This document contains comments about the subject "Inertial frame of reference" in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph Reflection I explain my own opinion.

### Contents

The article starts with the following sentence.
In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame or inertial space) is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner.
IMO the concepts homogeneously and isotropically have nothing to do with a reference frame. Both concepts define what is called the Cosmological Principle. See: Comments about: Cosmological principle
The combination "that the frame describes time" with "in a time-independent manner" does not make sense
All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration
The reader should understand that inertial frames do not exist. What exist are two trains which are in relative movement. Each of these trains you can mathematical define as a reference frame. The (abstarct) origins are in rectilinear motion.
In reality you can define many inertial frames of which one is called at rest.
Physical laws take the same form in all inertial frames.
Both concepts "Physical laws" and "inertial frames" are abstract concepts which cannot be tested.
What does it mean "the same form"? Why not identical.
The following sentence is much more specific:
All experiments (processes) are the same if they are performed in a train at rest or in a moving train
The question is if this is true.
By contrast, in a non-inertial reference frame the laws of physics vary depending on the acceleration of that frame with respect to an inertial frame, and the usual physical forces must be supplemented by fictitious forces.
The issue is that at this point no clear definition is given between an inertial versus a non-inertial frame.
The indirect conclusion of the text is that an inertial frame is in a constant linear motion and a non-inertail frame not (i.e. they have a variable speed). In reality the movement of all objects in the universe are in acceleration.
For example, a ball dropped towards the ground does not go exactly straight down because the Earth is rotating.
See: Reflection

### 1. Introduction

The motion of a body can only be described relative to something else - other bodies, observers, or a set of space-time coordinates. These are called frames of reference.
In order to describe the motion of a body only need one frame of reference (and one clock)
This frame represents the x,y,z coordinates relative to one reference point or origin.
The wording space-time coordinates is misleading and requires an explanation.
If the coordinates are chosen badly, the laws of motion may be more complex than necessary.
This information seems to be in conflict with what is claimed above: "Physical laws take the same form in all inertial frames." (1)
In an inertial frame, Newton's first law (the law of inertia) is satisfied: Any free motion has a constant magnitude and direction.
Such an inertial frame only exists in theory.
Newton's second law for a particle takes the form: F = m*a
See Next comment.
In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate O about an axis, takes the form: F' = m*a
A rotating reference frame is a non-inertial frame

### 2.1 A set of frames where the laws of physics are simple

According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation:
IMO special relativity has nothing to do with all physical laws
Special relativity describes the behaviour of more or less identical physical processes. For each physical law this is the same.
In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment (otherwise the differences would set up an absolute standard reference frame).
There are two issues:
• The first issue is to what extend an observer can establish his speed relative to a reference frame.
• The second issue is to what extend an observer can establish his speed relative to the speed of light.

### 2.2 Absolute space

Newton posited an absolute space considered well approximated by a frame of reference stationary relative to the fixed stars. An inertial frame was then one in uniform translation relative to absolute space.
What that means is that in practice Newton only used one frame i.e. the largest possible to describe the evolution of the entire universe.

### 3. Newton's inertial frame of reference

One approach is to argue that all real forces drop off with distance from their sources in a known manner, so we have only to be sure that a body is far enough away from all sources to ensure that no force is present.
That is only true when a source is at infinite distance from any source, implying that such a special place does not exist in the Universe.

### 4. Newtonian mechanics

Classical mechanics, which includes relativity, assumes the equivalence of all inertial reference frames.
Relativity (Relativistic Mechanics) does not belong to Classical mechanics
It is more the other way around: Relativistic mechanics assumes the equivalence of all reference frames. Next we read:
Newtonian mechanics makes the additional assumptions of absolute space and absolute time.
Newtonian mechanics and Clasical mechanics are one of the same.
Historical it is the other way around: Relativistic mechanics considers the difference between absolute space and time (Newton) versus relative space and time and introduces the concept space-time.
Given these two assumptions, the coordinates of the same event (a point in space and time) described in two inertial reference frames are related by a Galilean transformation.
r' = r - r0 - v*t
t' = t - t0
The problem is that IMO this assumption is clearly only theoretical. The issue is how do you demonstrate this relation in the reality.
The reader should be aware of two different concepts:
• Transformations which use the same origin. This type is purely mathematical.
• Transformations using different origins (reference frames). This type is much more difficult physical to demonstrate.

