Why the laws of nature are not inevitable, never have been, and never will be.

[Still from the 1956 movie The Ten Commandments]

No one has any idea why mathematics works so well to describe nature, but it is arguably an empirical fact that it works. A corollary of this is that you can formulate theories in terms of mathematical axioms and derive consequences from this. This is not how theories in physics have historically been developed, but it’s a good way to think about the relation between our theories and mathematics.

All modern theories of physics are formulated in mathematical terms. To have a physically meaningful theory, however, mathematics alone is not sufficient. One also needs to have an identification of mathematical structures with observable properties of the universe.

The maybe most important lesson physicists have learned over the past centuries is that if a theory has internal inconsistencies, it is wrong. By internal inconsistencies, I mean that the theory’s axioms lead to statements that contradict each other. A typical example is that a quantity defined as a probability turns out to take on values larger than 1. That’s mathematical rubbish; something is wrong.

Of course a theory can also be wrong if it makes predictions that simply disagree with observations, but that is not what I am talking about today. Today, I am writing about the nonsense idea that the laws of nature are somehow “inevitable” just because you can derive consequences from postulated axioms.

It is easy to see that this idea is wrong even if you have never heard the word epistemology. Consequences which you can derive from axioms are exactly as “inevitable” as postulating the axioms, which means the consequences are not inevitable. But that this idea is wrong isn’t the interesting part. The interesting part is that it remains popular among physicists and science writers who seem to believe that physics is somehow magically able to explain itself.

But where do we get the axioms for our theories from? We use the ones that, according to present knowledge, do the best job to describe our observations. Sure, once you have written down some axioms, then anything you can derive from these axioms can be said to be an inevitable consequence. This is just the requirement of internal consistency.

But the axioms themselves can never be proved to be the right ones and hence will never be inevitable themselves. You can say they are “right” only to the extent that they give rise to predictions that agree with observations.

This means not only that we may find tomorrow that a different set of axioms describes our observations better. It means more importantly that any statement about the inevitability of the laws of nature is really a statement about our inability to find a better explanation for our observations.

This confusion between the inevitability of conclusions given certain axioms, and the inevitability of the laws of nature themselves, is not an innocuous one. It is the mistake behind string theorists’ conviction that they must be on the right track just because they have managed to create a mostly consistent mathematical structure. That this structure is consistent is of course necessary for it to be a correct description of nature. But it is not sufficient. Consistency tells you nothing whatsoever about whether the axioms you postulated will do a good job to describe observations.

Similar remarks apply to the Followers of Loop Quantum Gravity who hold background independence to be a self-evident truth, or to everybody who believes that statistical independence is sacred scripture, rather than being what it really is: A mathematical axiom, that may or may not continue to be useful.

Another unfortunate consequence of physicists’ misunderstanding of the role of mathematics in science are multiverse theories.

This comes about as follows. If your theory gives rise to internal contradictions, it means that at least one of your axioms is wrong. But one way to remove internal inconsistencies is to simply discard axioms until the contradiction vanishes.

Dropping axioms is not a scientifically fruitful strategy because you then end up with a theory that is ambiguous and hence unpredictive. But it is a convenient, low-effort solution to get rid of mathematical problems and has therefore become fashionable in physics. And this is in a nutshell where multiverse theories come from: These are theories which lack sufficiently many axioms to describe our universe.

Somehow an increasing number of physicists has managed to convince themselves that multiverse ideas are good scientific theories instead of what they de facto are: Useless.

There are infinitely many sets of axioms that are mathematically consistent but do not describe our universe. The only rationale scientists have to choose one over the other is that the axioms give rise to correct predictions. But there is no way to ever prove that a particular set of axioms is inevitably the correct one. Science has its limits. This is one of them.

Is the Anthropic Principle scientific?

Today I want to explain why the anthropic principle is a good, scientific principle. I want to talk about this, because the anthropic principle seems to be surrounded by a lot of misunderstanding, especially for what its relation to the multiverse is concerned.


Let me start with clarifying what we are talking about. I often hear people refer to the anthropic principle to say that a certain property of our universe is how it is because otherwise we would not be here to talk about it. That’s roughly correct, but there are two ways of interpreting this statement, which gives you a strong version of the anthropic principle, and a weak version.

The strong version has it that our existence causes the universe to be how it is. This is not necessarily an unscientific idea, but so-far no one has actually found a way to make it scientifically useful. You could for example imagine that if you managed to define well enough what a “human being” is, then you could show that the universe must contain certain forces with certain properties and thereby explain why the laws of nature are how they are.

However, I sincerely doubt that we will ever have a useful theory based on the strong anthropic principle. The reason is that for such a theory to be scientific, it would need to be a better explanation for our observations than the theories we presently have, which just assume some fundamental forces and particles, and build up everything else from that. I find it hard to see how a theory that starts from something as complicated as a human being could possibly ever be more explanatory than these simple, reductionist theories we currently use in the foundations of physics.

Let us then come to the weak version of the anthropic principle. It says that the universe must have certain properties because otherwise our own existence would not be possible. Please note the difference to the strong version. In the weak version of the anthropic principle, human existence is neither necessary nor unavoidable. It is simply an observed fact that humans exist in this universe. And this observed fact leads to constraints on the laws of nature.

These constraints can be surprisingly insightful. The best-known historical example for the use of the weak anthropic principle is Fred Hoyle’s prediction that a certain isotope of the chemical element carbon must have a resonance because, without that, life as we know it would not be possible. That prediction was correct. As you can see, there is nothing unscientific going on here. An observation gives rise to a hypothesis which makes a prediction that is confirmed by another observation.

Another example that you often find quoted is that you can use the fact of our own existence to tell that the cosmological constant has to be within certain bounds. If the cosmological constant was large and negative, the universe would have collapsed long ago. If the cosmological constant was large and positive, the universe would expand too fast for stars to form. Again, there is nothing mysterious going on here.

You could use a similar argument to deduce that the air in my studio contains oxygen. Because if it didn’t I wouldn’t be talking. Now, that this room contains oxygen is not an insight you can publish in a scientific journal because it’s pretty useless. But as the example with Fred Hoyle’s carbon resonance illustrates, anthropic arguments can be useful.

To be fair, I should add that to the extent that anthropic arguments are being used in physics, they do not usually draw on the existence of human life specifically. They more generally use the existence of certain physical preconditions that are believed to be necessary for life, such as a sufficiently complex chemistry or sufficiently large structures.

So, the anthropic principle is neither unscientific, nor is it in general useless. But then why is the anthropic principle so controversial? It is controversial because it is often brought up by physicists who believe that we live in a multiverse, in which our universe is only one of infinitely many. In each of these universes, the laws of nature can be slightly different. Some may allow for life to exist, some may not.

(If you want to know more about the different versions of the multiverse, please watch my earlier video.)

If you believe in the multiverse, then the anthropic principle can be reformulated to say that the probability we find ourselves in a universe that is not hospitable to life is zero. In the multiverse, the anthropic principle then becomes a statement about the probability distribution over an ensemble of universes. And for multiverse people, that’s an important quantity to calculate. So the anthropic principle smells controversial because of this close connection to the multiverse.

However, the anthropic principle is correct regardless of whether or not you believe in a multiverse. In fact, the anthropic principle is a rather unsurprising and pretty obvious constraint on the properties that the laws of nature must have. The laws of nature must be so that they allow our existence. That’s what the anthropic principle says, no more and no less.

Dark energy might not exist after all

Last week I told you what dark energy is and why astrophysicists believe it exists. This week I want to tell you about a recent paper that claims dark energy does not exist.


To briefly remind you, dark energy is what speeds up the expansion of the universe. In contrast to all other types of matter and energy, dark energy does not dilute if the universe expands. This means that eventually all the other stuff is more dilute than dark energy and, therefore, it’s the dark energy that determines the ultimate fate of our universe. If dark energy is real, the universe will expand faster and faster until all eternity. If there’s no dark energy, the expansion will slow down instead and it might even reverse, in which case the universe will collapse back to a point.

I don’t know about you, but I would like to know what is going to happen with our universe.

So what do we know about dark energy. The most important evidence we have for the existence of dark energy comes from supernova redshifts. Saul Perlmutter and Adam Riess won a Nobel Prize for this observation in 2011. It’s this Nobel-prize winning discovery which the new paper calls into question.

