Exploring Time Dilation: A Case Study

[calculus_jy]

concept of time dilation

can someone tell me if i have any misconception in concept when i consider the following case, as i am really confused about the symmetry of time dilation.

suppose a train and a platform of the same length travel relative to each other at speed of 0.6c ie lorentz factor is .8

to consider the observer on the train measuring how long it takes for the train to travel pass the platform, we take the train as stationary and the platform moving, so if he says he takes 60s. Then the observer on platform will say this event takes 60s(.8) ie 48s?and does this observer(on platform) see the train travel pass the platform in 48s or the 38.4s below.

to consider the observer on platfrom measuring how long the train takes to travel pass the platform, we take the platform stationary and train moving, so if he says it takes 48s, then the observer on the train will say this event will take 48s(.8) ie 38.4s ? and does this observer(on train) see the platform travel past him in 38.4s or the 60s above?

I am so confused, please help

 

[calculus_jy]

--------------------------------------------------------------------------------

can someone tell me if i have any misconception in concept when i consider the following case, as i am really confused about the symmetry of time dilation.

suppose a train and a platform of the same length travel relative to each other at speed of 0.6c ie lorentz factor is .8

to consider the observer on the train measuring how long it takes for the train to travel pass the platform, we take the train as stationary and the platform moving, so if he says he takes 60s. Then the observer on platform will say this event takes 60s(.8) ie 48s?and does this observer(on platform) see the train travel pass the platform in 48s or the 38.4s below.

to consider the observer on platfrom measuring how long the train takes to travel pass the platform, we take the platform stationary and train moving, so if he says it takes 48s, then the observer on the train will say this event will take 48s(.8) ie 38.4s ? and does this observer(on train) see the platform travel past him in 38.4s or the 60s above?

please help

 

[otg]

--------------------------------------------------------------------------------
suppose a train and a platform of the same length travel relative to each other at speed of 0.6c ie lorentz factor is .8

to consider the observer on the train measuring how long it takes for the train to travel pass the platform, we take the train as stationary and the platform moving, so if he says he takes 60s. Then the observer on platform will say this event takes 60s(.8) ie 48s?and does this observer(on platform) see the train travel pass the platform in 48s or the 38.4s below.

to consider the observer on platfrom measuring how long the train takes to travel pass the platform, we take the platform stationary and train moving, so if he says it takes 48s, then the observer on the train will say this event will take 48s(.8) ie 38.4s ? and does this observer(on train) see the platform travel past him in 38.4s or the 60s above?

please help

The most important quality of the nature is symmetry [at least it's the most beautiful :)]
Thus will the observer on the platform [P] see things in the train happen in exactly the same way as the observer in the train [T] sees things happen on the platform.
Thus P will say that the event at T takes 48s, and T will say that the event at P takes 48s, but P will say that the event at P takes 60s [rest frame], and T will say that the event at T takes 60s [rest frame]

clearer?

 

[calculus_jy]

i dun quite get it

 

[calculus_jy]

so when T says he has traveled from point A to B of the platform in 60s
will P see the train at pt B at 48s?NO?
and is P's obervation of the event at P the arrival of the train at B at 60s?
also when considering the train moving and if the person on the train says 60s like the 1st case, then shouldn't P say this event >60s but in the 1st case (same things happen)when the train says 60s the platform says 48?

 

[otg]

so when T says he has traveled from point A to B of the platform in 60s
will P see the train at pt B at 48s?NO?
and is P's obervation of the event at P the arrival of the train at B at 60s?

Due to length contraction, P will see a train of length 0.8 that travels a distance of 1, while T will see himself traveling a distance of 0.8 [since from his perspective, the platform has length 0.8]. Both persons however agree on the speed being 0.6c, thus they will disagree on what they observe. P says it takes 1/0.6c for T to move from A to B, while he sees the watch of T only pass 0.8/0.6c.

T will see a person P that travels a distance of 1 [the train length measured by T], while P will see himself traveling a distance of 0.8 [since from his perspective, the train has length 0.8]
T says it takes 1/0.6c for P to move from C to D [the ends of the train] while he sees the watch of P only pass 0.8/0.6c.

