Last year I had the insight that my talks desperately need improvement, and attempted to list all the important things I should keep in might when I speak in front of people. After chewing a pen for a very long time, what I finally wrote was 'Breathe Normally'. I consider this to be a successful list. It's pinned to the wall in my office.
However, as Marcus has tried to communicate to me repeatedly, lists pretend structured thought. This together with the recent posts by Christine about the top 10 lists for String Theory (ST) and Loop Quantum Gravity (LQG), inspired me to write down my own top 10 list of unsolved questions in physics. For completeness I will also briefly summarize Christine's lists, which I felt free to shorten and reinterpret to suit my needs. While writing this post, I further came across several more or less related links, that you also find below.
Since I am neither a string theorist nor working on LQG, this is kind of an agnostic outside view, and should be read as such.
My Top 10
Unsolved Questions in Theoretical Physics
- 1) How can the apparent disagreement between general relativity (GR) and quantum gravity be resolved? Does it require to quantize gravity? If so, how? If not, see 2 and 3.
2) Do black holes destroy information? If not, what happens to the matter that collapses to a black hole?
3) Are there really singularities in GR (inside black holes/big bang)? If so, how can we understand what happens there? If not, how are they avoided?
4) How can we explain the data (supernovae, WMAP) which seems to indicate that the universe is filled with dark energy. Is there really dark energy? If so, what is it? Why does it become important just now (coincidence problem)?
5) How can we understand the rotation curves of galaxies, and the too large sizes of voids between galaxies. Does dark matter exist? If so, what is it made of?
6) What happened in the very early stages of the universe? How can we solve the horizon/flatness/homogeneity problem? Did inflation really take place? If so, what is the inflaton? How does electroweak symmetry breaking work? Where does the baryon-antibaryon asymmetry come from?
7) Why do we experience 3+1 dimensions? Are there extra dimensions? If so, why haven't we yet noticed them?
8) Are the electroweak and strong interaction unified at high energies? If so, are the currently known particles of the standard model (SM) elementary? Are there more yet unobserved particles? Why are the parameters of the SM what they are and are they in yet unknown ways related to each other (or are they related to 1. or 6.?). Why are the gauge groups of the SM what they are?
9) Can we understand quantization?
10) What causes particles to have masses and why are these so much smaller than the Planck mass (and hence the gravitational interaction so weak, alias the hierarchy problem)?
String Theory Top 10
This is a free interpretation of Lubos' list. For more details, references and links, please look up his post.
ST 1) Absence of free non-dynamical continuous dimensionless parameters in the underlying equations.
ST 2) Microscopic calculation of entropy of black holes and their other thermodynamical properties.
ST 3) The equivalence between conformal field theories and quantum gravity in anti de Sitter space, i.e. AdS/CFT correspondence.
ST 4) Unity of all consistent theories of quantum gravity in the maximal dimensions.
ST 5) Natural embedding of realistic vacua with all desirable features, SM spectrum gauge groups, SUSY, grand unification, neutrino masses, solutions to numerous particle physics problems within the simplest N=1 vacua of string theory.
ST 6) Matrix models and Matrix theory as alternative descriptions of second-quantized systems without second quantization, including the description of more complicated backgrounds such as 10D type IIA.
ST 7) Mirror symmetry and physical methods to solve difficult questions in algebraic geometry, and geometrization of particle physics processes such as gaugino condensation
ST 8) Detailed proofs that topology can change and description how it precisely occurs.
ST 9) Framework that generates helpful new concepts and ideas that might be relevant in bottom-up phenomenology even without the exact rules of string theory such as large extra dimensions, warped dimensions, application of quiver theories (deconstruction etc.), and others.
ST 10) Other implications for mathematics as encoded in topological string theory, a subsector of the full string theory
ST 11) Other mechanisms showing the emergent character of space, other dualities such as K3-heterotic, new transitions, new massless states [...]
ST 12) The existence of the landscape, a large enough set of metastable solutions that the cosmological constant can adjust to a value small enough as to allow organized structures
LQG Top 10
For details and references, look up Lee Smolin's paper or Christine's list. You also find extensive comments on that list at Lubos' post.
