Wednesday, January 17, 2018

Pure Nerd Fun: The Grasshopper Problem

illustration of grasshopper.
It’s a sunny afternoon in July and a grasshopper lands on your lawn. The lawn has an area of a square meter. The grasshopper lands at a random place and then jumps 30 centimeters. Which shape must the lawn have so that the grasshopper is most likely to land on the lawn again after jumping?

I know, sounds like one of these contrived but irrelevant math problems that no one cares about unless you can get famous solving it. But the answer to this question is more interesting than it seems. And it’s more about physics than it is about math or grasshoppers.

It turns out the optimal shape of the lawn greatly depends on how far the grasshopper jumps compared to the square root of the area. In my opening example this ratio would have been 0.3, in which case the optimal lawn-shape looks like an inkblot

From Figure 3 of arXiv:1705.07621

No, it’s not round! I learned this from a paper by Olga Goulko and Adrian Kent, which was published in the Proceedings of the Royal Society (arXiv version here). You can of course rotate the lawn around its center without changing the probability of the grasshopper landing on it again. So, the space of all solutions has the symmetry of a disk. But the individual solutions don’t – the symmetry is broken.

You might know Adrian Kent from his work on quantum foundations, so how come his sudden interest in landscaping? The reason is that problems similar to this appear in certain types of Bell-inequalities. These inequalities, which are commonly employed to identify truly quantum behavior, often end up being combinatorial problems on the unit sphere. I can just imagine the authors sitting in front of this inequality, thinking, damn, there must be a way to calculate this.

As so often, the problem isn’t mathematically difficult to state but dang hard to solve. Indeed, they haven’t been able to derive a solution. In their paper, the authors offer estimates and bounds, but no full solution. Instead what they did (you will love this) is to map the problem back to a physical system. This physical system they configure so that it will settle on the optimal solution (ie optimal lawn-shape) at zero temperature. Then they simulate this system on the computer.

Concretely, the simulate the lawn of fixed area by randomly scattering squares over a template space that is much larger than the lawn. They allow a certain interaction between the little pieces of lawn, and then they calculate the probability for the pieces to move, depending on whether or not such a move will improve the grasshopper’s chance to stay on the green. The lawn is allowed to temporarily go into a less optimal configuration so that it will not get stuck in a local minimum. In the computer simulation, the temperature is then gradually decreased, which means that the lawn freezes and thereby approaches its most optimal configuration.

In the video below you see examples for different values of d, which is the above mentioned ratio between the distance the grasshopper jumps and the square root of the lawn-area:

For very small d, the optimal lawn is almost a disc (not shown in the video). For increasingly larger d, it becomes a cogwheel, where the number of cogs depends on d. If d increases above approximately 0.56 (the inverse square root of π), the lawn starts falling apart into disconnected pieces. There is a transition range in which the lawn doesn’t seem to settle on any particular shape. Beyond 0.65, there comes a shape which they refer to as a “three-bladed fan”, and after that come stripes of varying lengths.

This is summarized in the figure below, where the red line is the probability of the grasshopper to stay on the lawn for the optimal shape:
Figure 12 of arXiv:1705.07621

The authors did a number of checks to make sure the results aren’t numerical artifacts. For example, they checked that the lawn’s shape doesn’t depend on using a square grid for the simulation. But, no, a hexagonal grid gives the same results. They told me by email they are looking into the question whether the limited resolution might hide that the lawn shapes are actually fractal, but there doesn’t seem to be any indication for that.

I find this a super-cute example for how much surprises seemingly dull and simple math problems can harbor!

As a bonus, you can get a brief explanation of the paper from the authors themselves in this brief video.

Tuesday, January 16, 2018

Book Review: “The Dialogues” by Clifford Johnson

Clifford Johnson is a veteran of the science blogosphere, a long-term survivor, around already when I began blogging and one of the few still at it today. He is professor at the Department of Physics and Astronomy at the University of Southern California (in LA).

I had the pleasure of meeting Clifford in 2007. Who’d have thought back then that 10 years later we would both be in the midst of publishing a popular science book?

Clifford’s book was published by MIT Press just two months ago. It’s titled The Dialogues: Conversations about the Nature of the Universe and it’s not just a book, it’s a graphic novel! Yes, that’s right. Clifford doesn’t only write, he also draws.

His book is a collection of short stories which are mostly physics-themed, but also touch on overarching questions like how does science work or what’s the purpose of basic research to begin with. I would characterize these stories as conversation starters. They are supposed to make you wonder.

But just because it contains a lot of pictures doesn’t mean The Dialogues is a shallow book. In contrast, a huge amount of physics is packed into it, from electrodynamics to the multiverse, the cosmological constant, a theory of everything and to gravitational waves. The reader also finds references for further reading in case they wish to learn more.

I found the drawings were put to good use and often add to the explanation. The Dialogues is also, I must add, a big book. With more than 200 illustrated pages, it seems to me that offering it for less than $30 is a real bargain!

I would recommend this book to everyone who has an interest in the foundations of physics. Even if you don’t read it, it will still look good on your coffee table ;)

Win a copy!

I bought the book when it appeared, but later received a free review copy. Now I have two and I am giving one away for free!

The book will go to the first person who submits a comment to this blogpost (not elsewhere) listing 10 songs that use physics-themed phrases in the lyrics (not just in the title). Overly general words (such as “moon” or “light”) or words that are non-physics terms which just happen to have a technical meaning (such as “force” or “power”) don’t count.

The time-stamp of your comment will decide who was first, so please do not send your list to me per email. Also, please only make a submission if you are willing to provide me with a mailing address.

Good luck!

The book is gone.

Wednesday, January 10, 2018

Superfluid dark matter gets seriously into business

very dark fluid
Most matter in the universe isn’t like the stuff we are made of. Instead, it’s a thinly distributed, cold, medium which rarely interacts both with itself and with other kinds of matter. It also doesn’t emit light, which is why physicists refer to it as “dark matter.”

A recently proposed idea, according to which dark matter may be superfluid, has now become more concrete, thanks to a new paper by Justin Khoury and collaborators.

Astrophysicists invented dark matter because a whole bunch of observations of the cosmos do not fit with Einstein’s theory of general relativity.

According to general relativity, matter curves space-time and, in return, the curvature dictates the motion of matter. Problem is, if you calculate the response of space-time to all the matter we know, then the observed motions doesn’t fit the prediction from the calculation.

This problem exists for galactic rotation curves, velocity distributions in galaxy clusters, for the properties of the cosmic microwave background, for galactic structure formation, gravitational lensing, and probably some more that I’ve forgotten or never heard about in the first place.

But dark matter is only one way to explain the observation. We measure the amount of matter and we observe its motion, but the two pieces of information don’t match up with the equations of general relativity. One way to fix this mismatch is to invent dark matter. The other way to fix this is to change the equations. This second option has become known as “modified gravity.”

There are many types of modified gravity and most of them work badly. That’s because it’s easy to break general relativity and produce a mess that’s badly inconsistent with the high-precision tests of gravity that we have done within our solar system.

However, it has been known since the 1980s that some types of modified gravity explain observations that dark matter does not explain. For example, the effects of dark matter in galaxies become relevant not at a certain distance from the galactic center, but below a certain acceleration. Even more perplexing, this threshold of acceleration is related to the cosmological constant. Both of these features are difficult to account for with dark matter. Astrophysicists have also established a relation between the brightness of certain galaxies and the velocities of their outermost stars. Named “Baryonic Tully Fisher Relation” after its discoverers, it is also difficult to explain with dark matter.

On the other hand, modified gravity works badly in other cases, notably in the early universe where dark matter is necessary to get the cosmic microwave background right, and to set up structure formation so that the result agrees with what we see.

