The science of the multiverse.

CMB aniotropies.
Image: NASA/WMAP

A new numerical study of bubble collisions makes a big step towards testing the multiverse hypothesis.

The multiverse might not be the most original or even surprising idea that physicists have proposed recently, but it certainly excelled in capturing the public imagination and in stirring up discussion. On the very top of the discussion list is the question whether the multiverse is a scientific idea at all, or whether it is simply a philosophical retreat for lazy physicists who’ve gotten tired hunting answers that didn’t come knocking on their door.

But there’s no simple answer to that question. Whether the multiverse is a scientific idea depends on what one means with multiverse. As I explained previously, the existence of “multiverses” in many theories is just a consequence of pushing models beyond their phenomenological reach. The only thing these types of multiverses demonstrate is that physicists don’t understand the limits of pure mathematics. In contrast, the best motivated multiverse is bubble universes in eternal inflation. And these can have observational consequences.

Eternal inflation is a variant of inflation, a phase of exponential growth in the early universe. Exactly how this phase proceeds depends on the properties of quantum fields that filled the universe back then. In eternal inflation, it is only parts of the whole space in which the rapid expansion comes to an end and structures like our galaxies form; these parts are referred to as “bubble universes”. In the rest of space, inflation continues and goes on to create new bubbles. This bubble production lasts eternally.

Most of these bubble universes are causally disconnected from ours and we have no chance to ever observe them. However, it is at least theoretically possible that some of these bubbles collide as they expand. This would mean that what is now our observable universe had, when we look back in time, not one seed, but two or more that later came to join. This type of bubble collision can have observable consequences for the formation of structures and leave imprints in the pattern of temperature fluctuations in the cosmic microwave background (CMB).

The accurate mathematical description of these bubble collisions is however difficult because Einstein’s field equations are non-linear. Solutions can normally only analytically be found in cases with many symmetries, and in the case of bubble collisions the geometry prevents one from using such a highly symmetric ansatz. Approximately valid analytical solutions have previously been put forward, but when one wants to make quantitative prediction one needs a sufficiently precise numerical simulation. Such a numerical simulation has to evolve forward in time the metric components, whose fluctuations eventually go to seed the perturbations in the CMB, which we then later measure.

Such a numerical simulation has recently been published in this paper

Simulating the universe(s): from cosmic bubble collisions to cosmological observables with numerical relativity
Carroll L. Wainwright, Matthew C. Johnson, Hiranya V. Peiris, Anthony Aguirre, Luis Lehner, Steven L. Liebling
arXiv:1312.1357 [hep-th]

The authors only study the simplest case, that is the collision of only two bubbles and in addition these bubbles are identical (they have the same vacuum state). This is clearly not the most general case, but even so their simulation allows them to calculate the effects on the CMB better than previously possible.

Roughly speaking, the bubble collision leaves a localized temperature fluctuation - a hot spot or a cold spot - in the CMB that fades off away from the center of the collision. Exactly how it fades is very important for the extraction of such a signal from the data, and yet this could only be estimated before this numerical simulation was completed. Notably, the authors found that the fall-off is faster than was expected from the analytic estimates.

The figure below shows the time-evolution for the scalar field (Φ) that drives the inflation and two functions (a and α) that quantify the behavior of the metric. The horizontal axis is one of the spatial coordinates the vertical axes a measure for the time.

Figure 7 from arXiv:1312.1357 [hep-th]

What you can see in the image is how the configuration starts out being initially split in two halves and then evolves towards a situation where the initial split slowly fades away. That the bubbles both originate at “the same” time can always be achieved by a suitable choice of time-coordinate. The time, or the initial distances between the bubbles, can later be changed to a free parameter by a coordinate transformation.

This numerical study demonstrates nicely that it is possible to connect the underlying model for eternal inflation to observable signatures. It is also valuable in suggesting a useful parameterization for the effects. I find this a very interesting paper which will provide a basis for further studies that are necessary to analyze cosmological data for signals that might show we live in a multiverse.

Trouble in the Ivory Tower: Not an academic problem.

The Ivory Tower.
Image from The Neverending Story.

“Science is the only news,” Stuart Brand told us. And the news is that research misconduct is on the rise while reproducible results are in decline. Peer review, the process in which scientific publications are evaluated by anonymous peers, has become a farce as scientists’ existential worries make it an exercise in forward defense with the occasional backhand offense. Scientists produce more papers now than ever, and then hide them behind journal subscriptions so costly nobody can read them – a good idea because most published research findings are probably false, though that too is probably false. Measures for scientific success have been criticized ever since they began being used, and the academic system chokes on social effects like herding, pluralistic ignorance and groupthink.

Yes, science works, no need to call me names. But science doesn’t work as good as it could, not as good as it should, not as good as we need it to work.

Scientific institutions and scientific management are stuck in the last century. The academic system today is in no shape to cope with the demands of high connectivity in a global and increasing workforce, is unable to deal with complex trans-national and interdisciplinary problems, and can’t handle the amplification of social feedback that information technology has brought.

The academic system, in brief, has the same problem as our political, social and economic systems.

The biggest challenge mankind faces today is not the development of some breakthrough technology. The biggest challenge is to create a society whose institutions integrate the knowledge that must precede any such technology, including knowledge about these institutions themselves. All of our big problems today speak of our failure, not to envision solutions, but to turn our ideas and knowledge into reality.

It’s not that we lack creativity. It’s that the kind of creativity that comes to us naturally does not latch upon problems evolution didn’t endow us to register to begin with. We do not comprehend the interplay of large crowds of people and are unable to individually beat our own psychology, rooted in groups of tens to hundreds, not billions. To arrange our living together in groups larger than we can intuit, we agree on rules of conduct and incentives that align our individual actions with collective trends so that both are to our benefit. This requires systems design. It requires science. And before that it requires we acknowledge the problem.

But we watch. We watch with bewilderment as a video of sunrise is broadcast on Tiananmen square where thick smog forces onlookers to wear breathing masks. We watch with horrified fascination video footages of the big garbage swirl and of birds dying from indigestible plastic pieces. We watch, hypnotized, replays of negotiation failures that make our adaptation to climate change more costly by the day. The way we have arranged, organized, policed and institutionalized our living together leaves us to watch ourselves watching, stunned at our own inability to change anything about it.

And scientists, the ones who should be able to analyze the situation and to devise a solution aren’t any better.

Scientists, of course, know exactly what is wrong with academia. Leaving aside that no two of them can agree on how to do it, they know how to solve the problem. There’s no shortage of proposals for how to fix peer review and scientific publishing and for how to better distribute resources. Futures markets, auction markets, lottery systems, open peer review, and dozens of alternative metrics have been suggested, we’ve seen it all. They write papers about it and send them for peer review. The rest is the same old he-said-she-said.

So far, scientists miserably failed to adapt the academic system to the changing demands of the 21st century. They belabor the problem and devise solutions, but are unable to implement them. And in the ocean of conference proceedings they watch the giant abstract swirl.

Academia mirrors the problem of our societies in a nutshell. The members of the academe, they’re all talk but no walk. We are being told that scientists are studying now the interconnectivity of the multi-layered networks that govern our societies, and we ask for answers and advice, we ask to be informed about how to solve our problems. There’s nobody else to solve these problems.

Social systems adapt to changing demands much like organisms do, by gradual modification and selection. But this process takes time – a lot of time – and it’s time we cannot afford. The only way to accelerate this adaption is the scientific method: a targeted, controlled, and recorded series of modifications. Many existing projects today aim to track and analyze the complex interactions of our highly interwoven networked world. But not a single one of these projects addresses the real problem, which is how to use this knowledge in the very systems that are being studied. It is this feedback of knowledge about the system back into the system that is necessary for our institutions to adapt. It requires a self-consistent scientific approach to institutional design, an approach that doesn’t exist and is nowhere near existence.

