# Great unsolved physics problems [closed]

We all know that some theoretical ideas lack experimental evidence while in other cases there's a lack of a suitable theory for known phenomena and established facts and concepts.

But what problem in physics, according to you, deserves a mention? And why you think solving that particular problem is of utmost importance and/or how far-reaching its effects/repercussions would be.

One unsolved problem per post.

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Some qualified person (i.e. not me) should write an answer about the AdS/CFT conjecture! – Greg P Dec 28 '10 at 19:14

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@arivero: perhaps. I just wanted to point out that in my opinion greatest unsolved problems are hiding in the nature not in the mathematical foundations of our theoretical models. But this was never intended as a criticism, just an amusing fact to note :) – Marek Jan 20 '11 at 14:34
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## closed as not constructive by David Zaslavsky♦May 15 '12 at 21:22

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or specific expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, see the FAQ for guidance.

## 33 Answers

A general existence and uniqueness theorem for the Navier-Stokes equations. The lack of one is probably the largest open problem in classical mechanics, considering that the study of fluid dynamics is based on the Navier-Stokes equations and generalizations thereof. If there were an equation of state/initial data set where the solution was either non-existent or non-unique, even if such a thing were not experimentally realizable (for instance, the "good" initial data formed a dense set in the space of possible initial data), it would still fundamentally change how we look at the evolution of classica systems.

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– user346 Jan 20 '11 at 6:00

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I would have thought the question was only of mathematical interest. Real fluids are not continuous, but made of particles. This makes the Navier-Stokes equations an approximation. – Hugh Allen Feb 7 '11 at 6:15
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Q: Are there magnetic monopoles?

Why: If there are, Maxwell's equations become more symmetric and, more important, it immediately explains why charge is quantized. If there aren't, then the interesting question might be: Why?

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– Robin Maben Nov 30 '10 at 4:45

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@user16307 Well, "explain" is relative. But we already know that angular momentum is quantized, and if magnetic monopoles exist, you can find a system whose EM field has an angular momentum that is proportional to the electric charge, so that then has to be quantized as well. – Lagerbaer Mar 4 at 16:00
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There is not (as far as I know) a satisfactory microscopic description of high-Tc superconductors.

Classical (s-wave) superconductors are described by BCS theory, which qualitatively assembles charge-carriers into phonon-mediated Cooper pairs, and successfully predicts many macroscopic phenomena like the Meissner effect. This theory has been known for over 50 years. The behavior of high-Tc superconductors seems to be a different animal, with substantially more complexity.

If we were to have a good grasp of the microscopic theory, this would be a major insight into the behavior of certain highly-correlated electronic systems, and one could perhaps build on such an understanding to analyze more complicated systems. On a more applications-oriented level, it is conceivable that we would have an easier time cooking up better-performing or more industrially economical superconductors.

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What makes up dark matter.

The existence of dark matter is well established cosmologically especially through recent gravitational lens observations of galaxies that collided. But we have no idea what it consists of. Ordinary baryonic matter is virtually rules out and galactic structure formation models suggest a weakly interacting massive particle is the best fit. So is that right and if so how do such particles fit into particle physics beyond the standard model?

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Is supersymmetry (SUSY) a symmetry of our world?

This has to do with many outstanding problems in modern physics, like hierarchy problem, nature of dark matter, cosmological constant problem and others. If true, it explains some of them in one stroke and for others it provides clues as to what to do next. But note that it would also bring many other questions (e.g. precisely what SUSY model is realized in nature and how exactly is spontaneous breaking of SUSY realized). It also points a way to quantum gravity (via supergravity).

In short, this symmetry is very appealing theoretically and many people are quite sure it is indeed correct despite not yet being observed (so, in this regard it is quite similar to Higgs boson). Now, not only is the resolution of this problem (in either way) very interesting but LHC should actually be able to give the answer in next few years and this makes it all the more exciting.

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A completely general method for overcoming the fermion sign problem in quantum monte carlo sampling.

As it is, any special circumstances in which we can guarantee the weights of a fermion path integral to be nonnegative are highly prized, but in general, in spatial dimensions greater than d = 1 we just can't accurately do QMC simulations for fermions.

