Issues with Feruchemical Iron

[Heilven he/him]

I have an issue with some of the fundamental physics behind F-Iron. Namely, what it actually does and how it interfaces with Conservation of Energy and Momentum.
As per the Coppermind, "Iron is used to store or retrieve (gain) physical mass. This is accomplished by changing the Skimmer's mass, not by changing the effect of gravity on the Skimmer, i.e. it does not modify weight directly ... The law of conservation of momentum still exists when using iron Feruchemy, so while tapping weight doesn't significantly increase the speed of falling (not considering air resistance), decreasing one's weight to half will double one's speed ... Feruchemical iron interferes with an individual's interaction with the Higgs field".

I want to break this down step by step, because I think there are pretty big fundamental problems with this explanation.

So, Iron changes the user's mass, not by changing the effect of gravity, Conservation of Momentum still applies.
If this were truly the case, (and it must be to see the effects we see) than F-Iron users would not fall slower when storing mass. This is evidently obvious by facts we know in real life, two objects of different mass fall at the same speed under the same gravitational conditions.
F = GMm/r^2, dp/dt = F, ma = m GM/r^2.
Mass cancels out of this equation, and has no effect on the acceleration felt. For a feruchemist to fall slower when storing weight, there would need to be a distinction between Inertial mass and Gravitational mass.
The relativistic explanation says that these masses are the same, meaning that iron feruchemy must be changing the effect of the gravitational field on a mass (ie gravitational acceleration) otherwise the change in mass would have no effect on the force felt due to gravity.
So either we go with the Newtonian explanation (mi and mg) or the Standard Theory explanation (only one m, but you feel the gravitational force differently). 

This causes problems with other effects. We can be very certain that F-Iron does effect mass, as we see Wax is able to push harder while tapping iron. He clearly requires more force to be accelerated when tapping iron, and less while storing.

F-Iron also cannot change both mass and gravity, as that would once again cancel any effect on falling speed.

There also might be an issue with conservation of energy as well, but I would have to do the math to find out. Conservation of momentum is fine under the canon explanation, but energy changes by the square of your speed, so a skimmer storing weight will require kinetic energy. This could theoretically be explained by just stealing energy from the environment like

Spoiler

what Radiants do

(Extremely minor SA spoilers) but that would be a bit counter to the idea of End-Neutral Feruchemy.

Please let me know if there's a hole in my logic or math somewhere or if I'm missing something, this is going to bug me for a while.

[alder24]

It's magic, it doesn't make sense.

23 minutes ago, Heilven said:

If this were truly the case, (and it must be to see the effects we see) than F-Iron users would not fall slower when storing mass. This is evidently obvious by facts we know in real life, two objects of different mass fall at the same speed under the same gravitational conditions.
F = GMm/r^2, dp/dt = F, ma = m GM/r^2.
Mass cancels out of this equation, and has no effect on the acceleration felt. For a feruchemist to fall slower when storing weight, there would need to be a distinction between Inertial mass and Gravitational mass.

They fall slower not because of gravitational acceleration, which doesn't change for them, but because of terminal velocity, which do change when they change mass (WoA Sazed did it). vt=sqrt(2mg/ρACd). Lower the mass, lower terminal velocity.

31 minutes ago, Heilven said:

There also might be an issue with conservation of energy as well, but I would have to do the math to find out.

There is an issue when changing weight mid fall, energy is disappearing or appearing, I've done the math, but it can be explained in few ways, like by Investiture - storing weight gives away energy (Investiture) to metalminds, tapping pulls energy (Investiture) from metalminds. Investiture is another form of matter/energy. Or that energy is simply transferred from Ek to Ep, and there is no loss of energy. There was a discussion about conservation of momentum and energy during freefall, where I did the math on energy, you can read it, but it's from Cosmere forum, so full Cosmere spoilers possible (no idea what was there, mostly about Skimmer from page 3)

Spoiler

Here is the post with the math:

https://www.17thshard.com/forum/topic/115297-how-busted-is-compounding/?do=findComment&comment=1440933

Here is the whole topic if you're interested (but I think the relevant part of discussion about storing weight starts at page 3)

https://www.17thshard.com/forum/topic/115297-how-busted-is-compounding

 

 

WoBs on F-iron:

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)

 

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)

 

[Heilven he/him]

Quote

They fall slower not because of gravitational acceleration, which doesn't change for them, but because of terminal velocity, which do change when they change mass (WoA Sazed did it). vt=sqrt(2mg/ρACd). Lower the mass, lower terminal velocity.

