Is COVID there before you measure it?

Today I want to talk about a peculiar aspect of quantum measurements that you may have heard of. It’s that the measurement does not merely reveal a property that previously existed, but that the act of measuring makes that property real. So when Donald Trump claims that not testing people for COVID means there will be fewer cases, rather than just fewer cases you know about, then that demonstrates his deep knowledge of quantum mechanics.

This special role of the measurement process is an aspect of quantum mechanics that Einstein worried about profoundly. He thought it could not possibly be correct. He reportedly summed up the question by asking whether the moon is there when nobody looks, implying that, certainly, the question is absurd. Common sense says “yes” because what does the moon care if someone looks at it. But quantum mechanics says “no”.



In quantum mechanics, the act of observation has special relevance. As long as you don’t look, you don’t know if something is there or just exactly what its properties are. Quantum mechanics, therefore, requires us to rethink what we even mean by “reality”. And that’s why they say it’s strange and weird and you can’t understand it and so on.

Now, Einstein’s remark about the moon is frequently quoted but it’s somewhat misleading because there are other ways of telling whether the moon is there that do not require looking at it in the sense of actually seeing it with our own eyes. We know that the moon is there, for example, because its gravitational pull causes tides. So the word “looking” actually refers to any act of observation.

You could say, but well, we know that quantum mechanics is a theory that is relevant only for small things, so it does not apply to viruses and certainly not to the moon. But well, it’s not so simple. Think of Schrödinger’s cat.

Erwin Schrödinger’s thought experiment with the cat demonstrates that quantum effects for single particles can have macroscopic consequences. Schrödinger said, let us take a single atom which can undergo nuclear decay. Nuclear decay is a real quantum effect. You cannot predict just exactly when it happens, you can only say it happens with a certain probability in a certain amount of time. Before you measure the decay, according to quantum mechanics, the atom is both decayed and not decayed. Physicists say, it is in a “superposition” of these states. Please watch my earlier video for more details about what superpositions are.

But then, Schrödinger says, you can take the information from the nuclear decay and amplify it. He suggested that the nuclear decay could releases a toxic substance. So if you put the cat in a box with the toxin device triggered by nuclear decay, is the cat alive or is it dead if you have not opened the box?

Well, it seems that the cat is somehow both, dead and alive, just like the atom is both decayed and not decayed. And, oddly enough, getting an answer to the question seems to depend on the very human act of making an observation. It is for this reason that people used to think consciousness has something to do with quantum mechanics.

This was something which confused physicists a lot in the early days of quantum mechanics, but this confusion has luckily been resolved, at least almost. First, we now understand that it is irrelevant whether a person does the observation in quantum mechanics. It could as well be an apparatus. So, consciousness is out of the picture. And we also understand that it is really not the observation that is the relevant part but the measurement itself. Things happen when the particle hits the detector, not when the detector spits out a number.

But that brings up the question what is a measurement in quantum mechanics? A measurement is the very act of amplifying the subtle quantum signal and creating a definite outcome. It happens because if the particle hits the detector it has to interact with a lot of other particles. Once this happens, the quantum effects are destroyed.

And here is the important thing. A measurement is not the only way that the quantum system can interact with many particles. Indeed, most particles interact with other particles all the time, just because there is air and radiation around us and there are constantly particles banging into each other. And this also destroys quantum effects, regardless of whether anyone actually measures any of it.

This process in which many particles lose their quantum effects is called “decoherence” because quantum effects come from the “coherence” of states in a superposition. Coherence just means these state which are in a superposition are all alike. But if the superposition interacts with a lot of other particles, this alikeness is screwed up, and with that the quantum effects disappear.

If you look at the numbers you find that decoherence happens enormously quickly, and it happens more quickly the larger the system and the more it interacts. A few particles in vacuum can maintain their quantum effects for a long time. A cat in a box, however, decoheres so quickly there isn’t even a name for that tiny fraction of a second. For all practical purposes, therefore, you can say that cats do not exist in quantum superpositions. They are either dead or alive. In Schrödinger’s thought experiment, the decoherence actually happens already when the toxin is released, so the superposition is never passed on to the cat to begin with.

Now what’s with viruses? Viruses are not actually that large. In fact, some simple viruses have been brought into quantum superpositions. But these quantum superpositions disappear incredibly quickly. And again, that’s due to decoherence. That’s what makes these experiments so difficult. If it was easy to keep large systems in quantum states, we would already be using quantum computers!

So, to summarize. The moon is there regardless of whether you look, and Schrödinger’s cat is either dead or alive regardless of whether you open the box, because the moon and the cat are both large objects that constantly interact with many other particles. And people either have a virus or they don’t, regardless of whether you actually test them.

Having said that, quantum mechanics has left us with a problem that so far has not been resolved. The problem is that decoherence explains why quantum effects go away in a measurement. But it does not explain how to make sense of the probabilities in quantum mechanics for single particles. Because the probabilities seem to suddenly change once you measure the particle. Before measurement, quantum mechanics may have said it would be in the left detector with 50% probability. After measurement, the probability is either 0% of 100%. And decoherence does not explain how this happens. This is known as the measurement problem in quantum mechanics.

Guest Post: “Who Needs a Giant New Collider?” by Alessandro Strumia

Size of 100km tunnel for CERN's planned new collider, the FCC. [Image:CERN]

For the first time in the history of particle physics the scientific program at a collider is mostly in the past light cone and there is no new collider in view. I would like to share my thoughts about this exceptional situation, knowing that many colleagues have negative options of those of us who publicly discuss problems, such as Peter Woit, Sabine Hossenfelder and even Adam Falkowski.

To understand present problems, let’s start from stone age. Something that happens only once in history happened about a century ago: physicists understood what matter is. During this golden period, progress in fundamental physics had huge practical relevance: new discoveries made people richer, countries stronger, and could be used for new experiments that gave new discoveries.

This virtuous cycle attracted the best people and allowed to recognise deep beautiful principles like relativity, quantum mechanics, gauge invariance. After 1945 nuclear physics got huge funds that allowed to explore energies higher than those of ordinary matter building bigger experiments.

This lead to discoveries of new forms of matter, but at energies so high that the new particles had little practical applications, not even for building new experiments. What practical use can have a particle that decays in a zeptosecond? As a result, colliders still use ordinary matter and got bigger because physics demands that the radius of a circular collider grows linearly with energy: R ≈ (4π/α)³ (energy)/(electron mass)² in natural units. This equation means that HEP (High Energy Physics) can explore energies much above the electron mass by becoming HEP (High Expenses Physics). Some people get impressed by big stuff, but it got bigger because we could not make it better.

For decades bigger and bigger colliders got funded thanks to past prestige, but prestige fades away while costs grew until hitting human resources and time-scales. European physicists saw this problem 60 years ago and joined national resources forming CERN. This choice paid: a few decades after WW2 Europe was again the center of high-energy physics. But energy and costs kept growing, and the number of research institutions that push the energy frontier declined as 6, 5, 4, 3, 2, 1.

