Tuesday, September 10, 2019

Book Review: “Something Deeply Hidden” by Sean Carroll

Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime
Sean Carroll
Dutton, September 10, 2019

Of all the weird ideas that quantum mechanics has to offer, the existence of parallel universes is the weirdest. But with his new book, Sean Carroll wants to convince you that it isn’t weird at all. Instead, he argues, if we only take quantum mechanics seriously enough, then “many worlds” are the logical consequence.

Most remarkably, the many worlds interpretation implies that in every instance you split into many separate you’s, all of which go on to live their own lives. It takes something to convince yourself that this is reality, but if you want to be convinced, Carroll’s book is a good starting point.

“Something Deeply Hidden” is an enjoyable and easy-to-follow introduction to quantum mechanics that will answer your most pressing questions about many worlds, such as how worlds split, what happens with energy conservation, or whether you should worry about the moral standards of all your copies.

The book is also notable for what it does not contain. Carroll avoids going through all the different interpretations of quantum mechanics in detail, and only provides short summaries. Instead, the second half of the book is dedicated to his own recent work, which is about constructing space from quantum entanglement. I do find this a promising line of research and he presents it well.

I was somewhat perplexed that Carroll does not mention what I think are the two biggest objections to the many world’s interpretation, but I will write about this in a separate post.

Like Carroll’s previous books, this one is engaging, well-written, and clearly argued. I can unhesitatingly recommend it to anyone who is interested in the foundations of physics.

[Disclaimer: Free review copy]

Sunday, September 08, 2019

Away Note

I'm attending a conference in Oxford the coming week, so there won't be much happening on this blog. Also, please be warned that comments may be stuck in the moderation queue longer than usual.

Friday, September 06, 2019

The five most promising ways to quantize gravity

Today, I want to tell you what ideas physicists have come up with to quantize gravity. But before I get to that, I want to tell you why it matters.

That we do not have a theory of quantum gravity is currently one of the biggest unsolved problems in the foundations of physics. A lot of people, including many of my colleagues, seem to think that a theory of quantum gravity will remain an academic curiosity without practical relevance.

I think they are wrong. That’s because whatever solves this problem will tell us something about quantum theory, and that’s the theory on which all modern electronic devices run, like the ones on which you are watching this video. Maybe it will take 100 years for quantum gravity to find a practical application, or maybe it will even take a 1000 years. But I am sure that understanding nature better will not forever remain a merely academic speculation.

Before I go on, I want to be clear that quantizing gravity by itself is not the problem. We can, and have, quantized gravity the same way that we quantize the other interactions. The problem is that the theory which one gets this way breaks down at high energies, and therefore it cannot be how nature works, fundamentally.

This naïve quantization is called “perturbatively quantized gravity” and it was worked out in the 1960s by Feynman and DeWitt and some others. Perturbatively quantized gravity is today widely believed to be an approximation to whatever is the correct theory.

So really the problem is not just to quantize gravity per se, you want to quantize it and get a theory that does not break down at high energies. Because energies are proportional to frequencies, physicists like to refer to high energies as “the ultraviolet” or just “the UV”. Therefore, the theory of quantum gravity that we look for is said to be “UV complete”.

Now, let me go through the five most popular approaches to quantum gravity.

1. String Theory

The most widely known and still the most popular attempt to get a UV-complete theory of quantum gravity is string theory. The idea of string theory is that instead of talking about particles and quantizing them, you take strings and quantize those. Amazingly enough, this automatically has the consequence that the strings exchange a force which has the same properties as the gravitational force.

This was discovered in the 1970s and at the time, it got physicists very excited. However, in the past decades several problems have appeared in string theory that were patched, which has made the theory increasingly contrived. You can hear all about this in my earlier video. It has never been proved that string theory is indeed UV-complete.

2. Loop Quantum Gravity

Loop Quantum Gravity is often named as the biggest competitor of string theory, but this comparison is somewhat misleading. String theory is not just a theory for quantum gravity, it is also supposed to unify the other interactions. Loop Quantum Gravity on the other hand, is only about quantizing gravity.

It works by discretizing space in terms of a network, and then using integrals around small loops to describe the space, hence the name. In this network, the nodes represent volumes and the links between nodes the areas of the surfaces where the volumes meet.

Loop Quantum Gravity is about as old as string theory. It solves the problem of combining general relativity and quantum mechanics to one consistent theory but it has remained unclear just exactly how one recovers general relativity in this approach.

3. Asymptotically Safe Gravity

Asymptotic Safety is an idea that goes back to a 1976 paper by Steven Weinberg. It says that a theory which seems to have problems at high energies when quantized naively, may not have a problem after all, it’s just that it’s more complicated to find out what happens at high energies than it seems. Asymptotically Safe Gravity applies the idea of asymptotic safety to gravity in particular.

This approach also solves the problem of quantum gravity. Its major problem is currently that it has not been proved that the theory which one gets this way at high energies still makes sense as a quantum theory.

4. Causal Dynamical Triangulation

The problem with quantizing gravity comes from infinities that appear when particles interact at very short distances. This is why most approaches to quantum gravity rely on removing the short distances by using objects of finite extensions. Loop Quantum Gravity works this way, and so does String Theory.

Causal Dynamical Triangulation also relies on removing short distances. It does so by approximating a curved space with triangles, or their higher-dimensional counterparts respectively. In contrast to the other approaches though, where the finite extension is a postulated, new property of the underlying true nature of space, in Causal Dynamical Triangulation, the finite size of the triangles is a mathematical aid, and one eventually takes the limit where this size goes to zero.

The major reason why many people have remained unconvinced of Causal Dynamical Triangulation is that it treats space and time differently, which Einstein taught us not to do.

5. Emergent Gravity

Emergent gravity is not one specific theory, but a class of approaches. These approaches have in common that gravity derives from the collective behavior of a large number of constituents, much like the laws of thermodynamics do. And much like for thermodynamics, in emergent gravity, one does not actually need to know all that much about the exact properties of these constituents to get the dynamical law.

If you think that gravity is really emergent, then quantizing gravity does not make sense. Because, if you think of the analogy to thermodynamics, you also do not obtain a theory for the structure of atom by quantizing the equations for gases. Therefore, in emergent gravity one does not quantize gravity. One instead removes the inconsistency between gravity and quantum mechanics by saying that quantizing gravity is not the right thing to do.

Which one of these theories is the right one? No one knows. The problem is that it’s really, really hard to find experimental evidence for quantum gravity. But that it’s hard doesn’t mean impossible. I will tell you some other time how we might be able to experimentally test quantum gravity after all. So, stay tuned.

Wednesday, September 04, 2019

What’s up with LIGO?

The Nobel-Prize winning figure.
We don’t know exactly what it shows.
[Image Credits: LIGO]
Almost four years ago, on September 14 2015, the LIGO collaboration detected gravitational waves for the first time. In 2017, this achievement was awarded the Nobel Prize. Also in that year, the two LIGO interferometers were joined by VIRGO. Since then, a total of three detectors have been on the lookout for space-time’s subtle motions.

By now, the LIGO/VIRGO collaboration has reported dozens of gravitational wave events: black hole mergers (like the first), neutron star mergers, and black hole-neutron star mergers. But not everyone is convinced the signals are really what the collaboration claims they are.

Already in 2017, a group of physicists around Andrew Jackson in Denmark reported difficulties when they tried to reproduce the signal reconstruction of the first event. In an interview dated November last year, Jackson maintained that the only signal they have been able to reproduce is the first. About the other supposed detections he said: “We can’t see any of those events when we do a blind analysis of the data. Coming from Denmark, I am tempted to say it’s a case of the emperor’s new gravitational waves.”

For most physicists, the 170817 neutron-star merger – the strongest signal LIGO has seen so-far – erased any worries raised by the Danish group’s claims. That’s because this event came with an electromagnetic counterpart that was seen by multiple telescopes, which can demonstrate that LIGO indeed sees something of astrophysical origin and not terrestrial noise. But, as critics have pointed out correctly, the LIGO alert for this event came 40 minutes after NASA’s gamma-ray alert. For this reason, the event cannot be used as an independent confirmation of LIGO’s detection capacity. Furthermore, the interpretation of this signal as a neutron-star merger has also been criticized. And this criticism has been criticized for yet other reasons.

