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Eivind
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What`s the difference between Lorentz- and Galileian-transformation?
bernhard.rothenstein said:one possible difference is that in galileo relativity light propagates with infinite velocity whereas in Einstein's relativity it propagates with finite invariant velocity.
In a recent paperEivind said:What`s the difference between Lorentz- and Galileian-transformation?
bernhard.rothenstein said:In a recent paper
Ralph Bayerlein, Two myths about special relativity," Am.J.Phys. 74(2) 2006 looks for an answer to the question "Does the Lorentz transformation reduce to the Galilean transformation when the ratio v/c is small"? The answer is no as the author shoes.
Lorentz transformations are a set of equations that describe how measurements of time and space change between two reference frames that are in relative motion. They take into account the principles of special relativity, such as the constancy of the speed of light. Galileian transformations, on the other hand, are a simpler set of equations that describe how measurements of time and space change between two non-accelerating reference frames. They are based on the principles of classical mechanics and do not take into account the effects of special relativity.
We need both Lorentz and Galileian transformations because they are applicable in different situations. Galileian transformations are useful for describing the motion of objects at relatively low speeds, while Lorentz transformations are necessary for accurately describing the motion of objects at high speeds, close to the speed of light. Using the appropriate transformation for a given scenario ensures that our measurements of time and space are accurate.
No, Lorentz and Galileian transformations cannot be used interchangeably. Galileian transformations are only valid for low speeds and do not take into account the effects of special relativity. If we try to use Galileian transformations at high speeds, we will get incorrect results. Lorentz transformations are more general and can be used for all speeds, but they reduce to Galileian transformations at low speeds.
Lorentz and Galileian transformations affect the measurement of time and space by accounting for the differences in how these quantities are perceived by observers in different reference frames. They take into account the fact that time and space are relative and can appear to be different depending on the observer's frame of reference. These transformations ensure that the laws of physics are consistent for all observers, regardless of their relative motion.
Lorentz and Galileian transformations are fundamental concepts in modern physics, particularly in the fields of special relativity and classical mechanics. They provide a mathematical framework for understanding how measurements of time and space change between different reference frames, and they have been extensively tested and confirmed through experiments. Without these transformations, our understanding of the fundamental laws of physics would be incomplete.