How CERN began.

Some institutions gave up, others tried. Around 2000 German physicists proposed a new collider, but the answer was nein. Around 2010 Americans tried, but the answer was no. Next Japanese tried, but the answer was “we express interest” which in Japanese probably means no. Europeans waited hoping that new technology will be developed while the Large Hadron Collider will discover new physics and motivate a dedicated new collider to be financed once the economic crisis is over. Instead of new technology and new physics we got a new virus and a possible new crisis.

The responsibility of being the last dinosaur does not help survival. Innovative colliders would need taking risks, but unexplored energies got so high that the cost of a failure is no longer affordable. But this leads to stagnation. CERN now choose a non-innovative strategy based on reliability. First, get time by running LHC ad nauseam. Second, be or appear so nice and reliable that politics might give the needed ≈30 billions. Third, make again ee and pp circular colliders but greater, 100 km instead of 27.

As a theorist I would enjoy a 100 TeV pp collider for my 100th birthday.

But would it be good for society? No discovery is warranted, but anyhow recent discoveries at colliders had no direct practical applications. Despite this, giving resources to best scientists often leads to indirect innovations. The problem is that building a 100 km phonograph seems not a project that can give a technology leap towards a small gadget with the same memory. Rather, collider physics got so gigantic that when somebody has a new idea, the typical answer no longer is “let’s do it” but “let’s discuss at the next committee”. Committees are filled by people who like discussing, while creative minds seem more attracted by different environments. I see many smart physicists voting with their feet.

But would it be good for physics? So far physics is a serious science. This happened because physics had objective data and no school or center ever dominated physics. But now getting more high-energy data needs concentrating most resources in one center that struggles for its survival. Putting all eggs in one basket seems to me a danger. Maybe I am too much sensitive because some time ago CERN removed sociological data that I presented (now accepted for publication) and warned me that its code of conduct restricts free speech if “prejudicial to the Organization”. Happily I am no longer subject to it, and I say what I think.

Extract from rules that CERN claims Strumia violated.

Even if CERN gets the billions, its 100 TeV pp collider is too far away in time: high-energy physics will fade away earlier. Good physicists cannot wait decades fitting Higgs couplings and pretending it’s interesting enough. The only hope is that China decides that their similar collider project is worthwhile and builds it faster and cheaper. This would force CERN to learn how to make a more innovative muon collider in the LHC tunnel or disappear.

How to tell science from pseudoscience

Is the earth flat? Is 5G is a mind-control experiment by the Russian government? What about the idea that COVID was engineered by the vaccine industry? How can we tell apart science from pseudoscience? This is what we will talk about today.

Now, how to tell science from pseudoscience is a topic with a long history that lots of intelligent people have written lots of intelligent things about. But this is YouTube. So instead of telling you what everybody else has said, I’ll just tell you what I think.

I think the task of science is to explain observations. So if you want to know whether something is science you need (a) observations and (b) you need to know what it means to explain something in scientific terms. What scientists mean by “explanation” is that they have a model, which is a simplified description of the real world, and this model allows them to make statements about observations that agree with measurements and – here is the important bit – the model is simpler than just a collection of all available data. Usually that is because the model captures certain patterns in the data, and any kind of pattern is a simplification. If we have such a model, we say it “explains” the data. Or at least part of it.

One of the best historical examples for this is astronomy. Astronomy has been all about finding patterns in the motions of celestial objects. And once you know the patterns, they will, quite literally, connect the dots. Visually speaking, a scientific model gives you a curve that connects data points.

This is arguably over-simplified, but it is an instructive visualization because it tells you when a model stops being scientific. This happens if the model has so much freedom that it can fit any data, because then the model does not explain anything. You would be better off just collecting the data. This is also known as “overfitting ”. If you have a model that has more free parameters as input than data to explain, you may as well not bother with that model. It’s not scientific.

There is something else one can learn from this simple image, which is that making a model more complicated will generally allow a better fit to the data. So if one asks what is the best explanation of a set of data, one has to ask when does adding another parameter not justify the slightly better fit to the data you’d get from it. For our purposes it does not matter just exactly how to calculate this, so let me say that there are statistical methods to evaluate exactly this. This means, we can quantify how well a model explains data.

Now, all of what I just said was very quantitative and not in all disciplines of science are models quantitative, but the general point holds. If you have a model that requires many assumptions to explain few observations, and if you hold on to that model even though there is a simpler explanation, then that is unscientific. And, needless to say, if you have a model that does not explain any observation, then that is also not scientific.

A typical case of pseudoscience are conspiracy theories. Whether that is the idea that the earth is flat but NASA has been covering up the evidence since the days of Ptolemais at least, or that 5G is a plan by the government to mind-control you using secret radiation, or that COVID was engineered by the vaccine industry for profit. All these ideas have in common that they are contrived.

You have to make a lot of assumptions for these ideas to agree with reality, assumptions like somehow it’s been possible to consistently fake all the data and images of a round earth and brainwash every single airline pilot, or it is possible to control other’s people’s mind and yet somehow that hasn’t prevented you from figuring out that minds are being controlled. These contrived assumptions are the equivalent of overfitting. That’s what makes these conspiracy theories unscientific. The scientific explanations are the simple ones, the ones that explain lots of observations with few assumptions. The earth is round. 5G is a wireless network. Bats carry many coronaviruses, these have jumped over to humans before, and that’s most likely where COVID also came from.

Let us look at some other popular example, Darwinian evolution. Darwinian evolution is a good scientific theory because it “connects the dots” basically by telling you how certain organisms evolved from each other. I think that in principle it should be possible to quantify this fit to data, but arguably no one has done that. Creationism, on the other hand, simply posits that Earth was created with everything in place. That means Creationism puts in as much information as you get out of it. It therefore does not explain anything. This does not mean it’s wrong. But it means it is unscientific.

Another way to tell pseudoscience from science is that a lot of pseudoscientists like to brag with making predictions. But just because you have a model that makes predictions does not mean it’s scientific. And the opposite is also true, just because a model does not make predictions does not mean it is not scientific.

This is because it does not take much to make a prediction. I can predict, for example, that one of your relatives will fall ill in the coming week. And just coincidentally, this will be correct for some of you. Are you impressed? Probably not. Why? Because to demonstrate that this prediction was scientific, I’d have to show was better than a random guess. For this I’d have to tell you what model I used and what the assumptions were. But of course I didn’t have a model, I just made a guess. And that doesn’t explain anything, so it’s not scientific.

And a model that does not make predictions can still be scientific if it explains a lot of already existing data. Pandemic models are actually a good example for scientific models which do not make predictions. It is basically impossible to make predictions for the spread of infectious diseases because that spread depends on policy decisions which themselves can’t be predicted.

