Comments about the book "Introduction to Special Relativity" by Wolgang Rindler.

This document contains comments about the book: "Introduction to Special Relativity" by Wolgang Rindler. Clarendon Press - Oxford 1982

To read the book select this link: https://kampungpadi.files.wordpress.com/2010/01/wolfgang-rindler-introduction-to-special-relativity.pdf

• The text in italics is copied from that url
  
• Immediate followed by some comments
  

In the last paragraph I explain my own opinion.

Contents

• 1. The Foudations of Special Relativity - page 1
• 3. Inertial frames in Special Reltivity - page 5
• 4. Einstein's two axioms for Special Relativity - page 8
• 2. Relativistic Kinematics -page 27
• 11. Time dilation - page 31
• 12. The Twin paradox - page 34

Reflection

• Reflection 1 - Physics versus Mathematics.
• Reflection 2 - Reference frame versus lineair frame
• Reflection 3 - What came first: the chicken or the egg?
• Reflection 4 - The world accordingly to a flat TV screen

page 1

3. Inertial frames in Special Reltivity - page 5

A frame of reference is a convential standard of rest relative to which measurements can be made and experiments described.

Okay.

For example if we choose a frame rigidly attached to the earth, the various points of earth remain at rest in this frame while the 'fixed' stars all trace out vast circles in the course of each day; if, on the other hand, we choose a frame attached to the fixed stars then these remain at rest while points on earth, other than those on its axis, trace out approximate circles in the course of each day, and the earth itself traces out an ellipse in the course of each year; and so on.

This discussion is rather misleading.

• If you choose a frame rigidly attached to the earth your primarly point of study can only be earth based processes.
• If you choose a frame including the stars of our galaxy then such a frame allows you the study all the stars of our galaxy, including the Sun and the earth.
  The initial state can reflect the positions of the stars based on a certain date.

Both frames can be considered at rest, but the objects included are not at rest.

An inertial frame is one in which spatial relations, as determined by rigid scales at rest in the frame, are Euclidean and in which there exist a universal time in terms of free particles remain at rest or continue to move with constant speed along straight lines (i.e. in terms of which free particles obey Newton's first law)

It is not clear what the difference is between an inertial frame and the frame mentioned previous.
What means universal time? Why mention Newton's first law?

page 6

We can further picture the difining particles as carrying clocks that indicate the universal time throughout the frame.

My understanding of this sentence implies:

• That the difining particles are by definition at rest in the inertial frame.
• That all the clocks are identical.
• That all the clocks (at any instance, now) show the same time.
• That two events which are identified by the same clock reading are simultaneous in the inertial frame.

Now let us see the relevance of this special relativity.

Okay

We shall adopt the modern view that a physical theory is an abstract mathematical model whose applications to the real world consist of correspondences between a subset of it and a subset of the real world.

This sentence seems overly complex. Why not use this definition:

We shall adopt the modern view that a physical theory is an abstract mathematical model of a subset of the real world.

Anyway, the main problem is that most of what is happening in the real world can not be understood by means of mathematics.
In fact the deeper issue is which physical processes can be described by mathematics.

In line with this view, special relativity is the theory of an ideal physics referred to an ideal set of infinitely extended gravity-freeinertial frames, such as we described above.

See also page 5
The question to answer is why do you need inertial frames i.e. more than one.

page 7

Our next axiom is that all inertial frames are spatially homogeneous and isotropic, not only in their assumed Euclidean geometry but for the performance of all physical experiments.

It is very tricky to put mathematical constraints on the performance of physical experiments without first explaining these constraints i.e. homogeneous and isotropic.

It already eleminates the possible existence of an ether drift in any inertial frame.

If a certain theory eliminates certain processes (possibilities) apriory, what is the purpose to demonstrate the validity of possiblities using the same theory?

4. Einstein's two axioms for Special Relativity - page 8

page 27

11. Time dilation - page 31

12. The Twin paradox - page 34

Reflection 1. - Physics versus Mathematics.

