Thursday, April 30, 2020

Book Review: “The Dream Universe” by David Lindley

The Dream Universe: How Fundamental Physics Lost Its Way
By David Lindley
Doubleday (March 17, 2020)

Let me be honest: I expected to dislike this book. For one because it looked like a remake of Lindley’s 1993 book The End of Physics which I already disliked. Also, physics didn’t end. Worse still, if you read the description of his new book, you can easily mistake it for a description of my book Lost in Math. On the website of Lindley’s publisher you find, for example, that The Dream Universe is about “how theoretical physics is returning to its unscientific roots” and that physicists have come to believe
“As we investigate realms further and further from what we can see and what we can test, we must look to elegant, aesthetically pleasing equations to develop our conception of what reality is. As a result, much of theoretical physics today is something more akin to the philosophy of Plato than the science to which the physicists are heirs.”
However, after reading Lindley’s book, I changed my mind. It is a good book and while I think that Lindley in the end draws the wrong conclusions, it is well worth the read. Let me explain.

First of all, The Dream Universe is dramatically better than The End of Physics. The latter struck me as a superficial and, ultimately, pointless attack on some trends in contemporary physics just because the author had other ideas for what physicists should do. There really wasn’t much to learn from the book. The Dream Universe is instead a historical analysis of the changing role of mathematics in the foundations of physics and the growing divide between theory and experiment in the field. In his new book, Lindley makes a well-reasoned case that something is going badly wrong.

Lindley’s book of course has some overlap with mine. Both discuss the problem that arguments from mathematical beauty have become widely accepted among physicists even though they are unscientific. But while I wrote a book about current events with only a short dip into history, and told this story as someone who works in the field, Lindley provides the perspective of an outsider, albeit one who is knowledgeable both about physics and the history of science.

As Lindley tells the reader in the preface, he started a research career in physics, but then left to become a science writer. The End of Physics was his first book after this career change. He then became interested in the history of science and wrote several historical books. Now he has taken on the foundations of physics again with a somewhat more detached view.

The Dream Universe begins with some rather general chapters about the scientific method and about how scientists use mathematics. You find there the story of Galileo, Copernicus, and the epicycles, as well reflections on the conflict-loaded relation between science and the church. Lindley then moves on to the invention of calculus, the development of electrodynamics, and the increasing abstraction of physics, all the way up to string theory and the idea that the universe is a quantum computer. He lists some successes of this abstraction – notably Dirac’s prediction of anti-matter – before showing where this trend has led us: To superstrings, multiverses, lots of empty blather, and a complete lack of progress in the field.

Lindley is a skilled writer and the book is a pleasure to read. He explains even the most esoteric physics concepts eloquently and without wasting the reader’s time. Overall, he maintains a good balance between science, history, and the lessons of both. Lindley also doesn’t leave you guessing about his own opinion. In several places he says very clearly what he thinks about other historians’, scientists’, or philosophers’ arguments which I find so much more valuable than pages of polite tip-toeing that you have to dissect with an electron microscope to figure out what’s really being said.

The reader also learns that Lindley’s personal mode of understanding is visualization rather than abstraction. Lindley, for example, expresses at some point his frustration with a professor who explained (entirely correctly, if you ask me) that “a tensor is an object that transforms as a tensor” with a transformation law that the professor presumably previously defined. Lindley reacts: “Here is how I would explain a tensor. Think of a cube of jellylike material.” It follows two paragraphs about jelly that I personally find entirely unenlightening. Goes to show, I guess, that different people prefer different modes of explanation.

In the end, Lindley puts the blame for the lack of progress in the foundations of physics on mathematical abstraction, a problem he considers insurmountable. “The unanswerable difficulty, as I hope has become clear by now, is that researchers in fundamental physics are exploring a world, or worlds, hopelessly removed from our experience… What defines those unknowable worlds is perfect order, mathematical rigor, even aesthetic elegance.”

