Mechanics

Serhii Stepanov

• Publisher: De Gruyter
• Year: 2018
• ISBN:
  9783110516005
• Edition: 1
• Topic: Ciencias físicas
• Subtopic: Relatividad en física

In contrast to other introductions to special relativity, this one aims at a conceptually clear presentation of the theory. While not shying away from the proper mathematics, an emphasis is placed on an easy understanding of the underlying concepts, rather than technical calulcations only. With an entertaining writing style, comic-like illustrations and instructive problems, this textbook makes the entry to special relativity a lot easier.

1The Lorentz Transformations

This chapter considers the initial statements of the theory of relativity. We start from a discussion of the measurement procedures which must be performed in order for observers to agree upon units of length and time. Observers fixed relative to each other are considered, as well as observers located in different inertial frames of reference.

The key section of the chapter is “The Lorentz transformations”. The derivation of these transformations used here is not well known, though it has already been known for over 100 years. The velocity-addition law will be derived with the help of the Lorentz transformations and the meaning of the fundamental constant c will be established. To make the picture complete, the traditional derivation is also considered; it is based on the postulate (in fact, a theorem) that the velocity of light is constant.

1.1Stationary observers

Physical processes take place in space and time. Defining these terms necessitates determining measurement procedures that allow one to move from feelings to numbers. This is not easy and requires a number of explicit or implicit assumptions.

We will have to speak constantly of observers, active participants of the physical theory. Despite the surrounding world being objective, physics is ultimately being created to explain human perception, and to decrease its “subjectivity”. So, the appearance of such projections of our “self” is more than likely unavoidable. Certainly, they may also be represented by some physical instruments or artificially constructed intelligent creatures.

▷ If a person did not have a memory, time would not exist for them. The perception of time is formed by our memory registering surrounding changes. These same changes are used to measure time changing. Periodic processes, the time durations of which are considered the same, are convenient for this purpose. People have been searching for the “correct” clock for all of human history.

What is however the correct clock, and how do we know that the duration of a periodic process is constant? It turns out that the simplicity principle [2] is the most practical way to answer this difficult question:

Time is defined so that motion looks simple.

For example, it is not us...