Lorentz time dilation problem.

[Benzoate]

Homework Statement

Supersonic jets achieve maximum speeds of about (3 *10^6)*c.

a)During a time of 1 y =3.16*10^7 seconds on your clock, how much time would elapse on the pilot's clock?

b)How many minutes are lost by the pilots clock in 1 year of your time.

Homework Equations

delta(t)=delta(t')/(sqrt(1-v^2/c^2)^.5), where delta(t') is the proper time interval

the proper time would be the time elapse(delta(t')) on my clock and the time dilated (delta (t)) would be the pilot's clock.

The Attempt at a Solution

to solved the first problem, I would have to apply the equations I mentioned and 2 and solved delta(t). delta(t)= (3.16e7)/(sqrt(1-(3e-6)^2)).

delta(t)=31600000.0001422000000095985 seconds . So I say the time dilated on the pilot's clock is very negligble.

The second part of the question just asked the time difference between my clock time and the pilot clock's time and that results to be. delta(t)=.0001422000000095985 seconds =2.37e-5 minutes .

 

[G01]

You have one mistake here, other than that your work seems great, assuming you have not made an error while crunching the numbers. You have the wrong time as the proper time. The proper time is time the pilot experiences. This is because the proper time is the time given by an inertial clock present and at both events. Your clock is always with you, but the pilots clock is actually there at the events you are measuring (the beginning and end of the plane's year long trip).

(I like this description of proper time, but I found it on Wikipedia I think, so I am a little suspicious that it may not be a complete description of proper time. The definition seems to be fine to me, but if someone finds that it is not complete, please add on to it.)

Remember that the pilot should experience less time relative to you since he is moving relative to you, yet your answer says the pilot experiences MORE time. This is what gave the mistake away.

Other than that, your solution seems correct. Nice Job!

 

[m2003]

This means that in 1 year of my time, the pilot's clock would lose approximately 0.0000237 minutes. This may seem like a very small amount, but it is a significant effect when considering the high speeds of supersonic jets. This is due to the phenomenon of time dilation, which is a consequence of Einstein's theory of relativity. The faster an object moves, the slower time passes for that object relative to a stationary observer. This is a fundamental concept in modern physics and has been experimentally confirmed countless times.