Penrose claims LIGO noise is evidence for Cyclic Cosmology

Noise is the physicists’ biggest enemy. Unless you are a theorist whose pet idea masquerades as noise. Then you are best friends with noise. Like Roger Penrose.

Correlated "noise" in LIGO gravitational wave signals: an implication of Conformal Cyclic Cosmology
Roger Penrose
arXiv:1707.04169 [gr-qc]

Roger Penrose made his name with the Penrose-Hawking theorems and twistor theory. He is also well-known for writing books with very many pages, most recently “Fashion, Faith, and Fantasy in the New Physics of the Universe.”

One man’s noise is another man’s signal.

Penrose doesn’t like most of what’s currently in fashion, but believes that human consciousness can’t be explained by known physics and that the universe is cyclically reborn. This cyclic cosmology, so his recent claim, gives rise to correlations in the LIGO noise – just like what’s been observed.

The LIGO experiment consists of two interferometers in the USA, separated by about 3,000 km. A gravitational wave signal should pass through both detectors with a delay determined by the time it takes the gravitational wave to sweep from one US-coast to the other. This delay is typically of the order of 10ms, but its exact value depends on where the waves came from.

The correlation between the two LIGO detectors is one of the most important criteria used by the collaboration to tell noise from signal. The noise itself, however, isn’t entirely uncorrelated. Some sources of the correlations are known, but some are not. This is not unusual – understanding the detector is as much part of a new experiment as is the measurement itself. The LIGO collaboration, needless to say, thinks everything is under control and the correlations are adequately taken care of in their signal analysis.

A Danish group of researchers begs to differ. They recently published a criticism on the arXiv in which they complain that after subtracting the signal of the first gravitational wave event, correlations remain at the same time-delay as the signal. That clearly shouldn’t happen. First and foremost it would demonstrate a sloppy signal extraction by the LIGO collaboration.

A reply to the Danes’ criticism by Ian Harry from the LIGO collaboration quickly appeared on Sean Carroll’s blog. Ian pointed out some supposed mistakes in the Danish group’s paper. Turns out though, the mistake was on his site. Once corrected, Harry’s analysis reproduces the correlations which shouldn’t be there. Bummer.

Ian Harry did not respond to my requests for comment. Neither did Alessandra Buonanno from the LIGO collaboration, who was also acknowledged by the Danish group. David Shoemaker, the current LIGO spokesperson, let me know he has “full confidence” in the results, and also, the collaboration is working on a reply, which might however take several months to appear. In other words, go away, there’s nothing to see here.

But while we wait for the LIGO response, speculations abound what might cause the supposed correlation. Penrose beat everyone to it with an explanation, even Craig Hogan, who has run his own experiment looking for correlated noise in interferometers, and who I was counting on.

Penrose’s cyclic cosmology works by gluing the big bang together with what we usually think of as the end of the universe – an infinite accelerated expansion into nothingness. Penrose conjectures that both phases – the beginning and the end – are conformally invariant, which means they possess a symmetry under a stretching of distance scales. Then he identifies the end of the universe with the beginning of a new one, creating a cycle that repeats indefinitely. In his theory, what we think of as inflation – the accelerated expansion in the early universe – becomes the final phase of acceleration in the cycle preceding our own.

Problem is, the universe as we presently see it is not conformally invariant. What screws up conformal invariance is that particles have masses, and these masses also set a scale. Hence, Penrose has to assume that eventually all particle masses fade away so that conformal invariance is restored.

There’s another problem. Since Penrose’s conformal cyclic cosmology has no inflation it also lacks a mechanism to create temperature fluctuations in the cosmic microwave background (CMB). Luckily, however, the theory also gives rise to a new scalar particle that couples only gravitationally. Penrose named it  “erebon” after the ancient Greek God of Darkness, Erebos, that gives rise to new phenomenology.

Erebos, the God of Darkness,
according to YouTube.

The erebons have a mass of about 10^-5 gram because “what else could it be,” and they have a lifetime determined by the cosmological constant, presumably also because what else could it be. (Aside: Note that these are naturalness arguments.) The erebons make up dark matter and their decay causes gravitational waves that seed the CMB temperature fluctuations.

Since erebons are created at the beginning of each cycle and decay away through it, they also create a gravitational wave background. Penrose then argues that a gravitational wave signal from a binary black hole merger – like the ones LIGO has observed – should be accompanied by noise-like signals from erebons that decayed at the same time in the same galaxy. Just that this noise-like contribution would be correlated with the same time-difference as the merger signal.

In his paper, Penrose does not analyze the details of his proposal. He merely writes:

“Clearly the proposal that I am putting forward here makes many testable predictions, and it should not be hard to disprove it if it is wrong.”

In my impression, this is a sketchy idea and I doubt it will work. I don’t have a major problem with inventing some particle to make up dark matter, but I have a hard time seeing how the decay of a Planck-mass particle can give rise to a signal comparable in strength to a black hole merger (or why several of them would add up exactly for a larger signal).

Even taking this at face value, the decay signals wouldn’t only come from one galaxy but from all galaxies, so the noise should be correlated all over and at pretty much all time-scales – not just at the 12ms as the Danish group has claimed. Worst of all, the dominant part of the signal would come from our own galaxy and why haven’t we seen this already?

In summary, one can’t blame Penrose for being fashionable. But I don’t think that erebons will be added to the list of LIGO’s discoveries.

Nature magazine publishes comment on quantum gravity phenomenology, demonstrates failure of editorial oversight

I have a headache and
blame Nature magazine for it.

For about 15 years, I have worked on quantum gravity phenomenology, which means I study ways to experimentally test the quantum properties of space and time. Since 2007, my research area has its own conference series, “Experimental Search for Quantum Gravity,” which took place most recently September 2016 in Frankfurt, Germany.

Extrapolating from whom I personally know, I estimate that about 150-200 people currently work in this field. But I have never seen nor heard anything of Chiara Marletto and Vlatko Vedral, who just wrote a comment for Nature magazine complaining that the research area doesn’t exist.

In their comment, titled “Witness gravity’s quantum side in the lab,” Marletto and Vedral call for “a focused meeting bringing together the quantum- and gravity-physics communities, as well as theorists and experimentalists.” Nice.

If they think such meetings are a good idea, I recommend they attend them. There’s no shortage. The above mentioned conference series is only the most regular meeting on quantum gravity phenomenology. Also the Marcel Grossmann Meeting has sessions on the topic. Indeed, I am writing this from a conference here in Trieste, which is about “Probing the spacetime fabric: from concepts to phenomenology.”

