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Apr
28
answered What are fields?
Apr
26
comment Could a fish in a sealed ball, move the ball?
Yes it could! ;-) for example it may jump outside the ball and push it by means of its tail. More seriously - yes it could even waving portions of the water without going outside the ball.
Apr
25
comment Causality and Determinism
So please remember - the maximality of seed of light is kind of experimental results ( from Maxwell theory of electrodynamics) whilst existence of maximal speed as a constant of nature is a effects of Galilean principle ( all inertial observers are equivalent) and certain mathematical assumption about symmetry ( linearity or affinity of coordinate transformations among them)
Apr
25
comment Causality and Determinism
SR is only geometry and mathematics. The only what You need for SR is as follows: (1) The laws of physics are the same for all inertial observers, (2) coordinates of different inertial observers transform in linear (affine) way. From that two postulates You will give Lorenz group of symmetry, with one constant - velocity of unknown value which is "largest possible velocity inertial observer may notice". Then You may turn on some physics. You may identify this velocity value with the speed of light by comparison with Maxwell equations which obeys Lorentzian symmetry.
Apr
25
answered Does Quantum Mechanics assume space and time are continuous?
Apr
25
comment Does Quantum Mechanics assume space and time are continuous?
Do not You think, that it leads to conclusion that QM is certain type of effective theory? It means that QM computations may be obtained by performing more adequate calculations in exact theory and then averaged over "very large volumes compared to discrete elements"? If so: do we have "hidden variables" here, which are inconsistent with Bell Theorem? For me it looks reasonable... but may be of course naive. Please take a note that this is completely different matter than "unification of QG and QM for ultra large energies" - where discretization of space may be some kind of dynamical effect.
Apr
14
comment Is there something similar to Noether's theorem for discrete symmetries?
Cont. Then we have theory that for Hamiltonian systems if N integrals of motion exists - system is "integrable" So Vladimir statement in a case of Hamiltonian dynamics is wrong. Of course that there exists constants of motion not related to symmetry. But they are not related to structure of phase space and there is no foliation so in certain meaning they are particular, accidental one. And the may be represented ( after mathematical transformation) as initial conditions of well defined system.
Apr
14
comment Is there something similar to Noether's theorem for discrete symmetries?
@anna_v - I am the old fashioned guy - and I have obtained old fashioned education;-) I suppose there is fundamental misunderstanding what kind of systems are disputed here (Hamiltonian or Lagrangian mechanics vs general mechanics etc.). In the former integral of motion means that trajectories lays on certain hypersurfaces which forms differential manifolds - and then Hamiltonian flow defines sufficient structure for forming Noether theorem (such mechanism is called foliation, please take a look here: en.wikipedia.org/wiki/… ).
Apr
13
comment Is there something similar to Noether's theorem for discrete symmetries?
Vladimir - but this N conserved quantities are just initial values of trajectory of motion ( chosen one, from infinite possibilities) so they are trivial, and completely different for different trajectories. Symmetry transform this trajectories among others, so there are interesting constants of motion, not only trivial ones.
Apr
2
comment Noether theorem with semigroup of symmetry instead of group
I have found this paper: arxiv.org/abs/math/0604561v1 "Genuine Lie semigroups and semi-symmetries of PDEs" Is it representative for the level of knowledge about this area? If so: it means that such semigroup action on PDE equation solutions are called semi-symmetries. Probably there is a plenty to discover in this area, I suppose;-)
Apr
1
comment Noether theorem with semigroup of symmetry instead of group
One more notice - I do not expect any new invariant of motion - rather kind of flow remaining Renormalization Group equations.
Apr
1
comment Noether theorem with semigroup of symmetry instead of group
Yer they are well defined but what about definition of tangent space of it? And infinitesimal generators? And expansion of small element? Probably You are right that this is well known example (from ergodic theory, for example), but what about such structure in context of Lie algebra etc?