The Alcubierre drive is a theoretical concept that suggests a method for achieving faster-than-light travel by distorting spacetime. While it's an intriguing idea, it is important to note that the Alcubierre drive is purely speculative at this point, and there are numerous challenges and theoretical issues associated with its implementation.
One of the key components of the Alcubierre drive concept is the requirement for negative mass or negative energy density. Negative mass is a hypothetical concept that has not been observed in nature, and its existence raises a number of questions and challenges, both from a theoretical and practical standpoint. It is not currently known how negative mass or energy density could be obtained or created.
In terms of time dilation, the Alcubierre drive concept involves the creation of a "warp bubble" that contracts spacetime in front of the spacecraft and expands it behind, allowing the spacecraft to effectively ride a wave of distorted spacetime. However, the presence of negative mass or energy density required for the Alcubierre drive would likely have significant effects on spacetime itself, including the possibility of causing time dilation.
In summary, while the Alcubierre drive is an interesting theoretical concept, it is still highly speculative and faces significant challenges in terms of the required negative mass or energy density. The exact effects of such negative mass on time dilation, assuming it is even possible to achieve, would need further investigation and understanding.