Marletto and Vedral point out that it would be great if one could measure gravitational fields in quantum superpositions to demonstrate that gravity is quantized. They go on to lay out their own idea for such experiments, but their interest in the topic apparently didn’t go far enough to either look up the literature or actually put in the numbers.

Yes, it would be great if we could measure the gravitational field of an object in a superposition of, say, two different locations. Problem is, heavy objects – whose gravitational fields are easy to measure – decohere quickly and don’t have quantum properties. On the other hand, objects which are easy to bring into quantum superpositions are too light to measure their gravitational field.

To be clear, the challenge here is to measure the gravitational field created by the objects themselves. It is comparably easy to measure the behavior of quantum objects in the gravitational field of the Earth. That has something to do with quantum and something to do with gravity, but nothing to do with quantum gravity because the gravitational field isn’t quantized.

In their comment, Marletto and Vedral go on to propose an experiment:

“Likewise, one could envisage an experiment that uses two quantum masses. These would need to be massive enough to be detectable, perhaps nanomechanical oscillators or Bose–Einstein condensates (ultracold matter that behaves as a single super-atom with quantum properties). The first mass is set in a superposition of two locations and, through gravitational interaction, generates Schrödinger-cat states on the gravitational field. The second mass (the quantum probe) then witnesses the ‘gravitational cat states’ brought about by the first.”

This is truly remarkable, but not because it’s such a great idea. It’s because Marletto and Vedral believe they’re the first to think about this. Of course they are not.

The idea of using Schrödinger-cat states, has most recently been discussed here. I didn’t write about the paper on this blog because the experimental realization faces giant challenges and I think it won’t work. There is also Anastopolous and Hu’s CQG paper about “Probing a Gravitational Cat State” and a follow-up paper by Derakhshani, which likewise go unmentioned. I’d really like to know how Marletto and Vedral think they can improve on the previous proposals. Letting a graphic designer make a nice illustration to accompany their comment doesn’t really count much in my book.

The currently most promising attempt to probe quantum gravity indeed uses nanomechanical oscillators and comes from the group of Markus Aspelmeyer in Vienna. I previously discussed their work here. This group is about six orders of magnitude away from being able to measure such superpositions. The Nature comment doesn’t mention it either.

The prospects of using Bose-Einstein condensates to probe quantum gravity has been discussed back and forth for two decades, but clear is that this isn’t presently the best option. The reason is simple: Even if you take the largest condensate that has been created to date – something like 10 million atoms – and you calculate the total mass, you are still way below the mass of the nanomechanical oscillators. And that’s leaving aside the difficulty of creating and sustaining the condensate.

There are some other possible gravitational effects for Bose-Einstein condensates which have been investigated, but these come from violations of the equivalence principle, or rather the ambiguity of what the equivalence principle in quantum mechanics means to begin with. That’s a different story though because it’s not about measuring quantum superpositions of the gravitational field.

Besides this, there are other research directions. Paternostro and collaborators, for example, have suggested that a quantized gravitational field can exchange entanglement between objects in a way that a classical field can’t. That too, however, is a measurement which is not presently technologically feasible. A proposal closer to experimental test is that by Belenchia et al, laid out their PRL about “Tests of Quantum Gravity induced non-locality via opto-mechanical quantum oscillators” (which I wrote about here).

Others look for evidence of quantum gravity in the CMB, in gravitational waves, or search for violations of the symmetries that underlie General Relativity. You can find a little summary in my blogpost “How Can we test Quantum Gravity”  or in my Nautilus essay “What Quantum Gravity Needs Is More Experiments.”

Do Marletto and Vedral mention any of this research on quantum gravity phenomenology? No.

So, let’s take stock. Here, we have two scientists who don’t know anything about the topic they write about and who ignore the existing literature. They faintly reinvent an old idea without being aware of the well-known difficulties, without quantifying the prospects of ever measuring it, and without giving proper credits to those who previously wrote about it. And they get published in one of the most prominent scientific journals in existence.

Wow. This takes us to a whole new level of editorial incompetence.

The worst part isn’t even that Nature magazine claims my research area doesn’t exist. No, it’s that I’m a regular reader of the magazine – or at least have been so far – and rely on their editors to keep me informed about what happens in other disciplines. For example with the comments pieces. And let us be clear that these are, for all I know, invited comments and not selected from among unsolicited submissions. So, some editor deliberately chose these authors.

Now, in this rare case when I can judge their content’s quality, I find the Nature editors picked two people who have no idea what’s going on, who chew up 30 years old ideas, and omit relevant citations of timely contributions.

Thus, for me the worst part is that I will henceforth have to suspect Nature’s coverage of other research areas is equally miserable as this.

Really, doing as much as Googling “Quantum Gravity Phenomenology” is more informative than this Nature comment.

Stephen Hawking’s 75th Birthday Conference: Impressions

I’m back from Cambridge, where I attended the conference “Gravity and Black Holes” in honor of Stephen Hawking’s 75th birthday.

First things first, the image on the conference poster, website, banner, etc is not a psychedelic banana, but gravitational wave emission in a black hole merger. It’s a still from a numerical simulation done by a Cambridge group that you can watch in full on YouTube.

What do gravitational waves have to do with Stephen Hawking? More than you might think.

Stephen Hawking, together with Gary Gibbons, wrote one of the first papers on the analysis of gravitational wave signals. That was in 1971, briefly after gravitational waves were first “discovered” by Joseph Weber. Weber’s detection was never confirmed by other groups. I don’t think anybody knows just what he measured, but whatever it was, it clearly wasn’t gravitational waves. Also Hawking’s – now famous – area theorem stemmed from this interest in gravitational waves, which is why the paper is titled “Gravitational Radiation from Colliding Black Holes.”

Second things second, the conference launched on Sunday with a public symposium, featuring not only Hawking himself but also Brian Cox, Gabriela Gonzalez, and Martin Rees. I didn’t attend because usually nothing of interest happens at these events. I think it was recorded, but haven’t seen the recording online yet – will update if it becomes available.

Gabriela Gonzalez was spokesperson of the LIGO collaboration when the first (real) gravitational wave detection was announced, so you have almost certainly seen her. She also gave a talk at the conference on Tuesday. LIGO’s second run is almost done now, and will finish in August. Then it’s time for the next schedule upgrade. Maximal design sensitivity isn’t expected to be reached until 2020. Above all, in the coming years, we’ll almost certainly see much better statistics and smaller error bars.

