GRAVITATION by MTW - 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 starts wth the following text:
Suppose you want to study the total evolution of the Universe, specific the stars in the Milky way. This raises two questions;
- Is the concept of "local inertial frames" the right concept to tackle this problem.
- Is the whole exercise to make accurate predictions about the future, really that simple.
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 7 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 1 .
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 is subdivided in 3 parts.
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.
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.
The message is easy to summarize:
- physics is always and everywhere Lorentzian: i.e., locally the laws of special relativity are valid
- this simplicity shows clearly in a Lorentz frame of reference ("inertial frame of reference": Figure 1.7; and
- 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.
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.
First Release: 4 August 2017
Back to my home page Contents of This Document