Jacobi's Principle and the Disappearance of Time

Understand

Jacobi's action principle is known to lead to a problem of time.

• For example, the timelessness of the Wheeler-DeWitt equation can be seen as resulting from using Jacobi's principle to define the dynamics of 3-geometries through superspace.
• In addition, using Jacobi's principle for non-relativistic particles is equivalent classically to Newton's theory but leads to a time-independent Schrodinger equation upon Dirac quantization.
• In this paper, we study the mechanism for the disappearance of time as a result of using Jacobi's principle in these simple particle models.