Physics Help Forum Example of length contraction and time dilation.

 Special and General Relativity Special and General Relativity Physics Help Forum

 Jul 6th 2017, 10:04 AM #1 Senior Member     Join Date: Feb 2017 Posts: 205 Example of length contraction and time dilation. Is my interpretation correct? When you travel at 0.999 speed of light then to you what 3 seconds has passed is actually 67.2 seconds to an observer on earth if you are in a spaceship that is traveling fast. Also 1 meter to you on the spaceship would be observed as 0.45 meters on earth. This way time dilation works and length contraction also. Also note time is time into gamma and length is length/gamma. Also gamma @ 0.999 speed of light is 22.4. Is this correct?
Jul 6th 2017, 12:42 PM   #2
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Join Date: Nov 2013
Location: New Zealand
Posts: 552
$\displaystyle \gamma = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

 When you travel at 0.999 speed of light then to you what 3 seconds has passed is actually 67.2 seconds to an observer on earth if you are in a spaceship that is traveling fast.
Close. I think its 67.1

 Also 1 meter to you on the spaceship would be observed as 0.45 meters on earth. This way time dilation works and length contraction also.
No, I think the contraction is observed by you on the spaceship, not by the person on the earth.

Gamma is "cooked up" so that all observers see the speed of light as the same. So one observer will measure light travelling across a distance x in time t as c = x/t and another observer travelling at velocity v will see light travelling across a distance x/gamma and taking time t/gamma so to keep the speed of light the same we would need to calculate the length contraction of 1 meter as 1/gamma(0.999).

Time dilation is a bit confusing because it refers to the time you would see viewing a clock on earth with a very good telescope from your spaceship. It's not the time you measure directly like length contraction. That's why we divide by gamma for both x and t to change distance and time on earth to results we would see from spaceship.

 Jul 6th 2017, 10:34 PM #3 Junior Member   Join Date: Jul 2017 Location: China Posts: 3 @avito009:I think you are right 1
 Jul 6th 2017, 10:36 PM #4 Junior Member   Join Date: Jul 2017 Location: China Posts: 3 @avito009:sorry, the time dilation that you caculated is right,but the length conctraction is 0.045m . Last edited by linxf; Jul 6th 2017 at 11:03 PM.
 Jul 6th 2017, 10:38 PM #5 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 552 I got a different result for the length contraction and explained in my last post why. Perhaps I wasn't clear on that.

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