For a long time I have been rather agnostic about this, because I am more interested in the structure of fundamental laws than in the laws themselves. Dark matter works by adding particles to the standard model of particle physics. Modified gravity works by adding fields to general relativity. But particles are fields and fields are particles. And in both cases, the structure of the laws remains the same. Sure, it would be great to settle just exactly what it is, but so what if there’s one more particle or field.

It was a detour that got me interested in this: Fluid analogies for gravity, a topic I have worked on for a few years now. Turns out that certain kinds of fluids can mimic curved space-time, so that perturbations (say, density fluctuations) in the fluid travel just like they would travel under the influence of gravity.

The fluids under consideration here are usually superfluid condensates with an (almost) vanishing viscosity. The funny thing is now that if you look at the mathematical description of some of these fluids, they look just like the extra fields you need for modified gravity! So maybe, then, modified gravity is really a type of matter in the end?

I learned about this amazing link three years ago from a paper by Lasha Berezhiani and Justin Khoury. They have a type of dark matter which can condense (like vapor on glass, if you want a visual aid) if a gravitational potential is deep enough. This condensation happens within galaxies, but not in interstellar space because the potential isn’t deep enough. The effect that we assign to dark matter, then, comes partly from the gravitational pull of the fluid and partly from the actual interaction with the fluid.

If the dark matter is superfluid, it has long range correlations that give rise to the observed regularities like the Tully-Fisher relation and the trends in rotation curves. In galaxy clusters, on the other hand, the average density of (normal) matter is much lower and most of the dark matter is not in the superfluid phase. It then behaves just like normal dark matter.

The main reason I find this idea convincing is that it explains why some observations are easier to account for with dark matter and others with modified gravity: It’s because dark matter has phase transitions! It behaves differently at different temperatures and densities.

In solar systems, for example, the density of (normal) matter is strongly peaked and the gradient of the gravitational field near a sun is much larger than in a galaxy on the average. In this case, the coherence in the dark matter fluid is destroyed, which is why we do not observe effects of modified gravity in our solar system. And in the early universe, the temperature is too high and dark matter just behaves like a normal fluid.

In 2015, the idea with the superfluid dark matter was still lacking details. But two months ago, Khoury and his collaborators came out with a new paper that fills in some of the missing pieces.

Their new calculations take into account that in general the dark matter will be a mixture of superfluid and normal fluid, and both phases will make a contribution to the gravitational pull. Just what the composition is depends on the gravitational potential (caused by all types of matter) and the equation of state of the superfluid. In the new paper, the authors parameterize the general effects and then constrain the parameters so that they fit observations.

Yes, there are new parameters, but not many. They claim that the model can account for all the achievements of normal particle dark matter, plus the benefits of modified gravity on top.

And while this approach very much looks like modified gravity in the superfluid phase, it is immune to the constraint from the measurement of gravitational waves with an optical counterpart. That is because both gravitational waves and photons couple the same way to the additional stuff and hence should arrive at the same time – as observed.

It seems to me, however, that in the superfluid model one would in general get a different dark matter density if one reconstructs it from gravitational lensing than if one reconstructs it from kinetic measurements. That is because the additional interaction with the superfluid is felt only by the baryons. Indeed, this discrepancy could be used to test whether the idea is correct.

Khoury et al don’t discuss the possible origin of the fluid, but I like the interpretation put forward by Erik Verlinde. According to Verlinde, the extra-fields which give rise to the effects of dark matter are really low-energy relics of the quantum behavior of space-time. I will admit that this link is presently somewhat loose, but I am hopeful that it will become tighter in the next years. If so, this would mean that dark matter might be the key to unlocking the – still secret – quantum nature of gravity.

I consider this one of the most interesting developments in the foundations of physics I have seen in my lifetime. Superfluid dark matter is without doubt a pretty cool idea.

Tuesday, January 09, 2018

Me, elsewhere

Beginning 2018, I will no longer write for Ethan Siegel’s Forbes collection “Starts With a Bang.” Instead, I will write a semi-regular column for Quanta Magazine, the first of which -- about asymptotically safe gravity -- appeared yesterday.

In contrast to Forbes, Quanta Magazine keeps the copyright, which means that the articles I write for them will not be mirrored on this blog. You actually have to go over to their site to read them. But if you are interested in the foundations of physics, take my word that subscribing to Quanta Magazine is well worth your time, not so much because of me, but because their staff writers have so-far done an awesome job to cover relevant topics without succumbing to hype.

I also wrote a review of Jim Baggott’s book “Origins: The Scientific Story of Creation” which appeared in the January issue of Physics World. I much enjoyed Baggott’s writing and promptly bought another one of his books. Physics World  doesn’t want me to repost the review in text, but you can read the PDF here.

Finally, I wrote a contribution to the proceedings of a philosophy workshop I attended last year. In this paper, I summarize my misgivings with arguments from finetuning. You can now find it on the arXiv.

If you want to stay up to date on my writing, follow me on Twitter or on Facebook.

Wednesday, January 03, 2018

Sometimes I believe in string theory. Then I wake up.

They talk about me.
Grumpy Rainbow Unicorn.
[Image Source.]

And I can’t blame them. Because nothing else is happening on this planet. There’s just me and my attempt to convince physicists that beauty isn’t truth.

Yes, I know it’s not much of an insight that pretty ideas aren’t always correct. That’s why I objected when my editor suggested I title my book “Why Beauty isn’t Truth.” Because, duh, it’s been said before and if I wanted to be stale I could have written about how we’re all made of stardust, aah-choir, chimes, fade and cut.

Nature has no obligation to be pretty, that much is sure. But the truth seems hard to swallow. “Certainly she doesn’t mean that,” they say. Or “She doesn’t know what she’s doing.” Then they explain things to me. Because surely I didn’t mean to say that much of what goes on in the foundations of physics these days is a waste of time, did I? And even if, could I please not do this publicly, because some people have to earn a living from it.

They are “good friends,” you see? Good friends who want me to believe what they believe. Because believing has bettered their lives.

And certainly I can be fixed! It’s just that I haven’t yet seen the elegance of string theory and supersymmetry. Don’t I know that elegance is a sign of all successful theories? It must be that I haven’t understood how beauty has been such a great guide for physicists in the past. Think of Einstein and Dirac and, erm, there must have been others, right? Or maybe it’s that I haven’t yet grasped that pretty, natural theories are so much better. Except possibly for the cosmological constant, which isn’t pretty. And the Higgs-mass. And, oh yeah, the axion. Almost forgot about that, sorry.

But it’s not that I don’t think unified symmetry is a beautiful idea. It’s a shame, really, that we have these three different symmetries in particle physics. It would be so much nicer if we could merge them to one large symmetry. Too bad that the first theories of unification led to the prediction of proton decay and were ruled out. But there are a lot other beautiful unification ideas left to work on. Not all is lost!

And it’s not that I don’t think supersymmetry is elegant. It combines two different types of particles and how cool is that? It has candidates for dark matter. It alleviates the problem with the cosmological constant. And it aids gauge coupling unification. Or at least it did until LHC data interfered with our plans to prettify the laws of nature. Dang.

And it’s not that I don’t see why string theory is appealing. I once set out to become a string theorist. I do not kid you. I ate my way through textbooks and it was all totally amazing, how much you get out from the rather simple idea that particles shouldn’t be points but strings. Look how much consistency dictates you to construct the theory. And note how neatly it fits with all that we already know.

But then I got distracted by a disturbing question: Do we actually have evidence that elegance is a good guide to the laws of nature?