He then classifies “fundamental physics today as a kind of philosophy” and explains it is now “less about a strictly rational understanding of the universe and more about finding a scenario that we deem intellectually respectable.” He sees no way out of this situation because “Observation, experiment, and fact-finding are no longer able to guide [researchers in fundamental physics], so they must set their path by other means, and they have decided that pure rationality and mathematical reasoning, along with a refined aesthetic sense, will do the job.”

I am sympathetic to Lindley’s take on the current status of research in the foundations of physics, but I think the conclusion that there is no way forward is not supported by his argument. The problem in modern physics is not the abundance of mathematical abstraction per se, but that physicists have forgotten mathematical abstraction is a means to an end, not an end unto itself. They may have lost sight of the goal, alright, but that doesn’t mean the goal has ceased to exist.

It is also simply wrong that there are no experiments that could guide physicists in the foundations of physics, and I say this as someone who has spent the past 20 years thinking about this very problem. It’s just that physicists are wasting time publishing papers about beautiful theories that have no relevance for nature instead of analyzing what is going wrong in their discipline and how to make progress.

In summary, Lindley’s book is not so much a competition to Lost in Math as a complement. If you want to understand what is going wrong in the foundations of physics, The Dream Universe is an excellent and timely introduction.

Disclaimer: Free review copy.

Book Review: “A Philosophical Approach To MOND” by David Merritt

A Philosophical Approach to MOND: Assessing the Milgromian Research Program in Cosmology
By David Merritt
Cambridge University Press (April 30, 2020)

Don’t get put off by the title of the book! Really it should have been called “A Scientific Approach To MOND,” and I am so glad someone wrote it. MOND, to remind you, stands for Modified Newtonian Dynamics, which is the competing hypothesis to dark matter. Dark matter explains a whole bunch of astrophysical observations by positing a new type of matter that makes itself noticeable only through its gravitational pull. MOND instead postulates that the laws of gravity change on galactic scales.

The vast majority of astrophysicists today think erroneously that dark matter has better support in observational evidence, but Merritt cleans up with this myth. Let me emphasize that Merritt is not originally a philosopher by training. He worked for decades in astrophysics before his interest turned to the philosophy of science in recent years. His book is not a verbose pamphlet, as – excuse me – philosophical treatises tend to be, but it’s an in-depth scientific analysis.

What makes Merritt’s book special is that he evaluates the evidence, both for MOND and the standard model of cosmology, according to the most widely accepted criteria put forward by Popper, Zahar, Musgrave, and Carrier. The physicists among you need not despair: Merritt’s book has an excellent (and blissfully short) introduction into the philosophy of science that contains everything you need to know to follow along.

The book is extremely well structured. Merritt first analyses MOND as a phenomenological idea, largely formulated in words, then MOND in the non-relativistic case, then relativistic completions, and then the hybrid theory of dark matter and modified gravity that can be interpreted as a type of superfluid dark matter. In each step, Merritt examines how the theory fares with respect to confirmed predictions and corroboration, which he summarizes in handy tables.

Along the way he cleans up with quite a number of mistakes that you encounter all over the published literature. Yes, this is hugely troubling, and it should indeed trouble you. There is for example the idea that MOND cannot explain the CMB power spectrum when indeed it made a correct prediction for the second peak, whereas dark matter did not. In fact, astrophysicists had to twiddle with the dark matter idea after the measurement to accommodate the new data. Another wrong but wide-spread conviction is that modified gravity has somehow been ruled out by observation on galaxy clusters.

Having said that, Merritt clearly points out that MOND (or its relativistic generalizations) has certain problems, notably the third peak of the CMB is a headache.

The most interesting part of the book, though, is that Merritt demonstrates by many quotations that astrophysicists who prefer dark matter are confusing the predictive power of a theory with the ability of the theory to accommodate new evidence.

I have found this book tremendously useful, though I want to warn you that this is clearly not a popular science book. The book is full with technical detail. However, I believe that the biggest part of it should be understandable for anyone who has an interest in the topic. There are some parts which will be incomprehensible if you don’t at least have an undergrad degree in physics, eg when Merritt goes on about the Lagrangian formulation of the relativistic completions. But I don’t think that these parts are really essential to understand Merritt’s argument.