The supposed correlations in the LIGO noise were worth a joke by the session’s chairman, and I had the pleasure of talking to another member of the LIGO collaboration who recognized me as the person who wrote that upsetting Forbes piece. I clearly made some new friends there^^. I’d have some more to say about this, but will postpone this to another time.

Back to the conference. Monday began with several talks on inflation, most of which were rather basic overviews, so really not much new to report. Slava Mukhanov delivered a very Russian presentation, complaining about people who complain that inflation isn’t science. Andrei Linde then spoke about attractors in inflation, something I’ve been looking into recently, so this came in handy.

Monday afternoon, we had Jim Hartle speaking about the No-Boundary proposal – he was not at all impressed by Neil Turok et al’s recent criticism – and Raffael Bousso about the ever-tightening links between general relativity and quantum field theory. Raffael’s was the probably most technical talk of the meeting. His strikes me as a research program that will still run in the next century. There’s much to learn and we’ve barely just begun.

On Tuesday, besides the already mentioned LIGO talk, there were a few other talks about numerical general relativity – informative but also somehow unexciting. In the afternoon, Ted Jacobson spoke about fluid analogies for gravity (which I wrote about here), and Jeff Steinhauer reported on his (still somewhat controversial) measurement of entanglement in the Hawking radiation of such a fluid analogy (which I wrote about here.)

Wednesday began with a rather obscure talk about how to shove information through wormholes in AdS/CFT that I am afraid might have been somehow linked to ER=EPR, but I missed the first half so not sure. Gary Gibbons then delivered a spirited account of gravitational memory, though it didn’t become clear to me if it’s of practical relevance.

Next, Andy Strominger spoke about infrared divergences in QED. Hearing him speak, the whole business of using soft gravitons to solve the information loss problem suddenly made a lot of sense! Unfortunately I immediately forgot why it made sense, but I promise to do more reading on that.

Finally, Gary Horowitz spoke about all the things that string theorists know and don’t know about black hole microstates, which I’d sum up with they know less than I thought they do.

Stephen Hawking attended some of the talks, but didn’t say anything, except for a garbled sentence that seems to have played back by accident and stumped Ted Jacobson.

All together, it was a very interesting and fun meeting, and also a good opportunity to have coffee with friends both old and new. Besides food for thought, I also brought back a conference bag, a matching pen, and a sinus infection which I blame on the air conditioning in the lecture hall.

Now I have a short break to assemble my slides for next week’s conference and then I’m off to the airport again.

To understand the foundations of physics, study numerology

Numbers speak. [Img Src]

Once upon a time, we had problems in the foundations of physics. Then we solved them. That was 40 years ago. Today we spend most of our time discussing non-problems.

Here is one of these non-problems. Did you know that the universe is spatially almost flat? There is a number in the cosmological concordance model called the “curvature parameter” that, according to current observation, has a value of 0.000 plus-minus 0.005.

Why is that a problem? I don’t know. But here is the story that cosmologists tell.

From the equations of General Relativity you can calculate the dynamics of the universe. This means you get relations between the values of observable quantities today and the values they must have had in the early universe.

The contribution of curvature to the dynamics, it turns out, increases relative to that of matter and radiation as the universe expands. This means for the curvature-parameter to be smaller than 0.005 today, it must have been smaller than 10^-60 or so briefly after the Big Bang.

That, so the story goes, is bad, because where would you get such a small number from?

Well, let me ask in return, where do we get any number from anyway? Why is 10^-60 any worse than, say, 1.778, or exp(67π)?

That the curvature must have had a small value in the early universe is called the “flatness problem,” and since it’s on Wikipedia it’s officially more real than me. And it’s an important problem. It’s important because it justifies the many attempts to solve it.

The presently most popular solution to the flatness problem is inflation – a rapid period of expansion briefly after the Big Bang. Because inflation decreases the relevance of curvature contributions dramatically – by something like 200 orders of magnitude or so – you no longer have to start with some tiny value. Instead, if you start with any curvature parameter smaller than 10¹⁹⁷, the value today will be compatible with observation.

Ah, you might say, but clearly there are more numbers smaller than 10¹⁹⁷ than there are numbers smaller than 10^-60, so isn’t that an improvement?

Unfortunately, no. There are infinitely many numbers in both cases. Besides that, it’s totally irrelevant. Whatever the curvature parameter, the probability to get that specific number is zero regardless of its value. So the argument is bunk. Logical mush. Plainly wrong. Why do I keep hearing it?

Worse, if you want to pick parameters for our theories according to a uniform probability distribution on the real axis, then all parameters would come out infinitely large with probability one. Sucks. Also, doesn’t describe observations^*.

And there is another problem with that argument, namely, what probability distribution are we even talking about? Where did it come from? Certainly not from General Relativity because a theory can’t predict a distribution on its own theory space. More logical mush.

If you have trouble seeing the trouble, let me ask the question differently. Suppose we’d manage to measure the curvature parameter today to a precision of 60 digits after the point. Yeah, it’s not going to happen, but bear with me. Now you’d have to explain all these 60 digits – but that is as fine-tuned as a zero followed by 60 zeroes would have been!

Here is a different example for this idiocy. High energy physicists think it’s a problem that the mass of the Higgs is 15 orders of magnitude smaller than the Planck mass because that means you’d need two constants to cancel each other for 15 digits. That’s supposedly unlikely, but please don’t ask anyone according to which probability distribution it’s unlikely. Because they can’t answer that question. Indeed, depending on character, they’ll either walk off or talk down to you. Guess how I know.

Now consider for a moment that the mass of the Higgs was actually about as large as the Planck mass. To be precise, let’s say it’s 1.1370982612166126 times the Planck mass. Now you’d again have to explain how you get exactly those 16 digits. But that is, according to current lore, not a finetuning problem. So, erm, what was the problem again?

The cosmological constant problem is another such confusion. If you don’t know how to calculate that constant – and we don’t, because we don’t have a theory for Planck scale physics – then it’s a free parameter. You go and measure it and that’s all there is to say about it.

And there are more numerological arguments in the foundations of physics, all of which are wrong, wrong, wrong for the same reasons. The unification of the gauge couplings. The so-called WIMP-miracle (RIP). The strong CP problem. All these are numerical coincidence that supposedly need an explanation. But you can’t speak about coincidence without quantifying a probability!

Do my colleagues deliberately lie when they claim these coincidences are problems, or do they actually believe what they say? I’m not sure what’s worse, but suspect most of them actually believe it.

