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Exercise:
A Klingon spaceship travels at beaO of the speed of light with respect to the Earth. The Klingon crew measures a time erval of dtO between two events on Earth. abcliste abc Calculate the time between the two events for an observer on the Earth. abc Calculate the time erval they would measure between the same two events if they travelled at bebO of the speed of light. abcliste

Solution:
abcliste abc The time erval for the observers on the spaceship is the dilated time: Delta t gamma Deltatau It follow for the proper time as measured by an observer on Earth Deltatau fracDelta tgamma taF dt times sqrt-bea^ resulttaP abc The time ervals between the two events can be expressed as Delta t_ gamma_Deltatau fracDeltatausqrt-beta_^ where the index refers to the first and the index to the second situation. It follows for the ratio between the two time ervals fracDelta t_Delta t_ sqrtfrac-beta_^-beta_^ The time erval measured in the second sitution is Delta t_ dtbF dt times sqrtfrac-bea^-beb^ resultdtbP abcliste
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Exercise:
A Klingon spaceship travels at beaO of the speed of light with respect to the Earth. The Klingon crew measures a time erval of dtO between two events on Earth. abcliste abc Calculate the time between the two events for an observer on the Earth. abc Calculate the time erval they would measure between the same two events if they travelled at bebO of the speed of light. abcliste

Solution:
abcliste abc The time erval for the observers on the spaceship is the dilated time: Delta t gamma Deltatau It follow for the proper time as measured by an observer on Earth Deltatau fracDelta tgamma taF dt times sqrt-bea^ resulttaP abc The time ervals between the two events can be expressed as Delta t_ gamma_Deltatau fracDeltatausqrt-beta_^ where the index refers to the first and the index to the second situation. It follows for the ratio between the two time ervals fracDelta t_Delta t_ sqrtfrac-beta_^-beta_^ The time erval measured in the second sitution is Delta t_ dtbF dt times sqrtfrac-bea^-beb^ resultdtbP abcliste
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special relativity
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time dilation
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Difficulty
(2, default)
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0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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