Yes, time dilation occurs in the vicinity of massive objects, such as the supermassive black hole at the center of our galaxy, known as Sagittarius A* (Sgr A*). This phenomenon is known as gravitational time dilation and is a consequence of general relativity, the theory of gravity proposed by Albert Einstein.
According to general relativity, the presence of mass and energy curves the fabric of spacetime, causing it to be distorted. In regions with stronger gravitational fields, time runs slower compared to regions with weaker gravitational fields. Therefore, near a massive object like Sgr A*, time would be dilated or slowed down relative to a location farther away from it.
In our case, being in the vicinity of Sgr A*, which has a mass of about four million times that of our Sun, would result in a gravitational time dilation effect. However, it's important to note that the time dilation in our everyday lives due to the gravitational field of Sgr A* is extremely small and not practically noticeable.
Significant time dilation effects typically occur in extreme environments, such as near black holes or in the vicinity of highly massive objects, where the gravitational fields are exceptionally strong. For example, near the event horizon of a black hole, time dilation becomes significant, leading to extreme time distortions.
On a cosmic scale, when comparing our Milky Way galaxy to other galaxies, there might be differences in the overall gravitational potential and distribution of matter. These differences could potentially result in variations in the time dilation effects between galaxies, but again, the magnitude of these effects would generally be very small and likely negligible for most practical purposes.
In conclusion, while gravitational time dilation does occur near massive objects like the galactic center, its effects on everyday life in the Milky Way or when comparing to other galaxies are typically negligible.