Galileo’s principle of relativity

Physics > Galileo-Newton relativity

Consider briefly Galileo s principle of relativity in inertial systems: invariance, Newton s laws of mechanics, the role of Maxwell s equations, formulas and scheme.

Galileo s invariance and relativity assert that the laws of motion do not change at all points of the inertial system.

Learning challenge

  • Explain why Galileo s invariance did not work in Maxwell s equations.

Key points

  • Galileo s invariance states that Newton s laws are preserved in all inertial frames.
  • Newtonian mechanics says that there is absolute space, and time is universal.
  • Special relativity was based on complete consistency with electromagnetism, where the Lorentz invariance replaced the Galilean invariance.


  • Lorentz invariance – the speed of light does not depend on the frame of reference.
  • Absolute space is the concept that space always remains stable and motionless.

Galileo s invariance and relativity assert that the laws of motion do not change at all inertial points. Galileo Galilei first described the principle of relativity in 1632, using a ship moving at a constant speed as an example. In calm water, it is difficult for an observer to know if movement is present.

Usually Galileo s invariance refers to the use of Newton in mechanics, that is, his laws are preserved in all systems. Among the axioms:

  • There is absolute space where Newton s laws are true. An inertial sensor is a frame of reference in relative uniform motion towards absolute space.
  • All inertial sensors have a universal time.


Let s take two points S and S . A physical event in S will have position coordinates r = (x, y, z) and time t. Everything is exactly the same for S . You can synchronize clocks in two systems and take t = t . Suppose that S is in relative uniform motion towards S at a speed v. Consider a point object whose position is given by r = r


This is called the transformation of Galileo. Now the particle velocity is derived from the time derivative of the position:

Newtonian mechanics is invariant under the Galilean transformation. This is Galileo invariance

Another differentiation offers acceleration in two sensors:

It is from this that Galileo s relativity follows. If we assume that the mass is invariant in all inertial frames, then this equation proves that Newton s laws of mechanics must be fulfilled in all systems. But they are also present in absolute space, therefore Galileo s relativity also exists.


In the 19th century, Newtonian mechanics and Maxwell s equations were well studied. The problem was that Galileo s invariance didn t want to work in Maxwell s equations. The decision was taken by Albert Einstein. He based the formulation of the special theory of relativity on the fact that mechanics should be revised. As a result, the Galileo invariance was replaced by the Lorentz invariance. At low relative speeds, they are almost the same, but for those close to light, they differ.

Physics Section

  • Galileo-Newton relativity
  • Einstein s postulates
  • Light speed
The meaning of the special theory of relativity
  • Simultaneity
  • Time dilation
  • Time dilation effects: the twin paradox
  • Length reduction
Relativistic quantities
  • Relativistic velocity addition
  • Relativistic momentum
  • Relativistic energy and mass
  • Matter and antimatter
  • Relativistic kinetic energy
Consequences of the special theory of relativity
  • A paradigm shift in physics
  • Four-dimensional space and time
  • Relativistic universe

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