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Thought exp. on time dilation

by Nakshatra
Tags: dilation, time
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Janus
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Dec30-11, 11:39 AM
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Quote Quote by Nakshatra View Post
ok i found something more in this.

one more problem...there are two elements in my arrangement.
the two clocks and and those two lasers attach to those clocks.
it is right that the clocks will be dilated by same amount that means the two lasers will shoot photon at same time but as i calculated the two photons will start their journey to censors together but will not reach together...

for the photon starting from clock1
will take
T(clock1) =r'/(c-v)
where r' is the contracted length and is equal to r'=r√1-(v2/c2)
putting the value or r' and solving we get
T(clock1)=(r/c)√(c+v)/(c-v)

and for the photon starting from clock 2
T(clock2)=r/√c2-v2 .

so the two photon will not reach the two censors simultaneously.
question is again the same..
It is not quite clear how you are arranging your clocks and sensors here, so I'll try to cover all the bases.

First, I'll assume that the clocks are located at the same spot and firing at sensors located some distance away in different directions and equal distances (as measured in the ship frame). In this case it will be true that according to the ground observer, the lasers will hit the sensors at different times. However, the sensors must then transfer this information to the device that kills the man.
If we place the device halfway between the sensors, we know that in the ship frame the signals from the sensors will arrive at the same time. In the ground frame, these signals, no matter how they are carried (wire etc.) will undergo the same effects as the laser pulses did, one signal taking longer to reach the device than the other. The result of this will be to completely cancel out the time difference in the laser arrivals. In other words, the signals will arrive at the device at the same time according to the ground frame also.

Second, we'll assume that the clocks are separated by some distance and the lasers are aimed at censors located at the same spot as the triggering device, which is halfway between the lasers. According to the ship frame, the lasers fire at the same time and the reach the sensors at the same time, but we don't have to worry about transmission time from sensors to device.

Now what happens according to the ground frame? The lasers take different times to reach the censors, however they still reach the censors at the same time. This is because even though the two clocks are undergoing the same time dilation, they are not synchronized according to the ground frame. They run at the same speed, but one clock will be ahead of the other, and by the same amount as difference in time that it takes for the lasers to travel to the sensors. This is due to the Relativity of Simultaneity. So the upshot is that in the ground frame, the lasers still reach the sensors at the same time, but they are not fired at the same time.

There is no way to arrange things so that a contradiction occurs between the frames.
Nakshatra
#20
Dec31-11, 03:42 AM
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here is the arrangement...
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Doc Al
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Dec31-11, 04:38 AM
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Quote Quote by Nakshatra View Post
here is the arrangement...
Since the two sensors are, for all practical purposes, at the same location, if the lasers strike the sensors at the same time in one frame they will be seen as striking the sensors at the same time in all frames. However, since the lasers of the two clocks are spatially separated, frames will disagree as to whether the laser pulses were fired at the same time or not.
DaleSpam
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Dec31-11, 07:13 AM
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Btw, sensors are devices which detect physical events or measurements and report them to experimenters. Censors are people which detect objectionable words or images and report them to the authorities.
Nakshatra
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Dec31-11, 01:57 PM
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it is actually not an answer to my question..
*cylinder will remain close only if the two lasers (or say a photon)reach those censors at same time.

*the clocks will be synchronised for the ground observerB if they are synchronised for the oberverA (as both will be dilated by same amt.)

Here the question is not only about the starting time of the two lasers,most important is that whether the two lasers(or a photon) reach their respective censors together or not.

~the two lasers will start at same time for observer A(in the cab)
~the two lasers will start at same time even for observer B (ground)as they will dilate by same amount.
~the two clocks are synch. in frame of observer A,
and they will remain synch. for observer B;as they will dilate by same amount.
Any kind of disturbance in their time will open the cylinder.
main motive of my paradox is to investigate the dependency of death and life on frames.

