Dear Dr B: What do physicists mean by “quantum gravity”?

[Image Source: giphy.com]

“please could you give me a simple definition of "quantum gravity"?

J.”

Dear J,

Physicists refer with “quantum gravity” not so much to a specific theory but to the sought-after solution to various problems in the established theories. The most pressing problem is that the standard model combined with general relativity is internally inconsistent. If we just use both as they are, we arrive at conclusions which do not agree with each other. So just throwing them together doesn’t work. Something else is needed, and that something else is what we call quantum gravity.

Unfortunately, the effects of quantum gravity are very small, so presently we have no observations to guide theory development. In all experiments made so far, it’s sufficient to use unquantized gravity.

Nobody knows how to combine a quantum theory – like the standard model – with a non-quantum theory – like general relativity – without running into difficulties (except for me, but nobody listens). Therefore the main strategy has become to find a way to give quantum properties to gravity. Or, since Einstein taught us gravity is nothing but the curvature of space-time, to give quantum properties to space and time.

Just combining quantum field theory with general relativity doesn’t work because, as confirmed by countless experiments, all the particles we know have quantum properties. This means (among many other things) they are subject to Heisenberg’s uncertainty principle and can be in quantum superpositions. But they also carry energy and hence should create a gravitational field. In general relativity, however, the gravitational field can’t be in a quantum superposition, so it can’t be directly attached to the particles, as it should be.

One can try to find a solution to this conundrum, for example by not directly coupling the energy (and related quantities like mass, pressure, momentum flux and so on) to gravity, but instead only coupling the average value, which behaves more like a classical field. This solves one problem, but creates a new one. The average value of a quantum state must be updated upon measurement. This measurement postulate is a non-local prescription and general relativity can’t deal with it – after all Einstein invented general relativity to get rid of the non-locality of Newtonian gravity. (Neither decoherence nor many worlds remove the problem, you still have to update the probabilities, somehow, somewhere.)

The quantum field theories of the standard model and general relativity clash in other ways. If we try to understand the evaporation of black holes, for example, we run into another inconsistency: Black holes emit Hawking-radiation due to quantum effects of the matter fields. This radiation doesn’t carry information about what formed the black hole. And so, if the black hole entirely evaporates, this results in an irreversible process because from the end-state one can’t infer the initial state. This evaporation however can’t be accommodated in a quantum theory, where all processes can be time-reversed – it’s another contradiction that we hope quantum gravity will resolve.

Then there is the problem with the singularities in general relativity. Singularities, where the space-time curvature becomes infinitely large, are not mathematical inconsistencies. But they are believed to be physical nonsense. Using dimensional analysis, one can estimate that the effects of quantum gravity should become large close by the singularities. And so we think that quantum gravity should replace the singularities with a better-behaved quantum space-time.

The sought-after theory of quantum gravity is expected to solve these three problems: tell us how to couple quantum matter to gravity, explain what happens to information that falls into a black hole, and avoid singularities in general relativity. Any theory which achieves this we’d call quantum gravity, whether or not you actually get it by quantizing gravity.

Physicists are presently pursuing various approaches to a theory of quantum gravity, notably string theory, loop quantum gravity, asymptotically safe gravity, and causal dynamical triangulation, for just to name the most popular ones. But none of these approaches has experimental evidence speaking for it. Indeed, so far none of them has made a testable prediction.

This is why, in the area of quantum gravity phenomenology, we’re bridging the gap between theory and experiment with simplified models, some of which motivated by specific approaches (hence: string phenomenology, loop quantum cosmology, and so on). These phenomenological models don’t aim to directly solve the above mentioned problems, they merely provide a mathematical framework – consistent in its range of applicability – to quantify and hence test the presence of effects that could be signals of quantum gravity, for example space-time fluctuations, violations of the equivalence principle, deviations from general relativity, and so on.

Thanks for an interesting question!

We understand gravity just fine, thank you.

Yesterday I came across a Q&A on the website of Discover magazine, titled “The Root of Gravity - Does recent research bring us any closer to understanding it?” Jeff Lepler from Michigan has the following question:

“Q: Are we any closer to understanding the root cause of gravity between objects with mass? Can we use our newly discovered knowledge of the Higgs boson or gravitational waves to perhaps negate mass or create/negate gravity?”