Supernovae give us information about dark energy because some of them are very regular. These are the so-called type Ia supernovae. Astrophysicists understand quite well how these supernovae happen. This allows physicists to calculate how much light these blasts emit as a function of time, so they know what was emitted. But the farther the supernova is away, the dimmer it appears. So, if you observe one of these supernova, you can infer its distance from the brightness.

At the same time, you can also determine the color of the light. Now, and this is the important point, this light from the supernova will stretch if space expands while the light travels from the supernova to us. This means that the wave-lengths we observe here on earth are longer than they were at emission or, to put it differently, the light arrives here with a frequency that is shifted to the red. This red-shift of the light therefore tells us something about the expansion of the universe.

Now, the farther away a supernova is, the longer it takes the light to reach us, and the longer ago the supernova must have happened. This means that if you measure supernovae at different distances, they really happened at different times, and you know how the expansion of space changes with time.

And this is, in a nutshell, what Perlmutter and Riess did. They used the distance inferred from the brightness and the redshift of type 1a supernovae, and found that the only way to explain both types of measurements is that the expansion of the universe is getting faster. And this means that dark energy must exist.

Now, Perlmutter and Riess did their analysis 20 years ago and they used a fairly small sample of about 110 supernovae. Meanwhile, we have data for more than 1000 supernovae. For the new paper, the researchers used 740 supernovae from the JLA catalogue. But they also explain that if one just uses the data from this catalogue as it is, one gets a wrong result. The reason is that the data has been “corrected” already.

This correction is made because the story that I just told you about the redshift is more complicated than I made it sound. That’s because the frequency of light from a distant source can also shift just because our galaxy moves relative to the source. More generally, both our galaxy and the source move relative to the average restframe of stuff in the universe. And it is this latter frame that one wants to make a statement about when it comes to the expansion of the universe.

How do you even make such a correction? Well, you need to have some information about the motion of our galaxy from observations other than supernovae. You can do that by relying on regularities in the emission of light from galaxies and galaxy clusters. This allow astrophysicist to create a map with the velocities of galaxies around us, called the “bulk flow” .

But the details don’t matter all that much. To understand this new paper you only need to know that the authors had to go and reverse this correction to get the original data. And *then they fitted the original data rather than using data that were, basically, assumed to converge to the cosmological average.

What they found is that the best fit to the data is that the redshift of supernovae is not the same in all directions, but that it depends on the direction. This direction is aligned with the direction in which we move through the cosmic microwave background. And – most importantly – you do not need further redshift to explain the observations.

If what they say is correct, then it is unnecessary to postulate dark energy which means that the expansion of the universe might not speed up after all.

Why didn’t Perlmutter and Riess come to this conclusions? They could not, because the supernovae that they looked were skewed in direction. The ones with low redshift were in the direction of the CMB dipole; and high redshift ones away from it. With a skewed sample like this, you can’t tell if the effect you see is the same in all directions.*

What is with the other evidence for dark energy? Well, all the other evidence for dark energy is not evidence for dark energy in particular, but for a certain combination of parameters in the concordance model of cosmology. These parameters include, among other things, the amount of dark matter, the amount of normal matter, and the Hubble rate.

There is for example the data from baryon acoustic oscillations and from the cosmic microwave background which are currently best fit by the presence of dark energy. But if the new paper is correct, then the current best-fit parameters for those other measurements no longer agree with those of the supernovae measurements. This does not mean that the new paper is wrong. It means that one has to re-analyze the complete set of data to find out what is overall the combination of parameters that makes the best fit.

This paper, I have to emphasize, has been peer reviewed, is published in a high quality journal, and the analysis meets the current scientific standard of the field. It is not a result that can be easily dismissed and it deserves to be taken very seriously, especially because it calls into question a Nobel Prize winning discovery. This analysis has of course to be checked by other groups and I am sure we will hear about this again, so stay tuned.

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* Corrected this paragraph which originally said that all their supernovae were in the same direction of the sky.

What is Dark Energy?

What’s the difference between dark energy and dark matter? What does dark energy have to do with the cosmological constant and is the cosmological constant really the worst prediction ever? At the end of this video, you will know.


First things first, what is dark energy? Dark energy is what causes the expansion of the universe to accelerate. It’s not only that astrophysicists think the universe expands, but that the expansion is actually getting faster. And, here’s the important thing, matter alone cannot do that. If there was only matter in the universe, the expansion would slow down. To make the expansion of the universe accelerate, it takes negative pressure, and neither normal matter nor dark matter has negative pressure – but dark energy has it.

We do not actually know that dark energy is really made of anything, so interpreting this pressure in the normal way as by particles bumping into each other may be misleading. This negative pressure is really just something that we write down mathematically and that fits to the observations. It is similarly misleading to call dark energy “dark”, because “dark” suggests that it swallows light like, say, black holes do. But neither dark matter nor dark energy is actually dark in this sense. Instead, light just passes through them, so they are really transparent and not dark.

What’s the difference between dark energy and dark matter? Dark energy is what makes the universe expand, dark matter is what makes galaxies rotate faster. Dark matter does not have the funny negative pressure that is characteristic of dark energy. Really the two things are different and have different effects. There are of course some physicists speculating that dark energy and dark matter might have a common origin, but we don’t know whether that really is the case.

What does dark energy have to do with the cosmological constant? The cosmological constant is the simplest type of dark energy. As the name says, it’s really just a constant, it doesn’t change in time. Most importantly this means that it doesn’t change when the universe expands. This sounds innocent, but it is a really weird property. Think about this for a moment. If you have any kind of matter or radiation in some volume of space and that volume expands, then the density of the energy and pressure will decrease just because the stuff dilutes. But dark energy doesn’t dilute! It just remains constant.

Doesn’t this violate energy conservation? I get this question a lot. The answer is yes, and no. Yes, it does violate energy conservation in the way that we normally use the term. That’s because if the volume of space increases but the density of dark energy remains constant, then it seems that there is more energy in that volume. But energy just is not a conserved quantity in general relativity, if the volume of space can change with time. So, no, it does not violate energy conservation because in general relativity we have to use a different conservation law, that is the local conservation of all kinds of energy densities. And this conservation law is fulfilled even by dark energy. So the mathematics is all fine, don’t worry.

The cosmological constant was famously already introduced by Einstein and then discarded again. But astrophysicists think today that is necessary to explain observations, and it has a small, positive value. But I often hear physicists claiming that if you try to calculate the value of the cosmological constant, then the result is 120 orders of magnitude larger than what we observe. This, so the story has it, is the supposedly worst prediction ever.

Trouble is, that’s not true! It just isn’t a prediction. If it was a prediction, I ask you, what theory was ruled out by it being so terribly wrong? None, of course. The reason is that this constant which you can calculate – the one that is 120 orders of magnitude too large – is not observable. It doesn’t correspond to anything we can measure. The actually measureable cosmological constant is a free parameter of Einstein’s theory of general relativity that cannot be calculated by the theories we currently have.

Dark energy now is a generalization of the cosmological constant. This generalization allows that the energy density and pressure of dark energy can change with time and maybe also with space. In this case, dark energy is really some kind of field that fills the whole universe.

What observations speak for dark energy? Dark energy in the form of a cosmological constant is one of the parameters in the concordance model of cosmology. This model is also sometimes called ΛCDM. The Λ (Lambda) in this name is the cosmological constant and CDM stands for cold dark matter.

The cosmological constant in this model is not extracted from one observation in particular, but from a combination of observations. Notably that is the distribution of matter in the universe, the properties of the cosmic microwave background, and supernovae redshifts. Dark energy is necessary to make the concordance model fit to the data.

At least that’s what most physicists say. But some of them are claiming that really the data has been wrongly analyzed and the expansion of the universe doesn’t speed up after all. Isn’t science fun? If I come around to do it, I’ll tell you something about this new paper next week, so stay tuned.

What can artificial intelligence do for physics? And what will it do to physics?

Neural net illustration. Screenshot from this video.

In the past two years, governments all over the world have launched research initiatives for Artificial Intelligence (AI). Canada, China, the United States, the European Commission, Australia, France, Denmark, the UK, Germany – everyone suddenly has a strategy for “AI made in” whatever happens to be their own part of the planet. In the coming decades, it is now foreseeable, tens of billions of dollars will flow into the field.

But ask a physicist what they think of artificial intelligence, and they’ll probably say “duh.” For them, AI was trendy in the 1980s. They prefer to call it “machine learning” and pride themselves having used it for decades.

Already in the mid 1980s, researchers working in statistical mechanics – a field concerned with the interaction of large number of particles – set out to better understand how machines learn. They noticed that magnets with disorderly magnetization (known as “spin glasses”) can serve as a physical realization for certain mathematical rules used in machine learning. This in turn means that the physical behavior of these magnets shed light on some properties of learning machines, such as their storage capacity. Back then, physicists also used techniques from statistical mechanics to classify the learning abilities of algorithms.

Particle physicists, too, were on the forefront of machine learning. The first workshop on Artificial Intelligence in High Energy and Nuclear Physics (AIHENP) was held already in 1990. Workshops in this series still take place, but have since been renamed to Advanced Computing and Analysis Techniques. This may be because the new acronym, ACAT, is catchier. But it also illustrates that the phrase “Artificial Intelligence” is no longer common use among researchers. It now appears primarily as an attention-grabber in the mass media.

Physicists avoid the term “Artificial Intelligence” not only because it reeks of hype, but because the analogy to natural intelligence is superficial at best, misleading at worst. True, the current models are loosely based on the human brain’s architecture. These so-called “neural networks” are algorithms based on mathematical representations of “neurons” connected by “synapses.” Using feedback about its performance – the “training” – the algorithm then “learns” to optimize a quantifiable goal, such as recognizing an image, or predicting a data-trend.

This type of iterative learning is certainly one aspect of intelligence, but it leaves much wanting. The current algorithms heavily rely on humans to provide suitable input data. They do not formulate own goals. They do not propose models. They are, as far as physicists are concerned, but elaborate ways of fitting and extrapolating data.

But then, what novelty can AI bring to physics? A lot, it turns out. While the techniques are not new – even “deep learning” dates back to the early 2000s – today’s ease of use and sheer computational power allows physicists to now assign computers to tasks previously reserved for humans. It has also enabled them to explore entirely new research directions. Until a few years ago, other computational methods often outperformed machine learning, but now machine learning leads in many different areas. This is why, in the past years, interest in machine learning has spread into seemingly every niche.

Most applications of AI in physics loosely fall into three main categories: Data analysis, modeling, and model analysis.

Data analysis is the most widely known application of machine learning. Neural networks can be trained to recognize specific patterns, and can also learn to find new patterns on their own. In physics, this is used in image analysis, for example when astrophysicists search for signals of gravitational lensing. Gravitational lensing happens when space-time around an object is deformed so much that it noticeably distorts the light coming from behind it. The recent, headline-making, black hole image is an extreme example. But most gravitational lensing events are more subtle, resulting in smears or partial arcs. AIs can learn to identify these.

Particle physicists also use neural networks to find patterns, both specific and unspecific ones. Highly energetic particle collisions, like those done at the Large Hadron Collider, produce huge amounts of data. Neural networks can be trained to flag interesting events. Similar techniques have been used to identify certain types of radio bursts, and may soon help finding gravitational waves.

Machine learning aids the modeling of physical systems both by speeding up calculations and by enabling new types of calculations. For example, simulations for the formation of galaxies take a long time even on the current generation of super-computers. But neural networks can learn to extrapolate from the existing simulations, without having to re-run the full simulation each time, a technique that was recently successfully used to match the amount of dark matter to the amount of visible matter in galaxies. Neural networks have also been used to reconstruct what happens when cosmic rays hit the atmosphere, or how elementary particles are distributed inside composite particles.

For model analysis, machine learning is applied to understand better the properties of already known theories which cannot be extracted by other mathematical methods, or to speed up computation. For example, the interaction of many quantum particles can result in a variety of phases of matter. But the existing mathematical methods have not allowed physicists to calculate these phases. Neural nets can encode the many quantum particles and then classify the different types of behavior.

Similar ideas underlie neural networks that seek to classify the properties of materials, such as conductivity or compressibility. While the theory for the materials’ atomic structure is known in principle, many calculations have so-far exceeded the existing computational resources. Machine learning is beginning to change that. Many hope that it may one day allow physicists to find materials that are superconducting at room temperature. Another fertile area for applications of neural nets is “quantum tomography,” that is the reconstruction of quantum state from the measurements performed on it, a problem of high relevance for quantum computing.

And it is not only that machine learning advances physics, physics can in return advance machine learning. At present, it is not well understood just why neural nets work as well as they do. Since some neural networks can be represented as physical systems, knowledge from physics may shed light on the situation.

In summary, machine learning rather suddenly allows physicists to tackle a lot of problems that were previously intractable, simply because of the high computational burden.

What does this mean for the future of physics? Will we see the “End of Theory” as Chris Anderson oracled in 2008?

I do not think so. There are many different types of neural networks, which differ in their architecture and learning scheme. Physicists now have to understand which algorithm works for which case and how well, the same way they previously had to understand which theory works for which case and how well. Rather than spelling the end of theory, machine learning will take it to the next level.

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Can we tell if there’s a wormhole in the Milky-Way?

This week I got a lot of questions about an article by Dennis Overbye in the New York Times, titled “How to Peer Through a Wormhole.” This article says “Theoretically, the universe may be riddled with tunnels through space and time” and goes on to explain that “Wormholes are another prediction of Einstein’s theory of general relativity, which has already delivered such wonders as an expanding universe and black holes.” Therefore, so Overbye tells his readers, it is reasonable to study whether the black hole in the center of our Milky Way is such a wormhole.


The trouble with this article is that it makes it appear as if wormholes are a prediction of general relativity comparable to the prediction of the expansion of the universe and the prediction of black holes. But this is most definitely not so. Overbye kind of says this by alluding to some “magic” that is necessary to have wormholes, but unfortunately he does not say it very clearly. This has caused quite some confusion. On twitter, for example, Natalie Wolchover, has put wormholes on par with gravitational waves.

But this paper concerns Thorne's calculations of what's theoretically possible in GR, rather than new claims about the foundations of physics. And consider the success of GW detection, also a wild and crazy idea by Thorne and others.

— Natalie Wolchover (@nattyover) November 13, 2019

So here are the facts. General Relativity is based on Einstein’s field equations which determine the geometry of space-time as a consequence of the energy and matter that is in that space-time. General Relativity has certain kinds of wormholes as solutions. These are the so-called Einstein-Rosen bridges. There are two problems with those.

First, no one knows how to create them with a physically possible process. It’s one thing to say that the solution exists in the world of mathematics. It’s another thing entirely to say that such a solution describes something in our universe. There are whole books full with solutions to Einstein’s field equations. Most of these solutions have no correspondence in the real world.

Second, even leaving aside that they won’t be created during the evolution of the universe, nothing can travel through these wormholes.

If you want to keep a wormhole open, you need some kind of matter that has a negative energy density, which is stuff that for all we know does not exist. Can you write down the mathematics for it? Yes. Do we have any reason whatsoever to think that this mathematics describes the real world? No. And that, folks, is really all there is to say about it. It’s mathematics and we have no reason to think it’s real.

In this, wormholes are very, very different to the predictions of the expanding universe, gravitational waves, and black holes. The expanding universe, gravitational waves and black holes are consequences of general relativity. You have to make an effort to avoid that they exist. It’s the exact opposite with wormholes. You have to bend over backwards to make the math work so that they can exist.

Now, certain people like to tell me that this should count as “healthy speculation” and I should stop complaining about it. These certain people are either physicists who produce such speculations or science writers who report about it. In other words, they are people who make a living getting you to believe this mathematical fiction. But there is nothing healthy about this type of speculation. It’s wasting time and money that would be better used on research that could actually advance physics.

Let me give you an example to see the problem. Suppose the same thing would happen in medicine. Doctors would invent diseases that we have no reason to think exist. They would then write papers about how to diagnose those invented diseases and how to cure those invented diseases and, for good measure, argue that someone should do an experiment to look for their invented diseases.

Sounds ridiculous? Yeah, it is ridiculous. But that’s exactly what is going on in the foundations of physics, and it has been going on for decades, which is why no one sees anything wrong with it anymore.

Is there at least something new that would explain why the NYT reports on this? What’s new is that two physicists have succeeded in publishing a paper which says that if the black hole in the center of our galaxy is a traversable wormhole then maybe we might be able to see this. The idea is that if there is stuff moving around the other end of the wormhole then we might notice the gravitational influence of that stuff on our side of the wormhole.