We need scientists to help us create social systems that organize our living together in groups so large that our evolutionary brains, trained to deal with small groups, cannot cope with. Trial and error will take too long and the errors are too costly now. But scientists are like the overweight doctor preaching the benefits of blood-pressure regulation, evidently unable to solve their own problems first. They presently can’t help us solve any problems, and we shouldn’t listen to their advice until they’ve solved their own problems.

Science is the only news, but it’s not only news. It’s the canary in the coal mine. Better watch it closely.

Loops vs Strings. Almost discovered for much longer.

I didn't attend this year's FQXi conference, but most of the talks will be uploaded sooner or later to the FQXi YouTube channel. The FQXi conferences always feature a mock debate with a role switch. I've never seen one with an actual exchange of arguments, but the debates have some amusement value. This year we have Carlo Rovelli defending String Theory ("You Loop people... insist that you cannot get any prediction from your theory. But we can't either.") and Raffael Bousso defending Loop Quantum Gravity ("What happened next was the string landscape. You've all heard of the string landscape. It's also known as 'The End of Science.'"). Enjoy.

Shooting strings

Shooting strings.
Source: Meez Forums.

String theory, once hailed as theory of everything, now struggles to demonstrate its use for anything at all.

Most string theorists today, if not working for banks, study the gauge-gravity correspondence. This celebrated idea, arguably one of the most interesting findings in string theory, relates a strongly coupled field theory in flat space to weakly coupled gravity in a higher dimensional space. These higher-dimensional spaces do not resemble our universe, so the interesting applications of the gauge-gravity correspondence are analytical calculations in strongly coupled field theory. Notoriously difficult problems of the field theory can become manageable by reformulating them in the language of gravity.

The most widely promoted use of this gauge-gravity correspondence has been the quark gluon plasma, which is produced in highly energetic collisions of heavy ions, previously at RHIC and now at the LHC. There has been a lot of hype about the low viscosity that was analytically found using the gauge-gravity correspondence and that fit well with observations. But heavy ion physics isn’t just viscosity. There are many other observables that a good model must be able to explain.

One of these observables is the energy loss that elementary particles experience when they travel through the plasma. Just by chance it can happen that a particle pair is created but only one of the two particles travels through the plasma and loses energy. The primary particles are unstable and eventually decay to form stable hadrons. By measuring and summing up the momentum of the decay products one can infer the energy loss that happened in the plasma.

We previously saw that the gauge-gravity correspondence seems to work well for the RHIC data, but misses the mark when the more recent LHC is also taken into account. The prediction is far outside the error margin of the data, both in terms of magnitude and in terms of slope. The gauge-gravity correspondence predicts too much energy loss. I call that a bad fit to the data. String theorists call it “qualitatively correct” which seems to mean their prediction has an upward slope.

But heavy ion physics is a messy business where many different processes come together and that makes it difficult to draw unambiguous conclusions. Clearly that situation doesn’t look good. However, as I mentioned earlier, last year I heard a talk by Steven Gubser about an upcoming paper of his addressing the energy loss in the gauge-gravity correspondence. Ficnar, Gubser and Gyulassy now recently posted their new paper on the arxiv:

Shooting String Holography of Jet Quenching at RHIC and LHC
Andrej Ficnar, Steven S. Gubser, Miklos Gyulassy
arXiv:1311.6160 [hep-ph]

In this paper, the authors propose a new description on the gravity side for the particle which on the field theory side loses energy while traveling through the plasma. Previously, this particle was modeled by a string parallel to the boundary that fell towards the black hole horizon. Ficnar et al instead model the particle by a string that ‘shoots up’ away from the horizon. They calculate the energy loss of the endpoint and find that the energy loss is reduced relative to the previous scenario.

They do not motivate the gravitational description and I am left wondering if not there should be an unambiguous procedure to find the gravitational analogue. If one can just choose a different setup and get a different energy loss that does not exactly increase my faith in the predictive value of the model.

Be that as it may, with their new model a sufficient reduction of the energy loss can only be achieved by pushing the crucial parameter (λ, the ‘t Hooft coupling) into a limit where the approximation actually breaks down. This is no good because then the results cannot be trusted.

So then they add higher curvature terms on the gravity side. This introduces an additional parameter, and a suitable choice for this second parameter allows the coupling to remain just about in the okay range. One would expect these higher-order terms to be present, but in principle I’d think the coupling shouldn’t be an independent parameter. In any case, this still doesn’t fit both the RHIC and the LHC data.

Since the interpretation of the data depends on the reconstruction of the effective temperature at the collision, they then speculate that maybe the temperature values are off by 10% or so, in which case their calculation would fit the data just fine.

This model is clearly an improvement though I can’t say I am terribly convinced. What seems to become increasingly clear though is that any successful model for highly energetic heavy ion collisions must use a suitable combination of both weakly and strongly coupled physics. The gauge-gravity correspondence still has a good chance to prove its use for the strongly coupled physics, but that will necessitate getting into all the messy details.

Why quantize gravity?

When I first read DNLee’s story, I mistakenly thought “ofek” is a four letter word, an internet slang for oh-what-the-fucken-heck. Ofek, then, is all I have to say about my recent grant proposals being declined, one after the other. Ah, scrape the word “recent” – the Swedish Research Council hasn’t funded any one of my project proposals since I moved to Sweden in 2009. So all I can do is to continue to write papers as what feels like the only person working on quantum gravity in Northern Europe. Most painfully, I have had to turn away many a skilled and enthusiastic student wanting to work on quantum gravity phenomenology.

To add insult to injury, the Swedish Research Council publicly lists the titles of the winning proposals. You win if your research contains either “nano” or “neuro”, promises a cure for cancer, green energy, or a combination of the above. The strategy is designed for a bad return on investment. Money goes where lots of people poke the always same questions. If many flies circle the same spot there must be shit to find, the thinking is, let’s throw money at it. Our condensed matter people have no funding issues.

As nations face economic distress and support for basic research dwindles, why would anybody want to work on quantum gravity. Srsly. This question keeps coming back to me; its recurrence time conspicuously coincides with the funding agencies’ call cycles. It factors into my reflection index that women, I read, are drawn to occupations that help others, also occupations where they can use their allegedly superior social and language skills. What’ wrong with me? Why quantize gravity if I could cure cancer instead? Or at least write proposals promising I will, superior languages skills and all.

Modern medicine wouldn’t exist without the technologies that have become possible by breakthroughs in physics. There wouldn’t be any nano or neuro without imaging and manipulating quantum things and without understanding atoms and nucleons. Without basic research in physics, there wouldn’t be CT scans, there wouldn’t be NMR, nuclear power, digital cameras, and there wouldn’t be optical fibers for endovenous laser treatment.

At this point in history we still build on the new ground discovered by physicists a century ago. But the only way we can continue improving our circumstances of living is to increase our understanding of the fundamental laws of nature. And at the very top of the list there’s the question what is space and time, and how can we manipulate quantum objects. In my mind, these questions are intimately related. In my mind, that’s the ground the technologies of the next centuries will be built upon. In my mind, that’s how my occupation contributes to society – not to this generation maybe, but to the coming ones. Quantum gravity, quantum information, and the foundations of quantum mechanics are what will keep medicine advancing when nano and neuro has peaked and busted. Which will happen, inevitably, sooner or later.

So why quantum gravity? Because we know our knowledge of nature is incomplete. There must be more to find than we have found so far.

The search for quantum gravity is often portrayed as a search for unification. All other interactions besides gravity are quantized, there’s no unifying framework and that’s what physicists are looking for. It’s an argument from aesthetics, and it’s an argument I don’t like. Yes, it is unaesthetic to have gravity stand apart, but the reason we look for a quantum theory of gravity is much stronger than that: We know that unquantized gravity is incomplete and it is inconsistent with quantum theory. It isn’t only that we don’t know how to quantize gravity and that bugs us, we actually know that the combination of theories we presently have does not describe space and time at the fundamental level.

