This little book concentrates on the foundations of modern physics (its “ABC's”) and its most fundamental constants: c — the velocity of light and ℏ — the quantum of action.
First of all, the book is addressed to professional physicists, but in order to achieve maximal concentration and clarity it uses the simplest (high school) mathematics. As a result many pages of the book will be useful to college students and may appeal to a more general audience.
Contents:
The Fundamentals
Units
A Minimum of Mathematics
Translational Motion
Rotation and Quantization
Particles as Corpuscles and Waves
More About Units
The Hydrogen Atom
Periodic Table of Chemical Elements
Substance
Quantum Electrodynamics — QED
Transition to Classical Theory
Gravitation
Other Galaxies
Big Bang
Quantum Gravidynamics — QGD
Intranuclear Forces
Particles in Cosmic Rays
Particles in Accelerators
Three Discrete Symmetries
Half a Century Later
On Quantum Chromodynamics
On the Electroweak Theory
Supersymmetry
Grand Unification
In the Vicinity of the Planck Mass
Concluding Remarks
Readership: College students and interested readers in the physical sciences.
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The purpose of this book is to explain within a hundred-odd pages how modern elementary particle physics allows us to understand the workings of the surrounding world. Two universal constants lie at the basis of the cosmos: the maximum speed of uniform rectilinear motion c and minimum quantum of rotational and oscillatory motion ħ. The words “rectilinear” and “uniform” seem to point to unbounded, infinite motion through space and to linearity of the time (the philosophy of the Occident). Rotation points to cyclical nature of time and to bounded, finite nature of motion (the philosophy of the Orient).
The matter I wish to present here is not philosophy but the way in which physicists quantitatively describe their observations and experiments using intuition as their tool. The main problem of modern physics is that the concepts of maximum speed and minimum quantum appear extremely anti-intuitive to those who do not work in fundamental physics.
1.2 Space and time*
Our space is three-dimensional: any observer can imagine a system of coordinates — three mutually orthogonal axes: back-to-forward (x), left-to-right (y), bottom-to-top (z). The observer typically places himself at the origin of coordinates.
Imagine an observer following the motion of a particle. He characterizes the position of the particle at the moment of time t by the radius vector r with its three coordinates: x, y, z. The coordinate system plus time form what we call the frame of reference. All points in space and time are equivalent: both space and time are uniform. In addition, space is isotropic: the three axes can be oriented in an arbitrary manner. Note that under such re-orientations the magnitude of the radius vector remains unchanged: r ≡ |r| = const.
1.3 Matter and substance*
Any change in the motion or behavior of a particle is a manifestation of elementary (i.e. the smallest and indivisible) particles of matter. We begin with three elementary particles of matter: the photon γ, the electron e and the proton p. We will first see how the simplest hydrogen atom emerges as a result of their interaction. We will then look at other atoms so as to understand how the matter around us emerges as a result of their interaction and formation of increasingly complex systems of interlinked particles. Then we will go deeper step by step and learn about all other elementary particles.
There is still no universally accepted definition of what should be called ‘substance’ and what should be called ‘matter’. Many authors use the term “material particle” only if the particle has nonzero mass. Suffice it to recall the term “material point” which is used in the literature by many authors (see e.g. Weinberg’s book [1]) where they discussed “massive points”, that is bodies whose size can be considered negligible in a specific problem. For these authors photons are particles of radiation, not of matter. The debate on what should be called which name will be solved some day. At the moment I will refer to all particles including photons as particles of matter. And I will call atoms and everything built of atoms as substance.
1.4 Motion*
Motion is the displacement of a particle in space. If the motion is translational (i.e. uniform and rectilinear) then the velocity v of displacement is given by the formula v = r/t where r is the path covered and t is the time the displacement took. The definition of velocity in the case of arbitrary motion will be given a little later.
Chapter 2
Units*
2.1 Standards
Every measurement is a comparison of what is being measured with a known standard. The generally accepted standards with which results of measurements are compared are called units.
2.2 Circle and angles
Angles are measured in degrees (minutes and seconds) or in radians. One degree of arc is the angle subtended at the center of a circle by the arc obtained by dividing the circle into 360 equal parts. The minute of arc: 1′=1°/60. The second of arc: 1″=1′/60. We know that the ratio of the circumference of the circle to its radius equals 2π, where π ≈ 3.14. One radian 1 rad= 360°/2π ≈ 57° is the angle subtended by the arc whose length equals that of the radius.
2.3 Units of time and length
Units of time are determined by the rotation of the Earth. A day and a night are 24 hours long. One hour = 60 minutes. One minute = 60 seconds. Although one hour and one degree of arc consist of 60 minutes and 3600 seconds, this is the only common feature between the units of angle and time.
Lengths are measured by comparing them against the established length standard. The meter is the typical unit for measuring lengths.
Chapter 3
A Minimum of Mathematics
Mathematics is often said to be the queen and a servant of all the natural sciences. But mathematics is also a powerful obstacle when people are introduced to these sciences. This is why authors of popular science books and articles avoid using mathematical notation. In my opinion, modern physics cannot be explained without mathematics. I will try to limit myself to a minimum of mathematical knowledge. But this minimum is necessary and unavoidable.
3.1 Four operations of school mathematics and the imaginary unit*
Two types of arithmetic operations will be needed here to reach understanding of the laws of nature: 1) addition/subtraction, 2) multiplication/division, and two types of algebraic operations: 3) raising to power and 4) finding the logarithm. It won’t be soon that we will need this last operation. We will also need the concept of the imaginary unit
and of complex numbers.
3.2 Powers of ten*
When studying nature, we constantly come across very large or very small numbers which are conveniently presented as powers of ten. Thus the speed of light is 3 · 105 km/s = 3 · 108 m/s, and the size of an atom is on the order of 10−10 m. Unlike authors of popular science books, I will not use expressions like “one thousandth of one millionth of”; I will write 10−9.
3.3 Prefixes of the powers of ten
Many physical terms include the following prefixes:
Deca
101
da
Deci
10−1
d
Hecto
102
h
Centi
10−2
c
Kilo
103
k
Milli
10−3
m
Mega
106
M
Micro
10−6
μ
Giga
109
G
Nano
10−9
n
Tera
1012
T
Pico
10−12
p
Peta
1015
P
Femto
10−15
f
Exa
1018
E
Atto
10−18
a
Zetta
1021
Z
Zepto
10−21
z
Yotta
1024
Y
Yocto
10−24
y
3.4 Differentiation and integration
The velocity of arbitrary motion is determined as the derivative of distance with respect to time: v = dr/dt. The quantity dt stands for a sufficiently small (“infinitely small”) difference between two very close points in time. The quantity dr has a similar meaning — the difference between two points in space very close to one another. Here the infinitely small distance between two points in space is divided by the infinitely short interval of time, which gives as a result the finite velocity of motion. This operation is called differentiation. Integration is an operation inverse to differentiation: r = ∫vdt.We won’t need these operations just yet. It would be very useful to readers — both familiar with the concepts of dif...
