## Comments about the book "Introducing Einstein's Relativity" by Ray d'Inverno

This document contains comments about the book: "Introducing Einstein's Relativity" by Ray d'Inverno. Reprinted 1998
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Paragraph 2.5 The principle of special relativity

This means that, if one inertial observer carries out some dynamical experiment and discovers a physical law, then any other inertial observer performing the same experiments must discover the same law.
This is tricky.
Put another way these laws must be invariant under a Galilean transformation.
That maybe is true, but does that say anything about the experiment itself? about the physical process involved? I doubt that.
In Newtonian theory, we cannot determine the absolute position in space of an event, but only its position relative to some other event.
This is an unlucky description of Newtonian theory. Newton's main discussion is about forces. When the sum of all the forces is zero than the speed (and direction) of an object stays the same *. When this is not the case the speed (and direction) of an object will change. (*) or be at rest.
Thus both position and velocity are relative concepts.
This sentence is empty. No content.
Einstein realized that the principle as stated above is empty because there is no such thing as a purely dynamical experiment.
The issue are the physical process and these processes are dynamic i.e. changing in time.
Even on every elementary level any dynamical experiment we think of performing involves observation, i.e. looking and looking is part of optics not dynamics.
That is why you should try to describe of processes all purely from the physical point of view and remove the step of looking i.e. human observations.
Postulte I. Principle of special relativity
All inertial observers are equivalent
But this does not say anything about the physical processes involved.

### Paragraph 2.6. The constancy of the velocity of light

However the approach of the k-calculus is to dispense with the rigid ruler and use radar methods for measuring distances.
The use of a rigid ruler is not very practical, specific if you want to measure distances in space. However rigid rulers have one big advantage: You can measure distances simultaneous and that is when you use light signals not the case.
What is rigidity anyway? If a moving frame appears non-rigid in another frame, which, if either is the rigid one?
Tricky sentence
IMO a frame along a straight track defines a rigid frame. A train on that track also.
Thus an observer measures the distance of an object by sending out a light signal which is reflected off the object and received back by the observer.
This sentence should mention the implication if the inner working of the clock used, also involves lightsignals.

### Paragraph 2.7. The k-factor

Let us assume we have two observers A at rest and B moving away from A with uniform constant speed.
It is tricky to use the word observers. In real it is one object A at rest and object B moving.
However you can also claim that B is at rest and A is moving.
Then in a space-time diagram the worldline of A will be represented by a vertical straight line and the worldline of B by a straightline at an angle to A's as shown in Fig 2.6
It is easy to make such a sketch, but this is very difficult to draw an accurate one based on observations.
 ``` Time ^ |A /B +3 | . | | / +2 | . | | / +1 | . | | / 0-------------- ``` The problem is in the units of the time axis. The Time axis shows the time in days. +1 is at day 1, +2 is at day 2 etc The line A is simple because object A is supposed to be at rest. Line B is much more complex. To draw this line you can send out each day a flash and monitor the reflection. When you send at t0 and you receive at t1 than the total duration of the signal is t1-t0. The maximum distance is at (t0+t1)/2 and the distance is (t1-t0)/2 * c. This calculation requires that the speed of light is c in both directions and that the line A is in "absolute" rest.

### Paragraph 2.8. Relative speed of two inertial observers

Hence, if v is the velocity of B relative to A we find
v = x/t = (k^2-1)/(k^2+1)

### Paragraph 2.11. Relative speed of two inertial observers

The moral is that in SR time is a more difficult concept to work with than the absolute time of Newton.
Newton does not use the concept of absolute time nor absolute space. He somehow uses the concepts of time and space and uses somehow only one reference frame. Within that frame everywhere the speed of light is c. I'am specific writing somehow because he only considers the solar system as his reference frame.

### Paragraph 2.12. The Lorentz transformations

Let event P have coordinates (t,x) relative to A and (t',x') relative to B (Fig 2.17)
How do you know that?

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Created: 22 August 2017

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