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To be more specific, do teleportation spells conserve momentum from before to after the obvious infinite violation of momentum conservation inherent in instantaneous magical travel? Credit to nitsua60 suggesting this sentence!

For instance, if I were to take a running leap and then Dimension Door forward, would I continue to be propelled forward by my momentum (assuming that I still have a number of feet of movement speed remaining), or would that dissipate as part of the spell.

Similarly, if I were to launch a cannon ball from a cannon and then Teleport it into the throne room of a local king, would the cannon ball continue traveling forward at the same velocity or would it simply drop to the ground (given that the Teleport spell was successful)?

This is a similar question, but the only conclusive answer was from the Pathfinder SRD. I'm wondering if there is anything specifically in dnd-5e text that explicitly answers this question.

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The answer here is "it depends, but likely no."

This is a little philosophical, but the answer here depends on how you interpret the role of the rules. Using the GNS framework, you can think of role-playing games as:

  1. Strictly A Game, or the game-ist interpretation. If this is you, you likely agree with Dale M's excellent answer: there are no rules for this, so the GM must make some sort of ruling on the spot. What works at one table doesn't at another.
  2. A simulation of some sort of reality, or the simulation-ist interpretation. After all, you know combat rounds represent a 6-second span of time (basic rules, page 63, under "time"), and distances are regularly referenced, so you can use the 5e rules as a terrible simulation of reality. Or, you can view it as "our world, plus magic" and derive all sorts of values and things from the inaccurate data the game gives you. If so, then no, teleportation does not conserve or maintain momentum in any way: you can teleport over long distances without having to worry about latitude, your position going around the sun, etc.
  3. A Vehicle for Telling Stories, or the narrative-ist interpretation. D&D is just a vehicle for telling a story, and this would be something you discuss with your GM. The GM, once again, makes a ruling on this. Does it contribute better to a better story to "conserve momentum?"

As far as I am aware of, however, there is no official ruling on teleportation conserving any physical values.

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  • \$\begingroup\$ I just now added an answer that mentions some previous official rulings on teleportation conserving physical values \$\endgroup\$ – Matt Vincent Aug 22 '18 at 0:20
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There is no velocity in D&D 5e and therefore no acceleration, momentum or kinetic energy.

"Speed" is a resource you expend to change your position and "movement" is the act of doing this. If you are not expending speed you are not moving.

Similarly, arrows and cannonballs take no time to move from their source to their destination.

Also, things like falling damage have nothing to do with velocity and kinetic energy. How could they? Falling damage is 1d6 per 10 feet fallen to 20d6 regardless of if you are in a vacuum or not, on a plane with lower or higher gravity or not etc.

... at least, this interpretation is perfectly in accordance with the rules.

D&D 5e is not a physics engine and strange things happen if you try to think it is. For example, a wizard who teleports from London to Reykjavík will find themselves travelling east 200 mph faster than the ground. Anyone foolish enough to teleport from the equator to the opposite side of the globe will arrive at over 2,000 mph.

This is something you have to deal with with rulings because there are no rules.

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    \$\begingroup\$ Without momentum or kinetic energy, there would be no falling damage. This point is pertinent, because the presence of falling damage creates the opportunity to use teleportation spells to (potentially) avoid that damage. I understand that you're saying the text does not serve as a physics textbook, but there is kinetic energy (see point about falling damage). It seems that from your perspective any sort of teleportation would prevent falling damage (given that the caster teleports to a reasonable location). If that's the case, no conservation of momentum. \$\endgroup\$ – Val Oct 21 '17 at 21:55
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    \$\begingroup\$ @Val There's falling damage because there are rules for falling damage. That's the point. \$\endgroup\$ – Miniman Oct 21 '17 at 22:12
  • \$\begingroup\$ Returning to this after a couple of years as a reminder. After re-reading this answer I realize I didn't understand Dale's point the first time. I see now that this perspective is looking at the consequences within the game being defined entirely as a product of the rules. Falling is a 'condition' defined by the rules, but momentum is not. \$\endgroup\$ – Val Oct 2 at 15:46
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No.

The game rules themselves never tell you, but the consequences of preserving momentum make doing so essentially not possible. Simply put, if momentum were conserved, casting a single teleportation spell would be suicidal unless you managed to perfectly match the momentum.

Why?

Because planets have momentum due to the fact that they rotate. The Earth rotates about 1,600 kph (~1,000 mph) at the equator.

Planets also have momentum due to the fact that they orbit a star. The Earth revolves at 107,000 kph (~67,000 mph).

Most solar systems have momentum due to the fact that they orbit the galactic core. The Sol solar system that the Earth inhabits revolves at about 800,000 kph (~500,000 mph) [based on an estimate distance to the core of 27,000 light years and an estimated period of rotation of 230 million years].

Galaxies have momentum due to the fact that galaxies are all moving with respect to each other and due to the big bang. The Milky Way galaxy is perhaps moving at about 2 million kph (~1.2 million mph). It's difficult to tell, however, because the only frame of reference are other galaxies. This is the speed of our galactic cluster with respect to the Hydra constellation.

