Shooting just enough mass at very high velocity is not much different than shooting a lot more mass at lower velocity, in terms of force.
Exactly. You try accelerating 200kg up to anywhere close to the speed of light (say 80%). That is a lot of force.
Technically even photons can exert force on objects, but they have such a small mass that it's a difficult effect to observe.
Opening comment said that you'd need absurd amounts of mass to accelerate a person to near light speed.
I said that the velocity of ejecting that mass mattered. That if you could push out mass at speed of light, you'd need a lot less mass.
Not that you'd push out the same mass at speed of light. Or that you could arbitrarily push things out at speed of light. Sheesh.
Wait, hang on, we have access to an appreciable-chunk of the world's knowledge at our fingertips...
https://en.wikipedia.org/wiki/Photon - "Photons are massless[...]In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p[...]Current commonly accepted physical theories imply or assume the photon to be strictly massless"
In more recent times, it has been seen as easier to use just one concept of mass, and to redefine momentum entirely. So, photons have a mass of 0, and we don't need to specify "rest mass". But they do have momentum.
Of course that .06 m/s velocity change would be near instant, so bad things would happen. Probably a humanity-ending but not life-ending disaster. Global tsunamis and incredibly large tectonic changes, for sure. Imagine the entire water column of the marianas trench jumping up in the air and slamming into the ground below.
If the energy was transferred at a single point, it'll be the worst extinction event ever (4000x worse than chicxulub) but I'd bet single-celled and maybe even some multicellular life would survive. Anything bigger than a mouse is fucked, though.
But if you're trying to avoid self-propulsion and want to launch from Earth, say, even a 200kg craft, anywhere "close to the speed of light", then that will most probably require a significant enough amount of force to knock the planet out of orbit.
If you can apply small force over a long time, that will get you up to speed, too.
Someone did the math in the thread, and suggested that a constant 1g of acceleration would get you to the centre of the galaxy in 20 years (as measured by the clocks traveling on your spaceships). 1g of acceleration for 200kg is about 1962 Newton.
(This back of the envelope calculation assumes you have eg someone fire a laser at your ship to give you the energy you need. If you need to bring your own fuel, the rocket equation increases the total mass needed. But the same principle still applies: something like an ion drive has very little force, even if the top speed it can reach can be enormous.)
Just need to build a parabolic reflector on one side of it and point it towards the opposite direction where we want to go. When the reflector shoots to far from the same, tilt the reflectors, drop down closer to the Sun by gravity, tilt them back, do it again.
We could be going places in a few billion years!
Btw, the sun is also an extremely inefficient engine. With a bit of extra engineering we could probably scoop up hydrogen from the sun, and 'burn' it much more efficiently.