Wednesday, April 27, 2016

If you fall into a black hole

If you fall into a black hole, you’ll die. That much is pretty sure. But what happens before that?

The gravitational pull of a black hole depends on its mass. At a fixed distance from the center, it isn’t any stronger or weaker than that of a star with the same mass. The difference is that, since a black hole doesn’t have a surface, the gravitational pull can continue to increase as you approach the center.

The gravitational pull itself isn’t the problem, the problem is the change in the pull, the tidal force. It will stretch any extended object in a process with technical name “spaghettification.” That’s what will eventually kill you. Whether this happens before or after you cross the horizon depends, again, on the mass of the black hole. The larger the mass, the smaller the space-time curvature at the horizon, and the smaller the tidal force.

Leaving aside lots of hot gas and swirling particles, you have good chances to survive crossing the horizon of a supermassive black hole, like that in the center of our galaxy. You would, however, probably be torn apart before crossing the horizon of a solar-mass black hole.

It takes you a finite time to reach the horizon of a black hole. For an outside observer however, you seem to be moving slower and slower and will never quite reach the black hole, due to the (technically infinitely large) gravitational redshift. If you take into account that black holes evaporate, it doesn’t quite take forever, and your friends will eventually see you vanishing. It might just take a few hundred billion years.

In an article that recently appeared on “Quick And Dirty Tips” (featured by SciAm), Everyday Einstein Sabrina Stierwalt explains:
“As you approach a black hole, you do not notice a change in time as you experience it, but from an outsider’s perspective, time appears to slow down and eventually crawl to a stop for you [...] So who is right? This discrepancy, and whose reality is ultimately correct, is a highly contested area of current physics research.”
No, it isn’t. The two observers have different descriptions of the process of falling into a black hole because they both use different time coordinates. There is no contradiction between the conclusions they draw. The outside observer’s story is an infinitely stretched version of the infalling observer’s story, covering only the part before horizon crossing. Nobody contests this.

I suspect this confusion was caused by the idea of black hole complementarity. Which is indeed a highly contest area of current physics research. According to black hole complementarity the information that falls into a black hole both goes in and comes out. This is in contradiction with quantum mechanics which forbids making exact copies of a state. The idea of black hole complementarity is that nobody can ever make a measurement to document the forbidden copying and hence, it isn’t a real inconsistency. Making such measurements is typically impossible because the infalling observer only has a limited amount of time before hitting the singularity.

Black hole complementarity is actually a pretty philosophical idea.

Now, the black hole firewall issue points out that black hole complementarity is inconsistent. Even if you can’t measure that a copy has been made, pushing the infalling information in the outgoing radiation changes the vacuum state in the horizon vicinity to a state which is no longer empty: that’s the firewall.

Be that as it may, even in black hole complementarity the infalling observer still falls in, and crosses the horizon at a finite time.

The real question that drives much current research is how the information comes out of the black hole before it has completely evaporated. It’s a topic which has been discussed for more than 40 years now, and there is little sign that theorists will agree on a solution. And why would they? Leaving aside fluid analogies, there is no experimental evidence for what happens with black hole information, and there is hence no reason for theorists to converge on any one option.

The theory assessment in this research area is purely non-empirical, to use an expression by philosopher Richard Dawid. It’s why I think if we ever want to see progress on the foundations of physics we have to think very carefully about the non-empirical criteria that we use.

Anyway, the lesson here is: Everyday Einstein’s Quick and Dirty Tips is not a recommended travel guide for black holes.

Wednesday, April 20, 2016

Dear Dr B: Why is Lorentz-invariance in conflict with discreteness?

Can we build up space-time from
discrete entities?
“Could you elaborate (even) more on […] the exact tension between Lorentz invariance and attempts for discretisation?



Dear Noa:

Discretization is a common procedure to deal with infinities. Since quantum mechanics relates large energies to short (wave) lengths, introducing a shortest possible distance corresponds to cutting off momentum integrals. This can remove infinites that come in at large momenta (or, as the physicists say “in the UV”).