It further fueled the critics’ fire when Michael Brooks reported last year for New Scientist that, according to two members of the collaboration, the Nobel-prize winning figure of LIGO’s seminal detection was “not found using analysis algorithms” but partly done “by eye” and “hand-tuned for pedagogical purposes.” To this date, the journal that published the paper has refused to comment.

The LIGO collaboration has remained silent on the matter, except for issuing a statement according to which they have “full confidence” in their published results (surprise), and that we are to await further details. Glaciers are now moving faster than this collaboration.

In April this year, LIGO started the third observation run (O3) after an upgrade that increased the detection sensitivity by about 40% over the previous run.  Many physicists hoped the new observations would bring clarity with more neutron-star events that have electromagnetic counterparts, but that hasn’t happened.

Since April, the collaboration has issued 33 alerts for new events, but so-far no electromagnetic counterparts have been seen. You can check the complete list for yourself here. 9 of the 33 events have meanwhile been downgraded because they were identified as likely of terrestrial origin, and been retracted.

The number of retractions is fairly high partly because the collaboration is still coming to grips with the upgraded detector. This is new scientific territory and the researchers themselves are still learning how to best analyze and interpret the data. A further difficulty is that the alerts must go out quickly in order for telescopes to be swung around and point at the right location in the sky. This does not leave much time for careful analysis.

With the still lacking independent confirmation that LIGO sees events of astrophysical origin, critics are having a good time. In a recent article for the German online magazine Heise, Alexander Unzicker – author of a book called “The Higgs Fake” – contemplates whether the first event was a blind injection, ie, a fake signal. The three people on the blind injection team at the time say it wasn’t them, but Unzicker argues that given our lack of knowledge about the collaboration’s internal proceedings, there might well have been other people able to inject a signal. (You can find an English translation here.)

In the third observation run, the collaboration has so-far seen one high-significance binary neutron star candidate (S190425z). But the associated electromagnetic signal for this event has not been found. This may be for various reasons. For example, the analysis of the signal revealed that the event must have been far away, about 4 times farther than the 2017 neutron-star event. This means that any electromagnetic signal would have been fainter by a factor of about 16. In addition, the location in the sky was rather uncertain. So, the electromagnetic signal was plausibly hard to detect.

More recently, on August 14th, the collaboration reported a neutron-star black hole merger. Again the electromagnetic counterpart is missing. In this case they were able to locate the origin to better precision. But they still estimate the source is about 7 times farther away than the 2017 neutron-star event, meaning it would have been fainter by a factor of about 50.

Still, it is somewhat perplexing the signal wasn’t seen by any of the telescopes that looked for it. There may have been physical reasons at the source, such that the neutron-star was swallowed in one bite, in which case there wouldn’t be much emitted, or that the system was surrounded by dust, blocking the electromagnetic signal.

A second neutron star-black hole merger on August 17 was retracted

And then there are the “glitches”.

LIGO’s “glitches” are detector events of unknown origin whose frequency spectrum does not look like the expected gravitational wave signals. I don’t know exactly how many of those the detector suffers from, but the way they are numbered, by a date and two digits, indicates between 10 and 100 a day. LIGO uses a citizen science project, called “Gravity Spy” to identify glitches. There isn’t one type of glitch, there are many different types of them, with names like “Koi fish,” “whistle,” or “blip.” In the figures below you see a few examples.

Examples for LIGO's detector glitches. [Image Source]

This gives me some headaches, folks. If you do not know why your detector detects something that does not look like what you expect, how can you trust it in the cases where it does see what you expect?

Here is what Andrew Jackson had to say on the matter:

Jackson: “The thing you can conclude if you use a template analysis is [...] that the results are consistent with a black hole merger. But in order to make the stronger statement that it really and truly is a black hole merger you have to rule out anything else that it could be.

“And the characteristic signal here is actually pretty generic. What do they find? They find something where the amplitude increases, where the frequency increases, and then everything dies down eventually. And that describes just about every catastrophic event you can imagine. You see, increasing amplitude, increasing frequency, and then it settles into some new state. So they really were obliged to rule out every terrestrial effects, including seismic effects, and the fact that there was an enormous lightning string in Burkina Faso at exactly the same time [...]”
Interviewer: “Do you think that they failed to rule out all these other possibilities?

Jackson: “Yes…”
If it was correct what Jackson said, this would be highly problematic indeed. But I have not been able to think of any other event that looks remotely like a gravitational wave signal, even leaving aside the detector correlations. Unlike what Jackson states, a typical catastrophic event does not have a frequency increase followed by a ring-down and sudden near-silence.

Think of an earthquake for example. For the most part, earthquakes happen when stresses exceed a critical threshold. The signal don’t have a frequency build-up, and after the quake, there’s a lot of rumbling, often followed by smaller quakes. Just look at the below figure that shows the surface movement of a typical seismic event.
Example of typical earthquake signal. [Image Source]

It looks nothing like that of a gravitational wave signal.

For this reason, I don’t share Jackson’s doubts over the origin of the signals that LIGO detects. However, the question whether there are any events of terrestrial origin with similar frequency characteristics arguably requires consideration beyond Sabine scratching her head for half an hour.

So, even though I do not have the same concerns as were raised by the LIGO critics, I must say that I do find it peculiar indeed there is so little discussion about this issue. A Nobel Prize was handed out, and yet we still do not have confirmation that LIGO’s signals are not of terrestrial origin. In which other discipline is it considered good scientific practice to discard unwelcome yet not understood data, like LIGO does with the glitches? Why do we still not know just exactly what was shown in the figure of the first paper? Where are the electromagnetic counterparts?

LIGO’s third observing run will continue until March 2020. It presently doesn’t look like it will bring the awaited clarity. I certainly hope that the collaboration will make somewhat more efforts to erase the doubts that still linger around their supposed detections.

Wednesday, August 28, 2019

Solutions to the black hole information paradox

In the early 1970s, Stephen Hawking discovered that black holes can emit radiation. This radiation allows black holes to lose mass and, eventually, to entirely evaporate. This process seems to destroy all the information that is contained in the black hole and therefore contradicts what we know about the laws of nature. This contradiction is what we call the black hole information paradox.

After discovering this problem 40 years ago, Hawking spent the rest of his life trying to solve it. He passed away last year, but the problem is still alive and there is no resolution in sight.

Today, I want to tell you what solutions physicists have so-far proposed for the black hole information loss problem. If you want to know more about just what exactly is the problem, please read my previous blogpost.

There are hundreds of proposed solutions to the information loss problem, that I can’t possibly all list here. But I want to tell you about the five most plausible ones.

1. Remnants.

The calculation that Hawking did to obtain the properties of the black hole radiation makes use of general relativity. But we know that general relativity is only approximately correct. It eventually has to be replaced by a more fundamental theory, which is quantum gravity. The effects of quantum gravity are not relevant near the horizon of large black holes, which is why the approximation that Hawking made is good. But it breaks down eventually, when the black hole has shrunk to a very small size. Then, the space-time curvature at the horizon becomes very strong and quantum gravity must be taken into account.

Now, if quantum gravity becomes important, we really do not know what will happen because we don’t have a theory for quantum gravity. In particular we have no reason to think that the black hole will entirely evaporate to begin with. This opens the possibility that a small remainder is left behind which just sits there forever. Such a black hole remnant could keep all the information about what formed the black hole, and no contradiction results.

2. Information comes out very late.

Instead of just stopping to evaporate when quantum gravity becomes relevant, the black hole could also start to leak information in that final phase. Some estimates indicate that this leakage would take a very long time, which is why this solution is also known as a “quasi-stable remnant”. However, it is not entirely clear just how long it would take. After all, we don’t have a theory of quantum gravity. This second option removes the contradiction for the same reason as the first.

3. Information comes out early.

The first two scenarios are very conservative in that they postulate new effects will appear only when we know that our theories break down. A more speculative idea is that quantum gravity plays a much larger role near the horizon and the radiation carries information all along, it’s just that Hawking’s calculation doesn’t capture it.

Many physicists prefer this solution over the first two for the following reason. Black holes do not only have a temperature, they also have an entropy, called the Bekenstein-Hawking entropy. This entropy is proportional to the area of the black hole. It is often interpreted as counting the number of possible states that the black hole geometry can have in a theory of quantum gravity.

