User:Nikodem0/Problems of Theoretical Physics

Here, I want to list my own view of the most important, current questions of theoretical physics. There exist some pages of this type, like this one "Physics Problems for the Next Millennium", but not allowing for an online discussion.

= Emergence of the classical world and decoherence =

A quatum system interacting weakly or strongly with the environment (which must be 'big enough') tends to a state which diagonalizes the free or the interaction hamiltonian, respectively. Does this explain the emergence of a classical 'state' (classical world) or the quantum measurement process?

= The electric charge =

It seems to be a miracle that all elementary charges in the physics are equal. The fact that electron and proton (and many others) have the same absolute value of the electric charge is an experimental fact and must be necessarily postulated in the construction of the Standard Model (which itself allows for any values of charges). How to explain this fact?


 * There exist attempts to construct the quatum theory of the electric charge based on the asymptotic (infrared) electromagnetic field [cite Staruszkiewicz]


 * How should we interpret the charges of quarks (e/3) and of quasiparticles in the fractional quantum Hall effect (FQHE) (e/(2n+1))?


 * There is an intriguing observation that the effective charges (pairs) in a superconductor do not 'feel' (the interaction with) the background.


 * How far the analogy between the magnetic moment and spin, magnetic field and rotation, electric charge and (?) can go?

= Geometization of fundamental forces =


 * There is the very intriguing observation of Kaluza and Klein that the 5-dimensional vacuum Einstein equations are equivalent to 4-dimensional Einstein equations with an electromagnetic field if the 5-D metric is split into a 4-D metric and components corresponding to the electromagnetic potential and 'cylindrical' symmetry in the 5th dimension is assumed. The same can be done for any Yang-Mills field (with electromagnetism as a U(1) case)


 * What is the interpretation of the gauge freedom? Are these fields a remnant of simplification of a more general theory? (which after this simplification become irrelevant?)


 * The most natural to formulate the General Relativity as a gauge theory, including local Poincare transformations, necessarily leads to torsion. However, it seems we do not need the concept of torsion when constructing our theories.


 * The commutation and anticommutation is a very important basic feature in the Quantum Field Theory. In geometry the non-vanishing of commutators of translations corresponds to curvature or torsion. In the algebra of Lie groups the non-vanishing of commutators of generators defines the structure constants. Are these concepts related? What corresponds to the anti-commutation in the geometry? (The Clifford algebra is defined via anti-commutation.)


 * In 1+1 dimensions the Cauchy-Riemann equations, guaranteeing complex differentiability, are a system of 1st order PDE's implying the 2nd order Laplace equation for every component. In 1+3 dimensions the analogue of the complex structure is realized by quaternions. Does the Dirac equation (1st order system of PDE's) have anything to do with the 4-dimensional Cauchy-Riemann equations for quaternions?

= Particles as excitations =


 * In Quantum Field Theory the particles and antiparticles are defined as excitations of the vacuum state. Similarly as quasiparticles are excitations of a mean field in some effective theories. Can the 'fundamental' particles be interpreted as 'quasiparticles' and the 'vacuum' as a 'meanfield'?

= Interpretation of quantum mechanics =


 * No determinism


 * Interference: Quantum Mechanics or Quantum Field Theory expressed in the language of trajectories leads to the exploration of all possible trajectories by a particle

= Mach's rule =
 * Can this be shown that among all possible elliptic orbits in a 1/r potential only some are 'resonant' and survive in long time evolution if some noise/perturbation is added? These might be the 'quantized' orbits as we have it in the Solar System. Or, in some stochastic sense, solutions of the stationary Schrödinger equation.


 * To what extent does the Einstein theory of Gravity (the General Relativity) satisfy the Mach's rule? And what is the 'most proper' formulation of this rule?

= Quantum anomalies =


 * What does this teach us, that some classical symmetries are not preserved in quantized theories? (here: classical conserved current, after quantization becomes a not conserved current)

= Masses (and spins) of elementary and composite particles =


 * Where do the masses of "elementary" particles come from? Is Higgs mechanism the only good model on the market?


 * How to understand (and calculate) masses of composite (bound state) particles, e.g. proton = quarks + gluons of which 98% of the mass is carried by (asymptotically massless in UV) gluons --> problem of bound states in QCD / QFT... (Dynamical Chiral Symmetry Breaking, In-Hadron Condensates, ...)