### 5. Special relativity

Einstein's theory of special relativity, like Newtonian mechanics, assumes the equivalence of all inertial reference frames, but makes an additional assumption, foreign to Newtonian mechanics, namely, that in free space light always is propagated with the speed of light c0,
This requires a clear definition of what is free space and what is it not. As such this sentence implies that the speed of light is not always equal to c0.
For example what happens if light (photons) are emitted from a heavy mass i.e. a blackhole.
a defined value independent of its direction of propagation and its frequency, and also independent of the state of motion of the emitting body.
What is not mentioned if the speed of a light ray (photons) is constant through his complete voyage through space.
This whole definition boils down to the question: how is c0 measured in one direction.
The problem with measuring the speed of light is that in order to measure this speeds clocks have to be used. These clocks have to be synchronised and in order to do that lightsignals have to be used. This makes the measuring of the speed of light in one direction almost impossible.
This second assumption has been verified experimentally and leads to counter-intuitive deductions including:
Specif what has be verified experimentally and how.
I expect the Michelson and Morison experiment, but this is nowhere mentioned.
Next:
1. time dilation (moving clocks tick more slowly)
2. length contraction (moving objects are shortened in the direction of motion)
3. relativity of simultaneity (simultaneous events in one reference frame are not simultaneous in almost all frames moving relative to the first).
1. Moving clocks tick more slowly is a physical process. The issue is what that has to do with the speed of light.
To demonstrate the effect the clock is positioned in an airplane and flown around the earth. This introduces all sorts of fictitious forces which should be investigated with great care.
2. length contraction, assuming this is also a physical process, should be demonstrated without the use of clocks.
3. When you discuss the concept of simultaneous events the first question to answer is if there are simultaneous events. I mean things that happen (completely independent of any human interference) which you call simultaneous but are not observed as such. IMO in the total universe million things are happening simultaneous all at the same time of which I'am completely unaware.
If you agree which that than it is very easy to accept that: for two observers to observe these two events simultaneous they have to be at a certain position at a certain moment (which can be different), but most probably that both will not observe these events simultaneous.
Incidentally, because of the limitations on speeds faster than the speed of light, notice that a rotating frame of reference (which is a non-inertial frame, of course) cannot be used out to arbitrary distances because at large radius its components would move faster than the speed of light.
The fact that you cannot rotate any arbitrary length rod has nothing to do with reference frames. This is a physical fact. The same is that you cannot rotate each disc with any arbitrary radius with every speed. This is also a physical (experimental) fact.
However in an expanding universe those speeds are possible?

### 6. General relativity

Einstein�s general theory modifies the distinction between nominally "inertial" and "noninertial" effects by replacing special relativity's "flat" Minkowski Space with a metric that produces non-zero curvature.
That is easy to write.
The problem is how do you that in reality, based on an actual situation.
In general relativity, the principle of inertia is replaced with the principle of geodesic motion, whereby objects move in a way dictated by the curvature of spacetime.
That is easy to write in principle but very difficult to perform in reality.
Please supply as an example the movement of the planets around the Sun.
As a consequence of this curvature, it is not a given in general relativity that inertial objects moving at a particular rate with respect to each other will continue to do so.
Why using concepts like: inertial objects and particular rate ? The universe evolves based on all the physical processes evolving in the past.
This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity.
Inertial frames are not something that exist. In physics you always need is a reference frame to describe the positions of the objects under investigation.
A different question to answer is: And what about geodesics. Are they local or global?

However, the general theory reduces to the special theory over sufficiently small regions of spacetime, where curvature effects become less important and the earlier inertial frame arguments can come back into play.
Is this also true considering the movement of the stars in the Milky way?
And what about the planets around the Sun?
Over a period of a million years?
Schwarzschild pointed out that that was invariably seen: the direction of the angular momentum of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar System.
This is not true for the planet Mercury?

