A new theory about iron feruchemy

[Thorneater]

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.

[alder24]

Welcome to the Shard. F-iron is the hardest to understand because it breaks so many crucial laws of Physics.

 

6 hours ago, Thorneater said:

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.

F-iron stores mass, but NEVER all of mass. You can store most of your mass but not all of it. No Feruchemical metal, except for copper and aluminum, allows you to store all of it. Therefore mass will be always conserved, as m1v1=m2v2, it never goes to 0. And Feruchemist stores only his own body's mass, nothing else, his clothes, metalminds, everything he has on him still has the same mass. Feruchemist can’t change the mass of another object. 

6 hours ago, Thorneater said:

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.

What is the relation between the system A and B? Are they tied together? Then the system A would drag the system B behind him, losing velocity in process by giving it to the system B until they both reach the same speed - you can consider those tied systems as just 1 system. Before the change it has 8 kg (2 objects both 4 kg in mass) and 2 m/s (speed doesn't add up), after you change only one one object's mass of 4 kg into 2 kg, the overall mass in combined system is now 6 kg, and it has v2=m1v1/m2 = 2.66 m/s. Momentum is conserved.

If there is no relation between the system A and B, then the System A would go twice as fast, and system B won't change his velocity, nor momentum, because no change was made in it. 

Wait, where did you get that 0 kg in system B? What is that? Where did that come from? I don't understand it. Explain this please. There is no way for system B to have a mass of 0 kg with or without F-iron.

6 hours ago, Thorneater said:

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.

Magic compensates for the rotation of the Earth. And you're looking at it from the observer located in space, a person on the planet, from his point of view has no momentum at all, and all Feruchemy is happening in his frame of reference, not some outside one. Therefore only his momentum is changed, not the momentum added by rotation, as from his point of view he isn't moving. That's the most logical explanation I can think of.

Just like when you calculate the momentum of two balls, you don't add the momentum of Earth's rotation, or Earth's orbit, or Sun's orbit or Galaxy etc etc. It doesn't matter from the frame of reference you're looking at. Only the momentum of balls relative to the ground matters. That's the case for F-iron too.

6 hours ago, Thorneater said:

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).

No, I don't know what you mean here (especially considering earlier 0 kg in the first example). But a Feruchemist can store ONLY his body's mass. Everything that he wears still has mass. His clothes, metalminds, backpack etc. But he can get with his mass so close to 0 (but never reaching 0), that you could only look at the mass of his clothes and stuff he wears for some calculations (like calculating terminal velocity).

So if a Feruchemist stores mass, and he holds another person, only his mass gets stored, and if they're moving together, tied by a rope, then you can consider them as a single system, add their mass together and do math on that mass. 140 kg (2x70 kg) * 10 m/s = 71 kg (70 kg + 1 kg of Feruchemist after storing mass) * x m/s; x = 19.7 m/s - that would be their speed after a Feruchemist stores his mass. Only his mass, the other person's mass is unchanged, but because they're tied together, you consider them as one system, and the other person is "dragged" by Feruchemist speed, adding him more momentum after Feruchemist's mass is changed, which cases Feruchemist to lose the momentum/speed he would have if he was alone..

Is that what you meant? I'm not fully understanding you here.

6 hours ago, Thorneater said:

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.

Again, from the Crasher's frame of reference he doesn't have any speed or momentum given to him by planet's rotation or planet's orbit. He went from being stationary on the ground, to jumping into the air with 10 m/s speed and then changing his momentum, which includes ONLY that momentum of his jump, no planet's rotation - he has none of it from his frame of reference. 

All of those problems you mentioned simply disappear when you take a proper frame of reference into the account.

 

Some WoBs: 

Spoiler

Questioner

So, Metalminds: if you store weight, how does that work, do you decrease your mass or...?

Brandon Sanderson

So, storing weight actually plays with your mass, because if you look at how we do the physics of it… This one is really screwy, because we are changing mass and playing with it. You watch, like with Wax decreases his weight while he's in motion he'll speed up, and if he increases it, he'll slow down. The conservation of momentum and things like that, but we'll doing really weird stuff. It's like, how can you store your mass… Well, in the magic system it works, but it’s one of the weirdest things we do. *pauses to sign book* We kind of play loose and free with the physics sometimes. Like the example that I often use is Wayne doing a speed bubble, the light that is trapped in the speed bubble...like if he turns on a flashlight would actually radiate because of the redshift, and you could just kill everybody by flashing that. So, we make the speed bubbles not cause a redshift for that reason. We kind of work with what is good storytelling first, and then work the physics around it, but we have to put in all these little breaks and things like that in there regularity in order to actually have the story.

Shadows of Self San Jose signing (Oct. 9, 2015)

 

Spoiler

Brandon Sanderson

Chapter Six

The fight in the ballroom

From the early days of the Mistborn books, I'd been planning how an Allomantic gunfight would go down. I felt it the next evolution in what has been stylistically a big part of these books.

There is a fine line to walk in a lot of these sequences. I've made something of a name for myself in the fantasy world by attempting to mix some scientific reasoning with my magic systems. At the same time, Allomancy was designed precisely with action sequences in mind. I wanted them to be powerful and cinematic—and a cinematic fight sequence is often at odds with realism. (Watch two people who really know what they're doing fight with swords sometime, then watch any fight sequence in a film. Most of the time, the film sequences stray far from what would really happen.)

So, as I said, I walk a line. Sometimes, there are things I just can't do because they violate what I've set up as the rules of the world. Other times, I design the setting and nature of the fight specifically to allow for certain types of cinematic sequences. One thing I like a lot about Wax’s abilities is the power he has to manipulate his weight. There's some realism to what he does—for example, increasing his weight doesn't make him fall more quickly, but it allows him to do some powerful things while falling. Destroying the chandeliers is an example.

At the same time, I acknowledge that the weight manipulation aspect of Feruchemy is one of its more baffling powers, scientifically. Is he changing his mass? If so, he should become more dense, which I don't actually make the case when it plays out in fights. (Otherwise, increasing his weight enough would make him impervious to bullets.) So, if it's not mass manipulation, is it gravity manipulation, like Szeth and Kaladin do? Well, again, not really—as when his weight increases, his strength and ability to uphold that weight increase as well. Beyond that, Wax can't make himself so light that he has no weight at all.

So . . . well, at this point, the ability to explain it scientifically breaks down. I do like what it does, but I have to set its boundaries and stick to them—and accept that some of what's going on is irrational. (And don't get me started on what should really be happening scientifically when Wayne speeds up time.)

Footnote: Brandon has stated that iron Feruchemy works by manipulating the Higgs field.
The Alloy of Law Annotations (March 14, 2014)

 

Spoiler

clyguy

If Wax were to go to Roshar, and--he's a Skimmer, right? So he can change his weight--if he got Lashed in a different direction if he Stored his weight would that nullify some of the Lashing?

Brandon Sanderson

Okay, you're going to make me think through this. *laughter* So Wax actually changes mass. And the Lashing only affects gravitational pull. So the answer is no because different things with different masses fall at the same speed.

Shadows of Self release party (Oct. 5, 2015)

 

Spoiler

Questioner

So if someone is storing weight-- Feruchemy-- Can you store enough that you can actually float like a balloon?

Brandon Sanderson

Uh, your clothing and stuff will still have weight.

Questioner

If you were, like, completely naked and just *unintelligible* your hand up a wall, you will?

Brandon Sanderson

Yes. You will-- You could float, yeah. That's-- I mean, you could get your weight so low that it's basically like being in microgravity, which is...q

Questioner

Like 99%? Like a vacuum balloon?

