Reciprocity of length contraction is a logical consequence of Special Relativity. The higher the speed and Lorentz factor, the easier to recognize the dubiousness of this SR prediction. Let us start with these premises:
As Lorentz factor of 0.99995 c is 100, the moving ruler is contracted (from 1 LY) to 0.01 LY in the rest-frame.
Common sense would suggest that with respect to the 100-fold contracted length-unit, rest-frame distances (in direction of motion) are or seem to be increased 100-fold, in our case from 100 LY to 10 000 LY. The reason is obvious: 10 000 rulers with nominal length of 1 LY, but actually contracted to 0.01 LY, must be put one next to another in order to fill the whole distance of 100 LY.
Special Relativity however states that with respect to the moving ruler, distance from us to the target is reduced from 100 LY to 1 LY (moving-frame). This is possible only if the length of the ruler increases 100-fold (i.e. from 1 LY to 100 LY in the rest-frame), as the 1-LY-ruler must cover the whole distance of 100 LY at the same time. This then means that with respect to the moving-frame, the ruler itself (with a nominal length of 1 LY) has the same length as the rest-frame distance of 100 LY. In this way a moving-frame length of only 1 LY can be attributed to the 100-LY-distance.
Here the question arises:
The answer is astonishingly simple:
With respect to rest-frame simultaneity, the distance between front and back end of the moving 1-LY-ruler is 0.01 LY. If from the center of the contracted ruler a light signal is sent to both ends then this signal needs tBack = 0.005 LY / (c + 0.99995 c) = 0.0025 Year to reach the back end. To reach the front end, the light signal needs tFront = 0.005 LY / (c - 0.99995 c) = 99.9975 Year. So in the rest-frame, the event of reaching the front end occurs dt = tFront - tBack = 99.995 years after having reached the back end.
These two signal-receiving events, occurring 99.995 years one after the other in the rest-frame, are declared simultaneous in the moving frame. So in order to use this ruler as a length unit with respect to moving-frame simultaneity, its front end must have moved at v = 0.99995c 99.995 years longer than its back end. Only during these 99.995 years of unchanged motion, the ruler can increase from 0.01 LY (rest-frame length, rest-frame simultaneity) to 100 LY (rest-frame length, moving-frame simultaneity) by adding 99.99 LY (equals v * dt).
Only insofar as the ruler is itself expanded to 100 LY, it covers with its own nominal length of 1 LY the whole 100-LY-distance, and thus theses 100 LY turn out be just 1 light year.
In our case, SR prediction of reciprocal length contraction would only make sense in case of unchanged (inertial) motion of the ruler front-end over at least 99.995 years!
Summary for Lorentz-Ether-Theory with SR interpretation:
For better understanding see also.
Cheers, Wolfgang
Veneration for the paradigm shifts of the past often affiliates with abhorrence for possible paradigm shifts in the present
- A distance of 100 light years, e.g. from our planetary system to a target 100 LY away (rest-frame)
- A ruler (i.e. length unit) with a nominal (or proper) length of 1 LY
- Measuring our rest-frame distance of 100 LY with the ruler moving at v = 0.99995 c (moving-frame)
As Lorentz factor of 0.99995 c is 100, the moving ruler is contracted (from 1 LY) to 0.01 LY in the rest-frame.
Common sense would suggest that with respect to the 100-fold contracted length-unit, rest-frame distances (in direction of motion) are or seem to be increased 100-fold, in our case from 100 LY to 10 000 LY. The reason is obvious: 10 000 rulers with nominal length of 1 LY, but actually contracted to 0.01 LY, must be put one next to another in order to fill the whole distance of 100 LY.
Special Relativity however states that with respect to the moving ruler, distance from us to the target is reduced from 100 LY to 1 LY (moving-frame). This is possible only if the length of the ruler increases 100-fold (i.e. from 1 LY to 100 LY in the rest-frame), as the 1-LY-ruler must cover the whole distance of 100 LY at the same time. This then means that with respect to the moving-frame, the ruler itself (with a nominal length of 1 LY) has the same length as the rest-frame distance of 100 LY. In this way a moving-frame length of only 1 LY can be attributed to the 100-LY-distance.
Here the question arises:
How can a ruler, contracted from a nominal length of 1 light year to 0.01 LY, be on the other hand expanded to 100 LY with respect to the same rest-frame length-units?
The answer is astonishingly simple:
Actual simultaneity has to follow Poincaré synchronization.
With respect to rest-frame simultaneity, the distance between front and back end of the moving 1-LY-ruler is 0.01 LY. If from the center of the contracted ruler a light signal is sent to both ends then this signal needs tBack = 0.005 LY / (c + 0.99995 c) = 0.0025 Year to reach the back end. To reach the front end, the light signal needs tFront = 0.005 LY / (c - 0.99995 c) = 99.9975 Year. So in the rest-frame, the event of reaching the front end occurs dt = tFront - tBack = 99.995 years after having reached the back end.
These two signal-receiving events, occurring 99.995 years one after the other in the rest-frame, are declared simultaneous in the moving frame. So in order to use this ruler as a length unit with respect to moving-frame simultaneity, its front end must have moved at v = 0.99995c 99.995 years longer than its back end. Only during these 99.995 years of unchanged motion, the ruler can increase from 0.01 LY (rest-frame length, rest-frame simultaneity) to 100 LY (rest-frame length, moving-frame simultaneity) by adding 99.99 LY (equals v * dt).
Only insofar as the ruler is itself expanded to 100 LY, it covers with its own nominal length of 1 LY the whole 100-LY-distance, and thus theses 100 LY turn out be just 1 light year.
In our case, SR prediction of reciprocal length contraction would only make sense in case of unchanged (inertial) motion of the ruler front-end over at least 99.995 years!
Summary for Lorentz-Ether-Theory with SR interpretation:
A ruler (i.e. length unit) of 1 light year moving at 0.99995 c is used to measure an ether distance of 100 LY. The moving ruler is obviously contracted to 0.01 LY. If all inertial movements enjoy equal rights then with respect to the moving ruler, ether distances must also be contracted 100-fold, i.e. the ruler with nominal length of 1 LY must cover our whole ether distance of 100 LY.
Such a 10000-fold length increase can be achieved by sending a signal from the center of the contracted ruler to both ends and by declaring signal-reception as simultaneous. Because of ether wind, the signal needs 99.995 years longer to the front-end than to the back-end. And during these 99.995 years of constant inertial motion, the distance between the ruler-ends increase from 0.01 LY to 100 LY, leading to an attribution of only 1 light year to the 100-LY-ether-distance.
For better understanding see also.
Cheers, Wolfgang
Veneration for the paradigm shifts of the past often affiliates with abhorrence for possible paradigm shifts in the present
via International Skeptics Forum http://ift.tt/1CDY7x0
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