My apologies for the mess of notes at this point but I am puting them here as stimulation for further thoughts. I will be writing a separate, more coherent, post on symmetry probably early next year.
Symmetries play an important part in modern physics for external spacetime and internal gauge symmetry structure.
starting with a free theory : Dirac-Lagrangian (LD), Noether's first theorem : conserved current, Noether's second theorem
Global phase transformations are not observable
In changing local operators, expectations are changed...local phase transformation is misinterpreted as empirical
Fiber bundles : rule to connect the different fibers
What are the rules that allow us to go from one fiber to the next fiber
Lagrangian view allows for a distinction between four groups
structural realism: both quantum and gravitational gauge theories display cases of ontological underdetermination.
All that exists and that can be known about the world is structure as opposed to individual object-like entitites.
SR is a most prominent position in modern philosophy of science which proposes to reject known anti-realistic objections such as the...
-pessimistic meta-induction: by retention of structure through theory change
- theory under-determination: by invariance of structure within rivaling theories to combine with the ontology of modern physics (quantum theory, general relativity, gauge theories)
epistemic structural realism: have epistemic access to the relata only. epistemically hidden
Ontic Special Relativity
relata is nothing more than structural properties
-non-empirical symmetry with no real instantiations
-only invariants allow for a realistic interpretation.
All particles are rreducible representations of the Poincaré group.
Astrophysics began in the Victorian era - technological/instrumental reasons - invention of the spectroscope.
Is there a possibility of an extra spacetime dimension that exists outside gauge fields?
fit including/excluding theory errors
extra dimensions to explain the range of fermion masses
Hierarchy problem in the evolution of the Higgs-boson mass
Dark Matter Candidates
Absence of Gravity