Many of my readers like jump to conclusions about my opinions. But you are not one of them. You and I, therefore, both know that I did not say that inflation is bunk. Rather I said that the most common arguments for inflation are bunk. There are good arguments for inflation, but that’s a different story and shall be told another time.

And since you are among the few who actually read what I wrote, you also understand I didn’t say the cosmological constant is not a problem. I just said its value isn’t the problem. What actually needs an explanation is why it doesn’t fluctuate. Which is what vacuum fluctuations should do, and what gives rise to what Niayesh called the cosmological non-constant problem.

Enlightened as you are, you would also never think I said we shouldn’t try to explain the value of some parameter. It is always good to look for better explanations for the assumption underlying current theories – where by “better” I mean either simpler or can explain more.

No, what draws my ire is that most of the explanations my colleagues put forward aren’t any better than just fixing a parameter through measurement  – they are worse. The reason is the problem they are trying to solve – the smallness of some numbers – isn’t a problem. It’s merely a property they perceive as inelegant.

I therefore have a lot of sympathy for philosopher Tim Maudlin who recently complained that “attention to conceptual clarity (as opposed to calculational technique) is not part of the physics curriculum” which results in inevitable confusion – not to mention waste of time.

In response, a pseudoanonymous commenter remarked that a discussion between a physicist and a philosopher of physics is “like a debate between an experienced car mechanic and someone who has read (or perhaps skimmed) a book about cars.”

Trouble is, in the foundations of physics today most of the car mechanics are repairing cars that run just fine – and then bill you for it.

I am not opposed to using aesthetic arguments as research motivations. We all have to get our inspiration from somewhere. But I do think it’s bad science to pretend numerological arguments are anything more than appeals to beauty. That very small or very large numbers require an explanation is a belief – and it’s a belief that has become adapted by the vast majority of the community. That shouldn’t happen in any scientific discipline.

As a consequence, high energy physics and cosmology is now populated with people who don’t understand that finetuning arguments have no logical basis. The flatness “problem” is preached in textbooks. The naturalness “problem” is all over the literature. The cosmological constant “problem” is on every popular science page. And so the myths live on.

If you break down the numbers, it’s me against ten-thousand of the most intelligent people on the planet. Am I crazy? I surely am.

---

*Though that’s exactly what happens with bare values.

Away Note

I’ll be traveling the next two weeks. First to Cambridge to celebrate Stephen Hawking’s 75th birthday (which was in January), then in Trieste for a conference on “Probing the spacetime fabric: from concepts to phenomenology.”  Rant coming up later today, but after that please prepare for a slow time.

Dear Dr B: Is science democratic?

“Hi Bee,

One of the often repeated phrases here in Italy by so called “science enthusiasts” is that “science is not democratic”, which to me sounds like an excuse for someone to justify some authoritarian or semi-fascist fantasy.

We see this on countless “Science pages”, one very popular example being Fare Serata Con Galileo. It's not a bad page per se, quite the contrary, but the level of comments including variations of “Democracy is overrated”, “Darwin works to eliminate weak and stupid people” and the usual “Science is not democratic” is unbearable. It underscores a troubling “sympathy for authoritarian politics” that to me seems to be more and more common among “science enthusiasts". The classic example it’s made is “the speed of light is not voted”, which to me, as true as it may be, has some sinister resonance.

Could you comment on this on your blog?

Luca S.”

Dear Luca,

Wow, I had no idea there’s so much hatred in the backyards of science communication.

Hand count at convention of the German
party CDU. Image Source: AFP

It’s correct that science isn’t democratic, but that doesn’t mean it’s fascistic. Science is a collective enterprise and a type of adaptive system, just like democracy is. But science isn’t democratic any more than sausage is a fruit just because you can eat both.

In an adaptive system, small modifications create a feedback that leads to optimization. The best-known example is probably Darwinian evolution, in which a species’ genetic information receives feedback through natural selection, thereby optimizing the odds of successful reproduction. A market economy is also an adaptive system. Here, the feedback happens through pricing. A free market optimizes “utility” that is, roughly speaking, a measure of the agents’ (customers/producers) satisfaction.

Democracy too is an adaptive system. Its task is to match decisions that affect the whole collective with the electorate’s values. We use democracy to keep our “is” close to the “ought.”

Democracies are more stable than monarchies or autocracies because an independent leader is unlikely to continuously make decisions which the governed people approve of. And the more governed people disapprove, the more likely they are to chop off the king’s head. Democracy, hence, works better than monarchy for the same reason a free market works better than a planned economy: It uses feedback for optimization, and thereby increases the probability for serving peoples’ interests.

The scientific system too uses feedback for optimization – this is the very basis of the scientific method: A hypothesis that does not explain observations has to be discarded or amended. But that’s about where similarities end.

The most important difference between the scientific, democratic, and economic system is the weight of an individual’s influence. In a free market, influence is weighted by wealth: The more money you can invest, the more influence you can have. In a democracy, each voter’s opinion has the same weight. That’s pretty much the definition of democracy – and note that this is a value in itself.

In science, influence is correlated with expertise. While expertise doesn’t guarantee influence, an expert is more likely to hold relevant knowledge, hence expertise is in practice strongly correlated with influence.

There are a lot of things that can go wrong with scientific self-optimization – and a lot of things do go wrong – but that’s a different story and shall be told another time. Still, optimizing hypotheses by evaluating empirical adequacy is how it works in principle. Hence, science clearly isn’t democratic.

Democracy, however, plays an important role for science.

For science to work properly, scientists must be free to communicate and discuss their findings. Non-democratic societies often stifle discussion on certain topics which can create a tension with the scientific system. This doesn’t have to be the case – science can flourish just fine in non-democratic societies – but free speech strongly links the two.

Science also plays an important role for democracy.

Politics isn’t done with polling the electorate on what future they would like to see. Elected representatives then have to find out how to best work towards this future, and scientific knowledge is necessary to get from “is” to “ought.”

But things often go wrong at the step from “is” to “ought.” Trouble is, the scientific system does not export knowledge in a format that can be directly imported by the political system. The information that elected representatives would need to make decisions is a breakdown of predictions with quantified risks and uncertainties. But science doesn’t come with a mechanism to aggregate knowledge. For an outsider, it’s a mess of technical terms and scientific papers and conferences – and every possible opinion seems to be defended by someone!

As a result, public discourse often draws on the “scientific consensus” but this is a bad way to quantify risk and uncertainty.