The starting point of view of the discussed book is: "We shall adopt the modern view that a physical theory is an abstract mathematical model of a subset of the real world." This immediate raises one question: What comes first the real world or the physical theory?
A simple answer is the physical world because all theories are human spinsels.
A much more bassic question is:
Is the physical theory (model) of each subset the same? (A subset defined as a separate physical process) I doubt that. My understanding is that a theory is relevant for a set of similar, almost identical processes.
Assuming that is the case we get the next question: How many theories are there and what makes them specific?
IMO there are a hugh number of Theories and Laws and each are relevant for specific physical domains.
According to Wikipedia Physics the following five fields can be considered:

nuclear and particle physics (13); atomic, molecular, and optical physics (3) ; condensed matter physics (7) ; astrophysics (6); and applied physics.

The number in between brackets are the major theories in each field. General Relativity and Newton's Law of universal gravitation belong to astrophysics.
In that same Wikipedia document we can read:

* The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with motion in the absence of gravitational fields and the general theory of relativity with motion and its connection with gravitation.

What this all means is that if you want to study physics, first of all you have to define what you want to investigate because generally speaking its area of interest involves its own theory or mathematics. This raises a new question: Can you use all forms of mathematics to describe the physical world? The answer is temporarily yes but finally no. With temporarily is meant: internal as part of a set of calculations.
For example: The final (calculated) length of an object is always positif. For example: Temporarly you can use complex numbers, but the final answer can not contain a complex number.

What is important that most physical processes can not be described or explained by mathematics or numbers.
Generally speaking something that does not change can be measured. Something that changes is difficult to measure. That is the problem because what we want to understand is why does something change, what are the interactions involved. If we understand that, we humans can interfer and change the future in a direction we want, for the good or for the worse.

The text above related to the theory of relativity raises an issue related to frames. See: *
Consider a moving observer A in a merry-go-round observing a different observer B in that same merry-go-round? In that case the reference frame of observer B is in motion with respect to observer A. At the same time also the reference frame of observer A is in motion with respect to observer B. Consider also a different observer C outside the merry-go-round. In that case the different reference frames of both A and B each are in motion with respect to observer C.
My concern is what is the use of all these frames why an approach based on one reference frame seems the most logical.
See for more: Reflection 2 - Reference frame versus lineair frame What is even more: Why consider multiple frames when the frames itself don't influence the physical processes which are evolving within each frame. What is even more the physical processes in each will influence each other, on a larger time scale. See for more: Reflection 2 - Reference frame versus lineair frame

Mathematics as a science follows a very rigid manner. It starts with a set of bassic axioms or laws. Using these axioms more complex axioms or laws are develloped all in the mathematical domain. (This text is on purpose kept simple).
Physics as a science is different. The leading component is the physical world, mainly based on observations. In order to describe (its behaviour) mathematics is used. Physics as a science is much less exact as mathematics because it involves uncertainties based on the physical state of the universe. The second component of physics is mathematics. Mathematics as a tool can be used to transform physical observations into single numbers, into a sequence of numbers in time. Secondly mathematical equations can be developped which establish the relations between different parameters which inturn are an image to the physical changes which happen in the real processes studied.
But that is in principle. In reality the physical results of mathematics used should not be in conflict of what is physical possible.
For example in certain theories parameters (forces) between objects are calculated using the distance between the objects. Within the same theory objects are considered as point masses, mainly to make 'things' simpler. This can raise physical problems when these objects approach each other. From a mathematical point of view the distance between the objects can be come zero which is physical impossible. Secondly in order to calculate the parameter (a force) involves dividing by zero which leads to infinities (singularities) which are also physical impossible. What this means is that in order to apply mathematics, certain physical constraints should be tested as part of the calculations, in order to prevent situations which are physical impossible.