Such hard cut-off procedures were quite common in the early days of quantum field theory. They have since been replaced with more sophisticated regulation procedures, but these don’t work for quantum gravity. Hence it lies at hand to use discretization to get rid of the infinities that plague quantum gravity.

Lorentz-invariance is the symmetry of Special Relativity; it tells us how observables transform from one reference frame to another. Certain types of observables, called “scalars,” don’t change at all. In general, observables do change, but they do so under a well-defined procedure that is by the application of Lorentz-transformations.We call these “covariant.” Or at least we should. Most often invariance is conflated with covariance in the literature.

(To be precise, Lorentz-covariance isn’t the full symmetry of Special Relativity because there are also translations in space and time that should maintain the laws of nature. If you add these, you get Poincaré-invariance. But the translations aren’t so relevant for our purposes.)

Lorentz-transformations acting on distances and times lead to the phenomena of Lorentz-contraction and time-dilatation. That means observers at relative velocities to each other measure different lengths and time-intervals. As long as there aren’t any interactions, this has no consequences. But once you have objects that can interact, relativistic contraction has measurable consequences.

Heavy ions for example, which are collided in facilities like RHIC or the LHC, are accelerated to almost the speed of light, which results in a significant length contraction in beam direction, and a corresponding increase in the density. This relativistic squeeze has to be taken into account to correctly compute observables. It isn’t merely an apparent distortion, it’s a real effect.

Now consider you have a regular cubic lattice which is at rest relative to you. Alice comes by in a space-ship at high velocity, what does she see? She doesn’t see a cubic lattice – she sees a lattice that is squeezed into one direction due to Lorentz-contraction. Who of you is right? You’re both right. It’s just that the lattice isn’t invariant under the Lorentz-transformation, and neither are any interactions with it.

The lattice can therefore be used to define a preferred frame, that is a particular reference frame which isn’t like any other frame, violating observer independence. The easiest way to do this would be to use the frame in which the spacing is regular, ie your restframe. If you compute any observables that take into account interactions with the lattice, the result will now explicitly depend on the motion relative to the lattice. Condensed matter systems are thus generally not Lorentz-invariant.

A Lorentz-contraction can convert any distance, no matter how large, into another distance, no matter how short. Similarly, it can blue-shift long wavelengths to short wavelengths, and hence can make small momenta arbitrarily large. This however runs into conflict with the idea of cutting off momentum integrals. For this reason approaches to quantum gravity that rely on discretization or analogies to condensed matter systems are difficult to reconcile with Lorentz-invariance.

So what, you may say, let’s just throw out Lorentz-invariance then. Let us just take a tiny lattice spacing so that we won’t see the effects. Unfortunately, it isn’t that easy. Violations of Lorentz-invariance, even if tiny, spill over into all kinds of observables even at low energies.

A good example is vacuum Cherenkov radiation, that is the spontaneous emission of a photon by an electron. This effect is normally – ie when Lorentz-invariance is respected – forbidden due to energy-momentum conservation. It can only take place in a medium which has components that can recoil. But Lorentz-invariance violation would allow electrons to radiate off photons even in empty space. No such effect has been seen, and this leads to very strong bounds on Lorentz-invariance violation.

And this isn’t the only bound. There are literally dozens of particle interactions that have been checked for Lorentz-invariance violating contributions with absolutely no evidence showing up. Hence, we know that Lorentz-invariance, if not exact, is respected by nature to extremely high precision. And this is very hard to achieve in a model that relies on a discretization.

Having said that, I must point out that not every quantity of dimension length actually transforms as a distance. Thus, the existence of a fundamental length scale is not a priori in conflict with Lorentz-invariance. The best example is maybe the Planck length itself. It has dimension length, but it’s defined from constants of nature that are themselves frame-independent. It has units of a length, but it doesn’t transform as a distance. For the same reason string theory is perfectly compatible with Lorentz-invariance even though it contains a fundamental length scale.

