Um.... no. Here's the thing: the universe isn't static. The universe is expanding. What that means is we live in the center of a radius of spacetime that has (for us) a finite boundary. Even if relativistic speeds were attainable (which because of the mass-energy equation, they are not for human-sized mass), the furthest we could ever travel is 18 billion light years, a fraction of the 46 billion light year radius we see around us. Beyond that, the rate of expansion (whichever of the two Hubble constants you choose to favor) exceeds the velocity of light from the perspective of a starting-point here on Earth. Thus beyond 18 billion light years, everything is forever beyond our reach. Furthermore, your math is wildly off. Assuming your putative human magically reaches 99% of the speed of light, what is for her a 56-year journey corresponds to approximately 400 years on Earth. So the idea that "the Earth wouldn't even be there any more" is the result of faulty math, not the result of the equations of General Relativity. Time only "ceases" for a particle traveling at lightspeed, not for anything traveling just below lightspeed, where the time dilation effects are dramatically attenuated relative to the experience of a photon.

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