But. Of course I have a “but”!

I think that Merritt does not pay enough attention to the problem that MOND, because it is non-relativistic, is incompatible with an extremely well-confirmed theory – General Relativity –, and that we have to date no relativistic completion that does not run into other problems with evidence. This means that MOND, simply put, does not live up to the current scientific standard in the field.

Let me be clear that this does not mean that MOND – as an approximation – is wrong. But I believe the lack of a controlled limit to recover General Relativity is the major reason why so many physicists presently reject MOND. I find it somewhat unfair to simply disregard the scientific standard. The standard is there for a reason, and that reason itself is based on evidence, namely: Certain types of theories have proved successful. MOND is not that type of theory, and no one has yet managed to improve it. It only reproduces General Relativity in the cases where we have precision tests by postulating that it does so, not because there is an actual derivation that demonstrates this is consistently possible. This is an extremely non-trivial problem.

This problem is solved by the hybrid version that can be interpreted as superfluid dark matter. In Merritt’s evaluation this option receives mediocre grades. But of course this is because he does not appreciate the need to remove the tension between MOND and general relativity to begin with. Superfluid dark matter does this.

In summary, I think that everyone who has a research interest in astrophysics and cosmology will benefit from reading this book. And I think that physics would much benefit from a similar analysis of inflation and other hypotheses for the early universe, quantum gravity, theories of everything and grand unification, and quantum foundations.

Disclaimer: Free review copy

Wednesday, April 29, 2020

The Raven Paradox

The scientific method is only a few hundred years old. This continues to amaze me. It seems so obvious, now, that you should go and test your theories and, if necessary, revise them. But for much of human history, coming up with a “theory” was merely about story-telling and sense-making, not about making quantitatively accurate predictions.

Then again, the scientific method is not set in stone. Scientists and philosophers both are still trying to understand just how to identify the best hypothesis or when to discard one. This is not as trivial as it sounds, and this difficulty is well illustrated by the Raven Paradox, which I want to talk about today.

The Raven Paradox was first discussed in the 1940s by the German philosopher Carl Gustav Hempel and it is therefore also known as Hempel’s paradox. Hempel was thinking about what type of evidence counts in favor of a hypothesis. As an example, he used the hypothesis “All ravens are black”. If you see a raven, and the raven is indeed black, then you’d say this counts as evidence in favor of the hypothesis. So far, so good.

Now, the hypothesis that all ravens are black can be expressed as a logical statement in the form “If something is a raven, then it is black.” This statement is then logically equivalent to saying “If something is not black, then it is not a raven.” But once you have reformulated the hypothesis this way, then anything not black that is not a raven counts in favor of your hypothesis. Say, you see a red bus, then that speaks for the hypothesis that ravens are black, because the bus is not black and it not a raven either. If you see a green apple, that’s even more evidence that ravens are black. Yellow post-its? Brown snails? White daisies? They’re all evidence that ravens are black!

To most of you this will sounds somewhat nuts, and that’s what’s paradoxical about it. The argument is logically entirely correct. And yet, it seems intuitively wrong. This is not how we actually go about collecting evidence for hypotheses. So what is going on? Do we maybe not understand how science works after all?

Hempel himself seems to have thought that our intuition is just wrong. But the more commonly accepted explanation is today that our intuition is right, at least in this case. This explanation has it that we think black ravens are better evidence for the hypothesis that ravens are black than non-black non-ravens because there are more non-black non-ravens than there are black ravens, and indeed we have seen a lot of non-black non-ravens in our lives already. So, if we see a green apple, that’s evidence, alright, but it’s not very interesting evidence. It’s not very surprising. It does not tell you much new.

This argument can be made more formal using Bayesian inference. Bayesian inference is a method to update your evaluation of the probability of a hypothesis if you get more information. And indeed, for the raven paradox the calculation seems to be showing that the non-black non-ravens *are evidence in favor of the hypothesis, but black ravens are better evidence. They help you gain more confidence in your hypothesis.