The brief answer is no, we have no evidence. The long answer is in my book and, yes, I will mention the-damned-book until everyone is sick of it. The summary is: Beautiful ideas sometimes work, sometimes they don’t. It’s just that many physicists prefer to recall the beautiful ideas which did work.

And not only is there no historical evidence that beauty and elegance are good guides to find correct theories, there isn’t even a theory for why that should be so. There’s no reason to think that our sense of beauty has any relevance for discovering new fundamental laws of nature.

Sure, if you ask those who believe in string theory and supersymmetry and in grand unification, they will say that of course they know there is no reason to believe a beautiful theory is more likely to be correct. They still work on them anyway. Because what better could they do with their lives? Or with their grants, respectively. And if you work on it, you better believe in it.

I consent, not all math is equally beautiful and not all math is equally elegant. I yet have to find anyone, for example, who thinks Loop Quantum Gravity is more beautiful than string theory. And isn’t it interesting that we share this sense of what is and isn’t beautiful? Shouldn’t it mean something that so many theoretical physicists agree beautiful math is better? Shouldn’t it mean something that so many people believe in the existence of an omniscient god?

But science isn’t about belief, it’s about facts, so here are the facts: This trust in beauty as a guide, it’s not working. There’s no evidence for grand unification. There’s no evidence for supersymmetry, no evidence for axions, no evidence for moduli, for WIMPs, or for dozens of other particles that were invented to prettify theories which work just fine without them. After decades of search, there’s no evidence for any of these.

It’s not working. I know it hurts. But now please wake up.

Let me assure you I usually mean what I say and know what I do. Could I be wrong? Of course. Maybe tomorrow we’ll discover supersymmetry. Not all is lost.

Monday, December 25, 2017

Merry Christmas!

We wish you all happy holidays! Whether or not you celebrate Christmas, we hope you have a peaceful time to relax and, if necessary, recover.

I want to use the opportunity to thank all of you for reading along, for giving me feedback, and for simply being interested in science in a time when that doesn’t seem to be normal anymore. A special “Thank you" to those who have sent donations. It is reassuring to know that you value this blog. It encourages me to keep my writing available here for free.

I’ll be tied up with family business during the coming week – besides the usual holiday festivities, the twins’ 7th birthday is coming up – so blogging will be sparse for some while.

Monday, December 18, 2017

Get your protons right!

The atomic nucleus consists of protons and neutrons. The protons and neutrons are themselves made of three quarks each, held together by gluons. That much is clear. But just how do the gluons hold the quarks together?

The quarks and gluons interact through the strong nuclear force. The strong nuclear force does not have only one charge – like electromagnetism – but three charges. The charges are called “colors” and often assigned the values red, blue, and green, but this is just a way to give names to mathematical properties. These colors have nothing to do with the colors that we can see.

Colors are a handy terminology because the charges blue, red, and green can combine to neutral (“white”) and so can a color and its anti-color (blue and anti-blue, green and anti-green, and so on). The strong nuclear force is mediated by gluons which each carry two types of colors. That the gluons themselves carry a charge means that, unlike the photon, they also interact among each other.

The strong nuclear force has the peculiar property that it gets stronger the larger the distance between two quarks, while it gets weaker on short distances. A handy metaphor for this is a rubber string – the more you stretch it, the stronger the restoring force. Indeed, this string-like behavior of the strong nuclear force is where string-theory originally came from.

The strings of the strong nuclear force are gluon flux-tubes, that are connections between two color-charged particles where the gluons preferably travel along. The energy of the flux-tubes is proportional to their length. If you have a particle (called a “meson”) made of a quark and an anti-quark, then the flux tube is focused on a straight line connecting the quarks. But what if you have three quarks, like inside a neutron or a proton?

According to the BBC, gluon flux-tubes (often depicted as springs, presumably because rubber is hard to illustrate) form a triangle.

This is almost identical to the illustration you find on Wikipedia:
Here is the proton on Science News:

Here is Alan Stonebreaker for the APS:

This is the proton according to Carole Kliger from the University of Maryland:

And then there is Christine Davies from the University of Glasgow who pictured the proton for Science Daily as an artwork resembling a late Kandinsky:

So which one is right?

At first sight it seems plausible that the gluons form a triangle because that requires the least stretching of strings that each connect two quarks. However, this triangular – “Δ-shaped” – configuration cannot connect three quarks and still maintain gauge-invariance. This means it violates the key principle of the strong force, which is bad and probably means this configuration is not physically possible. The Y-shaped flux-tubes on the other hand don’t suffer from that problem.

But we don’t have to guess around because this is physics and one can calculate it. This calculation cannot be done analytically but it is tractable by computer simulations. Bissey et al reported the results in a 2006 paper: “We do not find any evidence for the formation of a Delta-shaped flux-tube (empty triangle) distribution.” The conclusion is clear: The Y-shape is the preferred configuration.

And there’s more to learn! The quarks and gluons in the proton don’t sit still, and when they move then the center of the Y moves around. If you average over all possible positions you approximate a filled Δ-shape. (Though the temperature dependence is somewhat murky and subject of ongoing research.)

The flux-tubes also do not always exactly lie in the plane spanned by the three quarks but can move up and down into the perpendicular direction. So you get a filled Δ that’s inflated to the middle.

This distribution of flux tubes has nothing to do with the flavor of the quarks, meaning it’s the same for the proton and the neutron and all other particles composed of three quarks, such as the one containing two charm-quarks that was recently discovered at CERN. How did CERN picture the flux tubes? As a Δ:

Now you can claim you know quarks better than CERN! It’s either a Y or a filled triangle, but not an empty triangle.

I am not a fan of depicting gluons as springs because it makes me think of charged particles in a magnetic field. But I am willing to let this pass as creative freedom. I hope, however, that it is possible to get the flux-tubes right, and so I have summed up the situation in the image below :

Tuesday, December 12, 2017

Research perversions are spreading. You will not like the proposed solution.

The ivory tower from
The Neverending Story
Science has a problem. The present organization of academia discourages research that has tangible outcomes, and this wastes a lot of money. Of course scientific research is not exclusively pursued in academia, but much of basic research is. And if basic research doesn’t move forward, science by large risks getting stuck.

At the root of the problem is academia’s flawed reward structure. The essence of the scientific method is to test hypotheses by experiment and then keep, revise, or discard the hypotheses. However, using the scientific method is suboptimal for a scientist’s career if they are rewarded for research papers that are cited by as many of their peers as possible.

To the end of producing popular papers, the best tactic is to work on what already is popular, and to write papers that allow others to quickly produce further papers on the same topic. This means it is much preferable to work on hypotheses that are vague or difficult to falsify, and stick to topics that stay inside academia. The ideal situation is an eternal debate with no outcome other than piles of papers.

You see this problem in many areas of science. It’s origin of the reproducibility crisis in psychology and the life sciences. It’s the reason why bad scientific practices – like p-value hacking – prevail even though they are known to be bad: Because they are the tactics that keep researchers in the job.

It’s also why in the foundations of physics so many useless papers are written, thousands of guesses about what goes on in the early universe or at energies we can’t test, pointless speculations about an infinitude of fictional universes. It’s why theories that are mathematically “fruitful,” like string theory, thrive while approaches that dare introduce unfamiliar math starve to death (adding vectors to spinors, anyone?). And it is why physicists love “solving” the black hole information loss problem: because there’s no risk any of these “solutions” will ever get tested.

If you believe this is good scientific practice, you would have to find evidence that the possibility to write many papers about an idea is correlated with this idea’s potential to describe observation. Needless to say, there isn’t any such evidence.

What we witness here is a failure of science to self-correct.

It’s a serious problem.