The strongest evidence for this inconsistency are the occurrence of singularities in unquantized gravity and the black hole information problem. The singularities are a sign that the unquantized theory breaks down and is incomplete. The black hole information problem shows that combining unquantized gravity with quantized matter is inconsistent – the result of combining them is incompatible with quantum theory.

Most importantly, we know that quantum particles can exist in superposition states, they can be neither here nor there. We also know that all particles carry energy and all energy creates a gravitational field. We thus know that the gravitational field of a superposition must exist, but we don’t know what it is. If the electron goes through both the left and the right slit, what happens to its gravitational field? Infuriatingly, nobody knows.

Nobody knows isn’t to say that nobody has an answer. Everybody seems to have an answer, the flies are circling happily. So I’ve made it my job to find out how we can ever know, which leads me to the question how to experimentally test quantum gravity. Without finding observational evidence, quantum gravity should be taught in the math or philosophy departments, not in the physics departments.

The irony is that quantum gravity phenomenology is as safe an investment as it gets in science. We know the theory must exist. We know that the only way it can be scientific is to make contact to observation. Quantum gravity phenomenology will become reality as surely as volcanic ash will drift over Central Europe again.

Every time I go down this road of self-doubts, I come out at the same place, which is right here in my office with my notepad and the books and the piles of papers. Quantum gravity is the next level of fundamental laws. The theory has to be connected to experiment. Quantum gravity is my contribution to the future of our societies and to help advance life on planet Earth. And, so I hope, space exploration, eventually. Because I really want ask those aliens a few things.

Today I talked to a professional photographer. Between the apertures and external flash settings and my attempt to produce a smile, I learned that he too has to write proposals for project funding. In his case, that’s portraits taken by a method which, I gather, isn’t presently widely used and not very popular with the Swedes. It’s neither nano nor neuro and it wasn’t funded.

Money is time, and time flies, and so in the end the most annoying part is all the waste of time that I could have used better than searching for pretty adjectives to decorate my proposals. Your tax money at work. Neuro-gravity anybody? Nano is also a four-letter word.

Book review: “Free Radicals” by Michael Brooks

Free Radicals: The Secret Anarchy of Science
By Michael Brooks
Profile Books Ltd (2011)

“Free Radicals” is a selection of juicy bits from the history of science, telling stories about how scientists break and bend rules to push onward and forward, how they fight, cheat and lie to themselves and to others. The reader meets well-known scientists (mostly dead ones) who fudged data, ignored evidence, flirted their way to lab equipment, experimented on themselves or family members, took drugs, publicly ridiculed their colleagues, and wiggled their way out of controversy with rhetorical tricks.

The book is very enjoyable as a collection of anecdotes. It is fast flowing, does not drown the reader in historical, biographical or scientific details, and it is well-written without distracting from the content. (I’ve gotten really tired of authors who want to be terribly witty and can’t leave you alone for a single paragraph).

Michael Brooks tries to convince the reader that there is a lesson to be learned from these anecdotes, which is that science thrives only because of scientists behaving badly in one way or the other. He refers to this as the “secret anarchy of science”. He actually disagrees with himself on that, as it becomes very clear from his stories that far from being anarchic, science is an elitist meritocracy that grandfathers achievers and is biased against newcomers, in particular members of minorities. Anarchy is unstable – it’s a vacuum that gets rapidly filled with rules and hierarchies – and academia is full with these unwritten rules. Science is not and has never been anything like anarchic, neither secretly nor openly, though the house of science has arguably housed its share of rebels.

Worse than that misuse of the term ‘anarchy’ is that Brooks tries to construct his lesson from a small and hand-picked selection of examples and ignores the biggest part of science, which is business as usual. As we discussed in this earlier post, the question is not whether there are people who bent rules and were successful, but how many people bent rules and just wasted everybody’s time, a problem to which no thought is given in the book.

Luckily, Brooks does not elaborate on his lessons too much. The reader gets some of this in the beginning and then again in the end, where Brooks also uses the opportunity and tries to encourage scientists to engage more in policy making. Again he disagrees with himself. After he spent two hundred pages vividly depicting how scientists care about nothing but making progress on their research, arguing that this single-mindedness is the secret to scientific progress, in the last chapter he now wants scientists to engage more in politics, but that square block won’t fit through the round hole.

In summary, the book is a very enjoyable collection of anecdotes from the history of science. It would have benefitted if the author had refrained from trying to turn it into lessons about the sociology of science.

10 Misconceptions about Free Will

If somebody talks about a “question that science cannot answer” what they really mean is a question they don’t want an answer to. Science can indeed be very disrespectful to people’s beliefs. I accept the wish to believe rather than know, but I get pissed off if somebody wraps their wishful thinking as an actual argument.

“Do humans have free will?” is a question I care deeply about. It lies at the heart of how we understand ourselves and arrange our living together. It also plays a central role for the foundations of quantum mechanics. In my darker moods I am convinced we’re not making any progress in quantum gravity because physicists aren’t able to abandon their belief in free will. And from the foundations of quantum mechanics the roadblock goes all the way up to neuroscience and politics.

Yes, I just blamed the missing rational discussion about free will for most of mankind’s problems, including quantum gravity.

Suggesting the absence of free will is apparently still an upsetter in the 21st century. You’re not supposed say it because allegedly just saying it makes other people immoral. Do you feel it already? How the immorality creeps from my blogpost into your veins? Aren’t you afraid to read on?

There’s no need to worry. This angst stems from a misunderstanding of what it means not to have free will. In this blogpost I address the most common misunderstandings, but before that let me explain why, to our best present knowledge of the laws of nature, you do not have free will. So, first the facts.

Fact 1: Everything in the universe, including you and your brain, is composed of elementary particles. What these particles do is described by the fundamental laws of physics. Everything else follows from that, in principle.

It follows in principle, but it is arguably not very practical to describe, say, human anatomy in terms of quarks and electrons. Instead, scientists of other disciplines use larger constituents and try to describe their behavior. This practical usefulness of increasingly larger scales, variables, and constituents, and the approximate accuracy of that procedure, is called “emergence”. All of these properties however derive from the fundamental description – in principle. That’s what is called reductionism.

The idea that the emergent properties of large systems do not derive from the fundamental description is called “strong emergence”. Some people like to claim that just because a system (eg your brain) consists of many constituents it is somehow exempt from reductionism and something (free will) “strongly emerges”. But fact is, there exists no known example where this happens, and there exists no known theory – not even an untested one – for how strong emergence can work. It is entirely irrelevant if your large system has adjectives like open, chaotic, complex or self-aware. It’s still just a really large number of particles that obey the fundamental laws of nature. Presently, believing in strong emergence is on the same intellectual level as believing in an immortal soul or in ESP.

Fact 2: All known fundamental laws of nature are either deterministic or random. To our best present knowledge, the universe evolves in a mixture of both, but just exactly how that mixture looks like will not be relevant in the following.

Having said that, I need to explain just exactly what I mean by the absence of free will:

a) If your future decisions are determined by the past, you do not have free will.

b) If your future decisions are random, meaning nothing can influence them, you do not have free will.

c) If your decisions are any mixture of a) and b) you do not have free will either.

In the above, you can read “you” as “any subsystem of the universe”, the details don’t matter. It follows straight from Fact 1 and Fact 2 that according to the definition of the absence of free will in a), b), c) free will is incompatible with what we presently know about nature.

I acknowledge that there are other ways to define free will. Some people for example want to call a choice “free” if nobody else could have predicted it, but for what I am concerned this is just pseudo free will.

Right! I didn’t say anything about neurobiology, the consciousness or the subconsciousness or about people pushing buttons. I don’t have to. For free will to exist it is necessary that free will be allowed by the fundamental laws of physics. It is necessary, but not sufficient: If you could make free will compatible with the laws of physics, it might still be that neurobiology finds your brain can’t make use of that option. Physics cannot tell you that free will exists, but it can tell you that it doesn’t exist. And that’s what I just told you.

