This weekend at Caltech we had a small but very fun conference: the “Physics of the Universe Summit,” or POTUS for short. (The acronym is just an accident, I’m assured.) The subject matter was pretty conventional — particle physics, the LHC, dark matter — but the organization was a little more free-flowing and responsive than the usual parade of dusty talks.
One of the motivating ideas that was mentioned more than once was the famous list of important problems proposed by David Hilbert in 1900. These were Hilbert’s personal idea of what math problems were important but solvable over the next 100 years, and his ideas turned out to be relatively influential within twentieth-century mathematics. Our conference, 110 years later and in physics rather than math, was encouraged to think along similarly grandiose lines.
And indeed people had done exactly that, especially ten years ago when the century turned: see representative lists here and here. I asked the organizers if anyone was taking a swing at it this time, and was answered in the negative. I was scheduled to give one of the closing summaries, and this sounded more interesting than what I actually had planned, so naturally I had to step up.
Here are the slides from my presentation, where you can find some elaboration on my choices.
And here’s the actual list:
- What breaks electroweak symmetry?
- What is the ultraviolet extrapolation of the Standard Model?
- Why is there a large hierarchy between the Planck scale, the weak scale, and the vaccum energy?
- How do strongly-interacting degrees of freedom resolve into weakly-interacting ones?
- Is there a pattern/explanation behind the family structure and parameters of the Standard Model?
- What is the phenomenology of the dark sector?
- What symmetries appear in useful descriptions of nature?
- Are there surprises at low masses/energies?
- How does the observable universe evolve?
- How does gravity work on macroscopic scales?
- What is the topology and geometry of spacetime and dynamical degrees of freedom on small scales?
- How does quantum gravity work in the real world?
- Why was the early universe hot, dense, and very smooth but not perfectly smooth?
- What is beyond the observable universe?
- Why is there a low-entropy boundary condition in the past but not the future?
- Why aren’t we fluctuations in de Sitter space?
- How do we compare probabilities for different classes of observers?
- What rules govern the evolution of complex structures?
- Is quantum mechanics correct?
- What happens when wave functions collapse?
- How do we go from the quantum Hamiltonian to a quasiclassical configuration space?
- Is physics deterministic?
- How many bits are required to describe the universe?
- Will “elementary physics” ultimately be finished?
Clearly I cheated somewhat by squeezing multiple questions into single problems. But the real challenge was thinking sufficiently big to come up with problems that people a century from now would agree are interesting. And I stuck to “elementary physics” — particle physics, gravitation, cosmology — just because I’m not competent to pick out the important problems in any other fields. Twenty-four, of course, because Hilbert had 23, and we had to go one better. There was certainly no shortage of candidates; I was coming up with more good problems and throwing out old ones right up until the last minute. Any obvious ones I missed?
January 15th, 2010 at 9:04 am
Hey Sean,
I really liked (16) and (21). (16), because to be direct it’s actually really weird. Almost the whole of existence will be lived in a deSitter background, why not us?
(21) because it’s an interesting problem, even from a mathematical viewpoint. I never really thought about it. Even figuring out what is “the” quantisation of certain operators is hard enough, but figuring things out in reverse is something I haven’t really seen much on.
Thanks for that!
January 15th, 2010 at 9:32 am
Many of these problems might be approached by condensed matter/ ultra-cold atoms etc. Eg., (21) and (18). The quantum-classical boundary is now being experimentally probed. Wojciech Zurek has published lots of general interest stuff in this area.
http://public.lanl.gov/whz/
January 15th, 2010 at 9:57 am
I ♥ #14. That’s the question that originally got me into science.
January 15th, 2010 at 10:20 am
“Is quantum mechanics correct?”
Seriously? We already know it’s not: neither standard quantum mechanics or quantum field theory can include the effects of gravity. Quantum mechanics is certainly an approximation that works astoundingly well in the right regimes, but “correct” it’s obviously not.