The Earth and everything on it has a combined momentum from all that motion. We don't notice it, because we all share it and have the same frame of reference.

If teleportation conserves momentum and you're standing still and teleport across the room facing a different direction, your momentum and that of the planet's are going to be suddenly wildly different. You'll find yourself a stain on the floor or ceiling. Alternately, if you're unlucky enough to have been outdoors with the vectors pointing upward, you'll very quickly find yourself off-planet, or, more likely, vaporized due to friction with the atmosphere.

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    \$\begingroup\$ Since your destination is moving, wouldn't you have to take the local frame of reference into account regardless of which ruling you use? \$\endgroup\$ – Matt Vincent Aug 22 '18 at 21:31
  • \$\begingroup\$ @MattVincent Yes, this response seems more like an argument that momentum is conserved. If you didn't conserve your local momentum, then when you teleported 30 ft and arrived with zero inertial momentum into an incredibly fast rotating inertial frame, you'd die instantly. \$\endgroup\$ – Blaise Jan 20 at 15:27
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    \$\begingroup\$ @Blaise Remember that momentum is a vector, consisting of both a magnitude and a direction. The choice is not that either the spell preserves the caster's momentum or it eliminates it entirely. (Both of those would result in death.) The spell either preserves the caster's momentum or corrects the caster's momentum to the new frame of reference. By correcting it, you're changing it, and by changing it, you're by definition not preserving it. \$\endgroup\$ – Bacon Bits Jan 20 at 16:40
  • \$\begingroup\$ @BaconBits I don't think a 30ft teleport would result in death, since the angle difference in your vectors is going to be so small. For very long-range teleports, we'd get into the semantics of whether one teleport "corrects" your momentum while another does not. In a universe of the impossible that's also trying to appear intuitively accessible (e.g. falling damage's simplified modeling of increasing speed), it seems most logical that all teleports would simply correct your momentum as you say. Good point, hadn't thought of it that way. \$\endgroup\$ – Blaise Jan 20 at 18:16
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The most reasonable, safe, and consistent interpretation would be that teleportation would conserve momentum (and orientation) relative to your frame of reference. E.g. if you were stationary on the ground when you left, and lying prone, you would arrive stationary and lying prone in your new location. And if you were falling when you left, you would be falling when you arrived, perhaps to stain a new place.

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Conserving Relative Momentum has Precedence

tldr: the 3e and 4e writers ruled to conserve momentum, but either way the local frame of reference must be taken into account.

As always: it's a DM's call, especially since this particular issue has not yet been specifically addressed in 5e.

Still, it was addressed in previous editions, and for anyone interested in those historical rulings, the 3.5e FAQ stated:

If you’re plummeting toward the ground when you cast teleport to reach a safe spot, you’d still be “falling” and would therefore take damage as appropriate to the distance you actually fell before teleporting.

Also, the 4e Rules forum FAQ stated:

"Is momentum conserved when teleporting? The designers lean towards yes, which is also consistent with 3.5's FAQ answer ...

Further discussions in the 4e Rules Forum (now gone) also discussed this as relative motion (to account for teleporting to other continents/worlds/planes). And to be fair: all movement/momentum is relative to begin with. Teleporting wouldn't be viable using either method if you don't account for the local frame of reference.

The 4e designer(s) mentioned above wrote an article on the subject, which contained the following excerpts:

... If you throw a stone through a portal, it comes out the exit still flying through the air. I can't imagine anyone saying that the stone just drops to the ground with all of its momentum somehow absorbed by the portal. (If that were the case, you couldn't even step through. Force is force.) The same thing applies if you leap through; you come out the far end mid-leap...

... This type of teleportation, then, is intuitively correct—which means momentum is conserved...

... An important addendum to what's written above is that momentum should be conserved when jumping through a portal relative to the portal. If I step into a magic circle on a flying boat and emerge in a magic circle on the ground, I don't have the boat's momentum; I have my momentum relative to the circle I stepped into.

This seems in line with another 4e Teleportation clarification:

If a creature is prone when it teleports, is it still prone when it reaches the destination space? The answer is yes. Teleportation does not set a prone creature upright. The principle behind this rule is that effects are not terminated by teleportation...

Now, some may balk at using clarifications from previous editions as precedence, but the 5e writers certainly used those editions for precedence, and I've found no new rule or paradigm in 5e that would conflict with this.

But again: it's a DM's call (plus: magic is typically portrayed as more of an art than a science, and likely dependent on one's beliefs... which is apropos in a shared, imaginary RPG setting... maybe just have the caster make a Arcana roll to have it work as desired). This information is solely for those that desire it.

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    \$\begingroup\$ Thanks for the resources! This is what I was looking for, whether or not there was any sort of clarification from the developers. \$\endgroup\$ – Val Jan 30 at 5:36
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I am going to answer this in a different way, by justifying a re-framing of the question first.

When you try to justify how magic works in a role playing game that is not designed to cater for such things (such as D&D 5e) it leads you down a rabbit hole where the whole magic system, the whole game, starts unravelling and often becomes unplayable.

