Thorneater

Of course we could just say that momentum is only conserved by the reference frame of the feruchemist, but that's too simple and kind of misses the point of conservation of momentum.

Yeah but you can tap the metalmind in a specific time or 12 hours later and your momentum by the solar system's frame of reference will be in the opposite direction and still you won't be affected differently from the momentum that the mass in the metalmind has.(And in my first suggestion I referred to the fact that the mass comes from somewhere as a possible solution.)

sounds interesting. Do you remember the name of this thread? I also thought in this direction, but momentum is a vector and it causes a lot of complications when trying to use the mass that was stored at night during the day.

Not necessarily, instead of flying straight up he can fly at an angle where the push from the coin eliminates the effect of air friction. It doesn't have to be true. wax is not a physicist. When he says that his density does not change, he does not mean that his mass density does not change. (dm/dVol have to get changed) he means that his permeability to bullets and blades does not change (and he says it). That is, that the density of the particles in Wax does not change. he remains made of exactly the same particles, it's just that each of them weighs a little more or a little less.(so his density does change)

First thing: an example for the case you asked for: two people in a freight car traveling at a constant speed (without shaking) with closed and sealed walls but with an open roof. One of the people is Crasher, he jumps on a coin and flies to the sky (and stops there). As far as the second person in the freight car is concerned, the Crasher is at rest, it has no velocity and therefore no momentum. As far as the Crasher himself is concerned, he sees the freight car as a small and insignificant thing and therefore it is clear to him that it is in motion and therefore for him it has a momentum. Second thing: regarding your solution: the Crasher can't really change his mass only regarding parts of his movement. Mass is something related to many other things besides momentum. In the first era, Sazed tapped his metalmind to increase the force of gravity acting on it and also the friction acting on it so that he could block doors and gates, therefore iron feruchemy also affects the gravitational mass of the Crasher (the mass considered in the force of gravity). We notice that in the second era Wax thinks that gravity causes him to accelerate equally before and after he stores mass. Together with the previous conclusion regarding the gravitational mass, it follows that iron feruchemy also affects the inertial mass. All in all, it seems that it is not possible that only a part of his mass is affected by iron feruchemy. (Because the mass related to the constant moment is the inertial mass and we have already seen that it changes.) In addition, other people can try to measure his mass, so it cannot be said that it changes only regarding a certain movement. We will note that if another human measures Crasher's mass he will probably calculate his gravitational mass and we have already seen that it is affected. So your solution seems a bit illogical to me. Note that my theory also refers to Crasher's frame of reference. I know that my theory is also not very natural and I will explain the logic behind it. (Otherwise it just seems that I pulled out a complex solution that is not similar to what is described.) So my theory is that the Crasher doesn't really store mass, but by filling the metalmind, it actually transfers part of its mass to the organs of the system (with the momentum that corresponds to the mass with the speed of the system). Usually in such a situation, after the transfer, the energy in the system is smaller than the energy before the transfer, this energy difference is stored in the metalmind in the form of Investiture. When he wants to increase his mass he actually transfers mass from the other parts of the system to him, usually this way the general energy in the system after the transfer is higher and therefore he uses the Investiture he has in the metalmind. And yes, I know that it is very, very unlikely that my theory reflects how feruchemy really works. (It is apparently too complex) but in my opinion the usual view is too full of mistakes and maybe some of the ideas at the base of the theory are correct. P.S By the way, you have a small mistake when you analyze the case, you accidentally subtracted from the general system the speed of the subjective system when in the calculation of the subjective system you added it at the end.

I think I wasn't clear. I'll be more precise in the some of my points. I didn't mean that all of the mass has stored. I meant that even if just a fraction of the mass has gone, the momentum can't be conserved in all of the inertial systems. I explained it in the next example (I can see how I was unclear in my declaration and example and I'll explain my example. System A and system B are supposed to represent the same case but in different "frames", two different watchers that "look" in the same event. In system A the watcher saw at the beginning a object( maybe a feruchemist) with weight of 4 kg that moves 2 meters each second, so its momentum is 8 kg•m/s. After the storing the momentum of the object should conserve but now is mass is 2 kg so his velocity should be 4 meters per second. The watcher in system B saw at first the object(the feruchemist) at rest, so its momentum is zero, and after the storing it should stay at rest.(because of the momentum conservation) The watcher in system B moves at 2 meters per second in relation to the watcher in system A(because he's move like the object), but after the storing we got that the object moves at 4 meters per second in relation to the watcher in system A but at 0 meters per second in relation to the watcher in system B, but the watcher in system B moves at 2 meters per second in relation to the watcher in system A and we got a contradiction ans so the momentum can't be conserved in both of system A and system B. It's not 0 kg but the momentum (because the object is at rest) is 0 kg*m/s(the units of momentum). I didn't say the the feruchemist stored another object's mass but that because mass can't disappear and conserve momentum (as I've said). I suggested that the feruchemy actually transfers mass between objects in the system in a way that is similar to "mass disappearance" from the perspective of people who do not notice microscopic changes (because the planet is usually in the human perception system and serves as 'grounding'). That fits to my theory because the Crasher doesn't "think" he moves as the planet rotates so this movement don't count as part of the momentum that "stay" with him after the storing and it distributed among the parts of the system, including the planet which is huge and therefore receives most of the traffic from it and all its effects are microscopic and negligible. I hope now my theory is more clear. I'll be happy to get any feedbacks.

I can't believe I'm not sure after two eras, but what does iron Feruchemy actually do? In the second era, Khriss told Wax that iron Feruchemy conserves momentum, but if the mass is actually gone, then in two inertial systems that move at different velocities, the momentum cannot be conserved in both of them. For example, if there is an object that moves in system A with a mass of 4 kg and a velocity of 2 meters per second and system B moves along with it. In order to conserve momentum in system A, if the mass is decreased by half, the velocity would need to be 4 meters per second. However, to conserve momentum in system B, the velocity of the object would need to be maintained (its momentum is 0 kg*meters per second). Thus, momentum cannot be conserved in both system A and system B simultaneously. Here's another example: if momentum is conserved in the system that moves with the planet (Scadrial, in this case, apparently), but does not rotate with the planet, then if a person uses Feruchemy to increase or decrease their mass and is not located at the planet's poles, they would fly out of the planet due to the momentum conservation principle. Some people may argue that the mass and momentum are stored in the cognitive realm, but we know that if a person stores mass during the day and uses it at night, they wouldn't experience a push to the side. However, according to this theory, the momentum would throw them to the side (actually setting them in their place, but the planet would rotate). So, my guess is that it depends on the Feruchemist's point of view. I think that the Feruchemist sees themselves as a part of a system, and naturally, all the objects that they consider (on some deep level) to be in this system. When the Feruchemist stores mass, their mass is actually divided among the entire system. Maybe each object gets a portion based on its mass divided by the mass of the system (and the Feruchemist can have a portion of that, gaining back some of the mass) or maybe not. With this mass, the system's velocity moves (and then the momentum is conserved). For example, if a Crasher (an iron Feruchemist and steel Allomancer) throws a coin to the ground and then flies into the sky and reduces their mass by half, their velocity in relation to the system will be doubled (and probably move with the planet), and they will not be pushed to the side (as I had originally imagined). This is because the momentum that would have made the push was divided in the system, and the planet likely absorbed most of it (and the mass of the planet makes it negligible, like grounding in electricity). Their velocity in relation to the system (how they see their velocity) will then double, perhaps almost entirely if some of their mass returns to them in the process. The theory has some versions. Each has some implications and there are experiments that can determine which one is true, but it is a little long so I'll finish here for now.