Light clock - Galilean transformations

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SUMMARY

The discussion focuses on the calculation of time intervals for a photon traveling between two mirrors located at y=0 and y=l, as observed by stationary observer O and moving observer O' using Galilean transformations. The time measured by O for a full period is established as Δt=2l/c. The challenge arises in determining the time Δt' for observer O', who moves with speed v along the x-axis, and comparing it to Δt. The relationship Δt' = γΔt is introduced, with γ being a factor greater than 1, indicating time dilation effects in the context of relative motion.

PREREQUISITES
  • Understanding of Galilean transformations in classical mechanics
  • Knowledge of the speed of light and its invariance in different reference frames
  • Familiarity with basic geometry, particularly isosceles triangles
  • Concept of time dilation and the factor γ in relative motion
NEXT STEPS
  • Study the principles of Galilean transformations in detail
  • Explore the implications of time dilation in special relativity
  • Learn how to construct and analyze isosceles triangles in physics problems
  • Investigate the relationship between speed, distance, and time in different reference frames
USEFUL FOR

Students and educators in physics, particularly those focusing on classical mechanics and introductory relativity concepts, as well as anyone interested in the mathematical foundations of motion and light behavior.

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We have two parallel mirrors, which are located at y=0 and y=l in the (x,y) plane. A photon is traveling between the mirrors, up and down along the y-axis. Consider an observer O at rest w.r.t. the mirrors.

  1. What's the time (Δt) measure by O for the photon to make a full period.
Consider an observer O' which moves along the x-axis with a speed v, which is constant. Assume l' = l.

  1. Using Galilean transformations from Newt. mech. , what's the time measured by O' for the photon to make a full period (draw a picture to illustrate the logic). Compare this with the time measured by O.
  2. Now use the postulate that c=c'. Compute the period Δt' again and compare it to Δt, writing it as Δt' = γΔt, for some value of γ. Check γ>1. Interpret the results.
So for 1, the answer is Δt=2l/c. But I don't know how to do 2 (and as a result of that, 3). I don't know what to draw and the Galilean transformation eludes me. First I thought that you had to draw a triangle, with sides of 0.5vt, l and ct/2. But that accomplishes nothing. Can I get some help please.
 
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Do you have some notes about the galilean transformations?
Remember that for the second set, the speed of light is not c, but c'.
Apart from that the reasoning is fine... only you are asked for a full period, which would be an isoceles triangle.
Consider: what is the height of the triangle from base to apex?
 

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