If that is so, then the entropy must shrink when the black hole shrinks and this is not the case for the remnant and the quasi-stable remnant.

So, if you want to interpret the black hole entropy in terms of microscopic states, then the information must begin to come out early, when the black hole is still large. This solution is supported by the idea that we live in a holographic universe, which is currently popular, especially among string theorists.

4. Information is just lost.

Black hole evaporation, it seems, is irreversible and that irreversibility is inconsistent with the dynamical law of quantum theory. But quantum theory does have its own irreversible process, which is the measurement. So, some physicists argue that we should just accept black hole evaporation is irreversible and destroys information, not unlike quantum measurements do. This option is not particularly popular because it is hard to include additional irreversible process into quantum theory without spoiling conservation laws.

5. Black holes don’t exist.

Finally, some physicists have tried to argue that black holes are never created in the first place in which case no information can get lost in them. To make this work, one has to find a way to prevent a distribution of matter from collapsing to a size that is below its Schwarzschild radius. But since the formation of a black hole horizon can happen at arbitrarily small matter densities, this requires that one invents some new physics which violates the equivalence principle, and that is the key principle underlying Einstein’s theory of general relativity. This option is a logical possibility, but for most physicists, it’s asking for too much.

Personally, I think that several of the proposed solutions are consistent, that includes option 1-3 above, and other proposals such as those by Horowitz and Maldacena, ‘t Hooft, or Maudlin. This means that this is a problem which just cannot be solved by relying on mathematics alone.

Unfortunately, we cannot experimentally test what is happening when black holes evaporate because the temperature of the radiation is much, much too small to be measurable for the astrophysical black holes we know of. And so, I suspect we will be arguing about this for a long, long time.

Friday, August 23, 2019

How do black holes destroy information and why is that a problem?

Today I want to pick up a question that many of you asked, which is how do black holes destroy information and why is that a problem?

I will not explain here what a black hole is or how we that know black holes exist, for this you can watch my earlier video. Let me instead get right to black hole information loss. To understand the problem, you first need to know the mathematics that we use for our theories in physics. These theories all have two ingredients.

First, there is something called the “state” of the system, that’s a complete description of whatever you want to make a prediction for. In a classical theory, that’s one which is not quantized, the state would be, for example, the positions and velocities of particles. To describe the state in a quantum theory, you would instead take the wave-functions.

The second ingredient to the current theories is a dynamical law, which is also often called an “evolution equation”. This has nothing to do with Darwinian evolution. Evolution here just means this is an equation which tells you how the state changes from one moment of time to the next. So, if I give you a state at any one time, you can use the evolution equation to compute the state at any other time.

The important thing is that all evolution equations that we know of are time-reversible. This means it never happens that two states that differ at an initial time will become identical states at a later time. If that was so, then at the later time, you wouldn’t know where you started from and that would not be reversible.

A confusion that I frequently encounter is that between time-reversibility and time-reversal invariance. These are not the same. Time reversible just means you can run a process backwards. Time reversal invariance on the other hand means, it will look the same if you run it backwards. In the following, I am talking about time-reversibility, not time-reversal invariance.

Now, all fundamental evolution equations in physics are time-reversible. But this time-reversibility is in many cases entirely theoretical because of entropy increase. If the entropy of a system increases, this means that it if you wanted to reverse the time-evolution you would have to arrange the initial state very, very precisely, more precisely than is humanly possible. Therefore, many processes which are time-reversible in principle are for all practical purposes irreversible.

Think of mixing dough. You’ll never be able to unmix it in practice. But if only you could arrange precisely enough the position of each single atom, you could very well unmix the dough. The same goes for burning a piece of paper. Irreversible in practice. But in principle, if you only knew precisely enough the details of the smoke and the ashes, you could reverse it.

The evolution equation of quantum mechanics is called the Schroedinger equation and it is just as time-reversible as the evolution equation of classical physics. Quantum mechanics, however, has an additional equation which describes the measurement process, and this equation is not time-reversible. The reason it’s not time-reversible is that you can have different states that, when measured, give you the same measurement outcome. So, if you only know the outcome of the measurement, you cannot tell what was the original state.

Let us come to black holes then. The defining property of a black hole is the horizon, which is a one-way surface. You can only get in, but never get out of a black hole. The horizon does not have substance, it’s really just the name for a location in space. Other than that it’s vacuum.

But quantum theory tells us that vacuum is not nothing. It is full of particle-antiparticle pairs that are constantly created and destroyed. And in general relativity, the notion of a particle itself depends on the observer, much like the passage of time does. For this reason, what looks like vacuum close by the horizon does not look like vacuum far away from the horizon. Which is just another way of saying that black holes emit radiation.

This effect was first derived by Stephen Hawking in the 1970s and the radiation is therefore called Hawking radiation. It’s really important to keep in mind that you get this result by using just the normal quantum theory of matter in the curved space-time of a black hole. You do not need a theory of quantum gravity to derive that black holes radiate.

For our purposes, the relevant property of the radiation is that it is completely thermal. It is entirely determined by the total mass, charge, and spin of the black hole. Besides that, it’s random.

Now, what happens when the black hole radiates is that it loses mass and shrinks. It shrinks until it’s entirely gone and the radiation is the only thing that is left. But if you only have the radiation, then all you know is the mass, change, and spin of the black hole. You have no idea what formed the black hole originally or what fell in later. Therefore, black hole evaporation is irreversible because many different initial states will result in the same final state. And this is before you have even made a measurement on the radiation.

Such an irreversible process does not fit together with any of the known evolution laws – and that’s the problem. If you combine gravity with quantum theory, it seems, you get a result that’s inconsistent with quantum theory.

As you have probably noticed, I didn’t say anything about information. That’s because really the reference to information in “black hole information loss” is entirely unnecessary and just causes confusion. The problem of black hole “information loss” really has nothing to do with just exactly what you mean by information. It’s just a term that loosely speaking says you can’t tell from the final state what was the exact initial state.

There have been many, many attempts to solve this problem. Literally thousands of papers have been written about this. I will tell you about the most promising solutions some other time, so stay tuned.

Thursday, August 22, 2019

You will probably not understand this

Hieroglyps. [Image: Wikipedia Commons.]

Two years ago, I gave a talk at the University of Toronto, at the institute for the history and philosophy of science. At the time, I didn’t think much about it. But in hindsight, it changed my life, at least my work-life.

I spoke about the topic of my first book. It’s a talk I have given dozens of times, and though I adapted my slides for the Toronto audience, there was nothing remarkable about it. The oddity was the format of the talk. I would speak for half an hour. After this, someone else would summarize the topic for 15 minutes. Then there would be 15 minutes discussion.

Fine, I said, sounds like fun.

A few weeks before my visit, I was contacted by a postdoc who said he’d be doing the summary. He asked for my slides, and further reading material, and if there was anything else he should know. I sent him references.

But when his turn came to speak, he did not, as I expected, summarize the argument I had delivered. Instead he reported what he had dug up about my philosophy of science, my attitude towards metaphysics, realism, and what I might mean with “explanation” or “theory” and other philosophically loaded words.

He got it largely right, though I cannot today recall the details. I only recall I didn’t have much to say about what struck me as a peculiar exercise, dedicated not to understanding my research, but to understanding me.

It was awkward, too, because I have always disliked philosophers’ dissection of scientists’ lives. Their obsessive analyses of who Schrödinger, Einstein, or Bohr talked to when, about what, in which period of what marriage, never made a lot of sense to me. It reeked too much of hero-worship, looked too much like post-mortem psychoanalysis, equally helpful to understand Einstein’s work as cutting his brain into slices.

In the months that followed the Toronto talk, though, I began reading my own blogposts with that postdoc’s interpretation in mind. And I realized that in many cases it was essential information to understand what I was trying to get across. In the past year, I have therefore made more effort to repeat background, or at least link to previous pieces, to provide that necessary context. Context which – of course! – I thought is obvious. Because certainly we all agree what a theory is. Right?

