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May 19

Does Wikipedia contain a contradiction about whether, the speed of light is only constant in inertial frames of reference?

On the one hand, our article special relativity states:

• In the lead: "The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer".
• In the chapter background: "Two observers in relative motion receive information about two events via light signals traveling at constant speed, independent of either observer's speed".
• In the chapter History: "James Clerk Maxwell presented a theory of electromagnetism...The theory specifically predicted a constant speed of light in vacuum, no matter the motion (velocity, acceleration, etc.) of the light emitter or receiver."
• In the chapter Reference frames and relative motion: "the speed of light is constant in relativity irrespective of the reference frame".

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So it seems that the speed of light is constant, also in non-inertial frames of reference.

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On the other hand, that article also states:

• In that chapter: "light in vacuum propagates with the speed c (a fixed constant, independent of direction) in at least one system of inertial coordinates".
• In the chapter Basis: The two postulates both concern observers moving at a constant speed relative to each other.
• In the chapter Lack of an absolute reference frame: "the speed of light in vacuum is always measured to be c, even when measured by multiple systems that are moving at different (but constant) velocities".
• in our article Postulates of special relativity, in the chapter Postulates of special relativity: "As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same value c in all inertial frames of reference".
• In our article speed of light, in the lead: "Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference is a constant...Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer".
• In that article, in the chapter Fundamental role in physics: "The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer...In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light can differ from c when measured from a remote frame of reference".

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So it seems that the speed of light is only constant in inertial frames of reference.

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I wonder if the second set of quotes contradicts the first one. HOTmag (talk) 19:04, 19 May 2025 (UTC)[reply]

The implicit assumption in the first set is that the observer shares the frame of reference with the measuring instrument.  ​‑‑Lambiam 12:08, 20 May 2025 (UTC)[reply]

Of course, but what about two measuring instruments that accelerate relative to each other? Will they measure the same speed of light, according to each set of quotes mentioned in my original post? HOTmag (talk) 00:04, 23 May 2025 (UTC)[reply]

In an inertial frame of reference you can make a local clock by observing a light package bouncing between two parallel motionless mirrors, which can serve as the basis for setting up a coordinate system. The problem is really in how to define a non-local coordinate system from a non-inertial frame of reference. You can write in your lab notes, "Event E was observed at position (x₁, y₁, z₁) at time t₁." How did you measure the values of these non-local coordinates? Will they still be in any sense meaningful at time t₂? Is the space point (x₁, y₁, z₁) still "where it was" at time t₁?  ​‑‑Lambiam 16:31, 23 May 2025 (UTC)[reply]

I'm referring now to your last three questions: Why can they only be asked when the frame of reference is (non-locally) accelerating, and not when the frame of reference is (non-locally) moving without acceleration? HOTmag (talk) 10:28, 26 May 2025 (UTC)[reply]

@Lambiam: Before it's archived... HOTmag (talk) 06:29, 1 June 2025 (UTC)[reply]

At least according to the theory of special relativity, clocks at different locations in the same inertial frame run at the same rate. This allows the observer to set up a consistent time coordinate. And if A, B and C are at rest with respect to an inertial frame, with B halfway between A and C, it remains halfway. More generally, if their locations are collinear, their relative positions on the line remain unchanged. This suffices to set up a spatial coordinate system.  ​‑‑Lambiam 07:11, 1 June 2025 (UTC)[reply]

Do your last two responses only show, that measuring the speed of light in a non-inertial frame of reference - is not "meaningful" only (as implied by your middle question in your previous response before your last one), or you also think that - measuring the speed of light (in vacuum) in different non-inertial frames of reference - really result in different values? HOTmag (talk) 09:53, 1 June 2025 (UTC)[reply]

@Lambiam: I suspect it's going to be archived soon... HOTmag (talk) 18:41, 2 June 2025 (UTC)[reply]

Spacetime in the non-inertial frame has non-zero curvature, so the geodesic distance between A and B traversed by a light packet going from A to B is larger than the Euclidean distance between A and B in the coordinate system of an inertial frame. If an observer ignores this issue, they will generally get different results than when they try to account for the curvature. And two observers in the same inertial frame of reference trying to account for the effect may still get different outcomes, since they cannot measure the curvature directly.  ​‑‑Lambiam 20:03, 2 June 2025 (UTC)[reply]