## Comments about the book "Einsteins Theory Of Relativity" by Max Born

This document contains comments about the book: "Einsteins Theory Of Relativity" by Max Born. Dover Publications 1965
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### 2.6 Dynamics - The law of Iertia - page 29

After these preliminaries we revert to the question with which we started: How do forces generate motion?
You can also start with a different question: What is the cause of motion.
This question is much more based on what is physical observed. Forces are not. They are postulated.
Galileo was the first to take the right point of view.
Undoubtly Galileo was a very clever man, but how do we know that he took the right POW?
He observed that it is a fallacy to assume that wherever there is motion there must always be force.
Observed? How?
Rather it must be asked what quantitative property of motion is in a regular fixed relation to force, whether it be position of the moving body, its velocity, its acceleration, or some composite quantity dependent on all of these.
This is a very difficult sentence. A much simpler way is to demonstrate velocity in a simple experiment. Such an experiment consists of three parts:
1. A force to start the movement.
2. No force to keep the movement in progress
3. A force in the opposite direction to stop the movement.
It is important to remark that this experiment only requires one reference frame. This reference frame is considered at rest.
No amount of reflection will allow us to derive an answer from philosophy.
It would be better to write: No answer can be expected from a thought experiment. Philosophical considerations can be used to define the rules of the game; what is good or bad science.
We must address ourselves directly to nature.
This is a very doubtfull answer. To find an answer, you have to perform experiments.
The answer which she gives is that force has an influence in effecting changes of velocity but that no force is necessary to maintain a motion in which the magnitude and the direction of velocity remain unaltered
As explained in the above experiment.
The law of inertia (or persistence) is by no means so obvious as its simple expression might lead us to surmise.
In our experience we do not know of bodies that are really withdrawn from all external influences; and if we use our imaginations to picture how they travel in their solitary rectilinear paths with constant velocity through astronomic space, we are once confronted with the problem of the absolutely straight path in space absolutely at rest, which we shall have to deal later.
This sentence combines astronomic space with absolute space without explaining the difference. This makes this sentence not very clear

### Page 30

It has been established that in the absence of forces the velocity remains constant in direction and motion on the table.
By means of experiment, I assume.
Consequently the forces will be associated with the change of velocity, the acceleration.
I would write: Forces are the cause that the velocity of an object changes. When there is an increase in speed this is called acceleration. When there is a decrease: deacceleration.
In what way they are associated can again be decided only by experiment.
100% true. And not by nature, as is suggested on the previous page

### 2.7 Dynamics - Impulses - page 30

We have presented the acceleration of a uniform motion as a limiting case of sudden changes of velocity of brief uniform motions.
What should have been written that the concepts (sudden) change of velocity and (sudden) acceleration are the same.
Hence we shall first have to inquire how a single sudden change of velocity is produced by the application of a force.
It is better to write:
How the application of a force produces a (single sudden) change of velocity.
The force is the cause.

### 2.10 Force and Acceleration - page 35

Before pursuing the striking parallel between mass and weight mentioned in the foregoing section we shall apply the laws as far established to the case of forces that act continuously
Okay
A force that acts continuously generates a motion whose velocity alters continuously
This is the correct way to describe an experiment. A continuous force is the cause that the velocity changes
We now suppose the force replaced by a rapid succession of blows or impulses.
Okay. The assumption should be that each blow or impulse should the same i.e. incorporates the same force (power)
At each blow the velocity will then suffer a sudden change, and there will result a world line that is bent many times, as in Fig 10, which will approximate the true, uniformly curved, world line and may be used in place of the latter in the calculations.
The curve in Fig 10 does not represent anything what can be called continuous.

