Dear Dr. B: What are the requirements for a successful theory of quantum gravity?

“I've often heard you say that we don't have a theory of quantum gravity yet. What would be the requirements, the conditions, for quantum gravity to earn the label of 'a theory' ?

I am particularly interested in the nuances on the difference between satisfying current theories (GR&QM) and satisfying existing experimental data. Because a theory often entails an interpretation whereas a piece of experimental evidence or observation can be regarded as correct 'an sich'.

That aside from satisfying the need for new predictions, etc.

Thank you,

Best Regards,

Noa Drake”

Dear Noa,

I want to answer your question in two parts. First: What does it take for a hypothesis to earn the label “theory” in physics? And second: What are the requirements for a theory of quantum gravity in particular?”

What does it take for a hypothesis to earn the label “theory” in physics?

Like almost all nomenclature in physics – except the names of new heavy elements – the label “theory” is not awarded by some agreed-upon regulation, but emerges from usage in the community – or doesn’t. Contrary to what some science popularizers want the public to believe, scientists do not use the word “theory” in a very precise way. Some names stick, others don’t, and trying to change a name already in use is often futile.

The best way to capture what physicists mean with “theory” is that it describes an identification between mathematical structures and observables. The theory is the map between the math-world and the real world. A “model” on the other hand is something slightly different: it’s the stand-in for the real world that is being mapped by help of the theory. For example the standard model is the math-thing which is mapped by quantum field theory to the real world. The cosmological concordance model is mapped by the theory of general relativity to the real world. And so on.

But of course not everybody agrees. Frank Wilczek and Sean Carroll for example want to rename the standard model to “core theory.” David Gross argues that string theory isn’t a theory, but actually a “framework.” And Paul Steinhardt insists on calling the model of inflation a “paradigm.” I have a theory that physicists like being disagreeable.

Sticking with my own nomenclature, what it takes to make a theory in physics is 1) a mathematically consistent formulation – at least in some well-controlled approximation, 2) an unambiguous identification of observables, and 3) agreement with all available data relevant in the range in which the theory applies.

These are high demands, and the difficulty of meeting them is almost always underestimated by those who don’t work in the field. Physics is a very advanced discipline and the existing theories have been confirmed to extremely high precision. It is therefore very hard to make any changes that improve the existing theories rather than screwing them up altogether.

What are the requirements for a theory of quantum gravity in particular?

The combination of the standard model and general relativity is not mathematically consistent at energies beyond the Planck scale, which is why we know that a theory of quantum gravity is necessary. The successful theory of quantum gravity must achieve mathematical consistencies at all energies, or – if it is not a final theory – at least well beyond the Planck scale.

If you quantize gravity like the other interactions, the theory you end up with – perturbatively quantized gravity – breaks down at high energies; it produces nonsensical answers. In physics parlance, high energies are often referred to as “the ultra-violet” or “the UV” for short, and the missing theory is hence the “UV-completion” of perturbatively quantized gravity.

At the energies that we have tested so far, quantum gravity must reproduce general relativity with a suitable coupling to the standard model. Strictly speaking it doesn’t have to reproduce these models themselves, but only the data that we have measured. But since there is such a lot of data at low energies, and we already know this data is described by the standard model and general relativity, we don’t try to reproduce each and every observation. Instead we just try to recover the already known theories in the low-energy approximation.

That the theory of quantum gravity must remove inconsistencies in the combination of the standard model and general relativity means in particular it must solve the black hole information loss problem. It also means that it must produce meaningful answers for the interaction probabilities of particles at energies beyond the Planck scale. It is furthermore generally believed that quantum gravity will avoid the formation of space-time singularities, though this isn’t strictly speaking necessary for mathematical consistency.

These requirements are very strong and incredibly hard to meet. There are presently only a few serious candidates for quantum gravity: string theory, loop quantum gravity, asymptotically safe gravity, causal dynamical triangulation, and, somewhat down the line, causal sets and a collection of emergent gravity ideas.

Among those candidates, string theory and asymptotically safe gravity have a well-established compatibility with general relativity and the standard model. From these two, string theory is favored by the vast majority of physicists in the field, primarily because it has given rise to more insights and contains more internal connections. Whenever I ask someone what they think about asymptotically safe gravity, they tell me that would be “depressing” or “disappointing.” I know, it sounds more like psychology than physics.

Having said that, let me mention for completeness that, based on purely logical reasoning, it isn’t necessary to find a UV-completion for perturbatively quantized gravity. Instead of quantizing gravity at high energies, you can ‘unquantize’ matter at high energies, which also solves the problem. From all existing attempts to remove the inconsistencies that arise when combining the standard model with general relativity, this is the possibly most unpopular option.

