Travelling at high speeds does indeed affect time dilation according to the theory of special relativity. Time dilation refers to the phenomenon where time appears to pass differently for observers in relative motion to each other. Specifically, time will appear to run slower for an object or observer moving relative to another object or observer at a different velocity.
According to the theory of special relativity, the time dilation factor, γ, is given by the equation:
γ = 1 / sqrt(1 - (v^2 / c^2))
Here, v represents the velocity of the object or observer, and c represents the speed of light in a vacuum, which is a fundamental constant.
As an object or observer accelerates to high speeds, approaching the speed of light, the value of v^2 / c^2 in the equation approaches 1, resulting in a larger time dilation factor γ. This means that time appears to slow down for the moving object or observer relative to a stationary observer.
However, it's important to note that time dilation does not allow for time travel in the conventional sense. While time dilation can cause time to run differently for objects or observers in relative motion, it does not allow for backward time travel or changing events in the past.
The time dilation effect is a consequence of the geometry of spacetime, and it is consistent with the principle that the speed of light is an absolute maximum limit in the universe. While time dilation can affect the perception of time for observers in motion, it does not enable traveling back in time or altering the timeline.