### 2.12 Weight and Mass - page 41

At the beginning of this chapter when we introduced the concept of mass, we observed that mass and weight exhibit a remarkable parallelism.
Okay
Heavy bodies offer a stronger resistance to an accelerating force than light bodies.
To make the facts quite clear, let us again consider the experiment of setting into motion spheres on a smooth horizontal table by means of impacts or impulses
Experiments are the preferred way to do science.
We next apply equal blows to A and B on the table and observe the velocity attained

### Page 44

THe law of the proportionality of weight to mass is often expressed as follows:
Gravitational and inertial mass are equal.
Also know as the equivalence principle.

### 3.1 Absolute Space and Absolute Time - page 54

The principle of mechanics, as here developed, were parly suggested to Newton by Galileo's works and partly created by himself.
This means Newton did not start from nothing. His work is based on Galileo's achievements.
To Newton we owe above all the definitions and laws in such a generalized form that they appear detached from earth-bound experiments and can be applied to events in astronomic space.
Okay.
In arriving at these laws Newton had to preface the actual mechanical principles by making definite assertions about space and time.
Without any proof?
Without such determinations even the simplest law of mechanics that of inertia, makes no sense
See next sentence.
According to this law, a body on which no force is acting is to move uniformly in a straight line.
That means that this law only describes very specific experiments.
Let us consider the table upon which we first experimented with the rolling sphere
Strictly speaking a rolling sphere on a table is not the correct condition to demonstrate the law of inertia does not hold. Gravity is involved.
If the sphere rolls on the table in a straight line, an observer who follows and measures its path from another planet would have to assert that the path is not a straight line according to his point of view.
That is correct. Any observer, from an other planet, which observes motions here on earth, will observe that motions here on earth are much more completed than observed by an observer on earth.
This may be rougly illustrated as follows:
i.e. demonstrated.
Now turn the disk uniformly as possible and at the same time draw a pencil along the ruler with constant velocity so that the pencil marks its curve on the disk.
In principle you can define two experiments:
1. When you draw a line along a ruler fixed to a piece of paper the result will be a straight line.
2. When you draw a line along a ruler and the a piece of paper moves the result will not be a straight line.
That is easy to understand.

### Page 55

This example shows clearly that the law of inertia makes sense, indeed, only when the space, or rather, the system of reference in which the rectilinear character of the motion is to hold, is exactly specified.
If you assume one reference frame for both experiments (see above) than it is clear:
1. The mathematics (the law) used to describe experiment (1) are simple.
2. The mathematics (the law) used to describe experiment (2) are complex.

### Page 56

In experiments on the earth - for example, of the sphere rolling on the table - the path of the freely moving body is not actually straight but a little curved.
Tht is correct. The reason is because the surface of the earth is not accurately measured.
The fact that this escapes our immediate notice is due only to the shortness of the paths used in the experiments compared with the dimensions of the earth.
That means this is an accuracy problem.
Here, as often happened in science, the inaccuracy of observation led to the discovery of an important fact.
I don't understand this sentence.
IMO this is an observation issue. What the result of the experiment will show, performed over a much longer duration, that the predicted position does not match the observed position.
The observed position will show that the rolling sphere is on the surface of the earth. The predicted position will show that the sphere is above the earth.
There are two reasons for this discrepency:
1. The surface of the earth is not flat.
2. Gravity and friction have to be taken into account. The result will be that the sphere will stop rolling.
Newton was therefore confronted with the task of finding the system of reference in which the law of inertia and all the other laws of mechanics were to hold.
That is the wrong approach. The law of inertia only holds when are no other forces are involved. Generally speaking each experiment is performed in its own environment and has its own constraints. For example: in almost all experiments gravity is involved. Combining all these experiments in one physical landscape, can lead to additional problems.
The general phylosophy to follow is start simple and slowly make the experiments more complex.
Probably it was for such reasons that Newton arrived at the conviction that an empirical system of refence fixed by material bodies could never be the foundation of a law involving the idea of inertia.
The problem is what is the best way to start the development of any theory? Is this an empty universe with one object ? Is this an universe with many objects?
In both cases in principle you can start with one reference frame.
By the law itself, through its close connection with Euclid's doctrine of space, the element of which is a straight line, appears as the natural starting point of the dynamics of astronomic space.
• In Mathematics a straight line is a good starting point.
• In astronomy (Celestial Mechanics) a binary system is a good starting point.
If one were for instance to take the period of rotation of the earth as unit of time, the law of inertia would not be exactly valid because there are some irregularities in the motion of the earth.
To use the rotation period of the earth as the basis of a clock or to define time is not a very good idea, because such a clock is not accurate.
As a consequence to study celestial mechanics using such a clock is also not a good idea.