Note that I neither claim strong emergence does not exist, nor do I say that a fundamental law has to be a mixture of determinism and randomness. What I am saying is this: If you want to argue that free will exists because strong emergence works, or there is an escape from determinism or randomness, then I want to see an example for how this is supposed to work.

Then let me address the main misconceptions:

1. If you do not have free will you cannot or do not have to make decisions.
   
   Regardless of whether you have free will or not, your brain performs evaluations and produces results and that’s what it means to make a decision. You cannot not make decisions. Just because your thought process is deterministic doesn’t mean the process doesn’t have to be executed in real time. The same is true if it has a random component.
   
   This misconception stems from a split-personality perspective: People picture themselves as trying to make a decision but being hindered by some evil free-will-defying law of nature. That is nonsense of course. You are whatever brain process works with whatever input you receive. If you don’t have free will, you’ve never had free will and so far you’ve lived just fine. You can continue to think the same way you’ve always thought. You’ll do that anyway.
   
   
2. If you do not have free will you have no responsibility for your actions.
   
   This misconception also comes from the split-personality perspective. You are what makes the decisions (takes in information and processes it) and performs the actions (acts on the results). If your actions are problematic for other people, you are the source of the problem and they’ll take measures to solve that problem. It’s not like they have any choice… If the result of your brain processes makes other people’s lives difficult, it’s you who will be blamed, locked away, sent to psychotherapy or get kicked where it really hurts. It is entirely irrelevant that your faulty information processing was inscribed in the initial conditions of the universe, the relevant question is what your future will bring if others try to get rid of you. The word ‘responsibility’ is just a red herring because it’s both ill-defined and unnecessary.
   
   
3. People should not be told they don’t have free will because that would undermine the rules of morally just societies.
   
   This misconception goes back to the first two and is based the idea that if people don’t have free will they don’t have any reason to reflect on their actions and to consider other people’s wellbeing. This is wrong of course. Evolution has endowed us with the ability to estimate the future impact of our actions and natural selection preferred those who acted so that others were supportive of their needs, or at least not outright aggressive towards them. If people don’t have free will they still have to make decisions and they still will be blamed for making other peoples’ lives miserable.
   
   Occasionally somebody refers me to this study which allegedly shows that “Encouraging a Belief in Determinism Increases Cheating.” This study also encourages misconception 2, so the finding is hardly surprising. I would like to see this repeated with the added explanation that the test subjects are of course still making decisions, regardless of whether the outcome was predetermined or not, and of course it matters what that outcome is.
   
   
4. If you do not have free will your actions can be predicted.
   
   Even if your brain processes were predictable in principle it is highly questionable anybody could do this in practice. Besides, as I explained above, these processes might have a random component that is even in principle not predictable. It is presently not very well understood just exactly how relevant such a random component might be.
   
   
5. If you do not have free will the future is determined by the past.
   
   Same misconception that underlies 4. Randomness is for all we presently know a component of the fundamental laws. In this case the future is not determined by the past, but neither do you have free will because nothing can influence this randomness.
   
   
6. If we do not have free will we can derive human morals.
   
   I don’t know why people get so hung up on this. Morals and values are just thought patterns that humans use to make decisions. Their relevance stems from these thought patterns being shared by many in similar versions. If the fundamental laws of the universe are deterministic and if you were really good at computation, then you could in principle compute them. In practice nobody can do it.
   
   It is also not actually what people mean when they talk about ‘deriving morals’. What they actually mean is whether one can derive what humans “should do”. That however one can only do once a goal is defined – “should do” to achieve what? – and that just moves the question elsewere. Science can’t answer this question because it’s ill-defined. Science can’t tell what anybody should be doing because that’s a meaningless phrase. Science can, in the best case, just tell what they will be doing.
   
   More to the point is (as I explained in length in this earlier blogpost) that at any time there are questions that science cannot answer because the knowledge we have is insufficient. These are the questions we leave to political decision. All the “should do” questions are of this type.
   
   
7. Free will is impossible.
   
   Not necessarily. As I explained here (paper here) it is possible to conceive of laws of nature that are neither deterministic nor random and that can plausibly be said to allow for free will. Alas, we do not presently have any evidence whatsoever that this is realized in nature and neither is it known whether this is even compatible with the laws of nature that we know. Send me a big enough paycheck and give me some years and I’ll find out.
   
   
8. You need to be a neuroscientist to talk about free will.
   
   We associate free will with autonomous systems that make choices, with activation patterns in human brains, which is the realm of neurobiology. However, your brain as much as every other part of the universe obeys the fundamental laws of nature. That these fundamental laws allow for free will is a necessary condition for free will to exist, and these laws fall into the realm of physics.
   
   
9. You need to be a philosopher to be allowed to talk about free will.
   
   If you want to know how everybody and their dog throughout the history of mankind defined free will, you had better read several thousand years’ worth of discussion on the issue. But I don’t like to waste time on definitions and I don’t see the merit in listing all variants of free will that somebody sometime has come up with. I told you above very clearly what I mean with ‘absence of free will’ and that is the core of the problem in two paragraphs. If you want to name this other than “free will”, I don’t care, it’s still the core of the problem.
   
   
10. If we do not have free will we cannot do science.
    
    I added this misconception because this comes up every time I talk about superdeterminism in quantum mechanics. The basic reason we can do science is that our universe evolves so that we are able to extract regularities in that evolution. You need to be able to measure what happens to similar systems under similar conditions and find patterns in that. But just how these similar systems came about is entirely irrelevant. It does not matter, for example, whether the laboratory and all the detector settings were predetermined already at the beginning of the universe. All that matters is that there are similar systems, that detections can be done, and the results are processed by you (or some computer) to extract regularities.

Let me be very clear that I didn’t say free will doesn’t exist. I said it doesn’t exist according to our best present knowledge of how nature works. If you want to hang on to free will you better come up with a really good idea how to make that compatible with existing scientific knowledge. I want to see progress, I don’t just want to see smoke screens of “strong emergence” or “qualia” and other fantasies.

Next Year’s News

As the year nears its end, my feed is full with last year’s news. For balance, I want to give some space to next year’s news. What do you think will be in the news next year?

In the very short run, technological developments aren’t so difficult to foresee, mostly because our brains all tick similarly. But by the time I have an idea, it’s highly likely somebody is already working on it. I’m not much of an inventor.

After the babies were born for example I remarked to Stefan that it’s about time somebody comes up with a high-tech diaper that sends me an email if full. Done.

Or this: For some years now, I keep reading about transcranial magnetic stimulation that allegedly boosts learning ability or intelligence in general. However, intelligence is a highly complex trait and I don’t buy a word of this. But wouldn’t the world be a much better place if we’d just sleep better? And don’t we know so much more about the brain in sleep-mode than in learning-mode? So why not use transcranial magnetic stimulation to treat insomnia? Somebody somewhere is working on that.

Here are three of my speculations that I haven’t yet heard much about:

Robotic brain extension

Insects’ brains can hooked up to chips and be remote controlled. But rather than using a computer to control a biological neural network, it would be much cooler if one could integrate the bio-brain to improve the tasks that robots are typically bad at. Balance for example is such a case that is extremely difficult for robots, yet the smallest bird-brain can easily balance a body on one leg, thanks to million of years of evolution. Can one engineer the both to work together, provided some ethics committee nods approval?

Inaudibility shield

Forget about invisibility shields, nobody wants to be invisible, just look at youtube. What we really need in the days of iPhones and people talking to their glasses is an inaudibility shield. I neither want to hear your phone calls, nor do you want to hear mine. Somebody please work on this.

The conscious subconsciousness

I read all the time about computers that are brain-controlled or most recently brain to brain communication. However, the former is still far too cumbersome and will remain so for a long time, and the latter creeps out most people. So let’s stick with one head and just route signals from the unconscious parts of our brain activity to the conscious parts and vice versa. Imagine for a moment how dramatically the world might change if we had the ability to readjust hormonal balance or heart rate.

