It is a rare situation where we need to cast aside elementary assumptions that underpin our theories in order to advance them further. To be an advance two things are required: (1) any discarded assumption must be accounted for as a consequence of something deeper, and (2) the deeper cause must have consequences (predictions) that show it is necessary.
I suspect that advancing our understanding of the nature of time, and dynamics in particular, is a situation of this kind. Dynamics is conventionally assumed to be an elemental part of nature. It is incorporated axiomatically in physical theories through conservation laws and compliant equations of motion. If, however, the conservation laws and equations of motion were found to be due to deeper causes, the conventional view of dynamics being elemental would need reworking. I argue in the talk below how a violation of time reversal symmetry (T violation) of the kind observed in K and B meson decay might be such a cause.
I use a new quantum formalism based on the principle of superposition of multiple paths that treats time and space equally. The states of matter and fields are represented by paths over space and time. If there is no T violation, the formalism allows an object to be localized in both space and time, i.e. it would exist only in some small region of space and in some small interval of time. As the object would not exist before or after the time interval, there is no equation of motion and no conservation laws. The elementary assumption of dynamics has been clearly discarded here.
However, the same formalism with T violation is dramatically different. The T violation induces destructive interference between paths over time which makes it impossible for matter to remain localized at any one position. An equation of motion (the Schrodinger equation) emerges and conservation laws are obeyed. The discarded assumption is replaced with the emergence of dynamics as a consequence of T violation. Requirement 1 is satisfied.
Moreover, local variations in T violation induce corresponding variations in local clock time (like a quantum version of time dilation). In the video below I briefly discuss how this might lead to physical evidence of the necessity of the new formalism and how it might fulfil requirement 2.
Women in Physics Canada conference 2017