## Comments about the book "Astronomy and Cosmology - A Modern Course" by Fred Hoyle

This document contains comments about the book: "Astronomy and Cosmology - A Modern Course" by Fred Hoyle. W.H.Freeman and Company 1975
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### page 7

In describing their relative motions it makes no difference whether we consider the Earth to move around the Sun, or the Sun to move around the Earth, as in Figure 1.5
The question is does that physical makes no difference. Does it physical makes no difference if the Sun moves around the center of Our Galaxy or the center of Our Galaxy around the Sun.
The relative motion of the Earth and the Sun is the same in these two figures.
Okay
From a physical point of view, however, is the situation the same?
That is a very important question. But is this the right question? Is the Earth moving around the Sun or the Sun around the Earth? Is that question important? How are these speeds calculated
Accordingly to the physical theory developed from the work of Isaac Newton, the two are not the same; Figure 1.4 is correct.
The physical theory by Isaac Newton is based on observations, however the theory itself should be indepent of any human involvment. The demonstration if that theory is correct should be based on future observations.
Figure 1.5, although giving a correct description of the apparent motion of the Sun in the sky, does not lead to a correct understanding of the situation.
Important sentence.

### Figure 1.4

 ``` Sun ^ |. . .| V Earth In many problems it is useful to think of the Earth as a Speck moving in its annual orbit around the Sun ```

### Figure 1.5

 ``` Sun Earth ^ |. . .| V The relative motion of the Earth and Sun is the same here as in Figure 1.4 ```

### page 8

* By understanding we imply the ability to predict ahead of time what the relation of the Earth and Sun is going to be, not only to each other but to other bodies in the Universe.
Understanding has much more to do with a physical explanation of the details of the process studied. For a medical cure understanding means the details of the process, how the cure works that our health is restored.
Prediction is a far more powerful achievement than description since description, is nothing more than a restatement of what has already been observed to occur.
** A description are the facts in the past. A prediction are the facts in the future. If in the future the description and 'our' prediction are the same, 'we' understand.
However, according to the physical theory developed by Albert Einstein Figure 1.4 and Figure 1.5 are indeed physically equivalent to each other.
What is much more important that 'we understand'. See **
Since Einstein's theory is technically superior to Newton's, the two descriptions must therefore be regarded as entirely equivalent.
That is a wrong reason. The proof of the pudding is the eating i.e. See **
In Einstein's theory we could use Figure 1.5 as the basis for prediction if we wished to do so.
That is not true. The basis for prediction should be text at the top of this page. See *, and should include a much more complex situation.

### page 122

With the proviso that the single spatial dimension of Figure 4.5 should really be three spatial dimensions, we now have a representation of both space and time i.e. of spacetime
It should be understand that spacetime is not a physical concept. Nothing can be measured in space time. Every photo is an image of the surrounding space at a certain instant.
The path of the particle in this representation is often referred to as the wordline of the particle.

### 4.3 Time-Sense and Causality - 129

What determines which is the source particle and which is the detector?
Okay
The answer to this question is that radiative interactions always go forward in time.
This raises the question: What means forward in time and how is this established. The answer should be valid for the total of the universe.
In Figure 4.7 the motion of a particle at point P influences the motion of particle b at Q, because Q is later than P
In Figure 4.7 this is clear, but how do you establish this in the reality?
The answer to our Question, therefore, is that we distinquish the source particle from the detector through the time-sense of the interaction.
This raises a physical question: What is time?

### 4.4 Quantum Mechanics and Atomic Structure - 131

Two problems were described above that can be solved exactly, i.e. in precise mathematical terms.
Only a very limited number of physical systems or behavior can be descibed in mathematical terms.

