I'm having some very basic conceptual problems about tension. If you have a pulley where two masses are hanging on opposite ends of an ideal string, why is the upwards force that the one mass experiences the same as the upwards force that the other experiences? People have tried to explain this to me by saying that it's logical because it's the same string and it's massless, but I just don't get it. What I DO get is: (a) that the acceleration of the masses will be the same and (b) that if the masses are equal, they will be in equilibrium, and the tension will be equal to the weight. Is there perhaps a more mathematical answer to my original question (e.g. reciprocity or something?) Also, exactly how is tension defined? Is it by definition a scalar quantity, or is it a vector? If it's a vector, how is the direction defined?