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Additional Aspects and Applications
Published in Marlos A. G. Viana, Vasudevan Lakshminarayanan, Symmetry in Optics and Vision Studies, 2019
Marlos A. G. Viana, Vasudevan Lakshminarayanan
Any two symmetries within the same class are connected, but no Lorentz transformation in one component can be connected with another in a different component. L+↑ contains the identity matrix and defines a subgroup of L, called the restricted Lorentz group, whereas L↑=L+↑∪L−↑ defines the orthochronous Lorentz group. The orthochronous symmetries are the transformations consistent with the geometry of M, preserving time orientation: x4>y4 implies (Lx)4>(Ly)4. The proper Lorentz group is defined by L+=L+↑∪L+↓, whereas L0=L+↑∪L−↓ defines the orthochorous Lorentz group. When the symmetries of the Lorentz group are enlarged to include space time translations, we obtain the so-called inhomogeneous Lorentz group or Poincaré group8P4. The Poincaré group is basic to relativity theory in that all physical laws are invariant with respect to the action of a Poincaré group on space time.
Light propagation and local speed in the linear Sagnac effect
Published in Journal of Modern Optics, 2019
Gianfranco Spavieri, George T. Gillies, Espen Gaarder Haug, Arturo Sanchez
The conventionalist scenario implies that the Lorentz transformations can be substituted by transformations based on absolute simultaneity, a substitution hardly acceptable by physicists who have been using the symmetry properties of the Lorentz group for decades in applications in several branches of modern physics, such as elementary particle physics, astrophysics, and quantum physics. Moreover, epistemologists (29) claim that a theory is physically meaningless unless its basic postulates can be tested. From that perspective, it is crucial for the standing of the theory that the physical equivalence (or not) between preferred frame theories and SR be satisfactorily tested and verified, at least in principle. Advances have been made by Spavieri, Rodriguez and Sanchez (13) who have recently shown that, in general, Einstein and absolute synchronization predict different observable results, thus suggesting that the two synchronizations are not physically equivalent. It follows that, at least in principle, Einstein's second postulate of a universally constant speed of light can be verified experimentally. In this case, standard SR with Einstein synchronization maintains its unique physical meaning and can be tested against theories that assume the existence of an identifiable preferred frame.
Implications of causality for quantum biology – I: topology change
Published in Molecular Physics, 2018
Let us briefly describe the topological properties that can be computed. A first step is to generate the underlying manifold. This step is provided by solving the quantum dynamical manifold equations (QDMEs) described below. These equations consist of 4D Minkowski spacetime generators for configuration coordinate fields (CCFs). The generators have a 1D time and 3D spatial structure. There can be multiple generators combining to generate a mass-spacetime manifold. The group of transformations of each generator is the Lorentz group and affine translations as well as conformal maps. The physical spaces of interest are the past and future causal cones. This (1 + 3)D decomposition focuses on 3D submanifolds evolving through time. A well-known example of the kind of results is that described for 2D manifolds spanned by triangles having faces, edges and vertices. If the 2D manifold has say k holes, thenThe 3D manifolds generated are considered to be spanned by a simplicial net consisting of tetrahedra. The number and type of holes in the generated manifolds can be computed using (co) homology [22]. Large biomolecules are often twisted and linked together. A quantity called the writhe can be defined reflecting the fact that a DNA molecule will coil if it is twisted. This leads to the formula [25]The linking number can be computed using a method going back to Gauss. These results can only be computed if the manifold can be computed. The spacetime current J can then be computed from the wave function thereby providing the basis for topology computations. Other topological characterisations of manifolds employ knot theory [26]. As a time-dependent problem, the manifold can evolve re-linking.