Dude, who even knows.
Post reblogged from Tanadrin with 118 notes
Here is something I’ve wondered about for a while: if you could teleport superpower-style, what happens to the medium you teleport from/into? The boring answer is, the volume you jump to replaces the volume you jump from: this could have weird side effects though. If you jumped underwater, you’d dump a bunch of water at your starting location. If you jumped underground, you’d live long enough to jump out; but there’d be a rock statue from where you first departed. The air could just disappear where you arrive, and new air could be created where you left, but that’s boring! It also requires a superpower or magic power that interacts in detail with the environment, unless, like, it’s always leaving behind inert nitrogen gas (which, again, would have weird effects).
Some stories posit that if you teleport into solid matter, you die, since the matter intersects your body. This is stupid. If that’s the case then teleporting into air (or water) would do the same thing, which would also kill you, because dumping dozens of liters of air and whatever microscopic objects happen to float in it into the human body instantaneously is going to cause all kinds of problems. Not least the pressure in your body is going to shoot up, bubbles are going to form in your blood, and your cells’ chemistry is going to freak out.
So the most logical version of this superpower to me has always seemed to be that you swiftly, but gradually, displace the surrounding medium as you arrive. Perhaps you are gradually inserted from the 4th dimension. Humans aren’t 4-dimensional, so if you were just dropped, you would still have to displace air instantly. But if you were inserted into the spot at an oblique angle (in the 4th dimension), then gradually rotated into place, or if instead some kind of superpowered or magical interface rapidly spread from the center of the teleportation spot to your skin, the air could simply be pushed aside.
If it’s too hard to be displaced by the force of your teleportation power, either the teleport fails or (perhaps) you die in a bizarre and grisly fashion. But if you’re displacing air… wouldn’t that make a noise? This has led me to today’s science problem, which is, how loud should teleportation be?
The average volume of a human (according to Google; I google all my constants ‘cause I’m lazy) is 62 L. Surface area is 1.92 m^2. Using the ideal gas law, we can figure out, for air compressed into a certain volume as a layer just above the skin, how much overpressure is produced. But this is unsatisfying, because we’re not positing our teleportation ability immediately and magically moves all the medium we displace to an arbitrarily thick layer around us. That would make sense, but most teleportation powers don’t use it, and it would lead to certain weird results–imagine compressing water, or some very rigid medium, and producing an extremely powerful shock wave! You could blow holes in walls by teleporting into them (well, if the rebound didn’t kill you).
Just how compressible is air? Wikipedia informs me an object moving quickly through a medium creates what is called ram pressure; if the direction of motion is perpendicular to the surface, it seems to be just P = ρu^2, where ρ is density of the medium and u is the velocity. The density of air at NTP is around 1.29 * 10^-3 kg/L. Sound waves create overpressure in air; and we are essentially creating a blast overpressure by rapidly displacing a specific volume of air. If we assume minimal energy loss from any instantaneous rebound of the body of the teleporting person, and that the amount of overpressure is close to the sound pressure as the disturbance propagates away from our body, we can get sudden, basically arbitrarily high pressures at the surface of our skin for arbitrary velocities of displacement. At 1 m/s, the overpressure is a tiny 0.001293 Pascals, so a sudden sharp noise about talking volume. At 100 m/s, it’s 12 Pa, which is 116 dB, just below the “threshold of discomfort” according to this table. So potentially this is quite a loud noise! In the spirit of Randall Munroe, though, let’s go higher.
At 1 km/s, we hit 156 dB, which Wikipedia says runs the risk of “instantaneous hearing loss,” which I can only assume means your eardrums will probably explode. At 100 km/s–probably close enough to “instant teleportation” as makes no difference–the sound produced in the immediate vicinity is a whopping 236 dB, which is far, far beyond the top of this Wikipedia table (remember, decibels are a logarithmic measure!). According to this page, this suggests a sound louder than the Tsar Bomba. If we want our teleportation power to work truly instantaneously, or as close to it as possible, this would involve the teleportation interface moving at the speed of light. That would produce an immediate overpressure wave clocking in at 375 decibels. Krakatoa, according to the previous source, was only 310 dB (I assume they mean “as close to the source as you could theoretically be). This is many orders of magnitude beyond that. Let’s be realistic; at this point relativistic effects apply, so who knows what the actual result would be, but we would probably be better off measuring it on the Richter scale (or possibly Torino). You’d better use your teleport effectively; all that is left of you is likely to be a fine mist.
I am dissatisfied with assuming we could produce almost arbitrarily loud results in this way, because it seems unreasonable that displacing such small volumes of air could have such stupendous results. But momentum must be taken into account, I suppose; if you’re pushing air molecules at 100 km/s, you’re depositing quite a large sum of energy into the surrounding medium. More importantly, though, physically consistent, near-instantaneous teleportation is not a stealthy power! At the lower end of the estimate, it’s probably not loud enough to draw attention on a busy street, but you’re definitely gonna notice if somebody appears behind you. And people will notice when you leave: a similar noise will occur when you leave behind a person-shaped hole in the air, although the loudness will max out much lower (my naive guess is about 194 dB, the loudness of a Saturn V rocket launch; but since air is moving into a vacuum here, I am even more unsure of this number).
I encourage corrections from people better at math or with more relevant knowledge; what I tried to find is a table or graph relating overpressure at the point of an explosion to loudness recorded from a specific distance away, but I couldn’t find anything. But if anybody has some explosives, spare barometers, and a big empty field going spare, do let me know, that sounds like a fun weekend project.