### Page 57

In this way Newton came to the conclusion that there is an absolute space and an absolute time.
Did Newton really come to the conclusion that there is an absolute time?
Concerning time he, Newton, says:
Absolute, True and Mathematical Time, of itself, and from its own nature flows equably without regard to any thing external, and by another name is called Duration: Relative, Apparent, and Common Time is some sensible and external (whether accurate or unequable) measure of Duration by means of motion, which is commonly used instead of True time; such as an Hour, a Day, a Month a Year.
It may be that there is no such thing as an equable motion, whereby time may be accurately measured.
In the above quotations by Newton, he emphasis more that there exists a physical time which flows equable and that measuring the same (motion) gives an inaccurate result.
All motions may be acceleratated and retarded, but the True, or equable progress, of Absolute time is liable to no change.
When you replace that by a statement like: "The speed of light is the same in all directions" which also makes an absolute claim, then what is the difference?
Concerning space Newton expresses similar options. He says:
Absolute Space, in its own nature, without regard to anything external, remains always similar and immovable. Relative Space is some moveable dimension or measure of the absolute spaces; which our sense determine by the position to bodies; and which is vulagary taken for immoveable space....
My interpretation is that Absolute Space is the total physical space. Relative Space is a small part of Absolute Space.
Newton further says:
And so instead of absolute places and motions, we use realtive ones;and that whitout any inconvenience in common affairs: but in Philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest , to which the places and motions may be refeferred....
This final part related to 'at rest' is interesting.
The definite statement, both in the definition of absolute time and in that of absolute space, that these two quantities exist "without reference to any external object whatsoever" seems strange from one like Newton, for he often emphasizes that he wishes to investigate what is actual, what is ascertainable by observation.
If Newton his guiding phylosophy are actual facts and observations than there is nothing wrong when he starts his investigation slightly different.
But what exists "without reference to any external object whatsoever" is not ascertainable and is not a fact.
What is wrong with that? Why not call this a postulate?

### Page 68

This is called the relativity principle of classical mechanics, and it may be formulated in various ways.
This can easily lead to confusion.
For the present,we shall state the following:
Relative to a coordinate system moving rectilinearly and uniformly through absolute space, the laws of mechanics have exactly the same expression as when referred to a coordinate system at rest in space.
This sentence can only be understood if their exists a clear definition of what the laws of mechanics are and what is even more important on which specific physical processes they are based.
To see the truth of this law we need only keep clear in our minds the funadamental laws of mechanics, the law of impulsive forces, and the concepts that occur in it.
For the law of impulsive forces the same rule applies.
We now that a blow produces a change of velocity.
We know: that when introduce a force on an object the position of that object changes.
But a change is quite independent of whether the velocities before and after the blow, v1 and v2 are referred to absolute space or to a system of reference which is itself moving with the constant velocity a.
The first question is: is how is this constant velocity a measured? IMO in the same way as v1 and v2. That means in the absolute frame considered at rest.
If the moving body is moving before the blow in space with the velocity v1 = 5 cm/sec,then an observer moving with the velocity a = 2cm/sec in the same direction would measure only the relative velocity v' = v1-a = 5-2 = 3 cm/sec.
this is clearly not a measurement but a calculation!
If the body now experiences a blow in the direction of motion which increases its velocity to v2=7 cm/sec then the moving observer would measure the final velocity as v2'= v2-a= 7-2=5 cm/sec.
Again this is clearly not a measurement but a calculation! .
Thus the change of velocity produced by the blow is w = v2-v1 = 7-5 = 2 cm/sec in absolute space.
This is clearly a calculation.
On the other hand the moving observer notes the increase of velocity as:
w' = v2'-v1' = (v2-a) - (v1-a) = v2 - v1 = w = 5-3 = 2 cm/sec
This result is independent of the speed of the moving observer or moving reference frame.
 This result seems to prove that the laws of physics are the same in every reference frame. However it is not that simple. Let us perform the following experiment: (This experiment is based Consider an (absolute) frame at rest.
Exactly the same holds for continuous forces and for accelerations produced by them.

