• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

Introduction

The article starts with the following sentence.
In the theory of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
This implies all the test performed in a laboratory frame on earth are performed in principle in a non-inertial reference frame.

2. Development of gravitation theory

Objects in free-fall do not experience being accelerated downward (e.g. toward the earth or other massive body) but rather weightlessness and no acceleration.
The concept of experience is very much related to what humans experience and has almost no physical meaning. The same with weightlessness.
This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any.
I think the reverse is also true: If an accelerometer registers any acceleration then the object is not in free-fall.
In reality when an accelerator registers long enough or is very accurate it will always measure an acceleration: Free fall is a theoretical concept and in some sense applies to an empty Universe which does not exist.
As an example: an inertial body moving along a geodesic through space can be trapped into an orbit around a large gravitational mass without ever experiencing acceleration. This is possible because spacetime is radically curved in close vicinity to a large gravitational mass. In such a situation the geodesic lines bend inward around the center of the mass and a free-floating (weightless) inertial body will simply follow those curved geodesics into an elliptical orbit.
The issue is what is the actual path that two objects follow. To claim that it is a geodesic is too simple. What you want to understand what happens when two large masses are involved. To claim that accelererometer (on board) will not measure acceleration is also of no much help.
These considerations suggest the following corollary to the equivalence principle, which Einstein formulated precisely in 1911:
Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of each object, that observer is in an accelerated frame of reference.
I would like to understand how an observer comes to this conclusion? What is he supposed to do.
Einstein combined the equivalence principle with special relativity to predict that clocks run at different rates in a gravitational potential, and light rays bend in a gravitational field, etc.
This is a tricky sentence because special relativity and gravitation are two different physical concepts.
That the behaviour of mechanical clocks is influenced by gravity can also be described by Newton's Law.
Unfortunate this sentence does not write anything about the speed of light rays in a gravitational field.

3.1 The weak equivalence principle

• The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition and structure.
The idea of a point mass is to calculate the strength of the gravitational field at a certain position. Point masses are used because they will not influence the strength of the gravitational field of a massive object. The deeper thought about the sentence is that a point sized object has no mass.

3.1.1 Active, passive, and inertial masses

By definition of active and passive gravitational mass, the force on M1 due to the gravitational field of M0 is:
F1 = M0act * M1pass/r^2
Along that same line: the force on M0 due to the gravitational field of M1 is:
F0 = M1act * M0pass/r^2
Why should not F1 be the same as F0?
That being the case we get M0act * M1pass = M1act * M0pass or M0act / M0pass = M1act / M1pass
The importance of this assertion is not clear,

3.2 The Einstein equivalence principle

What is now called the "Einstein equivalence principle" states that the weak equivalence principle holds, and that:[35]
The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
It is very difficult to understand it, i.e. to understand the details.
Here "local" has a very special meaning: not only must the experiment not look outside the laboratory, but it must also be small compared to variations in the gravitational field, tidal forces, so that the entire laboratory is freely falling. It also implies the absence of interactions with "external" fields other than the gravitational field
This place hugh constraints on its applicability.

3.3 The strong equivalence principle

The strong equivalence principle suggests the laws of gravitation are independent of velocity and location. In particular,
The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution.
and
The outcome of any local experiment (gravitational or not) in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
The question is what has all of this to do if you want to study the movement of objects through space. When you study that the concept "Local" has no usage.

3.3.1 Tests of the strong equivalence principle

The strong equivalence principle can be tested by searching for a variation of Newton's gravitational constant G over the life of the universe, or equivalently, variation in the masses of the fundamental particles.
This is a very tricky exercise.
To determine variation in the masses of the fundamental particles you must be able to measure its trajectories.

Reflection 1 - Implications equivalence of inertial mass and gravitational mass

On of the first questions to ask is what exactly is the definition and the difference between inertial mass and gravitational mass(accordingly to Einstein). Secondly how is each measured or calculated.
The interesting thing is that using Newton's Law mass is calculated based on observations using Newton's Law. Newton's Law starts from the concept that the sum of all the forces is zero and based on that concept (law) the masses are calculated with best fit observations.

Reflection 2 - Free fall

What is the difference between a person jumping from a building and the movement of any planet around the Sun?
From the point of view of the concept 'Free fall' there is none. The behaviour of each is defined by the masses in there immediate environment.
For a person jumping from a building this is the earth. For the Moon this is also the Earth.
Both are free falling in the sense that there are no internal forces which influence their behaviour.
The same is the case for any rocket in space with their engines turned off.

The next question is how do we calculate the mass of each object?
The simplest solution is to monitor the position of all the masses involved at regular intervals and to use Newton's Law. See previous reflection.

The final question is: The mass calculated in this way is this the gravitational mass or the inertial mass? IMO the difference does not make much sense. Instead of a person jumping from a building you can also drop an iron ball from the building and the same way as the person you can calculate the masses of all the objects involved.
Using that iron ball as a yardstick and with a balance you can calculate the mass of any object you want.

A final remark: What happens in case the iron ball (you drop) has the same mass as the Earth? You have to take that effect into account.

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Created: 22 October 2017

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