To begin with, scientists are terribly disagreeable and the only consensuses I know of are those on thousand years-old questions. More important, counting the numbers of people who agree with a statement simply isn’t an accurate quantifier of certainty. The result of such counting inevitably depends on how much expertise the counted people have: Too little expertise, and they’re likely to be ill-informed. Too much expertise, and they’re likely to have personal stakes in the debate. Worse, still, the head-count can easily be skewed by pouring money into some research programs.

Therefore, the best way we presently have make scientific knowledge digestible for politicians is to use independent panels. Such panels – done well – can both circumvent the problem of personal bias and the skewed head count. In the long run, however, I think we need a fourth arm of government to prevent politicians from attempting to interpret scientific debate. It’s not their job and it shouldn’t be.

But those “science enthusiasts” who you complain about are as wrong-headed as the science deniers who selectively disregard facts that are inconvenient for their political agenda. Both of them confuse opinions about what “ought to be” with the question how to get there. The former is a matter of opinion, the latter isn’t.

That vaccine debate that you mentioned, for example. It’s one question what are the benefits of vaccination and who is at risk from side-effects – that’s a scientific debate. It’s another question entirely whether we should allow parents to put their and other peoples’ children at an increased risk of early death or a life of disability. There’s no scientific and no logical argument that tells us where to draw the line.

Personally, I think parents who don’t vaccinate their kids are harming minors and society shouldn’t tolerate such behavior. But this debate has very little to do with scientific authority. Rather, the issue is to what extent parents are allowed to ruin their offspring’s life. Your values may differ from mine.

There is also, I should add, no scientific and no logical argument for counting the vote of everyone (above some quite arbitrary age threshold) with the same weight. Indeed, as Daniel Gilbert argues, we are pretty bad at predicting what will make us happy. If he’s right, then the whole idea of democracy is based on a flawed premise.

So – science isn’t democratic, never has been, never will be. But rather than stating the obvious, we should find ways to better integrate this non-democratically obtained knowledge into our democracies. Claiming that science settles political debate is as stupid as ignoring knowledge that is relevant to make informed decisions.

Science can only help us to understand the risks and opportunities that our actions bring. It can’t tell us what to do.

Thanks for an interesting question.

If tensions in cosmological data are not measurement problems, they probably mean dark energy changes

Galaxy pumpkin.
Src: The Swell Designer

According to physics, the universe and everything in it can be explained by but a handful of equations. They’re difficult equations, all right, but their simplest feature is also the most mysterious one. The equations contain a few dozen parameters that are – for all we presently know – unchanging, and yet these numbers determine everything about the world we inhabit.

Physicists have spent much brain-power on the question where these numbers come from, whether they could have taken any other values than the ones we observe, and whether their exploring their origin is even in the realm of science.

One of the key questions when it comes to the parameters is whether they are really constant, or whether they are time-dependent. If the vary, then their time-dependence would have to be determined by yet another equation, and that would change the whole story that we currently tell about our universe.

The best known of the fundamental parameters that dictate the universe how to behave is the cosmological constant. It is what causes the universe’s expansion to accelerate. The cosmological constant is usually assume to be, well, constant. If it isn’t, it is more generally referred to as ‘dark energy.’ If our current theories for the cosmos are correct, our universe will expand forever into a cold and dark future.

The value of the cosmological constant is infamously the worst prediction ever made using quantum field theory; the math says it should be 120 orders of magnitude larger than what we observe. But that the cosmological constant has a small non-zero value is extremely well established by measurement, well enough that a Nobel Prize was awarded for its discovery in 2011.

The Nobel Prize winners Perlmutter, Schmidt, and Riess, measured the expansion rate of the universe, encoded in the Hubble parameter, by looking at supernovae distributed over various distances. They concluded that the universe is not only expanding, but is expanding at an increasing rate – a behavior that can only be explained by a nonzero cosmological constant.

It is controversial though exactly how fast the expansion is today, or how large the current value of the Hubble constant, H₀, is. There are different ways to measure this constant, and physicists have known for a few years that the different measurements give different results. This tension in the data is difficult to explain, and it has so-far remained unresolved.

One way to determine the Hubble constant is by using the cosmic microwave background (CMB). The small temperature fluctuations in the CMB spectrum encode the distribution of plasma in the early universe and the changes of the radiation since. From fitting the spectrum with the parameters that determine the expansion of the universe, physicists get a value for the Hubble constant. The most accurate of such measurements is currently that from the Planck satellite.

Another way to determine the Hubble constant is to deduce the expansion of the universe from the redshift of the light from distant sources. This is the way the Nobel-Prize winners made their discovery, and the precision of this method has since been improved. These two ways to determine the cosmological constant give results that differ with a statistical significance of 3.4 σ. That’s a probability of less than one in thousand to be due to random data fluctuations.

Various explanations for this have since been proposed. One possibility is that it’s a systematic error in the measurement, most likely in the CMB measurement from the Planck mission. There are reasons to be skeptical because the tension goes away when the finer structures (the large multipole moments) of the data is omitted. For many astrophysicists, this is an indicator that something’s amiss either with the Planck measurement or the data analysis.

Or maybe it’s a real effect. In this case, several modifications of the standard cosmological model have been put forward. They range from additional neutrinos to massive gravitons to changes in the cosmological constant.

That the cosmological constant changes from one place to the next is not an appealing option because this tends to screw up the CMB spectrum too much. But the currently most popular explanation for the data tension seems to be that the cosmological constant changes in time.

A group of researchers from Spain, for example, claims that they have a stunning 4.1 σ preference for a time-dependent cosmological constant over an actually constant one.

This claim seems to have been widely ignored, and indeed one should be cautious. They test for a very specific time-dependence, and their statistical analysis does not account for other parameterization they might have previously tried. (The theoretical physicist’s variant of post-selection bias.)

Moreover, they fit their model not only to the two above mentioned datasets, but to a whole bunch of others at the same time. This makes it hard to tell what is the reason their model seems to work better. A couple of cosmologists who I asked why this group’s remarkable results have been ignored complained that the data analysis is opaque.

Be that as it may, just when I put the Spaniards’ paper away, I saw another paper that supported their claim with an entirely independent study based on weak gravitational lensing.

Weak gravitational lensing happens when a foreground galaxy distorts the images of farther away galaxies. The qualifier ‘weak’ sets this effect apart from strong lensing which is caused by massive nearby objects – such as black holes – and deforms point-like sources to partials rings. Weak gravitational lensing, on the other hand, is not as easily recognizable and must be inferred from the statistical distribution of the shapes of galaxies.