Is it possible to look for this? Yes, it is also possible to look for alien spaceships coming through, and chances are, next week a paper will get published about this and the New York Times reports it.

On a more technical note, a quick remark about the paper, which you find here:

Observing a wormhole
De-Chang Dai, Dejan Stojkovic
Phys. Rev. D 100, 083513 (2019)
arXiv:1910.00429 [gr-qc]

The authors look at what happens with the gravitational field on one side of a non-traversable wormhole if a shell of matter is placed around the other side of the wormhole. They conclude:

“[T]he gravitational field can cross from one to the other side of the wormhole even from inside the horizon... This is very interesting since it implies that gravity can leak even through the non-traversable wormhole.”

But the only thing their equation says is that the strength of the gravitational field on one side of the wormhole depends on the matter on the other side of the wormhole. Which is correct of course. But there is no information “leaking” through the non-traversable (!) wormhole because it’s a time-independent situation. There is no change that can be measured here.

This isn’t simply because they didn’t look at the time-dependence, but because the spherically symmetric case is always time-independent. We know that thanks to Birkhoff’s theorem. We also know that gravitational waves have no monopole contribution, so there are no propagating modes in this case either.

The case that they later discuss, the one that is supposedly observable, instead talks of objects on orbits around the other end of the wormhole. This is, needless to say, not a spherically symmetric case and therefore this argument that the effect is measurable for non-traversable wormholes is not supported by their analysis. If you want more details, this comment gets it right.

Did scientists get climate change wrong?

On my recent trip to the UK, I spoke with Tim Palmer about the uncertainty in climate predictions.

How can we test a Theory of Everything?

How can we test a Theory of Everything? That’s a question I get a lot in my public lectures. In the past decade, physicists have put forward some speculations that cannot be experimentally ruled out, ever, because you can always move predictions to energies higher than what we have tested so far. Supersymmetry is an example of a theory that is untestable in this particular way. After I explain this, I am frequently asked if it is possible to test a theory of everything, or whether such theories are just entirely unscientific.


It’s a good question. But before we get to the answer, I have tell you exactly what physicists mean by “theory of everything”, so we’re on the same page. For all we currently know the world is held together by four fundamental forces. That’s the electromagnetic force, the strong and the weak nuclear force, and gravity. All other forces, like for example Van-der-Waals forces that hold together molecules or muscle forces derive from those four fundamental forces.

The electromagnetic force and the strong and the weak nuclear force are combined in the standard model of particle physics. These forces have in common that they have quantum properties. But the gravitational force stands apart from the three other forces because it does not have quantum properties. That’s a problem, as I have explained in an earlier video. A theory that solves the problem of the missing quantum behavior of gravity is called “quantum gravity”. That’s not the same as a theory of everything.

If you combine the three forces in the standard model to only one force from which you can derive the standard model, that is called a “Grand Unified Theory” or GUT for short. That’s not a theory of everything either.

If you have a theory from which you can derive gravity and the three forces of the standard model, that’s called a “Theory of Everything” or TOE for short. So, a theory of everything is both a theory of quantum gravity and a grand unified theory.

The name is somewhat misleading. Such a theory of everything would of course *not explain everything. That’s because for most purposes it would be entirely impractical to use it. It would be impractical for the same reason it’s impractical to use the standard model to explain chemical reactions, not to mention human behavior. The description of large objects in terms of their fundamental constituents does not actually give us much insight into what the large objects do. A theory of everything, therefore, may explain everything in principle, but still not do so in practice.

The other problem with the name “theory of everything” is that we will never know that not at some point in the future we will discover something that the theory does not explain. Maybe there is indeed a fifth fundamental force? Who knows.

So, what physicists call a theory of everything should really be called “a theory of everything we know so far, at least in principle.”

The best known example of a theory of everything is string theory. There are a few other approaches. Alain Connes, for example, has an approach based on non-commutative geometry. Asymptotically safe gravity may include a grand unification and therefore counts as a theory of everything. Though, for reasons I don’t quite understand, physicists do not normally discuss asymptotically safe gravity as a candidate for a theory of everything. If you know why, please leave a comment.

These are the large programs. Then there are a few small programs, like Garrett Lisi’s E8 theory, or Xiao-Gang Wen’s idea that the world is really made of qbits, or Felix Finster’s causal fermion systems.

So, are these theories testable?

Yes, they are testable. The reason is that any theory which solves the problem with quantum gravity must make predictions that deviate from general relativity. And those predictions, this is really important, cannot be arbitrarily moved to higher and higher energies. We know that because combining general relativity with the standard model, without quantizing gravity, just stops working near an energy known as the Planck energy.

These approaches to a theory of everything normally also make other predictions. For example they often come with a story about what happened in the early universe, which can have consequences that are still observable today. In some cases they result in subtle symmetry violations that can be measurable in particle physics experiments. The details about this differ from one theory to the next.

But what you really wanted to know, I guess, is whether these tests are practically possible any time soon? I do think it is realistically possible that we will be able to see these deviations from general relativity in the next 50 years or so. About the other tests that rely on models for the early universe or symmetry violations, I’m not so sure, because for these it is again possible to move the predictions and then claim that we need bigger and better experiments to see them.

Is there any good reason to think that such a theory of everything is correct in the first place? No. There is good reason to think that we need a theory of quantum gravity, because without that the current theories are just inconsistent. But there is no reason to think that the forces of the standard model have to be unified, or that all the forces ultimately derive from one common explanation. It would be nice, but maybe that’s just not how the universe works.

Have we really measured gravitational waves?

A few days ago I met a friend on the subway. He tells me he’s been at a conference and someone asked if he knows me. He says yes, and immediately people start complaining about me. One guy, apparently, told him to slap me.

What were they complaining about, you want to know? Well, one complaint came from a particle physicist, who was clearly dismayed that I think building a bigger particle collider is not a good way to invest $40 billion dollars. But it was true when I said it the first time and it is still true: There are better things we can do with this amount money. (Such as, for example, make better climate predictions, which can be done for as “little” as 1 billion dollars.)

Back to my friend on the subway. He told me that besides the grumpy particle physicist there were also several gravitational wave people who have issues with what I have written about the supposed gravitational wave detections by the LIGO collaboration. Most of the time if people have issues with what I’m saying it’s because they do not understand what I’m saying to begin with. So with this video, I hope to clear the situation up.

Let me start with the most important point. I do not doubt that the gravitational wave detections are real. But. I spend a lot of time on science communication, and I know that many of you doubt that these detections are real. And, to be honest, I cannot blame you for this doubt. So here’s my issue. I think that the gravitational wave community is doing a crappy job justifying the expenses for their research. They give science a bad reputation. And I do not approve of this.

Before I go on, a quick reminder what gravitational waves are. Gravitational waves are periodic deformations of space and time. These deformations can happen because Einstein’s theory of general relativity tells us that space and time are not rigid, but react to the presence of matter. If you have some distribution of matter that curves space a lot, such as a pair of black holes orbiting one another, these will cause space-time to wobble and the wobbles carry energy away. That’s what gravitational waves are.

We have had indirect evidence for gravitational waves since the 1970s because you can measure how much energy a system loses through gravitational waves without directly measuring the gravitational waves. Hulse and Taylor did this by closely monitoring the orbiting frequency of a pulsar binary. If the system loses energy, the two stars get closer and they orbit faster around each other. The predictions for the emission of gravitational waves fit exactly on the observations. Hulse and Taylor got a Nobel prize for that in 1993.

For the direct detection of gravitational waves you have to measure the deformation of space and time that they cause. You can do this by using very sensitive interferometers. An interferometer bounces laser light back and forth in two orthogonal directions and then combines the light.

Light is a wave and depending on whether the crests of the waves from the two directions lie on top of each other or not, the resulting signal is strong – that’s constructive interference – or washed out – that’s destructive interference. Just what happens depends very sensitively on the distance that the light travels. So you can use changes in the strength of the interference pattern to figure out whether one of the directions of the interferometer was temporarily shorter or longer.

A question that I frequently get is how can this interferometer detect anything if both the light and the interferometer itself deform with space-time? Wouldn’t the effect cancel out? No, it does not cancel out, because the interferometer is not made of light. It’s made of massive particles and therefore reacts differently to a periodic deformation of space-time than light does. That’s why one can use light to find out that something happened for real. For more details, please check these papers.

