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“Go at the speed of light and it only takes 4.5 years to get to the nearest star.”

Based on our current understanding of physics a physical object can’t reach light speed because the force used to accelerate gets converted to mass and less to velocity the closer you get to light speed.

There are other problems such as energy storage and G-force.

If you accelerate a spaceship at 1 G, it will take about 6 months to reach 1/2 the speed of light. You will need to decelerate for another six months before arriving at your destination. So, that’s 1 year in an Earth gravity environment, with an average speed during that year of 1/4 the speed of light.

This means it would take about 9 years to reach Proxima Centauri. During this time the ship would lose all contact with Earth using modern communications. If it successfully reached its destination, the message back to Earth would not be received until more than 13 years after departure. And if the ship returned right away, it would be 18 years from the original launch before the ship made it back to Earth.

During the year of accelerating and decelerating in a linear path, the inside of the ship would be indistinguishable from an Earth gravity environment.

I do not know how to calculate the effect of continued acceleration, but at least some of this would be converted to mass rather than velocity up to the midpoint of the trip there. But continued thrust throughout the journey would reduce the time of the trip more.

There might be some unpredictable consequences of traveling at such speeds in that the materials that the ship is comprised of might not hold together in the same way as mass begins to be added.

A manned ship would require artificial gravity if the ship is not accelerating or decelerating which could be simulated without energy consumption by spinning the ship. But this non-linear acceleration only approximates gravity due to the Correalis effect. It is assumedly much better for human health than extended time in zero gravity though.

Carrying an energy source capable of accelerating itself and the weight of the ship for sustained periods would be an entirely separate challenge.

If we assumed that the technology that allows for “gravitic propulsion” bends spacetime in such a way as to negate the effect of thrust being converted to mass at velocities approaching lightspeed, human travelers would still require a sustainable G-force that limits how quickly light speed could be reached. Negating time dilation, it would take about a year at 1 G. Anything beyond lightspeed is time travel, so we would assume the journey will take one year of accelerating and one year of decelerating. The average speed during these legs of the trip will be 1/2 the speed of light (approximately). So those two years get you 1 light year of travel. The remaining 3.25 light years would take 3.25 years, for a total of 5.25 years there and the equivalent back to Earth. This is the absolute best-case scenario unless time travel is achieved.

In my opinion, gravitic propulsion that relies on gravity waves or anti-gravity would bend space-time and would be a type of time travel. If that turns out to be possible, all bets are off. I don’t think there is any publicly known scientific expirimentation that supports this yet. But my gut instinct is to believe that it is possible.