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calebhoilday
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This is a thought experiment that best depicts my issue in understanding special relativity, particularly the congruency of the velocity addition and velocity subtraction formula with other aspects of the theory.
This experiment consists of two clocks; clock A and clock B.
Clock A consists of a cannon that fires a projectile every second at a wall. The distance between the wall and the clock is (0.75)^0.5 light-seconds. The velocity of a projectile is (0.75)^0.5 C. These parameters result in a collision between a projectile and the wall every second in the observing frame of reference.
Clock B consists of two cannons that fire a projectile every second at each other. The distance between the cannons is 2x(0.75)^0.5 light-seconds. The velocity of each projectile is (0.75)^0.5 C. These parameters result in a collision between projectiles every second.
The purpose of this experiment is to convert from the frame of an observer to that of a projectile and determine the duration between event 1 firing and event 2 collision.
I am lead to believe that duration in a moving frame, divided by the duration in a stationary frame is equal to (1- (V^2/C^2))^0.5 . If this is the case, a projectile from either clock can be expected to consider that 0.5 seconds pass between event 1 and event 2 as time is dilated for the projectile so that for every one second on an observer’s clock, 0.5 seconds pass on a projectile’s clock based on the velocity the projectiles have.
The process of determining the duration between event 1 and event 2 in the projectiles frame of reference consists of determining:
(1) The distance between projectile and object one that the projectile will collide with in the frame of the projectile.
(2) The velocity of the object that the projectile will collide with in the frame of the projectile.
(3) The duration between event 1 and event 2 in the projectiles frame of reference, by dividing the distance as determined in (1) by the velocity as determined in (2)
Clock A
(1)
D =Length in observers frame/ (length of projectile with velocity/ length of projectile when stationary) = 2(0.75)^0.5 light-seconds
(2)
U = (S-V)/(1-(SV/C^2)
= (0.75)^0.5
(3)
T=D/U
= 2(0.75)^0.5/(0.75)^0.5
= 2 seconds
Clock B
(1)
D =Length in observers frame/ (length of projectile with velocity/ length of projectile when stationary) = 4(0.75)^0.5 light-seconds
(2)
U = (S-V)/(1-(SV/C^2)
= 2(0.75)^0.5/(1+0.75)
=(8/7)*(0.75)^0.5
(3)
T=D/U
= 4(0.75)^0.5/(8/7)*(0.75)^0.5
= 3.5 seconds
As can be seen Clock A and Clock B produce different results for the duration between event 1 and event 2 in the projectiles frame of reference, when in both the duration for the observer is 1 second. Neither of them produced a result that was consistent with the formula derived duration of 0.5 seconds.
?
Please share your thoughts.
This experiment consists of two clocks; clock A and clock B.
Clock A consists of a cannon that fires a projectile every second at a wall. The distance between the wall and the clock is (0.75)^0.5 light-seconds. The velocity of a projectile is (0.75)^0.5 C. These parameters result in a collision between a projectile and the wall every second in the observing frame of reference.
Clock B consists of two cannons that fire a projectile every second at each other. The distance between the cannons is 2x(0.75)^0.5 light-seconds. The velocity of each projectile is (0.75)^0.5 C. These parameters result in a collision between projectiles every second.
The purpose of this experiment is to convert from the frame of an observer to that of a projectile and determine the duration between event 1 firing and event 2 collision.
I am lead to believe that duration in a moving frame, divided by the duration in a stationary frame is equal to (1- (V^2/C^2))^0.5 . If this is the case, a projectile from either clock can be expected to consider that 0.5 seconds pass between event 1 and event 2 as time is dilated for the projectile so that for every one second on an observer’s clock, 0.5 seconds pass on a projectile’s clock based on the velocity the projectiles have.
The process of determining the duration between event 1 and event 2 in the projectiles frame of reference consists of determining:
(1) The distance between projectile and object one that the projectile will collide with in the frame of the projectile.
(2) The velocity of the object that the projectile will collide with in the frame of the projectile.
(3) The duration between event 1 and event 2 in the projectiles frame of reference, by dividing the distance as determined in (1) by the velocity as determined in (2)
Clock A
(1)
D =Length in observers frame/ (length of projectile with velocity/ length of projectile when stationary) = 2(0.75)^0.5 light-seconds
(2)
U = (S-V)/(1-(SV/C^2)
= (0.75)^0.5
(3)
T=D/U
= 2(0.75)^0.5/(0.75)^0.5
= 2 seconds
Clock B
(1)
D =Length in observers frame/ (length of projectile with velocity/ length of projectile when stationary) = 4(0.75)^0.5 light-seconds
(2)
U = (S-V)/(1-(SV/C^2)
= 2(0.75)^0.5/(1+0.75)
=(8/7)*(0.75)^0.5
(3)
T=D/U
= 4(0.75)^0.5/(8/7)*(0.75)^0.5
= 3.5 seconds
As can be seen Clock A and Clock B produce different results for the duration between event 1 and event 2 in the projectiles frame of reference, when in both the duration for the observer is 1 second. Neither of them produced a result that was consistent with the formula derived duration of 0.5 seconds.
?
Please share your thoughts.