The first direct detection of gravitational waves was made by the LIGO collaboration in September 2015. LIGO consists of two separate interferometers. They are both located in the United States, some thousand kilometers apart. Gravitational waves travel at the speed of light, so if one comes through, it should trigger both detectors with a small delay that comes from the time it takes the wave to travel from one detector to the other. Looking for a signal that appears almost simultaneously in the two detectors helps to identify the signal in the noise.

This first signal measured by LIGO looks like a textbook example of a gravitational wave signal from a merger of two black holes. It’s a periodic signal that increases in frequency and amplitude, as the two black holes get closer to each other and their orbiting period gets shorter. When the horizons of the two black holes merge, the signal is suddenly cut off. After this follows a brief period in which the newly formed larger black hole settles in a new state, called the ringdown. A Nobel Prize was awarded for this measurement in 2017. If you plot the frequency distribution over time, you get this banana. Here it's the upward bend that tells you that the frequency increases before dying off entirely.

Now, what’s the problem? The first problem is that no one seems to actually know where the curve in the famous LIGO plot came from. You would think it was obtained by a calculation, but members of the collaboration are on record saying it was “not found using analysis algorithms” but partly done “by eye” and “hand-tuned for pedagogical purposes.” Both the collaboration and the journal in which the paper was published have refused to comment. This, people, is highly inappropriate. We should not hand out Nobel Prizes if we don’t know how the predictions were fitted to the data.

The other problem is that so far we do not have a confirmation that the signals which LIGO detects are in fact of astrophysical origin, and not misidentified signals that originated on Earth. The way that you could show this is with a LIGO detection that matches electromagnetic signals, such as gamma ray bursts, measured by telescopes.

The collaboration had, so far, one opportunity for this, which was an event in August 2017. The problem with this event is that the announcement from the collaboration about their detection came after the announcement of the incoming gamma ray. Therefore, the LIGO detection does not count as a confirmed prediction, because it was not a prediction in the first place – it was a postdiction.

It seems to offend people in the collaboration tremendously if I say this, so let me be clear. I have no reason to think that something fishy went on, and I know why the original detection did not result in an automatic alert. But this isn’t the point. The point is that no one knows what happened before the official announcement besides members of the collaboration. We are waiting for an independent confirmation. This one missed the mark.

Since 2017, the two LIGO detectors have been joined by a third detector called Virgo, located in Italy. In their third run, which started in April this year, the LIGO/Virgo collaboration has issued alerts for 41 events. From these 41 alerts, 8 were later retracted. Of the remaining gravitational wave events, 10 look like they are either neutron star mergers, or mergers of a neutron star with a black hole. In these cases, there should also be electromagnetic radiation emitted which telescopes can see. For black hole mergers, one does not expect this to be the case.

However, no telescope has so far seen a signal that fits to any of the gravitational wave events. This may simply mean that the signals have been too weak for the telescopes to see them. But whatever the reason, the consequence is that we still do not know that what LIGO and Virgo see are actually signals from outer space.

You may ask isn’t it enough that they have a signal in their detector that looks like it could be caused by gravitational waves? Well, if this was the only thing that could trigger the detectors, yes. But that is not the case. The LIGO detectors have about 10-100 “glitches” per day. The glitches are bright and shiny signals but do not look like gravitational wave events. The cause of some of these glitches is known. The cause of other glitches not. LIGO uses a citizen science project to classify these glitches and has given them funky names like “Koi Fish” or “Blip.”

What this means is that they do not really know what their detector detects. They just throw away data that don’t look like they want it to look. This is not a good scientific procedure. Here is why.

Think of an animal. Let me guess, it’s... an elephant. Right? Right for you, right for you, not right for you? Hmm, that’s a glitch in the data, so you don’t count.

Does this prove that I am psychic? No, of course it doesn’t. Because selectively throwing away data that’s inconvenient is a bad idea. Goes for me, goes for LIGO too. At least that’s what you would think.

If we had an independent confirmation that the good-looking signal is really of astrophysical origin, this wouldn’t matter. But we don’t have that either. So that’s the situation in summary. The signals that LIGO and Virgo see are well explained by gravitational wave events. But we cannot be sure that these are actually signals coming from outer space and not some unknown terrestrial effect.

Let me finish by saying once again that personally I do not actually doubt these signals are caused by gravitational waves. But in science, it’s evidence that counts, not opinion.

The crisis in physics is not only about physics

downward spiral

In the foundations of physics, we have not seen progress since the mid 1970s when the standard model of particle physics was completed. Ever since then, the theories we use to describe observations have remained unchanged. Sure, some aspects of these theories have only been experimentally confirmed later. The last to-be-confirmed particle was the Higgs-boson, predicted in the 1960s, measured in 2012. But all shortcomings of these theories – the lacking quantization of gravity, dark matter, the quantum measurement problem, and more – have been known for more than 80 years. And they are as unsolved today as they were then.

The major cause of this stagnation is that physics has changed, but physicists have not changed their methods. As physics has progressed, the foundations have become increasingly harder to probe by experiment. Technological advances have not kept size and expenses manageable. This is why, in physics today we have collaborations of thousands of people operating machines that cost billions of dollars.

With fewer experiments, serendipitous discoveries become increasingly unlikely. And lacking those discoveries, the technological progress that would be needed to keep experiments economically viable never materializes. It’s a vicious cycle: Costly experiments result in lack of progress. Lack of progress increases the costs of further experiment. This cycle must eventually lead into a dead end when experiments become simply too expensive to remain affordable. A $40 billion particle collider is such a dead end.

The only way to avoid being sucked into this vicious cycle is to choose carefully which hypothesis to put to the test. But physicists still operate by the “just look” idea like this was the 19th century. They do not think about which hypotheses are promising because their education has not taught them to do so. Such self-reflection would require knowledge of the philosophy and sociology of science, and those are subjects physicists merely make dismissive jokes about. They believe they are too intelligent to have to think about what they are doing.

The consequence has been that experiments in the foundations of physics past the 1970s have only confirmed the already existing theories. None found evidence of anything beyond what we already know.

But theoretical physicists did not learn the lesson and still ignore the philosophy and sociology of science. I encounter this dismissive behavior personally pretty much every time I try to explain to a cosmologist or particle physicists that we need smarter ways to share information and make decisions in large, like-minded communities. If they react at all, they are insulted if I point out that social reinforcement – aka group-think – befalls us all, unless we actively take measures to prevent it.

Instead of examining the way that they propose hypotheses and revising their methods, theoretical physicists have developed a habit of putting forward entirely baseless speculations. Over and over again I have heard them justifying their mindless production of mathematical fiction as “healthy speculation” – entirely ignoring that this type of speculation has demonstrably not worked for decades and continues to not work. There is nothing healthy about this. It’s sick science. And, embarrassingly enough, that’s plain to see for everyone who does not work in the field.

This behavior is based on the hopelessly naïve, not to mention ill-informed, belief that science always progresses somehow, and that sooner or later certainly someone will stumble over something interesting. But even if that happened – even if someone found a piece of the puzzle – at this point we wouldn’t notice, because today any drop of genuine theoretical progress would drown in an ocean of “healthy speculation”.

And so, what we have here in the foundation of physics is a plain failure of the scientific method. All these wrong predictions should have taught physicists that just because they can write down equations for something does not mean this math is a scientifically promising hypothesis. String theory, supersymmetry, multiverses. There’s math for it, alright. Pretty math, even. But that doesn’t mean this math describes reality.

Physicists need new methods. Better methods. Methods that are appropriate to the present century.

And please spare me the complaints that I supposedly do not have anything better to suggest, because that is a false accusation. I have said many times that looking at the history of physics teaches us that resolving inconsistencies has been a reliable path to breakthroughs, so that’s what we should focus on. I may be on the wrong track with this, of course. But for all I can tell at this moment in history I am the only physicist who has at least come up with an idea for what to do.

Why don’t physicists have a hard look at their history and learn from their failure? Because the existing scientific system does not encourage learning. Physicists today can happily make career by writing papers about things no one has ever observed, and never will observe. This continues to go on because there is nothing and no one that can stop it.

You may want to put this down as a minor worry because – $40 billion dollar collider aside – who really cares about the foundations of physics? Maybe all these string theorists have been wasting tax-money for decades, alright, but in the large scheme of things it’s not all that much money. I grant you that much. Theorists are not expensive.

But even if you don’t care what’s up with strings and multiverses, you should worry about what is happening here. The foundations of physics are the canary in the coal mine. It’s an old discipline and the first to run into this problem. But the same problem will sooner or later surface in other disciplines if experiments become increasingly expensive and recruit large fractions of the scientific community.