(*Don't get me wrong i am not arrogant;i am just trying to ruled out every possibility which is making me feel that i am right...searching for an answer which can fully satisfy me
go through the problem from starting again... if necessary.)
Doc Al
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Dec31-11, 02:21 PM
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Quote Quote by Nakshatra View Post
it is actually not an answer to my question..
*cylinder will remain close only if the two lasers (or say a photon)reach those censors at same time.

*the clocks will be synchronised for the ground observerB if they are synchronised for the oberverA (as both will be dilated by same amt.)

Here the question is not only about the starting time of the two lasers,most important is that whether the two lasers(or a photon) reach their respective censors together or not.

~the two lasers will start at same time for observer A(in the cab)
~the two lasers will start at same time even for observer B (ground)as they will dilate by same amount.
~the two clocks are synch. in frame of observer A,
and they will remain synch. for observer B;as they will dilate by same amount.
Any kind of disturbance in their time will open the cylinder.
main motive of my paradox is to investigate the dependency of death and life on frames.
Just because the light clocks both dilate by the same amount (for a round trip of the laser pulse) does not mean that they are synchronized in all frames. If the lasers start at the same time according to cab observers, they will not start at the same time according to ground observers. However, the one way travel time for the laser pulses (from starting point to the sensor) is not the same for both clocks according to the ground observer.

If the lasers start at the same time according to the cab frame, the pulses will reach the sensors simultaneously. The ground frame observers will agree that the pulses reached the sensors at the same time: According to the ground frame, laser 1 fired first, but the pulse from laser 1 took longer to reach the sensor, so both pulses reached their targets at the same time. No paradox.
Janus
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Dec31-11, 02:29 PM
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Quote Quote by Nakshatra View Post
it is actually not an answer to my question..
*cylinder will remain close only if the two lasers (or say a photon)reach those censors at same time.

*the clocks will be synchronised for the ground observerB if they are synchronised for the oberverA (as both will be dilated by same amt.)
No they will not. There is more than time dilation at play here. There is the Relativity of Simultaneity. The clocks if synchronized for A, will not be synchronized for B. The clocks will tick at the same rate, but will be offset from each other.

Here the question is not only about the starting time of the two lasers,most important is that whether the two lasers(or a photon) reach their respective censors together or not.
Both observers agree that the photons arrive together, they disagree as to whrther or not the lasers fired simultaneously or not.

~the two lasers will start at same time for observer A(in the cab)
~the two lasers will start at same time even for observer B (ground)as they will dilate by same amount.
No, see above
~the two clocks are synch. in frame of observer A,
and they will remain synch. for observer B;as they will dilate by same amount.
No, see above
Any kind of disturbance in their time will open the cylinder.
main motive of my paradox is to investigate the dependency of death and life on frames.

(*Don't get me wrong i am not arrogant;i am just trying to ruled out every possibility which is making me feel that i am right...searching for an answer which can fully satisfy me
go through the problem from starting again... if necessary.)
It seems that you have never grasped what the Simultaneity of Relativity means. It means that events that are simultaneous to A are not so for B in a very real sense if they are separated from each other in the direction of the Relative motion between A and B.
DaleSpam
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Dec31-11, 03:20 PM
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Quote Quote by Nakshatra View Post
reach those censors at same time ... their respective censors together
See post 22.
DaleSpam
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Dec31-11, 03:24 PM
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Quote Quote by Nakshatra View Post
*the clocks will be synchronised for the ground observerB if they are synchronised for the oberverA (as both will be dilated by same amt.)
This is not correct. See: http://en.wikipedia.org/wiki/Relativity_of_simultaneity

This is the single most difficult concept for new students of relativity to grasp. Whether or not two spatially separated events are simultaneous depends on the reference frame. You should pay close attention to what Doc Al and Janus tell you, they know their stuff.
Nakshatra
#28
Jan1-12, 05:08 AM
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Indeed...
i will try to do the mathematics related.
thanks for the suggestion.


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