But. The argument from Bayesian inference expects you to know how many non-black non-ravens there are compared to ravens. You might estimate this to be a large number, but where do you get the evidence for that number from? And how have you evaluated it? What do you even mean by a non-black non-raven. Come to think of it, just how do you define “raven”? And what does it mean for something to be “black”? And so on. You can debate this endlessly, if you want.

But you know me, I don’t want to debate this endlessly, I just want to inspire you to think about this paradox for a moment and maybe confuse some other people with it.

Tuesday, April 28, 2020

New blog feature: Chat with other commenters

Moderating comments on this blog is a constant pain. That’s partly because there are always commenters which ignore the comment rules, thus forcing me to step in and reprimand them. Trust me, I don’t enjoy it. But this is a minor hassle. The real trouble with comment sections, here and elsewhere, is that they fulfil two different roles which conflict with each other.

See, my main interest in the comment section is that it contributes to the topic of my blogpost and adds valuable information for other readers. Many commenters, however, would rather use the comment section to discuss their own ideas or have an exchange about something else entirely. Now, in principle I think it’s great if my writing stimulates discussion, but I don’t want it to clog my threads. This brings me in the unfortunate position that I constantly have to tell people to shut up and go elsewhere instead of encouraging them to discuss.

But I may have stumbled over a solution for this problem.

Late last year, I got an email from Ben Alderoty, who had been working on an app that allows website visitors to have private one-on-one conversations. The app is called “Conversful” and if you’re on a laptop or desktop you should see it appear in the bottom right corner of your screen.

Click on the icon, and you are asked to enter a name or pseudonym and a topic you want to have a chat about. I would suggest that you use the same pseudonym that you use for commenting here, so that others recognize you.

Since blogs tend to collect like-minded people, I hope the chances are good that you will find someone to exchange thoughts with, especially since many of you have gotten to know each other over the years already. This blog receives most of its traffic from the USA, Canada, the UK, and Germany. This means that the traffic is the highest between the morning and early afternoon Eastern Time, or between the early afternoon and evening Central European Time, respectively. During these times you are most likely to meet other commenters here.

I want to emphasize that this is a test-run of software which is not yet fully developed and does not have all the functionality you may want from it. But I believe that this idea has much potential. It essentially turns websites in virtual meeting places, where you can have conversations without blasting your words out to the whole world.

If you have feedback or comments on this feature, please let me know, most easily by leaving a comment on this thread. The feedback you provide will go directly to the Conversful team for them to make improvements to the app. If you are running a website yourself where this app might be useful, please get in touch with Ben at For more information about them and their vision, you can also check their website

No, physicists have not explained why there is more matter than anti-matter in the universe. It’s not possible.

Pretty? Get over it.
You would think that physicists finally understood that insisting the laws of nature must be beautiful is unscientific. Or at least, if they do not understand it, you would think science writers meanwhile understand it. But every couple of months I have to endure yet another media blast about physicists who may have solved a problem that does not exist in the first place.

The most recent installation of this phenomenon are loads of articles about the recent T2K results that hint at CP violation in the neutrino sector. Yes, this is an interesting result and deserves to be written about. The problem is not the result itself, the problem is scientists and science writers who try to make this result more important than it is.

Truth be told, few people care about CP violation in the neutrino sector. To sell the story, therefore, this turned into a tale about how the results supposedly explain why there is more matter than antimatter in the universe. But: The experiment does not say anything about why there is more matter than anti-matter in the universe. No, it does not. No, not a single bit. If you think it does, you need to urgently switch on your brain. I do not care what your professor said, please think for yourself. Start it right now.

You can see for yourself what the problem is by reading the reports in the media. Not a single one of them explains why anyone should think there ever were equal amounts of matter and anti-matter to begin with. Leah Crane, for example, writes for New Scientist: “Our leading theories tell us that, in the moments after the big bang, there was an equal amount of matter and antimatter.”

