Special relativity clocks observed from two frames

In summary: This will give you the time that S' records on their clock. However, the time that S actually sees through a telescope will be different due to the effects of relativity and the speed of the two frames. This can be calculated using the Lorentz transformation equations. Essentially, it will be a combination of the time dilation effect and the time delay due to the speed of the frames.
  • #1
wumple
60
0

Homework Statement


Observers S and S' stand at the origins of their respective frames, which are moving relative to each other with a speed of .6c. Each has a standard clock, which, as usual, they set to zero when the two origins coincide. Observer S keeps the S' clock visually in sight. (a) What time will the S' clock record when the S clock records 5 micro seconds? (b) What time will Observer S actually read on the S' clock when his own clock reads 5 micro seconds?


Homework Equations


time dilation: t = gamma (proper time)


The Attempt at a Solution


I can solve part A by using time dilation. My confusion comes in understanding how to interpret the conditions set on part b - how is part b different from part A? I know that for time dilation, the proper time is the time measured when the clock is at rest. But how can I calculate what one observer sees on a clock in another frame?
 
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  • #2
I assume that part a is in observer S's frame.
I guess they just want to make it clear
that the relativistically calculated time on the S' clock
is different from the time on clock S' as
actually physically observed by S through a telescope.

This is a common mistake by beginners and
they just want to make sure that everyone understands it correctly
 
  • #3
but how would I go about calculating what observer S sees on the clock of S' through a telescope? That's the part I don't understand.
 
  • #4
work backward
 
  • #5


For part B, we need to take into account the effects of length contraction as well. The observer S will see the S' clock as moving at a slower rate due to time dilation, but also as physically shorter due to length contraction. This means that the S' clock will appear to be ticking slower than the S clock, but also moving through space at a slower rate.

To calculate the time that observer S will actually read on the S' clock, we can use the equation for time dilation (t = gamma * t'), where t is the time measured by observer S and t' is the time measured by observer S'. We also need to consider the length contraction factor, which is given by L = L0 * sqrt(1 - v^2/c^2), where L0 is the proper length and v is the relative velocity between the two frames.

So, for part B, the time that observer S will read on the S' clock will be given by:

t = (gamma * t') / (sqrt(1 - v^2/c^2))

where t' is the time recorded by the S' clock when the S clock reads 5 micro seconds.

This shows that the time read by observer S on the S' clock will be less than 5 micro seconds, due to the combined effects of time dilation and length contraction.
 

Related to Special relativity clocks observed from two frames

1. What is the concept of "time dilation" in special relativity?

Time dilation is the phenomenon in which time appears to pass at different rates for observers in different inertial frames of reference. This is a fundamental principle in special relativity, stating that the passage of time is relative to the observer's frame of reference and is affected by the relative motion between frames.

2. How does the speed of light play a role in special relativity?

The speed of light, denoted as "c", is a constant in special relativity and is the maximum speed at which all matter and information can travel. This means that the speed of light is the same for all observers, regardless of their relative motion. It also plays a crucial role in the time dilation and length contraction effects observed in special relativity.

3. Can two clocks moving at different speeds show the same time?

No, according to the principles of special relativity, two clocks moving at different speeds relative to each other will not show the same time. This is because as an object's speed increases, time appears to slow down for that object. Therefore, the clock moving at a faster speed will appear to be ticking slower compared to the clock moving at a slower speed.

4. How does time dilation affect the concept of simultaneity?

In special relativity, the concept of simultaneity is relative to the observer's frame of reference. This means that two events that appear to happen at the same time for one observer may not appear to be simultaneous for another observer in a different frame. This effect is known as the relativity of simultaneity and is a direct consequence of time dilation.

5. Is special relativity only applicable to objects traveling at high speeds?

No, the principles of special relativity apply to all objects, regardless of their speed. However, the effects of time dilation and length contraction are only noticeable at speeds close to the speed of light. At everyday speeds, these effects are negligible and can be ignored in calculations.

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