assuming you got a vehicle of 1000kg (1 ton) into space and accelerated it to 0.9c (0.9 times the speed of light) it would take over 10^20 J of energy. That is a shitload of energy.
For a nifty comparison, to accelrate that car to 0.9c would take over 15% of the energy used by the ENTIRE HUMAN RACE IN THE YEAR 2008!!
and thats a car, accelerating a giant spaceship that weighed, lets say, 1 million tons to 0.9c would take 150,000 times the amount of energy the human race used last year.
so needless to say, interstellar travel at speeds approaching the speed of light is IMPOSSIBLE!
You put a sweeping statement where you should be more precise and nuanced. Interstellar travel of
heavy payloads at speeds approaching the speed of light
seems infeasible by today's standards.
If an inordinate amount of energy must be expended to move a ton, obviously, research will focus on reducing the payload. Pack the strict minimum of people like sardines in hibernation chambers, carry the strict minimum to keep them alive. Still too heavy? Carry skinny teenage female dwarves, or better yet, genetically engineer smaller humans. Still too heavy? Extract the travelers' brains and discard their bodies in favor of lightweight machine bodies. If we went to that extreme (I believe we could), we could possibly carry hundreds of people (well, brains) in a spaceship weighing a ton.
If the point of the trip is to colonize another planet, you don't even need to man a ship - pack in a small autonomous robot that can build stuff (including duplicates of itself) using materials readily available at the target site, along with genetic samples and construct a society from there. It is not a far stretch of the imagination that we could eventually make small, lightweight robots sufficiently advanced to build what's needed and seed us somewhere else. And it could all fit in under a kilogram, for all we know. If the human race was in danger, would you really bother making a colony ship rather than just send a couple thousand "seeder" lightweight ships?
Basically, my point is that if we can't possibly produce enough energy to ship a payload weighing a ton at 0.9c to a distant system, we'll just work on removing everything in the payload that isn't absolutely necessary until it weighs little enough. There won't necessarily be political or economical incentive to do it, but it could happen, if only as a byproduct of compact, advanced AI technology.
This said, if we somehow figured out how to produce antimatter cheaply (I'm not sure on what grounds we could discard this possibility), large payloads might be reasonable. And we can't discount the possibility of fuel-less propulsion either. I'm not sure if large solar sails could somehow be used to attain great speeds spiralling out of orbit (the ship would fly out too early, but maybe we could use auxiliary propulsion as a sort of centripetal force? It doesn't sound like a good idea). Another possibly crazy idea would be to ship the payload from a distant outpost emitting a powerful laser or maser towards it. If the line of sight can be conserved (which in itself sounds like a difficult technical challenge), the ship would receive a constant influx of energy that it could use to accelerate or decelerate without it counting against its payload as fuel.
I mean, I will readily admit that I don't really know my shit here but what appears like an impossibility might just be a lack of inventiveness.
NOTE: if anyone wants to argue, please actually know something about relativistic calculations and not just talk out of your ass
EDIT: ok to people like mr. indigo. if you are going to argue with me, have a fucking counter arguement. dont just say random shit without any information to back it up. thank you
Don't be so pre-emptively defensive.