I know it’s obvious. I am by no means the first to point out that academia is infected with perverse incentives. Books have been written about it. Nature and Times Higher Education seem to publish a comment about this nonsense every other week. Sometimes this makes me hopeful that we’ll eventually be able to fix the problem. Because it’s in everybody’s face. And it’s eroding trust in science.

At this point I can’t even blame the public for mistrusting scientists. Because I mistrust them too.

Since it’s so obvious, you would think that funding bodies take measures to limit the waste of money. Yes, sometimes I hope that capitalism will come and rescue us! But then I go and read things like that Chinese scientists are paid bonuses for publishing in high impact journals. Seriously. And what are the consequences? As the MIT technology review relays:
    “That has begun to have an impact on the behavior of some scientists. Wei and co report that plagiarism, academic dishonesty, ghost-written papers, and fake peer-review scandals are on the increase in China, as is the number of mistakes. “The number of paper corrections authored by Chinese scholars increased from 2 in 1996 to 1,234 in 2016, a historic high,” they say.”

If you think that’s some nonsense the Chinese are up to, look at what goes on in Hungary. They now have exclusive grants for top-cited scientists. According to a recent report in Nature:
    “The programme is modelled on European Research Council grants, but with a twist: only those who have published a paper in the past five years that counted among the top 10% most-cited papers in their discipline are eligible to apply.”
What would you do to get such a grant?

To begin with, you would sure as hell not work on any topic that is not already pursued by a large number of your colleagues, because you need a large body of people able to cite your work to begin with.

You would also not bother criticize anything that happens in your chosen research area, because criticism would only serve to decrease the topic’s popularity, hence working against your own interests.

Instead, you would strive to produce a template for research work that can easily and quickly be reproduced with small modifications by everyone in the field.

What you get with such grants, then, is more of the same. Incremental research, generated with a minimum of effort, with results that meander around the just barely scientifically viable.

Clearly, Hungary and China introduce such measures to excel in national comparisons. They don’t only hope for international recognition, they also want to recruit top researchers hoping that, eventually, industry will follow. Because in the end what matters is the Gross Domestic Product.

Surely in some areas of research – those which are closely tied to technological applications – this works. Doing more of what successful people are doing isn’t generally a bad idea. But it’s not an efficient method to discover useful new knowledge.

That this is not a problem exclusive to basic research became clear to me when I read an article by Daniel Sarewitz in The New Atlantis. Sarewitz tells the story of Fran Visco, lawyer, breast cancer survivor, and founder of the National Breast Cancer Coalition:
    “Ultimately, “all the money that was thrown at breast cancer created more problems than success,” Visco says. What seemed to drive many of the scientists was the desire to “get above the fold on the front page of the New York Times,” not to figure out how to end breast cancer. It seemed to her that creativity was being stifled as researchers displayed “a lemming effect,” chasing abundant research dollars as they rushed from one hot but ultimately fruitless topic to another. “We got tired of seeing so many people build their careers around one gene or one protein,” she says.”
So, no, lemmings chasing after fruitless topics are not a problem only in basic research. Also, the above mentioned overproduction of useless models is by no means specific to high energy physics:
    “Scientists cite one another’s papers because any given research finding needs to be justified and interpreted in terms of other research being done in related areas — one of those “underlying protective mechanisms of science.” But what if much of the science getting cited is, itself, of poor quality?

    Consider, for example, a 2012 report in Science showing that an Alzheimer’s drug called bexarotene would reduce beta-amyloid plaque in mouse brains. Efforts to reproduce that finding have since failed, as Science reported in February 2016. But in the meantime, the paper has been cited in about 500 other papers, many of which may have been cited multiple times in turn. In this way, poor-quality research metastasizes through the published scientific literature, and distinguishing knowledge that is reliable from knowledge that is unreliable or false or simply meaningless becomes impossible.”

Sarewitz concludes that academic science has become “an onanistic enterprise.” His solution? Don’t let scientists decide for themselves what research is interesting, but force them to solve problems defined by others:
    “In the future, the most valuable science institutions […] will link research agendas to the quest for improved solutions — often technological ones — rather than to understanding for its own sake. The science they produce will be of higher quality, because it will have to be.”
As one of the academics who believe that understanding how nature works is valuable for its own sake, I think the cure that Sarewitz proposes is worse than the disease. But if Sarewitz makes one thing clear in his article, it’s that if we in academia don’t fix our problems soon, someone else will. And I don’t think we’ll like it.

Wednesday, December 06, 2017

The cosmological constant is not the worst prediction ever. It’s not even a prediction.

Think fake news and echo chambers are a problem only in political discourse? Think again. You find many examples of myths and falsehoods on popular science pages. Most of them surround the hype of the day, but some of them have been repeated so often they now appear in papers, seminar slides, and textbooks. And many scientists, I have noticed with alarm, actually believe them.

I can’t say much about fields outside my specialty, but it’s obvious this happens in physics. The claim that the bullet cluster rules out modified gravity, for example, is a particularly pervasive myth. Another one is that inflation solves the flatness problem, or that there is a flatness problem to begin with.

I recently found another myth to add to my list: the assertion that the cosmological constant is “the worst prediction in the history of physics.” From RealClearScience I learned the other day that this catchy but wrong statement has even made it into textbooks.

Before I go and make my case, please ask yourself: If the cosmological constant was such a bad prediction, then what theory was ruled out by it? Nothing comes to mind? That’s because there never was such a prediction.

The myth has it that if you calculate the cosmological constant using the standard model of particle physics the result is 120 orders of magnitude larger than what is observed due to contributions from vacuum fluctuation. But this is wrong on at least 5 levels:

1. The standard model of particle physics doesn’t predict the cosmological constant, never did, and never will.

The cosmological constant is a free parameter in Einstein’s theory of general relativity. This means its value must be fixed by measurement. You can calculate a contribution to this constant from the standard model vacuum fluctuations. But you cannot measure this contribution by itself. So the result of the standard model calculation doesn’t matter because it doesn’t correspond to an observable. Regardless of what it is, there is always a value for the parameter in general relativity that will make the result fit with measurement.

(And if you still believe in naturalness arguments, buy my book.)

2. The calculation in the standard model cannot be trusted.

Many theoretical physicists think the standard model is not a fundamental theory but must be amended at high energies. If that is so, then any calculation of the contribution to the cosmological constant using the standard model is wrong anyway. If there are further particles, so heavy that we haven’t yet seen them, these will play a role for the result. And we don’t know if there are such particles.

3. It’s idiotic to quote ratios of energy densities.

The 120 orders of magnitude refers to a ratio of energy densities. But not only is the cosmological constant usually not quoted as an energy density (but as a square thereof), in no other situation do particle physicists quote energy densities. We usually speak about energies, in which case the ratio goes down to 30 orders of magnitude.

4. The 120 orders of magnitude are wrong to begin with.

The actual result from the standard model scales with the fourth power of the masses of particles, times an energy-dependent logarithm. At least that’s the best calculation I know of. You find the result in equation (515) in this (awesomely thorough) paper. If you put in the numbers, out comes a value that scales with the masses of the heaviest known particles (not with the Planck mass, as you may have been told). That’s currently 13 orders of magnitude larger than the measured value, or 52 orders larger in energy density.

5. No one in their right mind ever quantifies the goodness of a prediction by taking ratios.

There’s a reason physicists usually talk a about uncertainty, statistical significance, and standard deviations. That’s because these are known to be useful to quantify the match of a theory with data. If you’d bother writing down the theoretical uncertainties of the calculation for the cosmological constant, the result would be compatible with the measured value even if you’d set the additional contribution from general relativity to zero.

In summary: No prediction, no problem.

