Derive Phase difference between clocks with distance

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SUMMARY

The discussion focuses on deriving the phase difference between clocks based on the distance light travels in a moving rectangular box. The key equation discussed is ΔT = vD/c², where ΔT represents the time difference between two events detected at either end of the box. The user seeks clarification on how to derive this equation without using Lorentz Transformations, emphasizing the concepts of simultaneity and time dilation. The equations provided, cTr = L/2 - vTr and cTf = L/2 + vTf, serve as the foundation for understanding the relationship between the distances and times involved.

PREREQUISITES
  • Understanding of basic physics concepts such as simultaneity, time dilation, and length contraction.
  • Familiarity with the equations of motion and light propagation.
  • Knowledge of the relationship between velocity, distance, and time.
  • Basic understanding of the principles of special relativity.
NEXT STEPS
  • Research the derivation of the Lorentz Transformations and their applications in physics.
  • Study the concept of time dilation in special relativity and its mathematical implications.
  • Explore the relationship between velocity, distance, and time in the context of light propagation.
  • Investigate how phase differences are defined and calculated in wave mechanics.
USEFUL FOR

Students of physics, particularly those studying special relativity, educators explaining time dilation concepts, and anyone interested in the mathematical relationships between motion and light propagation.

Shiz
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Phase difference between clocks with distance

Homework Statement



Derive Phase difference between clocks with distance

Homework Equations



I honestly don't understand how this equation ΔT = vD/c2 is derived/figured out.

The Attempt at a Solution



We haven't covered Lorentz Transformations yet so is there a way to explain this to me without using it? I understand the concept of simultaneity, time dilation, and length contraction. This problem deals with the first two. The situation is a rectangular box with two detectors on either end marked with the left as A and the right as B. The box is centered along vertical axis where a flash of light in the center of the box flashes, and the light moves towards left and right towards the detectors. Now the box is moving at a constant velocity to the right.

A picture is attached because it's hard to explain. L is the length of the box, D is the distance between panel 2 and panel 3. Tr is the time it takes for the light to travel to the left detector (Event 1) and Tf is the time it takes for the light to travel to the right detector (Event 2).

I have equations from panel 1 to panel 2: cTr = L/2 - vTr
And from panel 1 to 3: cTf = L/2 + vTf

I just don't understand how to get to the phase difference between them with these equations.

unnamed.jpg
 
Last edited:
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Shiz said:

Homework Statement



Derive Phase difference between clocks with distance

Homework Equations



I honestly don't understand how this equation ΔT = vD/c2 is derived/figured out.

The Attempt at a Solution



We haven't covered Lorentz Transformations yet so is there a way to explain this to me without using it? I understand the concept of simultaneity, time dilation, and length contraction. This problem deals with the first two. The situation is a rectangular box with two detectors on either end marked with the left as A and the right as B. The box is centered along vertical axis where a flash of light in the center of the box flashes, and the light moves towards left and right towards the detectors. Now the box is moving at a constant velocity to the right.

A picture is attached because it's hard to explain. L is the length of the box, D is the distance between panel 2 and panel 3. Tr is the time it takes for the light to travel to the left detector (Event 1) and Tf is the time it takes for the light to travel to the right detector (Event 2).

I have equations from panel 1 to panel 2: cTr = L/2 - vTr
And from panel 1 to 3: cTf = L/2 + vTf

I just don't understand how to get to the phase difference between them with these equations.

unnamed.jpg


Your two expressions for panels 1 and 2 to 3, look right. Are you sure that D is defined as is shown in your figure?

Your next step is to get an expression for D (in terms of T_f, T_d and L).

By the way, a time interval is usually not called a "phase difference" so it is a confusing term to use here.
 
I figured I needed that relationship already. I was just unsure how to visualize it and needed explaining of the problem. The relationship was c = v(deltaT).

Simple enough but I just needed to understand the problem first.
 

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