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Voyager 2 recently left the solar system and registered an increase in plasma density. If light moved slower in this dense plasma, would it appear like events in other solar systems played out slower than they actually do?

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    $\begingroup$ "dense" is a relative word here. The interplanetary plasma is still a very very good vacuum, compared to most vacuums created on Earth. $\endgroup$
    – James K
    Dec 14 '19 at 8:27
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If light moved slower in this dense plasma, would it appear like events in other solar systems played out slower than they actually do?

First, the interstellar medium is not a "dense" plasma like the Sun's photosphere (which is also extremely tenuous compared to, say, water).

Let's ignore that for now and assume the plasma density was high enough to change the permittivity (thus, the index of refraction too) such that electromagnetic waves moved at a speed well below the speed of light in vacuum. This would not affect time, i.e., there would be no time dilation due to this propagation speed difference. The only difference is that it would take longer for the same electromagnetic wave to move through the dense plasma than a vacuum.

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