January 15th, 2010 at 10:25 am
How gravity works on macroscopic scales? Excuse me, but I thought that was pretty well known stuff
January 15th, 2010 at 10:51 am
I disagree with the opinion why because Hilbert has 23 problems, then we should propose 24 or one more than Hilbert’s. It is the quality of each problems which matter, not the number.
Furthermore, I found that some of the problems you propose are more or less a recantation of the other, or tend to be philosophical rather than physical/scientific.
#1-#5 are interrelated in some ways.
#6 OK.
#7 will not have a satisfying answer, related to #1-#5.
#8 ditto
#9 This is phenomenology, not fundamental theory.
#10 Don’t you believe in GR ?
#11 OK.
#12 Correspondence principle – GR.
#13 Quantum fluctuations – HUP.
#14 is not even wrong! Once we know what is beyond the observable universe – that part become observable!
#15 Boltzmann solved it already, also Shannon.
#16 don’t have enough understanding to comment.
#17 don’t have enough understanding to comment.
#18 Phenomenological – not fundamental.
#19 You should never doubt QM like this, because it works and it is very unlikely to change. What you should have asked if there is an even more fundamental theory than QM.
#20 Ditto.
#21 Correspondence principle.
#22 Philosophical.
#23 Technical – not fundamental – and what do you want to do with it ?
#24 Again, philosophical.
I think your list of 24 can be squeezed into a smaller list.
#1 What is the nature of electroweak symmetry breaking.
#2 What is the explanation behind dark sector (dark energy and dark sector) — from your number #6
#3 What is the fundamental topology of spacetime .. — from your #11.
#4 Is there an even more fundamental theory underlying QM.
#5 What is the quantum formulation of gravity.
My own:
#1 What is the origin of neutrino mass. We know that neutrinos have masses, and currently there is no testable/proven theory which explain the origin of neutrino mass.
#2 Is there a physical theory which unifies tachyonic universe (v > c) and non-tachyonic universe (v < c).
#3 What is the true origin of matter-antimatter asymmetry, CP violation, CKM matrix elements and all that.
#4 What is the true fundamental unit of electric charges [beyond ad hoc explanation about colour, generations, etc].
#5 Do magnetic monopoles exist, and if exists, which kind ?
All answers to those those must not just a theoretical answer, but also experimental results.
For purely mathematical physics ones, my problem is:
A rigorous and mathematically sound definition of functional integration (that’s path integral to physicists) — probably the most important discovery in 20th century
mathematics together with Noether’s theorem.
January 15th, 2010 at 11:02 am
I think just as the questions reveal much about Sean, the reactions to them reveal much about the readers. I guess I belong to the same basic tribe that Sean himself does, so I don’t find it surprising that I am mostly satisfied.
January 15th, 2010 at 11:04 am
@Random Guy
I share your sentiments about (14) – Perhaps it should be expressed: can we push the boundaries of what is currently observable, and if so what will we see.
For (21) you glibly state “correspondence principle” – but this is not currently well defined in many cases. I think at least the details, and maybe the fundamentals, are still an open problem.
January 15th, 2010 at 11:58 am
Isn’t gravity at macroscopic scale explained by general relativity as Per no 5 said?
Thanks
January 15th, 2010 at 12:11 pm
20
January 15th, 2010 at 12:50 pm
I often marvel at the strange observable similarities of watching powdered sugar being stirred in my coffee cup and looking at Hubble pictures of a typical galaxy wheel. Does “dark matter” have liquid-like properties that’s been “stirred” ?
January 15th, 2010 at 1:19 pm
I love the phrase “Why has effective field theory forsaken us?”
I also quite like the picture of Fritz Zwicky on the slide for question 7, about which symmetries are useful. Presumably it’s an established fact that the S^2 bastard symmetry is quite useful.
