Vrftjkry

Warning

This question is the first of a series about specific use of teleportation. It will concern only about momemtum and speed: other subjects will be exposed later.

Context

The story happens in our world and current era. The protagonist possesses the power of teleportation with the following characteristics:

• When teleporting, a volume including the protagonist is swapped with the same volume of matter in another place. For example, if the destination is in open air, the departure will receive the same volume of air.


• That result with no problem of collision of matter: if the
  destination is in a solid rock, the protagonist will arrive in the
  rock. And at the departure, there will be a volume of rock with the
  same shape as the protagonist.


• There are no collision problems, but there are still problems: the
  destination can override a part of something since what matters is
  the volume. It’s not a problem when swapping a part of a rock, but
  it’s one when swapping a part of a person.


• The volume of exchange has the same shape as the protagonist adding a
  layer around it. The layer is at minima 5cm, but can expand by
  willpower.


• There is no minimum time between two swaps: it can be as short as
  reflexes permits.


• The protagonist can teleport as long as it has willpower: think of it
  as a superhero power.


• The teleportation happens if the protagonist can picture it.
  Coordinate won’t work, but a memory, a picture/film will (no matter
  the distance). The protagonist could also teleport in a hidden part, even if what behind is unknown as long as the protagonist can
  guess it (for example behind a door or a rock).


• Both volume exchanged keep their momentum ignoring the difference in velocity of the Earth's rotation. Falling toward Earth on the south pole, and teleporting to the north pole will result in the protagonist still falling. Flying westward and teleporting to facing eastward, will cause the protagonist to shoot forward in the eastward direction at the same speed.


• If the destination is a moving structure (vehicle...), the protagonist will teleport at the coordinate where the structure was when teleporting. But the protagonist will keep its momentum, resulting in a possible speed difference. Comparison is like trying to jump in a car in your everiday life: there won't be too much problems if the car is slow or stopped, but there will if you are on foot and the car is at 90km/h.
  -If the destination is a picture or a memory of a moving structure, the destination will be at the coordinate when the picture/memory took place.

Question

As the title said, my question is about that last point: speed.

Are they possible downside with keeping momentum when teleporting?

The two major problems I could find are:

• Teleporting in a moving object when motionless or vice versa.


• Teleporting by accident above a pit resulting in a free fall, which
  another teleport won’t resolve (unless quick thinking).

Please try to not raise problems from other subject since there will be other questions for them.

Edit: see also the answer of Zeiss Ikon, which is a nice one.

From some of the comments, I believe you're wanting to discount / ignore the difference in velocity of the Earth's rotation. Beyond that, yes, you still have much to worry about.

It's not the slide that gets you. It's the sudden stop at the end.

Deceleration for Mr. Teleporter from a jet airplane traveling at about 570 mph (917 kmh) to 0 at home, assuming it takes 3 inches for the body to fully decelerate, would be over 43444 G of force. That's... way beyond merely fatal. Your traveler hits the wall hard enough to go through the wall and possibly the next wall. Though he won't know, since he cannot possibly even begin survive that at all. In fact, he'll be a rather disgusting smear mixed into the debris from the wall(s). I suspect there won't be enough solid mass (bones) left over to recognize he was even human. Picture a water balloon exploding against a brick wall.

Similarly, if he's at home and suddenly wakes up, realizes he missed his flight and somehow can mentally picture the right plane (given they all look alike, that's unlikely in the extreme), he's going to suddenly appear sitting calmly in a seat that's going 570 or so mph, but he's at complete rest. I suspect the forces involved are more than sufficient to rip an entire line of seats out of their moorings to the plane's floor and even rip them out the back of the plane. Either way, your teleporter (and probably many other people) just died horrifically. But, at least its over quickly. Again, his body will be converted into a gooey mess in the initial impact between his back and the chair.

That 570 mph sudden stop translates to about 29 823 142 Newtons or 6 704 511 pounds of force on impact. That's about 7 kg of TNT in equivalent energy you've just introduced into either Mr. Teleporter's home and/or airplane.

Maybe a less extreme example won't be so... messy?

Mr. Teleporter is in his car and realizes he forgot to grab his mug of coffee off the kitchen counter. Oops. Well, no problem. He's a commuter, but this week he's a passenger, not the drive. No one will mind if he pops back to the house, grabs his coffee, and then pops back into the car, right?

If their commute manages to get up to 70 mph on the highway (about 113 kph), he's going to appear in the kitchen going 70 mph and have a sudden and dramatically bad (but short) day. He will slide into the kitchen counter with roughly 655 Gs of force, give or take. If he has a kitchen counter that's well made at waist height, is upper body will be torn from the lower body, to impact somewhere else downrange with much less force. So the body will be recognizable and possibly even identifiable. But the bottom half just destroyed the kitchen counter, converting it all to a messy, gooey, pulp of debris.

