Hi! I'm studying special relativity and relativistic dynamics and I'm struggeling a little bit with the concept of 'covariance' of physical equations.(adsbygoogle = window.adsbygoogle || []).push({});

As far as I understand so far 'covariance' is related to the 'form invariance' of the equations of motions in relativity and the concept is important because of the principle of relativity, i.e. that all physical laws are the same in every reference frame.

Maybe a good example here is the rate of change of momentum in an electromagnetic field;

one observer might say that the circular motion of an electron is due to a pure magnetic field, while another observer with a relative velocity experiences it as being due to a mixture of magnetic and electric fields.

Is this then an example of something which is in contradiction to the principle of relativity and thus not a physical law, per definition?

Is the reason that we introduce the field tensor and write

[tex]m \frac{d^2 x^\mu}{d \tau^2} = F^{\mu \nu} \frac{d x^\nu}{d \tau}[/tex]

that this equation is covariant in the sence that ALL observers will agree that the proper acceleration of the space time position is due to the field tensor, so that THIS then is an example of a physical law?

I would really appreciate comments on my current understanding and start a discussion around this to get it straight.

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# Principle of relativity, covariance and physical law.

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