Why does it matter? Because this wrong narrative has prompted physicists to aim at the wrong target.

The real problem with the cosmological constant is not the average value of the standard model contribution but – as Niayesh Afshordi elucidated better than I ever managed to – that the vacuum fluctuations, well, fluctuate. It’s these fluctuations that you should worry about. Because these you cannot get rid of by subtracting a constant.

But of course I know the actual reason you came here is that you want to know what is “the worst prediction in the history of physics” if not the cosmological constant...

I’m not much of a historian, so don’t take my word for it, but I’d guess it’s the prediction you get for the size of the universe if you assume the universe was born by a vacuum fluctuation out of equilibrium.

In this case, you can calculate the likelihood for observing a universe like our own. But the larger and the less noisy the observed universe, the less likely it is to originate from a fluctuation. Hence, the mere fact that you have a fairly ordered memory of the past and a sense of a reasonably functioning reality would be exceedingly tiny in such a case. So tiny, I’m not interested enough to even put in the numbers. (Maybe ask Sean Carroll.)

I certainly wish I’d never have to see the cosmological constant myth again. I’m not yet deluded enough to believe it will go away, but at least I now have this blogpost to refer to when I encounter it the next time.

Thursday, November 30, 2017

If science is what scientists do, what happens if scientists stop doing science?

“Is this still science?” has become a recurring question in the foundations of physics. Whether it’s the multiverse, string theory, supersymmetry, or inflation, concerns abound that theoreticians have crossed a line.

Science writer Jim Baggott called the new genre “fairy-tale science.” Historian Helge Kragh coined the term “higher speculations,” and Peter Woit, more recently, suggested the name “fake physics.” But the accused carry on as if nothing’s amiss, arguing that speculation is an essential part of science. And I? I have a problem.

On the one hand, I understand the concerns about breaking with centuries of tradition. We used to followed up each hypothesis with experimental test, and the longer the delay between hypothesis and test, the easier for pseudoscience to take foothold. On the other hand, I agree that speculation is a necessary part of science and new problems sometimes require new methods. Insisting on ideals of the past might mean getting stuck, maybe forever.

Even more important, I think it’s a grave mistake to let anyone define what we mean by doing science. Because who gets to decide what’s the right thing to do? Should we listen to Helge Kragh? Peter Woit? George Ellis? Or to the other side, to people like Max Tegmark, Sean Carroll, and David Gross, who claim we’re just witnessing a little paradigm change, nothing to worry about? Or should we, heaven forbid, listen to some philosophers and their ideas about post-empirical science?

There have been many previous attempts to define what science is, but the only definition that ever made sense to me is that science is what scientists do, and scientists are people who search for useful descriptions of nature. “Science,” then, is an emergent concept that arises in communities of people with a shared work practices. “Communities of practice,” as the sociologists say.

This brings me to my problem. If science is what scientists do, then how can anything that scientists do not be science? For a long time it seemed to me that in the end we won’t get around settling on a definition for science and holding on to it, regardless of how much I’d prefer a self-organized solution.

But as I was looking for a fossil photo to illustrate my recent post about what we mean by “explaining” something, I realized that we witness the self-organized solution right now: It’s a lineage split.

If some scientists insist on changing the old-fashioned methodology, the communities will fall apart. Let us call the two sectors “conservatives” and “progressives.” Each of them will insist they are the ones pursuing the more promising approach.

Based on this little theory, let me make a prediction what will happen next: The split will become more formally entrenched. Members of the community will begin taking sides, if they haven’t already, and will make an effort to state their research philosophy upfront.

In the end, only time will tell which lineage will survive and which one will share the fate of the Neanderthals.

So, if science is what scientists do, what happens if some scientists stop doing science? You see it happening as we speak.

Sunday, November 26, 2017

Astrophysicist discovers yet another way to screw yourself over when modifying Einstein’s theory

Several people have informed me that has once again uncritically promoted a questionable paper, in this case by André Maeder from UNIGE. This story goes back to a press release by the author’s home institution and has since been hyped by a variety of other low-quality outlets.

From what I gather from Maeder’s list of publications, he’s an astrophysicist who recently had the idea to revolutionize cosmology by introducing a modification of general relativity. The paper which now makes headlines studies observational consequences of a model he introduced in January and claim to explain away the need for dark matter and dark energy. Both papers contain a lot of fits to data but no consistent theory. Since the man is known in the astrophysics community, however, the papers got published in ApJ, one of the best journals in the field.

For those of you who merely want to know whether you should pay attention to this new variant of modified gravity, the answer is no. The author does not have a consistent theory. The math is wrong.

For those of you who understand the math and want to know what the problem is, here we go.

Maeder introduces a conformal prefactor in front of the metric. You can always do that as an ansatz to solve the equations, so there is nothing modified about this, but also nothing wrong. He then looks at empty de Sitter space, which is conformally flat, and extracts the prefactor from there.

He then uses the same ansatz for the Friedmann Robertson Walker metric (eq 27, 28 in the first paper). Just looking at these equations you see immediately that they are underdetermined if the conformal factor (λ) is a degree of freedom. That’s because the conformal factor can usually be fixed by a gauge condition and be chosen to be constant. That of course would just give back standard cosmology and Maeder doesn’t want that. So he instead assumes that this factor has the same form as in de Sitter space.

Since he doesn’t have a dynamical equation for the extra field, my best guess is that this effectively amounts to choosing a weird time coordinate in standard cosmology. If you don’t want to interpret it as a gauge, then an equation is missing. Either way the claims which follow are wrong. I can’t tell which is the case because the equations themselves just appear from nowhere. Neither of the papers contain a Lagrangian, so it remains unclear what is a degree of freedom and what isn’t. (The model is also of course not scale invariant, so somewhat of a misnomer.)

Maeder later also uses the same de Sitter prefactor for galactic solutions, which makes even less sense. You shouldn’t be surprised that he can fit some observations when you put in the scale of the cosmological constant to galactic models, because we have known this link since the 1980s. If there is something new to learn here, it didn’t become clear to me what.

Maeder’s papers have a remarkable number of observational fits and pretty plots, which I guess is why they got published. He clearly knows his stuff. He also clearly doesn’t know a lot about modifying general relativity. But I do, so let me tell you it’s hard. It’s really hard. There are a thousand ways to screw yourself over with it, and Maeder just discovered the one thousand and first one.

Please stop hyping this paper.

Wednesday, November 22, 2017

How do you prove that Earth is older than 10,000 years?

Mesosaurus fossil. Probably dating back
to the early Permian Period, roughly
300 million years ago. [Image source]
Planet Earth formed around 4.5 billion years ago. The first primitive forms of life appeared about 4 billion years ago. Natural selection did the rest, giving rise to species increasingly better adapted to their environment. Evidence, as they say, is overwhelming.

Or is it? Imagine planet Earth began its existence a mere 10,000 years ago, with all fossil records in place and carbon-14 well into decaying. From there on, however, evolution proceeded as scientists tell us. How’d you prove this story wrong?

You can’t.

I know it hurts. But hang on there, band aid follows below.

You can’t prove this story wrong because of the way our current theories work. These theories need two ingredients: 1) A configuration at any one moment in time, called the “initial condition,” and 2) A hypothesis for how this initial configuration changes with time, called the “evolution law.”

You can reverse the evolution law to figure out from the present configuration what happened back in time. But there’s no way you can tell whether an earlier configuration actually existed or whether they are just convenient stories. In theories of this type – and that includes all theories in physics – you can therefore never rule out that at some earlier time the universe evolved by an entirely different law – maybe because God or The Programmer assembled it – and was then suddenly switched on to reproduce our observations.

