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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