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?
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!
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/
I ♥ #14. That’s the question that originally got me into science.
“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.
How gravity works on macroscopic scales? Excuse me, but I thought that was pretty well known stuff 🙂
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.
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.
@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.
Isn’t gravity at macroscopic scale explained by general relativity as Per no 5 said?
Thanks
20
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” ?
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.
Sean, you may be interested in this Wikipedia article on unsolved problems in physics:
http://en.wikipedia.org/wiki/Unsolved_problems_in_physics
What is the ultraviolet extrapolation of the Standard Model?
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).
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.
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
The book is free on the web
structureofexistence.com
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.
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!
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). 😉
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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?
Instead of #19 & 20:
Is the quantum world non-local, non-causal, or non-deterministic? (must be one…)
Somebody seems to be doing an awfully good job at keeping this conference secret. Is there a link for other talks?