This document contains comments about the book: "GRAVITATION" by Charles W. Misner Kip S Thorne wn John Archibald Wheeler. W.H. Freeman and Company 1973
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

## \$1.3 Weightlessness - page 19

This document discusses page 19 of the book GRAVITATION by C.W Misner, K.S Thorne and J.A Wheeler. The text of that page is subdivided in 4 parts.
• ### Part 1

Part 1 starts wth the following text:
In analyzing physics in a local inertial frame of reference, or following an ant on his little section of apple skin, one wins simplicity by foregoing every reference to what is far awy, Physics is simple only when viewed locally: that is Einstein's great lesson.
Suppose you want to study the total evolution of the Universe, specific the stars in the Milky way. This raises two questions;
1. Is the concept of "local inertial frames" the right concept to tackle this problem.
2. Is the whole exercise to make accurate predictions about the future, really that simple.
• ### Part 2

Part 2 starts wth the following text:
Newton spoke differently: "Absolute space, in its own nature, without relation to anything external, remains always similar and immovable." But how does one give meaning to Newton's absolute space, find its cornerstones, mark out its straight lines? In the real world of gravitation, no particle follows one of Newton's straight lines. His ideal geometry is beyond observation. "A comet going past the sun is deviated from an ideal line." No. There is no pavement on which to mark out that line, The "ideal straight line" is a myth. It never happened, and it never will.
The best book to study Newton's Law is the excelent book "Newton's Principia For the Common Reader" by S.Chandrasekhar.
Chapter 24 is about comets. When you read that chapter you get an impressive idea how well Newton understood the complex trajectorie of a comet. In this chapter the concept of a straight line is not mentioned and plays no role in the excelent explanation of the parabolic nature of the trajectory around the Sun.
Newton was very well aware of the concept a straight line: In Law I at page 22 we can read:
Every body continues in its state of rest or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
In realty when you study the solar system this is always the case.

I do not know if in this book the concept of "Absolute space" is anywhere mentioned. You get an idea about Newton's way of reasoning when you study definition III at page 19. Here he writes:
Resistance is usually ascribed to bodies at rest, to those in motion; but motion and rest, as commonly conceived are only relativily distinquished; nor are those bodies always truly at rest which commonly are taken to be so.
This same information is also discussed in paragraph 10c: "The Newtoninian principle of relativity" at page 42 of the same book
To important gravity is for Newton see Reflection part 1: Final page .
• ### Part 3

Part 3 starts wth the following text:
"It required a severe struggle [for Newton] to arrive at the concept of independent and absolute space, indispensible for the development of theory.... Newton's decision was, in the contemporary state of science, the only possible one, and particulary the only fruitful one. But the subsequent development of the problems, proceeding in a roundabout way which no one could then possible foresee, has shown the the resistance of Leibniz and Huygens, intuitively well-founded but supported by inadequate arguments, was actually justified.... It has required no less strenuous exertions subsequently to overcome this concept [of absolute space]"
[A. EINSTEIN (1954)].
In this text Einstein emphasysis the concept of absolute space support by Newton. He agrees that this concept makes sense in Newton's time but slowly was taken down under the influence of many. In some sense absolute space was replaced by relatif space. Simultaneity was replaced by relativity of simultaneity.

• ### Part 4

Part 4 is subdivided in 3 parts.
• #### part 4.1

What is direct and meaningful, according to Einstein, is the geometry in every local inertial frame. There every particle moves in a straight line with uniform velocity. DEFINE the local inertial frame so that this simplicity occurs for the first few particles (Figure 1.7). In the frame thus defined, every other free particle is observed also to move in a straight line with uniform velocity. Collision and disintegration processes follow the laws of conservation of momentum and energy of special relativity.
This whole paragraph show a much too simple picture. Elementary particles only move in straight where there are no electrical and magnetic fields are involved. When there is gravity involved the trajectories of (small) objects do not follow straight lines i.e. are bended. It are these bended trajectories that Newton discusses.
• #### part 4.2

That all these miracles come about, as attested by tens of thousands in elementary particle physics, is witness to the inner workings of the machinery of the world.
These trajectories of the elementary particles, if they are straight, do not describe the complexity involved in the trajectories of the planetary objects and stars. In reality many of the trajectories of the particles are bendend. What you can learn from individual experiments is that the reaction rates are a function of speed. To explain that you have to unravel the details of the reactions involved.
• #### part 4.3

The message is easy to summarize:
1. physics is always and everywhere Lorentzian: i.e., locally the laws of special relativity are valid
2. this simplicity shows clearly in a Lorentz frame of reference ("inertial frame of reference": Figure 1.7; and
3. to test for a local Lorentz frame, test for weightlessness!
The problem with this sentence is that in reality when you stay on the surface of earth you are not in an inertial frame.
At page 18 of the book GRAVITATION is written
Infact travel aboard a freely moving spaceship.Nothing could be more natural than what one sees: every free object moves in a straight line with uniform velocity.
That is only true to a certain extend. The path of the Sun is not a straight line. That is what Newton discusses.

