Atomic Clocks and Constraints on Variations of Fundamental Constants

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Fundamental constants play an important role in modern physics, being landmarks that designate different areas. We call them constants, however, as long as we only consider minor variations with the cosmological time/space scale, their constancy is an experimental fact rather than a basic theoretical principle. Modern theories unifying gravity with electromagnetic, weak, and strong interactions, or even the developing quantum gravity itself, often suggest such variations. Many parameters that we call fundamental constants,fundamental constants such as the electron charge and mass ( Chap. 1 and 1 ), are actually not truly fundamental constants but effective parameters that are affected by renormalization or the presence of matter 2 ; 3 . Living in a changing universe we cannot expect that matter will affect these parameters the same way during any given cosmological epoch. An example is the inflationary model of the universe, which states that in a very early epoch, the universe experienced a phase transition, which, in particular, changed a vacuum average of the so-called Higgs field, which determines the electron mass. The latter was zero before this transition and reached a value close or equal to the present value after the transition. The problem of variations of constants has many facets, and here we discuss aspects related to atomic clocks and precision frequency measurements. Other related topics may be found in 4 ; 5 .