I do not think that the data we have so far plus the requirement of mathematical consistency will allow us to derive one unique theory. This means that without additional data physicists have no reason to ever converge on any one approach to quantum gravity.

Thank you for an interesting question!

Hey Bill Nye, Please stop talking nonsense about quantum mechanics.

Bill Nye, also known as The Science Guy, is a popular science communicator in the USA. He has appeared regularly on TV and, together with Corey Powell, produced two books. On Twitter, he has gathered 2.8 million followers, by which he ranks somewhere between Brian Cox and Neil deGrasse Tyson. This morning, a video of Bill Nye explaining quantum entanglement was pointed out to me:



The video seems to be part of a series in which he answers questions from his fans. Here we have a young man by name Tom from Western Australia calling in. The transcript starts as follows:

Tom: Hi, Bill. Tom, from Western Australia. If quantum entanglement or quantum spookiness can allow us to transmit information instantaneously, that is faster than the speed of light, how do you think this could, dare I say it, change the world?

Bill Nye: Tom, I love you man. Thanks for the tip of the hat there, the turn of phrase. Will quantum entanglement change the world? If this turns out to be a real thing, well, or if we can take advantage of it, it seems to me the first thing that will change is computing. We’ll be able to make computers that work extraordinarily fast. But it carries with it, for me, this belief that we’ll be able to go back in time; that we’ll be able to harness energy somehow from black holes and other astrophysical phenomenon that we observe in the cosmos but not so readily here on earth. We’ll see. Tom, in Western Australia, maybe you’ll be the physicist that figures quantum entanglement out at its next level and create practical applications. But for now, I’m not counting on it to change the world.

I thought I must have slept through Easter and it’s already April 1st. I replayed this like 5 times. But it didn’t get any better. So what else can I do but take to my blog in the futile attempt to bring sanity back to earth?

Dear Tom,

This is an interesting question which allows one to engage in some lovely science fiction speculation, but first let us be clear that quantum entanglement does not allow to transmit information faster than the speed of light. Entanglement is a non-local correlation that enforces particles to share properties, potentially over long distances. But there is no way to send information through this link because the particles are quantum mechanical and their properties are randomly distributed.

Quantum entanglement is a real thing, we know this already. This has been demonstrated in countless experiments, and while multi-particle correlations are an active research area, the basic phenomenon is well-understood. But entanglement does not imply a spooky “action” at a distance – this is a misleading historical phrase which lives on in science communication just because it has a nice ring to it. Nothing ever acts between the entangled particles – they are merely correlated. That entanglement might allow faster-than-light communication was a confusion in the 1950s, but it’s long been understood that quantum mechanics is perfectly compatible with Einstein’s theory of Special Relativity in which information cannot be transmitted faster than the speed of light.

No, it really can’t. Sorry about that. Yes, I too would love to send messages to the other side of the universe without having to wait some billion years for a reply. But for all we presently know about the laws of nature, it’s not possible.

Entanglement is the relevant ingredient in building quantum computers, and these could indeed dramatically speed up information processing and storage capacities, hence the effort that is being made to build one. But this has nothing to do with exchanging information faster than light, it merely relies on the number of different states that quantum particles can be brought into, which is huge compared to those of normal computers. (Which also work only thanks to quantum mechanics, but normal computers don’t use quantum states for information processing.)

Now let us forget about the real world for a moment, and imagine what we could do if it was possible to send information faster than the speed of light, even though this is to our best present knowledge not possible. Maybe this is what your question really was?

The short answer is that you are likely to screw up reality altogether. Once you can send information faster than the speed of light, you can also send it back in time. If you can send information back in time, you can create inconsistent histories, that is, you can create various different pasts, a problem commonly known as “grandfather paradox:” What happens if you travel back in time and kill your grandpa? Will Marty McFly be born if he doesn’t get his mom to dance with his dad? Exactly this problem.

Multiple histories, or quantum mechanical parallel worlds, are a commonly used scenario in the science fiction literature and movie industry, and they make for some mind-bending fun. For a critical take on how these ideas hold up to real science, I can recommend Xaq Rzetelny’s awesome article “Trek at 50: The quest for a unifying theory of time travel in Star Trek.”

I have no fucking clue what Bill thinks this has to do with harnessing energy from black holes, but I hope this won’t discourage you from signing up for a physics degree.