## \$1.5 Time - page 26

Look at a bad clock for a good view how time is defined. Let t be the time on a "good" clock (time coordinate of a local inertial frame). it makes the tracks of free particles through the local region of space time look straight. let T(t) be the reading of the "bad" clock; it makes the world lines of free particles through the local region of space time look curved.
This is a rather theoretical discussion. How do you know in the first place that the particle follows a straight path through space with a constant velocity?
Only in that case the line f(x,t) is a straight line.
It is clear from this example of a "bad" time that Newton thought of a "good" time when he set up the principle that "Times flows uniformly".
Time is defined to make motion look simple!
I doubt if Newton had this in mind.
In the book "Newton's Principia" at page 41 we read
But to the extent the direction and the direction and the magtitude of the rectilinear motion are unspecified, to that extent we can refer the motion equally to another frame of reference obtained by the transformation:
(r)' = (R).(r) + (v)t + (d) and t'= t + tau (7)
where (v),(d) and tau are constants and (R) is any orthogonal matrix with constants coefficients.
If O and O' denote the unprimed and primed coordinate system, then for any stationary observer in O' the coordinate system O will appear as rotated by (R) and moving with a uniform velocity (v) dispaced at t=0 by (d); and further for the observer in O', the clock in O will be running behind his own by the time tau.
It is important to consider the simplicity of the language used.
IMO the importance is that Newton assumes that the ticking rate of a clock in O and O' are the same. A clock in Newton's time was a pendulum.

## \$ 16.4 The Rods and clocks used to measure space and time intervals. page 393

Rather, one must ask the laws of physics themselves what types of rods and clocks will do the job.
That means one must study the inner workings of a clock.
Put differently one defines an "ideal" rod or clock to be the one which measures proper length as given by ds = sqrt (gab dx^a dx^b) or proper time as given by dtau = sqrt (-gab dx^a dx^b) (the kind of clock to which one was led by physical arguments in \$1.5)
This whole procedure is not as simple as it sounds. What is gab in practice?
One must then determine the accuracy to which a given rod or clock is ideal under given circumstances by using the laws of physics to analyze its behavior.
This is a very important remark. That means IMO you must study the innerworkings of a clock to decide if a clock is "good" or "bad".
As an obvious example, consider a pendulum clock. If it is placed at rest on the Earth's surface, etc and time dilation effects due to the swinging velocity are negligible etc then the laws of physics report that the pendulum clock is "ideal"
This puts very strict rules on which is an "good" pendulum clock.
However, in any other context (e.g on a rocket journey to the moon), a pendulum clock should be far from ideal. Wildly changing accelerations or no acceleration at all will make it worthless
In short a moving pendulum will behave different then a pendulum at rest.
IMO the reason is the inner operation of the clock itself.
Almost at the end of page 393 we read:
Ofcourse any point has a "breaking point" beyond which it will cease to function properly. But that breaking point depends entirely on the construction of the clock -and not at all on any "universal influence of acceleration on the march of time". Velocity produces a universal time dilation;acceleration does not.
This piece of text emphasizes how important the construction of a clock is.
At the same time this raises also the phylosophical question if the concept "time dilation" truelly says something about the physical meaning of time or about the behaviour of a clock?

C. Analysis of Pendulum Motion
This means that the pendulum is an ideal clock when it is at rest on Earth's surface
This immediate raises the question: What is an ideal clock? more specific a moving clock?

Box 16.3 Response of clocks to acceleration and to tidal gravitational forces
When subjected to sufficiently strong accelerations or tidal forces such a clock will cease to measure proper time with its normal precision.
There is a distinction between temporary damage or permenent damage.
The issue is also a disctinction between in principle or in practice.
B. Influence of acceleration or tidal forces on the macroscopic structure of the clock - a structure dictated by current technology.
The crystal oscillator which produces the periodic output must be locked to the regulating process in some way.
IMO the issue is (in principle) the regulating process itself. Is this process influenced by accelerations (different speeds)? Yes or No.
Tidal forces are so small in the solar system that the clock manufacturer can ignore them
In practice.
However a 9173 atomic clock subjected to the tidal accelerations near a spacetime singularity, should break the "lock" to its atomic process long before the tidal forces become strong enough to influence the atomic process itself.
In principle?