### 4.5 Reflections on the Sophistication of Physical Theories - 145

As a reflection of this situation we can identify T with the classical theory of particles and radiation and T' with the form of quantum mechanics discovered in 1925 by Heisenberg and by Schrödinger.
Such a reflection makes only sense if you identify the experiments that these theories explain. If the type of experiments is the same and the results are the same than apparently there is no difference between T and T'.
If the results of T' are more accurate than T' has the preference.
If the number of experiments is larger (wider) than also T' has the preference.
Yet within only a few years T' became replaced by T''
Okay.
According to the 1925 form of the theory, the amplitude for a specific path to go from a point P to a point Q was represented by a complex number.
Any wave can mathematically be represented by a complex number, but the physical part is not a complex number.
Then Dirac found four complex numbers should be used. The resulting improved theory, T'', is known as relativistic quantum mechanics and the set of 4 complex numbers denting the amplitude is known as the spin of the particle.

### 5.3 The nature of Light Wave - page 184

Second, there is a spatial correlation between the up-and-down motions at different points,
The word correlation describes part of an accuracy issue.
This spatial ordering is measured by the wavelength(lambda), the distance between two adjacent wave crest, or two adjacent wave troughs.
To measure this distance at any instant is not easy. In real the positions of all crests have to be measured simultaneous.
As time proceeds, the whole spatial pattern moves along as shown in Figure 5.43
Figure 5.43 is an idealisation.
The time required to complete the oscillation at each point is simply the time required by the wave to travel through a distance equal to the wave length.
Also this 'picture' is too simple.
If the speed of travel of the wave is V, then the time required for the wave to move through the distance lamba is simple lambda/V.
This type of physical reasoning is wrong You always have to start from observations and using these observations you can calculate a certain parameter i.e the speed V.
At a clock time t0 you have to measure the position the position of the crest x0(to)
At t1 you have to measure the position of that same crest x1(t1)
The speed of the crest or wave is then: (x1-x0)/(t1-t0).

### Appendix II.4 "Local" Geometry and its relation to the Physical World - page 213

It might seem at first sight as if we now have a grip on the problem of what we mean physically by the numbers x,y,z, but a little consideration soon reveals difficulties.
Okay.
No such set of measurements could be carried out instantaneously; yet x,y,z, are to be measured at a specific moment of time, the moment when the particle is at the Point P of its path.
The second half is important the first half not. The problem is that you want to know the position and the Universal time when the particle is at a certain position. The only way to establish that, is when the universe consists of a grid, with a clock at each grid point.
When you do that for the same particle twice you can calculate the velocity of this particle. The whole problem is to what extend you can do that in the reality? Because performing both measurements raises still their own problems. One problem is to detect the particle twice, without disturbing the particle.

### page 215

 Figure II.20 The radiation from a particle in regular oscillation posses a wave structure. Radiation reaching a detector particle causes it to oscillate. The strength of a radiation field emitted from a particle in oscillation fluctuates from place to place. When such a field reaches an other particle that particle can also start to oscillate, specific when the two particles are identical. This is related about the concept: Your own frequency or eigen frequency.

### page 218

What we are saying is that observation and measurements show that certain tenets of of Euclidean geometry are valid in the actual world, provided the distances over which they are considered to hold are not too great.
I expect the same can be said for any type of geometry, specific the line segment PQ^2 defined at page 219.

### 7. Atoms, Nuclei, and the evolution of the Sun - Page 299

Becquerel repeated the experiment without shining light on his uranium material, and still the photographis plate became fogged.
The importance is that Becquerel performed an experiment.
So it followed that the uranium was doing "something" all by it self. But what?
Okay

### page 306

The nineteenth-century concept of indestructable atoms was dead. Atoms could change into one other
Okay.
When they did so , either an alpha-ray (helium or a beta-ray (electron) was emitted, and energy was released in the motion of these emitted particles
This leaves on overall question: Where did the original of this energy came from, at the creation of the universe.

### 15.2 Universal Time - 640

To deal with this question we consider that although our system of local geometry may fail for very distant galaxies, our local geometry remains valid valid for galaxies that are not too far away.
What is the physical reasoning behind this statement?
When something global geometry is not precise than local geometry is also not precieze. Local geometry can be defined as precise for all the distances measured on earth because a ruler can be used. All other distances can be defined as approximations because light signals are involved implying the use of clocks, which require synchronisation, which also involves light signals

### Appendix VI.2 - What is time? - Page 693

There are many ways to set up systems of time and space measurements, which can be connected with each other by mathematical formulas, in such a way that, if we know from observation how to describe our everday world in terms of one system, then we can work out how the world should be described in terms of any one of the other systems.
A very complex sentence.

