The level of time dilation experienced on Earth's surface compared to being in "deep space" can vary depending on the specific conditions and reference frames involved. Time dilation is a consequence of the theory of relativity, and it occurs due to differences in gravitational fields and relative velocities.
On Earth's surface, the dominant factor contributing to time dilation is the gravitational field. According to general relativity, clocks in a stronger gravitational field tick slower relative to clocks in a weaker field. As a result, someone living on the surface of the Earth experiences a slightly slower passage of time compared to someone in a region of weaker gravity, such as deep space.
The difference in time dilation between Earth's surface and deep space is relatively small, but measurable. To provide a rough estimate, a clock on the surface of the Earth would experience time dilation of about 1 part in 10^16 compared to a clock in deep space. This means that for every second experienced in deep space, a clock on the Earth's surface would tick approximately 1 × 10^-16 seconds slower.
It's important to note that this estimate assumes a stationary observer on Earth's surface. If an observer on Earth were in motion relative to deep space, additional time dilation due to relative velocity would come into play. However, for typical velocities on Earth's surface, this velocity-related time dilation is negligible compared to the gravitational time dilation.
Overall, the time dilation experienced on Earth's surface compared to being in deep space is extremely small and only becomes significant in extreme conditions, such as near a black hole or when considering highly precise measurements over long durations.