## 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.
• The text in italics is copied from the article.
• Immediate followed by some comments

### page 49

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.
Next:
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.
Next:

### 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 2

### Reflection 1 - 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 part 2 - 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