So with pandemic models we really make “projections” or we can look at certain “scenarios” that are if-then cases. If we do not cancel large events, then the spread will likely look like this. If we do cancel them, the spread will more likely look like that. It’s not a prediction because we cannot predict whether large events will be canceled. But that does not make these models unscientific. They are scientific because they accurately describe the spread of epidemics on record. These are simple explanations that fit a lot of data. And that’s why we use them in the first place.

The same is the case for climate models. The simplest explanation for our observation, the one that fits the data with the least amount of assumptions, is that climate change is due to increasing carbondioxide levels and caused by humans. That’s what the science says.

So if you want to know whether a model is scientific, ask how much data it can correctly reproduce and how many assumptions were required for this.

Having said that, it can be difficult to tell science from pseudoscience if an idea has not yet been fully developed and you are constantly told it’s promising, it’s promising, but no one can ever actually show the model fits to data because, they say, they’re not done with the research. We see this in the foundations of physics most prominently with string theory. String theory, if it would work as advertised, could be good science. But string theorists never seem to get to the point where the idea would actually be useful.

In this case, then, the question is really a different one, namely, how much time and money should you throw at a certain research direction to even find out whether it’s science or pseudoscience. And that, ultimately, is a decision that falls to those who fund that research.

How to search for alien life

Yes, I believe there is life on other planets, intelligent life even. I also think that the search for life elsewhere in the universe is THE most exciting scientific exploration ever. Why then don’t I work on it, you ask? Well, I think I do, kind of. I’ll get to this. But first let me tell you how scientists search for life that’s not on Earth, or “extraterrestrial”, as they say.


When I was a student in the 1990s, talking about extraterrestrial life was not considered serious science. At the time it was not even widely accepted that solar systems with planets like earth are a common occurrence in the universe. But in the past 10 years the mood among scientists has shifted dramatically, and that’s largely thanks to the Kepler mission.

The Kepler satellite was a NASA mission that looked for planets which orbit around stars in our galactic neighborhood. It has observed about 150,000 stars in a small patch of the sky, closely and for long periods of time. From these observations you can tell whether a stars dims periodically because a planet passes by in the line of sight. If you are lucky, you can also tell how big the planet is, how close it is to the star, and how fast it orbits, from which you can then extract its mass.

Kepler has found evidence for more than 4000 exoplanets, as they are called. Big ones and small ones, hot ones and cold ones, and also a few that are not too different from our own planet. Kepler is no longer operating, but NASA has followed up with a new mission, TESS, and several more missions to look for exoplanets are upcoming soon, for example there is another NASA Mission W-FIRST, there is the CHEOPS mission of the E.S.A, and the James Webb Space Telescope, which is a joint mission of NASA, the ESA, and the Canadian Space Agency.

So, we now know that other earth-like planets are out there. The next thing that scientists would like to know is whether the conditions on any of these planets are similar to the conditions on Earth. This is a very human-centered way of thinking about life, of course, but at least so far life on this planet is the only one we are sure exists, so it makes sense, to ask if other places are similar. Ideally, scientists would like to know whether the atmosphere of the earth-like exoplanets contains oxygen and methane, or maybe traces of chlorophyll.

They do already have a few measurements of atmospheres of exoplanets, but these are mostly of large and hot planets that orbit closely around their mother star, because in this case the atmosphere is easier to measure. The way you can measure what’s in the atmosphere is that you investigate the spectral composition of light that either passes through the atmosphere or that is emitted or reflected off the surface. For this too, there are more satellite missions planned, for example the ESA mission ARIEL.

Ok, you may say, but this will in the best case give us an indication for microbial life and really you’d rather know if there is intelligent life out there. For this you need an entirely different type of search. Such searches for extraterrestrial intelligence have been conducted for about century. They have largely relied on analyzing electromagnetic radiation in the radio or micro-wave range that reaches us from outer space. For one that’s because this part of the electromagnetic spectrum is fairly easy to measure without going into the upper atmosphere. But it’s also because our own civilization emits in this part of the spectrum. This electromagnetic radiation is then analyzed for any kind of pattern that is unlikely to be of natural, astrophysical origin.

As you already know, no one found any sign of intelligent life on other planets, except for some false alarms.

The search for intelligent, extraterrestrial life has, sadly enough, always been underfunded, but some people are not giving up their hopes and efforts. There is for example the SETI Institute in California. They have a new plan to look for aliens, which is to distribute 96 cameras on the surface of our planet so that they can look for LASER signals from outer space, 24 hours a day, all over the sky. Like with the search for radio signals, the idea is that LASER-light might be a sign of communication or a by-product of other technologies that extraterrestrial civilizations are using. From those 96 cameras so far one has been installed. The institute is trying to crowdfund the mission, for more information, check out their website.

A search that has no funding issues is the “Breakthrough Listen” project which is supported by billionaire Yuri Milner. This project has run since 2015 and will run through 2025. It employs two radio telescopes to searching for signs of intelligent life. The data that this project has collected so far are publicly available. However, they amount to about 2000 Terabytes, so it’s not exactly user-friendly. Milner has another alien project, which is the “Breakthrough Starshot”. Yes, Milner likes “Breakthroughs” and everything he does is Breakthrough Something; he is also the guy who set up the Breakthrough Prize. The vision of the Starshot project is to send an army of mini space-craft to Alpha Centauri. Alpha Centauri is a solar system in our galactic neighborhood, and “only” about 4 light years away. It is believed to have an earth-like planet. Milner’s mini-space craft are supposed to study this planet and send data back to earth. The scientists on Milner’s team hope to be ready for launch by 2036. It will take 20 to 30 years to reach Alpha Centauri, and then another four years to send the data back to Earth. So, maybe by 2070, we’ll know what’s going on there.

It’s unlikely, of course, that we should be so lucky to find intelligent life basically at the first place we look. Scanning the galaxy for signs of communication, I think, is much more promising. But. We should keep in mind that quite plausibly the reason we have not yet found evidence for extraterrestrial intelligent life is that we have not developed the right technology to pick up their communication. In particular, if there is any way to send information faster than the speed of light, then that’s what all the aliens are using. And, as I explained in an earlier video, in contrast to what you may have been told, there is nothing whatsoever wrong with faster-than-light messaging, except that we don’t know how to do that.

And here is where my own research area, the foundations of physics, becomes really important. If we ever want to find those aliens, we need to better understand space and time, and matter and information. Thanks for watching, see you next week.

Ode to Joy [I've been singing again]

You wanted me to sing in German. Your wish is my command.

Physicists still lost in math

My book Lost in Math was published two years ago, and this week the paperback edition will appear. I want to use the occasion to tell you why I wrote the book and what has happened since.


In Lost in Math, I explain why I have become very worried about what is happening in the foundations of physics. What is happening, you ask? Well, nothing. We have not made progress for 40 years. The problems we are trying to solve today are the same problems we were trying to solve half a century ago.

