Region the light never reaches the 'uniformly-accelerated' observer?

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Discussion Overview

The discussion revolves around whether there exists a region in spacetime that light never reaches a uniformly accelerated observer. Participants explore the implications of acceleration on light perception and the concept of the Rindler horizon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the existence of a region where light never reaches a uniformly accelerated observer, expressing confusion about the concept.
  • Another participant asserts that light from any star will eventually reach any observer, unless considering the expansion of space.
  • A different participant claims to have identified such a region, explaining that the asymptotic line of the hyperbola representing the uniformly accelerated observer intersects the x-axis, indicating that light emitted from behind this point will never reach the observer.
  • One participant challenges the previous assertion, referencing a Minkowski chart that illustrates how light from certain regions will not catch up with accelerating observers, introducing the concept of the Rindler horizon.
  • Another participant reiterates the existence of a region that a uniformly accelerating observer cannot see, describing the Rindler horizon as similar to a black hole horizon and noting its position relative to the observer.
  • A participant presents a spacetime diagram to illustrate the interaction between an accelerating observer and light beams, noting that the existence of the horizon is dependent on acceleration rather than velocity.

Areas of Agreement / Disagreement

Participants express differing views on the existence and implications of the Rindler horizon, with some asserting its existence and others questioning or challenging the conditions under which light reaches an observer. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

The discussion includes references to specific spacetime diagrams and concepts such as the Rindler horizon and Minkowski space, which may depend on particular definitions and assumptions about acceleration and light propagation.

johnahn
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Is there a region that the light never reaches the 'uniformly accelerated' observer?

Of course, light travels in the same direction the observer moves.

It sounds weird for me...

I derive the parameterization of t and x, and gets hyperbola.

So I try to find with drawing that in the ST diagram, but I cannot see any clues for the reason why there exists such things...
 
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I am not at all clear on what "region" you are talking about. Ignoring expansion of space itself, no observer can move faster than light with respect to any star so light from any star will eventually reach any observer.
 
Oh, I find such region... It was very simple. If we draw the asymtotic line of the hyperbola that is the uniformly accelerated observer, then that line will meet with the x-axis at a point. And the light emitted by the source behind that point, never reaches the observer forever because the world line of the light and the observer do not meet at all.

I throw a question, and I answer it lol
 
HallsofIvy said:
... . Ignoring expansion of space itself, no observer can move faster than light with respect to any star so light from any star will eventually reach any observer.

Not true. Have a look at the Minkoski chart in this post https://www.physicsforums.com/showpost.php?p=2858281&postcount=37 depicting accelerating observers in flat Minkowski space. Light emitted from the region to left of the diagonal dotted line will never catch up with the accelerating Rindler observers. The boundary of this region is known as the Rindler horizon and is an flat space analogue of the curved space Schwarzschild event horizon.
 
johnahn said:
Is there a region that the light never reaches the 'uniformly accelerated' observer?

Of course, light travels in the same direction the observer moves.

It sounds weird for me...

I derive the parameterization of t and x, and gets hyperbola.

So I try to find with drawing that in the ST diagram, but I cannot see any clues for the reason why there exists such things...

Yes, there is a region of space-time a uniformly acceleratig observer cannot see. The boundary between the region he can see and can't see is called the Rindler horizon. It's rather similar to a black hole horizon in many respects.

The Rindler horizon appears to be a constant distance behind the accelerating observer in his accelerated frame of reference (using the definition of simultaneity of a co-moving inertial observer to create said frame of reference).
 
Here's a spacetime diagram of the accelerating observer A. A and L have synchronised clocks and L sends a light beam to A at the time the acceleration starts. If A drops a device C, then C intercepts the light beam fairly quickly. It seems strange that the horizons existence depends on acceleration, not velocity. The moment the acceleration stops the horizon disappears.
 

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