A person by name Bill Andrews (unknown to me) gives the following answer:

“A: Sorry, Jeff, but scientists still don’t really know why gravity works. In a way, they’ve just barely figured out how it works.”

The answer continues, but let’s stop right there where the nonsense begins. What’s that even mean scientists don’t know “why” gravity works? And did the Bill person really think he could get away with swapping “why” for a “how” and nobody would notice?

The purpose of science is to explain observations. We have a theory by name General Relativity that explains literally all data of gravitational effects. Indeed, that General Relativity is so dramatically successful is a great frustration for all those people who would like to revolutionize science a la Einstein. So in which sense, please, do scientists barely know how it works?

For all we can presently tell gravity is a fundamental force, which means we have no evidence for an underlying theory from which gravity could be derived. Sure, theoretical physicists are investigating whether there is such an underlying theory that would give rise to gravity as well as the other interactions, a “theory of everything”. (Please submit nomenclature complaints to your local language police, not to me.) Would such a theory of everything explain “why” gravity works? No, because that’s not a meaningful scientific question. A theory of everything could potentially explain how gravity can arise from more fundamental principles similar to, say, the ideal gas law can arise from statistical properties of many atoms in motion. But that still wouldn’t explain why there should be something like gravity, or anything, in the first place.

Either way, even if gravity arises within a larger framework like, say, string theory, the effects of what we call gravity today would still come about because energy-densities (and related quantities like pressure and momentum flux and so on) curve space-time, and fields move in that space-time. Just that these quantities might no longer be fundamental. We’ve known since 101 years how this works.

After a few words on Newtonian gravity, the answer continues:

“Because the other forces use “force carrier particles” to impart the force onto other particles, for gravity to fit the model, all matter must emit gravitons, which physically embody gravity. Note, however, that gravitons are still theoretical. Trying to reconcile these different interpretations of gravity, and understand its true nature, are among the biggest unsolved problems of physics.”

Reconciling which different interpretations of gravity? These are all the same “interpretation.” It is correct that we don’t know how to quantize gravity so that the resulting theory remains viable also when gravity becomes strong. It’s also correct that the force-carrying particle associated to the quantization – the graviton – hasn’t been detected. But the question was about gravity, not quantum gravity. Reconciling the graviton with unquantized gravity is straight-forward – it’s called perturbative quantum gravity –  and exactly the reason most theoretical physicists are convinced the graviton exists. It’s just that this reconciliation breaks down when gravity becomes strong, which means it’s only an approximation.

“But, alas, what we do know does suggest antigravity is impossible.”

That’s correct on a superficial level, but it depends on what you mean by antigravity. If you mean by antigravity that you can let any of the matter which surrounds us “fall up” it’s correct. But there are modifications of general relativity that have effects one can plausibly call anti-gravitational. That’s a longer story though and shall be told another time.

A sensible answer to this question would have been:

“Dear Jeff,

The recent detection of gravitational waves has been another confirmation of Einstein’s theory of General Relativity, which still explains all the gravitational effects that physicists know of. According to General Relativity the root cause of gravity is that all types of energy curve space-time and all matter moves in this curved space-time. Near planets, such as our own, this can be approximated to good accuracy by Newtonian gravity.

There isn’t presently any observation which suggests that gravity itself emergens from another theory, though it is certainly a speculation that many theoretical physicists have pursued. There thus isn’t any deeper root for gravity because it’s presently part of the foundations of physics. The foundations are the roots of everything else.

The discovery of the Higgs boson doesn’t tell us anything about the gravitational interaction. The Higgs boson is merely there to make sure particles have mass in addition to energy, but gravity works the same either way. The detection of gravitational waves is exciting because it allows us to learn a lot about the astrophysical sources of these waves. But the waves themselves have proved to be as expected from General Relativity, so from the perspective of fundamental physics they didn’t bring news.

Within the incredibly well confirmed framework of General Relativity, you cannot negate mass or its gravitational pull. 

You might also enjoy hearing what Richard Feynman had to say when he was asked a similar question about the origin of the magnetic force:

This answer really annoyed me because it’s a lost opportunity to explain how well physicists understand the fundamental laws of nature.