Indeed, we see this beginning to happen in medicine and in ecology, too.

Small-scale drug trials have pretty much run their course. These are good only to find in-your-face correlations that are universal across most people. Medicine, therefore, will increasingly have to rely on data collected from large groups over long periods of time to find increasingly personalized diagnoses and prescriptions. The studies which are necessary for this are extremely costly. They must be chosen carefully for not many of them can be made. The study of ecosystems faces a similar challenge, where small, isolated investigations are about to reach their limits.

How physicists handle their crisis will give an example to other disciplines. So watch this space.

A Million Miles [I've been singing again]

Used the weekend to finish my most recent track.

What is the quantum measurement problem?

Today, I want to explain just what the problem is with making measurements according to quantum theory.

Quantum mechanics tells us that matter is not made of particles. It is made of elementary constituents that are often called particles, but are really described by wave-functions. A wave-function is a mathematical object which is neither a particle nor a wave, but it can have properties of both.

The curious thing about the wave-function is that it does not itself correspond to something which we can observe. Instead, it is only a tool by help of which we calculate what we do observe. To make such a calculation, quantum theory uses the following postulates.

First, as long as you do not measure the wave-function, it changes according to the Schrödinger equation. The Schrödinger equation is different for different particles. But its most important properties are independent of the particle.

One of the important properties of the Schrödinger equation is that it guarantees that the probabilities computed from the wave-function will always add up to one, as they should. Another important property is that the change in time which one gets from the Schrödinger equation is reversible.

But for our purposes the most important property of the Schrödinger equation is that it is linear. This means if you have two solutions to this equation, then any sum of the two solutions, with arbitrary pre-factors, will also be a solution.

The second postulate of quantum mechanics tells you how you calculate from the wave-function what is the probability of getting a specific measurement outcome. This is called the “Born rule,” named after Max Born who came up with it. The Born rule says that the probability of a measurement is the absolute square of that part of the wave-function which describes a certain measurement outcome. To do this calculation, you also need to know how to describe what you are observing – say, the momentum of a particle. For this, you need further postulates, but these do not need to concern us today.

And third, there is the measurement postulate, sometimes called the “update” or “collapse” of the wave-function. This postulate says that after you have made a measurement, the probability of what you have measured suddenly changes to 1. This, I have to emphasize, is a necessary requirement to describe what we observe. I cannot stress this enough because a lot of physicists seem to find it hard to comprehend. If you do not update the wave-function after measurement, then the wave-function does not describe what we observe. We do not, ever, observe a particle that is 50% measured.

The problem with the quantum measurement is now that the update of the wave-function is incompatible with the Schrödinger equation. The Schrödinger equation, as I already said, is linear. That means if you have two different states of a system, both of which are allowed according to the Schrödinger equation, then the sum of the two states is also an allowed solution. The best known example of this is Schrödinger’s cat, which is a state that is a sum of both dead and alive. Such a sum is what physicists call a superposition.

We do, however, only observe cats that are either dead or alive. This is why we need the measurement postulate. Without it, quantum mechanics would not be compatible with observation.

The measurement problem, I have to emphasize, is not solved by decoherence, even though many physicists seem to believe this to be so. Decoherence is a process that happens if a quantum superposition interacts with its environment. The environment may simply be air or, even in vacuum, you still have the radiation of the cosmic microwave background. There is always some environment. This interaction with the environment eventually destroys the ability of quantum states to display typical quantum behavior, like the ability of particles to create interference patterns. The larger the object, the more quickly its quantum behavior gets destroyed.

Decoherence tells you that if you average over the states of the environment, because you do not know exactly what they do, then you no longer have a quantum superposition. Instead, you have a distribution of probabilities. This is what physicists call a “mixed state”. This does not solve the measurement problem because after measurement, you still have to update the probability of what you have observed to 100%. Decoherence does not tell you to do that.

Why is the measurement postulate problematic? The trouble with the measurement postulate is that the behavior of a large thing, like a detector, should follow from the behavior of the small things that it is made up of. But that is not the case. So that’s the issue. The measurement postulate is incompatible with reductionism. It makes it necessary that the formulation of quantum mechanics explicitly refers to macroscopic objects like detectors, when really what these large things are doing should follow from the theory.

A lot of people seem to think that you can solve this problem by way of re-interpreting the wave-function as merely encoding the knowledge that an observer has about the state of the system. This is what is called a Copenhagen or “neo-Copenhagen” interpretation. (And let me warn you that this is not the same as a Psi-epistemic interpretation, in case you have heard that word.)

Now, if you believe that the wave-function merely describes the knowledge an observer has then you may say, of course it needs to be updated if the observer makes a measurement. Yes, that’s very reasonable. But of course this also refers to macroscopic concepts like observers and their knowledge. And if you want to use such concepts in the postulates of your theory, you are implicitly assuming that the behavior of observers or detectors is incompatible with the behavior of the particles that make up the observers or detectors. This requires that you explain when and how this distinction is to be made and none of the existing neo-Copenhagen approaches explain this.

I already told you in an earlier blogpost why the many worlds interpretation does not solve the measurement problem. To briefly summarize it, it’s because in the many worlds interpretation one also has to use a postulate about what a detector does.

What does it take to actually solve the measurement problem? I will get to this, so stay tuned.

Dark matter nightmare: What if we are just using the wrong equations?

Dark matter filaments. Computer simulation.
[Image: John Dubinski (U of Toronto)]

Einstein’s theory of general relativity is an extremely well-confirmed theory. Countless experiments have shown that its predictions for our solar system agree with observation to utmost accuracy. But when we point our telescopes at larger distances, something is amiss. Galaxies rotate faster than expected. Galaxies in clusters move faster than they should. The expansion of the universe is speeding up.

General relativity does not tell us what is going on.

Physicists have attributed these puzzling observations to two newly postulated substances: Dark matter and dark energy. These two names are merely placeholders in Einstein’s original equations; their sole purpose is to remove the mismatch between prediction and observation.

This is not a new story. We have had evidence for dark matter since the 1930s, and dark energy was on the radar already in the 1990. Both have since occupied thousands of physicists with attempts to explain just what we are dealing with: Is dark matter a particle, and if so what type, and how can we measure it? If it is not a particle, then what do we change about general relativity to fix the discrepancy with measurements? Is dark energy maybe a new type of field? Is it, too, made of some particle? Does dark matter have something to do with dark energy or are the two unrelated?

To answer these questions, hundreds of hypotheses have been proposed, conferences have been held, careers have been made – but here we are, in 2019, and we still don’t know.

Bad enough, you may say, but the thing that really keeps me up at night is this: Maybe all these thousands of physicists are simply using the wrong equations. I don’t mean that general relativity needs to be modified. I mean that we incorrectly use the equations of general relativity to begin with.

The issue is this. General relativity relates the curvature of space and time to the sources of matter and energy. Put in a distribution of matter and energy at any one moment of time, and the equations tell you what space and time do in response, and how the matter must move according to this response.

But general relativity is a non-linear theory. This means, loosely speaking, that gravity gravitates. More concretely, it means that if you have two solutions to the equations and you take their sum, this sum will not also be a solution.

Now, what we do when we want to explain what a galaxy does, or a galaxy cluster, or even the whole universe, is not to plug the matter and energy of every single planet and star into the equations. This would be computationally unfeasible. Instead, we use an average of matter and energy, and use that as the source for gravity.

Needless to say, taking an average on one side of the equation requires that you also take an average on the other side. But since the gravitational part is non-linear, this will not give you the same equations that we use for the solar system: The average of a function of a variable is not the same as the function of the average of the variable. We know it’s not. But whenever we use general relativity on large scales, we assume that this is the case.

So, we know that strictly speaking the equations we use are wrong. The big question is, then, just how wrong are they?

Nosy students who ask this question are usually told these equations are not very wrong and are good to use. The argument goes that the difference between the equation we use and the equation we should use is negligible because gravity is weak in all these cases.

But if you look at the literature somewhat closer, then this argument has been questioned. And these questions have been questioned. And the questioning questions have been questioned. And the debate has remained unsettled until today.

That it is difficult to average non-linear equations is of course not a problem specific to cosmology. It’s a difficulty that condensed matter physicists have to deal with all the time, and it’s a major headache also for climate scientists. These scientists have a variety of techniques to derive the correct equations, but unfortunately the known methods do not easily carry over to general relativity because they do not respect the symmetries of Einstein’s theory.