I often hear people argue such creation-stories are wrong because they can’t be falsified, but this makes about as much sense as organic salt. No, they are not wrong, but they are useless.

Last week, I gave a talk at the department of History and Philosophy at the University of Toronto. My talk was followed by a “response” from a graduate student who evidently spent quite some time digging through this blog’s archives to classify my philosophy of science. I didn’t know I have one, but you never stop learning.

I learned that I am sometimes an anti-realist, meaning I don’t believe in the existence of an external reality. But I’d say I am neither a realist nor an anti-realist; I am agnostic about whether or not reality exists or what that even means. I don’t like to say science unveils “truths” about “reality” because this just brings on endless discussions about what is true and what is real. To me, science is about finding useful descriptions of the world, where by “useful” I mean they allow us to make predictions or explain already existing observations. The simpler an explanation, the more useful it is.

That scientific theories greatly simplify the stories we tell about the world is extremely important and embodies what we even mean by doing science. Forget all about Popperism and falsification, just ask what’s the most useful explanation. Saying that the world was created 10,000 years ago with all fossils in place is useless in terms of explaining the fossils. If you, on the other hand, extrapolate the evolution law back in time 4 billion years, you can start with a much simpler initial condition. That’s why it’s a better explanation. You get more out of less.

So there’s your band aid: Saying that the world was created 10,000 years ago with everything in place is unfalsifiable but also useless. It is quantifiably not simple: you need to put a lot of data into the initial condition. A much simpler, and thus scientifically better, explanation, is that planet Earth is ages old and Darwinian evolution did its task.

I’m not telling you this because I’ve suddenly developed an interest in Creationism. I am telling you this because I frequently encounter similar confusions surrounding the creation of the universe. This usually comes up in reaction to me pointing out that there is nothing whatsoever wrong with finetuned initial conditions if you do not have a probability distribution to quantify why the conditions are supposedly unlikely.

People often tell me that a finetuned initial condition doesn’t explain anything and thus isn’t scientific. Or, even weirder, that if you’d accept finetuned initial conditions this would turn science itself ad absurdum.

But this is just wrong. Finetuned initial conditions are equally good or bad explanations than not-finetuned ones. What is decisive isn’t whether the initial condition is finetuned, but whether it’s simple. According to current nomenclature, that is not the same thing. Absent a probability distribution, for example, an initial value of 1.0000000[00] for the curvature density parameter is scientifically equally good as an initial value of 0.0000001[00]… because both are equally simple. Current thinking among cosmologists, in contrast, has it that the latter is much worse than the former.

This confusion about what it means for a scientific theory to be useful sits deep and has caused a lot of cosmologists to cook up stories about the early universe based on highly questionable extrapolations into the past.

Take, for example, inflation, the idea that the early universe underwent a phase of rapid expansion. Inflation conjectures that before a certain moment in our universe’s history there was a different evolution law, assigned to a newly invented scalar field called the “inflaton.” But this conjecture is scientifically problematic because it construes up an evolution law in the past where we have no way of testing it. It’s not so different from saying that if you’d roll back time more than 10,000 years, you wouldn’t find planet Earth but god waving a magic wand or what have you.

A bold conjecture like inflation can only be justified if it leads to an actually simpler story, but on that the jury is out. Inflation was meant to solve several finetuning problems, but this doesn’t bring a simplification, it’s merely a beautification. The price to pay for this prettier theory, though, is that you now have at least one, if not several, new fields and their potentials, and some way to get rid of them again, which is arguably a complication of the story.

I wrote in a recent post that inflation seems justifiable after all because it provides a simple explanation for certain observed correlations in the cosmic microwave background (CMB). Well, that’s what I wrote some weeks ago, but now I am not so sure it is correct, thanks in no small part to a somewhat disturbing conversation I had with Niayesh Afshordi at Perimeter Institute.

The problem is that in cosmology there really aren’t a lot of data. There are but a few numbers. It’s a simple story already without inflation. And so, the current status is that I just don’t know whether or not inflation is a good theory. (But check back next month.)

Let me emphasize that the concordance model (aka ΛCDM) does not suffer from this problem. Indeed, it makes a good example for a scientifically successful theory. Here’s why.

For the concordance model, we seek the combination of dark matter, normal matter, and cosmological constant (as well as a handful other parameters) that best fit current observations. But what do we mean by best fit? We could use any combinations of parameters to get the dynamical law, and then use it to evolve the present day observations back in time. And regardless of what the law, there is always an initial state that will evolve into the present one.

In general, however, the initial state will be a mess, for example because the fluctuations of the cosmic microwave background (radiation) are not related in any obvious way to the structures we observe (matter). Whereas, if you pick the parameters correctly, these two types of structures belong together (higher density of matter corresponding to hotter spots in the cosmic microwave background). This match is a great simplification of the story – it explains something.

But the more you try to turn back time in the early universe, the harder it becomes to obey the scientific credo of storytelling, that you should seek only simpler explanations, not more complicated ones. The problem is the story we presently have is already very simple. This really is my biggest issue with eternal inflation and the multiverse or cyclic cosmologies, bounces, and so on and so forth. They are stories, all right, but they aren’t simplifying anything. They just add clutter, like the programmer that set up our universe so that it looks the way it looks.

On some days I hope something scientific will eventually come out of these stories. But today I am just afraid we have overstepped the limits of science.

Sunday, November 12, 2017

Away Note

I am overseas the coming week, giving a seminar at Perimeter Institute on Tuesday, a colloq in Toronto on Wednesday, and on Thursday I am scheduled to “make sense of mind-blowing physics” with Natalie Wolchover in New York. The latter event, I am told, has a live webcast starting at 6:30 pm Eastern, so dial in if you fancy seeing my new haircut. (Short again.)

Please be warned that things on this blog will go very slowly while I am away. On this occasion I want to remind you that I have comment moderation turned on. This means comments will not appear until I manually approve them. I usually check the queue at least once per day.

(The above image is the announcement for the New York event. Find the seven layout blunders.)

Friday, November 10, 2017

Naturalness is dead. Long live naturalness.

I was elated when I saw that Gian Francesco Giudice announced the “Dawn of the Post-Naturalness Era,” as the title of his recent paper promises. The craze in particle physics, I thought, might finally come to an end; data brought reason back to Earth after all.

But disillusionment followed swiftly when I read the paper.

Gian Francesco Giudice is a theoretical physicist at CERN. He is maybe not the most prominent member of his species, but he has been extremely influential in establishing “naturalness” as a criterion to select worthwhile theories of particle physics. Together with Riccardo Barbieri, Giudice wrote one of the pioneering papers on how to quantify naturalness, thereby significantly contributing to the belief that it is a scientific criterion. To date the paper has been cited more than 1000 times.

Giudice was also the first person I interviewed for my upcoming book about the relevance of arguments from beauty in particle physics. It became clear to me quickly, however, that he does not think naturalness is an argument from beauty. Instead, Giudice, like many in the field, believes the criterion is mathematically well-defined. When I saw his new paper, I hoped he’d come around to see the mistake. But I was overly optimistic.

As Giudice makes pretty clear in the paper, he still thinks that “naturalness is a well-defined concept.” I have previously explained why that is wrong, or rather why, if you make naturalness well-defined, it becomes meaningless. A quick walk through the argument goes as follows.

Naturalness in quantum field theories – ie, theories of the type of the standard model of particle physics – means that a theory at low energies does not sensitively depend on the choice of parameters at high energies. I often hear people say this means that “the high-energy physics decouples.” But note that changing the parameters of a theory is not a physical process. The parameters are whatever they are.