Happy New Year! May it be a good one for you.

The finetuned cube

The standard model of parenthood.

The kids are almost three years now and I spend a lot of time picking up wooden building blocks. That’s good for your health in many ways, for example by the following brain gymnastics.

When I scan the floor under the couch for that missing cube, I don’t expect to find it balancing on a corner - would you? And in the strange event that you found it delicately balanced on a corner, would you not expect to also find something, or somebody, that explains this?

When physicists scanned the LHC data for that particle, that particle you’re not supposed to call the god-particle, they knew it would be balancing on a corner. The Higgs is too light, much too light, that much we knew already. And so, before the LHC most physicists expected that once they’d be able to see the Higgs, they’d also catch a glimpse of whatever it was that explained this delicate balance. But they didn’t.

It goes under the name ‘naturalness,’ the belief that a finely tuned balance requires additional explanation. “Naturally” is the physicist’s way of saying “of course”. Supersymmetry, neatified to Susy, was supposed to be the explanation for finetuning, but Susy has not shown up, and neither has anything else. The cube stands balanced on the corner, seemingly all by itself.

Of course those who built their career on Susy cross-sections are not happy. They are now about to discard naturalness, for this would mean Susy could hide everywhere or nowhere, as long as it’s not within reach of the LHC. And beyond the LHC there’s 16 orders of magnitude space for more papers. Peter Woit tells this tale of changing minds on his blog. The denial of pre-LHC arguments is so bold it deserves a book (hint, hint), but that’s a people-story and not mine to tell. Let me thus leave aside the psychological morass and the mud-throwing, and just look at the issue at hand: Naturalness, or its absence respectively.

I don’t believe in naturalness, the idea that finetuned parameter values require additional explanation. I recognize that it can be a useful guiding principle, and that apparent finetuning deserves a search for its cause, but it’s a suggestion rather than a requirement.

I don’t believe in naturalness because the definition of finetuning itself is unnatural in its focus on numerical parameters. The reason physicists focus on numbers is that numbers are easy to quantify - they are already quantified. The cosmological constant is 120 orders of magnitude too large, which is bad with countably many zeros. But the theories that we use are finetuned to describe our universe in many other ways. It’s just that physicists tend to forget how weird mathematics can be.

We work with manifolds of integer dimension that allow for a metric and a causal structure, we work with smooth and differentiable functions, we work with bounded Hamiltonians and hermitian operators and our fibre bundles are principal bundles. There is absolutely no reason why this has to be, other than that evidence shows it describes nature. That’s the difference between math and physics: In physics you take that part of math that is useful to explain what you observe. Differentiable functions, to pick my favorite example because it can be quantified, have measure zero in the space of all functions. That’s infinite finetuning. It’s just that nobody ever talks about it. Be wary whenever you meet the phrase “of course” in a scientific publication – infinity might hide behind it.

This finetuning of mathematical requirements appears in form of axioms of the theory – it’s a finetuning in theory space, and a selection is made based on evidence: differentiable manifolds with Lorentzian metric and hermitian operators work. But selecting the value of numerical parameters based on observational evidence is no different from selecting any other axiom. The existence of ‘multiverses’ in various areas of physics is similarly a consequence of the need to select axioms. Mathematical consistency is simply insufficient as a requirement to describe nature. Whenever you push your theory too far and ties to observation loosen too much, you get a multiverse.

My disbelief in naturalness used to be a fringe opinion and it’s gotten me funny looks on more than one occasion. But the world refused to be as particle physicists expected, naturalness rapidly loses popularity, and now it’s my turn to practice funny looks. The cube, it’s balancing on a tip and nobody knows why. In desparation they throw up their hands and say “anthropic principle”. Then they continue to produce scatter plots. But it’s a logical fallacy called ‘false dichotomy’, the claim that if it’s not natural it must be anthropic.

That I don’t believe in naturalness as a requirement doesn’t mean I think it a useless principle. If you have finetuned parameters, it will generally be fruitful to figure out the mechanism of finetuning. This mechanism will inevitably constitute another incidence of finetuning in one way or the other, either in parameter space or in theory space. But along the line you can learn something, while falling back on the anthropic principle doesn’t teach us anything. (In fact, we already know it doesn’t work.) So if you encounter finetuning, it’s a good idea to look for a mechanism. But don’t expect that mechanism to work without finetuning itself - because it won’t.

If that was too many words, watch this video:


It’s a cube that balances on a tip. If your resolution scale is the size of the cube, all you will find is that it’s mysteriously finetuned. The explanation for that finetuned balance you can only find if you look into the details, on scales much below the size of the cube. If you do, you’ll find an elaborate mechanism that keeps the cube balanced. So now you have an explanation for the balance. But that mechanism is finetuned itself, and you’ll wonder then just why that mechanism was there in the first place. That’s the finetuning in theory space.

Now in the example with the above video we know where the mechanism originated. Metaphors all have their shortcomings, so please don’t mistake me for advocating intelligent design. Let me just say that the origin of the mechanism was a complex multi-scale phenomenon that you’d not be able to extract in an effective field theory approach. In a similar way, it seems plausible to me that the unexplained values of parameters in the standard model can’t be derived from any UV completion by way of an effective field theory, at least not without finetuning. The often used example is that hundreds of years ago it was believed that the orbits of planets have to be explained by some fundamental principles (regular polygons stacked inside each other, etc). Today nobody would assign these numbers fundamental relevance.

Of course I didn’t find a cube balancing on a tip under the couch. I didn’t find the cube until I stepped on it the next morning. I did however quite literally find a missing puzzle piece – and that’s as much as a theoretical physicist can ask for.

Merry Christmas and Happy Holidays

I wish you all happy holidays and a peaceful Christmas time!

The next days will be a slow time on the blog as we're working our way through the holidays, the kid's 3rd birthday, and new year, with all the family and friend's visits that come with it. Back to business next year - enjoy the silence :)

Searching for Spacetime Defects

Defects in graphene.
Image source: IOP.

Whether or not space and time are fundamentally discrete is one of the central questions of quantum gravity. Discretization is a powerful method to tame divergences that plague the quantization of gravity, and it is thus not surprising that many approaches to quantum gravity rely on some discrete structure, may that be condensed matter analogies, triangulations, or approaches based on networks. One expects that discretization explains the occurrence of singularities in general relativity as unphysical, much like singularities in hydrodynamics are merely mathematical artifacts that appear because on short distances the fluid approximation for collections of atoms is no longer applicable.

But finding experimental evidence for space-time discreteness is difficult because this structure is at the Planck scale and thus way beyond what we can directly probe. The best tests for such discrete approaches thus do not rely on the discreteness itself but on the baggage it brings, such as violations or deformations of Lorentz-symmetry that can be very precisely tested. Alas, what if the discrete structure does not violate Lorentz-symmetry? That is the question I have addressed in my two recent papers.

In discrete approaches to quantum gravity, space-time is not, fundamentally, a smooth background. Instead, the smooth background that we use in general relativity – the rubber sheet on which the marbles roll – is only an approximation that becomes useful at long distances. The discrete structure itself may be hard to test, but in any such discrete approach one expects the approximation of the smooth background to be imperfect. The discrete structure will have defects, much like crystals have defects, just because perfection would require additional explanation.

The presence of space-time defects affects how particles travel through the background, and the defects thus become potentially observable, constituting indirect evidence for space-time discreteness.To be able to quantify the effects, one needs a phenomenological model that connects the number and type of defects to observables, and can in return serve to derive constraints on the prevalence and properties of the defects.

In my papers, I distinguished two different types of defects: local defects and non-local defects. The requirement that Lorentz-invariance is maintained (on the average) turned out to be very restrictive on what these defects can possibly do.

