söndag 22 maj 2016

Equivalence Principle as Definition: Experiment

Here is little experiment you can do yourself on the kitchen table supporting the idea that intertial mass is made equal to gravitational mass by definition as a result of a definition of force in terms of gravitational force:
Take two identical pieces of material, put one of the pieces on a horisontal table with frictionless surface and connect the other by a weightless rope as indicated in the picture and let go from rest.

Record the acceleration of the system. Observe that it is half of the gravitational acceleration of one of the pieces in free fall. Conclude that inertial mass = gravitational mass and that force ultimately is defined in terms of gravitational force as expressed by the green arrows.

Understand that what you test with the experiment is if mass = force/acceleration is independent of orientation of Euclidean coordinate system.

3 kommentarer:

  1. Where does the definition really enter in your opinion?

    If you use Newton's laws separately on the two bodies, and eliminate the string force, minor algebra gives

    a_2 = m1 / (m1 + m2) * g.

    This since the constraint gives a_2 = a_1 if it is assumed that the string is rigid. Newton's laws only gets you to this point.

    From here, a priori, you can not say anything until you actually perform the experiment. You need the empirical input to see if (m1 + m2) adds up to 2m1.

  2. Yes, the kitchen experiment shows that inertial mass = gravitational mass, as a result of invariance of Newton's 2nd with respect to orientation: vertical gravitational acceleration is equal to horisontal inertial acceleration under equal force. Right?
    But the EQUIVALENCE PRINCIPLE is something very much bigger and mysterious, right?

  3. Newton's 2nd law is not mysterious, nor the form of his gravitational law, but Einstein's Principles are strange and unphysical, including the Equivalence Principle. Newton is clear and Einstein is obscure.