Question 2: Relative events and space-time intervals

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SUMMARY

The discussion focuses on the application of space-time intervals in the context of Special Relativity (SR) and General Relativity (GR). The first question involves deriving the coordinates of a light ray in the S' system, leading to the conclusion that the coordinates are x' = - (sqrt3 / c)ct' and y' = - 1/2 ct'. The second question addresses the relationship between simultaneous events in different reference frames, confirming that the space-time interval is defined as (ds)^2 = -c^2(dt)^2 + (dx)^2, contrary to the incorrect formulation presented by the user.

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  • Understanding of Special Relativity (SR) and General Relativity (GR)
  • Familiarity with space-time intervals and Lorentz transformations
  • Knowledge of the speed of light (c) and its implications in relativity
  • Basic trigonometry, particularly in relation to angles and coordinates
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  • Study Lorentz transformations in detail to understand their application in different reference frames
  • Learn about the derivation and implications of the space-time interval in relativity
  • Explore the concept of simultaneity in different inertial frames
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Students and enthusiasts of physics, particularly those interested in the principles of relativity, as well as educators looking to clarify concepts related to space-time intervals and transformations.

yukcream
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I just a beginner for relativity (both GR & SR), so you find my question may be very simple but still hope you can help! THX~ :shy:

Q1. A light ray in the x'y'-plane arrives at the origin O' of the S' system at t'=0. it coms from a direction which makes an angle 30deg with O'x' and 60 deg with O'y'. Show that events on the front of the ray have coordinates is:

x' = - (sqrt3 / c)ct', y' = - 1/2 ct'
can I use the equation of transformation that x' = xo + ct' ? if yes how about the cos-function in fornt og ct'?

Q2. 2 events occur simultaneously at t=o in the reference frame S, at the origin and at the point (X,0,0). In the second frames S', the measured time-interval between the events is T. Prove that the distance beetween the points at which the events occur in S' is (X^2 + C^2T^2)

Am I right to use the space-time interval: (ds)^2= c^2(dt)^2+ (dx)^2? I have tried this method but the trem 1/[sqrt(1- v^2/c^2)] is left~~~ What's worng ??

yukyuk
 
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Am I right to use the space-time interval: (ds)^2= c^2(dt)^2+ (dx)^2?
No. (ds)^2= -c^2(dt)^2+ (dx)^2, or vice versa.

Question 1 is deceptively simple.
 
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