Consequences? Well, in addition to making my life (exponentially!) easier, it would also prove P=NP.

(see, e.g.: Phys. Rev. Lett. 94, 170201)

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What mechanism is responsible for the imbalance between matter and anti-matter in the universe?

Did the universe start with such an imbalance already in place or is it due to some CP violating mechanism at high energy that was significant in the early universe? If so what interactions are involved?

Currently known CP violating mechanisms do not appear to be strong enough to account for the observed amount of matter in the universe, so the explanation is liekly to be someting new beyond the known standard model.

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+1 Baryon asymmetry is definitely one of the most perplexing aspects of cosmology. – Noldorin Jan 22 '11 at 23:47

Since no one mentioned the confinement:
"no analytic proof exists that quantum chromodynamics should be confining"

Briefly: it turns out that one cannot isolate color-charged particles. Intuitively one can understand it -- gluons, being the carriers of strong interaction, carry the color-charge themselves. So they are "screening" the color-charge of a carrier. And when one tries to, say, separate two quarks, the "gluon tube" appears between them. Which leads to production of new quarks, and those new quarks combine with the quarks being separated, producing colorless states in the end.

Up to now there is no analytic calculation, that supports this picture.
I think that the solution of that would be a great achievement.

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One fundamental problem in mathematical physics that has to my knowledge not been resolved, but I might be mistaken since I haven't been working in this particular field for already 5 years and 5 years is a long time, is the following:

In macroscopic bodies, there are several laws existing describing transport phenomena like heat conduction. They are described by precise mathematical laws which are well established experimentally. A well-known one is Fourier's law:

$$c\frac{\partial}{\partial t}T(\vec{r},t)=\nabla \cdot \left(\kappa \nabla T(\vec{r},t)\right) \; ,$$

where $T(\vec{r},t)$ is the local temperature, $c=c(T)$ the specific heat and $\kappa=\kappa(T)$ the heat conductivity. There is however no rigorous mathematical derivation of this equation for any classical or quantum model with a Hamiltonian microscopic evolution. This problem is related to the question wether deterministic microscopic systems can fully explain the behaviour of macroscopic matter. (Remember this question, well basically, we have no rigorous proof that it's all just probability applied on huge amounts of microscopic particles. At least not for out of equilibrium processes, which transport phenomena are.)

Now, I don't expect anyone but mathematical physicists invested in this particular field to loose any sleep over it. We have a good heuristic understanding of how things work and there's nobody seriously doubting that the explanation of macroscopic phenomena lies in understanding the underlying microscopic phenomena (except maybe some crackpots and fringe physicists). Still, a mathematical derivation could bring us a deeper understanding of why it works.

The Green-Kubo relation gives $\beta V \int_0^\infty d\tau \left\langle J(0)J(\tau) \right\rangle$ for the transport coefficients. The time autocorrelation function can be computed using the closed time path formalism.

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Interesting. I had no idea that Fourier's law had no derivation from microscopic principles! – Noldorin Nov 30 '10 at 11:25
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What is the explanation of sonoluminescence? Under the right circumstances, sound waves can cause a bubble in a liquid to emit light. But the mechanism by which this happens is not understood.

Some of the theories proposed to explain it are impressively exotic and far-fetched. Who knows what could come out of it?

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What is the nature and parameters of the Higgs sector?

I.e.

Does the Higgs particle exist?

If so, what is its mass?

Are there Higgs multiplets e.g. as predicted by supersymmetry?

This is the last remaining question mark over the standard model and its resolution may take us to the next step beyond the standard model.

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I can't believe this answer (well, question) doesn't have more up-votes. How many billions of dollars were just spent building the LHC in an effort to answer it?? (Not to mention man-hours of the thousands of physicists contributing to it.) Needless to say, it gets my vote. – qftme May 10 '11 at 10:30

Why is the cosmological constant $10^{-120}$ times smaller than the Planck scale? Why is the electroweak scale so many orders of magnitude smaller than the Planck scale? Why is the QCD scale comparable to the electroweak scale?