Reflection 2 - reference frame versus inertial frame

Consider as your reference frame a frame linked to the center of our galaxy. This frame we can assume to be at rest. As such the frame is not moving and not rotating. The speed of light we assume to be the same in all directions.
Within that frame there are stars with are moving in circles around the center of our galaxy i.e. a Black Hole in Sagitarrius A.

Consider a second reference frame linked to the center of our Sun. From a local point of view this frame can be considered at rest, but from a global point of view this is a moving frame. You could also consider this frame as a frame with moves in a straight line. However this is an approximation because considering a longer period, this frame moves in a circle, undergoing continuous accelaration.

Reflection 3 - What came first: the chicken or the egg?

This question looks like a paradox, but it is not.

• The answer that the chicken came first is wrong, because how can you have a chicken without an egg.
• The answer that the egg came first is wrong, because how can you have an egg without a chicken.

To answer this question you have to consider the evolution of each chicken:

At any moment: You have a chicken or you have both or you have an egg

There after the process repeats itself. In both directions i.e. forward or backward in time.

Forward in time the process can evolve and become more complex.
Backward in time the process becomes simpler
Considering humans the same 'problem' exists.

The purpose of this question is an introduction to a slightly different question:

What came there first: the real world or the theory?

The problem with this question is that the question is not clear. The question does not make sense. The real world , the total universe in order to discus, requires a description at all levels of detail, of something that physical exists . A theory or law is not something that exists. It is a description of a subset of the real world in a mathematical notation. Both are invented and improved by humans, but the real world is physcical and mathematics is not. Mathematics is a tool specific used when the underlying processes are stable.

The fact that certain processes are stable and can de described by mathematics is not an explanation why these processes are stable. The explanation is in the detail of the processes discussed.

Reflection 4 - The world accordingly to a flat TV screen?

Consider we are performing a simulation of our solar system. What do we see on our TV screen? The answer is this depends on certain parameters.

• Suppose the program performs an update once every day at 12 o'clock.
  If that is the case the program displays a point indicating the position of each of the planets at 12 o'clock. When the program runs for one year the program shows one complete revolution for the earth and for the inner planets Mercury and Venus. For the outer planets it displays part of a revolution.
  
• The next issue is exactly what does the program displays? This depends about the mathematics (or laws) used in the programme.
  When the mathematics used is Newton's Law the program is based on the idea that after each cycle (when all the new positions are calculated) the time for all the positions is the same. This is also true after each next cycle. Also for each previous cycle, starting with cycle 1.
  What that means is that what we observe on the screen is not actual what we see. If you want to observe on the TV screen what we observe, you have to take the light travel time into account. In short what we see is the state of the universe in the past.

Now let us discuss a certain experiment implemented with a test program.

• When you start this program the first thing that you see is TV screen in Red . Next it changes to Orange , to Yellow , to Green , to Blue etc. All in all it changes to 16 colors and than it repeats it self. At the right hand side there is a clock, which shows clock counts. This counts increase each time when there is a color change.
• The purpose behind this program is to get an idea about the state of the total universe. Specific about the concept of time related to the total universe.

• To makes this clear the screen also contains a box, drawn with 12 white lines. The bottom plane corners are marked A,B,C and D. The top plane contains the corners are marked E,F,G and H. In mathematical notation the point A is marked as (0,0,0) and the point H as (1,1,1) The point A is considered the origin. The point H (1,1,1) is at the farthest distance from point A. However it easy to imagine that there are 7 more of thes points Three in the same plane as point H with z= 1, at the locations: (-1,1,1), (-1,-1,1) and (1,-1,1) And for at the plane z = -1 : (1,1,-1), (-1,1,-1), (-1,-1,-1) and (1,-1,-1)

  G--------H . | . | E | F | | | | | | | | | | | | | | | | | | D--------C | . | . A--------B

• Now we are performing an experiment.
  At a certain moment there is a flash of light at point A and this flash (in white) propagates in the sphere through our universe.
  At a certain moment this sphere will go through the points EBD. At that same moment the whole screen will

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