This worries me because if we do not make progress understanding nature on the most fundamental level, then scientific progress will eventually be reduced to working out details of applications of what we already know. This means that overall societal progress depends crucially on progress in the foundations of physics, more so than on any other discipline.

I know that a lot of scientists in other disciplines find that tremendously offensive. But if they object all I have to do is remind them that without breakthroughs in the foundations of physics there would be no transistors, no microchips, no hard disks, no computers, no wifi, no internet. There would be no artificial intelligence, no lasers, no magnetic resonance imaging, no electron microscopes, no digital cameras. Computer science would not exist. Modern medicine would not exist either because the imaging methods and tools for data analysis would never have been invented. In brief, without the work that physicists did 100 years ago, modern civilization as we know it today would not exist.

I find it somewhat perplexing that so few people seem to realize how big of a problem it is that progress in the foundations of physics has stalled. Part of the reason, I think, is that physicists in the foundations themselves have been talking so much rubbish that people have come to believe foundational work is just philosophical speculation and has lost any relevance for technological progress.

Indeed, I am afraid, most of my colleagues now believe that themselves. It’s wrong, needless to say. A better understand of the theories that we currently use to make all these fancy devices, will almost certainly lead to practical applications. Maybe not in 5 years or 10 years, but more in 100 or 500 years. But eventually, it will.

So, my book Lost in Math is an examination of what has gone wrong. As the subtitle says, the problem is that physicists rely on unscientific methods to develop new theories. These methods are variations of arguments from mathematical beauty, though many physicists are not aware that this is what they are doing.

This problem has been particularly apparent when it comes to the belief that the Large Hadron Collider (LHC) should see new fundamental particles besides the Higgs boson. The reason so many physicists believed this, is that if it had happened, if the LHC would have found other new particles, then the theories would have been much more beautiful. I explained in my book why this argument is unscientific and why therefore, we have no reason to think the LHC should see anything new besides the Higgs. And indeed that’s exactly what happened.

Since the publication of my book, it has slowly sunken in with particle physicists that they were indeed wrong and that their methods did not work. They have largely given up using this particular argument from beauty that led to those wrong LHC predictions. That’s good, of course, but it does not really solve the problem, because they have not analyzed how it could happen that they collectively – and we are talking here about thousands of people – believed in something that was obviously unscientific.

So this is where we stand today. The recognition that something is going wrong in the foundations of physics is spreading. But physicists still have not done anything to fix the problem.

How can we even fix the problem? Well, I explain this in my book. The key is to have a look at what has historically worked. Where have breakthroughs come from in the foundations of physics? Historically a lot of breakthroughs were driven by experimental discoveries. But the simple things have been done and new experiments now are so costly and take such a long time to build, that coincidental discoveries have become incredibly unlikely. You do not just tinker around with a 27 kilometer particle collider.

This means we have to look at the other type of breakthrough, where a theoretical prediction turned out to be correct. Think of Einstein and Dirac and of Higgs and the others who predicted the Higgs boson. What did these correct predictions have in common?

They have in common that they were based on theoretical advances which resolved an inconsistency in the then existing theories. What I mean by inconsistency here is an internal logical disagreement. Therefore, the conclusion I draw from looking at the history of physics is that we should stop trying to make our theories prettier, and instead focus on solving the real problems with these theories.

Some of the inconsistencies in the current theories are the missing quantization of gravity, the measurement problem in quantum mechanics, some aspects of dark energy and dark matter, and some issues with quantum field theories.

I don’t think physicists have really understood what I told them, or maybe they don’t want to understand it. Most of them claim there is no problem, which is patently ridiculous, because everyone who follows popular science news knows that they have been producing loads of nonsense predictions for decades and nothing ever panned out. Clearly, something is going wrong there.

But what I have found very encouraging is the reaction of young physicists to the book, students and postdocs. They don’t want to repeat the mistakes of the past, and they are frequently asking for practical advice. Which I am happy to give, to the extent that I can. The young people give me hope that things will change, eventually, though it might take some time.

“Lost in Math” contains several interviews with key people in the field, Frank Wilczek, Steven Weinberg, Gian Francesco Giudice, who was head of the CERN theory division at the time, Garrett Lisi. George Ellis. Chad Orzel. So you will not only get to hear my opinion, but also that of others. If you haven’t had a chance to read the hardcover, the paperback edition has just appeared, so check it out!

Understanding Quantum Mechanics #3: Non-locality

Locality means that to get from one point to another you somehow have to make a connection in space between these points. You cannot suddenly disappear and reappear elsewhere. At least that was Einstein’s idea. In quantum mechanics it’s more difficult. Just exactly how quantum mechanics is and is not local, that’s what we will talk about today.


To illustrate why it’s complicated, let me remind you of an experiment we already talked about in a previous video. Suppose you have a particle with total spin zero. The spin is conserved and the particle decays in two new particles. One goes left, one goes right. But you know that the two new particles cannot each have spin zero. Each can only have a spin with an absolute value of 1. The easiest way to think of this spin is as a little arrow. Since the total spin is zero, these two spin-arrows of the particles have to point in opposite directions. You do not know just which direction either of the arrows points, but you do know that they have to add to zero. Physicists then say that the two particles are “entangled”.

The question is now what happens if you measure one of the particles’ spins. This experiment was originally proposed as a thought experiment by Einstein, Podolsky, and Rosen, and is therefore also known as the EPR experiment. Well, actually the original idea was somewhat more complicated, and this is a simpler version that was later proposed by Bohm, but the distinction really doesn’t matter for us. The EPR experiment has meanwhile actually been done, many times, so we know what the outcome is. The outcome is... that if you measure the spin on the particle on one side, then the spin of the particle on the other side has the opposite value. Ok, I see you are not surprised. Because, eh, we knew this already, right? So what is the big deal?

Indeed, at first sight entanglement does not appear particularly remarkable because it seems you can do the same thing without quantum anything. Suppose you take a pair of shoes and put them in separate boxes. You don’t know which box contains the left shoe and which the right shoe. You send one box to your friend overseas. The moment the friend opens their box, she will instantaneously know what’s in your box. That seems to be very similar to the two particles with total spin zero.

But it is not, and here’s why. Shoes do not have quantum properties, so the question which box contained the left shoe and which the right shoe was decided already when you packed them. The one box travels entirely locally to your friend, while the other one stays with you. When she opens the box, nothing happens with your box, except that now she knows what’s in it. That’s indeed rather unsurprising.

The surprising bit is that in quantum mechanics this explanation does not work. If you assume that the spin of the particle that goes left was already decided when the original particle decayed, then this does not fit with the observations.