The Kilo Degree Survey (KiDS) has gathered and analyzed weak lensing data from about 15 million distant galaxies. While their measurements are not sensitive to the expansion of the universe, they are sensitive to the density of dark energy, which affects the way light travels from the galaxies towards us. This density is encoded in a cosmological parameter imaginatively named σ⁸. Their data, too, is in conflict with the CMB data from the Planck satellite.

The members of the KiDs collaboration have tried out which changes to the cosmological standard model work best to ease the tension in the data. Intriguingly, it turns out that ahead of all explanations the one that works best is that the cosmological constant changes with time. The change is such that the effects of accelerated expansion are becoming more pronounced, not less.

In summary, it seems increasingly unlikely the tension in the cosmological data is due to chance. Cosmologists are cautious and most of them bet on a systematic problem with the Planck data. However, if the Planck measurement receives independent confirmation, the next best bet is on time-dependent dark energy. It wouldn’t make our future any brighter though. The universe would still expand forever into cold darkness.

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[This article previously appeared on Starts With A Bang.]

Update June 21: Corrected several sentences to address comments below.

What’s new in high energy physics? Clockworks.

Clockworks. [Img via dwan1509].

High energy physics has phases. I don’t mean phases like matter has – solid, liquid, gaseous and so on. I mean phases like cranky toddlers have: One week they eat nothing but noodles, the next week anything as long as it’s white, then toast with butter but it must be cut into triangles.

High energy physics is like this. Twenty years ago, it was extra dimensions, then we had micro black holes, unparticles, little Higgses – and the list goes on.

But there hasn’t been a big, new trend since the LHC falsified everything that was falsifiable. It’s like particle physics stepped over the edge of a cliff but hasn’t looked down and now just walks on nothing.

The best candidate for a new trend that I saw in the past years is the “clockwork mechanism,” though the idea just took a blow and I’m not sure it’ll go much farther.

The origins of the model go back to late 2015, when the term “clockwork mechanism” was coined by Kaplan and Rattazzi, though Cho and Im pursued a similar idea and published it at almost the same time. In August 2016, clockworks were picked up by Giudice and McCullough, who advertised the model as a “a useful tool for model-building applications” that “offers a solution to the Higgs naturalness problem.”

Gears. Img Src: Giphy.

The Higgs naturalness problem, to remind you, is that the mass of the Higgs receives large quantum corrections. The Higgs is the only particle in the standard model that suffers from this problem because it’s the only scalar. These quantum corrections can be cancelled by subtracting a constant so that the remainder fits the observed value, but then the constant would have to be very finely tuned. Most particle physicists think that this is too much of a coincidence and hence search for other explanations.

Before the LHC turned on, the most popular solution to the Higgs naturalness issue was that some new physics would show up in the energy range comparable to the Higgs mass. We now know, however, that there’s no new physics nearby, and so the Higgs mass has remained unnatural.

Clockworks are a mechanism to create very small numbers in a “natural” way, that is from numbers that are close by 1. This can be done by copying a field multiple times and then coupling each copy to two neighbors so that they form a closed chain. This is the “clockwork” and it is assumed to have a couplings with values close to 1 which are, however, asymmetric among the chain neighbors.

The clockwork’s chain of fields has eigenmodes that can be obtained by diagonalizing the mass matrix. These modes are the “gears” of the clockwork and they contain one massless particle.

The important feature of the clockwork is now that this massless particle’s mode has a coupling that scales with the clockwork’s coupling taken to the N-th power, where N is the number of clockwork gears. This means even if the original clockwork coupling was only a little smaller than 1, the coupling of the lightest clockwork mode becomes small very fast when the clockwork grows.

Thus, clockworks are basically a complicated way to make a number of order 1 small by exponentiating it.

I’m an outspoken critic of arguments from naturalness (and have been long before we had the LHC data) so it won’t surprise you to hear that I am not impressed. I fail to see how choosing one constant to match observation is supposedly worse than introducing not only a new constant, but also N copies of some new field with a particular coupling pattern.

Either way, by March 2017, Ben Allanach reports from Recontres de Moriond – the most important annual conference in particle physics – that clockworks are “getting quite a bit of attention” and are “new fertile ground.”

Ben is right. Clockworks contain one light and weakly coupled mode – difficult to detect because of the weak coupling – and a spectrum of strongly coupled but massive modes – difficult to detect because they’re massive. That makes the model appealing because it will remain impossible to rule it out for a while. It is, therefore, perfect playground for phenomenologists.

And sure enough, the arXiv has since seen further papers on the topic. There’s clockwork inflation and clockwork dark matter, a clockwork axion and clockwork composite Higgses – you get the picture.

But then, in April 2017, a criticism of the clockwork mechanism appears on the arXiv. Its authors Craig, Garcia Garcia, and Sutherland point out that the clockwork mechanism can only be used if the fields in the clockwork’s chain have abelian symmetry groups. If the group isn’t abelian the generators will mix together in the zero mode, and maintaining gauge symmetry then demands that all couplings be equal to one. This severely limits the application range of the model.

A month later, Giudice and McCullough reply to this criticism essentially by saying “we know this.” I have no reason to doubt it, but I still found the Craig et al criticism useful for clarifying what clockworks can and can’t do. This means in particular that the supposed solution to the hierarchy problem does not work as desired because to maintain general covariance one is forced to put a hierarchy of scales into the coupling already.

I am not sure whether this will discourage particle physicists from pursuing the idea further or whether more complicated versions of clockworks will be invented to save naturalness. But I’m confident that – like a toddler’s phase – this too shall pass.

Dear Dr B: What are the chances of the universe ending out of nowhere due to vacuum decay?

“Dear Sabine,

my names [-------]. I'm an anxiety sufferer of the unknown and have been for 4 years. I've recently came across some articles saying that the universe could just end out of no where either through false vacuum/vacuum bubbles or just ending and I'm just wondering what the chances of this are occurring anytime soon. I know it sounds silly but I'd be dearly greatful for your reply and hopefully look forward to that

Many thanks

[--------]”

Dear Anonymous,

We can’t predict anything.

You see, we make predictions by seeking explanations for available data, and then extrapolating the best explanation into the future. It’s called “abductive reasoning,” or “inference to the best explanation” and it sounds reasonable until you ask why it works. To which the answer is “Nobody knows.”

We know that it works. But we can’t justify inference with inference, hence there’s no telling whether the universe will continue to be predictable. Consequently, there is also no way to exclude that tomorrow the laws of nature will stop and planet Earth will fall apart. But do not despair.

Francis Bacon – widely acclaimed as the first to formulate the scientific method – might have reasoned his way out by noting there are only two possibilities. Either the laws of nature will break down unpredictably or they won’t. If they do, there’s nothing we can do about it. If they don’t, it would be stupid not to use predictions to improve our lives.

