How wonderful would it be if the growth of scientific and technological innovation would come along with more equality and social inclusion. How wonderful would it be, while we discover faraway planets, to rediscover the needs of the brothers and sisters orbiting around us.”
I find this remarkable, not only because his attitude flies in the face of those who claim religion is incompatible with science. More important, Pope Francis succeeds where the vast majority of politicians fail. He listens to scientists, accepts the facts, and bases calls for actions on evidence. Meanwhile, politicians left and right bend facts to mislead people about what’s in whose interest.

And Pope Francis is a man whose word matters big time. About 1.3 billion people in the world are presently members of his Church. For the Catholics, the Pope is the next best thing to God. The Pope is infallible, and he can keep going until he quite literally drops dead. Compared to Francis, Tweety-Trump is a fly circling a horse’s ass.

Global distribution of Catholics.
[Source: Wikipedia. By Starfunker226CC BY-SA 3.0Link.]

This current Pope is demonstrably not afraid of science, and this gives me hope for the future. Most of the tension between science and religion that we witness today is caused by certain aspects of monotheistic religions that are obviously in conflict with science – if taken literally. But it’s an unnecessary tension. It would be easy enough to throw out what are basically thousand years old stories. But this will only happen once the religious understand it will not endanger the core of their beliefs.

Science advocates like to argue that religion is incompatible with science for religion is based on belief, not reason. But this neglects that science, too, is ultimately based on beliefs.

Most scientists, for example, believe in an external reality. They believe, for the biggest part, that knowledge is good. They believe that the world can be understood, and that this is something humans should strive for.

In the foundations of physics I have seen more specific beliefs. Many of my colleagues, for example, believe that the fundamental laws of nature are simple, elegant, even beautiful. They believe that logical deduction can predict observations. They believe in continuous functions and that infinities aren’t real.

None of this has a rational basis, but physicists rarely acknowledge these beliefs as what they are. Often, I have found myself more comfortable with openly religious people, for at least they are consciously aware of their beliefs and make an effort to prevent it from interfering with research. Even my own discipline, I think, would benefit from a better awareness of the bounds of human rationality. Even my own discipline, I think, could learn from the Pope to tell Is from Ought.

You might not subscribe to the Pope’s idea that “tenderness is the path of choice for the strongest, most courageous men and women.” Honestly, to me doesn’t sound so different from believing that love will quantize gravity. But you don’t have to share the values of the Catholic Church to appreciate here is a world leader who doesn’t confuse facts with values.