Dear Bill,

Every day I get emails from people who want to convince me that they have found a way to create a wormhole, harness vacuum energy, travel back in time, or that they know how to connect the conscious mind with the quantum, whatever that means. They often argue with quotes from papers or textbooks which they have badly misunderstood. But they no longer have to do this. Now they can quote Bill The Science Guy who said that quantum entanglement would allow us to harness energy from black holes and to travel back in time.

Maybe you were joking and I didn’t get it. But if it’s a joke, let me tell you that nobody in my newsfeed seems to have found it funny.

Seriously, man, fix that. Sincerely,

B.

Can we get some sympathy for the nerdy loners please?

“Mommy?”

“What is she doing?” – “She is sitting there.” – “Ye-es. But what is she do-ing?”

“She isn’t doing anything. She is just. Sitting there.”

“How long do we wait?” – “We wait until the clock is 29 and 10.”

I’m sitting there because I have a problem. The problem isn’t that I have children – children who, despite my best efforts, still can’t read the clock. I am sitting there because I have a problem with a differential equation. Actually, several of them.

You’d think two non-stop nagging kids would have cured me from getting eaten up by equations. But they’ve just made me better at zoning out. Hooked on a suitably interesting problem – it’s inevitably something-with-physics – I am basically incommunicable, sometimes for weeks at a time.

Not like that’s news. 20 years ago I was your stereotypical nerd. The student in an oversized hoodie, with glasses and an always overdue haircut. No matter where I went, I dragged around a huge backpack full of books – just in case I had to look up something about that problem I was on. Nobody was surprised I ended up with a PhD in theoretical physics.

I’ve since swapped the hoodies for mommy-wear that doesn’t make it quite as easy for toddlers to hide food in it. I’ve found a way to tie up the mess that is my hair. And I’ve learned to make conversation. Though my attempts at small-talk inevitably seem to start with “I recently read...”

But despite my efforts to hide it, I’m afraid I’m still your stereotypical nerd.

I get often asked if it’s difficult to be one of the few women in a field dominated by men. Yes, sometimes. But leaving aside the inevitable awkwardness that comes with hearing your own voice stand out an octave above everyone else’s, theoretical physics has always been my intellectual home, the go-to place when in need of likeminded people. The stories about the lone genius waiting to be hit by an apple, they didn’t turn me off, they were my aspiration. I just wanted to be left alone solving problems. And for the biggest part I have been left alone.

There’s a price to pay, of course, for wanting to be left alone. Which is that you might be left alone.

Ágnes Móscy is the exact opposite of your stereotypical nerd. She’s as intelligent as artsy, and she dabbles with ease between communities. She seems infinitely energetic and is a wonderful woman, warm and welcoming, cool and clever. In recent years, Ágnes has become very engaged in the good cause of supporting minorities in physics. She has gone about it as you expect of a scientist, with numbers and facts, with data and references, giving lectures and educating her colleagues. I admire her initiative.

I had to say some nice things about Ágnes first because next comes some criticism.

The other day she wrote a piece for Huffpo hitting on the supposed myth of the lonely genius.

I will agree that genius is as word as useless as overused. Nobody really knows what it means, and it has an unfortunate ring of “genetics” to it. That’s unfortunate because a recent study has found evidence that women shy away from fields that are believed to require inborn talent rather than hard work. Then there’s another study which demonstrated that students are more likely to associate “genius” with male professors than with female and black professors. And Ágnes is right of course when she says that most of us in physics aren’t geniuses, whatever exactly you think it means, so why use a label that is neither descriptive nor helpful?

I’d sign a petition to trashcan “genius,” together with “next Einstein.”

Then Ágnes makes a case that the loner in physics is as much a myth as the genius. You won’t be surprised to hear I disagree.

True, scientists always build on other’s work, and once they’ve built, they must tell their colleagues about it. Communication isn’t only a necessary part of research, it’s also the best way to make sure you’re not fooling yourself. That talking to other people about your problems can be useful is a lesson I first had to learn, but even I eventually learned it.

Still, there is a stage of research that remains lonely. That phase in which you don’t really know just what you know, when you have an idea but you can’t put into words, a problem so diffuse you’re not sure what the problem is.

Fields Medalist Michael Atiyah (who I now don’t dare to call a genius because you might think I want to discourage girls from studying math) put it this way in a recent interview with Siobhan Roberts for Quanta Magazine:

“Dreams happen during the daytime, they happen at night. You can call them a vision or intuition. But basically they’re a state of mind—without words, pictures, formulas or statements. It’s “pre” all that. It’s pre-Plato. It’s a very primordial feeling. And again, if you try to grasp it, it always dies. So when you wake up in the morning, some vague residue lingers, the ghost of an idea. You try to remember what it was and you only get half of it right, and maybe that’s the best you can do.”

Tell me how that’s not lonely work.

As I am raising two girls, I am all too aware of occupational stereotypes. Like many academics, my husband and I are fighting the pink/blue divide, the gender segregation that starts already in kindergarten. I don’t want my daughters to think following their interests isn’t socially appropriate because some professions aren’t for women.

I am therefore all in favor of initiatives targeting girls with science toys and educational games, because of course I hope that’s where my kids’ interests are. Also, I get to play with the stuff myself. (I recently bought a microscope that attaches to the phone because I thought the girls might want have a close look at some leaves. Instead my husband used it to inspect our gauze curtains and proceeded to use them as a refraction lattice. I’m still waiting to get my microscope and laser pointer back.)

But while I hope my children will go on to become scientists, I first and foremost want them to find out which profession they will be most happy with, whether that means physicist or midwife. And I don’t want young women to get talked into something they aren’t genuinely into, just because the statistics say there should be more women in physics. I don’t want them to be mislead by marketing physics as something it is not.

So let’s tell it like it is.

Physics isn’t all teamwork and communication skills, it’s not all collaboration and conferences, it’s not all chalk and talk. That’s some of it, but physics is also a lot of reading and a lot of thinking – and sometimes it’s lonely.

There are stages in your research in which you will hit on a problem that no one can help you with. Because that’s what research is all about – finding and solving problems that no one has solved before. And sometimes you will get stuck, annoyed about yourself, frustrated about your own inability to make sense of these equations. You will feel stupid and you will feel lonely and you will feel like nobody can understand you – because nobody can understand you.

That’s physics too.

Science only stands to benefit from more diversity. Different cultural and social backgrounds, different experiences and different personality traits serve to broaden our perspectives and may lead to new approaches to old problems. But attracting new customers shouldn’t scare away the regulars. We have use for the nerdy loners too.

Having reached almost 40 years of age, I’ve survived long enough to no longer care if people think I’m not normal. Not normal for leaving the party early, not normal for scribbling notes on my arm, not normal for spontaneously bursting into lectures about Lorentz-invariance violating operators.

Luckily, I am married to a man who doesn’t only have much understanding for my problems, but also seems to have textbooks on each and every obscure subfield of physics. There’s a reason he’s in the acknowledgements of almost all of my papers.

I hope that you, too, find a niche in life where you fit in. And if you want to be left alone, don’t let anyone tell you there is no place for loners in this world any more.

“29 and 10. That’s 39.”

She can’t yet read the clock. But she’s good at math.

Researchers propose experiment to measure the gravitational force of milli-gram objects, reaching almost into the quantum realm.

Neutrinos, gravitational waves, light deflection on the sun – the history of physics is full with phenomena once believed immeasurably small but now yesterday’s news. And on the list of impossible things turned possible, quantum gravity might be next.

Quantum gravitational effects have widely been believed inaccessible by experiment because enormously high energy densities are required to make them comparably large as other quantum effects. This argument however neglects that quantum effects of gravity can also become relevant for massive objects in quantum superpositions. Once we are able to measure the gravitational pull of an object that is in a superposition of two different places, we can determine whether the gravitational field is in a quantum superposition as well.

This neat idea has two problematic aspects. First, since gravity is very weak, measuring gravitational fields of small objects is extremely difficult. And second, bringing massive objects into quantum states is hard because the states rapidly decohere due to interaction with the environment. However, technological advances on both aspects of the problem have been stunning during the last decade.

In two previous posts we discussed some examples of massive quantum oscillators that can create location superpositions of objects as heavy as a nano-gram. The objects under consideration here are typically small disks made of silicon that are bombarded with laser light while trapped between two mirrors. A nano-gram might not sound much, but compared to the masses of elementary particles that’s enormous.

Meanwhile, progress on the other aspect of the problem - measuring tiny gravitational fields – has also been remarkable. Currently, the smallest mass whose gravitational pull has been measured is about 90g. But a recent proposal by the group of Markus Aspelmeyer in Vienna lays out a method for measuring the gravitational force of masses as small as a few milli-gram.

A micromechanical proof-of-principle experiment for measuring the gravitational force of milligram masses
Jonas Schmöle, Mathias Dragosits, Hans Hepach, Markus Aspelmeyer
arXiv:1602.07539 [physics.ins-det]

Their proposal relies on a relatively new field of technology that employs micro-mechanical devices, which basically means you make your whole measurement apparatus as small as you can, piling single atoms on atoms. This trend, which has itself become possible only by the nanotechnology required to to design these devices, allows measurements of unprecedented precision.

