The concept you're referring to is known as time dilation, which is a phenomenon predicted by Einstein's theory of relativity. Time dilation occurs due to differences in gravitational fields and relative velocities.
The time dilation between two places that are very close together, such as 1 millimeter apart, would be extremely minuscule and practically imperceptible. The effect of gravity and relative velocity at such a small distance would be negligible.
To put it into perspective, time dilation becomes more noticeable when there are significant differences in gravity or relative velocities. For instance, time dilation has been observed and measured between clocks on satellites and clocks on the Earth's surface due to the different gravitational fields and orbital speeds involved. However, even in those scenarios, the time differences are on the order of microseconds or even nanoseconds.
Therefore, the time difference between two places just 1 millimeter apart would be incredibly tiny, far beyond any currently measurable or perceivable scale.