We have a "problem" with simultaneity here, that T and P would not agree on *both* events "T is at A" and "T is at B". [or "P is at C" and "P is at D"] Thus we cannot say that "the event starts at t1 and ends at t2" without adding "with respect to T" or "P". But the symmetry of the situation is clear

hope I didn't mess anything up here :) having pain from kidney stones so I'm not thinking clearly

 

[Doc Al]

can someone tell me if i have any misconception in concept when i consider the following case, as i am really confused about the symmetry of time dilation.

The symmetry of time dilation is that both train and platform observers measure each other's clocks as running slow compared to their own.

suppose a train and a platform of the same length travel relative to each other at speed of 0.6c ie lorentz factor is .8

to consider the observer on the train measuring how long it takes for the train to travel pass the platform, we take the train as stationary and the platform moving, so if he says he takes 60s.

To avoid confusion we have to clearly define what it means for the train to "travel past the platform". Let's define two events: (A) The front of the platform passes the front of the train; (B) The rear of the platform passes the front of the train.

Given that understanding, the train observer says that the time between those two events is 60s. (Which implies that the length of the train is 36 light-seconds.)

Then the observer on platform will say this event takes 60s(.8) ie 48s?and does this observer(on platform) see the train travel pass the platform in 48s or the 38.4s below.

Since the above observations where made by the train observer in the front of the train using a single clock, the platform observer can apply time dilation to figure out the time that he would measure: According to platform clocks, the train clocks operate slowly thus the actual time should be 60s/.8 = 75 seconds. (He could also calculate the time from the trains speed and length as measured by the platform.)

Thus train observers and platform observers measure different times between the same two events. Note that the situation is not symmetric, since the platform observers require multiple clocks to make their measurements of the time: One at the front of the platform to measure the time of event A; one at the rear of the platform to measure the time of event B. So train observers can't mindlessly apply the time dilation formula to the platform measurement of 75 seconds since that measurement was not made on a single moving clock.

The symmetric situation would be this. Define two different events: (A) The front of the train passes the front of the platform; (C) The rear of the train passes the front of the platform. Compare these events (one of which is the same) with the two above and you'll see that they are an exact match, but with platform and train reversed. Since it's a completely equivalent situation (and we assume the rest length of platform and train are equal) the times will be the same: The platform observer at the front of the platform will measure the time between events A & C to be 60 seconds; the train observers will measure it to be 75 seconds.

I hope this helps a little.

 

[tiny-tim]

Hi calculus_jy!

I think this has all got needlessly complicated.

(Relativity usually does! )

This has nothing to do with time dilation … only length contraction.

To pass each other, each must go the length of the platform plus the length of the train.

Each measures its own length as the same, and the length of the other as contracted.

And each measures other's speed as the same.

Does that help?

 

[Doc Al]

Given tiny-tim's quite sensible definition of "the train passing the platform", you can see that both observers will measure the same time. But this does not contradict time dilation, since both frames must use multiple clocks to make their measurements.

In this case, the two events would be: (A') The front of the train passes the near end of the platform; (B') The rear of the train passes the far end of the platform.

You might want to ask yourself: How is this possible without some kind of contradiction? The full answer requires length contraction, time dilation, and--most importantly--the relativity of simultaneity (between those multiple clocks).

 

[calculus_jy]

thx all and no one has confused me more! i get cases when considering all the cases separate but when i reverse the situation i get different story!?
sorry for being a pain, but i am so fustrated i can't understand this

suppose the ends of the platfrom are A and B and the the train C and D
the front of the train C travels in direction A to B

so if the observer on the train measures the time it takes him to see A and then B is 60s
1)isn't he considering the platform to be moving, so the platform observer will say this event is shorter!?i kinda get y its 75s (longer) when u consider the train moving, so the platfrom will have a time dilated!??
2) if the obeserver on the platform does say it is 75s, but will he see C at B at this time?

 

[calculus_jy]

also, let's say there is obervers A and B moving relative to each other, B observes an event in his frame taking 10s, then A willl say this event has a time >10s?then if A observes a time >10s, shouldn't B consider A is moving and thus oberve a time >>10s contradicting to the original 10s he observed??(i know i have made this so confusing for u guys, sorry and thank you in advance)

 

[Doc Al]

suppose the ends of the platfrom are A and B and the the train C and D
the front of the train C travels in direction A to B

OK.

so if the observer on the train measures the time it takes him to see A and then B is 60s

So the two events are:

-The observer at the front of the train (C) passes platform end A;
-The observer at the front of the train (C) passes platform end B.​

[Note that this is the setup I described in post #7.]