Why do I say this? D&D 5e is only meant to loosely simulate the real world (find discussions on what hit points are or on falling damage to see that). It is far better described as a game that provides rules which help you collaboratively create heroic stories set in a fantasy world (though generally I wouldn't, it sounds far too pompous).

Within these rules there is a system for producing magical effects, things that just can't be done in the real world. Magic is the word we have for things that we can't explain using our current understanding of the laws of physics. Things just happen as a result of magic.

As soon as you try to use the "conservation of momentum" law about any one spell, then you are accepting the proposition that our real physical laws apply and then, to pick the most obvious spell, Wish stops working because it horribly violates the laws of thermodynamics.

So instead of asking "Do teleportation spells conserve momentum?" you need to ask a different question, as "momentum" is not a concept that exists in the game to explain how things work. The alternative question I would suggest is: "Does a moving target of a teleportation spell carry on moving once they change position?" and it is that question I will try to answer.

Movement by creatures in D&D is done in discrete "chunks". The story might be "The wizard ran from one side of the door to the other, casting a magic missile at the enemy as they past the opening, diving back into cover before getting filled full of arrows". However the game is run in discrete steps so this could be: wizard moves 10', casts a spell, moves 10' with no requirement for a character to continue moving at each stage no matter how fast they are going.

As such there is no momentum, no pre-determination. Where the character goes next can be decided by the player at each 5' step on a grid or any value if not using a grid. For instance the wizard's player could decide it stays in the door rather than go the final 5' of the second 10' move into cover due to the consequences of the spell cast.

Movement and Position (PHB p.190):

However you’re moving, you deduct the distance of each part of your move from your speed until it is used up or until you are done moving.

if you have a speed of 30 feet, you can move 10 feet, take your action, and then move 20 feet.

So what if the wizard used a Dash action to move 60', i.e. as fast as possible (as a story this would be "the wizard run as fast as they could"). However they get teleported by a trap they step on to a position directly in front of a wall after moving only 50' of the movement. What happens? Are they required to run into the wall at full tilt and take damage or can they just decide not to take the next 10' of movement?

The rules say they can just not take any more movement. That there is no momentum. The story may be "the wizard ran as fast as they could across the teleportation trap and disappeared. A moment later they were in front of a wall of spikes 30' away, but pulled up just in time to stop being skewered."

So applying all this to your first question:

if I were to take a running leap and then Dimension Door forward, would I continue to be propelled forward by my momentum (assuming that I still have a number of feet of movement speed remaining), or would that dissipate as part of the spell.

and bringing in a couple more rules:

Movement and Position (PHB p.190):

If you have more than one speed, such as your walking speed and a flying speed, you can switch back and forth between your speeds during your move. Whenever you switch, subtract the distance you've already moved from the new speed. The result determines how much farther you can move.

Jumping (PHB p.182):

LongJump. When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement

This would mean that if someone takes a running jump and go 10' of their possible 15' (say) jump distance, then they take an action to cast dimension door (we won't get into whether you can do this in the middle of a jump) and teleport 200' to a new position, then they are then free to use whatever speed they have remaining, say either the remaining 5' of their jump or, if they teleported onto a surface, some or all of their remaining walking movement. The rules do not require the use of the remaining 5' of jump, but you can. There is no momentum and the story description comes afterwards.

Your second question is actually a different case because it is about a moving object not a creature, which is handled differently in the rules:

Similarly, if I were to launch a cannon ball from a cannon and then Teleport it into the throne room of a local king, would the cannon ball continue traveling forward at the same velocity or would it simply drop to the ground (given that the Teleport spell was successful)?

The game says nothing about projectiles spending any time in the intervening space between source and target. An arrow hits as soon as the character shoots, a fireball explodes at the moment it is cast. Even a ready action cannot intercept the projectile mid-flight (PHB p.192 Ready: "When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger").

So this case cannot occur within the game rules as you cannot cast a spell on a projectile mid-flight. If a situation is set up that does not follow the normal game rules then it can do whatever the DM wants it to and the question becomes immaterial.

Finally the case where the projectile passes through a "gate" or a "portal" i.e. is teleported by passing through a pre-existing environmental magical effect rather than having a spell cast upon it, then it becomes the call of the DM whether it continues through and completes to move, as there is no RAW guidance about this situation that I know of. I believe that most DMs, like myself, would make the call that it did complete it's trajectory, though I can see how it could be justified otherwise.

In the end I think it is best to say that it is good to be reminded that the best story and consistency should rule. That almost always means that in 5e real world science as an explanation should lose out to "it is magic" every time.

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It's not a good idea to surprise the players, so all other things being equal, the best answer is that you always arrive at rest with respect to your immediate surroundings. If you teleport into mid-air, you're stopped, and then you begin to fall. If you teleport onto the deck of a moving airship, you arrive moving at the same speed as the airship and don't go tumbling aft. It's the most narratively useful answer, and it does what the human at the table expects the spell to do, without trying to figure out physics in a game world or opening the door to bizarre Portal-esque stunts*.

*I would be open to allowing somebody to try a Portal stunt, but I'd call for a fairly difficult arcana check to modify the spell on the fly to allow for it. If they succeed, I might let them write a brand new spell that specifically does that.

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