This is a continuation of previous posts on operational definition in SI 2019 of mass as gravitational mass.
In Newton's mechanics inertial mass is exactly equal to gravitational mass as an expression of both (i) universality of free fall and (ii) conservation of energy. A Universe without (i) and (ii) cannot exist.
In Einstein's mechanics this truly fundamental equality is no longer guaranteed by (i) and (ii), but has to be added as an independent Equivalence Principle EP, which has to be supported by experimental evidence. Accordingly major efforts have been made to find ever more precise experimental confirmation, where the current precision is $10^{-15}$, while new experiments are receiving funding to reach even better precision:
✅ Best Precision to Date:
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Experiment: MICROSCOPE (CNES, ESA)
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Method: Differential accelerometry in space (free-falling test masses of different materials)
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Result: Difference in acceleration between test masses of different compositions was less than 2 parts in $10^{15}$.
🚀 Future Target Precisions:
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Galileo Galilei (GG) satellite – proposed
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Target: $10^{-17}$
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STE-QUEST (atom interferometry in space) – proposed
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Target: $10^{-17}$ (depending on mission configuration)
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To a classical physicist these experiments are similar to precise testing of the validity of the equality 1+1 = 2.
Einstein presented his Special Theory of Relativity SR in 1905 in a desperate effort to get a university position, and followed up in 1915 with his General Theory of Relativity GR in a desperate attempt to keep the position he managed to get in 1909 under severe criticism of SR.
Einstein thus took on the role of challenging Newton's mechanics by connecting it to propagation of light which was not mechanics, and by assuming EP as a fundamental postulate of GR as a step away from Newton's mechanics.
Despite severe criticism of both SR and little acceptance of GR before his death in 1955, today Einstein is the undisputed hero of modern physics as the man who showed that Newton was wrong and so opened the door to all sorts of new physics desperately needed after the success of the atom bomb in 1945 had faded.
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