No. The problem is that as you approach the speed of light, your effective mass increases. This is a measured effect that has to be allowed for in particle accelerators where electrons and protons are regularly accelerated to better than 99 percent the speed of light. As the mass of the spaceship increases, so does the inertia of the spaceship and it takes a stronger thrust to keep increasing its velocity by one more kilometer per second. By the time you get really, really close to the speed of light for a rocket ship weighing many kilograms, you have to expend energy at a rate comparable to the output of all the nuclear power plants now in operation. In most designs, you have to bring the weight of the nuclear fuel and the power plants with you too! This adds more weight and so requires even more thrust. The only way out of this is to not bring the fuel with you. The ways that you could do this might include: 1) Solar sails - which are being developed and may be tested by 2005; 2) use a 'laser cannon' focused on the spacecraft to push it from Earth or 3) use the energy latent in the quantum fluctuations of local spacetime. Although the laser canon idea has been looked into and does not seem to require new technology, the vacuum energy concept seems to be pure science fiction. No one has demonstrated a way to extrace net energy from the vacuum as yet.
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