### Page 69

The root of this law is clearly the law of inertia, according to which a motion of translation occurs when no forces act.
Physical this means that the object moves in a straight line and that the distance between the positions measured at a regural interval is the same.
A system of bodies all of which travel through space with the same constant velocity is, therefore, not only at rest regards their mutual position, but also without actions of forces manifesting themselves on the bodies of the system in consequence of the motion.
A system of bodies all of which travel through space with the same constant velocity is an articial situation. This reflects typical a thought experiment. In real gravity will be involved.
But if the bodies of the system exert forces on one another, the motions therby produced will occur relatively just as if common motion of translation were not taking place.
When the system exert forces on one another the original straight lines will now be curved.
Thus for an observer moving with the system, it would not be distinquishable from one at rest.
The issue is much more if you have a system of bodies and each body also incorporates an observer will any of these observers measure different.
The experience, repeated daily and thousands of times, that we observe nothing of the translatory motion of the earth is an impressive proof of this law.
It should be mentioned that in this case we can not speak of clearly a system at rest (an observer at rest) versus a moving reference frame (an moving observer with a constant speed).
In fact what we have is a moving reference frame and a moving observer, which both experience a force at t0, at t1, at t2 etc. The result is that the observer experiences nothing, specific because the force acts continuous.

It should also be mentioned that if you consider all the planets of the solar system each observer on each planet can easily observe that his position compared with the position of the other planets continuously changes.

But the same fact is seen in motions on the earth.
I expect on the surface of the earth.
Everyone knows that in a ship or railway carriage moving uniformly mechanical events occur in the same way as on earth (considered at rest)
If you drive a car in a straight line and you turn your steering wheel you can make a turn and if you drive to hard you can flip over.
If you do exactly the same and you consider yourself at rest (in the car) the result seems 'strange'. To consider yourself at rest seems a wrong assumption.

### Page 290

But the result of the experimental researches was that it is impossible to detect motion with respect to the ether by physical means.
What this means that there exists no clear definition of the concept ether. As such ether has no physical meaning.
From this it follows that absolute simultaneity can likewise be ascertained in no way whatever.
From this conclusion nothing else can be concluded. In order to solve the issue absolute simulateity versus relative simultaneity we are back to zero.
The paradox contained in this assertion vanishes if we remind ourselves that to compare time by light signals we must know the exact value of the velicity of light, while the measurement of the latter again entails the determination of a length of time.
To solve this issue you must only use clocks as a measurement of clock-counts.
In order to measure clock-counts using light signals the only assumption is that the speed of light is the same in all directions.
When you compare clock-counts of two different clocks, and when you assume: (1) they should not and (2) one is at rest, than you can calculate the speed of the other clock.
Thus we are obviously moving in a vicious circle.
That is correct.
Even if we cannot attain absolute simultaneity, however, it is possible, as Einstein has shown, to define relative simultaneity for all clocks that are relative at rest with respect to one another without knowing the value of velocity of the signals.
This sentence is tricky because it uses both concept absolute and relative without any clear definition of each.