But, no, they do not. They cannot. You don’t even need to know what these “leading theories” look like in detail, except that, as all current theories in physics, they work by applying differential equations to initial values. Theories of this type can never explain the initial values themselves. It’s not possible. The theories therefore do not tell us there was an equal amount of matter and antimatter. This amount is a postulate. The initial conditions are always assumptions that the theory does not justify.

Instead, physicists think for purely aesthetic reasons it would have been nicer if there was an equal amount of matter and antimatter in the early universe. Trouble is, this does not agree with observation. So then they cook up theories for how you can start with an equal amount of matter and anti-matter and still end up with a universe like the one we see. You find a good illustration for this in a paper by Steigman and Scherrer with the title “Is The Universal Matter - Antimatter Asymmetry Fine Tuned?” (arXiv:1801.10059) They write:
“One possibility is that the Universe actually began in an asymmetric state, with more baryons and antibaryons. This is, however, a very unsatisfying explanation. Furthermore, if the Universe underwent a period of inflation (i.e., very rapid expansion followed by reheating), then any preexisting net baryon number would have been erased. A more natural explanation is that the Universe began in an initally [sic] symmetric state, with equal numbers of baryons and antibaryons, and that it evolved later to produce a net baryon asymmetry.”
They call it an “unsatisfying explanation” to postulate a number, but the supposedly better explanation still postulates a number!

People always complain to me that I am supposedly forgetting that science is all about “explaining”. These complainers do not listen. Nothing is being explained here. The two hypothesis on the table are: “The universe started with a ratio X of matter to anti-matter and the outcome is what we observe.” The other explanation is “The universe started with a ratio Y of matter to anti-matter, then many complicated things happened and the outcome is what we observe.” Neither of these theories explains the value of X or Y. If anything, you should prefer the former hypothesis because it’s clearly the simpler one. In any case, though, as I said, this type of theory cannot explain their own initial value.

But here is the mind-boggling thing: The vast majority of physicists think that the second explanation is somehow better because the number 1.0000000000 is prettier than the number 1.0000000001. That’s what it comes down to. They like some numbers better than others. But, look, a first grader can see the problem. Physicists are wondering why X=1.0000000001. But with the supposedly new explanation you then ask why Y=1.0000000000? How is that an improvement? Answer: It is not.

Let me emphasize once again that the problem here is not the experiment itself. The problem is that physicists mistakenly think something is being explained because they never bothered to think about what it even means to explain something.

You may disagree with me that scientists should not waste time on trying to prettify the laws of nature, alright. Maybe you think this is something scientists should do with tax money. But I expect that if a topic gets media coverage then the public hears the truth. So here is the truth: No problem has been solved. The problem is not solvable with the current theories of nature.

Friday, April 24, 2020

Understanding Quantum Mechanics #1: It's not about discreteness

This must be one of the most common misunderstandings about quantum mechanics, that quantum mechanics is about making things discrete. But is an understandable misunderstanding because the word “quantum” suggests that quantum mechanics is about small amounts of something. Indeed, if you ask Google for the meaning of quantum, it offers the definition “a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents.” Problem is that just because energy is proportional to frequency does not mean it is discrete. In fact, in general it is not.

The reason that quantum mechanics has become associated with discretization is entirely historical. The first signs that something was not quite right with the fundamental theories of the 19th century came from atomic spectral lines. Atoms can absorb and emit light only at certain frequencies. If you think that atoms are basically blobs of particles stuck together, which was what people thought at the time, then this makes absolutely no sense.

According to quantum mechanics now, the negatively charged electrons occupy shells around the positively charged nucleus. These shells cannot have any radius, but only certain values of the radius are allowed. Just what shape the shells have and how large they are can be calculated with quantum mechanics. And this explains why atoms can only absorb and emit light of certain frequencies. Because the energy of the light must fit to the energy that moves an electron from one shell to another.