But having written a public weblog for more than 12 years makes me a comparably simple subject of study. I have, over the years, provided explanations for just exactly what I mean when I say “scientific method” or “true” or “real”. So at least you could find out if only you wanted to. Not that I expect anyone who comes here for a 1,000 word essay to study an 800,000 word archive. Still, at least that archive exists. The same, however, isn’t the case for most scientists.

I was reminded of this at a recent workshop where I spoke with another woman about her attempts to make sense of one of her senior colleague’s papers.

I don’t want to name names, but it’s someone whose research you’ll be familiar with if you follow the popular science media. His papers are chronically hard to understand. And I know it isn’t just me who struggles, because I heard a lot of people in the field make dismissive comments about his work. On the occasion which the woman told me about, apparently he got frustrated with his own inability to explain himself, resulting in rather aggressive responses to her questions.

He’s not the only one frustrated. I could tell you many stories of renown physicists who told me, or wrote to me, about their struggles to get people to listen to them. Being white and male, it seems, doesn’t help. Neither do titles, honors, or award-winning popular science books.

And if you look at the ideas they are trying to get across, there’s a pattern.

These are people who have – in some cases over decades – built their own theoretical frameworks, developed personal philosophies of science, invented their own, idiosyncratic way of expressing themselves. Along the way, they have become incomprehensible for anyone else. But they didn’t notice.

Typically, they have written multiple papers circling around a key insight which they never quite manage to bring into focus. They’re constantly trying and constantly failing. And while they usually have done parts of their work with other people, the co-authors are clearly side-characters in a single-fighter story.

So they have their potentially brilliant insights out there, for anyone to see. And yet, no one has the patience to look at their life’s work. No one makes an effort to decipher their code. In brief, no one understands them.

Of course they’re frustrated. Just as frustrated as I am that no one understands me. Not even the people who agree with me. Especially not those, actually. It’s so frustrating.

The issue, I think, is symptomatic of our times, not only in science, but in society at large. Look at any social media site. You will see people going to great lengths explaining themselves just to end up frustrated and – not seldom – aggressive. They are aggressive because no one listens to what they are trying so hard to say. Indeed, all too often, no one even tries. Why bother if misunderstanding is such an easy win? If you cannot explain yourself, that’s your fault. If you do not understand me, that’s also your fault.

And so, what I took away from my Toronto talk is that communication is much more difficult than we usually acknowledge. It takes a lot of patience, both from the sender and the receiver, to accurately decode a message. You need all that context to make sense of someone else’s ideas. I now see why philosophers spend so much time dissecting the lives of other people. And instead of talking so much, I have come to think, I should listen a little more. Who knows, I might finally understand something.

Saturday, August 17, 2019

How we know that Einstein's General Relativity cannot be quite right

Today I want to explain how we know that the way Einstein thought about gravity cannot be correct.

Einstein’s idea was that gravity is not a force, but it is really an effect caused by the curvature of space and time. Matter curves space-time in its vicinity, and this curvature in return affects how matter moves. This means that, according to Einstein, space and time are responsive. They deform in the presence of matter and not only matter, but really all types of energies, including pressure and momentum flux and so on.

Einstein called his theory “General Relativity” because it’s a generalization of Special Relativity. Both are based on “observer-independence”, that is the idea that the laws of nature should not depend on the motion of an observer. The difference between General Relativity and Special Relativity is that in Special Relativity space-time is flat, like a sheet of paper, while in General Relativity it can be curved, like the often-named rubber sheet.

General Relativity is an extremely well-confirmed theory. It predicts that light rays bend around massive objects, like the sun, which we have observed. The same effect also gives rise to gravitational lensing, which we have also observed. General Relativity further predicts that the universe should expand, which it does. It predicts that time runs more slowly in gravitational potentials, which is correct. General Relativity predicts black holes, and it predicts just how the black hole shadow looks, which is what we have observed. It also predicts gravitational waves, which we have observed. And the list goes on.

So, there is no doubt that General Relativity works extremely well. But we already know that it cannot ultimately be the correct theory for space and time. It is an approximation that works in many circumstances, but fails in others.

We know this because General Relativity does not fit together with another extremely well confirmed theory, that is quantum mechanics. It’s one of these problems that’s easy to explain but extremely difficult to solve.

Here is what goes wrong if you want to combine gravity and quantum mechanics. We know experimentally that particles have some strange quantum properties. They obey the uncertainty principle and they can do things like being in two places at once. Concretely, think about an electron going through a double slit. Quantum mechanics tells us that the particle goes through both slits.

Now, electrons have a mass and masses generate a gravitational pull by bending space-time. This brings up the question, to which place does the gravitational pull go if the electron travels through both slits at the same time. You would expect the gravitational pull to also go to two places at the same time. But this cannot be the case in general relativity, because general relativity is not a quantum theory.

To solve this problem, we have to understand the quantum properties of gravity. We need what physicists call a theory of quantum gravity. And since Einstein taught us that gravity is really about the curvature of space and time, what we need is a theory for the quantum properties of space and time.

There are two other reasons how we know that General Relativity can’t be quite right. Besides the double-slit problem, there is the issue with singularities in General Relativity. Singularities are places where both the curvature and the energy-density of matter become infinitely large; at least that’s what General Relativity predicts. This happens for example inside of black holes and at the beginning of the universe.

In any other theory that we have, singularities are a sign that the theory breaks down and has to be replaced by a more fundamental theory. And we think the same has to be the case in General Relativity, where the more fundamental theory to replace it is quantum gravity.

The third reason we think gravity must be quantized is the trouble with information loss in black holes. If we combine quantum theory with general relativity but without quantizing gravity, then we find that black holes slowly shrink by emitting radiation. This was first derived by Stephen Hawking in the 1970s and so this black hole radiation is also called Hawking radiation.

Now, it seems that black holes can entirely vanish by emitting this radiation. Problem is, the radiation itself is entirely random and does not carry any information. So when a black hole is entirely gone and all you have left is the radiation, you do not know what formed the black hole. Such a process is fundamentally irreversible and therefore incompatible with quantum theory. It just does not fit together. A lot of physicists think that to solve this problem we need a theory of quantum gravity.

So this is how we know that General Relativity must be replaced by a theory of quantum gravity. This problem has been known since the 1930s. Since then, there have been many attempts to solve the problem. I will tell you about this some other time, so don’t forget to subscribe.

Tuesday, August 13, 2019

The Problem with Quantum Measurements

Have you heard that particle physicists want a larger collider because there is supposedly something funny about the Higgs boson? They call it the “Hierarchy Problem,” that there are 15 orders of magnitude between the Planck mass, which determines the strength of gravity, and the mass of the Higgs boson.

What is problematic about this, you ask? Nothing. Why do particle physicists think it’s problematic? Because they have been told as students it’s problematic. So now they want $20 billion to solve a problem that doesn’t exist.

Let us then look at an actual problem, that is that we don’t know how a measurement happens in quantum mechanics. The discussion of this problem today happens largely among philosophers; physicists pay pretty much no attention to it. Why not, you ask? Because they have been told as students that the problem doesn’t exist.

But there is a light at the end of the tunnel and the light is… you. Yes, you. Because I know that you are just the right person to both understand and solve the measurement problem. So let’s get you started.

Quantum mechanics is today mostly taught in what is known as the Copenhagen Interpretation and it works as follows. Particles are described by a mathematical object called the “wave-function,” usually denoted Ψ (“Psi”). The wave-function is sometimes sharply peaked and looks much like a particle, sometimes it’s spread out and looks more like a wave. Ψ is basically the embodiment of particle-wave duality.

The wave-function moves according to the Schrödinger equation. This equation is compatible with Einstein’s Special Relativity and it can be run both forward and backward in time. If I give you complete information about a system at any one time – ie, if I tell you the “state” of the system – you can use the Schrödinger equation to calculate the state at all earlier and all later times. This makes the Schrödinger equation what we call a “deterministic” equation.

But the Schrödinger equation alone does not predict what we observe. If you use only the Schrödinger equation to calculate what happens when a particle interacts with a detector, you find that the two undergo a process called “decoherence.” Decoherence wipes out quantum-typical behavior, like dead-and-alive cats and such. What you have left then is a probability distribution for a measurement outcome (what is known as a “mixed state”). You have, say, a 50% chance that the particle hits the left side of the screen. And this, importantly, is not a prediction for a collection of particles or repeated measurements. We are talking about one measurement on one particle.

