It is possible to figure out how time duration and space distance change when we are close to the speed of light - but I am not sure what happens to them if we travel in the speed of light.
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It is not possible for a massive object to move at the speed of light
see Accelerating particles to speeds infinitesimally close to the speed of light? for example
so the premise of your question is itself problematic. When we usually talk about time dilation or length contraction in a moving frame, we are referring to an observer measuring time or length in such a frame, and since it is not possible for an observer to move at the speed of light, it's unclear what the question means in the first place.
joshphysics
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