It’s admittedly an unsexy research topic. It’s technical and tedious and most physicists ignore it. And so, while there are thousands of physicists who simply assume that the correction-terms from averaging are negligible, there are merely two dozen or so people trying to make sure that this assumption is actually correct.

Given how much brain-power physicists have spent on trying to figure out what dark matter and dark energy is, I think it would be a good idea to definitely settle the question whether it is anything at all. At the very least, I would sleep better.

Further reading: Does the growth of structure affect our dynamical models of the universe? The averaging, backreaction and fitting problems in cosmology, by Chris Clarkson, George Ellis, Julien Larena, and Obinna Umeh. Rept. Prog. Phys. 74 (2011) 112901, arXiv:1109.2314 [astro-ph.CO].

What does the future hold for particle physics?

In my new video, I talk about the reason why the Large Hadron Collider, LHC for short, has not found fundamentally new particles besides the Higgs boson, and what this means for the future of particle physics. Below you find a transcript with references.


Before the LHC turned on, particle physicists had high hopes it would find something new besides the Higgs boson, something that would go beyond the standard model of particle physics. There was a lot of talk about the particles that supposedly make up dark matter, which the collider might produce. Many physicists also expected it to find the first of a class of entirely new particles that were predicted based on a hypothesis known as supersymmetry. Others talked about dark energy, additional dimensions of space, string balls, black holes, time travel, making contact to parallel universes or “unparticles”. That’s particles which aren’t particles. So, clearly, some wild ideas were in the air.

To illustrate the situation before the LHC began taking data, let me quote a few articles from back then.

Here is Valerie Jamieson writing for New Scientist in 2008:

“The Higgs and supersymmetry are on firm theoretical footing. Some theorists speculate about more outlandish scenarios for the LHC, including the production of extra dimensions, mini black holes, new forces, and particles smaller than quarks and electrons. A test for time travel has also been proposed.”

Or, here is Ian Sample for the Guardian, also in 2008:

“Scientists have some pretty good hunches about what the machine might find, from creating never-seen-before particles to discovering hidden dimensions and dark matter, the mysterious substance that makes up 25% of the universe.”

Paul Langacker in 2010, writing for the APS:

“Theorists have predicted that spectacular signals of supersymmetry should be visible at the LHC.” Michael Dine for Physics Today in 2007:

“The Large Hadron Collider will either make a spectacular discovery or rule out supersymmetry entirely.”

The Telegraph in 2010:

“[The LHC] could answer the question of what causes mass, or even surprise its creators by revealing the existence of a fifth, sixth or seventh secret dimension of time and space.”

A final one. Here is Steve Giddings writing in 2010 for phys.org:

“LHC collisions might produce dark-matter particles... The collider might also shed light on the more predominant “dark energy,”... the LHC may reveal extra dimensions of space... if these extra dimensions are configured in certain ways, the LHC could produce microscopic black holes... Supersymmetry could be discovered by the LHC...”

The Large Hadron collider has been running since 2010. It has found the Higgs boson. But why didn’t it find any of the other things?

This question is surprisingly easy to answer. There was never a good reason to expect any of these things in the first place. The more difficult question is why did so many particle physicists think those were reasonable expectations, and why has not a single one of them told us what they have learned from their failed predictions?

To see what happened here, it is useful to look at the difference between the prediction of the Higgs-boson and the other speculations. The standard model without the Higgs does not work properly. It becomes mathematically inconsistent at energies that the LHC is able to reach. Concretely, without the Higgs, the standard model predicts probabilities larger than one, which makes no sense.

We therefore knew, before the LHC turned on, that something new had to happen. It could have been something else besides the Higgs. The Higgs was one way to fix the problem with the standard model, but there are other ways. However, the Higgs turned out to be right.

All other proposed ideas, extra dimensions, supersymmetry, time-travel, and so on, are unnecessary. These theories have been constructed so that they are compatible with all existing observations. But they are not necessary to solve any problem with the standard model. They are basically wishful thinking.

The reason that many particle physicists believed in these speculations is that they mistakenly thought the standard model has another problem which the existence of the Higgs would not fix. I am afraid that many of them still believe this. This supposed problem is that the standard model is not “technically natural”.

This means the standard model contains one number that is small, but there is no explanation for why it is small. This number is the mass of the Higgs-boson divided by the Planck mass, which happens to be about 10^-15. The standard model works just fine with that number and it fits the data. But a small number like this, without explanation, is ugly and particle physicists didn’t want to believe nature could be that ugly.

Well, now they know that nature doesn’t care what physicists want it to be like.

What does this mean for the future of particle physics? This argument from “technical naturalness” was the only reason that physicists had to think that the standard model is incomplete and something to complete it must appear at LHC energies. Now that it is clear this argument did not work, there is no reason why a next larger collider should see anything new either. The standard model runs into mathematical trouble again at energies about a billion times higher than what a next larger collider could test. At the moment, therefore, we have no good reason to build a larger particle collider.

But particle physics is not only collider physics. And so, it seems likely to me, that research will shift to other areas of physics. A shift that has been going on for two decades already, and will probably become more pronounced now, is the move to astrophysics, in particular the study of dark matter and dark energy and also, to some extent, the early universe.

The other shift that we are likely to see is a move away from high energy particle physics and move towards high precision measurements at lower energies, or to table top experiments probing the quantum behavior of many particle systems, where we still have much to learn.

Has Reductionism Run its Course?

For more than 2000 years, ever since Democritus’ first musings about atoms, reductionism has driven scientific inquiry. The idea is simple enough: Things are made of smaller things, and if you know what the small things do, you learn what the large things do. Simple – and stunningly successful.

After 2000 years of taking things apart into smaller things, we have learned that all matter is made of molecules, and that molecules are made of atoms. Democritus originally coined the word “atom” to refer to indivisible, elementary units of matter. But what we have come to call “atoms”, we now know, is made of even smaller particles. And those smaller particles are yet again made of even smaller particles.

© Sabine Hossenfelder

The smallest constituents of matter, for all we currently know, are the 25 particles which physicists collect in the standard model of particle physics. Are these particles made up of yet another set of smaller particles, strings, or other things?

It is certainly possible that the particles of the standard model are not the ultimate constituents of matter. But we presently have no particular reason to think they have a substructure. And this raises the question whether attempting to look even closer into the structure of matter is a promising research direction – right here, right now.

It is a question that every researcher in the foundations of physics will be asking themselves, now that the Large Hadron Collider has confirmed the standard model, but found nothing beyond that.

20 years ago, it seemed clear to me that probing physical processes at ever shorter distances is the most reliable way to better understand how the universe works. And since it takes high energies to resolve short distances, this means that slamming particles together at high energies is the route forward. In other words, if you want to know more, you build bigger particle colliders.

This is also, unsurprisingly, what most particle physicists are convinced of. Going to higher energies, so their story goes, is the most reliable way to search for something fundamentally new. This is, in a nutshell, particle physicists’ major argument in favor of building a new particle collider, one even larger than the presently operating Large Hadron Collider.

But this simple story is too simple.

The idea that reductionism means things are made of smaller things is what philosophers more specifically call “methodological reductionism”. It’s a statement about the properties of stuff. But there is another type of reductionism, “theory reductionism”, which instead refers to the relation between theories. One theory can be “reduced” to another one, if the former can be derived from the latter.

Now, the examples of reductionism that particle physicists like to put forward are the cases where both types of reductionism coincide: Atomic physics explains chemistry. Statistical mechanics explains the laws of thermodynamics. The quark model explains regularities in proton collisions. And so on.

But not all cases of successful theory reduction have also been cases of methodological reduction. Take Maxwell’s unification of the electric and magnetic force. From Maxwell’s theory you can derive a whole bunch of equations, such as the Coulomb law and Faraday’s law, that people used before Maxwell explained where they come from. Electromagnetism, is therefore clearly a case of theory reduction, but it did not come with a methodological reduction.

Another well-known exception is Einstein’s theory of General Relativity. General Relativity can be used in more situations than Newton’s theory of gravity. But it is not the physics on short distances that reveals the differences between the two theories. Instead, it is the behavior of bodies at high relative speed and strong gravitational fields that Newtonian gravity cannot cope with.

