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WillO
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ItFirst: Despite appearances, this question has absolutely nothing to do with relativity, because it asks about the length of a traveler at various stages in the journey with all measurements made in a single frame (namely the earthbound frame). So the entire question comes down to: Does decelerating change your length?

The answer entirely depends on how the travelingtraveler twin decelerates. Suppose he's heading toward earth head-first, and he abruptly stops moving. If (in the earth-frame) his head stops before his feet do, he's going to contract. If his head and feet stop at the same moment, he's going to remain the same length he was while traveling. If his feet stops before his head does, he's going to stretch out.

Of course all the same things are true in the traveling frame. It's perfectly possible, for example, that his head and feet stop simultaneously in the earth frame but non-simultaneously in the traveling frame, so his length stays fixed in the earth frame and not in the traveling frame. Or vice versa. That's where relativity comes in, but it has nothing to do with the question that was asked.

It entirely depends on how the traveling twin decelerates. Suppose he's heading toward earth head-first, and he abruptly stops moving. If (in the earth-frame) his head stops before his feet do, he's going to contract. If his head and feet stop at the same moment, he's going to remain the same length he was while traveling. If his feet stops before his head does, he's going to stretch out.

Of course all the same things are true in the traveling frame. It's perfectly possible, for example, that his head and feet stop simultaneously in the earth frame but non-simultaneously in the traveling frame, so his length stays fixed in the earth frame and not in the traveling frame. Or vice versa.

First: Despite appearances, this question has absolutely nothing to do with relativity, because it asks about the length of a traveler at various stages in the journey with all measurements made in a single frame (namely the earthbound frame). So the entire question comes down to: Does decelerating change your length?

The answer entirely depends on how the traveler twin decelerates. Suppose he's heading toward earth head-first, and he abruptly stops moving. If (in the earth-frame) his head stops before his feet do, he's going to contract. If his head and feet stop at the same moment, he's going to remain the same length he was while traveling. If his feet stops before his head does, he's going to stretch out.

Of course all the same things are true in the traveling frame. It's perfectly possible, for example, that his head and feet stop simultaneously in the earth frame but non-simultaneously in the traveling frame, so his length stays fixed in the earth frame and not in the traveling frame. Or vice versa. That's where relativity comes in, but it has nothing to do with the question that was asked.

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WillO
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It entirely depends on how the traveling twin decelerates. Suppose he's heading toward earth head-first, and he abruptly stops moving. If (in the earth-frame) his head stops before his feet do, he's going to contract. If his head and feet stop at the same moment, he's going to remain the same length he was while traveling. If his feet stops before his head does, he's going to stretch out.

Of course all the same things are true in the traveling frame. It's perfectly possible, for example, that his head and feet stop simultaneously in the earth frame but non-simultaneously in the traveling frame, so his length stays fixed in the earth frame and not in the traveling frame. Or vice versa.