- LQG 1) The kinematical Hilbert space has been rigorously constructed. The Hilbert space of spatially diffeomorphism invariant (Hdiffeo) and gauge invariant states of a gauge field on a manifold Sigma has an orthonormal basis whose elements are in one to one correspondence with the diffeomorphism equivalence classes of embeddings of spin network into Sigma.
LQG 2) Certain spatially diffeomorphism invariant observables have been constructed. The spectra have been computed. The area and volume operators can be promoted to genuine physical observables, by gauge fixing the time gauge so that at least locally time is measured by a physical field.
LQG 3) Loop quantum gravity leads to a detailed microscopic picture of the quantum geometry of a black hole or cosmological horizon.
LQG 4) Among the operators that have been constructed and found to be finite on Hdiffeo is the Hamiltonian constrain. Not only can the Wheeler deWitt equation be precisely defined, it can be solved exactly. Several infinite sets of solutions have been constructed, as certain superpositions of the spin network basis states, for all values of the cosmological constant.
LQG 5) Evolution amplitudes corresponding to the quantization of the Einstein equations in 3 + 1 dimensions, are known precisely for vanishing and non-vanishing values of the cosmological constant, and for both the Euclidean and Lorentzian theories.
LQG 6) Spin foam models with matter have been extensively studied in 2+1 dimensions. At least in 2 + 1 dimensions the scattering of matter coupled to quantum gravity is described by a version of deformed special relativity.
LQG 7) Coupling to all the standard forms of matter fields are understood, including gauge fields, spinors, scalars and higher p-form gauge fields.
LQG 8) Spin foam models appropriate for Lorentzian quantum gravity, called causal spin foams, have quantum analogues of all the basic features of general relativistic spacetimes. These include dynamically generated causal structure, light cones and a discrete analogue of multifingered time.
LQG 9) For the case of non-vanishing cosmological constant, of either sign, there is an exact physical state, called the Kodama state, which is an exact solution to all of the quantum constraint equations, whose semiclassical limit exists. By studying excitations of these states one reproduces conventional quantum field theory, as well corrections to it which may be compared with experiment.
LQG 10) The inverse cosmological constant turns out to be quantized in integral units, so that k = 6pi/G is an integer.
You find a summary of unsolved problems in theoretical physics at Wikipedia
including problems I have never heard of, like the Corona heating problem.
Then there is the
which you also find in this paper.
For a refreshingly different list see N. David Mermin's article on this:
The best list I came across, with plenty of references and explanations, is the one by John Baez
First, I notice that both ST and LQG claim to be a solution to 1.
LQG 1,2,4,5,7,8 and ST 5,6,7,8,10,11 deal with the theories themselves and do not address any of my problems.
Both (ST 2, LQG 3) also claim to be crucial regarding the understanding of black hole evaporation (2). If one of both has successfully explained what happens to the matter that plunges into the black hole, the good news hasn't yet reached me.
I promoted Joe Polchinski's point about the minimalness of free parameters in ST to ST 1, because for me it is the most attractive feature. Maybe then someone could please derive the parameters of the SM from that underlying equation and address point 8?
AdS/CFT (ST 2) is nice, but to my eyes it relates two things that don't say anything about 1-10. However, it is certainly useful to occupy hundreds of postdocs.
ST 4 seems to me a very bold claim, since nobody has ever shown me what a consistent theory of quantum gravity looks like.
LQG 2 addresses point 3.
ST 12 does not explain anything.
LQG 9 and 10 are interesting, but I don't see how they help with my unsolved questions.
ST 9 and LQG 6 allow to examine phenomenological implications, which could in turn help us to learn something about the structure of the underlying theory. LQG 9 in principle sounds nice, but there seems to be plenty of disagreement around it. One way or the other, it doesn't help with 1-10.
Finally, notice how carefully I avoided to call the above ST and LQG points 'results'.
I think this is enough structured thought for today. I am afraid I have successfully depressed myself.
In case of a sudden loss of brain pressure, intriguing tasks will drop down directly in front of you. Pull task towards you, tighten strap around your head. BREATHE NORMALLY.