The processes that are physically possible at high energies decouple whenever effective field theories work, pretty much by definition of what it means to have an effective theory. But this is not the decoupling that naturalness relies on. To quantify naturalness you move around between theories in an abstract theory space. This is very similar to moving around in the landscape of the multiverse. Indeed, it is probably not a coincidence that both ideas became popular around the same time, in the mid 1990s.

If you now want to quantify how sensitively a theory at low energy depends on the choice of parameters at high energies, you first have to define the probability for making such choices. This means you need a probability distribution on theory space. Yes, it’s the exact same problem you also have for inflation and in the multiverse.

In most papers on naturalness, however, the probability distribution is left unspecified which implicitly means one chooses a uniform distribution over an interval of about length 1. The typical justification for this is that once you factor out all dimensionful parameters, you should only have numbers of order 1 left. It is with this assumption that naturalness becomes meaningless because you have now simply postulated that numbers of order 1 are better than other numbers.

You wanted to avoid arbitrary choices, but in the end you had to make an arbitrary choice. This turns the whole idea ad absurdum.

That you have to hand-select a probability distribution to make naturalness well-defined used to be well-known. One of the early papers on the topic clearly states
“The “theoretical license” at one’s discretion when making this choice [for the probability distribution] necessarily introduces an element of arbitrariness to the construction.” 
Anderson and Castano, Phys. Lett. B 347:300-308 (1995)

Giudice too mentions “statistical comparisons” on theory space, so I am sure he is aware of the need to define the distribution. He also writes, however, that “naturalness is an inescapable consequence of the ingredients generally used to construct effective field theories.” But of course it is not. If it was, why make it an additional requirement?

(At this point usually someone starts quoting the decoupling theorem. In case you are that person let me say that a) no one has used mass-dependent regularization schemes since the 1980s for good reasons, and b) not only is it questionable to assume perturbative renormalizability, we actually know that gravity isn’t perturbatively renormalizable. In other words, it’s an irrelevant objection, so please let me go on.)

In his paper, Giudice further claims that “naturalness has been a good guiding principle” which is a strange thing to say about a principle that has led to merely one successful prediction but at least three failed predictions, more if you count other numerical coincidences that physicists obsess about like the WIMP miracle or gauge coupling unification. The tale of the “good guiding principle” is one of the peculiar myths that gets passed around in communities until everyone believes it.

Having said that, Giudice’s paper also contains some good points. He suggests, for example, that the use of symmetry principles in the foundations of physics might have outlasted its use. Symmetries might just be emergent at low energies. This is a fairly old idea which goes back at least to the 1980s, but it’s still considered outlandish by most particle physicists. (I discuss it in my book, too.)

Giudice furthermore points out that in case your high energy physics mixes with the low energy physics (commonly referred to as “UV/IR mixing”) it’s not clear what naturalness even means. Since this mixing is believed to be a common feature of non-commutative geometries and quite possibly quantum gravity in general, I have picked people’s brains on this for some years. But I only got shoulder shrugs, and I am none the wiser today. Giudice in his paper also doesn’t have much to say about the consequences other than that it is “a big source of confusion,” on which I totally agree.

But the conclusion that Giudice comes to at the end of his paper seems to be the exact opposite of mine.

I believe what is needed for progress in the foundations of physics is more mathematical rigor. Obsessing about ill-defined criteria like naturalness that don’t even make good working hypotheses isn’t helpful. And it would serve particle physicists well to identify their previous mistakes in order to avoid repeating them. I dearly hope they will not just replace one beauty-criterion by another.

Giudice on the other hand thinks that “we need pure unbridled speculation, driven by imagination and vision.” Which sounds great, except that theoretical particle physics has not exactly suffered from a dearth of speculation. Instead, it has suffered from a lack of sound logic.

Be that as it may, I found the paper insightful in many regards. I certainly agree that this is a time of crisis but that this is also an opportunity for change to the better. Giudice’s paper is very timely. It is also merely moderately technical, so I encourage you to give it a read yourself.

Monday, November 06, 2017

How Popper killed Particle Physics

Popper, upside-down.
Image: Wikipedia.
Popper is dead. Has been dead since 1994 to be precise. But also his philosophy, that a scientific idea needs to be falsifiable, is dead.

And luckily so, because it was utterly impractical. In practice, scientists can’t falsify theories. That’s because any theory can be amended in hindsight so that it fits new data. Don’t roll your eyes – updating your knowledge in response to new information is scientifically entirely sound procedure.

So, no, you can’t falsify theories. Never could. You could still fit planetary orbits with a quadrillion of epicycles or invent a luminiferous aether which just exactly mimics special relativity. Of course no one in their right mind does that. That’s because repeatedly fixed theories become hideously difficult, not to mention hideous, period. What happens instead of falsification is that scientists transition to simpler explanations.

To be fair, I think Popper in his later years backpedaled from his early theses. But many physicists not only still believe in Popper, they also opportunistically misinterpret the original Popper.

Even in his worst moments Popper never said a theory is scientific just because it’s falsifiable. That’s Popper upside-down and clearly nonsense. Unfortunately, upside-down Popper now drives theory-development, both in cosmology and in high energy physics.

It’s not hard to come up with theories that are falsifiable but not scientific. By scientific I mean the theory has a reasonable chance of accurately describing nature. (Strictly speaking it’s not an either/or criterion until one quantifies “reasonable chance” but it will suffice for the present purpose.)

I may predict for example, that Donald Trump will be shot by an elderly lady before his first term is over. That’s compatible with present knowledge and totally falsifiable. But chances it’s correct are basically zero and that makes it a prophecy, not a scientific theory.

The idea that falsifiability is sufficient to make a theory scientific is an argument I hear frequently from amateur physicists. “But you can test it!” they insist. Then they explain how their theory reworks the quantum or what have you. And post their insights in all-caps on my time-line. Indeed, as I am writing this, a comment comes in: “A good idea need only be testable,” says Uncle Al. Sorry, Uncle, but that’s rubbish.

You’d think that scientists know better. But two years ago I sat in a talk by Professor Lisa Randall who spoke about how dark matter killed the dinosaurs. Srsly. This was when I realized the very same mistake befalls professional particle physicists. Upside-down Popper is a widely-spread malaise.

Randall, you see, has a theory for particle dark matter with some interaction that allows the dark matter to clump within galaxies and form disks similar to normal matter. Our solar system, so the idea, periodically passes through the dark matter disk, which then causes extinction events. Or something like that.

Frankly I can’t recall the details, but they’re not so relevant. I’m just telling you this because someone asked “Why these dark matter particles? Why this interaction?” To which Randall’s answer was (I paraphrase) I don’t know but you can test it.

I don’t mean to pick on her specifically, it just so happens that this talk was the moment I understood what’s wrong with the argument. Falsifiability alone doesn’t make a theory scientific.

If the only argument that speaks for your idea is that it’s compatible with present data and makes a testable prediction, that’s not enough. My idea that Trump will get shot is totally compatible with all we presently know. And it does make a testable prediction. But it will not enter the annals of science, and why is that? Because you can effortlessly produce some million similar prophecies.

In the foundations of physics, compatibility with existing data is a high bar to jump, or so they want you to believe. That’s because if you cook up a new theory you first have to reproduce all achievements of the already established theories. This bar you will not jump unless you actually understand the present theories, which is why it’s safe to ignore the all-caps insights on my timeline.

But you can learn how to jump the bar. Granted, it will take you a decade. But after this you know all the contemporary techniques to mass-produce “theories” that are compatible with the established theories and make eternally amendable predictions for future experiments. In my upcoming book, I refer to these techniques as “the hidden rules of physics.”

