An Accessible Formulation for Defining the SI Second Based on Multiple Atomic Transitions

The atomic transitions employed in the best of today's optical clocks are a strong foundation for the upcoming redefinition of the SI second. Including multiple transitions in the definition offers increased accuracy, a robust diversity of implementations and would drive continuous performance validation through frequency comparisons. The cost is that such a definition is more complex to articulate and feared to be challenging to implement. We show that it can be made more approachable to intuition, illustration and implementation through formulating this ensemble definition of the SI second in terms of the weighted arithmetic mean of normalized atomic transition frequencies. This definition produces the same results as the presently discussed option up to second order terms of order 10^-30 or below.