Final answer:
The bullet hitting the target is not affected by the ant's perception of time due to special relativity. While the ant experiences time dilation, the motion towards the target remains consistent across different reference frames. The laws of physics, including the speed of light, remain constant, thus the bullet strikes the target as observed by an external observer.
Step-by-step explanation:
The question you've asked involves concepts from the realm of special relativity, which is a branch of Physics dealing with objects moving at speeds close to the speed of light. Considering an ant on a bullet traveling at 99.9% the speed of light, we must apply the principles of time dilation and length contraction which are fundamental aspects of special relativity.
From the ant's perspective, time would indeed seem to move much slower relative to the target due to the effects of time dilation. However, this does not mean that the ant would witness the target dodging out of the way. To an external observer, the bullet would hit the target seemingly without delay because they are not subject to the same relativistic effects as the ant. The bullet's trajectory is not altered by the ant's perception of time; the bullet and ant are both traveling together at the same high velocity.
It's essential to understand that the ant doesn't have a different 'personal' time that allows it to see the target move out of the way. Special relativity tells us that both time and space are relative. This means that while the ant onboard the bullet might experience time at a slower rate when compared to an outside observer, the bullet's motion towards the target remains unchanged. The target would not have time to move significantly before the bullet hits. This is due to the fact that motion is relative, and the laws of physics, including the speed of light, remain consistent across different reference frames.
The analogy of the ruler and the ants moving apart at speeds proportional to their distances is akin to Hubble's law which describes the expansion of the universe but offers a good notion on relative velocities within the same frame. This stretching ruler shows that although the ants are not moving on their own, their relative speeds are a result of the ruler's expansion, somewhat similar to how time dilates and length contracts relative to the frame of reference of the moving observer. Nonetheless, in your scenario, the bullet's motion towards its target is not affected by these relative perceptions.