Talk:Equivalence principle

active, passive, and inertial masses

by definition of active and passive gravitational mass, the force on mass₁ due to the gravitational field of mass₀ is:

$F_{1}={\frac {Mass_{0}^{act}*Mass_{1}^{pass}}{r^{2}}}$

likewise the force on a second object of arbitrary mass₂ due to the gravitational field of mass₀ is:

$F_{2}={\frac {Mass_{0}^{act}*Mass_{2}^{pass}}{r^{2}}}$

By definition of inertial mass:

$F=mass^{inertial}*acc$

if mass₁ and mass₂ are the same distance r from mass₀ then by the experimentally proven Weak equivalence principle they fall at the same rate (their accelerations are the same)

$acc_{1}={\frac {F_{1}}{mass_{1}^{inertial}}}=acc_{2}={\frac {F_{2}}{mass_{2}^{inertial}}}$

hence:

${\frac {Mass_{0}^{act}*Mass_{1}^{pass}}{r^{2}*mass_{1}^{inertial}}}={\frac {Mass_{0}^{act}*Mass_{2}^{pass}}{r^{2}*mass_{2}^{inertial}}}$

therefore:

${\frac {Mass_{1}^{pass}}{mass_{1}^{inertial}}}={\frac {Mass_{2}^{pass}}{mass_{2}^{inertial}}}$

in other words, passive gravitational mass must be proportional to inertial mass for all objects.

Further by Newtons third law of motion:

$F_{1}={\frac {Mass_{0}^{act}*Mass_{1}^{pass}}{r^{2}}}$ must be equal and opposite to

$F_{0}={\frac {Mass_{1}^{act}*Mass_{0}^{pass}}{r^{2}}}$

it follows that:

${\frac {Mass_{0}^{act}}{Mass_{0}^{pass}}}={\frac {Mass_{1}^{act}}{Mass_{1}^{pass}}}$

in other words, passive gravitational masses must be proportional to active gravitational mass for all objects. Lemmiwinks2 (talk) 01:24, 27 September 2009 (UTC)

I have created a list of known places where the above comment appears. Brian Jason Drake 11:40, 29 September 2009 (UTC)

Lemmiwinks2 deleted the section on their talk page containing that list. Revision 318510298 was the list revision containing that list. A cleaned-up version of the above comment now appears in the article. Brian Jason Drake 07:41, 28 October 2009 (UTC)

Important details

"The equivalence principle proper was introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1g"

This statement is only true if the test masses used are lifted from the earth, so that the total mass of the system does not change. External test masses will always accelerate at more than one g, depending on their mass.

The equivalence principal does not refer to the relative acceleration of a mass and the earth. It refers to the acceleration of a mass relative their mutual center of gravity. When a heavier body is used, the center of mass shifts, and the *relative* acceleration increases. Only the acceleration of the body relative to the mutual barycenter is unchanged.

"g" is not the acceleration of a body relative to the earth. It is the acceleration of a body relative to their common center of gravity.

Acceleration is often mentioned without providing a reference frame. "Gravitational acceleration" is ambiguous. Acceleration can be relative to the two bodies, or relative to their common center of mass, or relative to an arbitary reference frame, or relative to an encompassing barycenter (such as the solar system barycenter, geocenter, etc).

Newton's second law describes acceleration relative to a local instantaneously unaccelerated frame. g*m/r^2 is acceleration relative to the mutual center of mass of two bodies. g*(m1+m2)/r^2 is the relative acceleration of the two masses.

Uniform gravitational fields do not exist in reality. This should be stressed early in the article to avoid confusion.

This is why modern treatments of the equivalence princpal rely on the concept of a limit. Nearly all of the "principals" mentioned are true only in the limit of some infinitesimal. For example, the weak equivalence principle is true only in the limit of an infinitesimaly small object with infinite rigidity and an infinitely small mass separated by an infinitesmally small distance during an infinesimally small time inverval.

These restrictions must also be applyied to Newton's law of universal gravitation before it can be applied to physical systems. However, they are implicit in Newton's law due to the non-physical assumption of "point masses". The same technique should be applied here.

Norbeck (talk) 02:00, 30 December 2009 (UTC)

Section "The weak equivalence principle"

The mention of capillarity appears to be complete nonsense, and much of the section on Eötvös and his torsion balance is irrelevant. Could this be restored to something like it was in April 2009 before Celebration1981 (a user subsequently blocked) put it into this form?--Keith Edkins ( Talk ) 11:01, 4 January 2010 (UTC)

Newton's Theory Applies Only to Point Masses?

The present article says Newton's theory applies only to point masses. What does this mean? On the face of it, the statement seems to be false. Newton himself, in the Principia, certainly did not consider "point masses" at all, he always insisted on finite density, so the mass of a single point would be zero. So what does it mean to say that Newtonian gravity applies only to point masses?Urgent01 (talk) 17:27, 19 April 2010 (UTC)

Recent work showing non-equivalence of gravitational and inertial mass

I am not qualified to update the article properly but I wanted to bring the following paper to the attention of someone who can do it justice. Recent work has shown that in the quantum world, these must be different and in fact can be significantly different. The paper describing this work is [1] while the blog describing it is [2]. --Sgaragan (talk) 13:00, 15 June 2010 (UTC)

Direction of weight in space elevator

Einstein inoculated general relativity with the help of equivalence principle and spaceship/space elevator but I don't understand in which direction a person feel sensation of his weight = mg?

Upward means towards the centre of elevator OR

Downward means towards the floor of elevator.

Further, shouldn't a person inside space-elevator moves towards its centre due to universal law of gravitation [F=GMm/R^2]-shell theorem?Khattak#1-420