The tension between discreteness and Lorentz-invariance appears always if you have objects that transform like distances or like areas or like spatial volumes. The Causal Set approach therefore is an exception to the problems with discreteness (to my knowledge the only exception). The reason is that Causal Sets are a randomly distributed collection of (unconnected!) points with a four-density that is constant on the average. The random distribution prevents the problems with regular lattices. And since points and four-volumes are both Lorentz-invariant, no preferred frame is introduced.

It is remarkable just how difficult Lorentz-invariance makes it to reconcile general relativity with quantum field theory. The fact that no violations of Lorentz-invariance have been found and the insight that discreteness therefore seems an ill-fated approach has significantly contributed to the conviction of string theorists that they are working on the only right approach. Needless to say there are some people who would disagree, such as probably Carlo Rovelli and Garrett Lisi.

Either way, the absence of Lorentz-invariance violations is one of the prime examples that I draw upon to demonstrate that it is possible to constrain theory development in quantum gravity with existing data. Everyone who still works on discrete approaches must now make really sure to demonstrate there is no conflict with observation.

Thanks for an interesting question!

Wednesday, April 13, 2016

Dark matter might connect galaxies through wormholes

Tl;dr: A new paper shows that one of the most popular types of dark matter – the axion – could make wormholes possible if strong electromagnetic fields, like those found around supermassive black holes, are present. Unclear remains how such wormholes would be formed and whether they would be stable.
Wormhole dress.
Source: Shenova.

Wouldn’t you sometimes like to vanish into a hole and crawl out in another galaxy? It might not be as impossible as it seems. General relativity has long been known to allow for “wormholes” that are short connections between seemingly very distant places. Unfortunately, these wormholes are unstable and cannot be traversed unless filled by “exotic matter,” which must have negative energy density to keep the hole from closing. And no matter that we have ever seen has this property.

The universe, however, contains a lot of matter that we have never seen, which might give you hope. We observe this “dark matter” only through its gravitational pull, but this is enough to tell that it behaves pretty much like regular matter. Dark matter too is thus not exotic enough to help with stabilizing wormholes. Or so we thought.

In a recent paper, Konstantinos Dimopoulos from the “Consortium for Fundamental Physics” at Lancaster University points out that dark matter might be able to mimic the behavior of exotic matter when caught in strong electromagnetic fields:
    Active galaxies may harbour wormholes if dark matter is axionic
    By Konstantinos Dimopoulos
    arXiv:1603.04671 [astro-ph.HE]
Axions are one of the most popular candidates for dark matter. The particles themselves are very light, but they form a condensate in the early universe that should still be around today, giving rise to the observed dark matter distribution. Like all other dark matter candidates, axions have been searched for but so far not been detected.

In his paper, Dimopoulos points out that, due to their peculiar coupling to electromagnetic fields, axions can acquire an apparent mass which makes a negative contribution to their energy. This effect isn’t so unusual – it is similar to the way that fermions obtain masses by coupling to the Higgs or that scalar fields can obtain effective masses by coupling to electromagnetic fields. In other words, it’s not totally unheard of.

Dimopoulos then estimates how strong an electromagnetic field is necessary to turn axions into exotic matter and finds that around supermassive black holes the conditions would just be right. Hence, he concludes, axionic dark matter might keep wormholes open and traversable.

In his present work, Dimopoulos has however not done a fully relativistic computation. He considers the axions in the background of the black hole, but not the coupled solution of axions plus black hole. The analysis so far also does not check whether the wormhole would indeed be stable, or if it would instead blow off the matter that is supposed to stabilize it. And finally, it leaves open the question how the wormhole would form. It is one thing to discuss configurations that are mathematically possible, but it’s another thing entirely to demonstrate that they can actually come into being in our universe.

So it’s an interesting idea, but it will take a little more to convince me that this is possible.

And in case you warmed up to the idea of getting out of this galaxy, let me remind you that the closest supermassive black hole is still 26,000 light years away.