Box 16.4 Ideal rods and clocks built from geodesic world lines
(3) Light rays (null geodesics) bounce back and forth between these parallel world lines; each round trip constitutes one "tick"
It are these "ticks" which are used to measure time intervals.
The issue is the ticking rate influenced when a clock is moved. IMO the answer is Yes.
(4) The proper time lapse tau between ticks is related to the interval AB by: etc.
where N1 and N2 are the number of ticks between the events shown in the diagrams.
My interpretation is that the propertime is the number of ticks between N2 and N1. As the rest of the text indicate this number in practice should be high, to improve accuracy.

## \$38.4 Tests for the existance of a metric governing length and time measurements and particle kinematics - page 1054

• SR, GR etc assume the existence of a metric field and predict that this field determines the rates of ticking of atomic clocks and the length of laboratory rods by the familiar relation -dt^2=ds^2 = gab dx^a dx^b (see original text)
• The experimental evidence for a metric comes largely from elementary particle physics. It is of two types: first experiments that measure the time intervals directly, eg measurements of the time dilation of the delay times of unstable particles. etc
• Notice what particle-physics experiments do and do not tell one about the metric tensor g etc
• Third elementary particle experiments do suggest that the times measured by atomic clocks depend only on velocity not on acceleration etc.
1. the above text uses the word governing in the sense of control, strongly influences, determine, guide or regulate (Webster)
IMO a metric does neither. A metric is a mathematical tool which first has to be measured by experiments and then can be used to predict other observations.
2. the above text uses the word dilation in the sense of stretching or enlarging (Webster). This shows a physical connotation (implication).

## \$39.1 Other Theories - page 1066

Among all bodies of physical law none has ever been found that is simpler or more beautiful than Einstein's geometric theory of gravity (Chapter 16 and Chapter 17); nor has any theory of gravity ever been discovered that is more compelling.
To call a theory beautiful has no scientific meaning; to call a theory compelling (WEBSTER: meaning calling for examination as in the sentence: new and compelling evidence) has scientific meaning.
As experiment after experiment has been performed, and one theory of gravity after another has fallen by the wayside a victim of the observation, Einstein's theory has stood firm. No purported inconsistency between experiment and Einstein's laws of gravity has ever surmounted the test of time.
Experiments are one part of the story. Certain implications of Einstein's Law are very diffecult or almost impossible experimental to test like length (Lorentz) contraction as mentioned at page 48.
No theory is complete if it postulates that atomic clocks measure the "interval" dtau = ( -gab dx^a dx^b)^1/2 constructed from a particular metric.
a = alpha and b = beta. Next we read:
Atomic clocks are complex systems whose behaviour must be calculated from the fundamental laws of quantum theory and electromagnetism.
That means they are not considered as part of special relavity.
No theory is complete if it postulates that planets move on geodesics. Planets are complex systems whose motion must be calculated from fundamental laws for the response of stressed matter of gravity. For further discussion see par 16.4, 20.6 and 40.9
As accepted.
Agreement with past experiment: The necessity that a theory agree, to within standard deviation, with the "four standard tests" (gravitational redshift, perihelion shift, electromagnetic-wave deflection, and radar time-delay) is obvious.
As accepted.

## \$40.1 Many experiments open to distinquish General Relativity from proposed metric theories of gravity - page 1096

At page 1096, at the bottom, we read:
* Of course from the point of view of Einstein's full general relativity theory, all that legalistically counts is the one and only curved-spacetime geometry of the real physical world. All these "individual fields" are mere bookkeepers' discourse, and they are best abandoned (they cease to be useful) when one passes from the post-Newtonian limit to the full Einstein theory.
This raises immediate the question: to what extend the full Einstein theory can be tested, in the sense that it gives better predictions (when applied) than the post-Newtonian limit.
The second lesson is, if you want to do a perfect job, the post-Newtonian limit should not be used.

