If a person were to travel at the speed of light towards Earth, several important considerations arise:
The speed of light is an absolute speed limit: According to the theory of special relativity, the speed of light in a vacuum is the maximum speed that any object with mass can achieve. As an object with mass approaches the speed of light, its relativistic mass increases, requiring an infinite amount of energy to reach or exceed that speed. Thus, it is not possible for a person or any object with mass to travel at the speed of light.
Time dilation and length contraction: As an object approaches the speed of light, time dilation occurs, meaning that time appears to slow down for the moving object relative to a stationary observer. Additionally, length contraction occurs, making the object appear shorter along its direction of motion as observed by a stationary observer.
Given these factors, let's consider a scenario where an object could hypothetically travel arbitrarily close to the speed of light. From the perspective of an observer on Earth, as the object approaches the speed of light, time dilation would cause the object's time to slow down relative to Earth's time. This means that the object would perceive time passing more slowly than the observer on Earth.
If the object were somehow able to reach the speed of light, time would effectively stop for it, and from the object's perspective, the entire universe would appear to contract into a single point. However, it is important to note that this scenario is purely hypothetical, as it is not possible for an object with mass to reach or exceed the speed of light.
In summary, due to the limitations imposed by the theory of relativity, a person cannot travel at the speed of light towards Earth or anywhere else. The speed of light acts as an absolute cosmic speed limit, and our understanding of physics does not allow for the scenarios you described.