Dr. Lind has been selected by NASA to act as a mission specialist for the testin

Question

Dr. Lind has been selected by NASA to act as a mission specialist for the testing of a brand new propulsion system for spaceships. The new drive is to be tested just beyond the orbit of Neptune (for safety concerns). After the grueling journey to the testing site, the brand new drive manages to successfully accelerate (without killing the astronauts inside) to 0.95 times the speed of light relative to a separate ship where Dr. Lind is monitoring information from the test vehicle. Specifically, he is able to compare how much time is passing on the test ship with his own clock. Does the test ship's clock run slower, faster, or the same as his? Can Dr. Lind measure the proper time, proper distance, or both?

Explanation / Answer

According to Lorentz transformation time in a moving frame will be seen to be running slow or diluted. Thus this time always be shortest as compare to rest frame. Hence we can say that ship’s clock run slower.

t = t0/(1-v2/c2)1/2

Where t0=time in moving frame

t= time measured in rest frame

c= velocity of light

v= velocity of moving frame

Plugging values,

t = t0/(1-(0.95)2/c2)1/2

t = 3.2t0

By relativity, time measured in rest frame is ‘proper time’. In this example Dr. Lind is in the rest frame and the astronaut in moving frame. Hence Dr. Lind can measure ‘ Proper time’.

Since proper time and proper distance can’t be measured in the same frame, Dr. Lind can’t measure ‘Proper distance’.

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