It’s better to prepare for a future that you don’t have than to not prepare for a future you do have. And science is based on this reasoning: We don’t know why the universe is comprehensible and why the laws of nature are predictive. But we cannot do anything about unknown unknowns anyway, so we ignore them. And if we do that, we can benefit from our extrapolations.

Just how well scientific predictions work depends on what you try to predict. Physics is the currently most predictive discipline because it deals with the simplest of systems, those whose properties we can measure to high precision and whose behavior we can describe with mathematics. This enables physicists to make quantitatively accurate predictions – if they have sufficient data to extrapolate.

The articles that you read about vacuum decay, however, are unreliable extrapolations of incomplete evidence.

Existing data in particle physics are well-described by a field – the Higgs-field – that fills the universe and gives masses to elementary particles. This works because the value of the Higgs-field is different from zero even in vacuum. We say it has a “non-vanishing vacuum expectation value.” The vacuum expectation value can be calculated from the masses of the known particles.

In the currently most widely used theory for the Higgs and its properties, the vacuum expectation value is non-zero because it has a potential with a local minimum whose value is not at zero.

We do not, however, know that the minimum which the Higgs currently occupies is the only minimum of the potential and – if the potential has another minimum – whether the other minimum would be at a smaller energy. If that was so, then the present state of the vacuum would not be stable, it would merely be “meta-stable” and would eventually decay to the lowest minimum. In this case, we would live today in what is called a “false vacuum.”

Image Credits: Gary Scott Watson.

If our vacuum decays, the world will end – I don’t know a more appropriate expression. Such a decay, once triggered, releases an enormous amount of energy – and it spreads at the speed of light, tearing apart all matter it comes in contact with, until all vacuum has decayed.

How can we tell whether this is going to happen?

Well, we can try to measure the properties of the Higgs’ potential and then extrapolate it away from the minimum. This works much like Taylor series expansions, and it has the same pitfalls. Indeed, making predictions about the minima of a function based on a polynomial expansion is generally a bad idea.

Just look for example at the Taylor series of the sine function. The full function has an infinite number of minima at exactly the same value but you’d never guess from the first terms in the series expansion. First it has one minimum, then it has two minima of different value, then again it has only one – and the higher the order of the expansion the more minima you get.

The situation for the Higgs’ potential is more complicated because the coefficients are not constant, but the argument is similar. If you extract the best-fit potential from the available data and extrapolate it to other values of the Higgs-field, then you find that our present vacuum is meta-stable.

The figure below shows the situation for the current data (figure from this paper). The horizontal axis is the Higgs mass, the vertical axis the mass of the top-quark. The current best-fit is the upper left red point in the white region labeled “Metastability.”

Figure 2 from Bednyakov et al, Phys. Rev. Lett. 115, 201802 (2015).

This meta-stable vacuum has, however, a ridiculously long lifetime of about 10⁶⁰⁰ times the current age of the universe, take or give a few billion billion billion years. This means that the vacuum will almost certainly not decay until all stars have burnt out.

However, this extrapolation of the potential assumes that there aren’t any unknown particles at energies higher than what we have probed, and no other changes to physics as we know it either. And there is simply no telling whether this assumption is correct.

The analysis of vacuum stability is not merely an extrapolation of the presently known laws into the future – which would be justified – it is also an extrapolation of the presently known laws into an untested energy regime – which is not justified. This stability debate is therefore little more than a mathematical exercise, a funny way to quantify what we already know about the Higgs’ potential.

Besides, from all the ways I can think of humanity going extinct, this one worries me least: It would happen without warning, it would happen quickly, and nobody would be left behind to mourn. I worry much more about events that may cause much suffering, like asteroid impacts, global epidemics, nuclear war – and my worry-list goes on.

Not all worries can be cured by rational thought, but since I double-checked you want facts and not comfort, fact is that current data indicates our vacuum is meta-stable. But its decay is an unreliable prediction based the unfounded assumption that there either are no changes to physics at energies beyond the ones we have tested, or that such changes don’t matter. And even if you buy this, the vacuum almost certainly wouldn’t decay as long as the universe is hospitable for life.

Particle physics is good for many things, but generating potent worries isn’t one of them. The biggest killer in physics is still the 2nd law of thermodynamics. It will get us all, eventually. But keep in mind that the only reason we play the prediction game is to get the best out of the limited time that we have.

Thanks for an interesting question!

Does parametric resonance solve the cosmological constant problem?

An oscillator too.
Source: Giphy.

Tl;dr: Ask me again in ten years.

A lot of people asked for my opinion about a paper by Wang, Zhu, and Unruh that recently got published in Physical Reviews D, one of the top journals in the field.

How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe
Qingdi Wang, Zhen Zhu, William G. Unruh
Phys. Rev. D 95, 103504 (2017)
arXiv:1703.00543 [gr-qc]  

Following a press-release from UBC, the paper has attracted quite some attention in the pop science media which is remarkable for such a long and technically heavy work. My summary of the coverage so far is “bla-bla-bla parametric resonance.”

I tried to ignore the media buzz a) because it’s a long paper, b) because it’s a long paper, and c) because I’m not your public community debugger. I actually have own research that I’m more interested in. Sulk.

But of course I eventually came around and read it. Because I’ve toyed with a similar idea some while ago and it worked badly. So, clearly, these folks outscored me, and after some introspection I thought that instead of being annoyed by the attention they got, I should figure out why they succeeded where I failed.

Turns out that once you see through the math, the paper is not so difficult to understand. Here’s the quick summary.

One of the major problems in modern cosmology is that vacuum fluctuations of quantum fields should gravitate. Unfortunately, if one calculates the energy density and pressure contained in these fluctuations, the values are much too large to be compatible with the expansion history of the universe.

This vacuum energy gravitates the same way as the cosmological constant. Such a large cosmological constant, however, should lead to a collapse of the universe long before the formation of galactic structures. If you switch the sign, the universe doesn’t collapse but expands so rapidly that structures can’t form because they are ripped apart. Evidently, since we are here today, that didn’t happen. Instead, we observe a small positive cosmological constant and where did that come from? That’s the cosmological constant problem.

The problem can be solved by introducing an additional cosmological constant that cancels the vacuum energy from quantum field theory, leaving behind the observed value. This solution is both simple and consistent. It is, however, unpopular because it requires fine-tuning the additional term so that the two contributions almost – but not exactly – cancel. (I believe this argument to be flawed, but that’s a different story and shall be told another time.) Physicists therefore have tried for a long time to explain why the vacuum energy isn’t large or doesn’t couple to gravity as expected.