Note added: As mentioned by a commenter (see below) the argument in the paper might be incorrect. I asked the author for comment, but no reply so far.
Another note: The author says he has revised and replaced the paper, and that the conclusions are not affected.

Thursday, April 07, 2016

10 Essentials of Quantum Mechanics

Vortices in a Bose-Einstein condensate.
Source: NIST.

Trying to score at next week’s dinner party? Here’s how to intimidate your boss by fluently speaking quantum.

1. Everything is quantum

It’s not like some things are quantum mechanical and other things are not. Everything obeys the same laws of quantum mechanics – it’s just that quantum effects of large objects are very hard to notice. This is why quantum mechanics was a latecomer in theoretical physics: It wasn’t until physicists had to explain why electrons sit on shells around the atomic nucleus that quantum mechanics became necessary to make accurate predictions.

2. Quantization doesn’t necessarily imply discreteness

“Quanta” are discrete chunks, but not everything becomes chunky on short scales. Electromagnetic waves are made of quanta called “photons,” so the waves can be thought of as a discretized. And electron shells around the atomic nucleus can only have certain discrete radii. But other particle properties do not become discrete even in a quantum theory. The position of electrons in the conducting band of a metal for example is not discrete – the electron can occupy any place within the band. And the energy values of the photons that make up electromagnetic waves are not discrete either. For this reason, quantizing gravity – should we finally succeed at it – also does not necessarily mean that space and time have to be made discrete.

3. Entanglement is not the same as superposition

A quantum superposition is the ability of a system to be in two different states at the same time, and yet, when measured, one always finds one particular state, never a superposition. Entanglement on the other hand is a correlation between parts of a system – something entirely different. Superpositions are not fundamental: Whether a state is or isn’t a superposition depends on what you want to measure. A state can for example be in a superposition of positions and not in a superposition of momenta – so the whole concept is ambiguous. Entanglement on the other hand is unambiguous: It is an intrinsic property of each system and the so-far best known measure of a system’s quantum-ness. (For more details, read “What is the difference between entanglement and superposition?”)

4. There is no spooky action at a distance

Nowhere in quantum mechanics is information ever transmitted non-locally, so that it jumps over a stretch of space without having to go through all places in between. Entanglement is itself non-local, but it doesn’t do any action – it is a correlation that is not connected to non-local transfer of information or any other observable. It was a great confusion in the early days of quantum mechanics, but we know today that the theory can be made perfectly compatible with Einstein’s theory of Special Relativity in which information cannot be transferred faster than the speed of light.

5. It’s an active research area

It’s not like quantum mechanics is yesterday’s news. True, the theory originated more than a century ago. But many aspects of it became testable only with modern technology. Quantum optics, quantum information, quantum computing, quantum cryptography, quantum thermodynamics, and quantum metrology are all recently formed and presently very active research areas. With the new technology, also interest in the foundations of quantum mechanics has been reignited.

6. Einstein didn’t deny it

Contrary to popular opinion, Einstein was not a quantum mechanics denier. He couldn’t possibly be – the theory was so successful early on that no serious scientist could dismiss it. Einstein instead argued that the theory was incomplete, and believed the inherent randomness of quantum processes must have a deeper explanation. It was not that he thought the randomness was wrong, he just thought that this wasn’t the end of the story. For an excellent clarification of Einstein’s views on quantum mechanics, I recommend George Musser’s article “What Einstein Really Thought about Quantum Mechanics” (paywalled, sorry).

7. It’s all about uncertainty

The central postulate of quantum mechanics is that there are pairs of observables that cannot simultaneously be measured, like for example the position and momentum of a particle. These pairs are called “conjugate variables,” and the impossibility to measure both their values precisely is what makes all the difference between a quantized and a non-quantized theory. In quantum mechanics, this uncertainty is fundamental, not due to experimental shortcomings.

