With our current technology, it isn't possible for us to accelerate any amount of tungsten to relativistic speeds except for a few atoms in particle accelerator

With our current technology, it isn't possible for us to accelerate any amount of tungsten to relativistic speeds except for a few atoms in particle accelerator. The rocket equation means needs ludicrous amounts of fuel to reach relativistic speeds. This includes near-term technology like fusion reactors. You could take Jupiter along for fuel but still not reaching 99% of light speed. For stationary launchers, they would be super long or require enormous amounts of energy. Giant arrays of lasers aren't "possible with current technology". Relativistic projectiles probably requires antimatter. Which are pretty far beyond our technology. There is big question is antimatter rockets are possible, they require producing and containing a lot of antimatter. Although, it instead of accelerating super fast, it is probably easier to send the antimatter.