Hi, I have the following problem: The formula for the Period of a classic pendulum is T=sqrt(L/g) Where: T: Period of the Pendulum suspended on a string. g: Earth's acceleration (=G*Mass_of_Earth/(Radius_of_Earth)^2 L: Length of the Pendulum String Now, let us put the whole experiment (Earth and Pendulum) in a reference frame which is travelling at speed v in a direction perpendicular to the Pendulum string. The period T of the pendulum should then dilate: T_newframe = T*GAMMA Where: GAMMA = 1/sqrt(1-v^2/c^2) c = speed of light v = speed of new reference frame However, looking at the calculated Period of the Pendulum in the new reference Frame, using, the formula for the period, one gets: T_newframe = sqrt(L/g_newframe) = T/sqrt(GAMMA). The pendulum length is not changed in the new frame of reference, because it hangs perpendicular to v. So relativity tells me that the period will become longer because of time dilation, but at the same time it tells me that it will become shorter due to mass increase! I admit that the Earth will contract into an ellipse or something in the new frame, and calculating g will be a bit more involved, but this does not change the validity of the argument: Instead of putting the pendulum on a spherical Earth, I could have placed it on top of a long, massive bar, which would not change shape due to relativistic effects, and would then give rise to a g_newframe of g_newframe =g*sqrt(GAMMA), as given in the above formula. Can you tell me where my mistake is? Thankful for any suggestions, Sebastian.