The local defects are similar to defects in crystals, except that they are localized both in space and in time. These local defects essentially induce a violation of momentum conservation. This leads to a fairly straight-forward modification of particle interactions whenever a defect is encountered that makes the defects potentially observable even if they are very sparse.

The non-local defects are less intuitive from the particle-physics point of view. They were motivated by what Markopoulou and Smolin called ‘disordered locality’ in spin-networks, just that I did not, try as I might, succeed in constructing a version of disordered locality compatible with Lorentz-invariance. The non-local defects in my paper are thus essentially the dual of the local defects, which renders them Lorentz-invariant (on the average). Non-local defects induce a shift in position space in the same way that the local defects induce a shift in momentum space.

I looked at a bunch of observable effects that the presence of defects of either type would lead to, such as CMB heating (from photon decay induced by scattering on the local defects) or the blurring of distant astrophysical sources (from deviations of photons from the lightcone caused by non-local defects). It turns out that generally the constraints are stronger for low-energetic particles, in constrast to what one finds in deformations of Lorentz-invariance.

Existing data give some pretty good constraints on the density of defects and the parameters that quantify the scattering process. In the case of local defects, the density is roughly speaking less than one per fm⁴. That’s an exponent, not a footnote: It has to be a four-volume, otherwise it wouldn’t be Lorentz-invariant. For the non-local defects the constraints cannot as easily be summarized in a single number because they depend on several parameters, but there are contour plots in my papers.

The constraints so far are interesting, but not overwhelmingly exciting. The reason is that the models are only for flat space and thus not suitable to study cosmological data. To make progress, I'll have to generalize them to curved backgrounds. I also would like to combine both types of defects in a single model. I am presently quite excited about this because there is basically nobody who has previously looked at space-time defects, and there’s thus a real possibility that analyzing the data the right way might reveal something unexpected. And into the other direction, I am looking into a way to connect this phenomenological model to approaches to quantum gravity by extracting the parameters that I have used. So, you see, more work to do...

Mathematics, the language of nature. What are you sinking about?

Swedish alphabet. Note lack of W. [Source]

“I was always bad at math” is an excuse I have heard many of my colleagues complain about. I’m reluctant to join their complaints. I’ve been living in Sweden for four years now and still don’t speak Swedish. If somebody asks me, I’ll say I was always bad with languages. So who am I to judge people for not wanting to make an effort with math?

People don’t learn math for the same reason I haven’t learned Swedish: They don’t need it. It’s a fact that my complaining colleagues are tiptoeing around but I think we’d better acknowledge it if we ever want to raise mathematic literacy.

Sweden is very welcoming to immigrants and almost everybody happily speaks English with me, often so well that I can’t tell if they’re native Swedes or Brits. At my workplace, the default language is English, both written and spoken. I have neither the exposure, nor the need, nor the use for Swedish. As a theoretical physicist, I have plenty of need for and exposure to math. But most people don’t.

The NYT recently collected opinions on how to make math and science relevant to “more than just geeks,” and Kimberly Brenneman, Director of the Early Childhood STEM Lab at Rutgers, informs us that

“My STEM education colleagues like to point out that few adults would happily admit to not being able to read, but these same people have no trouble saying they’re bad at math.”

I like to point out it’s more surprising they like to point this out than this being the case. Life is extremely difficult when one can’t read neither manuals, nor bills, nor all the forms and documents that are sometimes mistaken for hallmarks of civilization. Not being able to read is such a disadvantage that it makes people wonder what’s wrong with you. But besides the basics that come in handy to decipher the fine print on your contracts, math is relevant only to specific professions.

I am lying of course when I say I was always bad with languages. I was bad with French and Latin and as my teachers told me often enough, that was sheer laziness. Je sais, tu sais, nous savons - Why make the effort? I never wanted to move to France. I learned English just fine: it was useful and I heard it frequently. And while my active Swedish vocabulary never proceeded beyond the very basics, I quickly learned Swedish to the extent that I need it. For all these insurance forms and other hallmarks of civilization, to read product labels, street signs and parking tickets (working on it).

I think that most people are also lying when they say they were always bad at math. They most likely weren’t bad, they were just lazy, never made an effort and got away with it, just as I did with my spotty Latin. The human brain is energetically highly efficient, but the downside is the inertia we feel when having to learn something new, the inertia that’s asking “Is it worth it? Wouldn’t I be better off hitting on that guy because he looks like he’ll be able to bring home food for a family?”

But mathematics isn’t the language of a Northern European country with a population less than that of other countries’ cities. Mathematics is the language of nature. You can move out of Sweden, but you can’t move out of the universe. And much like one can’t truly understand the culture of a nation without knowing the words at the basis of their literature and lyrics, one can’t truly understand the world without knowing mathematics.

Almost everybody uses some math intuitively. Elementary logic, statistics, and extrapolations are to some extent hardwired in our brains. Beyond that it takes some effort, yes. The reward for this effort is the ability to see the manifold ways in which natural phenomena are related, how complexity arises from simplicity, and the tempting beauty of unifying frameworks. It’s more than worth the effort.

One should make a distinction here between reading and speaking mathematics.

If you work in a profession that uses math productively or creatively, you need to speak math. But for the sake of understanding, being able to read math is sufficient. It’s the difference between knowing the meaning of a differential equation, and being able to derive and solve it. It’s the difference between understanding the relevance of a theorem, and leading the proof. I believe that the ability to ‘read’ math alone would enrich almost everybody’s life and it would also benefit scientific literacy generally.

So needless to say, I am supportive of attempts to raise interest in math. I am just reluctant to join complaints about the bad-at-math excuse because this discussion more often than not leaves aside that people aren’t interested because it’s not relevant to them. And that what is relevant to them most mathematicians wouldn’t even call math. Without addressing this point, we’ll never convince anybody to make the effort to decipher a differential equation.

But of course people learn all the time things they don’t need! They learn to dance Gangnam style, speak Sindarin, or memorize the cast of Harry Potter. They do this because the cultural context is present. Their knowledge is useful for social reasons. And that is why I think to raise mathematic literacy the most important points are:

Exposure

Popular science writing rarely if ever uses any math. I want to see the central equations and variables. It’s not only that metaphors and analogies inevitably have shortcomings, but more importantly it’s that the reader gets away with the idea that one doesn’t actually need all these complicated equations. It’s a slippery slope that leads to the question what we need all these physicists for anyway. The more often you see something, the more likely you are to think and talk about it. That’s why we’re flooded with frequently nonsensical adverts that communicate little more than a brand name, and that’s why just showing people the math would work towards mathematic literacy.

I would also really like to see more math in news items generally. If experts are discussing what they learned from the debris of a plane crash, I would be curious to hear what they did. Not in great detail, but just to get a general idea. I want to know how the number quoted for energy return on investment was calculated, and I want to know how they arrived at the projected carbon capture rate. I want to see a public discussion of the Stiglitz theorem. I want people to know just how often math plays a role for what shapes their life and the lives of those who will come after us.

Don’t tell me it’s too complicated and people won’t understand it and it’s too many technical terms and, yikes, it won’t sell. Look at the financial part of a newspaper. How many people really understand all the terms and details, all the graphs and stats? And does that prevent them from having passionate discussions about the stock market? No, it doesn’t. Because if you’ve seen and heard it sufficiently often, the new becomes familiar, and people talk about what they see.

Culture

We don’t talk about math enough. The residue theorem in complex analysis is one of my favorite theorems. But I’m far more likely to have a discussion about the greatest songs of the 60s than about the greatest theorems of the 19th century. (Sympathy for the devil.) The origin of this problem is lack of exposure, but even with the exposure people still need the social context to put their knowledge to use. So by all means, talk about math if you can and tell us what you’re sinking about!