I have considered this possibility, but I find it very difficult to believe. Using that equation I ran a couple different numbers and it doesn't add up. I need to look at the exact chapter from WoA to see how much weight Sazed was storing, but we can do some basic calculations beforehand.
Ignoring air resistance, to fall from 100 meters (likely far further than Sazed actually fell) it takes 4.518 seconds to reach the ground. Upon hitting the ground, you would be moving at 44.276 m/s. An 80kg person has a terminal velocity of 101.71 m/s, so terminal velocity doesn't even come into effect here. In fact, you would need to be 15kg before your terminal velocity (44m/s) would be lower at all. This would be storing a massive portion of your mass, 81.5% of it.

Okay I grabbed the book and read the chapter, it definitely states that you fall slower due to air resistance. It doesn't seem like it has anything to do with terminal velocity though, since you are unlikely to fall far enough to reach that kind of speed. I guess the main advantage would be having lower kinetic energy, therefore hitting the ground with far less energy. That's exactly how it is described in the chapter.

Okay and I spent a long time looking over your energy math and I think your conclusion just doesn't work out. Your math was a little bit weird, but as soon as you begin to tap weight you should lose 317836.152 J. That energy has to go somewhere, and it can't be either KE or PE, those are both accounted for already. The reverse is true for storing weight, you should actually gain energy. If you began storing 40kg of your mass while moving you would suddenly gain a ton of kinetic energy from increasing your speed. Beyond the fact that you could create infinite energy by storing up a bunch of mass, stopping, and then just gaining height. By tapping that mass and jumping off, you will land with more kinetic energy than you expended walking to the higher point. Iron feruchemy completely breaks conservation of energy for a variety of reasons. I honestly don't see a good way to get away from that.

[IlstrawberrySeed]

14 minutes ago, Heilven said:

I have considered this possibility, but I find it very difficult to believe. Using that equation I ran a couple different numbers and it doesn't add up. I need to look at the exact chapter from WoA to see how much weight Sazed was storing, but we can do some basic calculations beforehand.
Ignoring air resistance, to fall from 100 meters (likely far further than Sazed actually fell) it takes 4.518 seconds to reach the ground. Upon hitting the ground, you would be moving at 44.276 m/s. An 80kg person has a terminal velocity of 101.71 m/s, so terminal velocity doesn't even come into effect here. In fact, you would need to be 15kg before your terminal velocity (44m/s) would be lower at all. This would be storing a massive portion of your mass, 81.5% of it.

Okay I grabbed the book and read the chapter, it definitely states that you fall slower due to air resistance. It doesn't seem like it has anything to do with terminal velocity though, since you are unlikely to fall far enough to reach that kind of speed. I guess the main advantage would be having lower kinetic energy, therefore hitting the ground with far less energy. That's exactly how it is described in the chapter.

Okay and I spent a long time looking over your energy math and I think your conclusion just doesn't work out. Your math was a little bit weird, but as soon as you begin to tap weight you should lose 317836.152 J. That energy has to go somewhere, and it can't be either KE or PE, those are both accounted for already. The reverse is true for storing weight, you should actually gain energy. If you began storing 40kg of your mass while moving you would suddenly gain a ton of kinetic energy from increasing your speed. Beyond the fact that you could create infinite energy by storing up a bunch of mass, stopping, and then just gaining height. By tapping that mass and jumping off, you will land with more kinetic energy than you expended walking to the higher point. Iron feruchemy completely breaks conservation of energy for a variety of reasons. I honestly don't see a good way to get away from that.

Wax gains speed by filling weight midair, but sazed filled, then stepped off. Kinetic energy doesn't increase if mass stays the same.

[Heilven he/him]

Sazed had less kinetic energy upon hitting the ground than he would have if he was not storing weight. That's all I meant by that.

Edited March 1, 2023 by Heilven

[cometaryorbit]

I figured Sazed was storing down to very low weight, to the point where his clothes and bracers/rings were a significant part of his weight if not the majority of it. I don't think storing down to 15kg is extreme at all - I see no reason why he wouldn't store (say) 98% of his weight - leaving him at maybe 2kg of his own weight + 2-3kg of clothes and metalminds = 4-5 kg total.

[alder24]

12 hours ago, Heilven said:

Ignoring air resistance, to fall from 100 meters (likely far further than Sazed actually fell) it takes 4.518 seconds to reach the ground. Upon hitting the ground, you would be moving at 44.276 m/s. An 80kg person has a terminal velocity of 101.71 m/s, so terminal velocity doesn't even come into effect here. In fact, you would need to be 15kg before your terminal velocity (44m/s) would be lower at all.

You can't ignore air resistance when considering terminal velocity. That is what makes it "terminal".

12 hours ago, Heilven said:

This would be storing a massive portion of your mass, 81.5% of it.