January 15th, 2010 at 2:14 pm
Sean, you may be interested in this Wikipedia article on unsolved problems in physics:
http://en.wikipedia.org/wiki/Unsolved_problems_in_physics
January 15th, 2010 at 2:49 pm
What is the ultraviolet extrapolation of the Standard Model?
January 15th, 2010 at 6:06 pm
RandomGuy: seriously? I don’t even do fundamental physics, and your comments still seem poorly thought-out to me. And… I’m pretty sure the one-upping Hilbert thing was a joke.
Among other things:
#15 has been a major component of Sean’s research for years, and on numerous occasions he’s explained why Boltzmann only solved half the problem (note Sean says boundary condition, not evolution).
#16 You know that you don’t understand this question. Congrats, but that should have tipped you off to the fact that you don’t understand #15 either. They’re linked.
#22 is philosophical, but also clearly a physics question. E.g., Bell’s inequality.
#23 could be fundamental – look at the holographic principle.
And I say all this as someone who does observational astrophysics, and generally considers himself unqualified to comment on fundamental physics. Apparently you don’t have the same feeling, despite not even being a physicist (inferring from your comment on physics lingo).
January 15th, 2010 at 10:33 pm
It’s an excellent list. However, as some others above, I don’t know what you mean with #10 though.
I have my top 10 here.
January 15th, 2010 at 11:26 pm
Here is the answer to number ten.
BLACK HOLES, EXPANSION, AND DARK ENERGY
In the continuum of space and time, exists the dichotomy of matter and energy. All things exist as both matter and energy, but are experienced as one or the other.
As energy, all things exist as wave patterns. Most wave patterns are interferences of simpler wave patterns. The simplest wave forms are those that do not interfere with other waves. These simplest wave forms hold their shape as they propagate. There are three such forms.
The first such wave form is seen in three dimensions as the spherical expansion wave of a bomb blast, and in two dimensions as the circular wave of expansion on the water where a rock was tossed in. The second wave form is seen in three dimensions as the cone of sonic boom following an aircraft traveling faster than sound, and in two dimensions as the V-wake on the water where the boat is traveling faster than the water wave. The third wave form is seen in three dimensions as the propagation torus of a smoke ring and is seen in two dimensions as the double vortexes of an oar stroke on the water.
The Torus is a particle of discrete exchange, from one point to another. The object exchanges position and momentum. While the spherical wave shows position, and the conic wave shows momentum, the torus shows both at the same time, and has a dynamic finite unbounded reality. The volumes of the cone, sphere, and torus are mathematically related as statics.
The Universe is a local density fluctuation. (a wave pulse) On this local density fluctuation wave, lesser wave forms may exist. All simple wave forms are also local density fluctuations, and as such are indeed universes in their own right, where other waves may exist.
Consider the torus as a universe. Einstein said that gravity is indistinguishable from acceleration. There is both linear acceleration and angular acceleration. Although the torus as a whole travels in a straight line, every local point on the torus travels in a circle and experiences angular acceleration.
The rubber sheet model of gravity and curved space translates directly to the propagating torus with angular acceleration. Acceleration is downward on the rubber sheet and outward on the torus. The tension field that separates the inside of the torus from the outside holds its shape as a simple two dimensional field of space and time just as the rubber sheet does.
Experimentally verifiable is that a big fat slow smoke ring generated in a room with very still air will eventually possess a bulge that travels in a circle on the surface of the smoke ring. This bulge, being a gravitational depression, gathers more of the energy of the field toward itself. Finally the bulge gathers enough material to collapse the field and eject a new, smaller smoke ring out in the same direction as the first torus. This collapse is a black hole to the first torus, and a white hole to the second torus, where the axes of space and time in that second torus have reversed.
While gravity tends to draw depressions together locally on a dynamic torus, even to the point of field collapse, other areas on a torus expand and contract globally as the torus propagates along without regard to local phenomenon on the surface. This is quintessence. The inertia of the torus to propagate is its dark energy. This is a two-dimensional example of the process that we experience in three dimensions.