1)isn't he considering the platform to be moving, so the platform observer will say this event is shorter!? i kinda get y its 75s (longer) when u consider the train moving, so the platfrom will have a time dilated!??

The platform observer sees the moving clock of the train observer at C to run slow, that means he measures the time to be longer. That's what time dilation means.

According to C's clock, the time between those two events is 60s. According to the platform observers, the time between those two events is 75s.

2) if the obeserver on the platform does say it is 75s, but will he see C at B at this time?

Sure. That's the second event.

 

[calculus_jy]

2) if the obeserver on the platform does say it is 75s, but will he see C at B at this time?

Sure. That's the second event.


so original train oberved 60s to second event
now working in reverse, isn't platfrom clock(s) moving relative to the train so the train will say the second event is >75s (this is the essence of what i dun get as it contradicts to what he original observes!)

 

[Doc Al]

also, let's say there is obervers A and B moving relative to each other, B observes an event in his frame taking 10s, then A willl say this event has a time >10s?then if A observes a time >10s, shouldn't B consider A is moving and thus oberve a time >>10s contradicting to the original 10s he observed??(i know i have made this so confusing for u guys, sorry and thank you in advance)

First things first: Events don't belong to a frame--they just happen. They are theoretically observable in any frame.

Second: Time intervals are measured between events.

Now imagine that two events occur at the same place according to frame A. An observer in A could just sit there and measure the time between those events by looking at his watch. If he measures the time interval to be 10s, then observers in frame B will measure a greater time. Note that according to B, these events do not happen at the same place.

Of course, there's nothing special about A. If two different events occurred at the same place according to B, and B measured the time between them to be 10s, then A would measure the time between those events to be greater than 10s.

It works both ways.

 

[Doc Al]

2) if the obeserver on the platform does say it is 75s, but will he see C at B at this time?

Sure. That's the second event.


so original train oberved 60s to second event
now working in reverse, isn't platfrom clock(s) moving relative to the train so the train will say the second event is >75s (this is the essence of what i dun get as it contradicts to what he original observes!)

No. There's no contradiction since there's no single platform clock collocated with the events that measures the interval to be 75s. Realize that multiple clocks are involved in the platform measurements: One at A and one at B. These clocks are synchronized according to platform observers, but not according to the train observers. That's the tricky part!

According to the train observers, the platform clocks are out of synch, they run slow, and the distance between them is contracted. All these factors work together.

 

[calculus_jy]

getting there, if you answer me this with clear explanaton, i think i shall get it , dun wanto annoyed u ppl much more
okay
train and platfrom same length
left end of train D and right C
left end of platform B and right A
train moves left to right

then if C measures the time interval he sees B then A is 60s----case 1 (at this time the ends of train and platfrom must be parallel)
B sees C at A when it is 75s

then B must measure the time interval he sees C and then D is 60s (symmertrical to Case 1 ) C sees B at D when it is 75s

this is right?
the poblem is that how can C observe C at A at 60s and the end of this train D is at B at 75s? or have this is due to time syrnc. and length contr again!?

 

[Doc Al]

The relativity of simultaneity is the key!

getting there, if you answer me this with clear explanaton, i think i shall get it , dun wanto annoyed u ppl much more
okay
train and platfrom same length
left end of train D and right C
left end of platform B and right A
train moves left to right

Here you swapped the ends of the platform from what you had defined in post #10 and I used in post #12. So I'm going to swap them back to avoid confusion:

(1) Train and platform are the same length when they are at rest. Of course, since they are moving, each observer measures the other to have contracted.
(2) Left end of train is D; right end is C. Train moves from left to right.
(3) Left end of platform is A; right end is B.

then if C measures the time interval he sees B then A is 60s----case 1 (at this time the ends of train and platfrom must be parallel)
B sees C at A when it is 75s

Let's assume that C's clock and A's clock both read time = 0 at the exact moment that they pass each other. At that moment, the right end of the train is lined up with the left end of the platform. Later, when C passes B (the right end of the train is lined up with the right end of the platform): C's clock reads 60s and B's clock reads 75s.

then B must measure the time interval he sees C and then D is 60s (symmertrical to Case 1 ) C sees B at D when it is 75s

this is right?

