The equation you mentioned, t' = -? (vx/c^2), is part of the Lorentz transformation, which describes how coordinates and time intervals appear to observers in different inertial reference frames. It is derived from the principles of special relativity.
In the equation, t' represents the time interval as observed in a different reference frame, t is the time interval measured in the spaceship's frame of reference, v is the relative velocity between the two frames, c is the speed of light, and ? (gamma) is the Lorentz factor given by ? = 1/â(1 - v^2/c^2).
When v approaches the speed of light (c), the Lorentz factor ? approaches infinity. This means that according to the Lorentz transformation, the time interval t' observed by an observer on Earth would become infinitely large, suggesting that the spaceship's clock would be infinitely in the past from the Earth's perspective.
However, it's important to note that this apparent "infinitely in the past" effect is not physically meaningful. It arises from the breakdown of the classical notion of simultaneity in special relativity. When objects move at relativistic speeds, time dilation and length contraction occur, leading to these counterintuitive effects.
From the perspective of an observer on the spaceship, their own clock would be running normally, and they would not experience any time travel effects. Each frame of reference has its own consistent and valid observations, but they may appear contradictory when compared directly.
It's worth noting that as an object with mass approaches the speed of light, the amount of energy required to accelerate it further also approaches infinity, making it physically impossible to reach or exceed the speed of light.