He strikes the kitchen with almost 450 000 Newtons of force (101 115 lb. or about 450 kJ... that's about 0.11 kg of TNT). As far as I can find via Google, it takes about 1500 lb of force to break a typical 2x4 wall stud. So at 70 mph, he's going way more than fast enough to go through a wall. But then everything gets way too messy to determine whether he retains sufficient mass or velocity to continue going through wall(s) after that.

We can slow him down further, of course. My morning commute, on interstates, often drags along at about 25 mph (40 kph). That same bounce-to-kitchen event results in about 83.4 G when going from 25 to 0 mph. That's still well into fatal territory, but maybe his now-widowed wife won't have to completely rebuild the kitchen out of his life insurance policy funds. Maybe.

As a point of reference, the highest Gs ever survived, according to Google, is 46.2 G. coming to a complete stop via impact from 25 mph is almost twice that, so well beyond survival range without some serious protective gear. Note that surviving high Gs requires physical training, so your typical office commuter won't make it out alive from that sudden 46 G event.

From this speed, he's going to strike with a force of about 57 370 Newtons (12 897 lb., 57 kJ, or about 14 g of TNT).

At 15 mph (24 kph), the impact Gs from suddenly sliding into a wall or other obstacle drop to a potentially survivable 30 G. But that's going to depend on what they hit (a wall spreads the force out more evenly, while striking a counter is probably completely fatal) and how tough they are. Regardless, they're going to suffer major, life-threatening injuries even at that relatively low speed.

Here, we've brought the impact force down to about a mere 20 653 Newtons (4 643 lb., 21 kJ or about 5 g of TNT).

At 10 mph (16 kph), we're down to about 13 G. That's painful but survivable, with about 9179 Newtons of impact force (2064 lb. or 2.2 g of TNT). But I wouldn't want to be going anywhere above that when I teleported.

Note, too, that if he's dumb enough to jump into the kitchen and misjudges his position, then there's now a mass from the kitchen that's sitting at rest in the car and about to strike the seat back he just left or the windshield with those same Gs, which will be destructive to the car and will likely pose a serious distraction to the driver.

If this power is held by a significant percentage of the population, there would be laws and public service announcements and stuff to prevent idiots from doing this sort of thing...

Teleporting with momentum is a bad idea.

Friends don't let friends teleport from moving vehicles.

I see potential issues with teleporting into a location that the protagonist doesn't know is moving. For instance, he remembers the interior of a travel trailer -- but doesn't know it's currently being towed at highway speed. Alternatively, he might teleport out of a vehicle without realizing it's moving (for instance, a very steady airliner flight, on straight and level course, might easily be mistaken for standing still, if you can't see outside).

Starting at 1000 km/hr is a bad thing, if you don't know it's the case. If you do, you could (assuming you have enough "remembered" destinations) teleport somewhere outdoors that puts that velocity straight up from ground, wait for the "wind" to die to as near zero as it gets, then 'port back to ground. The same method could be used (likely with prior planning as an emergency procedure) to deal with "Oh, I'm above a pit or just outside a tall building" situations.

Both volume exchanged keep their respective velocity relative to Earth.

Oh boy this is gonna be fun. Not to the teleporter though.

Which imply there won’t be any problem if the protagonist exchanges place between North Pole and equator

Nope :)

You see, there is a reason why the best places to launch a rocket into space are close to the equator. You get a boost to your orbital velocity by starting from a point on Earth that is moving faster linearly, relative to the rotation axis.

Such a rotation is on the order of 460 m/s over the equator. This is proportional to the cosine of the latitude; at the very poles, this speed is zero.

What this means is that should the teleporter do their thing departing from, say, Colombia, and arriving in Nunavut... They will be causing a sonic boom, for they will be flying eastwards faster than sound. They will be undergoing aerobraking - and since the human body was not built for naked supersonic flight, they will come to rest (in peace and in pieces) a few seconds and probably a few kilometers later.

Likewise, people in Colombia will see a burning mass of melting snow moving westwards. The snow will burn for the same reason meteorites do upon atmospheric entry - it is compressing the air in front of it to absurd pressures, there is no actual combustion involved. Bystanders may also become deaf.

Due to directions and geometry, the same effect may happen if the teleporter 'ports from northern Brazil to Indonesia.

If they move along the same latitude, but say 90 degrees East (Pickle Crow, Ontario to London) they will reappear moving straight upwards at $460 times cos(latitude) m/s$. Going 90 degrees west will cause them to splat against the ground at that speed.

Teleporting inside something means an impact against the inner wall of the cavity you create, at a potentially very high speed. Great fun indeed!