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Whether the speed of light can only be measured at the observer's place, in his local inertial frame of reference, that is, where the measurement is made. It is about the fact that the observer (that is, his measuring devices) are in his local reference frame, but he is measuring the speed of light in some distant reference frame.

If this is possible, will there be a difference in the speed of light between a local and such a remote measurement of the speed of light, and in what examples?

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    $\begingroup$ The speed of light always connects two different locations. It is not possible to even talk about it without referencing two distinct points in space. I don't know what you mean by "different flow of time". Time is always that which the clocks show. The only difference in time is being observed when we look at a second clock in a different reference system. $\endgroup$ Commented Apr 5, 2023 at 8:18
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    $\begingroup$ Do not edit a question in a way that invalidates answers you have already received to the original question. I have reverted your edit. That is against the site policies $\endgroup$
    – Dale
    Commented Apr 5, 2023 at 11:00
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    $\begingroup$ Only one clock is needed to measure the speed of light, but we also need a ruler, and that means the speed of light is not a local quantity. It requires at least two locations and the entire connecting line between them. So while clocks are, in some sense, entirely local, rulers and derived quantities are not. Of course an observer can measure the speed of light in another reference frame. All it takes is a bunch of mirrors and a ruler in that other frame. Whatever you do, though, you always need that ruler. $\endgroup$ Commented Apr 6, 2023 at 16:31
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    $\begingroup$ Physics with observers is, in general, not a good idea. It distracts from the physics. Negligible dimensions are also not "zero". They are simply physics speak for "tangent space". Unless there is no physics to first order (c is of first order in space and time), we can't go to second or higher order. $\endgroup$ Commented Apr 6, 2023 at 22:17
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    $\begingroup$ Relativity is all about different conditions. I don't know why that should be a problem? That is the core idea of it... how local physics "translates". The speed of light is the most important property that translates in a trivial fashion. Another thing are scalars in general. Whatever can be counted in one reference frame, will lead to the same count in another. $\endgroup$ Commented Apr 6, 2023 at 22:20

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Spigel asked: "Is there a possibility for that observer to measure the speed of light in some other frame of reference, where there is also a different gravity and flow of time? If there is, does the difference appear in the measurement of the speed of light?"

Locally light always has c, but far away it can have less, see the shapirodelayed velocity in the vicinity of a mass where light can even stay stationary at the horizon of a black hole, or more, see the recessional velocity to which it is added in an expanding universe. The laws of special relativity only hold in the immediate spatial and temporal neighbourhood.

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  • $\begingroup$ Since the general relativity tag in the question was edited out after I gave my answer and the new question now is only about special relativity my answer no longer fits, but it does in context of the original tag. $\endgroup$
    – Yukterez
    Commented Apr 5, 2023 at 14:56
  • $\begingroup$ Sorry, I changed the text because I assumed I didn't describe the question clearly. However, your answer suits me in any case. $\endgroup$
    – Spigel
    Commented Apr 5, 2023 at 19:04
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Is there a possibility for that observer to measure the speed of light in some other frame of reference, where there is also a different gravity and flow of time?

Of course that is possible. Simply build a device to measure the speed of light, and then have it transmit the results of the measurement to a distant observer or an observer moving relative to the device. Or even easier, make any measurement of the speed of light and simply analyze it from a different reference frame using a coordinate transform to a different frame.

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  • $\begingroup$ In your example, there are two observers (observer + measuring device). The point is that one observer looks from his reference frame into another reference frame and thus measures the speed of light. In that example, as stated by @Yukterez, the observer can perceive speeds other than c. Unfortunately, my question was not clear enough. $\endgroup$
    – Spigel
    Commented Apr 5, 2023 at 7:58

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