The core of the Sun and the surface of the Earth experience different levels of time dilation due to the gravitational fields they are subjected to. This means that time passes differently in these two locations. Specifically:
Time dilation at the core of the Sun: The Sun is a massive object, and its core experiences a very strong gravitational field due to its immense mass. According to general relativity, clocks closer to a massive object run slower compared to clocks farther away from it. Therefore, time passes more slowly at the core of the Sun compared to locations with weaker gravitational fields, such as the surface of the Earth.
Time dilation on the surface of the Earth: While the Earth has its own gravitational field, it is considerably weaker compared to that of the Sun. The time dilation experienced on the surface of the Earth is relatively small and not as significant as the time dilation in the Sun's core. However, it is still measurable, and sensitive instruments such as atomic clocks can detect this difference.
To quantify the exact difference in the passage of time between the core of the Sun and the surface of the Earth, detailed calculations are required. These calculations involve considering the mass and radius of the Sun and the Earth, as well as the principles of general relativity. The time dilation experienced at the core of the Sun will be greater than that experienced on the surface of the Earth, but the exact ratio will depend on the specific values and the distance from the respective gravitational sources.
It's worth noting that the time dilation between the core of the Sun and the surface of the Earth is relatively small in practical terms. However, it becomes more significant in extreme scenarios involving massive objects or near black holes, where the gravitational fields are much stronger.