Experimental Search for Quantum Gravity 2016

Research in quantum gravity is quite a challenge since we neither have a theory nor data. But some of us like a challenge.

So far, most effort in the field has gone into using requirements of mathematical consistency to construct a theory. It is impossible of course to construct a theory based on mathematical consistency alone, because we can never prove our assumptions to be true. All we know is that the assumptions give rise to good predictions in the regime where we’ve tested them. Without assumptions, no proof. Still, you may hope that mathematical consistency tells you where to look for observational evidence.

But in the second half of the 20th century, theorists have used the weakness of gravity as an excuse to not think about how to experimentally test quantum gravity at all. This isn’t merely a sign of laziness, it’s back to the days when philosophers believed they could find out how nature works by introspection. Just that now many theoretical physicists believe mathematical introspection is science. Particularly disturbing to me is how frequently I speak with students or young postdocs who have never even given thought to the question what makes a theory scientific. That’s one of the reasons the disconnect between physics and philosophy worries me.

In any case, the cure clearly isn’t more philosophy, but more phenomenology. The effects of quantum gravity aren’t necessarily entirely out of experimental reach. Gravity isn’t generally a weak force, not in the same way that, for example, the weak nuclear force is weak. That’s because the effects of gravity get stronger with the amount of mass (or energy) that exerts the force. Indeed, this property of the gravitational force is the very reason why it’s so hard to quantize.

Quantum gravitational effects hence were strong in the early universe, they are strong inside black holes, and they can be non-negligible for massive objects that have pronounced quantum properties. Furthermore, the theory of quantum gravity can be expected to give rise to deviations from general relativity or the symmetries of the standard model, which can have consequences that are observable even at low energies.

The often repeated argument that we’d need to reach enormously high energies – close by the Planck energy, 16 orders of magnitude higher than LHC energies – is simply wrong. Physics is full with examples of short-distance phenomena that give rise to effects at longer distances, such as atoms causing Brownian motion, or quantum electrodynamics allowing stable atoms to begin with.

I have spent the last 10 years or so studying the prospects to find experimental evidence for quantum gravity. Absent a fully-developed theory we work with models to quantify effects that could be signals of quantum gravity, and aim to test these models with data. The development of such models is relevant to identify promising experiments to begin with.

Next week, we will hold the 5th international conference on Experimental Search for Quantum Gravity, here in Frankfurt. And I dare to say we have managed to pull together an awesome selection of talks.

We’ll hear about the prospects of finding evidence for quantum gravity in the CMB (Bianchi, Krauss, Vennin) and in quantum oscillators (Paternostro). We have a lecture about the interface between gravity and quantum physics, both on long and short distances (Fuentes), and a talk on how to look for moduli and axion fields that are generic consequences of string theory (Conlon). Of course we’ll also cover Loop Quantum Cosmology (Barrau), asymptotically safe gravity (Eichhorn), and causal sets (Glaser). We’re super up-to-date by having a talk about constraints from the LIGO gravitational wave-measurements on deviations from general relativity (Yunes), and several of the usual suspects speaking about deviations from Lorentz-invariance (Mattingly), Planck stars (Rovelli, Vidotto), vacuum dispersion (Giovanni), and dimensional reduction (Magueijo). There’s neutrino physics (Paes), a talk about what the cosmological constant can tell us about new physics (Afshordi), and, and, and!

You can download the abstracts here and the timetable here.

But the best is I’m not telling you this to depress you because you can’t be with us, but because our IT guys still tell me we’ll both record the talks and livestream them (to the extent that the speakers consent of course). I’ll share the URL with you here once everything is set up, so stay tuned.

Update:Streaming link will be posted on the institute's main page briefly before the event. Another update: Lifestream is available here.

I’ve read a lot of books recently

[Reading is to writing what eating is to...]

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Dreams Of A Final Theory: The Scientist's Search for the Ultimate Laws of Nature
Steven Weinberg
Vintage, Reprint Edition (1994)

This book appeared when I was still in high school and I didn’t take note of it then. Later it seemed too out-of-date to bother, but meanwhile it’s almost become a historical document. Written with the pretty explicit aim to argue in favor of the Superconducting Supercollider (a US-proposal for a large particle collider that was scraped in the early 90s), it’s the most flawless popular science book about theoretical physics I’ve ever come across.

