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