### page 695

 Figure VI.5 The expansion and subsequent contraction of a local object without internal pressure follows the rules that are striking similar to those of a world geometry of type B. The local object begins by expanding (i)to a maximum size (ii) then falls back (iii), and continues to fall (iv) intil it eventfully becomes a black hole (v). The evolution of the universe and the evolution of a single object does not follow any rule.
These cosmological considerations have relevance to localized.
Cosmological considertions, including the evolution of the total Universe, have nothing to do with the possible evolution of a single
Consider a spherical distribution of material of uniform density suddenly set in outward expansion as in Figure VI.5. If this impulsive outward motion is violent enough, the object will dissipate itself, as in an explosion. But for a modest outward impulse, the motion will eventually by the checked by the gravitational attraction of the object on itself, and the expansion will be followed by contraction, just as in the cosmological example in Figure VI.4
The total evolution of the universe consisting of millions of stars and galaxies cannot be compared with the evolution of a single star, which is a single physical object, becoming a red giant, and which finaly becomes a Black Hole i.e. an object with a small size and large mass, approximate the same as the original star.

### Reflection 1 - Overview

The book: "Astronomy and Cosmology - A Modern Course" by Fred Hoyle is an excellent, understandable, clear book. The main reason why this is the case is because Mr Fred Hoyle himself understands the topics discussed very well. If that is not the case, the book will reflect this.

The main comments in this review are about the topics discussed, where I feel certain doubts.

### Reflection 2 - General Relativity

In page 7 and in page 8 specific in relation to the movement of the Sun and the Earth. IMO that situation is too simple.

### Figure Ref2a

 ``` Moon Earth Sun ^ ^ |. |. . .| .| V V Earth Moon Sun centered configuration ```

### Figure Ref2b

 ``` Sun Moon Earth ^ ^ |. |. . .| .| V V Moon Sun Earth centered configuration ```

### Figure Ref2c

 ``` Sun Sun Earth Moon ^ ^ ^ 1|. 2|. 1|. . .|2 .|1 .|2 V V V Earth Sun Sun Moon centered configuration ```

• Fig Ref 2A shows the Sun centered configuration.
The Earth revolves in a circle around the Sun, and the Moon in a circle around the Earth.
• Fig Ref 2B shows the Earth centered configuration.
Both the Sun and the Moon revolve in a circle around the Earth.
• Fig Ref 2C shows the Moon centered configuration.
The Earth revolves in a circle around the Moon.
The trajectory for the Sun is complex. On average the trajectory is a circle around the Moon. In reality the position of the Sun depents on the position of the Earth.
• When the Earth is in position 1 (left of the Moon), the Sun can only be in the two positions 1, left and right from the Sun.
• When the Earth is in position 2 (right of the Moon), the Sun can only be in the two positions 2, left and right from the Sun.
That means at the left side, Sun position 1 and position 2 are the Maximum and Mininum distances.
At the right side, Sun position 1 and position 2 are the Minimum and Maximum distances.
In reality the Sun follows a sinosoidale function between those two values.
The bottom line is, to call all the 3 Figures Ref2, equivalent is up to the reader.

### Reflection 3 - Time, Clock and Universal Time

The evolution of the universe is a continuous evolving process, implying that the 3D world of which we are a part is not static but dynamic.
The concept of Time, is a typical human related concept based on the idea that we can remember what has happened in the part and we can predict the future. This happens because we have a brain. Animals also have this capability, but it is less develloped.
Simply described, the capabilty to remember, is based on storing 3D images of our surroundings. The different images are identical of what you can call the time component in our existance. This component is not something personal but related to the whole of the universe. The present image which shows the whole of the universe we call: now. The previous images we call the past and expected images the future.
It is only the present moment that exist. The present nor the future exist.

In order to classify the images we use a clock. A clock is some sort of oscillator. Each count represent an image but infact any number of images can be considered inbetween two counts.
It is important that a clock or oscillator is a physical process and its behaviour can be subject of change or movement.
 ``` B --- /|\ / | \ / | \ / | \ t1/ |t2 \t1 / | \ / | \ / | \ -C--------A--------D- v1 v1 ``` Figure 1 - l=v1*t1
 ``` B --- /|\ / | \ / | \ / | \ t1/ |t2 \t1 / | \ / | \ / | \ -C--------A--------D- v2 v2 ``` Figure 2 - l=v2*t2
 ``` B -------------------- ^ /^\ ^ . / | \ . . / | \ . . / | \ . . / |t2 \ . . / | \ . . / | \ . ./ | \. -C--------A--------D- v2 v2 ``` Figure 3 - l=v2*t2