The moment you measure the particle, however, you know with 100% probability what you have got; in our example you now know which side of the screen the particle is. This sudden jump of the probability is often referred to as the “collapse” of the wave-function and the Schrödinger equation does not predict it. The Copenhagen Interpretation, therefore, requires an additional assumption called the “Measurement Postulate.” The Measurement Postulate tells you that the probability of whatever you have measured must be updated to 100%.

Now, the collapse together with the Schrödinger equation describes what we observe. But the detector is of course also made of particles and therefore itself obeys the Schrödinger equation. So if quantum mechanics is fundamental, we should be able to calculate what happens during measurement using the Schrödinger equation alone. We should not need a second postulate.

The measurement problem, then, is that the collapse of the wave-function is incompatible with the Schrödinger equation. It isn’t merely that we do not know how to derive it from the Schrödinger equation, it’s that it actually contradicts the Schrödinger equation. The easiest way to see this is to note that the Schrödinger equation is linear while the measurement process is non-linear. This strongly suggests that the measurement is an effective description of some underlying non-linear process, something we haven’t yet figured out.

There is another problem. As an instantaneous process, wave-function collapse doesn’t fit together with the speed of light limit in Special Relativity. This is the “spooky action” that irked Einstein so much about quantum mechanics.

This incompatibility with Special Relativity, however, has (by assumption) no observable consequences, so you can try and convince yourself it’s philosophically permissible (and good luck with that). But the problem comes back to haunt you when you ask what happens with the mass (and energy) of a particle when its wave-function collapses. You’ll notice then that the instantaneous jump screws up General Relativity. (And for this quantum gravitational effects shouldn’t play a role, so mumbling “string theory” doesn’t help.) This issue is still unobservable in practice, all right, but now it’s observable in principle.

One way to deal with the measurement problem is to argue that the wave-function does not describe a real object, but only encodes knowledge, and that probabilities should not be interpreted as frequencies of occurrence, but instead as statements of our confidence. This is what’s known as a “Psi-epistemic” interpretation of quantum mechanics, as opposed to the “Psi-ontic” ones in which the wave-function is a real thing.

The trouble with Psi-epistemic interpretations is that the moment you refer to something like “knowledge” you have to tell me what you mean by “knowledge”, who or what has this “knowledge,” and how they obtain “knowledge.” Personally, I would also really like to know what this knowledge is supposedly about, but if you insist I’ll keep my mouth shut. Even so, for all we presently know, “knowledge” is not fundamental, but emergent. Referring to knowledge in the postulates of your theory, therefore, is incompatible with reductionism. This means if you like Psi-epistemic interpretations, you will have to tell me just why and when reductionism breaks down or, alternatively, tell me how to derive Psi from a more fundamental law.

None of the existing interpretations and modifications of quantum mechanics really solve the problem, which I can go through in detail some other time. For now let me just say that either way you turn the pieces, they won’t fit together.

So, forget about particle colliders; grab a pen and get started.


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Saturday, August 10, 2019

Book Review: “The Secret Life of Science” by Jeremy Baumberg

The Secret Life of Science: How It Really Works and Why It Matters
Jeremy Baumberg
Princeton University Press (16 Mar. 2018)

The most remarkable thing about science is that most scientists have no idea how it works. With his 2018 book “The Secret Life of Science,” Jeremy Baumberg aims to change this.

The book is thoroughly researched and well-organized. In the first chapter, Baumberg starts with explaining what science is. He goes about this pragmatically and without getting lost in irrelevant philosophical discussions. In this chapter, he also introduces the terms “simplifier science” and “constructor science” to replace “basic” and “applied” research.

Baumberg suggests to think of science as an ecosystem with multiple species and flows of nutrients that need to be balanced, which is an analogy that he comes back to throughout the book. This first chapter is followed by a brief chapter about the motivations to do science and its societal relevance.

In the next chapters, Baumberg then focuses on various aspects of a scientist’s work-life and explains how these are organized in praxis: Scientific publishing, information sharing in the community (conferences and so on), science communication (PR, science journalism), funding, and hiring. In this, Baumberg make an effort to distinguish between research in academia and in business, and in many cases he also points out national differences.

The book finishes with a chapter about the future of science and Baumberg’s own suggestions for improvement. Except for the very last chapter, the author does not draw attention to existing problems with the current organization of science, though these will be obvious to most readers.

Baumberg is a physicist by training and, according to the book flap, works in nanotechnology and photonics. As most physicists who do not work in particle physics, he is well aware that particle physics is in deep trouble. He writes:
Knowing the mind of god” and “The theory of everything” are brands currently attached to particle physics. Yet they have become less powerful with time, attracting an air of liability, perhaps reaching that of a “toxic brand.” That the science involved now finds it hard to shake off precisely this layer of values attached to them shows how sticky they are.
The book contains a lot of concrete information for example about salaries and grant success rates. I have generally found Baumberg’s analysis to be spot on, for example when he writes “Science spending seems to rise until it becomes noticed and then stops.” Or
Because this competition [for research grants] is so well defined as a clear race for money it can become the raison d’etre for scientists’ existence, rather than just what is needed to develop resources to actually do science.
On counting citations, he likewise remarks aptly:
“[The h-index rewards] wide collaborators rather than lone specialists, rewards fields that cite more, and rewards those who always stay at the trendy edge of all research.”
Unfortunately I have to add that the book is not particularly engagingly written. Some of the chapters could have been shorter, Baumberg overuses the metaphor of the ecosystem, and the figures are not helpful. To give you an idea why I say this, I challenge you to make sense of this illustration:

In summary, Baumberg’s is a useful book though it’s somewhat tedious to read. Nevertheless, I think everyone who wants to understand how science works in reality should read it. It’s time we get over the idea that science somehow magically self-corrects. Science is the way we organize knowledge discovery, and its success depends on us paying attention to how it is organized.

Wednesday, August 07, 2019

10 differences between artificial intelligence and human intelligence

Today I want to tell you what is artificial about artificial intelligence. There is, of course, the obvious, which is that the brain is warm, wet, and wiggly, while a computer is not. But more importantly, there are structural differences between human and artificial intelligence, which I will get to in a moment.

Before we can talk about this though, I have to briefly tell you what “artificial intelligence” refers to.

What goes as “artificial intelligence” today are neural networks. A neural network is a computer algorithm that imitates certain functions of the human brain. It contains virtual “neurons” that are arranged in “layers” which are connected with each other. The neurons pass on information and thereby perform calculations, much like neurons in the human brain pass on information and thereby perform calculations.

In the neural net, the neurons are just numbers in the code, typically they have values between 0 and 1. The connections between the neurons also have numbers associated with them, and those are called “weights”. These weights tell you how much the information from one layer matters for the next layer.

The values of the neurons and the weights of the connections are essentially the free parameters of the network. And by training the network you want to find those values of the parameters that minimize a certain function, called the “loss function”.

So it’s really an optimization problem that neural nets solve. In this optimization, the magic of neural nets happens through what is known as backpropagation. This means if the net gives you a result that is not particularly good, you go back and change the weights of the neurons and their connections. This is how the net can “learn” from failure. Again, this plasticity mimics that of the human brain.

For a great introduction to neural nets, I can recommend this 20 minutes video by 3Blue1Brown.

Having said this, here are the key differences between artificial and real intelligence.

1. Form and Function

A neural net is software running on a computer. The “neurons” of an artificial intelligence are not physical. They are encoded in bits and strings on hard disks or silicon chips and their physical structure looks nothing like that of actual neurons. In the human brain, in contrast, form and function go together.

2. Size

The human brain has about 100 billion neurons. Current neural nets typically have a few hundred or so.

3. Connectivity

In a neural net each layer is usually fully connected to the previous and next layer. But the brain doesn’t really have layers. It instead relies on a lot of pre-defined structure. Not all regions of the human brain are equally connected and the regions are specialized for certain purposes.

4. Power Consumption

The human brain is dramatically more energy-efficient than any existing artificial intelligence. The brain uses around 20 Watts, which is comparable to what a standard laptop uses today. But with that power the brain handles a million times more neurons.

