Physics Special Relativity Time Dilation Question?

[justinh8]

Physics Special Relativity Time Dilation Question?

Homework Statement

Which of the following situations is the time interval between the two events in one frame equal to y(gamma) multiplied by the time interval in the other frame?

1. 2 Rocketships pass each other in space with high a high speed. In the first rocket ship, the captain opens a fridge door(event #1) and than closes the fridge door (event #2) 5 seconds later according to the watch of the captain The 2 rocketships are the two frames.

2. A high energy electron is emitted (event #1) by a far away star, and the star is moving fast away from the Earth. The electron is however moving toward Earth and is detected (event #2) upon arrival there. The Earth and the Star are the frames.

Homework Equations

Delta T (original) = delta T/y(gamma) where the time interval in which the event occurs at rest is Delta T (original) and Delta T is the time interval in which the observer sees it.

The Attempt at a Solution

So, i have to try to find when delta T in one frame equals delta t (original) x y(gamma) in the other frame. SO in general, the sequence where it includes time the event occurs at rest is when delta t = delta t (original) x y(gamma) right? Please help out, Thanks!

 

[RichardT]

Does delta t have to be moving?

 

[BruceW]

SO in general, the sequence where it includes time the event occurs at rest is when delta t = delta t (original) x y(gamma) right? Please help out, Thanks!

I don't know what you're trying to say here. The question essentially asks in what situations can you use the time dilation equation. You could either just state it, or prove it by using the (more general) Lorentz transformation equations.

 

[RichardT]

I might have gotten this (correct me if I am wrong). For the first one, i am assuming that the captain that measured 5 seconds is the same captain who opened the fridge door. Since the captain is in the frame of reference in which the event (opening and closing the fridge door) is occurring, this is the proper time or what you state T(original). Since T(original) = T/y(gamma), and the question asks for when is T = T(original) x y(gamma), the sequence given would NOT satisfy what the question asks for because T(original) is given when the question asks when will the time interval in one frame equal the time interval in another frame(The frame in which the observer is moving relative to the events) x gamma. Correct me if I am wrong

 

[BruceW]

The question asks Which of the following situations is the time interval between the two events in one frame equal to y(gamma) multiplied by the time interval in the other frame? The situations don't say which is the first frame and which is the second. So I would say the question is asking if either of these are true:
T(frame 1) = gamma x T(frame 2)
OR
T(frame 2) = gamma x T(frame 1)
You might think that one of these possibilities will always be true, but that is not always the case.

 

[justinh8]

I think i understand what you are saying. So you are saying that one of these situations you cannot use the time dilation equation, right? So since in sequence 1 since the event is not occurring at the same position relative to bothe of the frames being considered, it means time dilation is not applicable and you have to use a more general lorentz - einstein equation. Is this what you are trying to tell me? if not, I am lost.

 

[BruceW]

That's not quite right. Time dilation is applicable when the position does not change according to one of the frames. And according to the other frame, the position will change. (It would be pretty weird if the position did not change according to either frame, I guess this would only be true when the two events happen at the same place and time).

 

[justinh8]

Alright, i think i got it, So in sequence 1, since the event changes position in both frames (because both spaceships are moving), time dilation would not be applicable, right?. So to answer sequence 1, It is no, the time intervals between one frame will not equal the time interval x y(gamma) in the other frame because the events do not occur at the same position in either frame.

 

[justinh8]

And therefore for sequence 2, the time interval in one frame WILL equal the time interval in another frame x y(gamma) because according to one of the frames, the position in which the event is occurring does not change. Am i correct?

 

[RichardT]

I understand what the question asks now (thanks bruce), For sequence 2 however i am not positive that the equation will hold true. For it to be true, the position of the two events in one frame must be the same. But in the question where the star and Earth are the frames, the star is moving away from Earth and the Earth is at rest which means that one would see the events in a different position. Be my honor and correct me if its wrong

 

[justinh8]

I think i was wrong, I think the time dilation is applicable on the first sequence because the two frames are the two rocketships and since the captain is at rest relative to his rocketship where he measured the 5 seconds, the position of the two events did NOT change and stayed in the same position. However, in the second sequence where the two frames are the star and Earth, time dilation would not be applicable because both frames observe the two events in different positions.

 

[BruceW]

exactly :)

 

[justinh8]

What i don't understand about the second sequence is if I am an observer on earth, Will i not see event 1 and event 2 in the same position because relative to the earth, the Earth detects the electron at event 2 and since event 1 is not seen from the earth, couldn't the observer on Earth say that event 1 has also occurred where event 2 has occurred?

 

[BruceW]

Its true that the person might not see event 1 happening. But the question specifies that event 1 does happen on the star. So there is no problem about where event 1 happens, because it has been unambiguously defined as occurring at the star.

We might get a different question, where it says that event 1 happens when the electron is part-way through its journey to earth, and is passing by a meteorite. But now that we have defined event 1 differently, we will get a different answer for time differences between that event and event 2. In other words, we choose what the events are. There is nothing special about certain events.