So, yes, the energies of electrons which are bound to atoms are discrete. But the energies of electrons, or of any particle really, are not always discrete, and neither are other measureable quantities. The energy of a photon traveling through empty space, for example, can have any value according to quantum mechanics. The energy is not discrete. Or, if you look at an electron in the conducting band of a metal, it can be at any position. The position is not discrete.

What, then, does it mean to have a quantum theory as opposed to a non-quantum theory? A quantum theory is one in which you have observable quantities that obey Heisenberg’s uncertainty principle. Mathematically, this is not entirely the correct definition. More precisely a quantum theory has operators for observables which do not commute. But for what the physical consequences are concerned, the uncertainty principle is what tells quantum from non-quantum theories. The other important property of quantum theories is that you can have entanglement. We will talk about what this means another time.

For today, the lesson to take away is that quantizing a theory does not mean you make it discrete. This is important also when it comes to the quantization of gravity. Quantizing gravity does not necessarily mean that space and time have to be discrete. Thanks for watching, see you next week.

PS: I did not suddenly lose half my hair; I just messed up my lighting.

Thursday, April 16, 2020

How Heisenberg Became Uncertain

I have decided that my YouTube channel lacks a history part because there is so much we can learn from the history of science. So, today I want to tell you a story. It’s the story of how Werner Heisenberg got the uncertainty principle named after him.

Heisenberg was born in 1901 in the German city of Würzburg. He went on to study physics in Munich. In 1923, Heisenberg was scheduled for his final oral examination to obtain his doctorate. He passed mathematics, theoretical physics, and astronomy just fine, but then he run into trouble with experimental physics.

His examination in experimental physics was by Wilhelm Wien. That’s the guy who has Wien’s law named after him. Wien, as an experimentalist, had required that Heisenberg did a “Praktikum” which is a series of exercises in physics experimentation; it’s lab work for beginners, basically. But the university lacked some equipment and Heisenberg was not interested enough to find out where to get it. So he just moved on to other things without looking much into the experiments he was supposed to do. That, as it turned out, was not a good idea.

When Heisenberg’s day of the experimental exam came, it did not go well. In their book “The Historical Development of Quantum Theory”, Mehra and Rechenberg recount:
“Wien was annoyed when he learned in the examination that Heisenberg had done so little in the experimental exercise given to him. He then began to ask [Heisenberg] questions to gauge his familiarity with the experimental setup; for instance, he wanted to know what the resolving power of the Fabry-Perot interferometer was... Wien had explained all this in one of his lectures on optics; besides, Heisenberg was supposed to study it anyway... But he had not done so and now tried to figure it out unsuccessfully in the short time available during the examination. Wien... asked about the resolving power of a microscope; Heisenberg did not know that either. Wien questioned him about the resolving power of telescopes, which [Heisenberg] also did not know.”
What happened next? Well, Wien wanted to fail Heisenberg, but the theoretical physicist Arnold Sommerfeld came to Heisenberg’s help. Heisenberg had excelled in the exam on theoretical physics, and so Sommerfeld put in a strong word in favor of giving Heisenberg his PhD. With that, Heisenberg passed the doctoral examination, though he got the lowest possible grade.

But this was not the end of the story. Heisenberg was so embarrassed about his miserable performance that he sat down to learn everything about telescopes and microscopes that he could find. This was in the early days of quantum mechanics and it led him to wonder if there is a fundamental limit to how well one can resolve structures with a microscope. He went about formulating a thought experiment which is now known as “Heisenberg’s Microscope.”

This thought experiment was about measuring a single electron, something which was actually not possible at the time. The smallest distance you can resolve with a microscope, let us call this Δ x, depends on both the wave-length of the light that you use, I will call that λ, and the opening angle of the microscope, ε. The smallest resolvable distance is proportional to the wave-length, so a smaller wave-length allows you to resolve smaller structures. And it is inversely proportional to the sine of the opening angle. A smaller opening angle makes the resolution worse.

