Six not so easy pieces - by Richard P. Feynman - Book review

This document contains comments about the book "Six not so easy pieces" - by Richard P. Feynman written in 1997.



Chapter 3.

The Special Theory of Relativity - page 49

page 49

This page starts with the following text:
Newton's Second Law, which we have expressed by the equation:
F = d(m*v)/dt (3.0 a)
was stated with the tacit assumption that (the mass) m is a constant,
This sentence is "misleading". Equation indirectly assumes that the mass m is not constant.
Rewritten the same equation looks like:
F = d(m)/dt * v + m * dv/dt (3.0 b)
This equation when m = constant becomes:
F = m * a (3.0 c)
which in a larger context involves the study of accelaration motion (GR) and not linear motion (SR).
Immediate in the same sentence:
but we now know that this is not true and that the mass of a body increases with velocity.
In Einstein's corrected formula m has the value:
m = m0/ sqrt(1 - v^2/c^2) (3.1)
where the "rest mass" m0 represents the mass of a body that is not moving and c is the speed of light which is about 3 * 10^5 km/sec or 186000 miles/sec
The issue is what exactly does each parameter physical means. How are they calculated.
If you want to calulate the mass of a free floating object in space (like our earth) you need Newton's law or General relativity.
For those who want to learn enough about it so they can solve problems, that is all there is to the theory of relativity - it just changes Newton's laws by introducing a correction factor to the mass.
using equation 3.1 you can not solve any physical problem. The physical reality is much more complex.

page 50

From the formula itself it is easy to see that this mass increase is very small in ordinary circumstances.
When you consider equation all by it self you are doing mathematics. What you want is to understand motion and that is much more complex.
If the velocity is even as great as that of a satelite, which goes around the earth at 5 miles/sec then v/c = 5/186000: putting this value into the formula shows that the correction to the mass is only one part in two to three billion etc.
That is mathematical 100% correct.
But how do you know that the speed is 5 miles/sec or 500/186000 % of the speed of light?
These questions are very difficult to answer.
Actually the correctness of the formula has been amply confirmed by the observation of many kinds of particles moving at speeds ranging up to practically the speed of light.
I doubt if equation 3.1 has actually been confirmed by performing experiments.
See: Reflection 3 - Particles
The principle of relativity was first stated by Newton, in one of his corollaries to the laws of motion: "The motions of bodies included in a given space are among the same themselves, whether that space is at rest or moves uniformly forward in a straight line."
The problem this situation can only exist in theory. In reality objects never move in a straight line.
A different issue is how do you know that 'a given space' is at rest or in movement?
This means, for example, that if a space ship is drifting along at a uniform speed, all experiments performed in the space ship and all the phenomena in the space ship will appear the same as if the ship were not moving, provided, of course, that one does not look outside.
In real this discussion belongs to GR.
The most important question is how do you prove this principle.

Par 3.3

3.3 The Michelson-Morley experiment - page 54

page 55

If the apparatus is "at rest" in the ether, the times should be precisely equal, but if it is moving toward the right with a velocity u, there should be a difference in the times.
The most important thing to study is what happens with the light source, specific with the wavelength of the beam of light in the direction of movement.
From the earth perspective the position of the whole apparatus including the source is fixed on the surface of the earth.
As such what you should do is place the whole apparatus including the source on a moving platform and observe what is happening when this platform moves in a certain direction. One thing that will change is the wavelength of the source, which decreases. This is not taken into account in Figure 3-2.

page 57

The result of the experiment was null.
No change in interference fringes.
The result of the Michelson-Morley experiment was very puzzling and most disturbing.

page 58

THe first fruitful idea for finding a way out of the impasse came from Lorentz. He suggested that material bodies contract when they are moving, and that this foreshortening is only in the direction of motion, and also, that if the length is L0 when a body is at rest, then when it moves with speed u parallel to its length, the new length, which we call Lp (L-parallel) is given by:
Lp = l0* sqrt(1 - u^2/C^2)
One important question to answer is what is L0 and what is u.
IMO this is impossible to answer for any experiment on the surface of the earth.