8. Quantum effects are not necessarily small...

We do not normally observe quantum effects on long distances because the necessary correlations are very fragile. Treat them carefully enough however, and quantum effects can persist over long distances. Photons have for example been entangled over separations as much as several hundreds of kilometer. And in Bose-Einstein condensates, up to several million of atoms have been brought into one coherent quantum state. Some researchers even believe that dark matter has quantum effects which span through whole galaxies.

9. ...but they dominate the small scales

In quantum mechanics, every particle is also a wave and every wave is also a particle. The effects of quantum mechanics become very pronounced once one observes a particle on distances that are comparable to the associated wavelength. This is why atomic and subatomic physics cannot be understood without quantum mechanics, whereas planetary orbits are entirely unaffected by quantum behavior.

10. Schrödinger’s cat is dead. Or alive. But not both.

It was not well-understood in the early days of quantum mechanics, but the quantum behavior of macroscopic objects decays very rapidly. This “decoherence” is due to constant interactions with the environment which are, in relatively warm and dense places like those necessary for life, impossible to avoid. Bringing large objects into superpositions of two different states is therefore extremely difficult and the superposition fades rapidly.

The heaviest object that has so far been brought into a superposition of locations is a carbon-60 molecule, and it has been proposed to do this experiment also for viruses or even heavier creatures like bacteria. Thus, the paradox that Schrödinger’s cat once raised – the transfer of a quantum superposition (the decaying atom) to a large object (the cat) – has been resolved. We now understand that while small things like atoms can exist in superpositions for extended amounts of time, a large object would settle extremely rapidly in one particular state. That’s why we never see cats that are both dead and alive.

[This post previously appeared on Starts With A Bang.]

Sunday, April 03, 2016

New link between quantum computing and black hole may solve information loss problem

[image source: IBT]

If you leave the city limits of Established Knowledge and pass the Fields of Extrapolation, you enter the Forest of Speculations. As you get deeper into the forest, larger and larger trees impinge on the road, strangely deformed, knotted onto themselves, bent over backwards. They eventually grow so close that they block out the sunlight. It must be somewhere here, just before you cross over from speculation to insanity, that Gia Dvali looks for new ideas and drags them into the sunlight.

Dvali’s newest idea is that every black hole is a quantum computer. And not just any quantum computer, but a quantum computer made of a Bose-Einstein condensate that self-tunes to the quantum critical point. In one sweep, he has combined everything that is cool in physics at the moment.

This link between black holes and Bose-Einstein condensates is based on simple premises. Dvali set out to find some stuff that would share properties with black holes, notably the relation between entropy and mass (BH entropy), the decrease in entropy during evaporation (Page time), and the ability to scramble information quickly (scrambling time). What he found was that certain condensates do exactly this.

Consequently he went and conjectured that this is more than a coincidence, and that black holes themselves are condensates – condensates of gravitons, whose quantum criticality allows the fast scrambling. The gravitons equip black holes with quantum hair on horizon scale, and hence provide a solution to the black hole information loss problem by first storing information and then slowly leaking it out.

Bose-Einstein condensates on the other hand contain long-range quantum effects that make them good candidates for quantum computers. The individual q-bits that have been proposed for use in these condensates are normally correlated atoms trapped in optical lattices. Based on his analogy with black holes however, Dvali suggests to use a different type of state for information storage, which would optimize the storage capacity.

I had the opportunity to speak with Immanuel Bloch from the Max Planck Institute for Quantum Optics about Dvali’s idea, and I learned that while it seems possible to create a self-tuned condensate to mimic the black hole, addressing the states that Dvali has identified is difficult and, at least presently, not practical. You can read more about this in my recent Aeon essay.

But really, you may ask, what isn’t a quantum computer? Doesn’t anything that changes in time according to the equations of quantum mechanics process information and compute something? Doesn’t every piece of chalk execute the laws of nature and evaluate its own fate, doing a computation that somehow implies something with quantum?