Weinberg’s explanations are both comprehensible and remarkably accurate. The book contains no unnecessary clutter, is both well-structured and well written, and Weinberg doesn’t hold back with his opinions, neither on religion nor on philosophy.

It’s also the first time I’ve tried an audio-book. I listened to it while treadmill running. A lot of sweat went into the first chapters. But I gave up half through and bought the paperback which I read on the plane to Austin. Weinberg is one of the people I interviewed for my book.

Lesson learned: Audiobooks aren’t for me.

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Truth And Beauty – Aesthetics and Motivations in Science
Subrahmanyan Chandrasekhar
University of Chicago Press (1987)

I had read this book before but wanted to remind me of its content. It’s a collection of essays on the role of beauty in physics, mostly focused on general relativity and the early 20th century. Along historical examples like Milne, Eddington, Weyl, and Einstein, Chandrasekhar discusses various aspects of beauty, like elegance, simplicity, or harmony. I find it too bad that Chandrasekhar didn’t bring in more of his own opinion but mostly summarizes other people’s thoughts.

Lesson learned: Tell the reader what you think.

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Truth or Beauty – Science and the Quest for Order
David Orrell
Yale University Press (2012)

In this book, mathematician David Orrell argues that beauty isn’t a good guide to truth. It’s an engagingly written book which covers a lot of ground, primarily in physics, from helocentrism to string theory. But Orrell tries too hard to make everything fit his bad-beauty narrative. Many of his interpretations are over-the-top, like his complaint that

 “[T]he aesthetics of science – and particularly the “hard” sciences such as physics –have been characterized by a distinctly male feel. For example, feminist psychologists have noted that the classical picture of the atom as hard, indivisible, independent, separate, and so on corresponds very closely to the stereotypically masculine sense of self. If must have come as a shock to the young, male, champions of quantum theory when they discovered that their equations describing the atom were actually soft, fuzzy, and uncertain –in other words, stereotypically female.”

He further notes that many male physicists like to refer to nature as “she,” that Gell-Mann likes the idea of using particle accelerators to penetrate deeper (into the structure of particles), and quotes Lee Smolin’s remark that “the most cherished goal in physics, as in bad romance novels, is unification.” This is just to illustrate the, erm, depth of Orrell’s arguments.

In summary, it’s a nice book, but it’s hard to take Orrell’s argument seriously. Or maybe the whole thing was a joke to begin with.

Lesson learned: Don’t try to explain everything.

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The End Of Physics - The Myth Of A Unified Theory
David Lindley
Basic Books (1994)

This is a strange book. While reading, I got the impression that the author is constantly complaining about something, but it didn’t become clear to me what. Lindley tells the story of how physicists discovered increasingly more fundamental and also more unified laws of nature, and how they are hoping to finally develop a theory of everything. This, so he writes, would be the end of physics. Just that, as he explains in the next sentence, it of course wouldn’t be the end of physics.

Lindley likes words and likes to use a lot of them. Consequently the book reads like he wanted to cram in the whole history of physics, from the beginning to the end, with him having the last word.

His argument for why a theory of everything would remain a “myth” is essentially that it would be hard to test, something that nobody can really disagree on. But “hard to test” doesn’t mean “impossible to test,” and Lindley is clearly out of his water when it comes to evaluating experimental prospects of, say, probing quantum gravity, so he sticks with superficial polemics. Of course the book is 20 years old, and I can’t blame the author for not knowing what’s happened since, but from today’s perspective his rant seems baseless.

In summary, it’s a well-written book, but it has a fuzzy message. (Also, the reprint quality is terrible.)

Lesson learned: If you have something to say, say it.

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Why Beauty Is Truth – A History of Symmetry
Ian Stewart
Basic Books (2007)

This is a book, not about the physics, but the mathematics of symmetries, symmetry groups, Lie groups, Lie algebras, quaternions, global symmetries, local symmetries, and all that. Steward also discusses the relevance of these structure for physics, but his emphasis is on it being an application of mathematics. The book is held together by stories of the mathematicians who lead the way. The title of the book is somewhat misleading. Steward actually doesn’t discuss much the question “why” beauty is truth. He merely demonstrates along examples that many truths are beautiful.