5. Architecture

In a neural network, the layers are neatly ordered and are addressed one after the other. The human brain, on the other hand, does a lot of parallel processing and not in any particular order.

6. Activation Potential

In the real brain neurons either fire or don’t. In a neural network the firing is mimicked by continuous values instead, so the artificial neurons can smoothly slide from off to on, which real neurons can’t.

7. Speed

The human brain is much, much slower than any artificially intelligent system. A standard computer performs some 10 billion operations per second. Real neurons, on the other hand, fire at a frequency of at most a thousand times per second.

8. Learning Technique

Neural networks learn by producing output, and if this output is of low performance according to the loss function, then the net responds by changing the weights of the neurons and their connections. No one knows in detail how humans learn, but that’s not how it works.

9. Structure

A neural net starts from scratch every time. The human brain, on the other hand, has a lot of structure already wired into its connectivity, and it draws on models which have proved useful during evolution.

10. Precision

The human brain is much more noisy and less precise than a neural net running on a computer. This means the brain basically cannot run the same learning mechanism as a neural net and it’s probably using an entirely different mechanism.

A consequence of these differences is that artificial intelligence today needs a lot of training with a lot of carefully prepared data, which is very unlike to how human intelligence works. Neural nets do not build models of the world, instead they learn to classify patterns, and this pattern recognition can fail with only small changes. A famous example is that you can add small amounts of noise to an image, so small amounts that your eyes will not see a difference, but an artificially intelligent system might be fooled into thinking a turtle is a rifle.

Neural networks are also presently not good at generalizing what they have learned from one situation to the next, and their success very strongly depends on defining just the correct “loss function”. If you don’t think about that loss function carefully enough, you will end up optimizing something you didn’t want. Like this simulated self-driving car trained to move at constant high speed, which learned to rapidly spin in a circle.

But neural networks excel at some things, such as classifying images or extrapolating data that doesn’t have any well-understood trend. And maybe the point of artificial intelligence is not to make it all that similar to natural intelligence. After all, the most useful machines we have, like cars or planes, are useful exactly because they do not mimic nature. Instead, we may want to build machines specialized in tasks we are not good at.

Tuesday, August 06, 2019

Special Breakthrough Prize awarded for Supergravity

Breakthrough Prize Trophy.
[Image: Breakthrough Prize]
The Breakthrough Prize is an initiative founded by billionaire Yuri Milner, now funded by a group of rich people which includes, next to Milner himself, Sergey Brin, Anne Wojcicki, and Mark Zuckerberg. The Prize is awarded in three different categories, Mathematics, Fundamental Physics, and Life Sciences. Today, a Special Breakthrough Prize in Fundamental Physics has been awarded to Sergio Ferrara, Dan Freedman, and Peter van Nieuwenhuizen for the invention of supergravity in 1976. The Prize of 3 million US$ will be split among the winners.

Interest in supergravity arose in the 1970s when physicists began to search for a theory of everything that would combine all four known fundamental forces to one. By then, string theory had been shown to require supersymmetry, a hypothetical new symmetry which implies that all the already known particles have – so far undiscovered – partner particles. Supersymmetry, however, initially only worked for the three non-gravitational forces, that is the electromagnetic force and the strong and weak nuclear forces. With supergravity, gravity could be included too, thereby bringing physicists one step closer to their goal of unifying all the interactions.

In supergravity, the gravitational interaction is associated with a messenger particle – the graviton – and this graviton has a supersymmetric partner particle called the “gravitino”. There are several types of supergravitational theories, because there are different ways of realizing the symmetry. Supergravity in the context of string theory always requires additional dimensions of space, which have not been seen. The gravitational theory one obtains this way is also not the same as Einstein’s General Relativity, because one gets additional fields that can be difficult to bring into agreement with observation. (For more about the problems with string theory, please watch my video.)

To date, we have no evidence that supergravity is a correct description of nature. Supergravity may one day become useful to calculate properties of certain materials, but so far this research direction has not led to much.

The works by Ferrera, Freedman, and van Nieuwenhuizen have arguably been influential, if by influential you mean that papers have been written about it. Supergravity and supersymmetry are mathematically very fertile ideas. They lend themselves to calculations that otherwise would not be possible and that is how, in the past four decades, physicists have successfully built a beautiful, supersymmetric, math-castle on nothing but thin air.

Awarding a scientific prize, especially one accompanied by so much publicity, for an idea that has no evidence speaking for it, sends the message that in the foundations of physics contact to observation is no longer relevant. If you want to be successful in my research area, it seems, what matters is that a large number of people follow your footsteps, not that your work is useful to explain natural phenomena. This Special Prize doesn’t only signal to the public that the foundations of physics are no longer part of science, it also discourages people in the field from taking on the hard questions. Congratulations.

Update Aug 7th: Corrected the first paragraph. The earlier version incorrectly stated that each of the recipients gets $3 million.

Thursday, August 01, 2019

Automated Discovery

[Image: BuySellGraphic.com]

In 1986, Dan Swanson from the University of Chicago discovered a discovery.

Swanson (who passed away in 2012) was an information scientist and a pioneer in literature analysis. In the 1980s, he studied the distribution of references in scientific papers and found that, on occasion, studies on two separate research topics would have few references between them, but would refer to a common, third, set of papers. He conjectured that might indicate so-far unknown links between the separate research topics.

Indeed, Swanson found a concrete example for such a link. Already in the 1980s, scientists knew that certain types of fish oils benefit blood composition and blood vessels. So there was one body of literature linking circulatory health to fish oil. They had also found, in another line of research, that patients with Raynaud’s disease do better if their circulatory health improves. This led Swanson to conjecture that patients with Raynaud’s disease could benefit from fish oil. In 1993, a clinical trial demonstrated that this hypothesis was correct.

You may find this rather obvious. I would agree it’s not a groundbreaking insight, but this isn’t the point. The point is that the scientific community missed this obvious insight. It was right there, in front of their eyes, but no one noticed.

30 years after Swanson’s seminal paper, we have more data than ever about scientific publications. And just the other week, Nature published a new example for what you can do with it.

In the new paper, a group of researchers from California studied the materials science literature. They did not, like Swanson, look for relations between research studies by using citations, but they did a (much more computationally intensive) word-analysis of paper abstracts (not unlike the one we did in our paper). This analysis serves to identify the most relevant words associated with a manuscript, and to find relations between these words.

Previous studies have shown that words, treated as vectors in a high-dimensional space, can be added and subtracted. The most famous example is that the combination “King – Man + Woman” gives a new vector that turns out to be associated with the word “Queen”. In the new paper, the authors report finding similar examples in the materials science literature, such as “ferromagnetic −  NiFe + IrMn” which adds together to “antiferromagnetic”.

Even more remarkable though, they noticed that a number of materials whose names are close to the word “thermoelectric” were never actually mentioned together with the word “thermoelectric” in any paper’s abstract. This suggests, so the authors claim, that these materials may be thermoelectric, but so-far no one has noticed.

They have tested how well this works by making back-dated predictions for the discovery of new thermoelectric materials using only papers published until one of the years between 2001 and 2018. For each of these historical datasets, they used the relations between words in the abstracts to predict 50 thermoelectrical materials most likely to be found in the future. And it worked! In the five years after the historical data-cut, the identified materials were on average eight times more likely to be studied as thermoelectrics than were randomly chosen unstudied materials. The authors have now also made real predictions for new thermoelectric materials. We will see in the coming years how those pan out.

I think that analyses like this have lot of potential. Indeed, one of the things that keeps me up at night is the possibility that we might already have all the knowledge necessary to make progress in the foundations of physics, we just haven’t connected the dots. Smart tools to help scientists decide what papers to pay attention to could greatly aid knowledge discovery.

Sunday, July 28, 2019

The Forgotten Solution: Superdeterminism

Welcome to the renaissance of quantum mechanics. It took more than a hundred years, but physicists finally woke up, looked quantum mechanics into the face – and realized with bewilderment they barely know the theory they’ve been married to for so long. Gone are the days of “shut up and calculate”; the foundations of quantum mechanics are en vogue again.

It is not a spontaneous acknowledgement of philosophy that sparked physicists’ rediscovered desire; their sudden search for meaning is driven by technological advances.