Another example that belongs on this list is quantum mechanics. Quantum mechanics reproduces classical mechanics in suitable approximations. It is not, however, a theory about small constituents of larger things. Yes, quantum mechanics is often portrayed as a theory for microscopic scales, but, no, this is not correct. Quantum mechanics is really a theory for all scales, large to small. We have observed quantum effects over distances exceeding 100km and for objects weighting as “much” as a nanogram, composed of more than 10¹³ atoms. It’s just that quantum effects on large scales are difficult to create and observe.

Finally, I would like to mention Noether’s theorem, according to which symmetries give rise to conservation laws. This example is different from the previous ones in that Noether’s theorem was not applied to any theory in particular. But it has resulted in a more fundamental understanding of natural law, and therefore I think it deserve a place on the list.

In summary, history does not support particle physicists’ belief that a deeper understanding of natural law will most likely come from studying shorter distances. On the very contrary, I have begun to worry that physicists’ confidence in methodological reductionism stands in the way of progress. That’s because it suggests we ask certain questions instead of others. And those may just be the wrong questions to ask.

If you believe in methodological reductionism, for example, you may ask what dark energy is made of. But maybe dark energy is not made of anything. Instead, dark energy may be an artifact of our difficulty averaging non-linear equations.

It’s similar with dark matter. The methodological reductionist will ask for a microscopic theory and look for a particle that dark matter is made of. Yet, maybe dark matter is really a phenomenon associated with our misunderstanding of space-time on long distances.

The maybe biggest problem that methodological reductionism causes lies in the area of quantum gravity, that is our attempt to resolve the inconsistency between quantum theory and general relativity. Pretty much all existing approaches – string theory, loop quantum gravity, causal dynamical triangulation (check out my video for more) – assume that methodological reductionism is the answer. Therefore, they rely on new hypotheses for short-distance physics. But maybe that’s the wrong way to tackle the problem. The root of our problem may instead be that quantum theory itself must be replaced by a more fundamental theory, one that explains how quantization works in the first place.

Approaches based on methodological reductionism – like grand unified forces, supersymmetry, string theory, preon models, or technicolor – have failed for the past 30 years. This does not mean that there is nothing more to find at short distances. But it does strongly suggest that the next step forward will be a case of theory reduction that does not rely on taking things apart into smaller things.

Travel Update

The coming days I am in Brussels, for a workshop that I’m not sure where it is or what it is about. It also doesn’t seem to have a website. In any case, I’ll be away, just don’t ask me exactly where or why.

On Oct 15, I am giving a public lecture at the University of Minnesota. On Oct 17, I am giving a colloquium in Cleveland. On Oct 25, I am giving a public lecture in Göttingen (in German). On Oct 29, I’m in Genoa giving a talk at the “Festival della Scienza” to accompany the publication of the Italian translation of my book “Lost in Math.” I don’t speak Italian, so this talk will be in English.

On Nov 5th I’m speaking in Berlin about dark matter. On Nov 6th I am supposed to give a lecture at the Einstein Forum on Potsdam, though that doesn’t seem to be on their website. These two talks in Berlin and Potsdam will also be in German.

On Nov 12th I’m giving a seminar in Oxford, in case Britain still exists at that point. Dec 9th I’m speaking in Wuppertal, details to come, and that will hopefully be the last trip this year.

Next time I’m in the USA will probably be late March 2020. In case you are interested that I stop by at your place, please get in touch.

I am always happy to meet readers of my blog, so in case our paths cross, do not hesitate to say hi.

The Trouble with Many Worlds

Today I want to talk about the many worlds interpretation of quantum mechanics and explain why I do not think it is a complete theory.



But first, a brief summary of what the many worlds interpretation says. In quantum mechanics, every system is described by a wave-function from which one calculates the probability of obtaining a specific measurement outcome. Physicists usually take the Greek letter Psi to refer to the wave-function.

From the wave-function you can calculate, for example, that a particle which enters a beam-splitter has a 50% chance of going left and a 50% chance of going right. But – and that’s the important point – once you have measured the particle, you know with 100% probability where it is. This means that you have to update your probability and with it the wave-function. This update is also called the wave-function collapse.

The wave-function collapse, I have to emphasize, is not optional. It is an observational requirement. We never observe a particle that is 50% here and 50% there. That’s just not a thing. If we observe it at all, it’s either here or it isn’t. Speaking of 50% probabilities really makes sense only as long as you are talking about a prediction.

Now, this wave-function collapse is a problem for the following reason. We have an equation that tells us what the wave-function does as long as you do not measure it. It’s called the Schrödinger equation. The Schrödinger equation is a linear equation. What does this mean? It means that if you have two solutions to this equation, and you add them with arbitrary prefactors, then this sum will also be a solution to the Schrödinger equation. Such a sum, btw, is also called a “superposition”. I know that superposition sounds mysterious, but that’s really all it is, it’s a sum with prefactors.

The problem is now that the wave-function collapse is not linear, and therefore it cannot be described by the Schrödinger equation. Here is an easy way to understand this. Suppose you have a wave-function for a particle that goes right with 100% probability. Then you will measure it right with 100% probability. No mystery here. Likewise, if you have a particle that just goes left, you will measure it left with 100% probability. But here’s the thing. If you take a superposition of these two states, you will not get a superposition of probabilities. You will get 100% either on the one side, or on the other.

The measurement process therefore is not only an additional assumption that quantum mechanics needs to reproduce what we observe. It is actually incompatible with the Schrödinger equation.

Now, the most obvious way to deal with that is to say, well, the measurement process is something complicated that we do not yet understand, and the wave-function collapse is a placeholder that we use until we will figured out something better.

But that’s not how most physicists deal with it. Most sign up for what is known as the Copenhagen interpretation, that basically says you’re not supposed to ask what happens during measurement. In this interpretation, quantum mechanics is merely a mathematical machinery that makes predictions and that’s that. The problem with Copenhagen – and with all similar interpretations – is that they require you to give up the idea that what a macroscopic object, like a detector does should be derivable from theory of its microscopic constituents.

If you believe in the Copenhagen interpretation you have to buy that what the detector does just cannot be derived from the behavior of its microscopic constituents. Because if you could do that, you would not need a second equation besides the Schrödinger equation. That you need this second equation, then is incompatible with reductionism. It is possible that this is correct, but then you have to explain just where reductionism breaks down and why, which no one has done. And without that, the Copenhagen interpretation and its cousins do not solve the measurement problem, they simply refuse to acknowledge that the problem exists in the first place.

The many world interpretation, now, supposedly does away with the problem of the quantum measurement and it does this by just saying there isn’t such a thing as wavefunction collapse. Instead, many worlds people say, every time you make a measurement, the universe splits into several parallel worlds, one for each possible measurement outcome. This universe splitting is also sometimes called branching.

Some people have a problem with the branching because it’s not clear just exactly when or where it should take place, but I do not think this is a serious problem, it’s just a matter of definition. No, the real problem is that after throwing out the measurement postulate, the many worlds interpretation needs another assumption, that brings the measurement problem back.

The reason is this. In the many worlds interpretation, if you set up a detector for a measurement, then the detector will also split into several universes. Therefore, if you just ask “what will the detector measure”, then the answer is “The detector will measure anything that’s possible with probability 1.”

This, of course, is not what we observe. We observe only one measurement outcome. The many worlds people explain this as follows. Of course you are not supposed to calculate the probability for each branch of the detector. Because when we say detector, we don’t mean all detector branches together. You should only evaluate the probability relative to the detector in one specific branch at a time.

That sounds reasonable. Indeed, it is reasonable. It is just as reasonable as the measurement postulate. In fact, it is logically entirely equivalent to the measurement postulate. The measurement postulate says: Update probability at measurement to 100%. The detector definition in many worlds says: The “Detector” is by definition only the thing in one branch. Now evaluate probabilities relative to this, which gives you 100% in each branch. Same thing.

And because it’s the same thing you already know that you cannot derive this detector definition from the Schrödinger equation. It’s not possible. What the many worlds people are now trying instead is to derive this postulate from rational choice theory. But of course that brings back in macroscopic terms, like actors who make decisions and so on. In other words, this reference to knowledge is equally in conflict with reductionism as is the Copenhagen interpretation.

And that’s why the many worlds interpretation does not solve the measurement problem and therefore it is equally troubled as all other interpretations of quantum mechanics. What’s the trouble with the other interpretations? We will talk about this some other time. So stay tuned.