Why scalar-tensor equivalent theories are not physically equivalent?

Abstract

Whether Jordan's and Einstein's frame descriptions of F(R) theory of gravity are physically equivalent, is a long standing debate. However, practically none questioned on true mathematical equivalence, since classical field equations may be translated from one frame to the other following a transformation relation. Here we show that neither Noether symmetries, Noether equations, nor may quantum equations be translated from one to the other. The reason being, - conformal transformation results in a completely different system, with a different Lagrangian. Field equations match only due to the presence of diffeomorphic invariance. Unless a symmetry generator is found which involves Hamiltonian constraint equation, the mathematical equivalence between the two frames appears to be vulnerable. In any case, in quantum domain Mathematical and therefore physical equivalence can't be established.

14 pages, To appear in IJMPD (2017)

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• Noether symmetry in $f(T)$ teleparallel gravity
• Covariant singularities in Quantum Field Theory and Quantum Gravity
• On the equivalence between different canonical forms of F(R) theory of gravity
• A viable form of the metric Teleparallel F(T) theory of gravity
• Interplay of magnetic field and chemical potential induced anisotropy and frame dependent chaos of a $Q\bar{Q}$ pair in holographic QCD
• An issue with the classification of the scalar-tensor theories of gravity
• Weyl frames and canonical transformations in geometrical scalar-tensor theories of gravity
• Hubble Diagrams in the Jordan and Einstein Frames
• Some aspects of modified theory of gravity in Palatini formalism unveiled
• Thermodynamics of irreversible particle creation phenomena and its cosmological consequence
• Analyzing Conserved Currents in F(R) theory of gravity