## \$40.5 Perihelion Shift and Periodic Perturbations in geodesic Orbits - page 1110

Begin with the simplest of cases: the geodesic orbit of a test body in the sun's spherical gravitational field, ignoring all gravitational effects of the planets, of solar oblateness, and of motion relative to any preferred frame.
This makes this discussion maybe too simple.
The result, accurate to the order M0/r beyond Newtonian theory, is etc
equation (40.17)
where a and e are constants of integration and delta phi0 is defined by:
delta_phi0 = (2-beta-2*gamma)/3 * (6*pi*M0)/ (a*(1-e^2)) equation (40.18)
delta_phi0 = (6*pi*M0)/ (a*(1-e^2)) in general relativity
(For derivation see exercise 40.4)
In general relativity beta=1 and gamma=1.
Notice that if delta_phi0 were zero - as in the Newtonian limit - then the orbit (40.18) would be an ellipse with the semimajor axis a and eccentricity e (see Box 25.4).
This Notice makes a lot of sense.
The perihelion shift is not the only relativistic effect contained in the orbital motion for a test body.
Observe that we are discussing here a test body.
The periodic effects are not obvious in the PPN orbital equation (40.17); it looks like the simplest of precessing ellipses
Okay. Next:
But the quantities the observer measures directly are not a, e, and delta_phi0.
Instead, he measures the time evolution of round-trip radar travel times. delta_tau(tau) and the angular positions on the sky [theta0(tau), phi0(tau)].
It makes more sense that these type of parameters are measured.
The next sentence is not clear what is mentioned:
To compute these quantities is perfectly straightforward in principle, but in practice is a very complex task.
Which quantities are meant? I expect a, e and delta_phio. I start wandering: If this is already so difficult what if you want to perform the full Einstein theory? See page 1096
The most favorable orbits for experimental tests of the perihelion shift and of periodic effects are those that go nearest the sun and have the highest eccentricity [see equation (40.18)] - the orbits of Mercury, Venus Earth Mars and the asteroid Icarus.
It is interesting why Jupiter is missing.

### Reflection part 1: Final page

The following masterpiece of text is from the book: "Newton's Principia For the Common Reader" and demonstrates the issue of gravitation. What you can learn from this text is how important gravitation is and that absolute space is not an issue.

### Reflection part 2: Who is right Newton or Einstein or both

When you compare Newton with Einstein the most important difference is the speed of light. Newton does not discuss the speed of light. He assumes when you see a planet at a certain position the planet is actually there. (*)
What is also important for Einstein is the concept of inertial frames and the concept of rest. For Einstein an observer with a speed v =0 in an inertial frame is at rest in that frame.
For Newton that is not an issue. For Newton when the sum of all the forces (acting on an object) = 0 the object is either at rest or moves in a straight line.
For Einstein for an Observer at rest in an inertial frame the speed of light in both directions is the same.
Newton does not discus this issue, but IMO his opinion would be that the speed of light in our solar system would have been every where the same independent of any observer (as a first approximation).

When you study the book: "Newton's Principia For the Common Reader" a large part is related to solve the differential equations i.e to find analytical solutions. For a system of two bodies this is an ellipse. The many-body problem is discussed in paragraph 62 at page 215. The three-body problem: the foundations of Newton's lunar theory is discussed in Chapter 14 at the pages 235-267.
IMO what Newton's trys to find are analytical solutions of different n body situations. In general this is impossible. Only numerical solutions. In that sense it is quite easy to simulate all the planets around the Sun using Newton's Law. The problem is the predictions do not match observations.
In order to evaluate SR and GR you should try to do the same i.e. performing a simulation of all the planets around the sun, strictly using SR and GR and no approximations. This implies that you should also calculate the masses of all the planets. The reality is that this is that such a simulation is extremely difficult.

Newton is very much aware from the concept of time. Chapter 10a "The proportionality of mass and weight and the experiments on the pendulums" demonstrate the importance of time. The issue of what happens when clocks are moved is not discussed and is also of no direct importance for the study of the solar system.

What Newton does not discuss is that gravitational forces do not act instantaneous.
In Chapter 10 "On revolving orders" specific as part of Example 2 at page 196 he discusses different "forces of law".

(*) IMO when you want to understand the laws of nature you should start from the assumption that at any moment t any object considered has an instantaneous position x,y,z. Based on these instantaneous positions at many different moments t we can develop the necessary concepts and tools (laws) which are the basics to describe these positions. These instantaneous positions do not match with what we observe. That means certain mathematical transformations are necessary to transform what we observe into these instantaneous positions and to transform the predicted positions in what we should observe in the future. To perform these transformations the physical conditions of light (photons) should be considered.

### Reflection part 3: \$16.4 page 393

At page 393 the concepts "ideal" rods and clocks are defined. Pendulum clocks, atomic clocks and human clocks are discussed. Clocks which inner workings is based on the speed of light are not discussed.
At page 397 a clock based on a freely falling particle is discussed. Box 16.4 shows two figures:
• The top figure shows the worldline of a free falling particle.
• The bottom figure shows the worldline of a photon at rest.
In fact a free falling particle is identical with a moving clock which inner workings is based on light signals. Such a moving clock consists of two parallel mirrors which are placed perpendicular to the direction of motion between which one photon bounces back and forward. One of such cycles defines one tick.

The bottom figure defines a photon or clock at rest. The problem is both figures are not drawn at the same scale. In fact point Beta should be much closer towards point Alpha. (the same as the prallel worldlines above) When you do that you would see that the clock at rest ticks faster then the moving clock.

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