Time dilation: period of a clock

In summary, the proper time interval is the time on the clock in the ship as measured by the observer in the unprimed system.
  • #1
ephedyn
170
1
Relevant equations

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

where t' is the proper time interval, and t is the measured time interval in another reference frame.

Homework Statement /

Q: A spaceship is moving past us at a velocity of v = 3c/5. If, in our frame of reference, we measure a time interval of 1 second, what will be the time measured by clocks within the moving ship?

Actually, I'm questioning the solution that I'm given. I can get the same answer in both ways, but I want to confirm if I am correct in theory. So my question would be: should I assign t = 1 or t' = 1? The solution I was given suggests t = 1 such that t' = 0.8s.

The attempt at a solution

In my opinion, it's t' = 1 because each event (successive positions of the second hand; let's suppose it's analog) of the clock with us is observed to occur at the same position, while that of the clock(s) within the moving ship are observed to occur at different positions. Hence 1 second is the proper time interval. This gives me t = 1.25s, which is the measured period of the second hand's motion on the ship. Then taking 1/1.25 = 0.8, we have 0.8 of a cycle of the second hand's motion on the moving ship - the time showed on the clock on the ship is 0.8s.
 
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  • #2
Of course, they are equivalent.
Usually, one takes the unprimed system to be the "rest" system and the primed system the one moving with respect to it.
In this question, we are given that the elapsed time in our rest system is 1 second, and we are asked for the corresponding time in the moving system.

What you are doing is considering an observer on the spaceship and asking the question: if one second passes in the space ship, how much time will pass on ephedyns clock. The answer is indeed 1.25 second, so if this observer would time 1/1.25 seconds instead of 1/1 second, then 1 second would pass on your watch.
 
  • #3
OK, I understand now. Just to make sure, so am I correct to say that the proper time interval is the time on the clock in the ship as measured by the observer in the unprimed system (me)?

Thanks a lot!
 
  • #4
On second thoughts, forget that confirmation. I've got it. The proper time interval is the time on the clock in the ship as measured by the observer in the ship, since it would occur to the observer on the ship that the positions remain unchanged.

But thanks very much nonetheless for sorting out the idea of primed and unprimed frames of reference; I was referring to Halliday and it avoids this phrasing, which I find a little harder to grasp.
 

1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass at a slower rate for an observer who is in motion relative to another observer. This occurs due to the effects of special relativity, as described by Albert Einstein.

2. How does time dilation affect the period of a clock?

Time dilation affects the period of a clock by causing it to appear to tick slower for an observer who is in motion relative to the clock. This means that the period of the clock will be longer than the period measured by an observer who is stationary relative to the clock.

3. How is time dilation calculated?

Time dilation can be calculated using the equation t' = t√(1-v^2/c^2), where t is the time measured by an observer at rest, t' is the time measured by an observer in motion, v is the velocity of the moving observer, and c is the speed of light. This equation takes into account the effects of special relativity on the measurement of time.

4. What are some real-life examples of time dilation?

Some real-life examples of time dilation include the time dilation experienced by astronauts in space, as their high speeds cause time to pass slower for them than it does for people on Earth. Another example is the time dilation experienced by particles in a particle accelerator, as they move at incredibly high speeds. GPS satellites also experience time dilation, which must be corrected for in order for them to accurately provide location data.

5. Can time dilation be reversed or stopped?

No, time dilation cannot be reversed or stopped. It is a fundamental aspect of the universe and cannot be altered or controlled. However, its effects can be minimized or accounted for through precise measurements and calculations.

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