Lorentz and Doppler and signal pick up

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Discussion Overview

The discussion revolves around the application of Lorentz transformations and the Doppler effect in the context of two probes, A and B, which are sending signals to each other while moving at relativistic speeds. Participants explore the implications of time dilation, signal reception, and the effects of relative motion on the frequency of signals received.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes a scenario where two synchronized probes send signals to each other over a distance of 100 light-years, questioning the timing and reception of these signals based on their relative velocities.
  • Another participant introduces the concept of frequency shift due to the Doppler effect, providing a formula for calculating the frequency shift based on relative velocity.
  • There is a discussion about whether probe B experiences the Doppler effect immediately upon changing velocity, while probe A has to wait for the light from B's actions to reach it.
  • Some participants express uncertainty about the implications of relative motion and how it affects the timing of signal reception between the two probes.
  • One participant suggests that the situation creates an asymmetry in the experience of time between the two probes, leading to further questions about the nature of simultaneity in relativity.
  • Another participant attempts to clarify that an observer cannot perceive changes in motion until the light from those changes reaches them, emphasizing the role of the speed of light in these observations.

Areas of Agreement / Disagreement

Participants generally express differing views on the implications of the Doppler effect and the timing of signal reception. While some agree on the mechanics of how signals are sent and received, there is no consensus on the interpretation of the asymmetry in experiences between the two probes.

Contextual Notes

The discussion includes assumptions about the synchronization of clocks and the effects of relativistic speeds on time intervals, which may not be fully resolved. The mathematical steps involved in calculating signal reception times and frequency shifts are also subject to interpretation.

Who May Find This Useful

This discussion may be of interest to those studying special relativity, particularly in understanding the implications of the Doppler effect and time dilation in relativistic contexts.

  • #31
pervect said:
Stephanus said:
B will reach A at 115.4701 years.
I think you mean by this that A's clock will read 215.47years when B reaches A.
Because γ=2, then B will reach A according to B clock for 57.7350 years...
Very smart and meticulous of you, very careless of me! :smile: Yes that's right.
When A's clock read 215.47 year or 115.47 year from A's clock read 100 years which is the first time A receive signal from B.

pervect said:
B will receive a signal from A every γ(1−v/c) years as per wiki. There are several alternate equivalent formulae. I get this as a period of .2679 years, close to your figure.
Yes, thanks 0.2679 actually, just copied only 2 dec points.

pervect said:
A will send out a total of 216 plus a fraction signals that B will receive, the first signal A0 will be received by B when B starts the trip at B's time of 100. (Note that the set {0,1,...,215} contains 216 elements.) The first signal is numbered A0, the last A215. The spacing between signals is .2679 years. The last signal from A, A215, will be received at a time of 215*.2679 = 57.6 years according to B's clock, near the end of B's trip.

B will send out a total of 58 signals on the trip, the first signal B100, the last signal B157. A will receive the first signal, B100, at 200 years on A's clock due to propagation delays, the same time at which A will see B's rocket flare through a telescope (if A is looking).

A will receive signals from that point at the rate of 1 signal every .2679 years, so the last signal, B57, will arrive at 200+.269*57 = 215.27 on A's clock, shortly before B arrives.
Thank you, thank you. I learn much from this.
 

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