Hafele–Keating Experiment. What are the forces acting on the moving clock? According to the Hafele–Keating  Experiment, time dilation is the reason for the differences between the earth bound clock and the moving clock.
"General relativity predicts an additional effect, in which an increase in gravitational potential due to altitude speeds the clocks up. That is, clocks at higher altitude tick faster than clocks on Earth's surface."

https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
How does this “time dilation” manifest itself as a force to physically change the tick rate of the moving clock?
 A: Time dilation isn't a force, and moving clocks always tick at 1 tick per second. However, the "moving" clock and "stationary" clock take different paths through spacetime. This is why they end up showing different values when they are compared -- the clock measures the total elapsed spacetime "distance" (the proper time along the path the clock takes). The analogy is that a clock is like an odometer -- two cars which take different paths through space end up with different readings, just as two clocks which take different paths through spacetime end up with different readings too.
A: This is quite simple if you think in terms of a spacetime diagram. As an over-simplified version of the experiment, suppose there is an experimenter on an aircraft whose path is designed to follow that of an inertial motion, whose worldline is a timelike geodesic, and then there is a person on earth whose worldline is some spiral due to the rotation of the earth. Secondly, the arclength between two events $p_1$ and $p_2$ of an observer's worldline is their proper time: $\tau _2-\tau_1 = \int_{p_1}^{p_2}\sqrt{-ds^2}$, which is recorded by a standard clock that the observer carries. The proper time is exactly the internal aging experienced by an observer, and for the same observer it is always ticked away at the same rate, so there is no "force" influencing the clock rate (on the other hand, time dilation has to do with how one compares two clock readings on two worldlines in accordance with some choice of simultaneity). In all "twins paradox" situations, what is being compared are the two proper time readings that elapsed between two events. Because the plane's worldline is a timelike geodesic, the arclength of the plane's worldline between when it took off and when it lands is maximized, while the arclength of the worldline of the person on the ground between the same two events must always be smaller -- The plane experiences greater aging. So, once the plane lands, the one who went on the plane would have aged ever so slightly more than the one who stayed on the ground.