These hidden rules tell you how to add particles to the standard model and then make it difficult to measure them, or add fields to general relativity and then explain why we can’t see them, and so on. Once you know how to do that, you’ll jump the bar every time. All you have to do then is twiddle the details so that your predictions are just about to become measureable in the next, say, 5 years. And if the predictions don’t work out, you’ll fiddle again.

And that’s what most theorists and phenomenologists in high energy physics live from today.

There are so many of these made-up theories now that the chances any one of them is correct are basically zero. There are infinitely many “hidden sectors” of particles and fields that you can invent and then couple so lightly that you can’t measure them or make them so heavy that you need a larger collider to produce them. The quality criteria are incredibly low, getting lower by the day. It’s a race to the bottom. And the bottom might be at asymptotically minus infinity.

This overproduction of worthless predictions is the theoreticians’ version of p-value hacking. To get away with it, you just never tell anyone how many models you tried that didn’t work as desired. You fumble things together until everything looks nice and then the community will approve. It’ll get published. You can give talks about it. That’s because you have met the current quality standard.  You see this happen both in particle physics and in cosmology and, more recently, also in quantum gravity.

This nonsense has been going on for so long, no one sees anything wrong with it. And note how very similar this is to the dismal situation in psychology and the other life-sciences, where abusing statistics had become so common it was just normal practice. How long will it take for theoretical physicists to admit they have problems too?

Some of you may recall the book of philosopher Richard Dawid who claimed that the absence of alternatives speaks for string theory. This argument is wrong of course. To begin with there are alternatives to string theory, just that Richard conveniently doesn’t discuss them. But what’s more important is that there could be many alternatives that we do not know of. Richard bases his arguments on Bayesian reasoning and in this case the unknown number of unknown alternatives renders his no-alternative argument unusable.

But a variant of this argument illuminates what speaks against, rather than for, a theory. Let me call it the “Too Many Alternatives Argument.”

In this argument you don’t want to show that the probability for one particular theory is large, but that the probability for any particular theory is small. You can do this even though you still don’t know the total number of alternatives because you know there are at least as many alternatives as the ones that were published. This probabilistic estimate will tell you that the more alternatives have been found, the smaller the chances that any one of them is correct.

Really you don’t need Bayesian mysticism to see the logic, but it makes it sound more sciency. The point is that the easier it is to come up with predictions the lower their predictive value.

Duh, you say. I hear you. How come particle physicist think this is good scientific practice? It’s because of upside-down Popper! They make falsifiable predictions – and they believe that’s enough.

Yes, I know. I’m well on the way to make myself the most-hated person in high energy physics. It’s no fun. But look, even psychologists have addressed their problems by introducing better quality criteria. If they can do it, so can we.

At least I hope we can.

Thursday, November 02, 2017

Book Review: Max Tegmark “Our Mathematical Universe”

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality
Knopf (January 2014)

Max Tegmark just published his second book, “Life 3.0.” I gracefully declined reviewing it, seeing that three years weren’t sufficient to finish his first book. But thusly reminded of my shortfall, I made another attempt and finally got to the end. So here’s a late review or, if you haven’t made it through in three years either, a summary.

Tegmark is a cosmologist at MIT and his first book, “Our Mathematical Universe,” is about the idea that the world is not merely described by mathematics, but actually made of mathematics.

I told you ten years ago why this is nonsense and haven’t changed my mind since. It was therefore pretty clear I wouldn’t be fond of Max’s message.

But. Well. People like Max don’t grow on trees. I have much sympathy for his free-range ideas and also, even though I’ve met him several times, I never really figured out what he was tenured for. Probably not the mathematical universe. Once upon a time, I was sure, he must have done actual physics.

Indeed, as the book reveals, Tegmark did CMB analysis before everyone else did it. This solid scientific ground is also where he begins his story: With engaging explanations of contemporary cosmology, the evolution of the universe, general relativity, and all that. He then moves on to inflation, eternal inflation and the multiverse, to quantum mechanics in general and the many worlds interpretation in particular. After this, he comes to the book’s main theme, the mathematical universe hypothesis. At that point we’re at page 250 or so.

Tegmark writes well. He uses helpful analogies and sprinkles some personal anecdotes which makes the topic more digestible. The book also has a lot of figures, about half of which are helpful. I believe I have seen most of them on his slides.

Throughout the book, Tegmark is careful to point out where he leaves behind established science and crosses over into speculation. However, by extrapolating from the biased sample of people-he-spends-time-with, Tegmark seems to have come to believe the multiverse is much more accepted than is the case. Still, it is certainly a topic that is much discussed and worth writing about.

But even though Tegmark’s story flows nicely, I got stuck over and over again. The problem isn’t that the book is badly written. The problem is that, to paraphrase John Mellencamp, the book goes on long after the thrill of reading is gone.

Already in the first parts of the book, Tegmark displays an unfortunate tendency to clutter his arguments with dispensable asides. I got the impression he is so excited about writing that, while at it, he just also has to mention this other thing that he once worked on, and that great idea he had which didn’t work, and why that didn’t work, and how that connects with yet something else. And did I mention that? By the way, let me add this. Which is related to that. And a good friend of mine thinks so. But I don’t think so. And so on.

And then, just when you think the worst is over, Tegmark goes on to tell you what he thinks about alien life and consciousness and asteroid impacts and nuclear war and artificial intelligence.

To me, his writing exhibits a familiar dilemma. If you’ve spent years thinking about a topic, the major challenge isn’t deciding what to tell the reader. It’s deciding what to not tell them. And while some readers may welcome Tegmark’s excursions, I suspect that many of them will have trouble seeing the connections that he, without any doubt, sees so clearly.

As to the content. The major problems with Max’s idea that the universe is made of mathematics rather than merely described by mathematics are:
  1. The hypothesis is ill-defined without explaining what “is real” means. I therefore don’t know what’s the point even talking about it.

  2. Leaving this aside, Max erroneously thinks it’s the simplest explanation for why mathematics is so useful, and hence supported by Ockham’s razor (though he doesn’t explicitly say so). The argument is that if reality is merely described by mathematics rather than actually made of mathematics, then one needs an additional criterion to define what makes some things real and others not.

    But that argument is logically wrong. Saying that the universe is accurately described by mathematics makes no assumption about whether it “really is” mathematics (scare quotes to remind you that that’s ill-defined). It is unnecessary to specify whether the universe is mathematics or is something more, evidenced by scientists never bothering with such a specification. Ockham’s razor thus speaks against the mathematical universe.

  3. He claims that a theory which is devoid of “human baggage” must be formulated in mathematics. I challenge you to prove this, preferably without using human baggage. If that was too meta: Just because we don’t know anything better than math to describe nature doesn’t mean there is nothing.

  4. Max also erroneously thinks, or at least claims in the book, that the mathematical universe hypothesis is testable. Because, so he writes, it predicts that we will continue to find mathematical descriptions for natural phenomena.

    But of course if there was something for which we do not manage to find a mathematical description, that would never prove the mathematical universe wrong. After all, it might merely mean we were too dumb to figure out the math. Now that I think of it, maybe our failure to quantize gravity falsifies the mathematical universe.
There are further various statements in the book which I can’t make sense of. For example, I have no idea what an “element” of a mathematical structure is. I only know elements of sets. I also don’t understand why Tegmark believes accepting that our universe is a mathematical structure means that differential equations no longer need initial conditions. Or so he seems to say. Even more perplexing, he argues that the multiverse explains why the constants of nature seem finetuned for the existence of life. This is a misunderstanding of both finetuning and the anthropic principle.

There. I’ve done it again. I set out with the best intention to say nice things, but all that comes out is “wrong, wrong, wrong.”

To work off my guilt, I’ll now have to buy his new book too. Check back in three years.