Equivalence Principle

The Equivalence Principle is a fundamental principle of physics which states that gravity operates as if the observer was in an upwardly accelerating frame of reference. Despite that it takes more force to move a more massive object through space (Newton's Second Law), when in free-fall bodies of different masses 'fall' at the same rate without exhibition of different inertial resistances, just as if the bodies were inert and the Earth were accelerating upwards into them. The Equivalence Principle is also used to explain why observers in free-fall feel weightless, rather than feeling their own weight pulling them down (ie. while in a Zero G plane). Experiments with light and atomic clocks at various scales have further confirmed the nature of the Equivalence Principle.

=Description=

From Introduction to Cosmology by the 4th Cosmology School at Cracow, Portland, we see:



From p.112 of Introductory Physics: Building Models to Describe Our World (Archive) we see:

Classroom Aid - Equivalence Principle
The following video briefly describes the Equivalence Principle (Runtime: 5m):

=Examples=

Monkey and the Hunter
https://web2.ph.utexas.edu/~gleeson/RelativityNotesChapter8.pdf (Archive)

8.3.1 The Monkey and the Hunter



''Figure 8.3: Monkey and the Hunter A popular lecture demonstration is to fire a projectile at a hanging toy monkey. The monkey is released at the instant that the gun is fired.''

Science at the Amusement Park
https://web.archive.org/web/20200704180931/http://physics.gu.se/LISEBERG/callab.html

Carousel with Swings



Roland Eötvös
In Equivalence of Gravitational and Inertial Mass (Archive) by Benjamin Crowell, Ph.D. (bio), we read about Roland Eötvös' investigation into the Equivalence Principle:



''Figure a: The two pendulum bobs are constructed with equal gravitational masses. If their inertial masses are also equal, then each pendulum should take exactly the same amount of time per swing.''



Figure b: If the cylinders have slightly unequal ratios of inertial to gravitational mass, their trajectories will be a little different.



''Figure c: A simplified drawing of an Eötvös-style experiment. If the two masses, made out of two different substances, have slightly different ratios of inertial to gravitational mass, then the apparatus will twist slightly as the earth spins.''



''Figure d: A more realistic drawing of Braginskii and Panov's experiment. The whole thing was encased in a tall vacuum tube, which was placed in a sealed basement whose temperature was controlled to within 0.02°C. The total mass of the platinum and aluminum test masses, plus the tungsten wire and the balance arms, was only 4.4 g. To detect tiny motions, a laser beam was bounced off of a mirror attached to the wire. There was so little friction that the balance would have taken on the order of several years to calm down completely after being put in place; to stop these vibrations, static electrical forces were applied through the two circular plates to provide very gentle twists on the ellipsoidal mass between them.''

Experiments
A great many experiments have taken place in the effort to find violation of the Equivalence Principle. The following are of interest:


 * Gravitational Time Dilation - Time dilates in accordance with the uniform prediction of the Equivalence Principal to various heights
 * Time Dilation by Latitude - The Equivalence Principle is used to explain why time does not dilate at different latitudes due to the different latitudinal speeds of Earth
 * Vertical Michelson-Morley Experiment - Light velocity changes when photons are directed upwards or downwards
 * Pound-Rebka Experiment - The frequency of light red-shifts or blue-shifts when moving upwards or downwards in accordance with Doppler Shift

=General Relativity and Accelerating Upwards=

The Equivalence Principle is a fundamental tenet of General Relativity, which describes that the surface of the Earth is accelerating upwards through space-time to cause the EP effects as experienced on Earth.

From Gravity: A Very Short Introduction (Archive) by Cosmologist Timothy Clifton (bio), we read: