Newtonian spacetime can be modeled as a geometric object $M$ (affine space or manifold with connection with an absolute time function etc. etc.) that is symmetric under the action of the Galilean group $\mathrm{Gal}$, containing spatial & temporal translations, rotations, and Galilean boosts (shears) of arbitrary velocity $v$. A consequence of this is that we are unable to distinguish between inertial frames (i.e. reference frames in which isolated, non-interacting objects move inertially, as established by Newton's first law) by means of purely mechanical experiments.

One of the possible formulations of Mach's principle (please correct me if I am misled) is that we should similarly be unable to distinguish between rotating and non-rotating frames, contradicting Newton's assertion that the bucket experiment allows one to identify a privileged non-rotating frame. Could one interpret this as advocating for a different model of spacetime $M'$ whose symmetry group contains, along with the usual Galilean transformations, also "angular boosts" of arbitrary angular velocity $\omega$? What would their (supposedly conserved) observable generators be, and what would the structure of the resulting "Mach group" look like?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.