With quantum cryptography a reality and quantum computing on the horizon, questions once believed ephemeral are now butter and bread of the research worker. When I was a student, my prof thought it questionable that violations of Bell’s inequality would ever be demonstrated convincingly. Today you can take that as given. We have also seen delayed-choice experiments, marveled over quantum teleportation, witnessed decoherence in action, tracked individual quantum jumps, and cheered when Zeilinger entangled photons over hundreds of kilometers of distance. Well, some of us, anyway.

But while physicists know how to use the mathematics of quantum mechanics to make stunningly accurate predictions, just what this math is about has remained unclear. This is why physicists currently have several “interpretations” of quantum mechanics.

I find the term “interpretations” somewhat unfortunate. That’s because some ideas that go as “interpretation” are really theories which differ from quantum mechanics, and these differences may one day become observable. Collapse models, for example, explicitly add a process for wave-function collapse to quantum measurement. Pilot wave theories, likewise, can result in deviations from quantum mechanics in certain circumstances, though those have not been observed. At least not yet.

A phenomenologist myself, I am agnostic about different interpretations of what is indeed the same math, such as QBism vs Copenhagen or the Many Worlds. But I agree with the philosopher Tim Maudlin that the measurement problem in quantum mechanics is a real problem – a problem of inconsistency – and requires a solution.

And how to solve it? Collapse models solve the measurement problem, but they are hard to combine with quantum field theory which for me is a deal-breaker. Pilot wave theories also solve it, but they are non-local, which makes my hair stand up for much the same reason. This is why I think all these approaches are on the wrong track and instead side with superdeterminism.

But before I tell you what’s super about superdeterminism, I have to briefly explain the all-important theorem from John Stewart Bell. It says, in a nutshell, that correlations between certain observables are bounded in every theory which fulfills certain assumptions. These assumptions are what you would expect of a deterministic, non-quantum theory – statistical locality and statistical independence (together often referred to as “Bell locality”) – and should, most importantly, be fulfilled by any classical theory that attempts to explain quantum behavior by adding “hidden variables” to particles.

Experiments show that the bound of Bell’s theorem can be violated. This means the correct theory must violate at least one of the theorem’s assumptions. Quantum mechanics is indeterministic and violates statistical locality. (Which, I should warn you has little to do with what particle physicists usually mean by “locality.”) A deterministic theory that doesn’t fulfill the other assumption, that of statistical independence, is called superdeterministic. Note that this leaves open whether or not a superdeterministic theory is statistically local.

Unfortunately, superdeterminism has a bad reputation, so bad that most students never get to hear of it. If mentioned at all, it is commonly dismissed as a “conspiracy theory.” Several philosophers have declared superdeterminism means abandoning scientific methodology entirely. To see where this objection comes from – and why it’s wrong – we have to unwrap this idea of statistical independence.

Statistical independence enters Bell’s theorem in two ways. One is that the detectors’ settings are independent of each other, the other one that the settings are independent of the state you want to measure. If you don’t have statistical independence, you are sacrificing the experimentalist’s freedom to choose what to measure. And if you do that, you can come up with deterministic hidden variable explanations that result in the same measurement outcomes as quantum mechanics.

I find superdeterminism interesting because the most obvious class of hidden variables are the degrees of freedom of the detector. And the detector isn’t statistically independent of itself, so any such theory necessarily violates statistical independence. It is also, in a trivial sense, non-linear just because if the detector depends on a superposition of prepared states that’s not the same as superposing two measurements. Since any solution of the measurement problem requires a non-linear time evolution, that seems a good opportunity to make progress.

Now, a lot of people discard superdeterminism simply because they prefer to believe in free will, which is where I think the biggest resistance to superdeterminism comes from. Bad enough that belief isn’t a scientific reason, but worse that this is misunderstanding just what is going on. It’s not like superdeterminism somehow prevents an experimentalist from turning a knob. Rather, it’s that the detectors’ states aren’t independent of the system one tries to measure. There just isn’t any state the experimentalist could twiddle their knob to which would prevent a correlation.

Where do these correlations ultimately come from? Well, they come from where everything ultimately comes from, that is from the initial state of the universe. And that’s where most people walk off: They think that you need to precisely choose the initial conditions of the universe to arrange quanta in Anton Zeilinger’s brain just so that he’ll end up turning a knob left rather than right. Besides sounding entirely nuts, it’s also a useless idea, because how the hell would you ever calculate anything with it? And if it’s unfalsifiable but useless, then indeed it isn’t science. So, frowning at superdeterminism is not entirely unjustified.

But that would be jumping to conclusions. How much detail you need to know about the initial state to make predictions depends on your model. And without writing down a model, there is really no way to tell whether it does or doesn’t live up to scientific methodology. It’s here where the trouble begins.

While philosophers on occasion discuss superdeterminism on a conceptual basis, there is little to no work on actual models. Besides me and my postdoc, I count Gerard ‘t Hooft and Tim Palmer. The former gentleman, however, seems to dislike quantum mechanics and would rather have a classical hidden variables theory, and the latter wants to discretize state space. I don’t see the point in either. I’ll be happy if the result solves the measurement problem and is still local the same way that quantum field theories are local, ie as non-local as quantum mechanics always is.*

The stakes are high, for if quantum mechanics is not a fundamental theory, but can be derived from an underlying deterministic theory, this opens the door to new applications. That’s why I remain perplexed that what I think is the obvious route to progress is one most physicists have never even heard of. Maybe it’s just a reality they don’t want to wake up to.

Recommended reading:
  • The significance of measurement independence for Bell inequalities and locality
    Michael J. W. Hall
  • Bell's Theorem: Two Neglected Solutions
    Louis Vervoort
    FoP, 3,769–791 (2013), arXiv:1203.6587

* Rewrote this paragraph to better summarize Palmer’s approach.

Wednesday, July 24, 2019

Science Shrugs

Boris Johnson
The Michelson-Morley experiment of 1887 disproved the ether, a hypothetical medium that permeates the universe. By using an interferometer with perpendicular arms, Michelson and Morley demonstrated that the speed of light is the same regardless of how the direction of the light is oriented relative to our motion through the supposed ether. Their null result set the stage for Einstein’s theory of Special Relativity and is often lauded for heralding the new age of physics. At least that’s how the story goes. In reality, it was more complicated.

Thing is, Morley himself was not convinced of the results of his seminal experiment. Together with a new collaborator, Dayton Miller, he repeated the measurement a few years later. The two again got a negative result.

This seems to have settled the case for Morley, but Miller went on to build larger interferometers to achieve better precision.

Indeed, in the 1920s, Miller reported seeing an effect consistent with Earth passing through the ether! Though the velocity which he inferred from the data didn’t match expectations he remained convinced to have measured a partial drag caused by the ether.

Miller’s detection could never be reproduced by other experiments. It is today widely considered to be wrong, but just what exactly he measured has remained unclear.

And Miller’s isn’t the only measurement mystery.

In the 1960s, Joseph Weber built the first gravitational wave detectors. At a conference in 1969, he announced that he had measured two dozen gravitational wave events, and swiftly published his results in the Physical Review Letters.

It is clear now that Weber did not measure gravitational waves – those are much harder to detect than anyone anticipated back then. So what then did he measure?

Some have argued that Weber’s equipment was faulty, his data analysis flawed, or that he simply succumbed to wishful thinking. But just what happened? We may never know.

Then, 40 years ago, physicists at the Heavy Ion Society (GSI) in Germany bombarded uranium nuclei with curium. They saw an excess emission of positrons that they couldn’t explain. In a 1983 paper, the group wrote that the observation “cannot be associated with established dynamic mechanisms of positron production” and that known physics is “unlikely match to the data at a confidence level of better than 98%”.

This observation was never reproduced. We still have no idea if this was a real effect, caused by an odd experimental setup, or whether it was a statistical fluke.

Around the same time, in 1975, we saw the first detection of a magnetic monopole. Magnetic monopoles are hypothetical quasi-particles that should have been created in the early universe if the fundamental forces were once unified. The event in case was a track left in a detector sent to the upper atmosphere with a balloon. Some have suspected that the supposed monopole track was instead caused by a nuclear decay. But really, with only one event, who can tell? In 1982, a second monopole event was reported. It remained the last.*

Today we have a similar situation with the ANITA events. ANITA is the Antarctic Impulsive Transient Antenna, and its collaboration announced last year (to much press attention) that they have measured two upward-going cosmic ray events at high energy. Trouble is, according to the currently established theories, such events shouldn’t happen.

