A Relativistic Rocket

A couple of decades ago (programming in Basic on my TRS-80 computer with no hard drive), I tackled a similar problem. I wrote a numerical program for it, which I still have, but it's on a 5 1/2" floppy, which I can't read. I'm not really sure that I did it correctly. In case you feel like tackling the problem, I'll describe it in detail:

I postulated a laser-drive, converting matter & antimatter to laser energy with 100% efficiency. (The engine postulated by Michael is roughly twice as effective as mine. That is because it repeals the law of concervation of momentum, which my engine obeys.) The laser power is the mass-rate of fuel consumption times c^2. The reaction force is the laser power divided by c. You can use Newtonian equations to calculate delta v, delta M, etc., for a sufficiently small time interval; then apply SR to add velocities; also recalculate the mass, time, etc., with SR before going to the next small time interval.

For max efficiency, you chuck excess engines into the matter/antimatter converter while decelerating to zero at the destination. You can't use all your engines when the fuel gets low, anyway, because your acceleration would be more than the passengers can stand.

At some point, you will stop engines and coast until it is time to decelerate. To determine when to coast and when to decelerate, you must run the program from both ends of the journey toward the middle. After one time interval foreward from the start (with all engines ahead full and a full load of fuel), you run one time interval in reverse time from the destination (with one engine left and all the fuel burned up). When the foreward and reverse figures for fuel mass and number of engines are equal, you will have reached the ends of the coasting leg of the journey.

That is one iteration. Next you repeat the above using half the time interval. When successive iterations are within tolerance, you print out the results.

If you wish to return to Earth, plan on building new engines and generating new antimatter at the turn-around point. But why return? You would do well to stay where you are. You have aged a few years; your twin on Earth is a fossil. If mankind isn't extinct on Earth, your descendants on Earth may not be friendly to ET's like you. Besides, the money you borrowed to finance the journey will have accumulated compound interest for a couple of hundred thousand years. If your repayment is in gold, its gravity might swallow the solar system in a black whole. And those loan sharks have evolved into really nasty characters!

I have only vague memories of the results for specific journies, but very roughly speaking: It is possible to cross the galaxy in a lifetime if you first convert half of the Moon to antimatter and take all of it with you for fuel. All that mass will come in handy as shielding in case you hit a spec of sand along the way; that would cut into your available fuel, so start coasting a bit early or you won't be able to stop. To avoid collisions, it's best to plot a course well clear of the galactic center. As you begin your journey, please be careful where you point your exhaust; it could easily slice the Earth in two.

Notice that I didn't mention GR. The above numerical method should give the same result as GR; in fact a similar method could be used to verify whether GR is correctly derived from Einstein's assumptions. Of course, as TVF will tell you, GR may still be wrong if it is based on wrong assumptions.

Hey Phil

Agreed, the engine I described is not even feasible in theory. Conservation of momentum could be obtained by launching two rockets in opposite directions. But then acceleration of fuel really would become an issue if you want to drop the "instantaneous burn" clause. My rocket doesn't seem to mind accelerating fuel strangely enough. Two burns of d = 0.5 would have the same effect as one burn with d = 0.25

So let's take the moon and use it for fuel, why not? It's blocking the view for astronomers. We'll take an aluminium lawnchair as cockpit and one not too heavy pilot. Then d = 73 / 7.3 *10^22 = 10^-21 and GAMMA = 10^21
If we want to stop at our destination we must burn twice. That gives GAMMA = 3 *10^10
That's what we call high GAMMA , but the experiment has become absurd.

What I wanted to show with this oversimplistic rocket was that it's very unlikely for mass to be accelerated to high values of GAMMA (without help from outside) . Smaller masses have a higher chance I would say. And startravel is.. well .. a tall order.

A tall order, indeed! Practically speaking, there are only two ways to visit really far away places. One is to leave your physical body behind and take possession of a body that is already there. That's assuming that the human spirit is not a physical thing and therefore not governed by the laws of physics. The other is to put the physical body in stasis---a really deep hibernation---so it can wake up light centuries away from Earth, millennia later, but still youthful.

The latter method could be a good way to populate (or infest) the galaxy with humans, but there isn't much point to it from the traveler's point of view as an individual. What good is it to leave one of the few Garden of Eden spots in the universe to explore a distant solar system of dubious quality if you can't return to tell your friends what you found?

As for a galactic federation or empire, the best we can reasonably postulate is several groups striking out in different directions and returning to Earth at a predetermined time. They could then share their findings with one another; but there probably wouldn't be anyone or any intelligent thing on Earth willing or able to listen.

It's interesting to look at this at the various scales.

A galaxy is hard to move, that's obvious. There are nuclear processes going on, but they are scattered. An active core might be able to spit out big lumps at considerable speed.
A star is a good candidate to eject high GAMMA mass. It's one heavy nuclear reactor.
An atom is a very good nuclear device, however , due to it's small mass you could only expect tiny particles to be fast.
Maybe the best mass-to-kinetic-energy converter is a supernova explosion, a rare event.

We look through our telescopes and see all those galaxies and it may look chaotic but it's not a bowling alley.
I think most large scale accelerations are due to gravity, a local effect, which makes things stick together.
If a galaxy is moving fast for some reason it will collide with other ones eventually. Kinetic energie will be divided between the emerging galaxies. After a long time there's peace and quiet again.

Hmmm, another thing: How would you go about building a kinetic-energy-to-mass device?

Not an object, but a large volume of plasma: Matter in a disk spirals into some alleged black holes and jets of antimatter emerge from the poles at relativistic speeds---like c/2. Maybe you could thumb a ride on one of those jets. Of course, getting from here to the jet might present a small problem.

Great, the jets. I almost forgot about those. High energy beams emerging from the poles of very heavy objects, possibly spinning very fast too. Still, the mass is beaten to pulp in order to reach high v/c. I'll do a google on the jets. Hope i can find some searchwords because 'the jets' are probably a sixties band.

About the Ek-m converter:
I obviously didn't mean a Baron Von Munchhausen rocket that can decelerate gaining mass again. Actually mankind has already built particle accelerators, where new mass is created by fast collisions. I wonder where in nature mass is created this way and what would be the right ingredients to form let's say a neutron (ultimatly a hydrogen atom).