• Both Figure 1 and Figure 2 show a clock based on light signals.
• There is one light signal which moves from A to B, is reflected, and goes back to A. This signal represents a point at rest and the duration is t2. The length of AB = c * t2 with c the speed of light.
• There is one light signal which moves from C to B, is reflected and detected at point D. This signal represents a moving point and the total duration is 2 * t1. The length of CB (BD) = c * t1 with c the speed of light.
• Using CA = AD = l we come to the following equation: (c * t1)^2 = (c * t2)^2 + l^2 (1)
or t1^2 = t2^2 + (l/c)^2 or that t1>t2
This means, considering a fixed duration, that the number of ticks with the moving clocks (the light path CBD) is less than the number of ticks with the clock at rest (the light path ABA)
This is true for both Figure 1 and Figure 2
However there is also a difference between figure 1 and Figure 2.
• In Figure 1 the speed v of the moving object is expressed as a function of t1.
That means l = v1 * t1 Inserting that in equation 1 we get: (c * t1)^2 = (C * t2)^2 + (v1 * t1)^2
Or: (c^2 - v1^2) * t1^2 = c^2 * t2^2 or t1 = t2 * sqrt(c^2/(c^2 - v1^2)
Or with v1 = v we get t1= t2 *sqrt (1/ (1 - v^2/c^2)). (2)
This means also that t1>t2
• In Figure 2 the speed v of the moving object is expressed as a function of t2.
That means l = v2 * t2 Inserting that in equation 1 we get: (c * t1)^2 = (C * t2)^2 + (v2 * t2)^2
Or: c^2 * t1^2 = (c^2 + v2^2)* t2^2 or t1 = t2 * sqrt(1 + v2^2/c^2)
 Or with v2 = v we get t1= t2 *sqrt (1 + v^2/c^2)). width = 20%> (3)
This means also that t1>t2

Figure 1 is the simplest. One light signal is involved. Starting from C, reflecting at B and endding at D. The distance of the object is 2*l. The duration of the lightpath is 2*t1 and the speed v1 = 2 * l/2 * t1 = l/t1.
Figure 2 is much more complex. Because using a certain reasoning, three lightsignals or clocks are involved as shown in Figure 3. There is a clock at point C, point A and point D. All the clocks start simultaneous. They all are reflected simultaneous against the mirror and they all reach the bottom simultaneous.
The time measured by the clock at A is t2 and the distance moved by the object is l.
The time measured by the clcok at D is 2t2 and the distance moved by the object is 2l.
In both cases the speed by the object is 2l/2t2 = l/t2 = v2.

In fact that is the most difficult part of this experiment. You have an object which moves from C to D, with a certain speed, but how is this speed calculated. Figure 1 and Figure 2 show two different answers. General speaking you need two clocks, one at the start and one at the finish, which should run simultaneous. Both clocks should be synchronised. The physical aspect of these clocks is, that they should not move, because if they move, they run slower. This is the result of the whole experiment.

The conclusion is that a clock is a physical process and depending about its speed, compared with a clock at rest, can run faster or slower. What is more only clocks at rest should be used when speeds or accelarations are considered.

However the observation that a clock can run faster or slower, has nothing to do of what you can call the physical age of the universe. This age increases at a constant 'speed'
What is even more, the reaction rate of a process can be influenced by the particles involved. This can be the case for radioactive processes, when alpha or beta particles are emitted. This by itself can be an indication how long the process took place, but has no consequence related to the aging of the universe.

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Created: 23 December 2021

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