He stored most of his weight. It was hundreds of feet deep. If he stored 99.99% of his weight, he would reach terminal velocity very quickly. WoA ch 12:

Spoiler

Quote

He and Sazed stood on the crater's northern lip, before a drop of several hundred feet.

[...]

As he began to fall, he mentally reached into his ironmind, searching for the power he had stored therein. Filling a metalmind always had a cost: in order to store up sight, Sazed had been forced to spend weeks with poor eyesight. During that time, he had worn a tin bracelet, stowing away the excess sight for later use.

Iron was a bit different from the others. It didn't store up sight, strength, endurance—or even memories. It stored something completely different: weight.

This day, Sazed didn't tap the power stored inside the ironmind; that would have made him more heavy. Instead, he began to fill the ironmind, letting it suck away his weight. He felt a familiar sense of lightness—a sense that his own body wasn't pressing upon itself as forcefully. His fall slowed. The Terris philosophers had much to say on using an ironmind. They explained that the power didn't actually change a person's bulk or size—it just somehow changed the way that the ground pulled against them. Sazed's fall didn't slow because of his decrease in weight—it slowed because he suddenly had a relatively large amount of surface exposed to the wind of his fall, and a lighter body to go along with it.

Regardless of the scientific reasons, Sazed didn't fall as quickly. The thin metal bracelets on his legs were the heaviest things on his body, and they kept him pointed feet-downward. He held out his arms and bent his body slightly, letting the wind push against him. His descent was not terribly slow—not like that of a leaf or a feather. However, he didn't plummet either. Instead, he fell in a controlled—almost leisurely—manner. Clothing flapping, arms outspread, he passed Marsh, who watched with a curious expression.

As he approached the ground, Sazed tapped his pewtermind, drawing forth a tiny bit of strength to prepare. He hit the ground—but, because his body was so light, there was very little shock. He barely even needed to bend his knees to absorb the force of impact.

He stopped filling the ironmind, released his pewter, and waited quietly forMarsh.

 

There are problems with this, but they figured out how it should work by Era 2, but didn't change it:

Spoiler

ZealousidealBid3493

The way storing weight works in Feruchemy annoys me to no end, because regular laws of physics just don't work. Sazed once jumps from a height then reduces his weight to be light as a feather, but the energy should, in theory, stay the same, so his speed should increase to account for it, hence smashing into the ground at a massive speed. This is just one of the issues, there are many more like the one you present.

That being said, I just thought about storing of weight as storing energy, in a sense, so that would fix the kinetic energy issue.

Peter Ahlstrom

It depends on where in his jump he starts storing the weight. I’ll have to look at the scene. We worked on making this consistent for the Era 2 leatherbounds, but did not do it for the Era 1 leatherbounds.

General Reddit 2022 (Oct. 19, 2022)

 

 

12 hours ago, Heilven said:

Okay and I spent a long time looking over your energy math and I think your conclusion just doesn't work out. Your math was a little bit weird, but as soon as you begin to tap weight you should lose 317836.152 J. That energy has to go somewhere, and it can't be either KE or PE, those are both accounted for already. The reverse is true for storing weight, you should actually gain energy. If you began storing 40kg of your mass while moving you would suddenly gain a ton of kinetic energy from increasing your speed. Beyond the fact that you could create infinite energy by storing up a bunch of mass, stopping, and then just gaining height. By tapping that mass and jumping off, you will land with more kinetic energy than you expended walking to the higher point. Iron feruchemy completely breaks conservation of energy for a variety of reasons. I honestly don't see a good way to get away from that.

I disagree. Our equations for Ek and Ep are incomplete. In Cosmere they have their own versions (I think Brandon literally has someone working on physics of this), and those include Investiture as a part of the world. We can't replicate it with our equations. But energy can't be destroyed. It can't just disappear. It's ok if Ek doesn't match velocity, as energy conservation takes priority. 

However I do now think that the Ek remains unchanged after Iron is tapped - this energy isn't going back into Ep, because it shouldn't. The new increase of Ep can be explained by investiture from metalminds changing into energy to compensate for higher mass - thus gaining more Ep which would later be added to already existing Ek. So looking at numbers he should have 391 615,2J of Ek after 499 m of fall, and after tapping Iron, 77 695.2J should be added to Ep from drawing from metalminds, which all would be transferred into Ek and added to it - 391 615,2J+77 695.2J+784,8J=470 095.2J which should be the final energy, which would not correspond to velocity in a classical equation, because it's incomplete in Cosmere.

In the opposite scenario, when mid freefall you store weight, your Ep will decrease, and this energy is going into metalminds as Investiture. However in this case you're right, Ek is the problem, as speed doesn't match energy that was already accumulated during the fall.But here again I think, our Ek shouldn't change - energy doesn't match velocity. as there is a hidden part of the equation which includes Investiture and Spiritual Realm, and this is where change is happening.