Brandon Sanderson

Yeah.

Calamity release party (Feb. 16, 2016)

 

Spoiler

Brainless

You've always said that your favorite sort of magic was being a Coinshot or being a Windrunner because you really want to fly. So I thought that iron Feruchemy you can fly using just iron Feruchemy. So if you had a paraglider and a place to jump off of, you're paragliding, go downwards, your momentum increases, you increase your weight when you're going downwards. You pull upward and then you decrease your weight. Your velocity will increase and you'll go up--

Brandon Sanderson

We have thought about that. I'm not sure if the math-- Like, we're trying to conserve momentum. We're trying to follow the math of that. So the question is, would that work? It probably would, but I'd have to look at the math. Because I tried to make very clear in the Wax and Wayne books that we conserve momentum...

Really what we're doing is, we're breaking potential energy, right, when we're doing this. Because iron Feruchemy is just the weirdest of all of them. Because we're breaking potential energy, what you just said probably works, doesn't it.

Brainless

That was in context with the thing I was saying yesterday, about Feruchemical savants. If you did that every day for years, would you potentially get to the point where you could potentially make one side of your body heavier than the other side?

Brandon Sanderson

...There are many people in the cosmere who would think this idea has merit and they would want to test it.

MisCon 2018 (May 26, 2018)

 

[Thorneater]

I think I wasn't clear. I'll be more precise in the some of my points.

53 minutes ago, alder24 said:

F-iron stores mass, but NEVER all of mass. You can store most of your mass but not all of it. No Feruchemical metal, except for copper and aluminum, allows you to store all of it. Therefore mass will be always conserved, as m1v1=m2v2, it never goes to 0. And Feruchemist stores only his own body's mass, nothing else, his clothes, metalminds, everything he has on him still has the same mass. Feruchemist can’t change the mass of another object. 

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.

53 minutes ago, alder24 said:

What is the relation between the system A and B? Are they tied together? Then the system A would drag the system B behind him, losing velocity in process by giving it to the system B until they both reach the same speed - you can consider those tied systems as just 1 system. Before the change it has 8 kg (2 objects both 4 kg in mass) and 2 m/s (speed doesn't add up), after you change only one one object's mass of 4 kg into 2 kg, the overall mass in combined system is now 6 kg, and it has v2=m1v1/m2 = 2.66 m/s. Momentum is conserved.

If there is no relation between the system A and B, then the System A would go twice as fast, and system B won't change his velocity, nor momentum, because no change was made in it. 

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.

1 hour ago, alder24 said:

Wait, where did you get that 0 kg in system B? What is that? Where did that come from? I don't understand it. Explain this please. There is no way for system B to have a mass of 0 kg with or without F-iron.

It's not 0 kg but the momentum (because the object is at rest) is 0 kg*m/s(the units of momentum).

1 hour ago, alder24 said:

No, I don't know what you mean here (especially considering earlier 0 kg in the first example). But a Feruchemist can store ONLY his body's mass. Everything that he wears still has mass. His clothes, metalminds, backpack etc. But he can get with his mass so close to 0 (but never reaching 0), that you could only look at the mass of his clothes and stuff he wears for some calculations (like calculating terminal velocity).

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').

1 hour ago, alder24 said:

Again, from the Crasher's frame of reference he doesn't have any speed or momentum given to him by planet's rotation or planet's orbit. He went from being stationary on the ground, to jumping into the air with 10 m/s speed and then changing his momentum, which includes ONLY that momentum of his jump, no planet's rotation - he has none of it from his frame of reference. 

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.

[alder24]

Ok, I think I get it now.  I hope this response will look coherent, as I was adding things left and right after writing the whole post.

EDIT: Important note - I get it now for real, before writing any reply check out the edit at the end of the post. I explained everything there. You're right, different frame of reference messes up with conservation of momentum. But there is a very simple solution to that. 

 

3 hours ago, Thorneater said:

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.

What is the example where the Feruchemist (from his frame of reference) would consider himself to be moving and have speed, while some outside observer would see him at rest with no speed? I can't think of any example in real life that would work like that. The opposite, yes, a Feruchemist at rest in a moving train would not change his momentum at all (as it's 0), and a person outside the train would see him moving with some speed and no change to the momentum too. But the opposite, I can't think of anything like that, where from a Feruchemist's frame of reference he has a speed, but from an outside observer he has no speed. How? I think that's simply not possible to have that frame of references. Just give me an real life example, maybe I'm missing something. 

Technically an observer and a Feruchemist moving at the same speed together would consider their speed as 0 m/s relative to each other (from physics point of view), and they would think that the world around them is moving at a speed of 10 m/s. That's what you're talking about? But who thinks of himself as not moving when moving? We all know that we're moving and we have speed relative to the ground, and that's what is important. That's how we look at our speed, relative to the ground. Intent and perception in Cosmere matters a lot. Maybe if a Feruchemist considered himself as not moving (despite falling from the air) but he would view the world around him to be moving, then storing/tapping his mass wouldn't have any effect on his momentum or something weird would happen. No idea, because nobody who is falling would consider themself as not moving, we all know what is happening, our body instinctively too. Try to convince your body that it's not falling, good luck.

Here, something weird, which I thought of later while writing it. A Crusher, hovering above the train car's floor, would not change his speed nor momentum by changing his mass, as he considers himself stationary, with no speed and no momentum. Maybe if he would look at himself as having the train's speed and momentum (if that's even possible and if that would change how F-iron works), changing his mass might change his speed, as from his new perspective he has both speed and momentum now. From his new perspective momentum is conserved, but from all of passanger's perspective he suddenly gained speed and momentum out of nowhere. Yes. But they can explain that by making up some phantom momentum or force from investiture acting suddenly on that Crusher giving him that speed.

But I don't think that's even possible at all for a Crusher to change his frame of reference like that to that of outside the train, nor that his perception would matter with F-Iron. It would work like the WoB below states "relative to the mass/size of the object you're standing on" so no matter how hard the hovering Crusher is thinking of himself from the outside perspective, because he's on the massive train, he won't be able to change his momentum without actually moving inside the train in the first place. If you could make a person somehow stand on a coin, and launch himself and that coin into the air, and he would consider himself as standing on the coin (like standing on the train), than it wouldn't matter if he starts changing his mass, as the mass of the coin is too small to "anchor" him to that coin, so him changing his mass in that situation would change his momentum accordingly ignoring the coin fully, and acting as he isn't standing on that coin. Maybe I'm wrong. with all of those examples. Besides that one, involving a lot of mental gymnastics, I can't think of any example fitting your description. But you thinking of yourself as having a speed of the train, doesn't change the fact that relative to that train you have no speed.

 

 

It's not just about the frame of reference, but also perception. When you're falling there is now way for you to not know that you're falling, your senses would be screaming to you that you're falling, despite that from the physical frame of reference, you're kind of stationary and its the whole world that is moving towards you. But that's not something that your brain thinks. That's not something that you think. That's not something that you perceive. It's impossible for you to look at this differently, from the physics frame of reference, where you aren't falling, but the ground is moving towards you.

Something similar is happening with time bubbles, as they don't move, they're stationary. Marasi creating a bubble while being on the carriage creates a mess of an effect as the bubble stays on the ground, while the carriage moves out of it. But a time bubble on the train will be anchored to the train and move with it.

Spoiler

Questioner

Speed bubbles--

Brandon Sanderson

Yes. Ehhhh... these are the hardest ones.

Questioner

We've seen them work and move with trains, we've seen them not work with carriages: is there a size requirement, or is it how they view themselves?