It’s a pretty good book, both interesting and well-written, if somewhat too long for my taste. It doesn’t seem to have gotten the attention it deserves.

Lesson learned: It’s hard to write a popular science book that anyone will still recall a decade later.

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Eyes On The Sky: A Spectrum of Telescopes
Francis Graham-Smith
Oxford University Press (2016)

This is a book about telescopes, from then to now, from the radio regime to gamma rays. It’s not a book about astrophysics, it’s not a book about cosmology, and it’s not a book about history. It’s a book about telescopes. It is a thoroughly useful book, full of facts and figures and images, but you need to be really interested in telescopes to get through it. I read this book because I wanted to write a paragraph about the development of modern telescopes but figured I didn’t actually know much about modern telescopes. Now I’m much wiser.

Lesson learned: If you need to read a 200 pages book to write a single paragraph, you’ll never get done.

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Beauty and Revolution in Science
James McAllister
Cornell University Press (1999)

Philosopher James McAllister reexamines the Kuhnian idea of paradigm changes. He proposes that it should be amended, and argues that what characterizes a revolution is not the change of the entire scientific paradigm, but merely the change of aesthetic ideals. To back up his argument, he discusses several historical cases. This is not a popular science book, and it’s not always the most engaging read, but I have found it to be very insightful. It is somewhat unfortunate though that he didn’t spend more time illuminating the social dynamics that goes with the prevalence of beauty ideals in science.

Lesson learned: Philosophy isn’t dead.

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Higher Speculations
Helge Kragh
Oxford University Press (2011)

Kragh’s is a book about the failure of speculative ideas in physics. The steady state universe, mechanism, cyclic models of the universe, and various theories of everything are laid out in historical perspective. I have found this book both interesting and useful, but some parts are quite heavy reads. Kragh doesn’t offer an analysis or draws a lesson, and he mostly restrains from judgement. He simply tells the reader what happened.

Lesson learned: Even smart people sometimes believe really strange things.

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Supersymmetry: Unveiling The Ultimate Laws Of Nature
Gordy Kane
Basic Books (2001)

Particle physicist Gordon Kane explains why the supersymmetric extension of the standard model has become so popular and how it could be tested. Whether or not you are convinced by supersymmetry, you get to learn a lot about particle physics. It’s a straight-forward pop-science book that does a good job explaining why theorists have spent so much time on supersymmetry.

Lesson learned: You don’t need to write fancy to write well.

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Nature’s Blueprint - Supersymmetry and the Search for a Unified Theory of Matter and Force
Dan Hooper
Smithsonian (2008)

A book about high energy particle physics, the standard model, unification and the appeal of supersymmetry. It’s a well-written book that gives the reader a pretty good idea how particle physicists work and think. Hooper does a great job getting across the excitement that comes with the hope of being about to discovery a new fundamental law of nature. The book’s publication date was well timed, just before the LHC started taking data.

Lesson learned: Your book might become history faster than you think.

Sorry, the universe wasn’t made for you

Last month, game reviewers were all over No Man’s Sky, a new space adventure launched to much press attention. Unlike previous video games, this one calculates players’ environments from scratch rather than revealing hand-crafted landscapes and creatures. The calculations populate No Man’s Sky’s virtual universe with about 10¹⁹ planets, all with different flora and fauna – at least that’s what we’re told, not like anyone actually checked. That seems a giganourmous number but is still less than there’s planets in the actual universe, estimated at roughly 10²⁴.

User’s expectations of No Man’s Sky were high – and were highly disappointed. All the different planets, it turns out, still get a little repetitive with their limited set of options and features. It’s hard to code a universe as surprising as reality and run it on processors that occupy only a tiny fraction of that reality.

Theoretical physicists, meanwhile, have the opposite problem: The fictive universes they calculate are more surprising than they’d like them to be.

Having failed on their quest for a theory of everything, in the area of quantum gravity many theoretical physicists now accept that a unique theory can’t be derived from first principles. Instead, they believe, additional requirements must be used to select the theory that actually describes the universe we observe. That, of course, is what we’ve always done to develop theories – the additional requirements being empirical adequacy.