The smallest force that has so far been measured with nano-devices is around a zepto-Newton (zepto is 10^-21). That’s not yet the world-record in tiny-force measurements, which is currently held by a group in Berkely and lies at about a yocto-Newton (that’s 10^-24). But the huge benefit of the nano-devices is that you can get them close to the probe, whereas the experiment holding the record relies on precisely tracking the motion of a cloud of atoms in a trap. Not only doesn’t the cloud-tracking mean that it’s difficult to scale up the mass without ruining precision. The necessity to trap the particles also means that it’s difficult to get the source of the force-field close to the probe. The use of micro-mechanical devices in contrast does not have the same limitations and thus lends itself better to the task of measuring the gravitational force exerted by quantum systems.

The Aspelmeyer group sketches their experiment as shown in the figure below

[From arXiv:1602.07539]

The blue circles are the masses whose gravitational interaction one wants to measure, with the source mass to the right and the test-mass to the left. The test-mass is attached to the micro-mechanical oscillator, whereas the source-mass is driven by another oscillator close by the systems’ resonance frequency. The gravitational pull between the two masses transfers the oscillation of the source-mass to the test-mass, where it can be picked up by the detector.

In their paper, the experimentalists argue that it should be possible by this method to measure the gravitational force of a source mass not heavier than a few milli-grams. And that’s the conservative estimate. With better detector efficiency even that limit could be improved on.

There are still a few orders of magnitude between a milli-gram and a nano-gram, which is the current maximum mass for which quantum superpositions have been achieved. But in typical estimates for quantum gravitational effects you end up at least 30 orders of magnitude away from measurement precision. Now we are talking about five orders of magnitude – and that in a field with rapid technological developments for which there is no fundamental limit in sight.

What is most remarkable about this development is that this proposal relies on technology that until a few years ago literally nobody in quantum gravity ever talked about. It’s not even that the technological development has been faster than anticipated, it’s a possibility that plainly wasn’t on the radar. Now there is a Nobel Prize waiting here, for the first experimental measurement of quantum gravitational effects.

And as the Prize comes within reach, competition will speed up the pace. So stay tuned, I am sure we will hear more about this soon.

A new era of science

[img source: changingcourse.com]

Here in basic research we all preach the gospel of serendipity. Breakthroughs cannot be planned, insights not be forced, geniuses not be bred. We tell ourselves – and everybody willing to listen – that predicting the outcome of a research project is more difficult than doing the research in the first place. And half of all discoveries are made while tinkering with something else anyway. Now please join me for the chorus, and let us repeat once again that the World Wide Web was invented at CERN – while studying elementary particles.

But in theoretical physics the age of serendipitous discovery is nearing its end. You don’t tinker with a 27 km collider and don’t coincidentally detect gravitational waves while looking for a better way to toast bread. Modern experiments succeed by careful planning over the course of decades. They rely on collaborations of thousands of people and cost billions of dollars. While we always try to include multipurpose detectors hoping to catch unexpected signals, there is no doubt that our machines are built for very specific purposes.

And the selection is harsh. For every detector that gets funding, three others don’t. For every satellite mission that goes into orbit, five others never get off the ground. Modern physics isn’t about serendipitous discoveries – it’s about risk/benefit analyses and impact assessments. It’s about enhanced design, horizontal integration, and progressive growth strategies. Breakthroughs cannot be planned, but you sure can call in a committee meeting to evaluate their ROI and disruptive potential.

There is no doubt that scientific research takes up resources. It requires both time and money, which is really just a proxy for energy. And as our knowledge increases, new discoveries have become more difficult, requiring us too pool funding and create large international collaborations.

This process is most pronounced in basic research in physics – cosmology and particle physics – because in this area we deal with the smallest and the most distant objects in the universe. Things that are hard to see, basically. But the trend towards Big Science can be witnessed also in other discipline’s billion-dollar investments like the Human Genome Project, the Human Brain Project, or the National Ecological Observatory Network. “It's analogous to our LHC, ” says Ash Ballantyne, a bioclimatologist at the University of Montana in Missoula, who has never heard of physics envy and doesn’t want to be reminded of it either.

These plus-sized projects will keep a whole generation of scientists busy - and the future will bring more of this, not less. This increasing cost of experiments in frontier research has slowly, but inevitably, changed the way we do science. And it is fundamentally redefining the role of theory development. Yes, we are entering a new era of science – whether we like that or not.

Again, this change is most apparent in basic research in physics. The community’s assessment of a theory’s promise must be drawn upon to justify investment in an experimental test of that theory. Hence the increased scrutiny that theory-assessment gets as of recently. In the end it comes down to the question where we should put our money.

