So do we have any equation for Time that combines mass or energy?

The first mathematical formula to link time and energy that comes to my mind is [T, H] = iI,

where

T - time operator,

H - hamiltonian (energy operator),

i - imaginary unit,

I - identity matrix,

[T, H] = TH - HT and this operation is called a commutator.

The above formula is related to the famous Heisenberg uncertainty principle for time and energy. It more or less says that time and energy cannot be measured simultaneously with any accuracy. However, it is not about simultaneity in time, but about the fact that the more accurately one of these quantities has been measured, the less accurately we can measure the latter.

Probably this pattern came to my mind because yesterday, together with Ark, we sent a paper on the time operator for publication. Our article can be found here:

[2202.10393] Time of arrival operator in the momentum space
What exactly is this time operator? In classical mechanics, we simply have physical quantities. If the conditions of the experiment do not change, we will obtain the same result. In quantum mechanics, so-called observables (linear operators with strictly defined properties) correspond to physical quantities. If the conditions of the experiment do not change, we will not necessarily obtain the same results, but the probability distributions of these results will be the same. Despite the existence of observables in quantum mechanics, time is usually considered a parameter anyway. In our paper, we show the conditions under which a time operator can exist.