The cosmological constant problem is especially acute because of zero-point energy corrections coming from quantum field theory. In a nonsupersymmetric theory, with a mismatch between the number of bosonic and fermionic fields, this would require an incredible fine-tuning. Even in a nonsupersymmetric theory where the number of bosonic and fermionic fields match, unless the masses also match, we still require an enormous fine-tuning. Even if we have supersymmetry, it has to be broken below the TeV scale.

Dynamical mechanisms to solve this problem typically run into problems with the renormalization group.

Do the anthropic principle and the multiverse answer these questions?

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Shucks - i just repeat the question that M. Veltman asks about a dozen times in Facts and Mysteries - WHY ARE THERE THREE GENERATIONS OF FERMIONS ? Halzen & Martin ask the same, as do a dozen others I could find.

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What is the explanation for all the seemingly arbitrary dimensionless parameters?

This is the biggest mystery of science today I think

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– Gordon Feb 3 '11 at 23:49

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Given that the fine structure constant is a running constant that scales with energy, it's worth noting that it has this value only at zero energy. – qftme May 10 '11 at 10:25
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I think one important problem (at least from the point of mathematical physics) is to establish the Standard Model as a mathematically complete and consistent quantum field theory. This is related to: http://www.claymath.org/millennium/Yang-Mills_Theory/.

The point is that the Standard Model of particle physics deals with fundamental structures of matter and is one of the most successful models in physics in terms of accuracy of predictions. However it seems to consist of a bunch of unjustified rules, people argue using undefined objects etc. Up to now there is no conceptual clear, mathematical and logical consistent description of the Standard Model available. So I think it would give us a quite deeper understanding how nature works if we had such a consistent formualtion of the Standard Model.

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I don't think this is an important problem because I don't think it is true that the Standard Model is mathematically complete and consistent. The Clay prize refers only to QCD, which is asymptotically free. Other parts of the Standard Model (the U(1) gauge part, the Higgs sector) are not asymptotically free and thus need a UV completion. This is one of the reasons why people think the Standard Model is only an effective field theory, valid at low energies rather than a theory that makes mathematical sense at all distance scales. – pho Jan 20 '11 at 0:49

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I think any theory that needs renormalizations and IR problem resolving is physically and mathematically inconsistent by definition. A consistent theory calculates energies, scattering cross sections, etc., from the fundamental constants, not "renormalizes" them. – Vladimir Kalitvianski Jan 20 '11 at 11:29

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Vladimir, you'll have to admit this is a minority opinion. – pho Jan 20 '11 at 13:05
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Find a consistent and complete theory of quantum gravity combining quantum mechanics with general relativity.

Clearly, our universe is described by both quantum mechanics and general relativity. So, a more complete theory of the universe would have to incorporate quantum gravity somehow. However, combining the two has resisted decades of effort so far, and consistency and completeness turn out to be extremely stringent criteria in this case.

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@Marek: It may be too general, but as we are not really sure what form the final theory of quantum gravity will look like, making it more specific might run the risk of excluding the final correct theory. – QGR Jan 20 '11 at 9:49
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Is physical world ultimately describable by a renormalizable theory?

Most physicists tend to assume that this has to be so. The truth is that this assumption is just a convenience so we can add a cutoff that will keep the low-energy models safe from interacting with features of the high-energy underlying models.

There is nothing that will force this; in fact, is not out of the park to believe that most of the (27? 28? can't remember) "free" parameters in the standard model might be predicted by a non-perturbative nonrenormalizable high-energy model

More importantly though, this very assumption is directly related to the fact that current physical theories have remained largely unfalsifiable in practical terms. So this assumption (may) eventually turn out to be a self-induced dead-end

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Are there extra spatial dimensions?

Since many problems become exceptionally easier to solve with an assumption of extra spatial dimensions, I think this is one of the greatest questions of all time.

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I would like to know how to compute the charge of an electron from first principles. This would likely have major implications that would depend on the form of the solution.