Yes! I'll restate it with the corrected letters. According to A, 60s go by between the time that he passes C and the time that he passes D. According to the train observers, this takes 75s.

the poblem is that how can C observe C at A at 60s and the end of this train D is at B at 75s? or have this is due to time syrnc. and length contr again!?

Let's view what going on in detail during case 1 as seen by both observers. Let's assume, for concreteness, that C passes A when both clocks read 1200 hours. (High noon!)

According to train observers:

When C passes A:
- Clock C reads 1200:00
- Clock A reads 1200:00
- Clock B reads 1200:27 (Clock B is ahead of clock A by 27 seconds!)

When C passes B:
- Clock C reads 1201:00 (60s later.)
- Clock A reads 1200:48
- Clock B reads 1201:15 (Clock B is ahead of clock A by 27 seconds!)

Note that according to the train observer C, only 48 seconds elapsed on the platform clocks between the two events (not 75s like the platfrom observers think). Applying time dilation, 48s/.8 = 60s. So that makes perfect sense.


According to platform observers:

When C passes A:
- Clock C reads 1200:00
- Clock A reads 1200:00
- Clock B reads 1200:00 (Clock B is synchronized with clock A!)


When C passes B:
- Clock C reads 1201:00
- Clock A reads 1201:15
- Clock B reads 1201:15 (Clock B is synchronized with clock A!)

Note that according to the platform observers, 60s seconds elapsed on train clock C between the two events. Applying time dilation, 60s/.8 = 75s. So that makes perfect sense.

The relativity of simultaneity is the key!

 

[tiny-tim]

… clear and right, or clear and wrong … ?

… if you answer me this with clear explanaton, i think i shall get it …

Hi calculus_jy!

I'm going to give a clear explanation … but I'm not sure whether it's the right one!

Each says "the other has to travel my length, plus his length, both at the same speed; my length takes 60 seconds, his length is contracted, so at the same speed takes 48 seconds; total 108 seconds."

Am I missing something, or making an assumption I shouldn't?

 

[Doc Al]

Each says "the other has to travel my length, plus his length, both at the same speed; my length takes 60 seconds, his length is contracted, so at the same speed takes 48 seconds; total 108 seconds."

Am I missing something, or making an assumption I shouldn't?

You are using the (perfectly fine) definition of "train passing the platform" that you introduced in post #8. In your version, the two events are:

The front of the train (C) passes the left end of the platform (A)
The rear of the train (D) passes the right end of the platform (B)​

But that's a bit different than the situation discussed in the last couple of posts. The advantage of defining the two events as you did is that, as you point out, the situation is perfectly symmetric--both observers measure the same total time.

But then you don't have the fun of dealing with time dilation, which I thought was the topic of the thread! (If it comes up, you could remedy that by describing--like I attempted in my last post--exactly what all the clocks read for each event according to each observer.)

Note added: I think you made an error in your calculation of the total time. The 60s was the time it took the train to go from one end of the platform (A) to the other (B). That would give you a total time of 135s, not 108s.

 

[tiny-tim]

But then you don't have the fun of dealing with time dilation, which I thought was the topic of the thread!

hmm … yes … I'd forgotten that was the title of the thread!

Though if calculus_jy is happy with the concept of time dilation, and only worrying about the symmetry, then I think this problem is one of those examples that turn out to be a complication, rather than a clarification.

The clock readings are too indirectly relevant to make this a clarification … the length aspect obscures the time aspect … the more you try to understand it, the more complicated it seems.

This may be a good example for clarifying symmetry of length contraction, but "travelling twin" examples would give a much more direct clarification of time dilation symmetry.

 

[Doc Al]

But it's a golden opportunity to show that time dilation works the same for both observers. And to show how all three relativistic "effects"--time dilation, length contaction, & the relativity of simultaneity--work in concert.

But you're probably right--that might make things appear more complicated.