Light clock - Galilean transformations

In summary, the conversation discusses two parallel mirrors located at y=0 and y=l in the (x,y) plane with a photon traveling between them along the y-axis. The time measured by observer O for the photon to make a full period is Δt=2l/c. The conversation then introduces a second observer, O', who is moving along the x-axis with a constant speed v. Using Galilean transformations, the time measured by O' for the photon to make a full period is found to be Δt' = γΔt, for some value of γ. The postulate that c=c' is then used to compute Δt' again and compare it to Δt. The conversation ends with a request for
  • #1
Achmed
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0
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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  • #2
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?
 

Related to Light clock - Galilean transformations

1. What is a light clock and how does it work?

A light clock is a theoretical device used to illustrate the concept of time dilation in Einstein's theory of relativity. It consists of a light source bouncing between two mirrors at a constant speed. The time it takes for the light to make one round trip is measured as one "tick" of the clock.

2. What are Galilean transformations and how are they related to light clocks?

Galilean transformations are a set of equations used to convert measurements of time and space from one reference frame to another. They were developed by Galileo in the 17th century and were used to describe the laws of motion before Einstein's theory of relativity. Light clocks are used to demonstrate how these transformations break down when dealing with the speed of light, leading to the development of Einstein's theory.

3. How does the speed of light affect the measurement of time on a light clock?

The speed of light is a constant in all reference frames, meaning it does not change regardless of the observer's perspective. This leads to time dilation, where the measurement of time on a moving light clock appears slower to an outside observer compared to a stationary light clock. This phenomenon is a key principle in Einstein's theory of relativity.

4. Can a light clock be used to measure time accurately?

While a light clock is a useful illustration of time dilation, it is not a practical device for measuring time. This is because it relies on the constant speed of light, which is difficult to maintain in real-world conditions. However, atomic clocks, which use the oscillations of atoms to measure time, have been shown to be accurate to within a few nanoseconds over billions of years.

5. How does the concept of time dilation impact our understanding of space and time?

Einstein's theory of relativity revolutionized our understanding of space and time. It showed that the two are not separate entities but are interconnected and can be affected by gravity and motion. Time dilation allows for the possibility of time travel and has significant implications for our understanding of the universe and the laws of physics.

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