Galileo Transformation

principle of relativity in mechanics

Covariance of Newton's equations

Classic velocity addition principle

Maxwell gave that the propagation speed of electromagnetic waves in vacuum has nothing to do with the reference system and the movement of the light source, which is inconsistent with the velocity addition theorem of classical physics.

The speed of light propagating in the v direction relative to the earth

The speed of light propagating in the opposite direction v is v'

The speed of light perpendicular to v direction c'

experimental device

The speed of light does not depend on the observation frame of reference

The speed of light does not satisfy the classical speed addition theorem. The speed in all inertial systems is c

principle of relativity in physics

The principle of constant speed of light

Two events that are judged to be simultaneous in one inertial frame are judged to be different times in another inertial frame.

A point (x, y, z, w) represents the space-time coordinates of a physical event that occurs at a point at time t and becomes a world point.

The motion of an object can be represented by a continuous curve in space, called a world line

Two physical events that define coordinates have an interval

The interval between the emission of light waves and the arrival of light waves in the S frame is 0. The interval between two events connected by light signals is zero and has nothing to do with the reference frame.

The correct space-time coordinate transformation relationship between the two inertial systems must be linear

The length perpendicular to the direction of motion does not change due to the observation reference system

The relationship between the space-time coordinates in two different inertial systems at the same time is given.

Space and time can only be measured by specific objects and specific physical processes.

Simultaneity is relative. Events that are simultaneous in one inertial system may not be simultaneous in another inertial system.

The length of the ruler measured by an observer in a frame of reference that is at rest relative to the stick is the rest length or intrinsic length.

The observer measures the length of motion relative to the ruler's motion reference system.

The shrinkage of the moving ruler is a relativistic kinematic effect. If it is only between inertial frames, this effect is also relative.

The length of an object is a relative quantity and depends on the choice of the observation reference system.

Define the duration of the nuclear decay process measured by a clock that is stationary relative to the radioactive nucleus as the intrinsic time (stationary time)

The time measured relative to the movement of radioactive nuclei is the movement time

In fact, the physical processes occurring inside the moving object slow down.

The time interval between two physical events or the duration of a physical process is a relative quantity

The causality of the development of things is absolute and should be established in any observation reference system.

The speed of light in vacuum is the limit of the speed of all objects or signals, which is called the principle of terminal speed.

The theory of relativity guarantees that the order of two events in the theory of causality is absolute, but it is absolutely impossible for events to have a causal relationship. The order of events is relative, so the theory of relativity does not violate the law of causality.

void-like

temporal

light-like

Only physical laws that comply with the requirements of special relativity, that is, remain unchanged in form under the Lorentz transformation, can be correct.

A four-dimensional scalar is a zero-order tensor

A four-dimensional vector is a first-order tensor

The four-dimensional matrix is ​​a second-order tensor

The mathematical form of physical laws that meet the requirements of the principle of special relativity is Zhang Liang's equation in four-dimensional space. Examining whether a physical law meets the requirements of special relativity, that is, the covariant under the Lorentz transformation, boils down to whether the physical law can Expressed as a tensor equation in four-dimensional space

Mass is a quantity related to speed

Define four-dimensional momentum

The rest energy and kinetic energy of the particle should be equal to the total energy of the particle

quality loss

binding energy of atoms

Electromagnetic waves are photon fields, and photon rest mass is zero

formula

longitudinal doppler effect

Transverse Doppler Effect

The direction of light propagation observed in different inertial systems is different.

The light aberration formula of relativity

The amount of charge is a Lorentz scalar