Brandon Sanderson

That's a good question. So I build in this thing, right? I'm like "Oooh, speed bubbles! Speed bubbles are cool!" but the Delorean problem, right? You're like "I'm going to go back in time: to the middle of SPACE", because the planet is in the same position, right? This is stuff that science fiction writers have been having fun with since the silver age of science fiction. So I'm like "Alright, I need to deal with the Delorean problem". And so I'm like "Alright, we're going to have to say that frame of reference is a big part of it: so perception and frame of reference is a big part of it; and also size of the thing that you're on". So it would be possible to use kind of cosmere cognitive training to get that speed bubble moving with you-- And someone asked me a question about this on tour, I believe, so it would be in one of the reports-- Not this exact same thing, but "Could they learn to move their speed bubble with them?" And yes you can.

Questioner

So it is how the allomancer views it, not how the thing views itself?

Brandon Sanderson

That's a part of it. Partially how it view itself, *garbled* It's really also mass. Big thing-- The speed bubbles required all kinds of physics-gymnastics. I'm sorry physicists, but once you start playing with time the stuff you gotta do. It's just crazy stuff you gotta do.

Questioner

We actually sat down and worked out what the metric would have to do to have a speed bubble-- Yeah, it was gnarly.

Brandon Sanderson

...We did run the math on these things, and stuff like that. And Peter, y'know, he rais-- "Redshift" and stuff like this we talked about. And all kinds of fun stuff about speed bubbles that I then had to--

Bystander

Khriss asked about that?

Brandon Sanderson

Yeah. So this is-- This one and manipulating weight... Those are the math ones. So these are the ones where-- They create the fun things to talk about, but they are where this is fantasy and not science fiction. Like a lot of these questions I could answer and you'd be like "Alright, if there were this alternate power source, we could buy this" but in this case we're like exception-list-of-asterisks to make it work. But they're too fun to not do, right? And I knew I was doing gravity on Stormlight, so I'm like "I gotta do weight separately".

Arcanum Unbounded Chicago signing (Dec. 6, 2016)

Another fact to consider is that in Cosmere there is a third component to Matter-Energy, it's Investiture. Investiture=Matter=Energy. And that's how Brandon solves his physics problems. F-iron breaks laws of thermodynamics and potential energy? Not in his world, as Investiture compensates for all of that, and everything works fine. Speed bubbles should cause redshift/blueshift and fry people with microwaves? Not in his world, as Investiture compensates for that and absorbs excess energy. If you find the example that you're describing (A Feruchemist having speed from his frame of reference, a person B from a different frame of reference not seeing Feruchemist with any speed), then you can guarantee that Investiture is the explanation and momentum is still conserved.

Spoiler

Steeldancer (paraphrased)

 According to General Relativity, there should be spatial distortion in speed bubbles. So, why does no one notice it?

Brandon Sanderson (paraphrased)

There is spatial distortion in speed bubbles, that's why bullets are refracted when they enter a bubble. However, I played with it a bit, and ignore the redshift that should happen. The barrier of the bubble absorbs it, otherwise everyone would just be irradiated. 

FanX Spring 2019 (April 19, 2019)

 

3 hours ago, Thorneater said:

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.

That creates a problem because that's not how it works. A Feruchemist storing his mass changes it into investiture which is stored in his metalminds as investiture. That investiture is 100% retrievable. If that mass was simply shifted and added to the planet or other things, he wouldn't be able to get that back, as it was used up by something else - a planet for example. There is no way for that Investiture to wait for Feruchemist in his metalmind at the same time as it's added as mass to the planet's mass. Because as soon as a Feruchemist stores his mass, it stops being mass and is turned into Investiture. So there is no way for it to exist at two places at once - in his metalminds, and added to the "bigger system".

Tbf I am just confused by my own response here in a few places. But the main part I started to write is for you to find me a real life example of two frames of reference, when a Feruchemist A has a speed from A's frame of reference, but person B looking at person A would say A has no speed form B's frame of reference. Find me something like that, that doesn't involve mental gymnastics of perception (as with hovering Crusher in the train) and stuff like that. I really can't think of a real life example that you proposed.

The opposite is true for all I can think of. From A's frame of reference he isn't moving, but B sees him as moving (A is in the train, B is outside the train). In that case perception matters as A clearly knows he views his speed relative to the train and can't view his speed relative to the ground or person B outside of the train. So he can't view his momentum as that of the train (like I was arguing in the hovering Crusher example, 3rd paragraph, I was really grasping at straws at that point to come up with something matching your description). 

In real life if there is an observer B, who views person A as not moving from B's frame of reference, then that means that there are ONLY two possible scenarios. Either they both are not moving relative to the ground, or they both moving at the same speed and direction relative to the ground. There is no way (that I can think of) for person A to have speed from A's frame of reference, and for person B to see A with no speed from B's frame of reference.

 

Edit:

@Thorneater I cannot stop thinking about it. I cannot let it go. Let's consider a Crusher inside the train. That crusher has 80 kg, and is steel pushing himself in the same direction the train is moving. Crusher's speed of steel push is 1 m/s, the train is moving at 28 m/s. The momentum of Crusher in his reference frame is 80 kg * 1 m/s = 80 kgm/s, Crusher's momentum form outside reference frame is 80 kg * (1+28) m/s = 2320 kgm/s. Because he's moving with the train, right?

Now the Crusher drops his mass by half. From his reference frame he still has the same momentum, so his speed doubles up to 2 m/s. From the outside's reference frame there is a problem that you noted. If the momentum is conserved, then his speed would be 2320 kgm/s  = (80 kg / 2) * (x+28) m/s ; x = 2320 kgm/s / (80 kg / 2) - 28 m/s ; x = 88 m/s - that's the total speed the Crusher should have after his mass change that an outside observer expects. But that not the case, an outside observer would see the Crusher moving at 28 + 2 = 30 m/s, so to calculate Crusher's new momentum as viewed from the outsider's perspective, while taking Crusher's real speed of 2 m/s + 28 m/s into the account  P = (80 kg / 2) * (2 m/s + 28 m/s) = 1200 kgm/s - so you were right in the first place, the Crusher lost almost half of his momentum from the outside frame of reference. That's not good. That's not a momentum conserved. But there is a problem. Did you see it?

The Crusher didn't touch his train momentum and speed at all. Those are separate to his movement and not in his frame of reference. For him it's like they don't even exist. A momentum is a sum of components, a sum of all different momenta. He has his own momentum based on his steel push (80 kgm/s), and his momentum based on the train speed of 28 m/s (2320 - 80 = 2240 kgm/s). Those are separate to him because of his reference frame. So for an outside observer, the frame of reference in which our Crusher stores his mass takes priority, and separates itself from the outside observer's frame of reference. An outside observer would conclude that the Crusher changes only the mass of his steel push related momentum, not the mass of his train movement momentum. And thus the sum of components conserves the momentum.

So his starting momentum would be calculated by this equation P = 80 kg * 28 m/s + 80 kg * 1 m/s = 2320 kgm/s - a sum of all individual momenta, and after he changes his mass, only the mass of his reference frame is changed, so the mass related to the train momentum isn't changing, as he doesn't consider himself to be moving as the train is. So the way to calculate his new speed is by this: 2320 kgm/s = 80 kg * 28 m/s +(80 kg /2) * x m/s ; 2320 kgm/s - 80 kg * 28 m/s = (80 kg /2) * x m/s ; (2320 kgm/s - 80 kg * 28 m/s) / (80 kg /2) = x m/s ; 2 m/s = x. The same value as calculated based only on Crusher's own reference frame. Everything works fine. The problem is fixed. Right? 

