Long-distance teleportation is hard, you guys.

I was not expecting this to be this hard.

The question is: Given only teleportation and no other superpowers, can you reliably travel transcontinental distances without instantly dying?

The reason it’s hard is that the point you start from and the point you end at are not stationary relative to each other. The Earth is rotating on its axis. It’s also revolving around the sun and whirling around the galaxy and for all I know it’s disco dancing through the cosmic microwave background, but the rest of those aren’t relevant.

Here’s why the earth’s rotation is a problem, helpfully explained in comic form:

Little did Calvin know that if he ever invented teleportation his life would depend on this very thing.

The point toward the middle of the record is a point toward one of the poles, closer to the axis of rotation. The point on the edge is a point on the equator, away from the axis. They’re moving at different speeds. Say you’re in San Antonio, and you teleport to Mexico City. Well, Mexico City is moving seventy-eight miles per hour faster than San Antonio. The nearest wall rushes you at 80mph from the west, and I don’t like your chances. And that’s two cities that are pretty close together.

But that’s with cities that are basically on the same line north to south. If they’re not, then it’s both more complicated and way more dangerous. Places at different latitudes are moving at different speeds, but places at different longitudes are moving different directions.

Suppose this diagram represents the earth, with us looking down on it from above the North Pole. (This is in fact exactly what it represents.) The earth rotates counterclockwise around its axis, which is helpfully labeled A. There’s nothing at point C; don’t bother going there. It’s spinning counterclockwise: If you’re at point D then your current movement is directly left.

Your speed is based on your latitude: at the equator it’s about 1080 miles per hour, where I am in Los Angeles it’s about 895, at the North or South Pole it’s zero. So if you’re at point D, you’re moving to the left very fast. If you then teleport to point B, you’re still moving to the left very fast. You smash into the earth instantly and die.

The obvious solution is to teleport to the point precisely ninety degrees east of you. For instance, from B to D on that diagram (Just pretend they’re ninety degrees apart.) Then the direction you’re currently traveling in is straight up. You go up, eventually gravity turns you around, and you come back down into the middle of the Atlantic. Bring a parachute and a life raft. Or, if you’re Indiana Jones, just a life raft.

This doesn’t work. Partly because the very fast speeds in question are in fact faster than the speed of sound. You’re not surviving that. More importantly, even if you do use that trick, it just cancels out the momentum you already had. It doesn’t get you moving in the direction Point D already is. Stopping only helps if you’re aiming for one of the poles; you need to match the speed and direction of your destination.

OK, next obvious solution (spoiler: this one doesn’t work either). You can try to get to the point 180 degrees across from you like this: Teleport 90º east, as before. You fly up. When gravity remembers to pull you back, you start falling. Note that, if you started at the bottom of the circle, you are now on the far right, and “falling” means falling left. At some point before you hit the ground, teleport straight up and keep falling. You speed up, gaining 22 miles per hour each second. (I’m starting to regret not using metric for this post.) Eventually you’re moving at the right speed. Since you’re already going in the right direction, you can now safely teleport to your destination. (This can get you to one of two points: The farthest point on Earth from where you started, or the point that corresponds to that one but on the other side of the equator.)

Except that it doesn’t work. It doesn’t work because of one of the most annoying things in the history of physics, air resistance. Human terminal velocity is around 120 mph, and you can’t get much faster than that while falling through air on earth. Depending on where you want to go, you might need to be moving several times that.

So you do it from higher up, outside Earth’s atmosphere. On the bright side, there’s no air. It won’t interfere with your attempts to speed up. On the less bright side, there’s no air. If you know enough to not hold your breath, you’ll survive with no permanent damage for up to ten uncomfortable seconds. But by fifteen you’ll lose consciousness, presumably lose your ability to teleport, and then die. So let’s keep it under ten seconds of vacuum exposure.

Unfortunately, this can’t work. Earth’s gravity can give you 22 miles per hour extra speed for each second you spend in freefall, but you only have ten seconds. Say you’re falling at 120 miles per hour the regular way, then get another 220 from doing that insanely dangerous thing for ten seconds. That’s still not fast enough. If you’re aiming for somewhere equatorial, you need to be able to reach 1080 mph.

The problem here is that Earth’s gravity can’t accelerate you enough. (And no, you don’t get to bring rockets with you.) So, it’s time for another obvious solution: Teleport to Jupiter! This involves some major headaches, because it turns out that your departure and destination cities are not actually in the same orbit as Jupiter. So now we actually do have to think about position relative to the sun as well as position relative to Earth’s axis.

The plan is the same as before: Teleport to a specific point above Jupiter. Spend up to ten seconds letting its gravity pull you toward the planet. This will never take more than ten seconds thanks to Jupiter’s gravity; exactly how long it takes depends on how close to Earth’s equator your destination is. Pick the point above the planet in such a way that the line from where you are toward Jupiter is the vector that will, in a few seconds, make your velocity match the velocity of your destination. Once you’re going at the right speed in the right direction, teleport to where you want to go. You’re travelling at insane speeds, your destination is travelling at insane speeds, and if you did the math right then you’ll match up perfectly.

We can’t always do this. Earth and Jupiter are moving at up to 100,000 mph relative to each other depending on the time of year, and it would really suck if you forgot about that and burned up in its atmosphere. In order to avoid complicated math, let’s say you only do it when Earth and Jupiter are moving along parallel lines. This happens about twenty-two times every twelve years.