But, said Heisenberg, if light is made of particles, that’s the photons, and I try to measure the position of an electron with light, then the photons will kick the electron. But you need some opening angle for the microscope to work, which means you don’t know exactly where the photon is coming from. Therefore, the act of measuring the position of the electron with a photon actually makes me less certain about where the electron is because I didn’t know where the photon came from.

Heisenberg estimated that the momentum that would be transferred from the photon to the electron to is proportional to the energy of the photon, which means inversely proportional to the wavelength, and proportional to the sine of the opening angle. So if we call that momentum Δ p we have Δ p is proportional to sine ε over λ. And the constant in front of this is Planck’s constant, because that gives you the relation between the energy and the wave-length of the photon.

Now you can see that if you multiply the two uncertainties, the one in position and the one in momentum of the electron, you find that it’s just Planck’s constant. This is Heisenberg’s famous uncertainty principle. The more you know about the position of the particle, the less you know about the momentum and the other way round.

We know today that Heisenberg’s argument for microscopes is not quite correct but, remarkably enough, the conclusion is correct. Indeed, this uncertainty has nothing to do with microscopes in particular. Heisenberg’s uncertainty is far more than that: It’s a general property of nature. And it does not only hold for position and momenta but for many other pairs of quantities.

Many years later Heisenberg wrote about his insight: “So one might even assume, that in the work on the gamma-ray microscope and the uncertainty relation I used the knowledge which I had acquired by this poor examination.”

I like this story because it tells us that if there is something you don’t understand, then don’t be ashamed and run away from it, but dig into it. Maybe you will find that no one really understands it and leave your mark in science.

Thursday, April 09, 2020

What is Reductionism?

Last week, we spoke about emergence, this week, we will speak about the opposite: Reductionism. Reductionism, loosely speaking, is the idea that you can understand things by taking them apart into smaller things. This definition of reductionism, as we will see, is not quite correct, but it’s not too far off. Before we get to the details, however, a few words about how enormously important reductionism is for scientific understanding.

A lot of people seem to think that reductionism is a philosophy. But it most definitely is not. That reductionism is correct is a hypothesis about the properties of nature and it is a hypothesis that has so far been supported by every single experiment that has ever been done. I cannot think of *any scientific fact that is better established than that the properties of the constituents of a system determine how the system works.

To be sure, taking things apart into pieces to understand how they work is not always a good idea. Even leaving aside that taking apart a living organism typically kills it, the problem is that the connection between the theory for the constituents and the theory for the whole system may just be too complicated to be useful. Indeed, this is more often the case than not, which is why figuring out how an organism works from studying its components is not a fruitful strategy. Studying the living organism as a whole is dramatically more useful, so this is what scientists normally do in practice.

But if you really want to *understand what an organism does and how it does it, you will look for an explanation on the level of constituents. Like this part sends a signal to that part. This part stores and releases energy. This piece produces something and does this to another piece, and so on. If we want to really understand something, we look for a reductionist theory. Why? Because we know from experience that reductionist theories have more explanatory power. They lead to new predictions rather than just allowing us to reproduce already observed regularities.

Indeed, the whole history of science until now has been a success story of reductionism. Biology can be reduced to chemistry, chemistry can be reduced to atomic physics, and atoms are made of elementary particles. This is why we have computers today. But, again, this does not mean it is always practical to use a theory for the constituents to describe the composite system. For example, you would not use the standard model of particle physics to predict election outcomes. And why not? Because that would not be useful. The computation would take too long. So what’s the use of reductionism then? The use is that at each level of reduction that scientists have discovered, they gained new insights about how nature works and that has enabled us to make both intellectual and technological progress.

But here is the important point. There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determine the behavior of the whole. Theory reductionism on the other hand means that you have levels of theories where the higher – emergent – levels can be derived from the lower – more fundamental – levels. But in this case, a high level does not necessary mean the theory is about large things, and a low level does not necessarily mean it’s about small things.

So what type of reductionism is it that has been so successful in the history of science? The funny thing is that it’s a combination of both. Methodological reductionism has so far gone hand in hand with theory reductionism. As we have looked at smaller things we have found more fundamental theories.

