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It won't work. Rather, it won't work for long. Remember, we have assumed that conservation holds.
The motor's exhaust velocity is the ship's own limiting velocity if we use teleportation to fuel the ship. Jupiter's atmosphere wouldn't expand fast enough to be useful. Even with a fusion drive, we lose momentum every time a droplet of hydrogen reaches the fuel tank. We have to get it back by firing the droplet through the rocket motor. When the two velocities balance... we can't go any faster.
Total conversion of matter to light does give us unlimited velocity. Then we have only the problem of what to do with the incoming fuel. We always have that problem. A droplet of hydrogen moving at a tenth of lightspeed would vaporize any fuel tank we can build today. Maybe in the future... with new materials... plenty of padding... springs...
Let's try something else.
THE ASSUMPTIONS: The distance one can teleport is relatively restricted. The greater the curvature of space-that is, the greater the proximity to a large mass-the shorter is the limiting distance.
We will assume that on Earth the limiting distance is two feet; around Mars's orbit, some miles; between stars, a few light minutes. Attempt to send a mass beyond the limiting distance, and it will emerge from the receiver as a fluid or a fine dust. The curvature of space distorts the relationships between atoms too greatly.
Again, we assume the conservation laws hold.
THE RESULTS: Feeble as far as true teleportation is concerned. We can teleport fluids, so fuel tanks disappear except for storage tanks and spacecraft. The best we can do for spacecraft is fuel a booster, with a heavily armored fuel tank, designed to lift spacecraft out of a gravity well at low speed. But we can use the system to build a ship...
See Figure 4 (page 103). We'll call this peculiar object the "end-teleport drive," and we'll say that it teleports itself onto its own front end. I invented it many years ago, but I never had the nerve to write a story about it.
Notice that if you push the button, the ship teleports onto its own front end; but if you hold the button down, it will teleport repeatedly, in a steady stream of images. One jump brings the ship to position 2; but the moment it begins to occupy position 2 it wants to be at position 3; as that image starts to form the ship wants to be at position 4, et cetera. If teleportation is rapid enough we can use it for transportation.
You refuse to believe in my ship? Then think of it as an exercise in speculation. Ridiculous as it may seem, we do get results.
1) Rate-of-travel of the ship is limited only by mechanical difficulties, that is, by the rate of successive teleportation. The end-teleport drive does not affect the ship's kinetic energy. We change only the position. So there is none of this nonsense about relativity.
2) We must assume a mechanical limit on rate-of-travel. Otherwise the ship goes off the edge of the universe.
3) You can take your ffinger off the button. Kinetic energy is teleported along with everything else; and as a perfect image you have free will.
4) The longer the ship is, the faster it will go, with a given rate-of-teleportation. But: the longer the ship is, the greater is the danger of getting too near a large mass. To land on Earth the ship would have to be less than two feet long.
In fact, you can't land it anywhere with the end-teleport drive. As with the inertialess drives in Doe Smith's LENSMAN series, you keep an intrinsic velocity which reappears when the drive goes off. To land the ship anywhere you need either inboard auxiliary rockets, or rocket tugs.
5) What happens if something gets in the way of the ship?
Good question. Many things definitely will. Light, for example.
A light beam crosses interstellar space. Suddenly, for an instant, the end-teleport ship is occupying that space. The ship's walls can't stop it, for the light never encountered the walls. A human eye can stop it if the light reaches that eye in time.
Result: everything on the ship is transparent. If we assume that some light will be picked up by the teleportation field and carried along with the ship, then how transparent everything is will depend on two things: the rate of travel, and the distance of an object from the passenger's eye. His hand is nearly opaque. The further wall is nearly invisible, because so much light is being picked up in the space between wall and eye...and dropped between wall and eye. The cabin in Figure 4 is u
If the teleportation field will not transport light, the situation becomes more serious. At a useful rate of travel a light beam would have just time to traverse the diameter of a human eye before the eye disappears. So a human eye will still function. But the ship and all its contents, including the passenger, are totally invisible, and each passenger becomes a disembodied viewpoint falling between the stars.
Travel even faster, and a light beam may have time to touch the retina without first entering the lens of the eye. Now everything becomes a blur. On arrival the passenger becomes a psychiatric patient.
6) Interstellar dust would also be picked up en route. Most of it could be handled by a tough air conditioning system; but a certain proportion would appear already inside the transitory space occupied by the passenger. Definitely he would need medical attention on arrival.
7) Interstellar hydrogen would be swept up by the moving ship. Aboard an end-teleport drive there would be absolutely no smoking. Drinking, yes...
8) As for meteors and larger bodies... we'll use a trick.
Let's say we're going toward the galactic core, i.e. toward Sagitarius. Okay: Before we leave the system, we take our ship to within a few million miles of the Sun, on the Sagitarius side; and we hover.
We hover by end-teleporting outward as the Sun's gravity draws us inward. Half an hour of this should give us a respectable intrinsic velocity Sunward. Now we take off toward Sagitarius.
So we ram something en route. It can happen.
But... it takes energy to make two solid masses occupy the same space. Chances are we ca
So the ship backs up at hundreds of miles per second!
Even if we ram a planet, our intrinsic velocity is higher than escape velocity, and we're safe.
9) Conservation of energy rears its head once more. The ship becomes fiendishly cold as it leaves the solar system, and body temperature drops simultaneously.
The reverse occurs as we enter a system. It's a good thing we built a heavy air conditioning system to get rid of all that dust. We'll need it for temperature control.
VII
Why do I persist in assuming that the conservation laws hold?
This question caused a series of soapbox speeches, mostly in my defense (thanks, friends), along the back wall of my Boston audience. The assumptions are important, and I'm going to try to justify them.
1) The behavior of the universe does not change. In all known cases the laws of conservation of energy and momentum hold rigorously. Now we use them for prediction. The existence and most of the properties of the neutrino were predicted by use of these and other conservation laws. Later the neutrino itself was detected through judicious use of its own proposed properties.