Well, that's my explanation of this. You did identify the problem correctly - in different reference frames, the conservation of momentum enforces enormous gains/losses of speed, which aren't observable, thus momentum can't be conserved. But we know momentum must be conserved, so a change in mass should launch people into space. That doesn't happen either. So we have a problem. A paradox? Right? Not really. My explanation to this is what I have written above in the edited section - Crusher's frame of reference, his perspective, takes priority. His frame of reference is the one in which his change of mass is happening. That's the only momentum affected by his change. So an outsider observing the train passing by would say the Crusher has two separate and the Crusher only changed his mass in one of them, the inside one, related to his steel push, not to the train movement. Basically our Crusher isolated both movements and changed his mass only in one of them, without touching the other. Weird? Not really, he isn't aware of his other movement, from his reference frame he is moving with the speed of 1 m/s in the train, while the world outside is moving with a whooping speed of 28 m/s, like a treadmill. But from his point of view, he doesn't have that train related momentum at all, therefore there is no change to the mass of that momentum. Nothing changes there. Different frame of reference and the Crusher's perspective is all that matters when he changes mass. All that an outside observer needs to do is to separate the total momentum of the Crusher into the sum of momenta, and isolate one the one in which the Crusher changed his mass. The Crusher changes his mass only in a specific frame of reference, only related to the speed he has in that frame of reference, without touching speeds and mass that he has in a broader frame of reference - those observing in a broader frame of reference must separate Crusher's momentum in to sum of momenta in different frame of reference and isolate only the one in which Crusher is changing his mass. That's my solution to the problem which you saw first. 

And it's supported by WoBs too, like the one copied above: "for time bubbles the frame of reference and the perspective matters a lot". Now my explanation begs a question - can that Crusher change his frame of reference, his perspective, to that of the outside observer's? Can he stand on the roof of the train, thinking really hard that the outsider's frame of reference is his now, and he is moving with 28 m/s, then store his mass down to 1 kg launching himself forward with an unrealistic speed of 2240 m/s (Mach 6.5) ahead of the train? Can he do that? The WoB posted above said that a time bubble's anchor can be changed based on Slider's perspective, a Slider can learn to anchor it to himself, so maybe a Crusher, or any F-iron Feruchemist, can learn to change his perspective and a frame of reference to store mass in that frame of reference? I don't think this is the case, because that would go into ridiculous extremes in which Feruchemist could store his mass in the frame of reference related to Scadrial's orbit around their sun and launch himself into space with impossible speeds. Brandon's magic is all about limitations, and having a person who can launch himself into space with whatever speeds he wants just by changing his perspective would be too ground breaking. But on the other hand we have Windrunners, who do exactly that, and Sliders and Pulsers who can anchor their speed bubbles to them based on perspective, so why not Skimmers too? Maybe it would be as said in the WoB about time bubbles - depending on the size/mass of the object they're on, they can't change their mass in frame of reference outside of that object (like I was kind of arguing in the section before the edit), and thus their lock to that frame of reference. It's an interesting idea that may be worth asking. Or at least we should ask Peter how Crusher's momenta and speeds behaves in different reference frames - maybe Brandon and Peter aren't even aware of that and you're the first one who noticed that problem.

 

I hope this explains everything. I hope it's clear and easy to understand. And I hope I haven't made any glaring mistakes.

Edited June 4, 2023 by alder24

[Thorneater]

On 4.6.2023 at 9:35 PM, alder24 said:

Tbf I am just confused by my own response here in a few places. But the main part I started to write is for you to find me a real life example of two frames of reference, when a Feruchemist A has a speed from A's frame of reference, but person B looking at person A would say A has no speed form B's frame of reference. Find me something like that, that doesn't involve mental gymnastics of perception (as with hovering Crusher in the train) and stuff like that. I really can't think of a real life example that you proposed.

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.

On 4.6.2023 at 9:35 PM, alder24 said:

Well, that's my explanation of this. You did identify the problem correctly - in different reference frames, the conservation of momentum enforces enormous gains/losses of speed, which aren't observable, thus momentum can't be conserved. But we know momentum must be conserved, so a change in mass should launch people into space. That doesn't happen either. So we have a problem. A paradox? Right? Not really. My explanation to this is what I have written above in the edited section - Crusher's frame of reference, his perspective, takes priority. His frame of reference is the one in which his change of mass is happening. That's the only momentum affected by his change. So an outsider observing the train passing by would say the Crusher has two separate and the Crusher only changed his mass in one of them, the inside one, related to his steel push, not to the train movement. Basically our Crusher isolated both movements and changed his mass only in one of them, without touching the other. Weird? Not really, he isn't aware of his other movement, from his reference frame he is moving with the speed of 1 m/s in the train, while the world outside is moving with a whooping speed of 28 m/s, like a treadmill. But from his point of view, he doesn't have that train related momentum at all, therefore there is no change to the mass of that momentum. Nothing changes there. Different frame of reference and the Crusher's perspective is all that matters when he changes mass. All that an outside observer needs to do is to separate the total momentum of the Crusher into the sum of momenta, and isolate one the one in which the Crusher changed his mass. The Crusher changes his mass only in a specific frame of reference, only related to the speed he has in that frame of reference, without touching speeds and mass that he has in a broader frame of reference - those observing in a broader frame of reference must separate Crusher's momentum in to sum of momenta in different frame of reference and isolate only the one in which Crusher is changing his mass. That's my solution to the problem which you saw first. 

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

On 4.6.2023 at 9:35 PM, alder24 said:

From the outside's reference frame there is a problem that you noted. If the momentum is conserved, then his speed would be 2320 kgm/s  = (80 kg / 2) * (x+28) m/s ; x = 2320 kgm/s / (80 kg / 2) - 28 m/s ; x = 88 m/s - that's the total speed the Crusher should have after his mass change that an outside observer expects. But that not the case, an outside observer would see the Crusher moving at 28 + 2 = 30 m/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.

[alder24]

43 minutes ago, Thorneater said:

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.

Not really, the Crusher would lose all of car's momentum and stay behind due to air drag, so in reality relative to the Crusher he would consider the car to be in motion away from him, the person inside the car would see himself stationary, while considering the Crusher to be moving away from him. They would both consider each other in motion, relative to themself.

55 minutes ago, Thorneater said:

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.

And F-iron breaks the laws of physics, as changing mass doesn't affect ones density ρ=m/v. So we already have a clear example of storing mass acting selectively. So we know F-iron doesn't store "all types" of mass. I've just extended it to frame of reference. In the case of F-iron, mass just doesn't work like in physics.

 

Spoiler

Brandon Sanderson

Chapter Six

The fight in the ballroom

From the early days of the Mistborn books, I'd been planning how an Allomantic gunfight would go down. I felt it the next evolution in what has been stylistically a big part of these books.

There is a fine line to walk in a lot of these sequences. I've made something of a name for myself in the fantasy world by attempting to mix some scientific reasoning with my magic systems. At the same time, Allomancy was designed precisely with action sequences in mind. I wanted them to be powerful and cinematic—and a cinematic fight sequence is often at odds with realism. (Watch two people who really know what they're doing fight with swords sometime, then watch any fight sequence in a film. Most of the time, the film sequences stray far from what would really happen.)

So, as I said, I walk a line. Sometimes, there are things I just can't do because they violate what I've set up as the rules of the world. Other times, I design the setting and nature of the fight specifically to allow for certain types of cinematic sequences. One thing I like a lot about Wax’s abilities is the power he has to manipulate his weight. There's some realism to what he does—for example, increasing his weight doesn't make him fall more quickly, but it allows him to do some powerful things while falling. Destroying the chandeliers is an example.

