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In this hypothetical, an experiment is going to be conducted concerning the repositioning of clocks.

two clocks are placed at the leading end of a vessel, that is 1 light second long, to an observer at rest relative to it.

This vessel is shot into space from an observation station at 0.9C. As these clocks occupy essentially the same position, it can be safely assumed that these clocks in both the vessel frame and the observing station frame, that they are synchronised to each other enough that the difference is negligible between the frames.

One of the clocks is going to be shot from the leading end to the trailing end at a velocity of

-1/2.8 C according to the vessel or decelerate to a velocity of 0.8 to the observing station, where upon hitting the trailing end will return to the velocity of the vessel.

Before this occurs predictions based on special relativity are conducted as to what the difference between the clocks will be in each frame.

(Trailing - leading) in observing frame = duration of event in frame x (dilation of trailing - dilation of leading)

(Trailing - leading) in vessel frame = duration of event in frame x (dilation of trailing - dilation of leading)

special relativity suggests that any frame of reference can be treated as though it is an absolute frame, considering itself to have a velocity of 0. For relativity to hold when one translates the goings on in a particular frame to another, it must be consistent with what the frame would predict.

for this situation it means, that the difference in clocks in the observing station frame converted into the vessel frame through the use of Lorentz transformations, should equal the difference in clocks in the vessel frame:

difference in observing frame -simultaneity adjustment = difference in vessel frame

or

(((1-VS)/|S-V|)*(((1-((S-V)/(1-VS))^2)^0.5)-1))=(((1-V^2)^0.5/(V-S))*(((1-S^2)^0.5)-((1-V^2)^0.5))-V

V: velocity of vessel / speed of light

S: velocity of trailing clock / speed of light

my calculations show in this instance

(((1-VS)/|S-V|)*(((1-((S-V)/(1-VS))^2)^0.5)-1)) = -0.18466 seconds

V-(((1-V^2)^0.5/(V-S))*(((1-S^2)^0.5)-((1-V^2)^0.5)) = -0.18466 seconds

So it did work out in my calculations.

two clocks are placed at the leading end of a vessel, that is 1 light second long, to an observer at rest relative to it.

This vessel is shot into space from an observation station at 0.9C. As these clocks occupy essentially the same position, it can be safely assumed that these clocks in both the vessel frame and the observing station frame, that they are synchronised to each other enough that the difference is negligible between the frames.

One of the clocks is going to be shot from the leading end to the trailing end at a velocity of

-1/2.8 C according to the vessel or decelerate to a velocity of 0.8 to the observing station, where upon hitting the trailing end will return to the velocity of the vessel.

Before this occurs predictions based on special relativity are conducted as to what the difference between the clocks will be in each frame.

(Trailing - leading) in observing frame = duration of event in frame x (dilation of trailing - dilation of leading)

(Trailing - leading) in vessel frame = duration of event in frame x (dilation of trailing - dilation of leading)

special relativity suggests that any frame of reference can be treated as though it is an absolute frame, considering itself to have a velocity of 0. For relativity to hold when one translates the goings on in a particular frame to another, it must be consistent with what the frame would predict.

for this situation it means, that the difference in clocks in the observing station frame converted into the vessel frame through the use of Lorentz transformations, should equal the difference in clocks in the vessel frame:

difference in observing frame -simultaneity adjustment = difference in vessel frame

or

(((1-VS)/|S-V|)*(((1-((S-V)/(1-VS))^2)^0.5)-1))=(((1-V^2)^0.5/(V-S))*(((1-S^2)^0.5)-((1-V^2)^0.5))-V

V: velocity of vessel / speed of light

S: velocity of trailing clock / speed of light

my calculations show in this instance

(((1-VS)/|S-V|)*(((1-((S-V)/(1-VS))^2)^0.5)-1)) = -0.18466 seconds

V-(((1-V^2)^0.5/(V-S))*(((1-S^2)^0.5)-((1-V^2)^0.5)) = -0.18466 seconds

So it did work out in my calculations.

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