The Comeback of Massive Gravity

Massive gravity, a modification of general relativity in which gravitons have mass, has an interesting history. Massive gravity was long believed to be internally inconsistent, but physicists at Stockholm University now claim to have constructed a consistent theory for massive gravity. This theory is a viable alternative to general relativity and can address some of its problems.

In Einstein’s theory of general relativity gravitational waves spread with the speed of light, and the quanta of the gravitational field, the gravitons, are expected to do the same*. To be more precise, gravitons move with the speed of massless particles because they are assumed to be massless. But whether or not a particle is indeed massless is in the end a question of experiment.

Neutrinos were long believed to be massless, but we know today that at least two of them have tiny non-zero masses (whose absolute value has not yet been determined). The mass of the photon is known to be zero to extremely high precision on experimental grounds. But what about gravity? This is a timely question because a small mass would lead to a long-distance modification of general relativity, and present observational evidence left physicists with some puzzles at these long distances, notably dark energy and dark matter.

However, to be able to even properly ask whether gravitons have masses, we need a consistent theory for massive gravity. But making gravitons massive is a challenge for the theoretical physicist. In fact, it was long believed to be impossible.

The problems start when you want to introduce a mass-term into general relativity. For vector fields, you can take a contraction of fields of the form A^νA_ν to stand in front of the mass term. In general relativity the field is the metric tensor, and the only full contractions that you can create without using derivatives are constant: they create a cosmological constant, not a graviton mass. If you want a mass-term in general relativity you need a second two-tensor, that is a field which looks like a metric but isn’t the metric. Theories of this type are also known as ‘bi-metric’. Massive gravity is thus intimately related to bi-metric gravity.

But that’s only the beginning of the problems, a beginning that dates back more than 70 years.

In 1939, Fierz and Pauli wrote down a theory of massive gravity in the perturbative limit. They found that for the theory to be consistent – meaning free of ‘ghosts’ that lead to unphysical instabilities – the parameters in the mass-terms must have specific values. With these values, the theory is viable.

In 1970 however, van Dam and Veltman and, independently, Zukharov, showed that in the Fierz-Pauli approach, the limit in which the mass of the graviton is taken to zero is not continuous and does, contrary to naïve expectations, not reproduce general relativity. Any graviton mass, regardless how small, leads to deviations that can contribute factors of order one to observables, which is in conflict with observation. The Fierz-Pauli theory now seemed theoretically fine, but experimentally ruled out.

Two years later, in 1972, Vainshtein argued that this discontinuity is due to the treatment of the gravitational degrees of freedom in the linearization procedure and can be cured in a full, non-linear, version of massive gravity. Unfortunately, in the same year, Deser and Boulware claimed that any non-linear completion of the Fierz-Pauli approach reintroduces the ghost. So now massive gravity was experimentally fine but theoretically sick.

Nothing much happened in this area for more than 30 years. Then, in the early 2000s, the wormy can was opened again by Arkani-Hamed et al and Creminelli et al, but they essentially confirmed the Deser-Boulware problem.

The situation began to look brighter in 2010, when de Rahm, Gabadadze and Tolley proposed a theory of massive gravity that did not suffer from the ghost-problem in a certain limit. Needless to say, after massive gravity had been thought dead and buried for 40 years, nobody really believed this would work. The de Rahm-Gabadadze approach did not make many friends because the second metric was treated as a fixed background field, and the theory was shown to allow for superluminal propagation (and, more recently, acausality).

However, starting in 2011, Fawad Hassan and Rachel Rosen from Stockholm University (ie next door), succeeded in formulating a theory of massive gravity that does not suffer from the ghost instability. The key to success was a generalization of the de Rahm-Gabadadze approach in which the second metric is also fully dynamic, and the interaction terms between the two metrics take on a specific form. The specific form of the interaction terms is chosen such that it generates a constraint which removes the ghost field. The resulting theory is to best present knowledge fully consistent and symmetric between the two metrics.

(Which, incidentally, explains my involvement with the subject, as I published a paper with a fully dynamic, symmetric, bi-metric theory in 2008, though I wasn’t interested in the massive case and don’t have interaction terms. The main result of my paper is that I ended up in defense committees of Fawad’s students.)

In the last years, the Stockholm group has produced a series of very interesting papers that not only formalizes their approach and shows its consistency, but they also derived specific solutions. This is not a small feat as it is already difficult to find solutions in general relativity if you have only one metric and having two doesn’t make the situation easier. Indeed, not many solutions are presently known, and the known ones have quite strong symmetry assumptions. (More students in the pipe...)

Meanwhile, others have studied how well this modification of general relativity fares as an alternative to ΛCDM. It has been found that massive gravity can fit all cosmological data without the need to introduce an additional cosmological constant. But before you get too excited about this, note that massive gravity has more free parameters than ΛCDM, that being the coupling constants in the interaction terms.

What is missing right now though is a smoking-gun signal, some observation that would allow to distinguish massive gravity from standard general relativity and could be used to distinguish between both. This is presently a very active area of research and one that I’m sure we’ll hear more about.

---

* To be precise, in the classical theory we should be speaking of gravitational waves instead. The frequent confusion between gravitational waves and gravitons, the latter of which only exist in quantized gravity, is a bad habit but forgivable. Far worse are people who say ‘gravity wave’ when they refer to a gravitational wave. A gravity wave is a type of cloud formation and has nothing to do with linearized gravity.

Are irreproducible scientific results okay and just business as usual?

That I even have to write about this tells you how bad it is.

During the last years a lot of attention has been drawn to the prevalence of irreproducible results in science. That published research findings tend to weaken or vanish over time is a pressing problem in particular in some areas of the life sciences, psychology and neuroscience. On the face of it, the issue is that scientists work with too small samples and frequently cherry-pick their data. Next to involuntarily poor statistics, the blame has primarily been put on the publish-or-perish culture of modern academia.

While I blame that culture for many ills, I think here the finger is pointed at the wrong target.

Scientists aren’t interested in publishing findings that they suspect to be spurious. That they do it anyway is because a) funding agencies don’t hand out sufficient money for decent studies with large samples b) funding agencies don’t like reproduction studies because, eh, it’s been done before and c) journals don’t like to publish negative findings. The latter in particular leads scientists to actively search for effects, which creates a clear bias. It also skews meta-studies against null results.

That’s bad, of course.

I will not pretend that physics is immune to this problem, though in physics the issue is, forgive my language, significantly less severe.

A point in case though is the application of many different analysis methods to the same data set. Collaborations have their procedures sorted out to avoid this pitfall, but once the data is public it can be analyzed by everybody and their methods, and sooner or later somebody will find something just by chance. That’s why, every once in while we hear of a supposedly interesting peculiarity in the cosmic microwave background, you know, evidence for a bubble collision, parallel universes, a cyclic universe, a lopsided universe, an alien message, and so on. One cannot even blame them for not accounting for other researchers who are trying creative analysis methods on the same data, because that’s unknown unknowns. And theoretical papers can be irreproducible in the sense of just being wrong, but the vast majority of these just get ignored (and if not the error is often of interest in itself).

So even while the fish at my doorstep isn’t the most rotten one, I think irreproducible results are highly problematic, and I welcome measures that have been taken, eg by Nature magazine, to improve the situation.

And then there’s Jared Horvath, over at SciAm blogs, who thinks irreproducibility is okay, because it’s been done before. He lists some famous historical examples where scientists have cherry-picked their data because they had a hunch that their hypothesis is correct even if the data didn’t support it. Jared concludes:

“There is a larger lesson to be gleaned from this brief history. If replication were the gold standard of scientific progress, we would still be banging our heads against our benches trying to arrive at the precise values that Galileo reported.”

You might forgive Jared, who is a is a PhD candidate in cognitive neuroscience, for cherry picking his historical data, because he’s been trained in today’s publish-and-perish culture. Unfortunately, he’s not the only one who believes that something is okay because a few people in the past succeeded with it. Michael Brooks has written a whole book about it. In “Free Radicals: The Secret Anarchy of Science”, you can read for example

“It is the intuitive understanding, the gut feeling about what the answer should be, that marks the greatest scientists. Whether they fudge their data or not is actually immaterial.”