At the same time, I acknowledge that the weight manipulation aspect of Feruchemy is one of its more baffling powers, scientifically. Is he changing his mass? If so, he should become more dense, which I don't actually make the case when it plays out in fights. (Otherwise, increasing his weight enough would make him impervious to bullets.) So, if it's not mass manipulation, is it gravity manipulation, like Szeth and Kaladin do? Well, again, not really—as when his weight increases, his strength and ability to uphold that weight increase as well. Beyond that, Wax can't make himself so light that he has no weight at all.

So . . . well, at this point, the ability to explain it scientifically breaks down. I do like what it does, but I have to set its boundaries and stick to them—and accept that some of what's going on is irrational. (And don't get me started on what should really be happening scientifically when Wayne speeds up time.)

Footnote: Brandon has stated that iron Feruchemy works by manipulating the Higgs field.
The Alloy of Law Annotations (March 14, 2014)

 

Spoiler

Phantine

I actually asked Peter Ahlstrom (who tends to handle math and magic system interactions with physics for Team Sanderson) about this a little while ago

A couple of friends and I are discussing if the iron feruchemy causing changes in speed is a retcon (since there's a mention in AoL that "increasing his weight manyfold would not affect his motion"), or if the effect is just more complicated (like only causing an instant change in speed if Wax changes weight while actively pushing on something).

Are you willing to weigh in on that, or is it just something we shouldn't be thinking too hard about?

Thanks

And his response was

I just don't know the answer to this question.

So I personally think the explanation is either 'Brandon thought it would be cooler for shifting your weight to change your velocity, and forgot he had mentioned it a couple times' or 'this is Wax's twinborn perk'. I'm leaning towards the latter, since the person who writes the magic system summaries at the end of the book specifically interrogated Wax about the effects, and mentioned she specifically was interested in his very unusual power combination.

As for the density thing, there is an explicit mention that you appear to get stronger when tapping, but only to the extent that you can still stand up and walk around - you still have more difficulty moving around overall. So (to pull out random numbers), if you're at 200% normal mass, you have 180% normal strength, and at 50% mass you have 60% normal strength. That means Wax habitually going around at 75% weight so he's 'light on his feet' makes sense - even if he's weaker overall, he's proportionally stronger.

The way I personally think about things for bullets or whatever, anything 'inside' the body (where 'inside' is defined in the same way that pushing/pulling metal 'inside' the body uses it) interacts with your body as if it were normal. So tapping iron doesn't cause your ultra-massive blood to be impossible for your heart to pump, but it also doesn't prevent a bullet from passing through your flesh. That seems to be consistent with how it's portrayed in the books.

Brandon Sanderson

Just a note: in the quote of mine above, I was trying (I believe) to find a way for Wax to indicate that weight doesn't influence the rate at which he falls. IE, acceleration in regards to gravity. It's tough, and I made the call (perhaps incorrectly) not to use modern physics terminology in the W&W books. It has been very hard then to explain:

1). Wax changing his weight doesn't change the pull of gravity on him, or the rate at which he falls. 2) He DOES follow the laws of conservation of momentum.

My talking around these things has let me to tie a few paragraphs in knots.

General Reddit 2016 (Feb. 19, 2016)

 

Spoiler

Questioner

Does Iron store mass or weight?

Brandon Sanderson

Excellent question. The thing is it really does involve mass, but I’m breaking some physics rules, basically. I have to break a number of physics rules in order to make Magic work in the first place. Those whole laws of Thermodynamics, I’m like “You are my bane!” (laughter) But I try to work within the framework, and I have reasonings built up for myself, and some of them have to be kind of arbitrary. But the thing is, it does store mass if you look at how it interacts, but when a Feruchemist punches someone, you’re not having a mass transference of a 1000 pounds transferring the mass into someone else.

So there are a few little tweaks. You can go talk to Peter, because Peter has the actual math. Oh Peter’s back there. Peter is dressed up as Allomancer Jak from the broadsheet. In fact we’re giving some out broadsheets, aren’t we Peter. So when you come through the line, we’re giving out Broadsheets. Please don’t take fifty—I think we might have enough for everybody. The broadsheets are the newspaper from the Alloy of Law time. It’s an inworld newspaper. It’s actually reproduced in the book in four different pages, and we put it together in one big broadsheet.

So anyway, you can talk with him, he’s got more of the math of it. I explained the concept to Peter and he’s better with the actual math, so he said “We’ll figure it out.”

Alloy of Law release party (Nov. 7, 2011)

 

[Thorneater]

9 hours ago, alder24 said:

Not really, the Crusher would lose all of car's momentum and stay behind due to air drag, so in reality relative to the Crusher he would consider the car to be in motion away from him, the person inside the car would see himself stationary, while considering the Crusher to be moving away from him. They would both consider each other in motion, relative to themself.

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.

9 hours ago, alder24 said:

And F-iron breaks the laws of physics, as changing mass doesn't affect ones density ρ=m/v. So we already have a clear example of storing mass acting selectively. So we know F-iron doesn't store "all types" of mass. I've just extended it to frame of reference. In the case of F-iron, mass just doesn't work like in physics

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)

[therunner he/him]

24 minutes ago, Thorneater said:

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)

Except that would not work. If the mass of the particles is now higher, bullet penetration would go down.
I did some numbers on it in one of previous threads, and if he just ~15x his mass, even modern bullets would not penetrate more than ~3 cm or something like that.

Which since he is storing all the time, he should be able to do for brief moments of being bullet proof in fight. But it is not happening, and per WoBs it cannot happen.
So Iron Feruchemy breaks a lot of things.

Edit: @alder24

Quote

Not really, the Crusher would lose all of car's momentum and stay behind due to air drag, so in reality relative to the Crusher he would consider the car to be in motion away from him, the person inside the car would see himself stationary, while considering the Crusher to be moving away from him. They would both consider each other in motion, relative to themself.

Consider it in vacuum then. Thorneater has a point, you cannot conserve momentum like Wax describes it in different reference frames.

If in frame A, Wax is moving at v_A = 10 m/s , and he drops his weight to 1/10, then his speed should increase to v_A2 = 100 m/s to conserve momentum.

But an observer frame B which is moving at 5m/s with respect to frame A, and from which perspective Wax is moving only at v_B = 5 m/s, would expect that after dropping his weight to 1/10, he should start moving at v_B2 = 50m/s to preserve momentum, which is just 55m/s in frame A.

So there is discrepancy there, and Iron Feruchemy is breaking principle of relativity, and we have a momentum deficit to explain. It would work far better if Iron Feruchemy stored momentum and not weight, which would also make it an interesting counterpart for Steel which stores speed or velocity.

@Thorneater good point on the issue with different reference frames! I guess there must be some different kind of relativity in Cosmere that takes into account Investiture for it to work.
At the end of the day though, it is fictional magic, and it will most likely never be actually consistent, despite best attempts. It will look consistent, unless you poke it too hard.

Edited June 6, 2023 by therunner

[Thorneater]

55 minutes ago, therunner said:

Except that would not work. If the mass of the particles is now higher, bullet penetration would go down.
I did some numbers on it in one of previous threads, and if he just ~15x his mass, even modern bullets would not penetrate more than ~3 cm or something like that.

sounds interesting. Do you remember the name of this thread?

56 minutes ago, therunner said:

It would work far better if Iron Feruchemy stored momentum and not weight, which would also make it an interesting counterpart for Steel which stores speed or velocity.

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.

[therunner he/him]

56 minutes ago, Thorneater said:

sounds interesting. Do you remember the name of this thread?

