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).

Chaper 39 Other Thories of Gravity and the Post-Newtonian Approximation - page 1066

$39.1 Other Theories - page 1066

At page 1066 we read:
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.
See also below related to: "four standard tests"
At page 1066 we read:
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.

Chapter 40 Solar-System Experiments - page 1096

$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

At page 1110 we read:
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.
At page 1111 we read:
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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First Release: 4 August 2017

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