Strictly speaking, however, the vacuum energy density is not constant, but – as you expect of fluctuations – it fluctuates. It is merely the average value that acts like a cosmological constant, but the local value should change rapidly both in space and in time. (These fluctuations are why I’ve never bought the “degravitation” idea according to which the vacuum energy decouples because gravity has a built-in high-pass filter. In that case, you could decouple a cosmological constant, but you’d still be stuck with the high-frequency fluctuations.)

In the new paper, the authors make the audacious attempt to calculate how gravity reacts to the fluctuations of the vacuum energy. I say it’s audacious because this is not a weak-field approximation and solving the equations for gravity without a weak-field approximation and without symmetry assumptions (as you would have for the homogeneous and isotropic case) is hard, really hard, even numerically.

The vacuum fluctuations are dominated by very high frequencies corresponding to a usually rather arbitrarily chosen ‘cutoff’ – denoted Λ – where the effective theory for the fluctuations should break down. One commonly assumes that this frequency roughly corresponds to the Planck mass, m_p. The key to understanding the new paper is that the authors do not assume this cutoff, Λ, to be at the Planck mass, but at a much higher energy, Λ >> m_p.

As they demonstrate in the paper, massaged into a suitable form, one of the field equations for gravity takes the form of an oscillator equation with a time- and space-dependent coupling term. This means, essentially, space-time at each place has the properties of a driven oscillator.

The important observation that solves the cosmological constant problem is then that the typical resonance frequency of this oscillator is Λ²/m_p which is by assumption much larger than the main frequency of fluctuations the oscillator is driven by, which is Λ. This means that space-time resonates with the frequency of the vacuum fluctuations – leading to an exponential expansion like that from a cosmological constant – but it resonates only with higher harmonics, so that the resonance is very weak.

The result is that the amplitude of the oscillations grows exponentially, but it grows slowly. The effective cosmological constant they get by averaging over space is therefore not, as one would naively expect, Λ, but (omitting factors that are hopefully of order one) Λ* exp (-Λ²/m_p). One hence uses a trick quite common in high-energy physics, that one can create a large hierarchy of numbers by having a small hierarchy of numbers in an exponent.

In conclusion, by pushing the cutoff above the Planck mass, they suppress the resonance and slow down the resulting acceleration.

Neat, yes.

But I know you didn’t come for the nice words, so here’s the main course. The idea has several problems. Let me start with the most basic one, which is also the reason I once discarded a (related but somewhat different) project. It’s that their solution doesn’t actually solve the field equations of gravity.

It’s not difficult to see. Forget all the stuff about parametric resonance for a moment. Their result doesn’t solve the field equations if you set all the fluctuations to zero, so that you get back the case with a cosmological constant. That’s because if you integrate the second Friedmann-equation for a negative cosmological constant you can only solve the first Friedmann-equation if you have negative curvature. You then get Anti-de Sitter space. They have not introduced a curvature term, hence the first Friedmann-equation just doesn’t have a (real valued) solution.

Now, if you turn back on the fluctuations, their solution should reduce to the homogeneous and isotropic case on short distances and short times, but it doesn’t. It would take a very good reason for why that isn’t so, and no reason is given in the paper. It might be possible, but I don’t see how.

I further find it perplexing that they rest their argument on results that were derived in the literature for parametric resonance on the assumption that solutions are linearly independent. General relativity, however, is non-linear. Therefore, one generally isn’t free to combine solutions arbitrarily.

So far that’s not very convincing. To make matters worse, if you don’t have homogeneity, you have even more equations that come from the position-dependence and they don’t solve these equations either. Let me add, however, that this doesn’t worry me all that much because I think it might be possible to deal with it by exploiting the stochastic properties of the local oscillators (which are homogeneous again, in some sense).

Another troublesome feature of their idea is that the scale-factor of the oscillating space-time crosses zero in each cycle so that the space-time volume also goes to zero and the metric structure breaks down. I have no idea what that even means. I’d be willing to ignore this issue if the rest was working fine, but seeing that it doesn’t, it just adds to my misgivings.

The other major problem with their approach is that the limit they work in doesn’t make sense to begin with. They are using classical gravity coupled to the expectation values of the quantum field theory, a mixture known as ‘semi-classical gravity’ in which gravity is not quantized. This approximation, however, is known to break down when the fluctuations in the energy-momentum tensor get large compared to its absolute value, which is the very case they study.

In conclusion, “bla-bla-bla parametric resonance” is a pretty accurate summary.

How serious are these problems? Is there something in the paper that might be interesting after all?

Maybe. But the assumption (see below Eq (42)) that the fields that source the fluctuations satisfy normal energy conditions is, I believe, a non-starter if you want to get an exponential expansion. Even if you introduce a curvature term so that you can solve the equations, I can’t for the hell of it see how you average over locally approximately Anti-de Sitter spaces to get an approximate de Sitter space. You could of course just flip the sign, but then the second Friedmann equation no longer describes an oscillator.

Maybe allowing complex-valued solutions is a way out. Complex numbers are great. Unfortunately, nature’s a bitch and it seems we don’t live in a complex manifold. Hence, you’d then have to find a way to get rid of the imaginary numbers again. In any case, that’s not discussed in the paper either.

I admit that the idea of using a de-tuned parametric resonance to decouple vacuum fluctuations and limit their impact on the expansion of the universe is nice. Maybe I just lack vision and further work will solve the above mentioned problems. More generally, I think numerically solving the field equations with stochastic initial conditions is of general interest and it would be great if their paper inspires follow-up studies. So, give it ten years, and then ask me again. Maybe something will have come out of it.

In other news, I have also written a paper that explains the cosmological constant and I haven’t only solved the equations that I derived, I also wrote a Maple work-sheet that you can download and check the calculation for yourself. The paper was just accepted for publication in PRD.

For what my self-reflection is concerned, I concluded I might be too ambitious. It’s much easier to solve equations if you don’t actually solve them.

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I gratefully acknowledge helpful conversation with two of this paper’s authors who have been very, very patient with me. Sorry I didn’t have anything nicer to say.

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.

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:

Signatures of extra dimensions in gravitational waves
David Andriot and Gustavo Lucena Gómez
arXiv:1704.07392 [hep-th]

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.]

“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.

[Bridge]
Every symmetry
Has to be broken,
Every harmony
Has to decay.

[Chorus]
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.

[Interlude]
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]