Sadly no, probably one of the vs. threads.
But roughly the argument comes down to old Newton approximation of impact depth (https://en.wikipedia.org/wiki/Impact_depth). So basically once the human body has density of the same order as the bullet, bullet can penetrate only as about as far as its length.
Since human body has density of ~1g/cm^3 and lead has about ~12 g/cm^3, increasing mass 15x means that bullet basically goes only its length inside the body. Still painful, but no life-threatening.

56 minutes ago, Thorneater said:

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.

True, perhaps storing magnitude of the momentum then? That would clear up that complication.

But it still has to be the somehow tied to the reference frame of planet/solar system/galaxy, which just makes it more complicated not less :/

Edited June 6, 2023 by therunner

[alder24]

3 hours ago, therunner said:

Thorneater has a point, you cannot conserve momentum like Wax describes it in different reference frames.

If in frame A, Wax is moving at v_A = 10 m/s , and he drops his weight to 1/10, then his speed should increase to v_A2 = 100 m/s to conserve momentum.

But an observer frame B which is moving at 5m/s with respect to frame A, and from which perspective Wax is moving only at v_B = 5 m/s, would expect that after dropping his weight to 1/10, he should start moving at v_B2 = 50m/s to preserve momentum, which is just 55m/s in frame A.

So there is discrepancy there, and Iron Feruchemy is breaking principle of relativity, and we have a momentum deficit to explain. It would work far better if Iron Feruchemy stored momentum and not weight, which would also make it an interesting counterpart for Steel which stores speed or velocity.

Right, there is. I agree. I realized this later when thinking about it more, did some math and edited the post and proposed a solution. That part about "find me an example" doesn't matter anymore, as I've found it myself.

 

1 hour ago, therunner said:

Sadly no, probably one of the vs. threads.
But roughly the argument comes down to old Newton approximation of impact depth (https://en.wikipedia.org/wiki/Impact_depth). So basically once the human body has density of the same order as the bullet, bullet can penetrate only as about as far as its length.
Since human body has density of ~1g/cm^3 and lead has about ~12 g/cm^3, increasing mass 15x means that bullet basically goes only its length inside the body. Still painful, but no life-threatening.

This one?

Spoiler

On 17.03.2023 at 10:05 AM, therunner said:

So, I did a little digging into ballistics, and actually becoming bulletproof is easier then I thought. (This was the primary source for math http://panoptesv.com/RPGs/Equipment/Weapons/Projectile_physics.php)

Humans are basically water, even average tissue density is like ~1.098 g/cm^3, so barely above water. The equations for penetration depth are linear in sectional density (so we can treat them as linear in volume density but multiplied by unit of length).
Since, eve 50. cal sniper rifle basically disintegrates after just 3 feet (~91 cm) in water ( Mythbusters episode), that means that increasing density ~93x times would make you bullet proof to 50. cal sniper rifle (well, it would penetrate ~1cm).
Interestingly enough, slower bullets actually get further in, but become non-lethal much sooner.

Some experimented with shooting into sand (density at most 2g/cm^3, https://www.theboxotruth.com/threads/the-box-o-truth-7-the-sands-o-truth.299/ ).
There no bullet penetrated more than 6 inches (~15 cm). So in this case tapping at ~27x increase makes you basically bulletproof (penetration at most 1cm). This assumes the person used the densest sand they could find, using average value (1.7g/cm^3) would bring the tapping needed down to ~23x.

I would assume that in some sense tissue would behave somewhere between water and sand (being more viscous than water, but less then sand in container), so anywhere between 23-93x tapping makes your soft tissue bullet proof up to 50. cal sniper rifles. Bones would become bullet proof far sooner. And this does not even consider the elastic properties of tissue, which would bring it down by some amount.

So at 2-3x tapping bullets would still pass through, but some just barely (I mean even IRL bullets can get stuck in wounds). At 10x tapping bullets would get about 3 cm in at most.
Someone who is on the bulkier side could effectively use this as emergency armor then.

 

[therunner he/him]

2 hours ago, alder24 said:

This one?

  Reveal hidden contents

 

 

Yep, thank you!
So compared to the 'naive' scaling due Newton, 'bulletproofiness' would be actually improving even faster, most likely due to the complex interactions with the environment (e.g. hydrodynamics and what not).

[Heilven he/him]

Ah Iron Feruchemy, my old nemesis. I think I've been on the path to discovering the issue with different reference frames before, but I had to stop thinking about it to save my sanity. Good work on what you've found though.

I think a major part of our issue is that we have no physical basis to draw on for changing your mass. It's not possible to just "change" your mass in the real world, so we really can't even be sure that our equations are correct. Take for instance, m1v1 = m2v2. This comes from considering that you are "ejecting" mass off of an object, or perhaps two objects coming together and exchanging mass. The full equation is more like m1v1 + m2v2 = m1'v1'+m2'v2' . We don't have a good basis for saying that Iron feruchemy follows this example. We can imagine taking our mass and attaching it/converting it to investiture, which is sort of similar to something like black body radiation, or perhaps any kind of decay. If we were to assume that the investiture actually has momentum, meaning that it can exert force (which makes sense, seeing as it clearly can do that) then really we shouldn't need to follow momentum conservation at all. We do, so we can follow that the investiture helps solve for our issues. Except that, of course, you lose investiture when storing and gain it when tapping. That's what makes this solution not work for energy conservation. Tapping mass doesn't give you energy, you actually lose more kinetic energy from slowing down than you gain from having an increased mass. Or no, I am wrong. In the case of momentum it actually works.

If an iron feruchemist were to store mass, an outside observer not moving with the planet would expect the iron feruchemist to go shooting up into space. If the investiture took some of the momentum in every direction, then the feruchemist could observe no change to their velocity. When tapping mass, they could be given momentum back in those directions, fixing our issues again. And as momentum is a linear transformation, momentum would actually be conserved, unlike energy.

The other issue with the two reference frames problem is that we are assuming that Galilean relativity even holds. The process of exchanging mass with the spiritual realm might not actually be upheld by Galilean relativity. I think if we assume that the investiture can provide a force on the iron feruchemist to deal with this problem, then galilean relativity is actually fine. All of the forces work themselves out.

There is a different problem however. If momentum is truly conserved, then we would expect the iron feruchemist to feel no force when storing or tapping mass (They might still in the other directions in order to conserve their velocity compared to the system, but in the direction of their velocity this argument holds). There is no change to their momentum, so they should feel no force. But there is a change in velocity, and thus an acceleration. But you cannot have an acceleration without a force, it's simply not possible. This is at the core of the problem with iron feruchemy, the idea that momentum does not change, yet there is a change in velocity. The idea of mass changing makes no physical sense, and so I'm not sure if we have a model capable of making sense of it.

[IlstrawberrySeed]

On 6/4/2023 at 11:35 AM, alder24 said:

Well, that's my explanation of this. You did identify the problem correctly - in different reference frames, the conservation of momentum enforces enormous gains/losses of speed, which aren't observable, thus momentum can't be conserved. But we know momentum must be conserved, so a change in mass should launch people into space. That doesn't happen either. So we have a problem. A paradox? Right? Not really. My explanation to this is what I have written above in the edited section - Crusher's frame of reference, his perspective, takes priority. His frame of reference is the one in which his change of mass is happening. That's the only momentum affected by his change. So an outsider observing the train passing by would say the Crusher has two separate and the Crusher only changed his mass in one of them, the inside one, related to his steel push, not to the train movement. Basically our Crusher isolated both movements and changed his mass only in one of them, without touching the other. Weird? Not really, he isn't aware of his other movement, from his reference frame he is moving with the speed of 1 m/s in the train, while the world outside is moving with a whooping speed of 28 m/s, like a treadmill. But from his point of view, he doesn't have that train related momentum at all, therefore there is no change to the mass of that momentum. Nothing changes there. Different frame of reference and the Crusher's perspective is all that matters when he changes mass. All that an outside observer needs to do is to separate the total momentum of the Crusher into the sum of momenta, and isolate one the one in which the Crusher changed his mass. The Crusher changes his mass only in a specific frame of reference, only related to the speed he has in that frame of reference, without touching speeds and mass that he has in a broader frame of reference - those observing in a broader frame of reference must separate Crusher's momentum in to sum of momenta in different frame of reference and isolate only the one in which Crusher is changing his mass. That's my solution to the problem which you saw first. 

