Do moving clocks always run slow?
It’s a very common sentence found in textbooks on special relativity: “Moving clocks run slow”. But—even in the context of special relativity—is it always true? The answer is no. It’s only true when the clocks’ ageing is measured in an inertial frame. This assumption of inertiality might not always be stated explicitly in textbooks, but it’s always there. A frame qualifies as inertial if, when you hold a mass in front of you and let it go, it hovers there indefinitely. In such a frame, you can indeed say that all moving clocks run slow. But if your frame is not inertial, the situation becomes much more complicated. One way to see how moving clocks might not run slow is to consider an inertial clock being orbited by another that is so close as to be almost touching. This close separation means we can reduce almost to zero any complications that would be caused by having to account for the finite speed of signals passed from one clock to the other. The inertial clock measures the orbitin
