Maxwell equation are derived in which coordinate system

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Discussion Overview

The discussion revolves around the coordinate systems in which Maxwell's equations are derived and their validity across different reference frames. Participants explore the implications of coordinate choice on the equations, particularly in the context of classical electrodynamics and special relativity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the coordinate system used in deriving Maxwell's equations, noting that many textbooks do not specify it and suggesting that multiple equivalent coordinate systems exist.
  • Another participant asserts that Maxwell's equations are valid in all inertial reference frames, linking this to the principles of special relativity and referencing the Michelson-Morley experiment as evidence of the absence of deviations in Newtonian physics.
  • A participant states that any inertial coordinate system is acceptable for the application of Maxwell's equations.
  • One participant expresses confusion about the choice of origin and axes in solving differential equations, specifically regarding how curl and divergence relate to the coordinates used.
  • Another participant encourages working through the mathematics of transforming coordinates to understand the implications for Maxwell's equations, suggesting a substitution approach to clarify the relationship between different coordinate systems.

Areas of Agreement / Disagreement

Participants generally agree that Maxwell's equations hold in all inertial reference frames, but there is disagreement regarding the implications of coordinate choice and the relevance of relativity in the context of deriving these equations.

Contextual Notes

The discussion highlights limitations in understanding how coordinate transformations affect the application of Maxwell's equations, particularly in relation to the choice of origin and axes, and the assumptions underlying these transformations.

Matt Smith
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Ignoring special relativity theory,maxwell equation are deduced in which coordinate system?In most electrodynamics textbook,maxwell equation are deduced without specifying which coordinate we are using.For example,when we are solving poisson equation in static case,it seems we can freely choose the original point,and 3 direction without contradict maxwell equation.It seems when we are deducting maxwell equation ,there are many equivlent coordinate system in which maxwell equation holds.When we are developing special relativity theory,we want to find the coordinate system in which maxwell equation holds,or in which system light have speed c.But it seems weird because we should know this coordinate system for a long time,because it should be the coordinate system in which we observe the electromagnetism phenomenon and deduce maxwell equation.
 
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The Maxwell equations are valid in all (inertial) reference frames. This is a result of special relativity. In Newtonian physics there must be deviations from the Maxwell equations in some reference frames - people searched for it but didn't find a deviation. Today we know why. The Michelson-Morley experiment is the most prominent example of an experiment that looked for deviations.
 
Any inertial coordinate system will do
 
mfb said:
The Maxwell equations are valid in all (inertial) reference frames. This is a result of special relativity. In Newtonian physics there must be deviations from the Maxwell equations in some reference frames - people searched for it but didn't find a deviation. Today we know why. The Michelson-Morley experiment is the most prominent example of an experiment that looked for deviations.
I just want to know when we solve differential equation ,why choosing a different original point and axes won't make any difference.Curl and divergence rely on the x,y,z.So please ingore the relativity chapter in Jackson's book or griffiths,and take chapter3,or 4 as an example.In the first several chapter we never mention the reference frame but with a lot of using curl and divergence.So in the first several chapter,when we do partial differentiation,we are doing it relative to which"x,y,z"?It is not a problem about relativity.
 
Matt Smith said:
why choosing a different original point and axes won't make any difference.Curl and divergence rely on the x,y,z.
This is just straight math. You should work this out for yourself. Transform from some T, X, Y, Z coordinate system to
T=t+t0
X=x+x0
Etc.
Substitute into Maxwell’s equations and simplify. What do you get?
 

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