If a pair of entangled particles is created and one of them is subjected to gravitational time dilation, it will have an effect on the clock of the other entangled particle. However, the precise nature of this effect depends on the specific details of the entanglement and the experimental setup.
Entanglement is a phenomenon in quantum mechanics where two or more particles become correlated in such a way that the state of one particle is dependent on the state of the other(s), regardless of the distance between them. When measuring certain properties of one entangled particle, such as its spin or polarization, the state of the other particle becomes instantly correlated or "entangled" with the measurement outcome of the first particle.
In the scenario you described, if one of the entangled particles is subjected to gravitational time dilation, it will experience a slower passage of time compared to the other particle that is not influenced by the gravitational field. This time dilation can affect the measurements of properties or observables related to the particle's internal clock or any other time-dependent characteristic.
As a result, the entangled particle experiencing gravitational time dilation will effectively have its time "stretched" or slowed down compared to its entangled partner. When measurements are made on the other particle, they will be influenced by the time dilation of the first particle. This means that the entangled partner's clock will appear to run slower from the perspective of an observer measuring its properties or observing its behavior.
It's important to note that this effect depends on the entanglement and the specific measurements being performed. The entangled particles may exhibit other quantum phenomena, such as quantum superposition, which can complicate the interpretation and effects of time dilation. Additionally, the exact details of the experimental setup, including the strength and duration of the gravitational time dilation, will influence the observed results.
Overall, the entangled particle's clock that is subjected to gravitational time dilation will have an impact on the behavior and measurements of the other entangled particle. This interplay between quantum entanglement and time dilation is a subject of ongoing research and exploration in the field of quantum mechanics.