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Imagine a situation where I'm moving at the same velocity as the electrons in a conducting wire. In this scenario, from my frame of reference, the electrons appear to be stationary and thus there is no current from my POV.

Now, for a brief moment, these "stationary" electrons come into contact with (or pass right next to) a light bulb in the vacuum of space and closes the circuit for a brief moment, causing it to illuminate, and then we all continue moving together. (water this down as much as possible to reach "spherical cows in a vaccuum" state for the purposes of this problem)

Question:

From my perspective, the light bulb lights up even though the electrons (which I observe as stationary) aren't "flowing" in the traditional sense. How is this phenomenon explained? Would I effectively be seeing a light bulb illuminating without any observable current thus creating something out of thin air (obviously no). Or rather, what do i have to "give up" for the laws of physics to be consistent.

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The issue with your analysis is that the electrons do not flow at a constant velocity through the lightbulb filament.

The lightbulb filament is a resistor, which means it gets in the way of electron flow in a circuit. If you were to pick a particular electron to follow you would both move along at the same constant velocity for a time, but then some time after you enter the filament the electron would collide with an atom. From your perspective the electron would suddenly accelerate backwards.

But this acceleration is not what causes the light from the lightbulb. Instead, the collisions heat up the filament over time, turning it into a black-body radiator.

There is no "spherical cow" model here where the electrons all move at a steady rate. The function of the lightbulb depends on extracting energy from the electrons through collisions.

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The effect on a current by going to a moving frame of reference is covered by special relativity, and any change in the current as of the order, v/c. By moving to a frame where the average velocity of the electrons is <<c, there is no significant change in the current.

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In the given scenario the electrons are moving with respect the light bulb and flow through the filament. Thus although the moving observer sees no current, the light bulb experiences one. Another way to look at it is that, from the point of view of the observer, the light bulb moves through the electrons and the observer sees the electrons scattering off the light bulb filament, which heats up. Also one would expect the light bulb to "slow down" with respect to the observer (or start moving in the direction of the observer and the original current) since it has lost energy to the electrons and has lost energy as heat and light in the filament.

In practise, however, electrons don't move uniformly through a wire because they are continuously scattered from defects in the metal crystal lattice, at grain boundaries and by thermal vibrations (phonons). Thus, although one can ascribe an average motion of electrons in the wire (current), the actual motion is almost random. The scattering transfers energy to the lattice which we observe as heat. It is this scattering in the light bulb filament that heats it up and makes it glow. With a potential difference applied to the ends of a wire (a voltage source), the electrons accelerate between scattering. The scattering acts as a frictional force opposing the acceleration. Thus without a driving force, the average motion of the electrons will quickly become zero and there will be no current. So in the light bulb scenario, most of the electrons will be scattered in the filament and no longer propagate forward.

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