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dr.fluis
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I have recently attempted quantifying relativity of simultaneity and I was wondering if my attempt has been successful.
Watch the below link before reading, as the calculations are based on the same type of event.
As the video has no parameters, I have made my own.
The velocity of the train: (0.75)^0.5 C or
Length of train: 2 light seconds in the man’s frame of reference.
lighting strike 1: the lightning strike that hits the leading end of the train.
lighting strike 2: the lightning strike that hits the trailing end of the train.
lighting strike occurrence in man’s frame of reference: time on clock 0s
Outline of process:
(a) Determine when light from lighting strike 1 and lighting strike 2 collides with the woman in the man’s frame of reference.
(b) Determine the duration between these collisions and convert from man’s frame to woman's frame using the Lorentz time transformation.
This process should result in the duration between lightning 1 and lighting 2 occurring in the woman’s frame of reference as she is equidistant from the occurrences.
Part A
Collision 1 = 1 light-second / ( speed of light + velocity of train)
= 1 CS/ (1 C + (0.75)^0.5 C)
=0.536 seconds /3dp/
Collision 2 = 1 light-second / ( speed of light - velocity of train)
= 1 CS/ (1 C - (0.75)^0.5 C)
= 7.464 seconds /3dp/
Part B
Collision 2 - Collision 1 = (1 CS/ (1 C - (0.75)^0.5 C)) - 1 CS/ (1 C + (0.75)^0.5 C)
= 6.928 seconds /3dp/
Conversion to woman’s frame of reference = (Collision 2 - Collision 1) x time transformation
= 6.928s x (1 - 0.75)^0.5
= 3.464 seconds /3dp/
In the woman’s frame of reference lighting strike 1 hits the train 3.464 seconds before lighting strike 2
Is this correct?
Watch the below link before reading, as the calculations are based on the same type of event.
As the video has no parameters, I have made my own.
The velocity of the train: (0.75)^0.5 C or
Length of train: 2 light seconds in the man’s frame of reference.
lighting strike 1: the lightning strike that hits the leading end of the train.
lighting strike 2: the lightning strike that hits the trailing end of the train.
lighting strike occurrence in man’s frame of reference: time on clock 0s
Outline of process:
(a) Determine when light from lighting strike 1 and lighting strike 2 collides with the woman in the man’s frame of reference.
(b) Determine the duration between these collisions and convert from man’s frame to woman's frame using the Lorentz time transformation.
This process should result in the duration between lightning 1 and lighting 2 occurring in the woman’s frame of reference as she is equidistant from the occurrences.
Part A
Collision 1 = 1 light-second / ( speed of light + velocity of train)
= 1 CS/ (1 C + (0.75)^0.5 C)
=0.536 seconds /3dp/
Collision 2 = 1 light-second / ( speed of light - velocity of train)
= 1 CS/ (1 C - (0.75)^0.5 C)
= 7.464 seconds /3dp/
Part B
Collision 2 - Collision 1 = (1 CS/ (1 C - (0.75)^0.5 C)) - 1 CS/ (1 C + (0.75)^0.5 C)
= 6.928 seconds /3dp/
Conversion to woman’s frame of reference = (Collision 2 - Collision 1) x time transformation
= 6.928s x (1 - 0.75)^0.5
= 3.464 seconds /3dp/
In the woman’s frame of reference lighting strike 1 hits the train 3.464 seconds before lighting strike 2
Is this correct?
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