ANITA’s two events are statistically significant, and I have no doubt they actually measured something. But it’s so little data there’s a high risk this will remain yet another oddity, eternally unresolved. Though physicists certainly try to get something out of it.

In all of these cases it’s quite possible the observations had distinct causes, just that we do not know the circumstances sufficiently well and do not have enough data to make a sober inference. Science is limited in this regard: It cannot reliably explain rare events that do not reproduce, and in these cases we are left with speculation and story-telling.

How did the world end up with Donald Trump as President of the United States and Boris Johnson as Prime Minister of the United Kingdom? In politics as in physics, some things defy explanation.

* Rewrote this paragraph after readers pointed out the second reference, see comments.

Tuesday, July 23, 2019

When they ask us [I’ve been singing again]

Prompted by last week’s conference (sorry, I meant “unconference”) which saw a lot of climate-related talks, climate modeling, geoengineering, biodiversity, and so on. Wrote this on the plane back home. Loosely inspired by this and this. Enjoy, while it lasts.

Friday, July 19, 2019

M is for Maggot, N is for Nonsense

wormy apple
[image: pinclipart.com]
Imagine you bite into an apple and find a beheaded maggot. Yuck! But it could have been worse. Had you found only half a maggot, you’d have eaten more of it. Worse still, you may have found only a quarter of a maggot, or a hundredth, or a thousandth. Indeed, if you take the limit maggot to zero, the worst possible case must be biting into an apple and not finding a maggot.

Wait, what? That doesn’t make sense. Certainly a maggot-free apple is not maximally yucky. Where did our math fail us?

It didn’t, really. The beheaded maggot is an example of a discontinuous or “singular” limit and originally due to Michael Berry*. You know you have a discontinuous limit if the function whose limit you are taking (that’s the increasing “yuck factor” of the maggot) does not approach the value of the function at the limit (unyucky).

A less fruity example is taking the y-th power of x and sending y to infinity. If x is any positive number smaller than 1, taking its exponent to infinity will give zero. If x is equal to one, all values of y will give back 1. If x is larger than one, the result of taking y to infinity will return infinity. If you plot the limit y to infinity as a function of x, it’s discontinuous.

Such singular limits are not just mathematical curiosities. We have them in physics too.

For example in thermodynamics, when we take the limit in which the number of constituents of a system becomes infinitely large, we see phase transitions where some quantities, such as the derivative of specific heat, become discontinuous. This is, of course, strictly speaking an unrealistic limit because the number of constituents may become very large, but never actually infinite. However, the limit isn’t always unrealistic.

Take the example of massive gravity. In general relativity, gravitational waves propagate with the speed of light and the particle associated with them – the graviton – is massless. You can modify general relativity so that the graviton has a mass. However, if you then let the graviton mass go to zero, you do not get back general relativity. The reason is that if the graviton mass is not zero, then it has additional polarizations and those are independent of the mass as long as the mass isn’t zero**.

The same issue appears if you have massless fields that can propagate in additional dimensions of space. This too gives rise to additional polarization which don’t necessarily disappear even if you take the size of the extra dimensions to zero.

Discontinuous limits are often a sign that you have forgotten to keep track of global, as opposed to local properties. If you for example take the radius of a sphere to infinity the curvature will go to zero, but the result is not an infinitely extended plane. For this reason, there are certain solutions in general relativity that will not approximate each other as you think they should. In a space with a negative cosmological constant, for example, black hole horizons can be infinitely extended planes. But these solutions no longer exist if the cosmological constant vanishes. In this case, black hole horizons have to be spherical.

Why am I telling you that? Because discontinuous limits should make you skeptical about any supposed insights gained into quantum gravity by using calculations in Anti de Sitter space.

Anti De Sitter (AdS) space, to remind you, is a space with a negative cosmological constant. It is popular among string theorists because they know how to make calculations in this space. Trouble is, the cosmological constant in our universe is positive. And there is no reason to think the limit of taking the cosmological constant from negative values to positive values is continuous. Indeed, it almost certainly is not because the very reason that string theorists prefer calculations in AdS is that this space provides additional structure that exists for any negative value of the cosmological constant, and suddenly vanishes if the value is zero.

String theorists usually justify working with a negative cosmological constant by arguing it can teach us something about quantum gravity in general. That may be so or it may not be so. The case with the negative cosmological constant resembles that of finding a piece of a maggot in your apple. I find it hard to swallow.

* ht Tim Palmer
** there are ways to fix this limiting behavior so that you do get back general relativity.

Wednesday, July 10, 2019

Away Note

I will be away for a week to attend SciFoo 2019. Please expect blogging to be sparse and comments to be stuck in the queue longer than usual.

Tuesday, July 09, 2019

Why the multiverse is religion, not science.

This is the 5th and last part in my series to explain why the multiverse is not a scientific hypothesis. The other parts are: 1. Does the Higgs-boson exist? 2. Do I exist? 3. Does God exist? and 4. The multiverse hypothesis.

I put together these videos because I am frustrated that scientists discard the issue unthinkingly. This is not a polemical argument and it’s not meant as an insult. But believing in the multiverse is logically equivalent to believing in god, therefore it’s religion, not science.

To see why, let me pull together what I laid out in my previous videos. Scientists say that something exists if it is useful to describe observations. By “useful” I mean it is simpler than just collecting data. You can postulate the existence of things that are not useful to describe observations, such as gods, but this is no longer science.

Universes besides our own are logically equivalent to gods. They are unobservable by assumption, hence they can exist only in a religious sense. You can believe in them if you want to, but they are not part of science.

I know that this is not a particularly remarkable argument. But physicists seem to have a hard time following it, especially those who happen to work on the multiverse. Therefore, let me sort out some common misunderstandings.

First. The major misunderstanding is that I am saying the multiverse does not exist. But this is not what I am saying. I am saying science does not tell us anything about universes we cannot observe, therefore claiming they exist is not science.

Second. They will argue the multiverse is simple. Most physicists who are in favor of the multiverse say it’s scientific because it’s simpler to assume that all universes of a certain type exist than it is to assume that only one of them exist.

That’s a questionable claim. But more importantly, it’s beside the point. The simplest assumption is no assumption. And you do not need to make any statement about the existence of the multiverse to explain our observations. Therefore, science says, you should not. As I said, it’s the same with the multiverse as with god. It’s an unnecessary assumption. Not wrong, but superfluous.

You also do not need to postulate the existence of our universe, of course. No scientist ever does that. That would be totally ridiculous.

Third. They’ll claim the existence of the multiverse is a prediction of their theory.

It’s not. That’s just wrong. Just because you can write down a theory for something, doesn’t mean it exists*. We determine that something exists, in the scientific sense, if it is useful to describe observation. That’s exactly what the multiverse is not.

Fourth. But then you are saying that discussing what’s inside a black hole is also not science

That’s equally wrong. Other universes are not science because you cannot observe them. But you can totally observe what’s inside a black hole. You just cannot come back and tell us about it. Besides, no one really thinks that the inside of a black hole will remain inaccessible forever. For these reasons, the situation is entirely different for black holes. If it was correct that the inside of black holes cannot be observed, this would indeed mean that postulating its existence is not scientific.

Fifth. But there are types of multiverses that have observable consequences.

That’s right. Physicists have come up with certain types of multiverses that can be falsified. The problem with these ideas is conceptually entirely different. It’s that there is no reason to think we live in such multiverses to begin with. The requirement that a hypothesis must be falsifiable is certainly necessary to make the hypothesis scientific, but not sufficient. I previously explained this here.

To sum it up. The multiverse is certainly an interesting idea and it attracts a lot of public attention. There is nothing wrong with that in principle. Entertainment has a value and so has thought-stimulating discussion. But do not confuse the multiverse with science, because it is not.

* Revised this sentence after two readers misunderstood the previous version.

Update: The video now has German and Italian subtitles. To see those, click on "CC" in the YouTube toolbar. Choose language under settings/gear icon.