The way that you can show this is to not measure the spin in the same direction on both sides, but to measure them in two different directions. In quantum mechanics, the spin in two orthogonal directions has the same type of mutual uncertainty as the position and momentum. So if you measure the spin in one direction, then you don’t know what’s with the other direction. This means if you on the left side measure the spin in up-down direction and on the right side measure in a horizontal direction, then there is no correlation between the measurements. If you measure them in the same direction, then the measurements are maximally correlated. Where quantum mechanics becomes important is for what happens in between, if you dial the difference in directions of the measurements from orthogonal to parallel. For this case you can calculate how strongly correlated the measurement outcomes are if the spins had been determined already at the time the original particle decayed. This correlation has an upper bound, which is known as Bell’s inequality. But, and here is the important point: Many experiments have shown that this bound can be violated.

And this creates the key conundrum of quantum mechanics. If the outcome of the measurement had been determined at the time that the entangled state was created, then you cannot explain the observed correlations. So it cannot work the same way as the boxes with shoes. But if the spins were not already determined before the measurement, then they suddenly become determined on both sides the moment you measure at least one of them. And that appears to be non-local.

So this is why quantum mechanics is said to be non-local. Because you have these correlations between separated particles that are stronger than they could possibly be if the state had been determined before measurement. Quantum mechanics, it seems, forces you to give up on determinism and locality. It is fundamentally unpredictable and non-local.

Ok, you may say, cool, then let us build a transmitter, forget our frequent flyer cards and travel non-locally from here on. Unfortunately, that does not work. Because while quantum mechanics somehow seems to be non-local with these strong correlations, there is nothing that actually observably travels non-locally. You cannot use these correlations to send information of any kind from one side of the experiment to the other side. That’s because on neither side do you actually know what the outcome of these measurements will be if you chose a particular setting. You only know the probability distribution. The only way you can send information is from the place where the particle decayed to the detectors. And that is local in the normal way.

So, oddly enough, quantum mechanics is entirely local in the common meaning of the word. When physicists say that it is non-local, they mean that particles which have a common origin but then were separated can be stronger correlated than particles without quantum properties could ever be. I know this sounds somewhat lame, but that’s what quantum non-locality really means.

Having said this, let me add a word of caution. The conclusion that it is not possible to explain the observations by assuming the spins were already determined at the moment the original particle decays requires the assumption that this decay is independent of the settings of the detectors. This assumption is known as “statistical independence”. If is violated, it is very well possible to explain the observations locally and deterministically. This option is known as “superdeterminism” and I will tell you more about this some other time.

Is faster-than-light travel possible?

Einstein said that nothing can travel faster than the speed of light. You have probably heard something like that. But is this really correct? This is what we will talk about today.


But first, a quick YouTube announcement. My channel has seen a lot of new subscribers in the past year. And I have noticed that the newcomers are really confused each time I upload a music video. They’re like oh my god she sings, what’s that? So, to make it easier for you, I will no longer post my music videos here, but I have set up a separate channel for those. This means if you want to continue seeing my music videos, please go and subscribe to my other channel.

Now about faster than light travel. To get the obvious out of the way, no one currently knows how to travel faster than light, so in this sense it’s not possible. But you already knew that and it’s not what I want to talk about. Instead, I want to talk about whether it is possible in principle. Like, is there anything actually preventing us from ever developing a technology for faster than light travel?

To find out let us first have a look at what Einstein really said. Einstein’s theory of Special Relativity contains a speed that all observers will measure to be the same. One can show that this is the speed of massless particles. And since the particles of light are, for all we currently know, massless, we usually identify this invariant speed with the speed of light. But if it turned out one day that the particles of light have a small, nonzero mass, then we would still have this invariant speed in Einstein’s theory, it just would not be the speed of light any more.

Next, Einstein also showed that if you have any particle which moves slower than the speed of light, then you cannot accelerate it to faster than the speed of light. You cannot do that because it would take an infinite amount of energy. And this is why you often hear that the speed of light is an upper limit.

However, there is nothing in Einstein’s theory that forbids a particle to move faster than light. You just don’t know how to accelerate anything to such a speed. So really Einstein did not rule out faster than light motion, he just said, no idea how to get there. However, there is a problem with particles that go faster than light, which is that for some observers they look like they go backwards in time. Really, that’s what the mathematics says.

And that, so the argument goes, is a big problem because once you can travel back in time, you can create causal paradoxes, the so-called “grandfather paradoxes”. The idea is, that you could go back in time, kill your own grandfather – accidentally, we hope – so that you would never be born and could not have travelled back in time to kill him, which does not make any sense whatsoever.

So, faster than light travel is a problem because it can lead to causal inconsistencies. At least that’s what most physicists will tell you or maybe have already told you. I will now explain why this is complete nonsense.

It’s not even hard to see what’s wrong with this argument. Imagine you have a particle that goes right to left backwards in time, what would it look like? It would look like a particle going left to right forward in time. These two descriptions are mathematically just entirely identical. A particle does not know which direction of time is forward.

*Our observation that forward in time is different than backward in time comes from entropy increase. It arises from the behavior of large numbers of particles together. If you have many particles together, you can still in principle reverse any particular process in time, but the reversed process will usually be extremely unlikely. Take the example of mixing dough. It’s very easy to get it mixed up and very difficult to unmix, though that is in principle possible.

In any case, you probably don’t need convincing that we do have an arrow of time and that arrow of time points towards more wrinkles. One direction is forward, the other one is not. That’s pretty obvious. Now the reason for the grandfather paradox is not faster than light travel, but it’s that these stories screw up the direction of the arrow of time. You are going back in time, yet you are getting older. *That is the inconsistency. But as long as you have a consistent arrow of time, there is nothing physically wrong with faster-than-light travel.

So, really, the argument from causal paradoxes is rubbish, they are easy to prevent, you just have to demand a consistent arrow of time. But there is another problem with faster-than-light travel and that comes from quantum mechanics. If you take into account quantum mechanics, then a particle that travels faster than light will destroy the universe, basically, which would be unfortunate. Also, it should already have happened, so the existence of faster-than-light particles seems to not agree with what we observe.

The reason is that particles which move faster than light can have negative energy. And in quantum mechanics you can create pairs of new particles provided you conserve the total energy. Now, if you have particles with negative energy, you can pair them with particles of positive energy, and then you can create arbitrarily many of these pairs from nothing. Physicists then say that the vacuum is unstable. Btw, since it is a common confusion, let me mention that anti-particles do NOT have negative energy. But faster than light particles can have negative energy.

This is clearly something to worry about. However, the conclusion depends on how seriously you take quantum theory. Personally I think quantum theory is not itself fundamental, but it is only an approximation to a better theory that has not yet been developed. The best evidence for this is the measurement problem which I talked about in an earlier video. So I think that this supposed problem with the vacuum instability comes from taking quantum mechanics too seriously.

Also, you can circumvent the problem with the negative energies if you travel faster than light by using wormholes because in this case you can use entirely normal particles. Wormholes are basically shortcuts in space. Instead of taking the long way from here to Andromeda, you could hop into one end of a wormhole and just reappear at the other end. Unfortunately, there are good reasons to think that wormholes don’t exist which I talked about in an earlier video.

