The discussion centers on how an accelerating observer measures the velocity of light compared to an observer at rest or moving at constant velocity. It explores the implications of acceleration on measurements of light speed, including distinctions between local and distant observations, and the effects of linear versus radial acceleration.
Participants express differing views on the implications of acceleration on light speed measurements and the nature of spacetime curvature. There is no consensus on whether the curvature of spacetime is observer-dependent or independent, indicating ongoing debate.
The discussion includes various interpretations of local versus distant measurements of light speed and the effects of acceleration on these measurements. Some assumptions about the nature of spacetime and the definitions of curvature remain unresolved.
brightonb said:Will an accelerating observer obtain the same value for light velocity as one at rest or moving at constant velocity? Will the measurement be the same for linear and radial (circular motion) acceleration?
When people say that the speed of light is constant, they mean that if any inertial (non-accelerating) observers measures the speed of light using rulers and clocks at rest relative to themselves, with the clocks synchronized using the Einstein synchronization convention, they will all find it moves at c.
Yes.Is the difference that the first refers to local frames, while the second refers to extended (distant) frames as well??
No.Does the accelerating observer have accelerating clocks?
An accelerating observer measures the local speed of light to be c in all directions.
Will an accelerating observer obtain the same value for light velocity as one at rest or moving at constant velocity?
All things being equal, yes. I.e. both observers must be at the same place at the same time, measuring light "locally" i.e. at their own location.brightonb said:Will an accelerating observer obtain the same value for light velocity as one at rest or moving at constant velocity?
Don't confuse space-time curvature with non-inertial ("accelerating") observers. The two often occur hand-in-hand but they have different effects.Naty1 said:While the local speeds of light will be measured as c by each observer, distant observations will yield different results for the speed of light between the two observers. The constant velocity inertial observer will see all light as c; for her, all spacetime is straight.
The accelerating observer will observe things as if immersed in a gravitational field where spacetime is curved; his observations change since curvature (gravitational strength) becomes apparent with increasing distance.
Inertial observers (a.k.a. free-falling observers) in the presence of gravitation do not see "all spacetime" as straight -- it only looks straight locally. The curvature or flatness of spacetime is an intrinsic property of spacetime itself and does not depend on the motion of observers. An inertial observer can tell if spacetime is flat or curved by looking at other, non-local inertial observers and seeing if they all move at constant velocity or if some don't.
No, the boldefaced statement is exactly right, the curvature of spacetime is observer independent.Naty1 said:I have been puzzled by the boldface part for sometime...and I think it does depend on frame...
What we call the "curvature of spacetime" has a technical meaning; the equations that describe it are very similar to the equations that describe, say, the curvature of the Earth's surface in terms of latitude and longitude coordinates, or any other pair of coordinates you might choose. This "curvature" need not manifest itself as a physical curve "in space".Naty1 said:I have been puzzled by the boldface part for sometime...and I think it does depend on frame...Let me disagree for discussion: A free falling inertial observer in the presence of gravitation sees local spacetime as flat; all other frames will observe the same local space as curved.DrGreg said:Inertial observers (a.k.a. free-falling observers) in the presence of gravitation do not see "all spacetime" as straight -- it only looks straight locally. The curvature or flatness of spacetime is an intrinsic property of spacetime itself and does not depend on the motion of observers. An inertial observer can tell if spacetime is flat or curved by looking at other, non-local inertial observers and seeing if they all move at constant velocity or if some don't.
In fact, when light is observed from a distance approaching a black hole and slowing, blue shifting, as viewed say from earth, and never reaching the event horizon, (curved space) while a local free falling observer sees that same light proceed to the event horizon and disappear (flat space)...isn't that an example of different observers seeing different shape spacetime??
If we switch to a non-inertial frame (but still in the absence of gravitation), we are now drawing a curved grid, but still on the same flat sheet of paper. Thus, relative to a non-inertial observer, an inertial object seems to follow a curved trajectory through spacetime, but this is due to the curvature of the grid lines, not the curvature of the paper which is still flat.
Do I understand what it means?When we introduce gravitation, the paper itself becomes curved. (I am talking now of the sort of curvature that cannot be "flattened" without distortion. ... Now we find that it is impossible to draw a square grid to cover the whole of the curved surface. The best we can do is draw a grid that is approximately square over a small region,...
An accelerating observer measures the local speed of light to be c in all directions.
This implies that for any local observer the velocity of light is isotropic and is equal to c, providing that it is measured by propagating a light beam in a small neighborhood of the observer, using Einstein synchronized clocks. This is also true for an observer in curved spacetime...,
A free-falling object (either a massive particle or a photon) has a worldline (trajectory in spacetime) that is "as straight as possible" constrained only by the curvature of "the paper on which it is drawn". Usually curved trajectories through space (rather than spacetime) are due to the proper-acceleration of the observer (remember someone stood on the Earth's surface is properly-accelerating). The "as straight as possible" line seems to be curved but that's relative to the observer's curved gridlines (which the accelerating observer perceives to be straight). Relative to a free-falling observer's locally-inertial frame (=locally square grid), the worldline is locally as-good-as straight (but curves in the distance).Naty1 said:It seems the same boldface concept should also apply with gravity (right?) : an inertial object seems to follow a (slightly different) curved trajectory through space...one slightly different from the physical curvature... hence a value for lightspeed different from c?
An accelerating observer measures the local speed of light to be c in all directions.
This is true by definition. Q: How does a non-inertial observer measure local distance and local time? A: by asking a co-moving (i.e. relatively stationary) inertial observer to make the measurement for him/her. This is how local distance and time are defined for a non-inertial observer.