• 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.
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames.
This implies that all processes are independent of which inertial frame is selected.
This seems very reasonable, but does not claim anything about the processes them selves.
Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ship was moving or stationary.
Above the deck this is also tricky. The true issue is: is the ship moving or stationary. How do you decide that.
This is a phylosophical question.

### 1. Formulation

Among the axioms from Newton's theory are:
1. There exists an absolute space, in which Newton's laws are true. An inertial frame is a reference frame in relative uniform motion to absolute space.
2. All inertial frames share a universal time.
There exists no guarantee that the clocks in both reference frames tick at the same rate.
By the second axiom above, one can synchronize the clock in the two frames and assume t = t' .
You should synchronize two clocks in both frames when your trip starts and compare both clocks when the round trip is finished.

### 1.1 Newton's theory versus special relativity

Some of the assumptions and properties of Newton's theory are:
1. The existence of infinitely many inertial frames. Each frame is of infinite size (the entire universe may be covered by many linearly equivalent frames). Any two frames may be in relative uniform motion. (The relativistic nature of mechanics derived above shows that the absolute space assumption is not necessary.)
2. The inertial frames may move in all possible relative forms of uniform motion.
3. There is a universal, or absolute, notion of time.
4. Two inertial frames are related by a Galilean transformation.
5. In all inertial frames, Newton's laws, and gravity, hold.
See: Reflection 1 - Newton's Law versus Special Relativity.
In comparison, the corresponding statements from special relativity are as follows:
1. The existence, as well, of infinitely many non-inertial frames, each of which referenced to (and physically determined by) a unique set of spacetime coordinates. Each frame may be of infinite size, but its definition is always determined locally by contextual physical conditions. Any two frames may be in relative non-uniform motion (as long as it is assumed that this condition of relative motion implies a relativistic dynamical effect -and later, mechanical effect in general relativity- between both frames).
2. Rather than freely allowing all conditions of relative uniform motion between frames of reference, the relative velocity between two inertial frames becomes bounded above by the speed of light.
3. Instead of universal time, each inertial frame possesses its own notion of time.
4. The Galilean transformations are replaced by Lorentz transformations.
5. In all inertial frames, all laws of physics are the same.
See: Reflection 1 - Newton's Law versus Special Relativity.
Notice both theories assume the existence of inertial frames. In practice, the size of the frames in which they remain valid differ greatly, depending on gravitational tidal forces.
To understand this sentence you must understand what gravitational tidal forces are.
Gravity is the field of General relativity. See: Reflection 1 - Newton's Law versus Special Relativity.
In the appropriate context, a local Newtonian inertial frame, where Newton's theory remains a good model, extends to, roughly, 10^7 light years.
Why? What is the background of this text?
To get some idea: The diameter of our Galaxy is about 10^5 light Years. THe distance to the Andromeda Galaxy is 2.5*10^6 light year.
To apply Newton's Law you need one reference frame or coordination system.
In special relativity, one considers Einstein's cabins, cabins that fall freely in a gravitational field. According to Einstein's thought experiment, a man in such a cabin experiences (to a good approximation) no gravity and therefore the cabin is an approximate inertial frame. However, one has to assume that the size of the cabin is sufficiently small so that the gravitational field is approximately parallel in its interior.
This can greatly reduce the sizes of such approximate frames, in comparison to Newtonian frames. For example, an artificial satellite orbiting around earth can be viewed as a cabin. However, reasonably sensitive instruments would detect "microgravity" in such a situation because the "lines of force" of the Earth's gravitational field converge.
The first part (about Einstein's thought experiment) belongs not to SR but to General Relativity.
The main problem with this text is that different situations are compared.

As mentioned before Newton mainly discusses the planets around the sun. At first approximation all these objects fall freely in the gravitational field of the Sun. However none of the planets move in a straight line. If you take a small object ( a cabin) also such an object will not move (fall) in a straight line through the gravitational field of the Sun (disturbed by the individual fields of the planets).

In general, the convergence of gravitational fields in the universe dictates the scale at which one might consider such (local) inertial frames.

### Reflection 1 - Newton's Law versus Special Relativity.

A comparisson between Newton's Law and Special Relativity does not make sense. Newton's Law bassis is the force of gravity acting upon mutual atracted objects in space. When you want to study the same objects using relativity, you should study General Relativity. Special Relativity studies the behaviour of objects and phenomena on the surface of the Earth.

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Created: 5 March 2019

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