### Page 229

But when two claim what, by its very meaning, can belong to only one, it must be concluded that the claim ifself is meaningless
Both claims can also be wrong But that does not mean that under certain conditions one can be right.
There is no such thing as absolute simulataneity
That means there exists no Now.
Whoever has once grasped this will find it difficult to understand why it took many years of exact research for this simple fact to be recognized.
Because it is not a simple fact. A simple fact should be explained by a simple example.
It is the repetition of the old story of Columbus egg.
Columbus egg has nothing to do with this.
At the same time Columbus egg is a very interesting tool to study physics, special related to Stellar Mechanics

### Page 231

On the other hand an observer moving with the system can with equal right assert that A1',B1' are simultaneous events (world points)
If an observer at rest and a moving observer both make the same claim of events which are physical not the same in the frame of the observer at rest i.e. A1 and B1 versus A1' and B1', than both identical claims (being both simultaneous events) can not be true.

The reader is advised to read this document: The purpose of Science In that document is explained that the two events A1,B1 and two events A1',B1' are physical different when those events are used to start an engine.

### Page 291

An interesting application of the transformation formula of p and E is made in quantum theory, of which we shall speak briefly

### 7.1 Relativity in the Case of Arbitrary Motions - page 309

In dealing with classical mechanics we discussed in detail the reasons that led Newton to conceive the idea of absolute space and absolute time.
Reading the text at page 57 you get the idea that absolute is the physical situation and relative has to do what is physical measured. There is nothing wrong with that.
The unsatisfactory features of this theory may be recognized from the following example:
Okay
Suppose two bodies S1 and S2 of the same deformable (fluid) material and the same size to be present in astronomic space at such a distance from each other that ordinary gravitational effects of the one on the other are inappreciably small (Fig 134)
The exclusion of gravitational effects can be important.
It is not clear if both bodies are physical connected to each other and if and how they are 'hanging' in space.
Each of these bodies is to be in equilibrium under the action of the gravitation of its parts on each other and the remaining physical forces so that no relative motions of its parts with respect to each other occur.
This sentence is also not very clear. What is meant with: "remaining physical forces".
To mention 'in equilibrium' and the final part of the sentence, seems to be double.
But the two bodies are to execute a relative motion of rotation with constant velocity about the line connecting their centers.
That means you need a common reference frame which allows an outside observer to make this observation.
This signifies that an observer on the body S1 notes a uniform rotation of the other body S2 with regard his own system of reference, and vice versa.
I assume that observer S1 is on the South Pole of object S1 (above).
I assume that observer S2 is on the North Pole of object S2 (below).
1. I don't under stand how observer S1 can establish that body S2 is rotating assuming that body S1 is rotating with the same velocity. In that case the relative velocity = 0
2. In case the relative velocity is non zero, each observer can establish that the other one is rotating, however in opposite directions. This is in conflict with Fig 134.
Now suppose each of these observers determines the shape of the body on which he stands and that it is found S1 (above) is a sphere and S2 is a flattened ellipsoid of rotation.
This clearly raises the question: what are all the actions involved as part of this experiment, before the sketch portrayed in Fig 134, was drawn.

### Fig 134

Two originally spherical liquid bodies S1 and S2 in relative rotation about a common axis
Fig 134 Shows two spheres S1 (above) and S2 (blow). Sphere S2 seems to be more elliptical. The common axis is rotating anti-clockwise.

Newton mechanics would infer from the different shapes of the two bodies that S1 is at rest in absolute space but that S2 executes an absolute rotation.
The words absolute can be eliminated. As such we get:
"that S1 is at rest and that S2 rotates."
The flattening of S2 is then explicable by centrifugal forces.
First you have to explain what centrifugal forces are.
This example illustrates clearly how absolute space is introduced as the (fictitious) cause.
No, it does not. This example is in fact much more complicated, to explain it in a simple way. You can read this in next and on page 311

