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In my magic system, sorcerers can absorb magical energy from another plane of existence, called Ether, in order to convert it into kinetic and thermal energy; they can also dispel these types of energy, which is converted back into magical energy and returned directly to Ether. Now, this means that a sorcerer could dispel say, a bullet's kinetic energy, but from my understanding its momentum would remain. If the sorcerer were to do this to the bullet, would it just stop accelerating, but still maintain its momentum, and still cause damage should it hit a target?

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    $\begingroup$ Bullets only accelerate whilst they're in the barrel of a gun. Only rockets and other self-propelled projectiles will keep accelerating in the air. $\endgroup$ – Starfish Prime Mar 12 at 12:25
  • $\begingroup$ @StarfishPrime technically Acceleration=Velocity/Time so bullets accelerate at different rates along their trajectory $\endgroup$ – depperm Mar 12 at 12:45
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    $\begingroup$ @depperm StarfishPrime is correct, once the bullet leaves the barrel the acceleration is zero and velocity stays at what is called muzzle velocity. There will be some deceleration after the bullet leaves the barrel due to air resistance which will eventually stop the bullet. $\endgroup$ – mwarren Mar 12 at 13:32
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    $\begingroup$ @mwarren deceleration is a type of acceleration though, just with a negative rate of increase. $\endgroup$ – zackit Mar 12 at 13:38
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    $\begingroup$ Such questions bemuse a physicist. You can't really pick physics apart like that. The concepts are all connected to each other: any change to how one part of physics works changes everything. $\endgroup$ – John Doty Mar 13 at 13:09
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I think you have some confusion: kinetic energy, in the non relativistic regime, is $K=$$1\over2$$ mv^2$. Momentum is $M=mv$.

Neither of them has to do with acceleration. If the mage can remove kinetic energy, it means the velocity (or the mass) is set to 0, and therefore also the momentum goes to 0.

For a bullet nullifying its velocity would mean that it would drop to the ground, Neo style

Neo stops bullets

Nullifying the mass instead would make the bullets vanish mid air. On the other, that much mass-energy going into Ether would have interesting applications

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    $\begingroup$ Of course, you can fix the 0 kinetic energy without 0 momentum thing by just setting the mass term to zero. Of course, by converting a bullet into photons you may have brought about some new problems, but they don't involve being shot as such. $\endgroup$ – Starfish Prime Mar 12 at 12:24
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    $\begingroup$ I cast "absorb momentum" on the incoming bullet. The bullet transmutes into photons, causing an EM burst equivalent to a small nuclear weapon, incinerating everything in a 100m radius (including me). But hey, at least I wasn't shot! 😁 $\endgroup$ – Matthew Mar 12 at 13:26
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    $\begingroup$ I rather dislike the bit where you say has nothing to do with acceleration. I suppose taken statically no they don't. But the velocity is in any way altered, acceleration is by definition, involved. Acceleration function is the integral of the velocity function. $\endgroup$ – Gault Drakkor Mar 12 at 19:39
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    $\begingroup$ @Rottweileronmarket-day. - you wouldn't have to stand out in the rain. Stand outdoors. Steal thermal (molecular kinetic) energy. $\endgroup$ – jdunlop Mar 12 at 22:09
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    $\begingroup$ @GaultDrakkor> derivative, not integral. Still, if the speed is magically removed instantly, then the acceleration is not defined (discontinuous) at the moment this happens. That is, not only it has nothing to do with acceleration, but it disregards it entirely. $\endgroup$ – spectras Mar 13 at 2:48
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Momentum has to go somewhere.

As @L.Dutch - Reinstate Monica said, there are strict formulae for momentum and kinetic energy, and we can't strip kinetic energy from an object and leave its momentum intact, not without fundamentally altering physics. So, when we remove the kinetic energy from an object, it would stop flying - unless we are stripping the energy by stripping mass. Stripping the mass while leaving object visibly intact may be an interesting idea, but it's totally unscientific, so I won't discuss it now.

Thus, if we want to stay within the realm of science, we are lent with the question - "If kinetic energy goes to Ether, where does the momentum go?" One option is for the momentum to go to Ether as well, so in physical world, the object just drops, and that's it. Another option is for the momentum to be transferred to another object in physical world, a more massive one. This would be an equivalent of bullet hitting a bottle, only all excessive energy is sucked away, bottle stays whole and just getting knocked at a much slower that the bullet speed.

