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?
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
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
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.
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.
- 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
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.)
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.
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).