From structureofexistence.com by Dan Echegoyen 951-204-0201
–
Dan Echegoyen
author of StructureOfExistence.com
(951) 204-0201
January 15th, 2010 at 11:29 pm
The book is free on the web
structureofexistence.com
January 16th, 2010 at 3:36 am
Sean, it is interesting to compare your list of 24 points to this one:
http://www.motionmountain.net/research/index.html#mill
This other list, which also claims completeness, is more muted.
And it contains some points that you do not list, such as finding
the origin of the least action principle.
January 16th, 2010 at 4:16 am
Interesting list. The other two are as well.
There is also an wikipedia article called “Unsolved problems in physics”. You and the readers here should contribute!
January 16th, 2010 at 5:43 am
Most of Hilbert’s problems are very well-defined mathematical statements, to be proven true or untrue. Fundamental physics is not quite so clear-cut, so this kind of list doesn’t quite seem as appropriate. I think this is reflected in the fact that most of your problems are quite vague, or ambiguous. Still, it’s interesting to think about these things.
I think problems 1, 2, and 7 are all interesting, reasonably well-defined, at least partially resolvable, and potentially fascinating, so I will endorse those three!
@Dan Echegoyen
Oh dear…
@ SU(N) is FU(N)…
FU(2).
January 16th, 2010 at 6:20 am
[...] Los 24 problemas de Sean Carroll para la físicos de partículas del s. XXI blogs.discovermagazine.com/cosmicvariance/2010/01/15/24-ques… por mezvan hace 2 segundos [...]
January 16th, 2010 at 7:56 am
I’m an engineer not a scientist, but I think that #18 will be the next major thrust in physics once a satisfactory theory of the micro world is developed: How do we go from fundamental particles to human brains or other complex structures. Are there emergent “laws” of organization?
January 16th, 2010 at 8:10 am
Instead of #19 & 20:
Is the quantum world non-local, non-causal, or non-deterministic? (must be one…)
January 16th, 2010 at 10:35 am
Somebody seems to be doing an awfully good job at keeping this conference secret. Is there a link for other talks?
January 16th, 2010 at 12:29 pm
[...] another such list (this time of 24 problems) by Sean [...]
January 16th, 2010 at 5:10 pm
There is only one question of modern physics that anyone who isn’t specialist cares about and that is: Time? Maybe some of the questions you meantioned are part of that, but time is what people care about.
January 16th, 2010 at 9:38 pm
I’m even more interested in question #25. A generation ago when I was studying physics, some of Sean’s 24 questions hadn’t yet even been fathomed. What questions will we be asking some 30 years hence?
January 17th, 2010 at 2:32 am
@Ben Lillie:
What is the ‘bastard S^2 symmetry’? I can’t find any reference to S^2 symmetry on google. S^2 the sphere isn’t a group.
is there something i’m missing? i can’t find anything on wikipedia about an S^2 symmetry
January 17th, 2010 at 5:59 am
Some more;
Science assumes Law of Uniformity of Nature and Law of Causality.What if it is not so?
If our receiving light from distant stars prove the existence of objects in the past, what about our existence?Are we in the past, present or future?
Why can’t we conceive more geometric patterns other than what we have now,like Square,Rectangle,Modifications of these two,Circle?
What is Time and Space?
In the light of Quantum Theory,should we not change our Perception of Physics and our understanding of Laws as we know of them now.
January 17th, 2010 at 7:30 am
Is spacetime a manifold – and if not why does it mostly look like one ?
Is there a fundamental mathematical idea that would revolutionize physics ?
Why is ordinary arithmetic so unreasonably effective ?
Is Math just a tool in the service of Physics ?
January 17th, 2010 at 8:44 am
@eigenlambda
Zwicky coined the term “Spherical Bastard”, i.e. a bastard any way you look at them. Bit of a strained joke on my part, and you’re right, I should have called it the O(3) bastard symmetry.