### 8.1.1 Theory

Inertial and non-inertial reference frames can be distinguished by the absence or presence of fictitious forces, as explained shortly
That means an inertial frame is not subject of fictitious forces
The important issue is what are fictitious forces.
The presence of fictitious forces indicates the physical laws are not the simplest laws available so, in terms of the special principle of relativity, a frame where fictitious forces are present is not an inertial frame
Again what are fictitious forces.
How do you decide that laws are the simplest?
Bodies in non-inertial reference frames are subject to so-called fictitious forces (pseudo-forces); that is, forces that result from the acceleration of the reference frame itself and not from any physical force acting on the body.

### 8.1.2 Applications

Inertial navigation systems used a cluster of gyroscopes and accelerometers to determine accelerations relative to inertial space.
I would rephrase this sentence as:
Inertial navigation systems use a cluster of gyroscopes and accelerometers to determine positions and velocities relative to their own inertial reference frame.
After a gyroscope is spun up in a particular orientation in inertial space, the law of conservation of angular momentum requires that it retain that orientation as long as no external forces are applied to it.
It is the other way around:
After a gyroscope is spun up in a particular orientation, it retains that orientation as long as no external forces are applied.
This behaviour is described by the law of conservation of angular momentum.
The issue is how to design (if you do not know) such an apparatus.

### Reflection - Rest frame

A ball dropped towards the ground does not go exactly straight down because the Earth is rotating.
Which of the two sentences is correct:
• A ball dropped does not follow straight line because the Earth is rotating.
• A ball dropped follows a straight line from the viewpoint of the center of the earth.
The problem with both sentences is that the ball does not move in a straight line considered from the center of the Sun.
Considered from the center of our galaxy the movement is even more complicated.

The point I'm trying to make is that in order to understand the movement of objects you should take the largest possible frame. To be more specific the difference between an inertial frame and non-inertial frame does not make much sense because in all processes accelerations are involved which have to be taken into account.

### Reflection 2 - Local versus global frame

The object of physical science is to try to describe physical phenomena in its most simplest form. Starting point is a reference frame, i.e. a coordination system to describe the positions of the objects involved.
• A local frame is the "smallest" point of view or frame used to describe a physical process. This can be a train or airplane or rocket.
In the case of a moving train the observer in the train is at rest but environment of the train is moving. To describe this moving environment is very complex.
• A global frame is a larger frame to describe the same physical process.
In the case of a moving train the frame is the surface of the earth. In this frame only the train is moving. The result is a much more simple description.
• But also the earth is moving around the Sun. The next step is a frame centered around the Sun.
• But also the sun is moving. The next step is the center of galaxy which finally should encompass the total universe
Starting point to describe the movement of the objects is Newton's Law. In case of Newton's Law the objests are considered point masses. In order to describe the physical processes within the objects them self (rotating, expanding and contracting) additional laws have to be used.

### Reflection 3 - Why this discussion of inertial frames ?

What we as humans what to understand is the evolution of the Universe. That means we want to understand the evolution of the galaxies and stars surrounding us at present and in the past. One important tool to describe that is a (reference) frame i.e. only one. Most important a fixed frame. Clocks in this fixed frame at fixed positions show the Universal Time or the age of the universe. Secondly we want to investigate identical processes and what are the reasons that these seemingly identical processes are different. In short we want to understand the laws of nature.
Objects even the whole universe can rotate. There are two ways to describe this behaviour:
From within this rotating object or from outside this object.
1. From within this rotating object the observer and the object is at rest and the whole universe is rotating. Light rays do not follow straight lines.
2. From outside this rotating object the whole universe and the observer are at rest and only the object is rotating. Light rays in general follow straight lines
The second way is the most simple.
The same reasoning applies why it is simpler to take the Sun as a reference point versus the Earth. It is even simpler to take the center of our Galaxy or the center of the local cluster.

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Created: 7 January 2015

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