But this does not necessarily have to remain this way. There is no reason to think that the next better theory of nature will be found by studying shorter distances. Just because the two types of reductionism have been tied together for a while does not mean it will remain this way.

Indeed, some of the biggest currently open problems in physics manifest themselves on large scales, not on small scales. Besides dark energy and dark matter there is also the measurement problem in quantum mechanics. I have told you about those problems in some earlier videos. They are not in any obvious way short-distance phenomena.

So the next time a particle physicist tries to tell you that we need higher energies to probe shorter distances because that’s where progress will come from, remind them that methodological reductionism is not the same as theory reductionism.

Friday, April 03, 2020

What is emergence? What does “emergent” mean?

The word “emerging” is often used colloquially to mean something like “giving rise to” or “becoming apparent”. But emerging, emergent, and emergence are also technical terms. So, today I want to explain what physicists mean by emergence, which is also the way that the expression is often, but not always, used by philosophers.

Emergent broadly speaking refers to novel types of behavior in systems with many interacting constituents. A good example is the “La ola” wave that you sometimes see in the audience of sporting events. It’s not something you can do alone. It only becomes possible because of the interaction between people and their neighbors.

Indeed, something very similar happens in many condensed-matter systems, where the interactions between atomic constituents gives rise to certain types of collective behavior. These can be waves, like with la ola. The simplest example of this are sound waves. Sound waves are really just a simple, collective description for atoms in a gas that move periodically and so create a propagating mode.

But we know that in quantum mechanics waves are also particles and the other way round. This is why in condensed matter systems one can have “quasi-particles” which behave like particles – with quantum properties and wave-behavior and all that – but are actually a collective that moves together. Quasi-particles are emergent from the interactions of many fundamental particles.

And this is really the most relevant property of emergence. Something is emergent if it comes about from the collective behavior of many constituents of a system, be that people or atoms. If something is emergent, it does not even make sense to speak about it for individual elements of the system.

There are a lot of quantities in physics which are emergent. Think for example of conductivity. Conductivity is the ability of a system to transport currents from one end to another. It’s a property of materials. But it does not make sense to speak of the conductivity of a single electron. It’s the same for viscosity, elasticity, even something as seemingly simple as the color of a material. Color is not a property you find if you take apart a painting into elementary particles. It comes from the band structure of molecules. It’s an emergent property.

You will find that philosophers discuss two types of emergence, that is “strong emergence” and “weak emergence”. What I just talked about is “weak emergence”. Weak emergence means that the emergent property can be derived from the properties the system’s constituents and the interactions between the constituents. An electron or a quark may not have a conductivity, but in principle you can calculate how they form atoms, and molecules, and metals, and then the conductivity is a consequence of this.

In physics the only type of emergence we have is weak emergence. With strong emergence philosophers refer to the hypothetical possibility that a system with many constituents displays a novel behavior which cannot be derived from the properties and the interactions of the constituents. While this is logically possible, there is not a single known example for this in the real world.

The best analogy I can think of are photographic mosaics, that are photos made up of smaller photos. If I gave you all the individual photos and their properties you’d have no idea what the “emergent” picture will be. However, this example is hardly a natural phenomenon. To make a photographic mosaic, you start with the emergent image you want to get and then look for photos that will fit. In other words, the “strong emergence” which you have here works only thanks to an “intelligent designer” who had a masterplan.

The problem with strong emergence is not only that we have no scientific theory for it, it’s worse. Strong emergence is incompatible with what we already know about the laws of nature. That’s because if you think that strong emergence can really happen, then this necessarily implies that there will be objects in this world whose behavior is in conflict with the standard model of particle physics. If that wasn’t so, then really it wouldn’t be strong emergence.

A lot of people seem to think that consciousness or free will should be strongly emergent, but there is absolutely no reason to think that this is the case. For all we currently know, consciousness is weakly emergent, as any other collective phenomenon in large systems.