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Do mean the value of e? At what energy scale? – pho Jan 20 '11 at 2:37

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I mean I want to derive the fine structure constant from first principles. – Matt Mar 2 '11 at 7:07

Greg P asked, so here it is. I think a proof of the AdS/CFT conjecture relating $N=4$ SYM with gauge group $SU(N_c)$ to IIB string theory on $AdS_5 \times S^5$ with $N_c$ units of five-form flux would be extremely important, even if the proof was only a proof by physics standards. I say this not because I think the conjecture may be false, indeed there is overwhelming evidence that the conjecture is true. Rather I think it would be important because many of the most important applications of gauge/gravity duality require going beyond AdS/CFT to theories without supersymmetry or conformal symmetry (such as gravity duals of QCD) or to theories without Lorentz invariance (various condensed matter applications) or to theories on the gravity side which are not asymptotically AdS. For example there are proposals for a de Sitter correspondence and Verlinde has proposed "emergent gravity" bases on holographic ideas which as far as I can tell do not involve the input of data from the boundary of spacetime as one needs in AdS. A proof of the original conjecture might indicate more clearly whether these extensions of the idea are correct, or whether at some point things go wrong when you try to generalize.

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Is information preserved in evaporating black holes in quantum gravity?

I know there are already too many answers here relating to quantum gravity, but I think this question is important.

According to quantum field theory in curved spacetime, information crossing the event horizon will end up at the singularity where it will be destroyed. If we produce a pair of entangled particles outside the black hole, and throw one of them inside, it might appear as if we have converted a pure state into a mixed state, which is extremely problematic.

A lot of weird and undesirable things will happen if unitary time evolution is violated in quantum mechanics, which is why it's likely a complete theory of quantum gravity will lead to unitary time evolution. So, the question is now where is the information hidden?

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A mathematical solution of the plasma physics that causes the reversal of the sun's magnetic field every 11.5 years.

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Why was the initial state of the universe so special? Why was the initial entropy so low? See recent book by Sean Carroll.

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Why is the expansion of the universe accelerating?

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What is mass/Inertia? What is gravity?

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What the heck happens when we do a measurement in quantum theory? That is why should the system jump to an Eigen state?

Why should nice unitary evolution suddenly do something weird just because someone did a measurement? What exactly is a measurement anyway?

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The Fundamental Properties of Space and Time at an Event.

Some specifics are:

1. Is Time a logical derivable construct from some non-time based fundamental theory?
2. Is Time discrete or continuous?
3. Is Space(-Time) discrete - and if so at the Planck level?
4. Directionality (and perhaps dimensionality) of Time
5. Dimensionality of Space (the String Theory issue)
6. Substructure (and any physics) below any Planck scale "minimum distance"

These kinds of issues are of course at the root of many conceptual and calculational issues in the theories around today.

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What is the exact form of Exchange-correlation (xc) functional in Density Functional Theory (DFT)?

The entire community of Condensed Matter Physics and Quantum Chesmitry want to know that answer. (:

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Quantum Mechanics gives us a mathematical framework for making predictions at the quantum level, which agree perfectly with experiment. However, no one knows what physical model (if any) that math represents. What does quantum mechanics really mean?

Disturbingly, many physics students do not realize that the Copenhagen Interpretation - that particles do not actually have a position or momentum until they are physically measured - is only one of many interpretations of quantum mechanics, none of which we have any reason to believe over any other. All the interpretations lead to the same math, and thus, the same experimental results.

Somewhat surprising to many, there are even some interpretations that do allow particles to have both definite positions and momentums (though other, equally-unintuitive assumptions must be made).

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This unanswered question was one of the biggest shocks on my undergraduate Quantum Mechanics courses. This actually was the motivation by which I became so interested in probability theory and, particularly, in the work of E.T. Jaynes. – Néstor May 12 '12 at 5:45

Does it make sense to talk about quantum gravity? Is it possible that gravity is a classical field or a condensate which appears largely classical, but where the underlying quantum physics is entirely different. Thirring fermions ~ sine Gordon solitons, where the SG solitons are a Euclideanize form of the hyperbolic dynamics on $AdS_2$. The $AdS_2~\sim~ CFT_1$ tells us the isometry of the spacetime is equivalent to the group for conformal quantum mechanics on the boundary. Might it then be the actual quantization is not with the spacetime, but with an underlying fermionic physics? If so can this be generalized to $AdS_n$, for $n~>~2$?

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## protected by David Zaslavsky♦Jun 4 '11 at 20:45

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