In summary, there is no reason in principle why faster than light travel or faster than light communication is impossible. Maybe we just have not figured out how to do it.

Talk To Me [I've been singing again]

This is for the guy who recommended I “release” my “inner Whitney Houston”.

Book Update

The US version of my book "Lost in Math" is about to be published as paperback. You can now pre-order it, which of course you should.

I am quite pleased that what I wrote in the book five years ago has held up so beautifully. There has been zero further progress in the foundations of physics and, needless to say, there will be zero progress until physicists understand that they need to change their methodology. Chances that they actually understand this are not exactly zero, but very close by.

In other news, on Monday I gave an online seminar about Superdeterminism, which was recorded and is now available on YouTube. Don't despair if Tim doesn't quite make sense to you; it took me a year to figure out that he isn't as crazy as he sounds.

The How The Light Gets in Festival which is normally in Hay-on-Wye has also been moved online. I think that's great, because Hay-on-Wye is a tiny village somewhere in the middle of nowhere and traveling there has been somewhat of a pain. Indeed, I had actually declined the invitation months ago. But since I can now attend without having to sit on a car, a bus, a plane, a train, and a taxi, I will be in a debate about Supersymmetry tomorrow (May 23) at 11:30am BST (not CEST) and giving a 30 mins talk about my book at 2pm (again that's BST).

[Guest Post] Conversful 101: Explaining What’s In The Bottom Corner Of Your Screen

[This post is written by Ben Alderoty from Conversful.]

You may have noticed something new in the bottom corner of BackRe(action) recently. It appears only if you’re on a computer. So if you’re on a phone or tablet right now, finish reading this post, but then come back another time from a computer to see what I’m talking about. That thing is called Conversful & myself with a team of a few others are behind it. I wanted to take a second to give some context as to what Conversful is & how it works.

We built Conversful to create new conversations. We believe that people on the same website at the same time probably have a lot in common. So much so that if they were to meet randomly at a conference, an airport or a bar, they would probably get into a fantastic conversation. But nothing exists right now to make these spontaneous connections happen. With Conversful, we’re trying to create a space where these connections can happen - a “virtual meeting place” of sorts to borrow Sabine’s words.

To open Conversful, just click the globe icon in the bottom corner. With the app open you can do one of two things; start a new conversation or join a conversation. 1️) To start a new conversation, all you’ll need is a topic and your first name. Topics can be anything. So far we’ve seen topics range from “Physics” to “Stephen Wolfram thinks he is close to a unified theory of physics unifying QM and GR. Some opinions?”. Both of these work. There’s no need to overthink a topic, keep it short, and submit it. 2) Joining a conversation is even easier. With the app open, click ‘Join Conversation’ and enter your first name.

Here’s a few other things:

• Conversations on Conversful are 1-1. They are between the person who started the conversation and the person who joined it.
• Conversations on Conversful are real-time. If you post a topic and then leave before someone joins, your topic will disappear. When you come back to the website at a later time you will not have any responses.
• Conversful is for everyone. We designed Conversful to make it feel like you’re texting a friend. Be yourself, share your thoughts, there’s always someone online to hear them out as long as you’re willing to hear theirs.

Today we rolled out a handful of new features to make it easier for conversations to happen. You’re probably seeing some of them right now. If you’ve already tried Conversful and it didn’t end in a conversation, I ask you to please give it another try!

P.S. To make Conversful the best it can be, I would love to hear from you. If you have any thoughts/ideas/feedback on what’s working (or not) and what else you’d like to see, please feel free to email me at (ben@conversful.com). Cheers from NYC & happy conversing!

Understanding Quantum Mechanics #2: Superposition and Entanglement

If you know one thing about quantum mechanics, it’s that Schrödinger’s cat is both dead and alive. This is what physicists call a “superposition”. But what does this really mean? And what does it have to do with entanglement? This is what we will talk about today.


The key to understanding superpositions is to have a look at how quantum mechanics works. In quantum mechanics, there are no particles and no waves and no cats either. Everything is described by a wave-function, usually denoted with the Greek letter Ψ (Psi). Ψ is a complex valued function and from its absolute square you calculate the probability of a measurement outcome, for example, whether the cat is dead or whether the particle went into the left detector, and so on.

But how do you know what the wave-function does? We have an equation for this, which is the so-called Schrödinger equation. Exactly how this equation looks like is not so important. The important thing is that the solutions to this equation are the possible things that the system can do. And the Schrödinger equation has a very important property. If you have two solutions to the equation, then any sum of those two solutions with arbitrary pre-factors is also a solution.

And that’s what is called a “superposition”. It’s a sum with arbitrary pre-factors. It really sounds more mysterious than it is.

It is relevant because this means if you have two solutions of the Schrödinger equation that reasonably correspond to realistic situations, then any superposition of them also reasonably corresponds to a realistic situation. This is where the idea comes from that if the cat can be dead and the cat can be alive, then the cat can also be in a superposition of dead and alive. Which some people interpret to means, it’s neither dead nor alive but somehow, both, until you measure it. Personally, I am an instrumentalist and I don’t assign any particular meaning to such a superposition. It’s merely a mathematical tool to make a prediction for a measurement outcome.

Having said that, talking about superpositions is not particularly useful, because “superposition” is not an absolute term. It only makes sense to talk about superpositions of something. A wave-function can be a superposition of, say, two different locations. But it makes no sense to say it is a superposition, period.

To see why, let us stick with the simple example of just two solutions, Ψ₁ and Ψ₂. Now let us create two superpositions, that are a sum and a difference of the two original solutions, Ψ₁ and Ψ₂. Then you have two new solutions, let us call them Ψ₃ and Ψ₄. But now you can write the original Ψ₁ and Ψ₂ as a superposition of Ψ₃ and Ψ₄. So which one is a superposition? Well, there is no answer to this. Superposition is just not an absolute term. It depends on your choice of a specific set of solutions. You could say, for example, that Schrodinger’s cat is not in a superposition of dead and alive, but that it is instead in the not-superposed state dead-and-alive. And that’s mathematically just as good.

So, superpositions are sums with prefactors, and it only makes sense to speak about superpositions of something. In some sense, I have to say, superpositions are really not terribly interesting.

Much more interesting is entanglement, which is where the quantum-ness of quantum mechanics really shines. To understand entanglement, let us look at a simple example. Suppose you have a particle that decays but that has some conserved quantity. It doesn’t really matter what it is, but let’s say it’s the spin. The particle has spin zero, and the spin is conserved. This particle decays into two other particles, one flies to the left and one to the right. But now let us assume that each of the new particles can have only spin plus or minus 1. This means that either the particle going left had spin plus 1 and the particle going left had spin minus 1. Or it’s the other way round, the particle going left had spin minus 1, and the particle going right had spin plus 1.

