Why Inertial Mass = Gravitational Mass

In equilibrium the spring force = gravitational force/weight.

The Equivalence Principle EP states that: 

• Inertial Mass = Gravitational Mass.  

EP means that all material bodies react the same way to gravitational force as to other forces, or specifically that they react to inertial force the same way as to gravitational force. In Newton's mechanics this follows from the fact that the size of any force ultimately is determined by comparison with gravitational force. 

For example, the force exerted by an elastic spring under extension is determined by hanging different bodies in the spring and measuring the extension, see above picture. This means that in Newtonian mechanics the gravitational force is used as reference for all types of force and so EP is valid by definition/agreement. Gravitation is the common denominator. 

In Newtonian mechanics it is thus meaningless to seek to verify EP by an experiment, and senseless to seek to do that in a very expensive experiment, like the MICROSCOPE.  It would be the same as to seek to experimentally verify that there are 100 centimeters on a 1 meter. Most people would say that this would not be meaningful, even if very high precision could be reached.  

EP is thus a consequence of Newton's mechanics, but it is different in Einstein's mechanics, where EP in instead serves as a postulate, which then in principle can be subject to experimental testing. This is what was reported in the previous post: A very high-precision experiment confirming EP! Like testing that there are 100 centimeters on 1 meter, to very high precsision? 

On top of that the experiment is supposed to verify not only EP as postulate of Einstein's mechanics (General Theory of Relativity GR), but also serve as a confirmation of the profound revolution brought to humanity by GR. This is mind-boggling. If EP is nothing but an agreement, then GR would also simply be an agreement, and so not real science.

The very high-precision of the experimental verification of EP supports a suspicion that what is tested is in fact a definition/agreement rather than a law/theory of physics. The consequences as concerns the physicality of GR are possibly far-reaching...

Compare with the low precision of the value of the gravitational constant $G$: less than 5 decimals. 

Recall that in the new SI units standard, agreements take the role of laws of physics when defining meter in terms of prescribed speed of light, and kg in terms of prescribed equivalence with energy. However, this is not anything which modern physicists want to agree on: the prescriptions/agreements are also laws of physics! The Best of Worlds! Compare with posts on SI 2019 standard.