Let's say there's a light wave travelling in vacuum, and it travels forever because it does not hit any object in its way. This light ray will produce oscillating magnetic and electric fields, but producing electric and magnetic field needs energy. So, how is it that the light can go on forever (which it will), when it's not as if that light wave has infinite energy? Shouldn't the light kind of just fade away, being wholly converted into magnetic and electric field?
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$\begingroup$ It does not work that way. You have to study the solutions of Maxwell equations to understand the electromagnetic wave. $\endgroup$– anna vApr 14, 2022 at 19:06
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3$\begingroup$ TLDR: The oscillation is the energy. It would be a violation of conservation of energy if the oscillation could simply "die out" without delivering the energy to an atom somewhere in the Universe. $\endgroup$– Solomon SlowApr 14, 2022 at 19:32
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$\begingroup$ Do you also expect a mass that is hurling through empty space without anything ever impeding it to also eventually slow down or fade away? I doubt it. So why is light different? The light might spread out so the same energy gets distributed over a wider area so it becomes very faint and difficult to detect, but the energy is still there and still moving. I do not know where you are drawing the conclusion that the light should eventually decay to just a magnetic or just an electric field. Consider that a fly wheel which is spinning (a kind of oscillation) can also spin forever. $\endgroup$– DKNguyenApr 14, 2022 at 19:36
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2 Answers
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Light does not produce oscillations in the electric and magnetic fields; Oscillations in the electric and magnetic fields are light. The reason these oscillations (i.e. light) do not violate conservation of energy is because the energy content of the fields ($\int\mathrm{d}^3r\,\tfrac12(\epsilon_0 E^2+\frac{1}{\mu_0}^2 B^2)$) does not change when the fields evolve according to Maxwell's equations; i.e. energy is conserved.
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$\begingroup$ @johnywhy In general, oscillations in the electric and magnetic fields are caused by things like moving charges or spinning magnetic dipoles, but that's really a separate question. $\endgroup$– SandejoNov 2, 2022 at 22:47
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$\begingroup$ @Sanjejo Separate question? But isn't propagation of light the topic? How does light approaching earth from alpha centauri produce moving charges or spinning magnetic dipoles? $\endgroup$ Nov 4, 2022 at 2:11
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A changing electric field induces a magnetic field. The changing magnetic field induces an electric field. So they can indeed just keep going "on forever".