That’s right. But when physicists speak of quantum computers, they mean a particularly powerful collection of entangled states, assemblies that allow to hold and manipulate much more information than a largely classical state. It’s this property of quantum computers specifically that Dvali claims black holes must also possess. The chalk just won’t do.

If it is correct what Dvali says, a real black hole out there in space doesn’t compute anything in particular. It merely stores the information of what fell in and spits it back out again. But a better understanding of how to initialize a state might allow us one day – give it some hundred years – to make use of nature’s ability to distribute information enormously quickly.

The relevant question is of course, can you test that it’s true?

I first heard of Dvali’s idea on a conference I attended last year in July. In his talk, Dvali spoke about possible observational evidence for the quantum hair due to modifications of orbits nearby the black hole. At least that’s my dim recollection almost a year later. He showed some preliminary results of this, but the paper hasn’t gotten published and the slides aren’t online. Instead, together with some collaborators, he published a paper arguing that the idea is compatible with the Hawking, Perry, Strominger proposal to solve the black hole information loss, which also relies on black hole hair.

In November then, I heard another talk by Stefan Hofmann, who had also worked on some aspects of the idea that black holes are Bose-Einstein condensates. He told the audience that one might see a modification in the gravitational wave signal of black hole merger ringdowns. Which have since indeed been detected. Again though, there is no paper.

So I am tentatively hopeful that we can look for evidence of this idea in the soon future, but so far there aren’t any predictions. I have an own proposal to add for observational consequences of this approach, which is to look at the scattering cross-section of the graviton condensate with photons in the wave-length regime of the horizon-size (ie radio-waves). I don’t have time to really work on this, but if you’re looking for one-year project in quantum gravity phenomenology, this one seems interesting.

Dvali’s idea has some loose ends of course. Notably it isn’t clear how the condensate escapes collapse, at least it isn’t clear to me and not clear to anyone I talked to. The general argument is that for the condensate the semi-classical limit is a bad approximation, and thus the singularity theorems are rather meaningless. While that might be, it’s too vague for my comfort. The idea also seems superficially similar to the fuzzball proposal, and it would be good to know the relation or differences.

After these words of caution, let me add that this link between condensed matter, quantum information, and black holes isn’t as crazy as it seems at first. In the last years, a lot of research has piled up that tightens the connections between these fields. Indeed, a recent paper by Brown et al hypothesizes that black holes are not only the most efficient storage devices but indeed the fastest computers.

It’s amazing just how much we have learned from a single solution to Einstein’s field equations, and not even a particularly difficult one. “Black hole physics” really should be a research field on its own right.

Friday, April 01, 2016

3 Billion Years Old Math Problem Solved by Prodigy Fetus

[image source:]
For Berta’s mother, the first kick already made clear that her daughter was extraordinary: “This wasn’t just any odd kick, it was a p-wave cross-correlation seismogram.” But this pregnancy exceeded even the most enthusiastic mother’s expectations. Still three months shy of her due date, fetus Berta just published her first paper in the renown mathematics journal “Reviews in Topology.” And it isn’t just any odd cohomological invariance that she has taken on, but one of the thorniest problems known to mathematicians.

Like most of the big mathematical puzzles, this one is easy to understand, and yet even the greatest minds on the planet have so far been unsuccessful proving it. Consider you have a box of arbitrary dimension, filled with randomly spaced polyhedra that touch on exactly three surfaces each. Now you take them out of the box, remove one surface, turn the box by 90 degrees around Donald Trump’s belly button, and then put the polyhedral back into the box. Put in simple terms this immediately raises the question: “Who cares?”

Berta’s proof demonstrates that the proposition is correct. Her work, which has been lauded by colleagues as “masterwork of incomprehensibility” and “a lucid dream caught in equations,” draws upon recent research in fields ranging from differential geometry to category theory to volcanology. The complete proof adds up to 5000 pages. “It’s quite something,” says her mother who was nicknamed “next Einstein’s mom” on Berta’s reddit AMA last week. “We hope the paper will be peer reviewed by the time she makes her driver’s license.”