We often act like knowledge discovery is a luxury. We act like it’s something societies can support optionally, to the extent that they feel like funding it. We act like it’s something that will continue, somehow, anyway. The situation, however, is much scarier than that.

At every level of knowledge we have the capability to exploit only a finite amount of resources. To unlock new resources, we have to invest the ones we have to discover new knowledge and develop new technologies. The newly unlocked resources can then be used for further exploration. And so on.

It has worked so far. But at any level in this game, we might fail. We might not succeed in using the resources we have smartly enough to upgrade to the next level. If we don’t invest sufficiently into knowledge discovery, or invest into the wrong things, we might get stuck – and might end up unable to proceed beyond a certain level of technology. Forever.

And so, when I look at the papers on hep-th and gr-qc, I don’t think about the next 3 years or 5 years, as my funding agency wants me to. I think about the next 3000 or 5000 years. Which of this research holds the promise of discovering knowledge necessary to get to the next level? The bigger and more costly experiments become, the larger the responsibility of theorists who claim that testing a theory will uncover worthwhile new insights. Do we live up to this responsibility?

I don’t think we do. Worse, I think we can’t because funding pressures force theoreticians to overemphasize the promise of their own research. The necessity of marketing is now a reality of science. Our assessment of research agendas is inevitably biased and non-objective. For most of the papers I see on hep-th and gr-qc, I think people work on these topics simply because they can. They can get this research published and they can get it funded. It tells you all about academia and very little about the promise of a theory.

While our colleagues in experiment have entered a new era of science, we theorists are still stuck in the 20st century. We still believe our task is being fighters for our own ideas, when we should instead be working together on identifying those experiments most likely to advance our societies. We still pretend that science is somehow self-correcting because a failed experiment will force us to discard a hypothesis – and we ignore the troubling fact that there are only so many experiments we can do, ever. We better place our bets very carefully because we won’t be able to bet arbitrarily often.

The reality of life is that nothing is infinite. Time, energy, manpower – all of this is limited. The bigger science projects become, the more carefully we have to direct our investments. Yes, it’s a new era of science. Are we ready?

Dear Dr. B: What is the difference between entanglement and superposition?

The only photo in existence
that shows me in high heels.

This is an excellent question which you didn’t ask. I’ll answer it anyway because confusing entangled states with superpositions is a very common mistake. And an unfortunate one: without knowing the difference between entanglement and superposition the most interesting phenomena of quantum mechanics remain impossible to understand – so listen closely, or you’ll forever remain stuck in the 19th century.

Let us start by decoding the word “superposition.” Physicists work with equations, the solutions of which describe the system they are interested in. That might be, for example, an electromagnetic wave going through a double slit. If you manage to solve the equations for that system, you can then calculate what you will observe on the screen.

A “superposition” is simply a sum of two solutions, possibly with constant factors in front of the terms. Now, some equations, like those of quantum mechanics, have the nice property that the sum of two solutions is also a solution, where each solution corresponds to a different setup of your experiment. But that superpositions of solutions are also solutions has nothing to do with quantum mechanics specifically. You can also, for example, superpose electromagnetic waves – solutions to the sourceless Maxwell equations – and the superposition is again a solution to Maxwell’s equations. So to begin with, when we are dealing with quantum states, we should more carefully speak of “quantum superpositions.”

Quantum superpositions are different from non-quantum superpositions in that they are valid solutions to the equations of quantum mechanics, but they are never being measured. That’s the whole mystery of the measurement process: the “collapse” of a superposition of solutions to a single solution.

Take for example a lonely photon that goes through a double slit. It is a superposition of two states that each describe a wave emerging from one of the slits. Yet, if you measure the photon on the screen, it’s always in one single point. The superposition of solutions in quantum mechanics tells you merely the probability for measuring the photon at one specific point which, for the double-slit, reproduces the interference pattern of the waves.

But I cheated...

Because what you think of as a quantum superposition depends on what you want to measure. A state might be a superposition for one measurement, but not for another. Indeed the whole expression “quantum superposition” is entirely meaningless without saying what is being superposed. A photon can be in a superposition of many different positions, and yet not be in a superposition of momenta. So is it or is it not a superposition? That’s entirely due to your choice of observable – even before you have observed anything.

All this is just to say that whether a particle is or isn’t in a superposition is ambiguous. You can always make its superposition go away by just wanting it to go away and changing the notation. Or, slightly more technical, you can always remove a superposition of basis states just by defining the superposition as a new basis state. It is for this reason somewhat unfortunate that superpositions – the cat being both dead and alive – often serve as examples for quantum-ness. You could equally well say the cat is in one state of dead-and-aliveness, not in a superposition of two states one of which is dead and one alive.

