• 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.

### 2 Einstein's use of the principle

There is a fundamental issue in relativity theory. If all motion is relative, how can we measure the inertia of a body?
The fundamental issue is: What means that something is at rest. How can something in a frame linked to earth called at rest, while the planets seem to rotate? The issue is how can we measure the mass of a body? How can we measure the mass of a body at rest?
Ofcourse first you must answer the question: what means inertia?
We must measure the inertia with respect to something else.
Correct. We must measure based on a standard.
But what if we imagine a particle completely on its own in the universe?
That is physical not possible.
If a bucket is filled with water *, and made to rotate, initially the water remains still, but then, gradually, the walls of the vessel communicate their motion to the water, making it curve and climb up the borders of the bucket, because of the centrifugal forces produced by the rotation.
Correct. That means this is physical process performed on earth can controlled by the gravity forces on earth.
Immediate next:
This thought experiment demonstrates that the centrifugal forces arise only when the water is in rotation with respect to the absolute space (represented here by the earth's reference frame, or better, the distant stars) instead, when the bucket was rotating with respect to the water no centrifugal forces were produced, this indicating that the latter was still with respect to the absolute space.
There are certain remarks:
• The previous text can not be considered a thought experiment.
• There is a huge physical different between the three concepts: absolute space, the earth's reference frame and the distant stars. You should not speak about absolute space, but about the total mass of the whole universe.
• What is important is that both the bucket and the water are rotating, with respect to the surface of the earth, or the earth, or the sun (within its frame) or all the stars (with the frame of 'absolute' space i.e. the universe)
Mach, in his book, says that:
the bucket experiment only demonstrates that when the water is in rotation with respect to the bucket no centrifugal forces are produced, and that we cannot know how the water would behave if in the experiment the bucket's walls were increased in depth and width until they became leagues big.
When you stir water in a large cup with a flat surface the water will behave the same.
Immediate next:
In Mach's idea this concept of absolute motion should be substituted with a total relativism in which every motion, uniform or accelerated, has sense only in reference to other bodies (i.e., one cannot simply say that the water is rotating, but must specify if it's rotating with respect to the vessel or to the earth).
In this view, the apparent forces that seem to permit discrimination between relative and "absolute" motions should only be considered etc.
IMO the concept of absolute versus relative should be dropped. As part of the text it should be clear what is mentioned.
When you write: Two trains approach an observer on a platform. One with a speed of 100 km/hour from the left and one with a speed of 100 km/hour from the right.
The most important question is exactly how are these calculated and not if the speeds are relative or absolute

### 3 Mach's principle in general relativity

Einstein, before completing his development of the general theory of relativity, found an effect which he interpreted as being evidence of Mach's principle.
evidence?
We assume a fixed background for conceptual simplicity, construct a large spherical shell of mass, and set it spinning in that background.
It is very tricky to start too simple.
Better is: We assume a massif homogeneous background, construct a sphere or shell of mass and set it spinning in that background.
In principle it does not matter if the background rotates or not. In practice it cannot rotate, neither initially the sphere or shell.
The spinning of that mass must have a cause.
The reference frame in the interior of this shell will precess with respect to the fixed background.
To demonstrate precession this experiment is much more complex.
You need something 'fixed' and heavy, like the surface of the earth.
You need some small and assymetric, like a top (toy, gyroscope).
The top will precession when its axis of rotation itself also rotates.

To demonstrate precession, starting from nothing is not as simple as it sounds. See: Reflection 2 - Precession

### Reflection 1 - Physical laws.

Generally speaking the physical laws can be divided in two groups: Local Physical laws and Global Physical Laws.
Local Physical laws are also called: Single Objects Laws. A single object can be the Earth. That means Local Physical Laws describe the processes that take place on the Earth, On the Sun or Inside a Black Hole. Special Relativity is typical a Local Physical Law.
Global Physical laws are also called: Multiple Object Laws. The Objects considered are not physical connected. A typical example of multiple objects is our Solar system or our Galaxy. The first consist of the Sun and many planets, the second of many stars rotating around a black. Newton's Law and General Relativity are Global Physical Laws.
One important concept that is treated different in the two types of laws is the concept mass.
The processes here on earth are described by local physical processes, but that does not mean that the earth is an indivisible object. That is not true. As long as these smaller objects are physical linked to the earth, it is okay.
When different objects are considered, the mass of each can be measured by using a standard mass and a balance. The working of a balance is based on the concept of gravity.
To calculate the masses of the solar system Newton's law is used or general relativity. The result is the mass of ech (single) object.

The experiment with a bucket (See * is typical a local physical problem and not global. The fact (observation) that surface of the water in the basket is flat or hollow, has nothing to do with the stars. The initial state of the basket is at rest. This is caused by the total mass of the basket and the water in the basket being attracted towards the mass of the earth. The turning of the basket is caused by an outside source. The result is also that the water starts to turn. etc.

### Reflection 2 - precession

What is the simplest experiment to demonstrate precession.
Starting point for this dicussion, will be an universe, homogeneous and uniformly filled with matter. This universe can be finite. The shape should be a sphere. When this is the case there is no effective gravitational field. The force of gravity is the same in all directions. The universe such depicted is not the same as empty (absolute) space.
From within this universe I consider one round object. IMO such an object can not rotate, when you start from a state when it is not rotating. When you apply an outside force the object will move, but not rotate.
In order to rotate the object should be 'flat'.

IMO when you want to demonstrate precession you need at least two objects. One large one and one small one. The small one should be positioned at the surface of the large one. When that is the case you can rotate the smaller object, by applying two forces in opposite positions (at the equator), in opposite directions. The force of gravity will keep the small one in position. This rotation is easier when the shape is not round, shorter in the direction of rotation (i.e. the vertical direction) and longer in the horizontal plane (along the equator).
When the axis of rotating is vertical you can apply a force at the top to bring the vertical axis in rotation.

When the small object is not connected to the large one you can have the situation like the Moon ( a satellite) circling around the Earth. To demonstrate precession is more complex, because each force applied to the satellite will also change its position and not always its rotation. When the satellite is someway locked like our Moon (keeping always the same 'face' towards the Earth) to increase the rotation is easier.

This subject is not finished and requires more thoughts.

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Created: 2 March 2019

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