Register to reply 
Thought exp. on time dilation 
Share this thread: 
#19
Dec3011, 11:39 AM

Emeritus
Sci Advisor
PF Gold
P: 2,361

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. 


#20
Dec3111, 03:42 AM

P: 12

here is the arrangement...



#21
Dec3111, 04:38 AM

Mentor
P: 41,304




#22
Dec3111, 07:13 AM

Mentor
P: 16,951

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.



#23
Dec3111, 01:57 PM

P: 12

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.) 


#24
Dec3111, 02:21 PM

Mentor
P: 41,304

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. 


#25
Dec3111, 02:29 PM

Emeritus
Sci Advisor
PF Gold
P: 2,361




#26
Dec3111, 03:20 PM

Mentor
P: 16,951




#27
Dec3111, 03:24 PM

Mentor
P: 16,951

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. 


#28
Jan112, 05:08 AM

P: 12

Indeed...
i will try to do the mathematics related. thanks for the suggestion. 


Register to reply 
Related Discussions  
Time dilation thought experiment clarification  Special & General Relativity  9  
Time dilation/ light speedthought experiments  Special & General Relativity  37  
Very simple thought experiment re: time dilation  Special & General Relativity  15  
A Thought Experiment with Time Dilation  Special & General Relativity  2 