Par 3.4

3.4 Transformation of time - page 59

page 60

Before the man took abroad, he agreed that it was a nice, standard clock, and when he goes along in the space ship he will not see anything peculiar.
It is important to know exactly what he observes. For example is it true that he does not observe anything peculiar with the "light clock"?
If he did, he would know he was moving - if anything at all changed because of the motion, he could tell he was moving.
Did the observer realy try to observe if nothing was strange on board of the space ship. He did not perform any test to see that in some sense he was also free floating in space?
This seems the observer was in some sense brainwashed.
But the principle of relativity says this is impossible in a uniformly moving system, so nothing has changed.
But is a trip with a space ship a test in a uniformly moving system? No.
There is acceleration involved, at the start, at the turn around point and at the end
This is important because this changing in speed is in fact the cause of the different behaviour of the clock.
A whole different issue is, that the magnitude of the receiving signal, after each cycle, will decrease, because the path is longer. This implies that the observer can detect motion.

page 61

From the figure it is also apparent that the greater u is, the more slowly the moving clock appears to run.
Okay. But why mention: 'appears to run' and not simple: 'runs'?
Not only does this particular kind of clock run more slowly, but if the theory of relativity is correct, any other clock, operating on any principle whatsoever, would also appear to run slower, and in the same proportion - we can say this without further analysis. Why is this so?
In this particular case, the light flash moves (initially) 'perpendicular' to the (supposed) direction of movement.
It is also possible that the light flash moves forward (and backward) in the direction of movement. The behaviour of these clocks is different.
See also: Reflection 1 - The philosophy of science
One of these clocks is taken into the space ship, along with the first kind.
Perhaps this clock will not run slower, but will continue to keep the same time as its stationary counterpart, and thus disagree with the other moving clock.
This type of reasoning requires a phylosophical discussion.
See also: Reflection 1 - The philosophy of science
Ah no, if that should happen, the man in the ship could use this mismatch between his two clocks to determine the speed of his ship, which we have been supposing is impossible.
Who are the we?
We need not know anything about the machinery of the new clock that might cause the effect - we simply know that whatever the reason, it will appear to run slow, just like the first one.
IMO this type of reasoning is not very scientific.
Now if all moving clocks run slower, if no way of measuring time gives anything but a slower rate, we shall just have to say, in a certain sense, that time itself appears to be slower in a space ship.
The fact that moving clocks run slower has nothing to do with the concept time i.e. the fact that all what surrounds us, all objects in the universe, exist in time. The concept that moving clocks run slower is a common accepted fact. It is known by people in navigation that in order to keep track about the position of a ship, you need an accurate clock.
All the phenomena there - the man's pulse rate, his thought processes, the time it takes to light a cigar etc - all these things must be slowed down in the same proportion, because he cannot tell he is moving.
In process therminology this is the called the reaction rate, that is the rate how fast (or slow) certain changes take place. In many cases just by stirring the reaction, the rate can be improved (goes faster).
All of this has nothing to do with the concept time.

page 62

Reflection 1 - The philosophy of science

At Page 50 The principle of relativity is discussed.
This raises a phylosophical question: how do you prove a principle?
There exists also different approach: A principle can not be proven. Instead a principle can only be invalidated by using some form of reasoning which leads to a logical contradiction

At Page 61 a different approach is followed in two occasions. Here it is assumed that the The principle of relativity is valid which leads to the conclusion that all clocks behave the same.
The question is if such logical reasoning is correct.

A similar issue is involved in case of an perpetum mobile. A perpetum mobile is a appartus which moves continues in a closed space. The principle is: that a perpetum mobile does exist. The prove is to build one to invalidate the principle.

Reflection 2 - equation 3.1

The purpose of this document is to study equation 3.1
From a mathematical point of view there is nothing wrong with this equation. The same with any mathematical equation. The problem is: which physical processes are described by this equation. What are the physical conditions and constraints if any.
If you have a process which uses light in order to operate than it seems reasonable that its functionalty depends about the speed of light. For example a clock which uses light to operate. Such a clock theoretical can not operate or tiCk when the speed of clock reaches the speed of light. This raises the physical question when exactly does the clock stops tickking.
The behavior of a clock is also symmetrical that means when the speed decreases the rate of the clock will increase.

In equation 3.1 the mass is influenced by the speed of light. The mass increases when the speed increases. This requires a physical explanation. Why light i.e. why photons?.
Rather similar comments apply when length is considerd. However here a different physical(?) phenomena is at stake: the length decreases when the speed increases.

The most difficult part of the equation is m0. This is the mass of a body that is not moving. But how do you know that? What is the rest mass of the earth? of the Sun?. Both are moving objects in our Galaxy, as such the issue is not trivial.
In the context of Newton's Law, mass is a calculated parameter. The mass of each object is calculated based on the movements of a group of objects over a certain period of time. During this period the mass of each object is considered constant (and no collisions are considered). In order to calculate each mass equation 3.0c is used. This is a rather straight forward method.

Reflection 3 - Particles

Using fast moving particles is the strategy to test Time Dilation. For a discussion select: Comments about "Time dilation" in Wikipediapar 5.4 "Muon Lifetime"

Created: 13 April 2015
updated: 5 May 2019 Major Revision.

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