Now to entanglement.

Entanglement is a correlation between different parts of a system. The simplest case is a correlation between particles, but really you can entangle all kinds of things and properties of things. You find out whether a system has entanglement by dividing it up into two subsystems. Then you consider both systems separately. If the two subsystems were entangled, then looking at them separately will inevitably reduce the information. In physics speak, you “trace out” one subsystem and are left with a mixed state for the other subsystem.

The best known example is a pair of particles, each with either spin +1 or -1. You don’t know which particle has which spin, but you do know that the sum of both has to be zero. So if you have your particles in two separate boxes, you have a state that is either +1 in the left box and -1 in the right box, or -1 in the left box and +1 in the right box.

Now divide the system up in two subsystems that are the two boxes, and throw away one of them. What do you know about the remaining box? Well, all you know is that it’s either +1 or -1, and you have lost the information that was contained in the link between the two boxes, the one that said “If this is +1, then this must be -1, and the other way round.” That information is gone for good. If you crunch the numbers, you find that correlations between quantum states can be stronger than correlations between non-quantum states could ever be. It is the existence of these strong correlations that tests of Bell’s theorem have looked for – and confirmed.

Most importantly, whether a system has entanglement between two subsystems is a yes or no question. You cannot create entanglement by a choice of observable, and you can’t make it go away either. It is really entanglement – the spooky action at a distance – that is the embodiment of quantum-ness, and not the dead-and-aliveness of superpositions.

[For a more technical explanation, I can recommend these notes by Robert Helling, who used to blog but now has kids.]

Tim Gowers and I have something in common. Unfortunately it’s not our math skills.

Heavy paper.

What would you say if a man with British accent cold-calls you one evening to offer money because he likes your blog?

I said no.

In my world – the world of academic paper-war – we don’t just get money for our work. What we get is permission to administrate somebody else’s money according to the attached 80-page guidelines (note the change in section 15b that affects taxation of 10 year deductibles). Restrictions on the use of funds are abundant and invite applicants to rest their foreheads on cold surfaces.

The German Research Foundation for example, will – if you are very lucky – grant you money for a scientific meeting. But you’re not allowed to buy food with it. Because, you must know, real scientists don’t eat. And to thank you for organizing the meeting you don’t yourself get paid – that wouldn’t be an allowed use of funds. No, they thank you by requesting further reports and forms.

At least you can sometimes get money for scientific meetings. But convincing a funding agency to pay a bill for public outreach or open access initiatives is like getting a toddler to eat broccoli: No matter how convincingly you argue it’s in their own interest, you end up eating it yourself. And since writing proposals sucks, I mean, sucks up time, at some point I gave up trying to make a case that this blog is unpaid public outreach that you'd think research foundations should be supportive of. I just write – and on occasion I carefully rest my forehead on cold surfaces.

Then came the time I was running low on income – unemployed between two temporary contracts – and decided to pitch a story to a magazine. I was lucky and landed an assignment instantly. And so, for the first time in my life, I turned in work to a deadline, wrote an invoice, and got paid in return. I. Made. Money. Writing. It was a revelation. Unfortunately, my published masterwork is now hidden behind a paywall. I am not happy about this, you are not happy about this, and the man with the British accent wasn’t happy about it either. Thus his offer.

But I said no.

Because all I could see was time wasted trying to justify proper means of spending someone else’s money on suitable purposes that might be, for example, a conference fee that finances the first class ticket of the attending Nobel Prize winner. That, you see, is an allowed way of spending money in academia.

My cold-caller was undeterred and called again a week later to inquire whether I had changed my mind. I was visiting my mom, and mom, always the voice of reason, told me to just take the damn money. But I didn’t.

I don’t like being reminded of money. Money is evil. Money corrupts. I only pay with sanitized plastic. I swipe a card through a machine and get handed groceries in return – that’s not money, that’s magic. I look at my bank account statements so rarely I didn’t notice for three years I accidentally paid a gym membership fee in a country I don’t even live. In case my finances turn belly-up I assume the bank will call and yell at me. Which, now that I think of it, seems unlikely because I moved at least a dozen times since opening my account. And I’m not good updating addresses either. I did call the gym though and yelled at them – I got my money back.

Then the British man told me he also supports Tim Gowers new journal. “G-O-W-ers?,” I asked. Yes, that Tim. That would be the math guy responsible for the equations in my G+ feed.

