Relative Error We continue with our example of time dilation in GPS satellite operation. We started with the following formula from special relativity: T Tm = � 1− v2 c2 and used a linear approximation to ﬁnd that: � � �� 1 v2 Tm ≈ T 1 + . 2 c2 This formula describes the diﬀerence due to time dilation between clocks on the ground and on the satellite. Algebraically, the diﬀerence is ΔT = Tm − T ; it turns out that there’s a very simple relation between T , ΔT , v and c: � � �� 1 v2 Tm ≈ T 1 + 2 c2 � � 1 v2 Tm ≈ T + T 2 c2 � 2� 1 v Tm − T ≈ T 2 c2 � � 1 v2 ΔT ≈ T 2 c2 � � ΔT 1 v2 ≈ T 2 c2 In other words, the relative or percent error ΔTT caused by time dilation is v2 proportional to the ratio 2 , which relates the speed of the satellite to the c speed of light. As in the example of falling stock prices, this value ΔTT gives us an idea of the relative size of the error introduced by time dilation.

Relative Error

Related Documents

Recommended Documents

Description

Related Documents

Want to Download This Document?

Free up your schedule!

Take 5 seconds to unlock