And it's supported by WoBs too, like the one copied above: "for time bubbles the frame of reference and the perspective matters a lot". Now my explanation begs a question - can that Crusher change his frame of reference, his perspective, to that of the outside observer's? Can he stand on the roof of the train, thinking really hard that the outsider's frame of reference is his now, and he is moving with 28 m/s, then store his mass down to 1 kg launching himself forward with an unrealistic speed of 2240 m/s (Mach 6.5) ahead of the train? Can he do that? The WoB posted above said that a time bubble's anchor can be changed based on Slider's perspective, a Slider can learn to anchor it to himself, so maybe a Crusher, or any F-iron Feruchemist, can learn to change his perspective and a frame of reference to store mass in that frame of reference? I don't think this is the case, because that would go into ridiculous extremes in which Feruchemist could store his mass in the frame of reference related to Scadrial's orbit around their sun and launch himself into space with impossible speeds. Brandon's magic is all about limitations, and having a person who can launch himself into space with whatever speeds he wants just by changing his perspective would be too ground breaking. But on the other hand we have Windrunners, who do exactly that, and Sliders and Pulsers who can anchor their speed bubbles to them based on perspective, so why not Skimmers too? Maybe it would be as said in the WoB about time bubbles - depending on the size/mass of the object they're on, they can't change their mass in frame of reference outside of that object (like I was kind of arguing in the section before the edit), and thus their lock to that frame of reference. It's an interesting idea that may be worth asking. Or at least we should ask Peter how Crusher's momenta and speeds behaves in different reference frames - maybe Brandon and Peter aren't even aware of that and you're the first one who noticed that problem.

 

I hope this explains everything. I hope it's clear and easy to understand. And I hope I haven't made any glaring mistakes.

That then begs the question of what happens when you change your frame of refrence? If your crasher is steelpushing backwards down a train with the car doors open, and drops mass midway, then what happens when they are no longer in the train? (Would they be flung back, toward the train?) What if they instead stop filling as soon as the "frame swap" happens?

13 hours ago, therunner said:

Except that would not work. If the mass of the particles is now higher, bullet penetration would go down.
I did some numbers on it in one of previous threads, and if he just ~15x his mass, even modern bullets would not penetrate more than ~3 cm or something like that.

Which since he is storing all the time, he should be able to do for brief moments of being bullet proof in fight. But it is not happening, and per WoBs it cannot happen.
So Iron Feruchemy breaks a lot of things.

Edit: @alder24

Consider it in vacuum then. Thorneater has a point, you cannot conserve momentum like Wax describes it in different reference frames.

If in frame A, Wax is moving at v_A = 10 m/s , and he drops his weight to 1/10, then his speed should increase to v_A2 = 100 m/s to conserve momentum.

But an observer frame B which is moving at 5m/s with respect to frame A, and from which perspective Wax is moving only at v_B = 5 m/s, would expect that after dropping his weight to 1/10, he should start moving at v_B2 = 50m/s to preserve momentum, which is just 55m/s in frame A.

So there is discrepancy there, and Iron Feruchemy is breaking principle of relativity, and we have a momentum deficit to explain. It would work far better if Iron Feruchemy stored momentum and not weight, which would also make it an interesting counterpart for Steel which stores speed or velocity.

@Thorneater good point on the issue with different reference frames! I guess there must be some different kind of relativity in Cosmere that takes into account Investiture for it to work.
At the end of the day though, it is fictional magic, and it will most likely never be actually consistent, despite best attempts. It will look consistent, unless you poke it too hard.

I don't think observational issues are nearly as important as what happens when one switches references, literally (leaving the train) or mentally (anchoring to the sun).

3 hours ago, Heilven said:

Ah Iron Feruchemy, my old nemesis. I think I've been on the path to discovering the issue with different reference frames before, but I had to stop thinking about it to save my sanity. Good work on what you've found though.

I think a major part of our issue is that we have no physical basis to draw on for changing your mass. It's not possible to just "change" your mass in the real world, so we really can't even be sure that our equations are correct. Take for instance, m1v1 = m2v2. This comes from considering that you are "ejecting" mass off of an object, or perhaps two objects coming together and exchanging mass. The full equation is more like m1v1 + m2v2 = m1'v1'+m2'v2' . We don't have a good basis for saying that Iron feruchemy follows this example. We can imagine taking our mass and attaching it/converting it to investiture, which is sort of similar to something like black body radiation, or perhaps any kind of decay. If we were to assume that the investiture actually has momentum, meaning that it can exert force (which makes sense, seeing as it clearly can do that) then really we shouldn't need to follow momentum conservation at all. We do, so we can follow that the investiture helps solve for our issues. Except that, of course, you lose investiture when storing and gain it when tapping. That's what makes this solution not work for energy conservation. Tapping mass doesn't give you energy, you actually lose more kinetic energy from slowing down than you gain from having an increased mass. Or no, I am wrong. In the case of momentum it actually works.

If an iron feruchemist were to store mass, an outside observer not moving with the planet would expect the iron feruchemist to go shooting up into space. If the investiture took some of the momentum in every direction, then the feruchemist could observe no change to their velocity. When tapping mass, they could be given momentum back in those directions, fixing our issues again. And as momentum is a linear transformation, momentum would actually be conserved, unlike energy.

The other issue with the two reference frames problem is that we are assuming that Galilean relativity even holds. The process of exchanging mass with the spiritual realm might not actually be upheld by Galilean relativity. I think if we assume that the investiture can provide a force on the iron feruchemist to deal with this problem, then galilean relativity is actually fine. All of the forces work themselves out.

There is a different problem however. If momentum is truly conserved, then we would expect the iron feruchemist to feel no force when storing or tapping mass (They might still in the other directions in order to conserve their velocity compared to the system, but in the direction of their velocity this argument holds). There is no change to their momentum, so they should feel no force. But there is a change in velocity, and thus an acceleration. But you cannot have an acceleration without a force, it's simply not possible. This is at the core of the problem with iron feruchemy, the idea that momentum does not change, yet there is a change in velocity. The idea of mass changing makes no physical sense, and so I'm not sure if we have a model capable of making sense of it.

This is true, but I don't know that it is an issue. Sure, a scientist needs to keep track of what frame of reference the person is in, but it shouldn't be that difficult.
 

 

If changing frame of reference while filling/tapping iron switches your delta momentum to match the new frame of reference with no additional forces, then they can hop off and on moving objects much more effectively.

[therunner he/him]

23 minutes ago, IlstrawberrySeed said:

I don't think observational issues are nearly as important as what happens when one switches references, literally (leaving the train) or mentally (anchoring to the sun).

It is not 'observational issue', it fundamentally means that momentum is not conserved. It is only conserved in some preferred reference frame, however that alone breaks even just Galilean relativity, which means that not even Newtonian physics is applicable.

