Comments about the book "GRAVITATION" by MTW

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
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.

$1.5 Time - page 26

At page 26 we read:
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

At page 393 we read:
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.
Next we read:
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?

At page 395 we read:

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?

At page 396 we read:

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?

At page 397 we read:

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

At page 1054 we read:
  • 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).

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 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: 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.

First Release: 4 August 2017

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