Redshift of a light pulse between 2 accelerating rockets

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    Light Pulse Redshift
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SUMMARY

The discussion focuses on the behavior of a light pulse emitted from a trailing rocket to a leading rocket, both accelerating with the same acceleration, denoted as ##a##. The light pulse travels a distance ##z## as perceived in the background frame, but the leading rocket moves forward during this time, complicating the actual distance the light must cover. The participants clarify that the first-order approximation simplifies the situation by ignoring higher-order terms, leading to the conclusion that the light pulse effectively reaches the leading rocket without accounting for the additional distance due to its acceleration.

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  • Understanding of special relativity concepts, particularly light propagation in accelerating frames.
  • Familiarity with basic kinematics, including acceleration and displacement equations.
  • Knowledge of reference frames and their significance in physics.
  • Ability to interpret mathematical approximations and their implications in physical scenarios.
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This discussion is beneficial for physicists, students of relativity, and anyone interested in the dynamics of light in accelerating frames, particularly in the context of special relativity and kinematics.

sphyrch
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I'm reading book from here. Suppose two rockets are accelerating with the same acceleration ##a## and are separated by some distance ##z##. At time ##t_0## the trailing rocket emits a light pulse. The book tells that pulse reaches leading box after time ##z/c## as seen in background frame. But won't the pulse actually have to cover a distance more than ##z## to reach the front rocket since the front rocket would've moved forward in that time? This on pg 65
 
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Yes, that is a first order approximation.
 
Dale said:
Yes, that is a first order approximation.
It like this? If front ship moved extra ##x## dist by the time (say ##t##) light reached, then ##ct-z=ut+at^2/2##. and then we say ##u<<c## so we ignore, and we say that time taken is super short so we ignore ##t^2## too. So every thing gets ignored and we get ##ct-z=0##. This the author logic?
 
More or less, yes. The only other thing is that usually they choose the reference frame where ##u=0##. So the displacement due to acceleration is 2nd order (##at^2/2##)
 
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