With the two planets moving in the same direction, or in directly opposite directions, you just have to pick the time of day when that direction is the vector you want. (Or, once again, the exact opposite direction.) Then you teleport directly in front of or directly behind Jupiter, get the velocity to match your target city, and there you go. Because “teleport interplanetary distances instantaneously and use a gas giant’s gravity to change your velocity at 10g for a few seconds in hard vacuum before teleporting back to the planet you started from” is totally a reasonable thing.

10 thoughts on “Long-distance teleportation is hard, you guys.”

1. Roxolan

In case you haven’t heard of it already, you might enjoy the internet fiction http://www.sagaofsoul.com/ where this little trick is weaponized. Open your second portal inside a distant ocean and you get to spray water at very high speed indeed. Open it into the crust and you’ll blow up a city.

1. Nate Gabriel Post author

I made sure to reread it before writing this. It’s a fun story. I think there should have been a lot more collateral damage when she used this particular trick, though; from the sonic boom if nothing else.

(And she can just add whatever kinetic energy she needs to, no messing around with Jupiter required.)

2. Stuart Armstrong

I had various suggestions involving multiple teleportations where you use air resistance to slowly change your trajectory as you work your way around the world… But if you can use multiple teleportations, why not teleport directly from X to Y – and then teleport back within a microsecond. The huge air pressure difference should be perfectly survivable for that short a time. Then you teleport back again. The idea is that your teleportations should be so quick that you only feel the average air pressure (and ground pressure!) between X and Y, weighted by the time you spend at each. So initially, you spend almost all your time at X, and just feel a gentle tug in the direction of Y’s air pressure. You gradually spend more time in Y, until your velocity becomes more compatible with Y, upping that proportion gradually until you can stay in Y entirely.

So after a few million teleportation, you’re done!

1. Nate Gabriel Post author

Wait, that’s awesome. Would it work?

Just from guessing at some of the numbers, the force exerted from ramming into the air should be around a thousand Newtons, but I’m not sure how to use that. That’s for if it’s directly opposite and both points are on the equator, and if you’re trying to minimize your cross section. I used .2 for the drag coefficient, and .01 m for the cross-section. That should give a lower answer than the real one, but most of the number comes from the wind speed anyway.

You still have to go from 480 m/s one way to 480 m/s the other way. If it takes you 1s, that’s almost 100g average acceleration. Estimating from the chart in this wired article (Link: http://www.wired.com/2011/04/crashing-into-wall/ , We’ll have to use the “eyeballs out” number.”), the g-forces will be survivable if the deceleration takes six seconds or more.

I thought of something to do with the force number. Convert it to pressure, and it’s 114,000 N/m^2, or 16.5 psi. The CDC says (Link: http://www.cdc.gov/niosh/docket/archive/pdfs/NIOSH-125/125-ExplosionsandRefugeChambers.pdf ) that if the pressure peaks that high it will *usually* kill you. But not always! Although the teleporter needs to withstand that for a longer time than someone sitting through an explosion, and I’m also still assuming that a human diving into the wind is more than twice as aerodynamic than a sphere.

1. Nate Gabriel Post author

Wait, never mind. That CDC thing was estimating the damage assuming there’s stuff flying around to kill you. You can totally just teleport to directly above where you want to go and use air resistance to slow you down from Mach 3 to terminal velocity, and I don’t think the wind pressure will kill you. The pressure itself is at the high end of what amateur scuba divers are allowed to do routinely. And you don’t have to worry about the bends since you can start the fall with a lungfull of regular-pressure air. Which is good, because I somehow managed to overestimate Jupiter’s surface gravity by a factor of four.

So the thing with jumping back and forth every microsecond shouldn’t kill you by pressure, either.

1. Nate Gabriel Post author

It probably wouldn’t kill you.

It’s only got about 1/50 the kinetic energy of a bullet (9mm pistol according to Wikipedia), but it’s concentrated in a much smaller area. You get a fly-sized puncture wound wherever it hits you, and it probably splashes against the bone or muscle. I don’t think it could seriously damage bone, but wouldn’t want to test it.

If you’re lucky, the puncture is all that happens. If you’re not, it hits some important blood vessel. And having an inside-out fly underneath your skin has to be a great way to get infected. But it compares very favorably to being shot and it’s unlikely to kill you directly.

3. Toph

Just do the teleports in a lot of small steps. As long as you don’t go too far in a single jump, the difference in velocities between your origin and your destination will be fairly small. I estimate that a jump of 150km directly east will have you moving up at 1km/h (0.3 m/s) relative to your destination. Regardless of your latitude, oddly enough, as long as you’re more than a few hundred km from the poles.

That’s a tiny hop, enough to trip you up but not enough to do serious harm. Two hundred of those hops will take you around the world. Teleporting too fast in quick succession will cause the vertical speed to add up, but you only need to wait 0.03 seconds for gravity to cancel it out.

Come to think of it, you don’t need to touch the ground here, since your centrifugal force will be enough to counter gravity on its own. So you don’t need to worry about teleporting into the middle of inhabited areas or oceans – you have enough margin of error to chain-teleport through the air above them. Going west is trickier, since the 1km/h boost will be pushing you down instead, and going north or south will force you to the side (depending on which hemisphere you’re in) which is probably even harder to deal with. But you can definitely cross intercontinental distances faster than any other method of travel.

1. Toph

Wait, I miscalculated somewhere.

Correction: You can jump about 8km east-west and get a 1km/h up-down jolt. Not instant but it’s definitely fast travel.

1. Estella

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