Is speed or momentum preserved if a moving object is shrunken or if the shrinking is dispelled?

Question

Shrinking a projectile and then removing the effect after launching it (for example, shooting it across an anti-magic field) raises the question whether the now restored (and larger) projectile continues flying with the same velocity. Or, if not speed but momentum is preserved, then it just drops to the ground?

For example, one could carry lots of ballista bolts shrunken down to the size of crossbow bolts, then firing them from a crossbow, but after the bolts pass through an antimagic field (either prepared before the fight, or mounting a magic item with a short range antimagic field at the tip of the crossbow), they get turned back into huge ballista bolts. Or shrinking down cannonballs down to a size where they could be fired from handheld muskets, and having effectively a handheld siege weapon of great destruction.

Are you looking for a history of this tactic throughout editions? Because that's a lot of work: Since I'm pretty sure no edition solves this with a general rule (although each should—the question certainly arises in every edition except maybe 4th), it means finding every way to change the sizes of stuff then determine how the game physics interacts with each different way. Consider narrowing this to just one of the game's editions. — Hey I Can Chan, Jun 29 '23 at 20:49
Related: Can the Enlarge/Reduce and Catapult spells be combined to hurl boulders? — Nobody the Hobgoblin, Jun 29 '23 at 21:44
Also related: Is speed or momentum preserved if a moving objext is shrunken or if the shrinking is dispelled? — Nobody the Hobgoblin, Jun 29 '23 at 21:54
@Matthieu : that one has many simple solutions, the most obvious is that the last peasant just throws it as if he was the first one to pick it up. Turn-based video games which allow picking up items and throwing them do it the same way (for example, the original Xcom or the Jagged Alliance series). You can use that to bring a grenade from one end of the map to the other one by using a series of soldiers to throw them to each other, but the last one throws it with the exact same force as if he had started the turn with it. — vsz, Jul 01 '23 at 18:37

Dale M · Answer 1 · 2023-06-30T09:10:28.747

Velocity and momentum are not concepts in the rules

D&D is not a physics engine. The game world works according to the game rules, not according to the physical laws of the universe.

Magic is magic.

By definition, it doesn't follow the rules of the real universe. That's what makes it magic. What it does and how it does it is up to the DM to decide.

Magical shrinking and enlarging are not concepts in the real world

The real world is not a magic engine. Magic does not exist in the universe, so the laws of physics don't deal with it.

Assuming this is something that could happen, what would be the effect?

The atmosphere for a large volume around the projectile would freeze solid.

Assuming the object is moving in a flat spacetime (close enough assumption for most game worlds) at non-relativistic speeds (again, a fair assumption for a crossbow bolt or cannonball), it has an energy of approximately:

$$ E={1 \over 2} m_ov^2+m_oc^2 $$

Any increase in rest mass will linearly increase the object's energy. A reduction in its velocity can obtain some of that energy. But \$c>>v\$, so the kinetic energy is negligible and can be ignored. A typical 30g crossbow bolt travelling at 100m/s has 150J of kinetic energy and 2,700,000,000,000,000J of rest energy.

That means the energy has to come from the environment of the projectile. If our 30g crossbow bolt becomes a 26kg ballista bolt, we need to find an additional 2,300,000,000,000,000,000J of energy.

Is that a lot? Well, it's about as much as is released in a magnitude 8.5 earthquake or about 67,000 Hiroshima-sized bombs. Which, coincidentally, is in the ballpark of the yield of the estimated 9,600 nuclear warheads currently in existence. So, big on a human scale, pretty big on a planetary scale, but quite small on a solar-system scale.

The kinetic energy of an ideal gas at room temperature is about 3500J/mole, and there are about 4000 moles/m³. So, we would freeze about 200 square kilometres of the air - a hemisphere about 7km in radius. This is an underestimate because the gasses would not actually get to absolute zero - frozen air still contains quite a lot of kinetic energy.

Of course, the reverse process would release the same amount of energy. Imagine standing with all the nuclear bombs and detonating them all at once. That would be pretty close. It's estimated that this would totally devastate an area about the size of South America and, obviously, have global repercussions.

And you thought Fireball was a powerful spell - Enlarge/Reduce laughs at its pathetic energy release.

This is why physics and magic don’t play nice together.

+1 This is the most interesting answer I've read in some time. — Nobody the Hobgoblin, Jul 01 '23 at 22:00
Enlarge/reduce specifically reduces an object to one-eighth of its original weight, so your 26kg bolt would actually reduce to just over 3kg. So you're actually only looking at a release of around 2,000,000,000,000,000,000J. Much more manageable lol. — smbailey, Aug 03 '23 at 15:49

score 2 · Answer 2 · answered Jul 01 '23 at 00:10

Agreed with Dale and the comments that D&D is not a physics engine. If a player wanted to do this, here's how I'd potentially rule this in play:

As a one-time event,

In 5e, Reduce is a 2nd level spell with a casting time of 1 action. Look for a single-target 2nd level spell like Scorching Ray. If targeting single enemy, Scorching Ray is a ranged spell attack that does up to 3x2d6. That's our starting point, and now we need to adjust from that.

If the player is relatively new to D&D, or the game is more of a lighthearted game, I'd probably try to encourage their creativity, by saying okay, make a ranged spell attack, and if it hits it'll do 6d6 to a single target and knock them back 5 ft. Having a player say "I want to do something crazy and cool, will you let me?" is something I personally always want to encourage.

If the group is experienced and power-gamey, I'd be more likely to say, okay you can try it but this isn't a spell you've practiced, so roll your spell attack with disadvantage.

As a reocurring thing

If your player really likes these kinds of physics hypotheticals, or starts pulling out equations to argue that the damage should be more than 6d6, then I think you have a few choices. First, I think it's appropriate to remind them of game balance, and how D&D isn't physically correct, it's about telling a story, and 'your wizard doesn't know what a railgun is', and most players will probably accept it.

But I think the carrot is to offer this as a potential character arc. "Your wizard doesn't know how to make firearms or particle accelerators yet, but maybe finding a way to break magical physics could be a good longterm project? When you get back from adventures and level up we can talk about how your research is progressing". As the player and GM, you can work to define homebrewed/reskinned spells or class-features for 'physics mage' features that are balanced for their level.

This is intuition I have from GMing PBTA games (which frequently have a move like "when you want to do the seemingly-impossible, describe it. You can do it, but you'll need [the gm sets requirements as fitting]") and BitD (which has long-term projects that enable you to break rules after investing downtime resources into them). But I think it translates well to D&D so long as you make sure to keep things reasonably in line with standard spells (at least in combat) — Kaia, Jul 01 '23 at 00:21
The biggest exploit and biggest balance problem is that spells can be only used a small number of times per day, but one could prepare a huge number of these projectiles over a longer time period (as the items remain shrunken until the effect is removed) and unleash them in a single encounter. — vsz, Jul 01 '23 at 18:33