January 17th, 2010 at 10:05 am
On Space and Time Kindly read my blog under Time a Non- Linear theory at ramanan50.wordpress.com and offer your views.
January 17th, 2010 at 6:15 pm
This is a great list. Many of them stump me. Dumb me.
Comments:
#16. Is this the unfunny haha way of asking “I am a Boltzmann Brain?”
#21. This seems to be a very general question in statistical mechanics.
More questions (some of them wacko, but fun)
1. You should add a cool question about time (you are now a man about from eternity to here). How about “Does time have the same characteristics (effects) on all length scales?”
2. Maybe too fuzzy and weird is “Is there an elementary particle equivalent of a ratchet?” That is, are space and time different only because of the characteristics of what they contain? An answer might lead to a resolution between objectiivism and a weakened sort of subjectivism.
3. People (not just physicists) devote a lot of time thinking about time travel in the sense of going back to a previous point in time, but has anybody thought about how hard (quantitatively) it is for us humans stuck to earth to travel back to the same point in space?
Finally, I think that the acceleration of galaxies away from each other is the most important cosmological problem of the century. So is there an easy way to lay the following idea to rest?
4. The acceleration of the galaxies away from each other is caused by positive static electrical charges on matter in galaxies screened by an equal amount (but more spread out) of screening negative charges in intergalactic space, and this imbalance is a simple result of stellar formation and Boltzmann statistics (more fast electrons than protons leak out of galaxies into intergalactic space). Forgive me if I’m wrong but didn’t Poincare posit an electromagnetically dominated universe? Has Gravity’s century dispelled Poincare’s ghost?
January 17th, 2010 at 6:43 pm
Sorry, I noticed the link to the slides themselves after I posted. You already have a cool question about time, and my comment about #16 also applies to #17. If #16 and #17 are Boltzmann Brain questions, my take is that simulations be damned, there’s nothing fruitful to be learned by the Russel paradox and the simple answer is that it is easier (by some large cardinal number) to make a big universe with many observers (but much smaller than that cardinal number) than a very small self aware universe.
January 17th, 2010 at 7:35 pm
Liked that post! I’ve also written about these questionable assumptions just here
http://bruceleeeowe.wordpress.com/2009/08/01/our-questionable-assumptions/
I think these are nice…
January 18th, 2010 at 8:40 am
more fiendish questions
Is it even possible to explain why space is 3d without also explaining Hydrogen ?
Why do particles have a complex phase ?
Is the good behavior of the universe contingent on Alternativitity ?
January 19th, 2010 at 5:15 pm
A lot of people have jumped on the question “10: How does gravity work on macroscopic scales?” and glibly said “Don’t you believe in GR” or related answers.
This totally glosses over the fact that GR only describes how gravity *behaves*, but doesn’t do squat to explain the mechanism.
How does the Andromeda Galaxy create a gravitational field that affects our galaxy? What’s the mechanism? Do gravitons exist? If so, where do they fit in the Standard Model? If it’s just curved spacetime with no mediator particle, how do other locations “know” that a mass is in motion? Consider tidal effects on earth due to the sun and moon – as things move in their orbits, what mechanism makes the curves in spacetime move to match? So many questions, so little time….
January 20th, 2010 at 10:04 am
I see some questions that hit all around it, but unless I’m missing something fundamental and a question that you included that I don’t understand covers this, there is an obvious question that is missing from your list:
What CAUSED the big bang?
I get the impression that physicists don’t want to think about this question either because they think it was god, and they don’t want to be ridiculed, or they think any attempt to investigate the question is in the realm of theology instead of physics and they don’t want to be ridiculed. Well, I don’t buy the “god” theory, but neither do I believe the question is inherently unanswerable.