In this case, quantum mechanics tells you that the state is in a superposition of the two possible outcomes of the decay. But, and here is the relevant point, now the solutions that you take a superposition of each contain two particles. Mathematically this means you have a sum of products of wave-functions. And in such a case we say that the two particles are “entangled”. If you measure the spin of the one particle, this tells you something about the spin of the other particle. The two are correlated.

This looks like it’s not quite local, but we will talk about just how quantum mechanics is local or not some other time. For today, the relevant point is that entanglement does not depend on the way that you select solutions to the Schrödinger equation. A state is either entangled or it is not. And while entanglement is a type of superposition, not every superposition is also entangled.

A curious property of quantum mechanics is that superpositions of macroscopic non-quantum states, like the dead and alive cat, quickly become entangled with their environment, which makes the quantum properties disappear in a process called “decoherence”. We will talk about this some other time, so stay tuned.

Thanks for watching, see you next week. Oh, and don’t forget to subscribe.

A brief history of black holes

Today I want to talk about the history of black holes. But before I get to this, let me mention that all my videos have captions. You turn them on by clicking on “CC” in the YouTube toolbar.


Now about the black holes. The possibility that gravity can become so strong that it traps light appears already in Newtonian gravity, but black holes were not really discussed by scientists until it turned out that they are a consequence of Einstein’s theory of general relativity.

General Relativity is a set of equations for the curvature of space and time, called Einstein’s field equations. And black holes are one of the possible solution to Einstein’s equations. This was first realized by Karl Schwarzschild in 1916. For this reason, black holes are also sometimes called the “Schwarzschild solution”.

Schwarzschild of course was not actually looking for black holes. He was just trying to understand what Einstein’s theory would say about the curvature of space-time outside an object that is to good precision spherically symmetric, like, say, our sun or planet earth. Now, outside these objects, there is approximately no matter, which is good, because in this case the equations become particularly simple and Schwarzschild was able to solve them.

What happens in Schwarzschild’s solution is the following. As I said, this solution only describes the outside of some distribution of matter. But you can ask then, what happens on the surface of that distribution of matter if you compress the matter more and more, that is, you keep the mass fixed but shrink the radius. Well, it turns out that there is a certain radius, at which light can no longer escape from the surface of the object, and also not from any location inside this surface. This dividing surface is what we now call the black hole horizon. It’s a sphere whose radius is now called the Schwarzschild radius.

Where the black hole horizon is, depends on the mass of the object, so every mass has its own Schwarzschild radius, and if you could compress the mass to below that radius, it would keep collapsing to a point and you’d make a black hole. But for most stellar objects, their actual radius is much larger than the Schwarzschild radius, so they do not have a horizon, because inside of the matter one has to use a different solution to Einstein’s equations. The Schwarzschild radius of the sun, for example, is a few miles*, whereas the actual radius of the sun is some hundred-thousand miles. The Schwarzschild radius of planet Earth is merely a few millimeters.

Now, it turns out that in Schwarzschild’s original solution, there is a quantity that goes to infinity as you approach the horizon. For this reason, physicists originally thought that the Schwarzschild solution makes no physical sense. However, it turns out that there is nothing physically wrong with that. If you look at any quantity that you can actually measure as you approach a black hole, none of them becomes infinitely large. In particular, the curvature just goes with the inverse of the square of the mass. I explained this in an earlier video. And so, physicists concluded, this infinity at the black hole horizon is a mathematical artifact and, indeed, it can be easily removed.

With that clarified, physicists accepted that there is nothing mathematically wrong with black holes, but then they argued that black holes would not occur in nature because there is no way to make them. The idea was that, since the Schwarzschild solution is perfectly spherically symmetric, the conditions that are necessary to make a black hole would just never happen.

But this too turned out to be wrong. Indeed, it was proved by Stephen Hawking and Roger Penrose in the 1960s that the very opposite is the case. Black holes are what you generally get in Einstein’s theory if you have a sufficient amount of matter that just collapses because it cannot build up sufficient pressure. And so, if a star runs out of nuclear fuel and has no new way to create pressure, a black hole will be the outcome. In contrast to what physicists thought previously, black holes are hard to avoid, not hard to make.

So this was the situation in the 1970s. Black holes had turned from mathematically wrong, to mathematically correct* but non-physical, to a real possibility. But there was at the time no way to actually observe a black hole. That’s because back then the main mode of astrophysical observation was using light. And black holes are defined by the very property that they do not emit light.

However, there are other ways of observing black holes. Most importantly, black holes influence the motion of stars in their vicinity, and the other stars are observable. From this one can infer the mass of the object that the stars orbit around and one can put a limit on the radius. Black holes also swallow material in their vicinity, and from the way that they swallow it, one can tell that the object has no hard surface. The first convincing observations that our own galaxy contains a black hole came in the late 1990s. About ten years later, there were so many observations that could only be explained by the existence of black holes that today basically no one who understands the science doubts black holes exist.

What makes this story interesting to me is how essential it was that Penrose and Hawking understood the mathematics of Einstein’s theory and could formally prove that black holes should exist. It was only because of this that black holes were taken seriously at all. Without that, maybe we’d never have looked for them to begin with. A friend of mine thinks that Penrose deserves a Nobel Prize for his contribution to the discovery of black holes. And I think that’s right.

* Unfortunately, a mistake in the spoken text.

Predictions are overrated

Fortune Teller. Image: Vecteezy.

The world, it seems, is full with people who mistakenly think that a theory which makes correct predictions is a good theory. This is rubbish, of course, and it has led to a lot of unnecessary confusion. I blame this confusion on the many philosophers, notably Popper and Lakatos, who have gone on about the importance of predictions, but never clearly said that it’s not a scientific criterion.

You see, the philosophers wanted a quick way to figure out whether a scientific theory is good or not that would not require them to actually understand the science. This, needless to say, is not possible. But the next best thing you can do is to ask how much you can trust the scientists. It is for this latter purpose, to evaluate the trust you can put in scientists, that predictions are good. But they cannot, and should not, ultimately decide what the scientific value of a theory is.

The problem is well illustrated by a joke that my supervisor used to make. He liked to tell his students that whenever you predict something, you should also predict the opposite, because this way you can never be wrong. Haha. In case you are a student, let me warn you that this is bad career advice; You’d also inevitably be wrong, and it tends to be the dirt that sticks. So, don’t /end{advice}. But this joke makes clear that just because a theory makes a correct prediction doesn’t mean it’s good science.

Oh, you may say, you can get away with this once, but then you wouldn’t be able to make several correct predictions. If you said that, you’d be wrong. Because repeated correct predictions, too, are easy to accomplish. In fact, your naïve belief that correct predictions somehow speak for a theory is commonly exploited by scammers.