Possibly the book gets better after this, but I haven’t progressed beyond this page because every time I see that paragraph I want to cry.

The “gut feeling about what the answer should be” does mark great scientists, yes. It also marks pseudoscientists and crackpots, just that you don’t find these the history books. The argument that fudging data is okay because great scientists did it and time proved them right is like browsing bibliographies and concluding that in the past everybody was famous.

I’m not a historian and I cannot set that record straight, but I can tell you that the conclusion that irreproducibility is a necessary ingredient to scientific progress is unwarranted.

But I have one piece of data to make my case, a transcript of a talk given by Irwin Langmuir in the 1950s, published in Physics Today in 1989. It carries the brilliant title “Pathological Science” and describes Langmuir’s first-hand encounters with scientists who had a gut feeling about what the answer should be. I really recommend you read the whole thing (pdf here), but just for the flavor here’s an excerpt:

“Mitogenic rays.
About 1923 there was a whole series of papers by Gurwitsch and others. There were hundreds of them published on mitogenic rays. There are still a few of them being published [in 1953]. I don’t know how many of you have ever heard of mitogenic rays. They are given off by growing plants, living things, and were proved, according to Gurwitsch, to be something that would go through glass but not through quarz. They seemed to be some sort of ultraviolet light… If you looked over these photographic plates that showed this ultraviolet light you found that the amount of light was not so much bigger than the natural particles of the photographic plate, so that people could have different opinions as to whether or not it showed this effect. The result was that less than half of the people who tried to repeat these experiments got any confirmation of it…”

Langmuir relates several stories of this type, all about scientists who discarded some of their data or read output to their favor. None of these scientists has left a mark in the history books. They have however done one thing. They’ve wasted their and other scientist’s time by not properly accounting for their methods.

There were hundreds of papers published on a spurious result – in 1953. Since then the scientific community has considerably grown, technology has become much more sophisticated (not to mention expensive), and scientists have become increasingly specialized. For most research findings, there are very few scientists who are able to conduct a reproduction study, even leaving aside the problems with funding and publishing. In 2013, scientists have to rely on their colleagues much more than was the case 60 years ago, and certainly in the days of Millikan and Galileo. The harm being caused by cherry picked data and non-reported ‘post-selection’ (a euphemism for cherry-picking), in terms of waste of time has increase with the community. Heck, there were dozens of researchers who wasted time (and thus their employers money...) on ‘superluminal neutrinos’ even though everybody knew these results to be irreproducible (in the sense that they hadn’t been found by any previous measurements).

Worse, this fallacious argument signals a basic misunderstanding about how science works.

The argument is based on the premise that if a scientific finding is correct, it doesn’t matter where it came from or how it was found. That is then taken to justify the ignorance of any scientific method (and frequently attributed to Feyerabend). It is correct in that in the end it doesn’t matter exactly how a truth about nature was revealed. But we do not speak of a scientific method to say that there is only one way to make progress. The scientific method is used to increase the chances of progress. It’s the difference between letting the proverbial monkey hammer away and hiring a professional science writer for your magazine’s blog. Yes, the monkey can produce a decent blogpost, and if that is so then that is so. But chances are eternal inflation will end before you get to see a good result. That’s why scientists have quality control and publishing ethics, why we have peer review and letters of recommendation, why we speak about statistical significance and double-blind studies and reproducible results: Not because in the absence of methods nothing good can happen, but because these methods have proven useful to prevent us from fooling ourselves and thereby make success considerably more likely.

Having said that, expert intuition can be extremely useful and there is nothing wrong with voicing a “gut feeling” as long as it is marked as such. It is unfortunate indeed that the present academic system does not give much space for scientists to express their intuition, or maybe they are shying away from it. But that’s a different story and shell be told another time.

So the answer to the question posed in the title is a clear no. The question is not whether science has progressed despite the dishonest methods that have been employed in the past, but how much better if would have progressed if that had not been so.

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I stole that awesome gif from over here. I don't know its original source.

The three phases of space-time

If life grows over your head, your closest pop psy magazine recommends dividing it up into small, manageable chunks. Physicists too apply this method in difficult situations. Discrete approximations – taking a system apart into chunks – are enormously useful to understand emergent properties and to control misbehavior, such as divergences. Discretization is the basis of numerical simulations, but can also be used in an analytic approach, when the size of chunks is eventually taken towards zero.

Understanding space and time in the early universe is such a difficult situation where gravity is misbehaved and quantum effects of gravity should become important, yet we don’t know how to deal with them. Discretizing the system and treating it similar to other quantum systems is the maybe most conservative approach one can think of, yet it is challenging. Normally, discretization is used for a system within space and time. Now it is space and time themselves that are being discretized. There is no underlying geometry as reference on which to discretize.

Causal Dynamical Triangulations (CDT), pioneered by Loll, Ambjørn and Jurkiewicz, realizes this most conservative approach towards quantum gravity. Geometry is decomposed into triangular chunks (or their higher-dimensional versions respectively) and all possible geometries are summed over in a path integral (after Wick-rotation) with the weight given by the discretized curvature. The curvature is encoded in the way the chunks are connected to each other. The term ‘causal’ refers to a selection principle for geometries that are being summed over. In the end, the continuum limit can be taken, so this approach in an by itself doesn’t mean that spacetime fundamentally is discrete, just that it can be approximated by a discretization procedure.

The path integral that plays the central role here is Feynman’s famous brain child in which a quantum system takes all possible paths, and observables are computed by suitably summing up all possible contributions. It is the mathematical formulation of the statement that the electron goes through both slits. In CDT it’s space-time that goes through all allowed chunk configurations.

Evaluating the path integral of the triangulations is computationally highly intensive, but simple universes can now be simulated numerically. The results that have been found during the last years are promising: The approach produces a smooth extended geometry that appears well-behaved. This doesn’t sound like much, but keep in mind that they didn’t start with anything resembling geometry! It’s discrete things glued together, but it reproduces a universe with a well-behaved geometry like the one we see around.

Or does it?

The path integral of CDT contains free parameters, and most recently the simulations found that the properties of the universe it describes depend on the value of the parameters. I find this very intriguing because it means that, if space-time's quantum properties are captured by CDT, then space-time has various different phases, much like water has different phases.

In the image below you see the phase-diagram of space-time in CDT.

CDT phase diagram of space-time.
After Fig 5 in 1302.2173

The parameter κ is proportional to the inverse of Newton’s constant, and the parameter Δ quantifies the (difference in the) abundance of two different types of chunks that space-time is built up of. The phase marked C in the upper left, with the Hubble image, is where one finds a geometry resembling our universe. In the phase marked A to the right space-time falls apart into causally disconnected pieces. In the phase marked B at the bottom, space-time clumps together into a highly connected graph with a small diameter that doesn’t resemble any geometry. The numerical simulations indicate that the transition between the phases C and A is first order, and between C and B it’s second order.

In summary, in phase A everything is disconnected. In phase B everything is connected. In phase C you can share images of your lunch with people you don’t know on facebook.

Now you might say, well, but the parameters are what they are and facebook is what it is. But in quantum theory, parameters tend to depend on the scale, that is the distance or energies by which a system is probed. Physicists say “constant’s run”, which just rephrases the somewhat embarrassing statement that a constant is not constant. Since our universe is not in thermal equilibrium and has cooled down from a state of high temperature, constants have been running, and our universe can thus have passed through various phases in parameter space.

Of course it might be that CDT in the end is not the right way to describe the quantum properties of gravity. But I find this a very interesting development, because such a geometric phase transition might have left observable traces and brings us one step closer to experimental evidence for quantum gravity.

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You can find a very good brief summary of CDT here, and the details eg in this paper.

Images used in the background of the phase-diagram, are from here, here and here.