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Photon travel 8 minutes (with speed $c$) from the sun to reach the earth. Any particle (or space-ship) with velocity $0.99 c$ covers the same distance (93 millions km) within less than 2 minutes (according to SR). Does this make sense?

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Possible duplicate: physics.stackexchange.com/q/32003/2451 –  Qmechanic Jan 9 '13 at 20:58
You can't talk about SR without specifying reference frames. Times and distances are different in different frames - that's the whole point of SR... –  Sklivvz Jan 9 '13 at 23:18
The question is simply comparing observations of two different observers. –  SS-3.1415926535897932384626433 Jan 9 '13 at 23:24

1 Answer 1

For rest observer (w.r.t. Sun), light takes 8 minutes to reach Earth. 8 minutes is simply $distance(AU)/c$. You can calculate (result would be in approx).

For the same observer, anything would take atleast 8 minutes to reach Earth. A particle with speed $0.99c$ would take more time than that of light. You can calculate with the same previous formula. So, 2 minutes is simply wrong.

If you switch to another inertial observer (non-rest), the space will be contracted too. If you're talking about reference frame of the particle with $0.99c$ speed, the particle would need to travel less distance to reach Earth. For light, it wouldn't be 8 minutes then (8 minutes is only for rest observer). If particle takes 2 minutes in that reference frame, light would take less than 2 minutes. Remember, light always takes least time for any observer. Don't compare observations of two different observers.

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Downvoters should aware that the question is confused with time dilation which isn't applicable here. You shouldn't be confused, too. –  SS-3.1415926535897932384626433 Jan 9 '13 at 23:00
In addition to travel time being 8 minutes (not 2), the Astronomical Unit (AU) is ~ 150 million kilometers, not 93 million km as stated in the Question. –  Eugene Seidel Jan 9 '13 at 23:05
The <2 minute answer is referring to the time measured in the rest frame of a traveler from the earth to the sun moving at 0.99c with respect to the sun's rest frame, and as the speed approaches c the measured time approaches zero. In this sense, time dilation does play a role in explaining part of the question. You may wish to clarify this in your answer. Your answer is correct in the sense that any travel time will be greater than 8 minutes as measured in the rest frame of the sun. –  kleingordon Jan 9 '13 at 23:22
Okay, I don't think my comment above applies any more to the updated answer. –  kleingordon Jan 9 '13 at 23:42
@kleingordon Thanks for the comment.. –  SS-3.1415926535897932384626433 Jan 9 '13 at 23:45

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