So basically it means that when it comes to Iron Feruchemy, we can throw away literally any IRL analogue, since Iron Feruchemy breaks the most basic of assumptions (that different observers agree on what is going on ).

E.g. for person on train, momentum is conserved, for person off-train momentum is not conserved, and the only way to square that circle is well, magic.

Edited June 6, 2023 by therunner

[IlstrawberrySeed]

6 minutes ago, therunner said:

It is not 'observational issue', it fundamentally means that momentum is not conserved. It is only conserved in some preferred reference frame, however that alone breaks even just Galilean relativity, which means that not even Newtonian physics is applicable.

So basically it means that when it comes to Iron Feruchemy, we can throw away literally any IRL analogue, since Iron Feruchemy breaks the most basic of assumptions (that different observers agree on what is going on ).

E.g. for person on train, momentum is conserved, for person off-train momentum is not conserved, and the only way to square that circle is well, magic.

Ah. And how exactly would storing momentum instead help? It could be that they thin k it stores mass, when it actually stores mass and momentum, and the magic delta mass doesn't effect the magic delta momentum and vice versa.

[cometaryorbit]

I don't think what F-Iron stores is really mass in the usual sense.

I also think that the attempt to make it more like mass than weight, to synergize with Wax's Pushing, opened more problems than it solved*; if it just was "how much gravity affects you" I think none of these problems would exist.

I think to make it work with the observed behavior, it needs to be heavily Spiritual (ie pure magic).

It has to do something odd, like what's actually being stored is a kind of Spiritual spiritweb variable for your overall mass, which doesn't really affect things that happen on a smaller scale (like bullet impact depth issues); or it only affects your effective mass for forces like gravity and Steelpushes, not for ordinary collisions;  or something like that.

The second one would be really weird, but I think it'd explain what we see quite well. It'd be like decoupling gravitational from inertial mass, except that Steelpushes/Ironpulls work off gravitational mass. That would make bullets pierce high-weight people just fine, since impact depth is an inertia/momentum thing.

The cosmere likely does have a preferred frame of reference IMO - it would make FTL easier, and the Cognitive Realm might provide one - but that doesn't explain the bullet piercing/impact depth issues, or the lack of super powerful punches, IMO.

*I wouldn't be surprised if Era 1 was written with the idea that it's just (gravitational) weight. Sazed says it is in WoA, and in HoA he fights with it by tackling and dropping his fists (boosted by gravity) not by super punching. When he uses it as an anchor (like the gates of Luthadel) he's touching the ground, so gravitational weight would help there.

Edited June 7, 2023 by cometaryorbit

[IlstrawberrySeed]

1 hour ago, cometaryorbit said:

The cosmere likely does have a preferred frame of reference IMO - it would make FTL easier, and the Cognitive Realm might provide one - but that doesn't explain the bullet piercing/impact depth issues, or the lack of super powerful punches, IMO.

Wouldn't it? As soon as it splits the skin, the frame of reference of the bullet is the body, and therefore inducted into higher mass.

[Underwater_Worldhopper he/him]

I have no idea what's going on in this thread since I tend to just ignore anything concerning F-Iron, but there was something someone said that I thought I should just throw in here, without reading the actual conversation, just to see what happens.

Anyway, the person's theory was that F-Iron doesn't change your mass at all; It only changes what the world around you thinks your mass is. So you could become heavier and do all the conservation of momentum tricks that Wax performs without ever actually gaining or losing mass. That will be all, continue whatever was going on here

[Argenti he/him]

please don't, Alder doesn't need anymore grey hairs

[AirsickAviar he/him]

@alder24 actually the way f-iron can't ever be exactly zero almost makes sense at a quantum level for me. Like how if one could store body heat, I would imagine it would never be able to be zero entirely. There is no absolute zero, even empty space has stuff appearing and disappearing, energies. Nature abhors a vacuum/nothing. Even with nothing there is almost always something, even if little. That's what I see with this logic. And now I just realized how fun it would have been to have a f-body heat power, lol.

[DrPhysics he/him]

On 6/6/2023 at 1:23 AM, therunner said:

If in frame A, Wax is moving at v_A = 10 m/s , and he drops his weight to 1/10, then his speed should increase to v_A2 = 100 m/s to conserve momentum.

But an observer frame B which is moving at 5m/s with respect to frame A, and from which perspective Wax is moving only at v_B = 5 m/s, would expect that after dropping his weight to 1/10, he should start moving at v_B2 = 50m/s to preserve momentum, which is just 55m/s in frame A.

There's a big piece of information that is missing from this discussion. You are all forgetting that the mass has to come from/go to somewhere,  and that some where has a speed. If you set that speed so that it is zero in what is considered "at rest" for the feruchemist,  it fixes all of these problems. 

The Ugly Math Way

Let's say the crasher has mass m and increases his mass by dm (getting lighter just changes the sign to minus). You get the momentum equation:

m*v_A1 = (m +dm) v_A2

But there's actually a hidden term and the full equation is:

m*v_A1+dm*0= (m+dm)v_A2

Now let's shift to reference frame moving at a speed -v' relative to the first, so that v_B1 = v_A2 + v', and anything at rest in the original frame now has a speed v'

The new momentum term before the weight change is actually:

mv_B1+dm*v'

Substitute in v_B1:

m(v_A1+v')+dm*v' = m*v_A1+m*v'+dm*v'= m*v_A1+(m+dm)v'

But, we know from our first equation that

m*v_A1 = (m +dm) v_A2

So subbing that in gives:

(m +dm) v_A2 +(m+dm)v' = (m+dm)*(v_A2+v') =(m+dm)v_B2

which is exactly what we'd expect as a new velocity.

 

Conceptual Examples

Lets take the example of a person riding a train. If they suddenly increase their mass, but all of that mass is traveling at the speed of the train, they arent going to chang speeds. If you drop a lot of mass going the speed of the train, you still aren't going to speed up.  (What happens to your speed if you pick up or put down a heavy piece of luggage on a train? Nothing).

 

Now, say you are running forward on the train and reduce your weight. To get that lost mass back to the speed of the train, you have to push backward on it, which pushes you forward, speeding you up.

[therunner he/him]

7 hours ago, DrPhysics said:

There's a big piece of information that is missing from this discussion. You are all forgetting that the mass has to come from/go to somewhere,  and that some where has a speed. If you set that speed so that it is zero in what is considered "at rest" for the feruchemist,  it fixes all of these problems.

Yeah, that seems to work, good catch.

Though it opens a new can of worms, in that the Investiture stores inside the metalmind have 'momentum' with respect to other observers, but this momentum is always exactly zero with respect to Feruchemist tapping.
And this Investiture momentum does not interact with anything else but the Feruchemist (e.g. Wax running into an obstacle, ignores any 'Investiture' momentum of the metalminds).

[DrPhysics he/him]

1 hour ago, therunner said:

the Investiture stores inside the metalmind have 'momentum' with respect to other observers, but this momentum is always exactly zero with respect to Feruchemist tapping

The investiture itself doesn't have to have momentum. We're dealing with an infinite energy supply that can increase/ decrease mass at will.

Whatever that process is, we just have to imagine that it creates mass which is at rest in the reference frame that the feruchemist considers at rest, not that the investiture has momentum already.

 

Momentum is only conserved when there are no external forces, and that process could easily involve an external force.

[Koloss17 She/They]

This might be just the thread to ask this question, or this might be yet another tangent.

Dumbing things down for the people at home, and also keeping in mind that I’m a biology student, not a physics student, what happens to your movement when storing? I would think you get some amount faster due to muscles needing to push less than usual, but I also wouldn’t be surprised if the magic be weirder than that.