### Page 311

If we ask "What is the cause of centrifugal forces?" the answer is: "Absolute space."
Who was the first person to give that answer? Space can never be the cause of any physical force.
Let us now again consider two bodies S1 and S2
Okay
If space is not accepted as the cause of their different shapes we must look for other and more convincing causes.
That is correct.
One ofcourse is a very serious question: Is this experiment a true description of a real experiment?
Let it be supposed that there are no other material bodies outside the two bodies S1 and S2.
This information is not explicit mentioned at page 309 . But I doubt if that is enough to explain the bevior of this experiment.
The different shapes of S1 and S2 would then be really inexplicable.
It makes this whole discussion worthless?
But is this difference in shapes, then, an empirical fact?
If you have any discussion, in any way, about an experiment, showing results which are physical not possible, then, such a discussion is senseless.
We have never had the experience of observing two bodies that are poised alone in the universe.
Strictly speaking that is true. However discussing a binary system, which consists of two stars, planets or blackholes is not senseless.
The assumption that two real bodies S1 and S2 would behave differently under these circumstances is supported by no evidence at all.
Rather, we must demand of a satisfactory mechanics that it exclude this assumption.

### Page 312

But if we observe in the case of two real bodies S1 and S2 the different behavior above described (we know that the planets), we can take as the cause of this only distant masses.
Distant masses can already be assumed at the start of the experiment. It is impossible that two objects are in relative rotation about a commom axis. When this is the case gravity will take care that they will collide. Only external masses (gravity) can prevent this, like
In the real world such masses are actual present, namely, the countless legion of stars.
100% correct.
The idea that the totality of distant masses must be the cause of the centrifugal forces was first expressed by the philosopher-physicist Ernst Mach, whose writing had a profound influence on Einstein.
The most important consequence of the distant masses is that you can have a binary star system of two rotating stars.
This also explains why you can have 'in principle' two objects S1 and S2 rotating among a common axis.
In fact in order to explain the whole experiment you should start from one reference frame which includes a background of stars in all directions.
The flattening of a planet is the greater, the greater its velocity of rotation with respect to this system of reference attached to the distant masses.
Here they speak about one reference frame. That seems the most logical.
Accordingly we shall demand that the laws of mechanics - and, indeed of physics in general - involve only the relative positions and motions of bodies.
We can not demand anything. The only thing that we can proclaim as good science is that the laws are a good description of the physical processes they describe i.e. are based on observations. In principle there is nothing wrong to use only one reference frame.
The biggest error is to use the concept as Absolute Space (as a cause) to explain any physical process.
No system of reference may be favored a priori with the inertial systems of Newton mechanics and Einstein's special theory of relativity; otherwise absolute accelerations with respect to these favored systems of reference and not only relative motions of bodies would enter into physical laws.
This sentence is not clear. Newton's Law includes distance and acceleration. Both are relative calculated concepts based on 'absolute' observations. What is wrong with that?
We thus arrive at the postulate that the true laws of physics must hold in exactly the same way in systems of reference that are moving arbitrary.
Again like I mentioned before: What is wrong when you study everything in one reference frame.
To be more specific: If all the laws of physics are all in agreement with this postulate is that a guarantee that the law is correct?

### 7.2 The principle of Equivalence - page 312

Fullfillment of this postulate requires an entirely new formulation of the law of inertia, since this is what inertial systems their favored position.
Okay, lets wait and see.
The inertia of a body is to be regarded no longer as an effect of absolute space but rather as due to other bodies.
IMO inertia is typical considered as an earth based concept and that is wrong.
In that sense

### Page 313

Earlier we discussed the law of equality of gravitational and inertial mass
See page 44
For events on earth it states that all bodies fall equally quickly; for motions of heavenly bodies it says that acceleration is independent of the mass of the moving body.
It is impossible that there exist a law which is specific for our earth
This law plays a fundamental part not only in mechanics but, indeed, in the whole of physics.
How can a law that claim that two concepts are the same, become fundamental, because in fact the whole law can be eliminated.
A law should describe something which includes physical change.

