Such experiments are challenging. The first problem is that the laboratory apparatus itself may be sensitive to changes in the constants. The size of all atoms could be increasing, but if the ruler you are using to measure them is getting longer, too, you would never be able to tell. Experimenters routinely assume that their reference standards--rulers, masses, clocks--are fixed, but they cannot do so when testing the constants. They must focus their attention on constants that have no units--they are pure numbers--so that their values are the same irrespective of the units system. An example is the ratio of two masses, such as the proton mass to the electron mass.
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