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    $\begingroup$ Could easily just say the magic spell also nullifies momentum. Or the momentum is transferred to the caster (low-mass high-speed objects like bullets have relatively small momentum. That will be like feeling the recoil from a gun, which, as we know, is much less bad than being shot. $\endgroup$ – user253751 Mar 12 at 20:46
  • $\begingroup$ Ooo... If you send the momentum to another object, you end up with something like sympathy from Kingkiller Chronicle. $\endgroup$ – Morgan Mar 12 at 22:43
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Momentum is given by mass times velocity, while kinetic energy is given by mass times velocity squared.

It follows that, in order to reduce kinetic energy while retaining momentum, the mage would need to decrease velocity while increasing mass.

So to remove 50% of the kinetic energy while preserving momentum he would need to halve the velocity while doubling the mass. Or if he wanted to remove 99% of the kinetic energy he would end up increasing mass 100-fold.

Some points;

  • While you could follow this to arbitrarily small, but positive, energies, going to 0 kinetic energy would require providing infinite mass.
  • As the object gains mass gravity will dominate how the object interacts with surrounding matter. Extending an event horizon beyond the object is something that most people would think of, but for objects that the mage interacts with spagettification would kick in much before this point. And you would potentially see fusion due to high pressure of the surrounding air.
  • Removing energy in this manner would require a staggering amount of energy as input.

Final remarks; Assuming the mage can resist the temptation to make the projectile heavy enough that it will cause havoc through gravity; as the kinetic energy decreases the lethality of the impact should also decrease. A soccer ball and a bullet has about the same momentum. According to Wolfram Alpha

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  • $\begingroup$ "A soccer ball and a bullet has about the same kinetic energy. According to Wolfram Alpha" No, they have about the same momentum. The bullet has much more kinetic energy. $\endgroup$ – Joseph Sible-Reinstate Monica Mar 13 at 4:16
  • $\begingroup$ Thanks, embarrassing typo. The argument would go the other way if they had the same kinetic energy. $\endgroup$ – Taemyr Mar 13 at 7:06
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If your magic can thus separately kinetic energy from momentum, what would happen is that the bullet would then lose its momentum from colliding with air molecules as it has no energy to push them aside.

The bullets could keep flying in a vacuum, but not in air.

(This all turns on the notion of their being separate, which doesn't occur in non-magical physics.)

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  • $\begingroup$ I'm not sure what it would mean for an object to still have momentum (and so have velocity) but not have kinetic energy (as Kinetic energy is 0.5mv^2). I.e. if something has mass and velocity it has kinetic energy by definition $\endgroup$ – Richard Tingle Mar 13 at 14:13
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Or for objects with mass the sudden/instantaneous loss of kinetic energy could simply be matter of converting velocity into heat.

As shown above a 'Neo' style sudden deceleration of a bullet (or stream of bullets) simply results in the bullets becoming hotter as they drop to the ground in direct proportion to their mass and velocity. Your magicians still pay a price for doing this in the form of the 'strain' involved in making this happen. Alternately perhaps the ether (which exists in 'parallel' to our reality) experiences a drop in local energy density when the magician casts the spell making it harder to perform similar spells in the same location in the immediate future and so greater effort/train' is imposed on the Magician if they immediately try to do the same thing again.) Either way at least Issac Newton still gets to sleep at night because the energy involved in decelerating the bullets actually went somewhere (as heat) in this plane of existence and the laws of energy conservation/thermodynamics still apply.

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  • $\begingroup$ On second thought you could run the process I described in reverse if you prefer i.e. reducing the velocity of the bullets to zero by transferring the energy of their inertia into heat in a parallel volume of the ether. That local part of the ether suddenly heats up in parallel to the bullets slowing down then dropping to the floor - at room temperature. $\endgroup$ – Mon Mar 18 at 4:41
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The reason why you have reached a contradictory conclusion with your thought experiment is because there is no reason why the momentum should be conserved.

You are describing a magical system which conserves energy, but has no constraint as to how the energy must flow. This violates the second law of thermodynamics, and therefore also violates the conservation of momentum.

So I disagree that the momentum has to go somewhere. The bullet should just stop and lose its momentum to nowhere. While this seems uncomfortable, I think this is actually an incredible idea which enables time travel (e.g. TENET).

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