### 7.13 The Unified Field Theory - page 370

In spite of this, Einstein began, a short time after finishing the general theory of relativity, to work on a unified field theory of relativity, to work on a unified field theory, which was to combine the laws of electromagnetism and gravitation in one system of formulae, always hoping that he could obtain in this way not only a formal unification but an explanation of the existence of elementary particles and their strange behavior which is commonly described with the help of quantum theory.
This is a very important (clever) exercise. The problem is that it is very difficult (if not impossible) to explain the why related to the existence of elementary particles.

### Page 371

It is impossible to give an idea of quantum theory in the frame of this book (See page: page 291 )

### Page 372

There are two directions of research
Okay
One accepts only special relativity and tries to construct the universal law from the facts of observation, in particular from the most general symmetry properperties of the interaction of elementary particles as revealed by experiment.
That is one way. A different way is even not to accept special relativity
The other direction of research tends to establish laws which are invariant in regard to general transformations, and follows there fore Einstein's general relativity in its procedure.
This raises the question why universal laws have to be invariant to general transformations.

### Index

Absolute Space page 57, page 68, page 309, 310, 311
Absolute time page 57, page 309
At rest page 57, page 68, page 310
Centrifugal force page 310, page 312,
Clock page 56, page 57
Columbus egg page 229
Elementary particles page 371
Equivalence principle page 44, page 312, page 313
Experiment page 45
Galileo page 54
General theory of Relativity page 370,
Inertia - the law of page 54, page 312
Invariant page 372,
Law of impulsive forces page 68
Law of mechanics page 68
Mach page 312
Michelson and Morley page 298
Newton, Quotations from, page 57
Observation page 372, page 372
Quantum theory page 291, page 371
Special Relativity page 372
Unified field theory page 370

### Reflection 1 - General.

The greatest adventage of this book is that it is clear. Almost all the different parts of the book are clear and easy to follow what Max Born means
However that does not mean that I understand every thing in the sense that I agree with everything or that I have no questions. Part of the problem can be lack of carefull reading from my part. The most important issues in this book which fall in this cathegory are written in red .

One of the most important part of the book are the Experiments. In order to discus experiments you have to follow certain rules: You have to describe them as complete as possible from start to finish.
It is not enough to start a description that two objects are in relative motion. By preference you must start from a situation that all objects are in the same initial state (at the same position and 'at rest') and by preference the final state should be the same. As part of the experiment forces can be used to introduce different speeds.
As part of any experiment it is also important how the speeds are measured. Specific if different reference frames are used. Also it is important to make a clear distinction between a measurement and a calculation. If you write w = v1 + v2 than the speed w is a calculated value.
Strictly speaking a speed is also a calculated value, based on the measurements of two positions and two events linked to one object. However there is nothing wrong to call a speed a measurement when it is a speed linked to one object.

### Reflection 2 - Experiment portrayed in Fig 134

Fig 134 at page 310 shows an experiment which involves two liquid bodies S1 and S2. What the text mentiones and what Fig 134 shows is that S1 is a sphere and S2 a flattened ellipsoid. What the text near Fig 134 shows is this original are two spherical liquid bodies.
What this means is that this experiment is surrounded with uncertainties, which should not be the case.
What you need, when you discuss an experiment, is all the details involved as part of the experiment. That means its initial state and all the actions that were involved as part of the experiment, to reach the final state. This is clearly missing.
As such, any mentioning that (absolute) space is involved to explain any physical effect, as written on page 310 , does not make any sense.

However what becomes clear after studying page page 311 , the explanation of this behavior can not be found by considering both bodies in isolation. That is wrong. The whole universe in some sense has to be taken into account. In short this experiment is part of celestial mechanics. That means all the text written at the second half of page 309, at page 310 and the top part of page 311 is misleading, including everything related to reference frames and (absolute) space.

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