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I understand that a moving particle creates an electric field due to the frame of reference.

I have watched several animations on YouTube about the negatively charged object being repelled by the electric current if the observer is stationary and the same object being repelled by the magnetic force, if the observer is moving at the same speed as the object and electrons.

How does that principle connect to real life? If you have a wire with a current it has a magnetic field outside.

What creates the magnetic field if the observer of the wire is standing still?

How does that not mean if you are standing still, a wire should not have a magnetic field, because you are a stationary observer?

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    $\begingroup$ Moving charges create MAGNETIC FIELDS. Your severely confused. If an observer is moving at the same speed as electrons in the wire, Then relative to the observer, charges in the wire are not moving and thus there is no magnetic field. for a stationary observer they will see charges moving with a velocity and thus measure there IS a magnetic field. $\endgroup$ Dec 7, 2021 at 12:25
  • $\begingroup$ In classical electrodynamics you can learn that electric and magnetic fields also transform under Lorentz transformation. They actually "mix" in some sense. This is how you can kind of "transform out" a magnetic field from a problem. But then you also change the electric field. Check this link : en.wikipedia.org/wiki/Electromagnetic_tensor $\endgroup$
    – zltn.guba
    Dec 7, 2021 at 12:48
  • $\begingroup$ @jensenpaull A wire with a current has a current in it and a magnetic field around it. According to every observer. Current in a wire is an absolute thing. $\endgroup$
    – stuffu
    Dec 8, 2021 at 16:51
  • $\begingroup$ No, you are wrong.velocity is relative and so is current density . $\endgroup$ Dec 8, 2021 at 17:35
  • $\begingroup$ Well I guess the protons are now moving so there would be, however current density in general is not constant and IS observer dependant $\endgroup$ Dec 8, 2021 at 17:37

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I will try to reply without going into math first. I think your mind is kinda confused, but relativity often is confusing.

You are speaking of stationary observer, but in relativity an observer is stationary only with respect to some reference frame, there is no absolutely stationary observer. This is one of the fundamental principles of special relativity, when you say the observer is standing still you need to say also in which reference frame.

Now consider a electrostatically charged wire of infinite length with a constant linear density of charge. This produces and cylindrically symmetric electric field that can easily be calculated by means of Gauss theorem and I leave the computation to you as an exercise. When we are saying the wire is charged we are stating that in our reference frame the charges in the wire are not moving, hence we are standing still with respect to the charges.

Say the wire is along the z axis and we start moving in the negative z direction at constant speed, i.e. we perform a Lorentz boost in the negative z direction. The charges in our reference frame are moving in the positive z direction, hence in the observers (us) reference frame what earlier was a charge density is now a current density. This current density sources a magnetic field. In this scenario we are not standing still with respect to the charges. Even though you might be looking at a wire standing still in the lab, hence still with respect to the lab you are not necessarily still wrt the charges.

Mathematically all of this is encoded in the transformation laws for the 4-current and electromagnetic field strength tensor

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Good question. Just the first paragraph appears somewhat confused, or maybe very confused.

So the answer to the question in the the last paragraph is:

Whenever you are trying to measure a magnetic field, you are absolutely not standing still.

Because you use a compass, and the compass needle contains "surface currents". Or you use an electro-magnet, which contains moving electrons.

So those moving things are attracted or repelled by the wire.

So we can say that the observer is not standing still, because the observer uses a device that has moving parts.

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