We understand what causes TNT to explode, what causes a volcano to erupt, what causes a big cloud of hydrogen in space to ignite in a fusion reaction, and what causes that cloud of hydrogen to eventually explode and spew heavy metals all over the local galaxy. What we don’t know, as far as I’ve heard, is what caused the big bang. (Please correct my ignorance if the question has already been answered.) It seems like a very interesting question to me. After all, if “that” caused it, what’s stopping “that” from causing another one halfway between the Earth and the Moon the day after tomorrow? Or is nothing stopping it?
January 22nd, 2010 at 1:44 pm
Everybody seems to be grappling with #10. I would be willing to bet ( unless I am missing something here) that he is referring to how General Relativity either needs to explain or must still be valid despite the discovery of “dark energy”. The universe is expanding at an increasing rate….. Why? Gravity is supposed to be an attractive force so why isn’t the expansion slowing down? Does gravity just ‘magically’ generate negative pressure at large distances (i.e. macroscopic perspectives)? If so, why? If not, what is this other energy and how is it related to gravity? General relativity doesn’t address this but it should.
January 22nd, 2010 at 1:50 pm
@ DP in CA (Post 39)
I would imagine most physicists avoid the question “What caused the big bang” because it is an inherently nonsensical question. If we can conclude that time is inseparable from space (i.e. space-time) and we also conclude that space-time didn’t “exist” until after the expansion, then words like ‘before’ are inconsistent and meaningless.
Hell, I would argue that the question, “How does one correctly think about and/or phrase questions relating to the big bang?” could be added to the list, provided of course that I thought it was possible to answer, which I don’t.
January 26th, 2010 at 7:24 am
Was Lee Smolin there? I just happen to be reading his 2006 ‘The Trouble with Physics’, decrying the general lack of progress in the field over the past 3-4 decades since the Standard Model, a troubling groupthink regarding string theory, and his 5 great problems in theoretical physics (1. unification of GR and QM into quantum gravity; 2. foundational problems of QM (relationship between the real and the formal worlds); 3. unification of the particles and forces; 4. the bases for the setting of the free constants in the Standard Model in nature; and 5. explanation of dark matter and dark energy). It’s interesting to consider the philosophical debate between someone like Lisa Randall and Smolin – both believe theory has to be tied to experimental data, not just beauty of the theory – but she seems to promote building up understanding from solving small problems, while he seems to think that approaching from small problems or big problems depend on the times, and these times call for thinking about the big problems.
January 26th, 2010 at 7:46 am
[...] information about this that seems to be available on the web is Sean Carroll’s blog posting here, where he gives a link to the slides of his [...]
January 26th, 2010 at 9:28 am
The current Big Bang Model is a QFT in a curved spacetime. Unfortunately, no such theory is mathematically well-defined; in spite of this, theoreticians claim to extract information from this hypothetical theory. On the other hand, the super-classical limit of the not mathematically well-defined QED in a curved spacetime is the mathematically well-defined Einstein-Maxwell-Dirac system. (One could get a similar system for the standard model.) As a super theory, EMD violates the positivity condition in the Penrose-Hawking Singularity Theorem. Thus, it is possible that there would be complete solutions without any singularities-Yau has in fact constructed some. Furthermore, it is known that the Einstein-Maxwell-Dirac system admits of solitonic solutions, i.e., classical electrons and photons. This is the kind of theory Einstein was hoping for. EMD is also a totally geometricized theory as a non-commutative geometry; here, the charge e and the mass m of the electron are geometric invariants of the non-commutative geometry analogous to pi!
January 26th, 2010 at 1:33 pm
I think the ultimate questions do hover on the edge of nonsense. Decrying questions like “what caused the big bang” seems to violate the spirit of a conference that encourages experts to ask big questions. If they are to go out on a limb in asking these questions, we must keep our part of the bargain by not mercilessly attacking them for doing so. The fundamental questions, i.e. “why is there something instead of nothing” are the most interesting, the reason that many people care about theoretical physics to devote their lives to it, and the most difficult to state as a question using concrete language that may lead to a falsifiable theory.
February 25th, 2010 at 1:01 pm
[...] 24 Questions for Elementary Physics [...]