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Taemyr
Taemyr
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YouYour conclusion, that an explorer can travel a distance that in our reference frame is 4 ly, in a time span that he can messure as less than 4 years, is correct.

However;

"Not only does time pass more slowly for the ship-board explorer, but as she accelerates, distances in the direction parallel to the direction of movement appear to shrink."

This is not quite accurate.

Only length contraction will be visible to the traveller.

Both length contraction and time contraction is visible for an observer moving with zero speed relative to an inertial frame observing objects having a nonzero speed relative to that frame.

So for an observer on earth observing the explorer you would not see length contraction. - Because the sun and target star is not moving at relativistic speed relative to your reference frame.

While for the explorer, he will not see time dilation. - His speed is zero in his reference frame. However he will see length contraction, because the stars have relativistic speeds in comparison with his reference frame.

So the two effects will be visible to different observers. The observer on earth will see the clock of the explorer running slower while the length between the two stars remain constant, while the explorer will observer the length between the two stars as shorter - while of course seeing his clock as running at regular speed.

You conclusion, that an explorer can travel a distance that in our reference frame is 4 ly, in a time span that he can messure as less than 4 years, is correct.

However;

"Not only does time pass more slowly for the ship-board explorer, but as she accelerates, distances in the direction parallel to the direction of movement appear to shrink."

This is not quite accurate.

Only length contraction will be visible to the traveller.

Both length contraction and time contraction is visible for an observer moving with zero speed relative to an inertial frame observing objects having a nonzero speed relative to that frame.

So for an observer on earth observing the explorer you would not see length contraction. - Because the sun and target star is not moving at relativistic speed relative to your reference frame.

While for the explorer, he will not see time dilation. - His speed is zero in his reference frame. However he will see length contraction, because the stars have relativistic speeds in comparison with his reference frame.

So the two effects will be visible to different observers. The observer on earth will see the clock of the explorer running slower while the length between the two stars remain constant, while the explorer will observer the length between the two stars as shorter - while of course seeing his clock as running at regular speed.

Your conclusion, that an explorer can travel a distance that in our reference frame is 4 ly, in a time span that he can messure as less than 4 years, is correct.

However;

"Not only does time pass more slowly for the ship-board explorer, but as she accelerates, distances in the direction parallel to the direction of movement appear to shrink."

This is not quite accurate.

Only length contraction will be visible to the traveller.

Both length contraction and time contraction is visible for an observer moving with zero speed relative to an inertial frame observing objects having a nonzero speed relative to that frame.

So for an observer on earth observing the explorer you would not see length contraction. - Because the sun and target star is not moving at relativistic speed relative to your reference frame.

While for the explorer, he will not see time dilation. - His speed is zero in his reference frame. However he will see length contraction, because the stars have relativistic speeds in comparison with his reference frame.

So the two effects will be visible to different observers. The observer on earth will see the clock of the explorer running slower while the length between the two stars remain constant, while the explorer will observer the length between the two stars as shorter - while of course seeing his clock as running at regular speed.

Source Link
Taemyr
Taemyr
  • 1.8k
  • 11
  • 12

You conclusion, that an explorer can travel a distance that in our reference frame is 4 ly, in a time span that he can messure as less than 4 years, is correct.

However;

"Not only does time pass more slowly for the ship-board explorer, but as she accelerates, distances in the direction parallel to the direction of movement appear to shrink."

This is not quite accurate.

Only length contraction will be visible to the traveller.

Both length contraction and time contraction is visible for an observer moving with zero speed relative to an inertial frame observing objects having a nonzero speed relative to that frame.

So for an observer on earth observing the explorer you would not see length contraction. - Because the sun and target star is not moving at relativistic speed relative to your reference frame.

While for the explorer, he will not see time dilation. - His speed is zero in his reference frame. However he will see length contraction, because the stars have relativistic speeds in comparison with his reference frame.

So the two effects will be visible to different observers. The observer on earth will see the clock of the explorer running slower while the length between the two stars remain constant, while the explorer will observer the length between the two stars as shorter - while of course seeing his clock as running at regular speed.