* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lorentz Invaiance Violation and Granularity of space time
Renormalization wikipedia , lookup
Double-slit experiment wikipedia , lookup
Quantum dot wikipedia , lookup
Wave–particle duality wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Matter wave wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Hydrogen atom wikipedia , lookup
Path integral formulation wikipedia , lookup
Elementary particle wikipedia , lookup
Quantum field theory wikipedia , lookup
Many-worlds interpretation wikipedia , lookup
Quantum fiction wikipedia , lookup
Quantum entanglement wikipedia , lookup
Quantum computing wikipedia , lookup
Quantum chromodynamics wikipedia , lookup
Orchestrated objective reduction wikipedia , lookup
Bell's theorem wikipedia , lookup
Identical particles wikipedia , lookup
Quantum machine learning wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Quantum teleportation wikipedia , lookup
Quantum key distribution wikipedia , lookup
Scalar field theory wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Renormalization group wikipedia , lookup
EPR paradox wikipedia , lookup
Quantum group wikipedia , lookup
History of quantum field theory wikipedia , lookup
Quantum state wikipedia , lookup
Hidden variable theory wikipedia , lookup
Canonical quantization wikipedia , lookup
Event symmetry wikipedia , lookup
A Different Approach (?) Collaboration with D Sudarsky Let us take up the notion that space-time contains some granular/discrete aspect with characteristic scale given by MPlanck The lesson from the previous studies is that such structure, if exists, can not lead to breakdown of Lorentz Invariance. It is of course hard to envision something like that while thinking classically about a spacetime. But what is space-time in a quantum world? We do not know! 1 When faced with total Ignorance proceed by analogy Consider a physicist trying to get information about the granular structure of a crystal. Assume that the fundamental crystal lattice has some symmetry, say cubic. We know that the fundamental granular structure will not become manifest through a breakdown of the symmetry if one studies a macroscopic, but similarly cubic crystal. However, if the macroscopic crystal does not share the lattice symmetry, we might be able to detect it. 2 Phenomenology The results so far indicate that the granular structure, if any, would have to respect the Lorentz symmetry. This would explain why we have not seen the “expected” violation of L.I. : There is none. So what would be the signature of the discrete structure of space time? In analogy with the crystal, we consider a macroscopic space-time that is Not Fully Lorentz Invariant. 3 There lies the hope of seeing something A space-time that is not Minkowski on an extended realm could exhibit the mismatch between the symmetry of the fundamental structure and that of the macroscopic domain. The departure from Minkowski spacetime is characterized by the Riemman. tensor: R . 4 The effects in question should represent a coupling of Riemman to ordinary matter. Furthermore: part of Riemman is determined by the local T : R - (R/2 )g =8G T and thus would look like a self coupling. That is not the most interesting. We need to consider couplings of the Weyl tensor W (Riemman without R or R). 5 The direct approach indicates that all such couplings are highly suppressed A more open minded approach exists: Extract from Weyl some aspects and couple them to matter: One possibility: Find eigenforms and eigenvalues of Weyl: W X = X And use these objects to couple to matter fields. 6 Consider the coupling to fermions The least suppressed term is : L = (1/MPlanck) ∑a a (a) Can this ideas be experimentally explored? In the non-relativistic regime the dominant new term in the Hamiltonian for the spin 1/2 particle H= (1/MPlanck) ∑a a0i(a) i This looks like a coupling of the spin with magnetic field. Can it be distinguished from that ? Could the suppression be 1/M instead of 1/Mplanck ? 7 Comments: Magnitude: is of the order of the gravitational gradients GM/r3. A non zero 0i implies a special direction and a time asymmetry (rotation). On the other hand the effect should be associated with the gravitational sources and thus susceptible of control. It should affect even particles with no electromagnetic couplings like Neutrinos. 8 Other comments Something like this could originate from some QG aspects of holonomic degrees of freedom (i.e. LQG (?)), or from QG bounds in the sectional curvatures (?)... It is worth noting that no real tests of Quantum Mechanics in the presence of curvature exists up to date! 9 THE CHALLENGE According to the GR view, COW experiment & the experiments with neutrons at Grenoble are ``just” tests of QM in a non inertial frame… but gravity lies only in the curvature, i.e. in the fact that inertial frames at different events do not coincide. Other tests, such as those using Quantum Gravity gradiometers, rely only on quantum aspects that are purely local ( no quantum description needed in the domain covered by different Local Inertial frames). The challenge, from my point of view, is to detect curvature (i.e. tidal forces) using quantum aspects of 10 matter. Further Ideas Point particles move along geodesics, but how do extended/quantum objects move? What is the operational definition of geodesic, when we test the world with extended objects? The path of the center of mass? NO! What are in principle the geodesics of the geometry, or the geometry itself, when all we have to explore it, are quantum particles ( in fact, quantum fields)? There is too much we do not understand! We need to be open minded when we explore! 11