(d) Consider the two curves for some fixed . The identification (2) makes each of these curves into a circle. Find the invariant circumference of this circle by integrating the appropriate root of between two neighboring identified points. Give your answers in terms of and . Answer: .
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Identification (2):
, where .
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Choose a segment on which .
The lower limit should be smaller than the upper limit.
— Me@2022-01-05 02:40:45 PM
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2022.01.05 Wednesday (c) All rights reserved by ACHK
To form an object (an observer), the component particles cannot all always move at light speed in the same direction, for that would prevent the object as a whole from feeling time.
Anything moving at the speed of light cannot feel the passage of time. If a set of particles all moves at light speed in the same direction all the time, they cannot feel time either as individuals or as a whole; so they cannot form an “object”.
To form an object (an observer), the component particles need to interact. So some component particles need to move in other directions sometimes.
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An object requires an internal structure to exist and evolve. The component particles need to interact in order to evolve as a single identity. So different particles need to move in different directions sometimes. As a result, the component particles as a whole, aka “the object”, will move slower than light.
— Me@2021-12-08 08:09:17 AM
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2022.01.05 Wednesday (c) All rights reserved by ACHK