The new twist is that many of these physicists think the missing observational input is the existence of life in our universe. I hope you just raised an eyebrow or two because physicists don’t normally have much business with “life.” And indeed, they usually only speak about preconditions of life, such as atoms and molecules. But that the sought-after theory must be rich enough to give rise to complex structures has become the most popular selection principle.

Known as “anthropic principle” this argument allows physicists to discard all theories that can’t produce sentient observers on the rationale that we don’t inhabit a universe that lacks them. One could of course instead just discard all theories with parameters that don’t match the measured values, but that would be so last century.

The anthropic principle is often brought up in combination with the multiverse, but logically it’s a separate argument. The anthropic principle – that our theories must be compatible with the existence of life in our universe – is an observational requirement that can lead to constraints on the parameters of a theory. This requirement must be fulfilled whether or not universes for different parameters actually exist. In the multiverse, however, the anthropic principle is supposedly the only criterion by which to select the theory for our universe, at least in terms of probability so that we are likely to find ourselves here. Hence the two are often discussed together.

Anthropic selection had a promising start with Weinberg’s prescient estimate for the cosmological constant. But the anthropic princple hasn’t solved the problem it was meant to solve, because it does not single out one unique theory either. This has been known at least since a decade, but the myth that our universe is “finetuned for life” still hasn’t died.

The general argument against the success of anthropic selection is that all evidence for the finetuning of our theories explores only a tiny space of all possible combinations of parameters. A typical argument for finetuning goes like this: If parameter X was only a tiny bit larger or smaller than the observed value, then atoms couldn’t exist or all stars would collapse or something similarly detrimental to the formation of large molecules. Hence, parameter X must have a certain value to high precision. However, these arguments for finetuning – of which there exist many – don’t take into account simultaneous changes in several parameters and are therefore inconclusive.

Importantly, besides this general argument there also exist explicit counterexamples. In the 2006 paper A Universe Without Weak Interactions, Harnik, Kribs, and Perez discussed a universe that seems capable of complex chemistry and yet has fundamental particles entirely different from our own. More recently, Abraham Loeb from Harvard argued that primitive forms of life might have been possible already in the early universe under circumstances very different from today’s. And a recent paper (ht Jacob Aron) adds another example:

Stellar Helium Burning in Other Universes: A solution to the triple alpha fine-tuning problem
By Fred C. Adams and Evan Grohs
1608.04690 [astro-ph.CO]

In this work the authors show that some combinations of fundamental constants would actually make it easier for stars to form Carbon, an element often assumed to be essential for the development of life.

This is a fun paper because it extends on the work by Fred Hoyle, who was the first to use the anthropic principle to make a prediction (though some historians question whether that was his actual motivation). He understood that it’s difficult for stars to form heavy elements because the chain is broken in the first steps by Beryllium. Beryllium has atomic number 4, but the version that’s created in stellar nuclear fusion from Helium (with atomic number 2) is unstable and therefore can’t be used to build even heavier nuclei.

Hoyle suggested that the chain of nuclear fusion avoids Beryllium and instead goes from three Helium nuclei straight to carbon (with atomic number 6). Known as the triple-alpha process (because Helium nuclei are also referred to as alpha-particles), the chances of this happening are slim – unless the Helium merger hits a resonance of the Carbon nucleus. Which it does if the parameters are “just right.” Hoyle hence concluded that such a resonance must exist, and that was later experimentally confirmed.

Adams and Groh now point out that there are other sets of parameters altogether in which case Beryllium is just stable and the Carbon resonance doesn’t have to be finely tuned. In their paper, they do not deal with the fundamental constants that we normally use in the standard model – they instead discuss nuclear structure which has constants that are derived from the standard model constants, but are quite complicated functions thereof (if known at all). Still, they have basically invented a fictional universe that seems at least as capable of producing life as ours.

This study is hence another demonstration that a chemistry complex enough to support life can arise under circumstances that are not anything like the ones we experience today.

I find it amusing that many physicists believe the evolution of complexity is the exception rather than the rule. Maybe it’s because they mostly deal with simple systems, at equilibrium or close by equilibrium, with few particles, or with many particles of the same type – systems that the existing math can deal with.

It makes me wonder how many more fictional universes physicists will invent and write papers about before they bury the idea that anthropic selection can single out a unique theory. Fewer, I hope, than there are planets in No Man’s Sky.