Tim Gowers. [Not sure whose photo, but not mine]

Tim Gowers, of course, also writes a blog. Besides that, he’s won the 1998 Fields Medal which makes him officially a genius. I sent him an email inquiring about our common friend. Tim wrote back he reads my blog. He reads my blog! A genius reads my blog! I mean, another genius – besides my mom who gets toddlers to eat broccoli.

Thusly, I thought, if it’s good enough for Gowers, it’s probably good enough for me. So I said yes. And, after some more weeks of consideration, sent my bank account details to the British man. You have to be careful with that kind of thing, says my mom.

That was last year in December. Then I forgot about the whole story and returned to my differential equations.

Tim, meanwhile, got busy setting up the webpage for his new journal “Discrete Analysis” which covers the emerging fields related to additive combinatorics (not to be confused with addictive combinatorics, more commonly known as Sudoku). His open-access initiative has attracted some attention because the journal’s site doesn’t itself host the articles it publishes – it merely links to files which are stored on the arXiv. The arXiv is an open-access server in operation since the early 1990s. It allows researchers in physics, math, and related disciplines to upload and share articles that have not, or not yet, been peer-reviewed and published. “Discrete Analysis” adds the peer-review, with minimal effort and minimal expenses.

Tim’s isn’t the first such “arxiv-overlay” journal – I myself published last year in another overlay-journal called SIGMA – but it is still a new development that is eyed with some skepticism. By relying on the arXiv to store files, the overlays render server costs somebody else’s problem. That’s convenient but doesn’t make the problem go away. Another issue is that the arXiv itself already moderates submissions, a process that the overlay journals have no control over.

Either way, it is a trend that I welcome because overlays offer scientists what they need from journals without the strings and costs attached by commercial publishers. It is, most importantly, an opportunity for the community to reclaim the conditions under which their research is shared, and also to innovate the format as they please:

“I wanted it to be better than a normal journal in important respects,” says Tim, “If you visit the website, you will notice that each article gives you an option to click on the words ‘Editorial introduction.’ If you do so, then up comes a description of the article (not on a new webpage, I hasten to add), which sets it in some kind of context and helps you to judge whether you want to find out more by going to the arXiv and reading it.”

But even overlay journals don’t operate at zero cost. The website of “Discrete Analysis” was designed by Scholastica’s team, and their platform will also handle the journal’s publication process. They charge $10 per submission and there are a couple of other expenses that the editorial board has to cover, such as services necessary to issue article DOIs. Tim wants to avoid handing on the journal expenses to the authors. Which brings in, among others, the support from my caller with the British accent.

In the two months that passed since I last heard from him, I found out that 10 years ago someone proved there is no non-trivial solution to the equations I was trying to solve. Well, at least that explains why I couldn’t find one. My hence scheduled two-day cursing retreat was interrupted by a message from The British Man. Did the money arrive?, he wanted to know. This way forced to check my bank account, it turned out not only didn’t his money arrive, but neither did I ever receive salary for my new job.

This gives me an excuse to lecture you on another pitfall of academic funding. Even after you have filed five copies of various tax-documents and sent the birth dates of the University President and Vice-president to an institution that handles your grant for another institution and is supposed to wire it to a third institution which handles it for your institution, the money might get lost along the way – and frequently does.

In this case they simply forgot to put me on the payroll. Luckily, the issue could be resolved quickly, and the next day also the wire transfer from Great Britain arrived. Good thing because, as mommy guilt reminded me, this bank account pays for the girls’ daycare and lunch. My writer friends won’t be surprised to hear however that I also had to notice several payments for my freelance work did not come through. When I grow up, I hope someone tells me how life works. /lecture

Tim Gowers invited submissions for “Discrete Analysis” starting last September, and the website of the new journal launched today; you can read his own blogpost here. For the community, they key question is now whether arxiv-overlay journals like Tim’s will be able to gain a status similar to that of traditional journals. The only way to find out is to try.

Public outreach in general, and science blogging in particular, is vital for the communication of science, both within our communities and to the public. And so are open access initiatives. Even though they are essential to advance research and integrate it into our society, funding agencies have been slow to accept these services as part of their mission.

While we wait for academia to finally digest the invention of the world wide web, it is encouraging to see that some think forward. And so, I am happy today to acknowledge this blog is now supported by the caller with the British accent, Ilyas Khan of Cambridge Quantum Computing. Ilyas has quietly supported a number of scientific endeavors. Although he is best known for enabling Wittgenstein's Nachlass to become openly and freely accessible by funding the project that was implemented by Trinity College Cambridge, he is also a sponsor of Tim Gowers' new journal Discrete Analysis.