See, suppose I plan to convince someone that I can correctly predict the stock market. What do I do? Well, I pick, say, 3 stocks and make “predictions” for a week ahead, but that are really just guesses which cover all reasonably possible trends. I then select a large group of victims. To each of them I send one of my guesses. Some of them will coincidentally get the correct guess. A week later, I know which people got the correct guess. To this group, I then send another set of guesses for the week ahead. Again, some people will get the correct guess by coincidence, and a week later I will know which one it was. I do this a third time, and then I have a group of people who have good “evidence” that I can tell the future.

Amazing, no?

What’s the problem here? The problem is that correct predictions don’t tell you whether someone’s theory is good science.

As we have just seen, one of the problems with relying on predictions is that they may be correct just by coincidence. The larger the pool of predictions – or the pool of scientists making predictions! – the more likely this is to happen. The other problem is that relying on predictions makes fundamentally no sense. If I have a scientific theory, it is either a good description of nature, or it is not. At which time someone made a calculation for an observable quantity is entirely irrelevant for a theory’s relation to nature.

This is a point which is often raised by string theorists, and they are correct to raise it. String theorists say that since string theory gives rise to general relativity, it deserves as much praise as general relativity. That’s because, if string theory had been discovered before general relativity, it would have made the same predictions: light deflection on the sun, precession of Mercury, black holes, gravitational waves, and so on.

And indeed, this would be a good argument in favor of string theory – if it was correct. But it isn’t. String theory does not give rise to general relativity. It gives rise to general relativity in 10 dimensions, with supersymmetric matter, a negative cosmological constant, and dozens of additional scalar fields. All this extra clutter conflicts with observations. To fix this conflict with observations, string theorists then have to make several additional assumptions. With that you get a theory that is considerably more complicated than general relativity, but that does not explain the data any better. Hence, Occam’s razor tells you that general relativity is preferable.

Of course, it’s this adding of ad hoc assumptions to fix a mismatch with observation that the philosophers were trying to prevent when they requested testable predictions. But it’s the ad hoc assumptions themselves that are the problem, not the time at which they were made. To decide whether a scientific theory is any good what matters is only its explanatory power. Explanatory power measures how much data you can fit from which number of assumptions. The fewer assumption you make and the more data you fit, the higher the explanatory power, and the better the theory.

Ok, I admit, it’s somewhat more complicated than that. That’s because it also matters how well you fit the data. If you make more assumptions, you will generally be able to fit the data better. So there is a trade-off to be made, which needs to be quantified: At which point is the benefit you get from more assumptions not worth a somewhat better fit to the data? There are statistical tools to decide that. One can argue which one of those is the best for a given purpose, but that’s a fight that experts can fight in the case at hand. What is relevant here is only that the explanatory power of a theory is quantifiable. And it’s the explanatory power that decides whether a theory is good or not.

That’s obvious, I know. But why then do philosophers go on (and on and on) about predictability? Because it’s a convenient rule of thumb. It prevents scientists from adding details to their theory after they have new data, and doing so tends to reduce explanatory power. So, in many cases, asking for predictions is a good idea.

However, if you rely on predictions, you may throw out the baby with the bathwater. Just because no one made a prediction doesn’t mean they necessarily will add assumptions after an observation. In fact, the very opposite can happen. Scientists sometimes remove unnecessary assumptions when they get new data. A theory, therefore, can become better when it has been updated.

Indeed, this has happened several times in the history of physics.

Remember Einstein introducing the cosmological constant and then calling it a blunder? He had mistakenly made a superfluous assumption and then removed it after he learned of the observations. This increased, not decreased, explanatory power. Or think of Dirac’s supposed discovery of anti-particles. When his mathematics revealed a positively charged equivalent of the electron, he argued it would be the proton, which had already been observed at the time. This required the ad hoc assumption that somehow the difference in the masses between the electron and proton didn’t matter. When the positron was discovered later, Dirac could remove the ad hoc hypothesis, thereby improving his theory.

By now I hope it is clear that you should not judge the scientific worth of a theory by looking at the predictions it has made. It is a crude and error-prone criterion. Unfortunately, it has become widely mistaken as a measure for scientific quality, and this has serious consequences, way beyond physics.

Epidemic models, for example, have been judged erroneously by their power to correctly predict the trends of new cases and deaths. But such predictions require modellers to also know what actions society takes to prevent the spread. They require, basically, to predict the minds of political leaders. This, needless to say, is asking for somewhat too much. But, yell the cranks, if it doesn’t make predictions, it’s not science! Nonsense. You should judge epidemic models – any model, really – by how much data they have been able to describe well, and how many assumptions were needed for this. The fewer assumptions and the better the fit to data, the higher the scientific value of the model.

A closely related confusion is the idea that scientists should not update a theory when new data comes in. This can also be traced back to Popper & Co who proclaimed that it is bad scientific practice. But of course a good scientist updates their theory when they get new data. That, after all, is the essence of the scientific method! You update your theory so that it has the highest explanatory power. In practice, this usually means recalibrating free parameters if new information is available.

Another example where this misunderstanding matters are climate models. Climate models have correctly predicted many observed trends, from surface temperature increase, to stratospheric cooling, to sea ice melting. That’s an argument commonly used against climate change deniers. But the deniers then go and dig up some papers that made wrong predictions. This, so their claim, demonstrates that really anything is possible and you can’t trust predictions.

In defense, the scientists say the wrong predictions were few and far between. The deniers then respond – entirely correctly – that there may have been all kinds of reasons for the skewed number of papers that have absolutely nothing to do with their scientific merit.

By now we are arguing about the integrity of scientists and the policies of their journals instead about science. The scientists are clearly losing the argument. And why is that? Because relying on predictions is not a scientific argument. It is inherently a sociological argument. It’s like claiming that a study must be wrong because the lead author has a conflict of interest. That’s reason to be skeptical, yes. But it does not follow that the study is necessarily wrong. That would be a logically faulty conclusion.

What, then, is the scientific answer for the climate change deniers? It’s that climate models explain loads of data with few assumptions. The simplest explanation for our observations is that the trends are caused by human carbon dioxide emission. It’s the hypothesis that has the highest explanatory power.

To add an example that is closer to home: Many non-physicists ridicule hypotheses like supersymmetry and certain types of particle dark matter because they can be eternally amended and hence make no predictions. But that is not the problem with these models. Updating a theory when new data comes in is totally fine. The problem with these models is that they have assumptions that were entirely unnecessary to explain any data to begin with.

Adding supersymmetry to the standard model or details about dark matter particles to the concordance model is superfluous. It lowers the explanatory power of these theories, instead of increasing it. That’s what’s unscientific about it. And of course once you have an assumption that was superfluous in the first place, you can eternally fiddle with it. But it’s the use of superfluous assumptions that’s the unscientific part, not updating them.

In brief, I think the world would be better place if scientists talked less about predictions and more about explanatory power.

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

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.