Hey guys, I've been learning about relativity recently and have a few thought experiments I'm pondering over. I'd appreciate input on the errors and validities of the consequences I've arrived at in my thoughts. The first thought experiment involves measurement of time. If we have an analog clock, we can look at its state twice and get the initial angle and the final angle. If the angle is , then the change in angle can be said to be Δθ. Now, since I've learned about relativity, it seems to me to be a presumption to say that a change in angle of clock hands correlates to a change in time ΔT. We would say Δθ=ΔT or that the slope of the variables theta and T is one in arbitrary but consistent units of T. That make sense to me. However, the problem comes in when you're comparing time between two clocks. If we had to clocks that we observed for a million years, and Δθ was the same for both clocks, we would say Δθ=Δθ for both clocks. Again, no problem. The problem comes from the presumption that the rate of change Δθ/ΔT for both clocks is equal, because all we have observed is simply comparable change in motion-for instance, if the unit of time were different for the clocks, but from your observation point one clock was traveling faster through time, you would observe Δθ=Δθ for the clocks, but you're canceling the change in time ΔT to presume this. Now, you could normally throw a clock between the two points and (switching from infinitesimals to differentials) you observe d^2θ on the freely falling clock relative to dθ of a stationary clock and know the time dilation between the two points. However, there seems to be a problem here: how do you start with two clocks that you are absolutely sure measure the same unit of time? Wouldn't that require an observation of two clocks in the exact same space? Another experiment I pondered is asymmetrical gravity on a sphere. Say, for instance, that you had a perfect sphere with variable gravity at constant height h. Let's say you can't jump or throw anything, so you can't observe free fall. All you have is a clock in your hand. Since you can't observe acceleration due to gravity, the only method you have to measure it's acceleration is with a scale. So now we take Newton's law of gravitational force. Height h is constant, so r^2 is the same for all measurements. Your mass isn't changing, so m is constant, and obviously the gravitational constant is constant. This means that force is changing only with respect to the variable gravitational field. We also know that force=mass dot acceleration, or mass dot length over seconds squared. So let's look at this equation: we know force is changing. We know that mass is constant. This means that acceleration is changing with respect to force. Force is length over seconds squared. Since time dilates with respect to gravitational force, does this imply that an increase in gravitational force changes gravity because length is changing, or because time is changing? It seems to me that length would be constant in all still frames of reference on the sphere. If gravitational force increases but time slows down-meaning the rate of change of what you observe speeds up-then wouldn't the units of T decrease in your reference frame? In other words, the point I am getting at is if all of your observations are at height h-do you actually notice the changing force with respect to gravity? Sorry if my math is confusing, but hopefully you can help me figure out these problems more accurately. Thank you.