But until we get full math from Brandon, we really don't have anything to do math with. So keep in mind our laws are broken, but Cosmere laws are not, because there is Investiture that makes any loss and gain of energy.

Spoiler

MoriWillow

When a Steelrunner taps speed, does it work by breaking the laws of motion, letting their speed be higher than it should be when considering their kinetic energy during movement or the force they impart upon impact with something (and inversely while storing)?

Brandon Sanderson

A lot of [Feruchemy] breaks the laws of thermodynamics, and this is indeed an example.

Skyward Pre-Release AMA (Oct. 22, 2018)

 

[Heilven he/him]

So the calculation I did ignoring air resistance was as a baseline to determine what velocity he would be moving at, then compared that to theoretical terminal velocity at any given mass. Terminal velocity decreases by the sqrt of mass, so it really doesn't decrease very quickly and under almost all conditions it takes a while to reach vt. 

When I went and actually reread the quoted chapter I saw that I am very clearly wrong. I figured it was silly to imagine an iron ferring storing 99% of their mass, but that was a bad assumption. However the chapter still describes sazed as falling relatively quickly, just slower than a normal person due to air resistance combating the lower force from gravity. I still don't think he reached terminal velocity, it's more that he had less kinetic energy upon reaching the ground, and used his pewtermind to help absorb whatever force he did feel.

So I am very clearly wrong, but it's probably still not terminal velocity unless you are falling for a very long distance, more just your acceleration decreasing due to a proportional increase of the force due to air resistance.

On the energy front, I hope you are correct. I've spent hours at this point thinking about it, and I can't come up with any in universe explanation for how energy is conserved. However, if investiture will factor into these equations in a way we cannot predict, it's possible.

There also might be more restrictions to using iron feruchemy than we have seen, like perhaps storing mass while having a higher potential energy uses more investiture. The example of infinite energy by storing mass at ground level, going back to normal, walking up a slight distance, tapping that mass, and jumping off would be fixed this way.

When it comes to changing mass with regards to momentum and kinetic energy I honestly don't know. I think there's clearly something deeper going on, seeing as we still don't have a good answer for how acceleration works while storing or tapping mass.

So I guess the only satisfactory answer is "rafo" and hope that the physics does actually get figured out eventually.

Oh and on thermodynamics I am completely fine with breaking thermodynamics. Magic as a method of breaking the laws of thermodynamics is normal, and I think the laws of thermodynamics are broken in almost every cosmere book. The laws of thermodynamics are more like guidelines anyway, they are backed in experimentation and probability, not facts of the universe.

Edited March 2, 2023 by Heilven
Suddenly figured I should talk about thermo since I missed that

[alder24]

1 hour ago, Heilven said:

I still don't think he reached terminal velocity

It's possible, but the drop was hundreds of feet, and using terminal velocity calculator, if he decreased his mass to 1kg, he would have a 10.5 m/s  terminal velocity, 5x lower than normal average terminal velocity for a person. Normally you fall for 12s and need 450m drop to reach terminal velocity, it seems to me he could reach it before getting to the ground. But we don't have numbers so.

1 hour ago, Heilven said:

On the energy front, I hope you are correct. I've spent hours at this point thinking about it, and I can't come up with any in universe explanation for how energy is conserved. However, if investiture will factor into these equations in a way we cannot predict, it's possible.

 

It's probably the best explanation there is right now. 

Spoiler

Questioner

Have you ever considered the energy density of Stormlight compared to real world substances? Example: nuclear fuels. Is it kind of on that level?

Brandon Sanderson

I have a little group of cosmerenauts, fans of the books that I’ve known for the long time who are themselves physicists. And I have asked them to start helping me quantify these things. Right now, I don’t have them exactly quantified. The place we’re starting with is: which forms of Investiture in the cosmere, how much fantastical-unit-of-energy do they have, and how does that relate to a real-world joule, or something like that. And that’s something we’re in the process of doing, because we’ll need it by space age cosmere. But I’ve told them they have years to figure it out.

The nice thing is, in our world, we have conservation of energy. I’ve talked about this in the cosmere: because we can go from energy to matter to Investiture (and any of the three can transfer between), we can pop energy out in interesting ways to fuel things if we need to. We can draw directly from the Spiritual Realm, or you can have some of this matter transferred into energy through becoming Investiture first, in a way that’s a little less explosive than normally getting energy out of matter is, in our world.

That said, the magic system of Dragonsteel (which I wrote long ago, which is not released), one of the primary magic systems of that was actual nuclear physics. And nuclear fission was part of the magic system, being able to see the atoms and manipulate them. I don’t know if I’ll ever do that in actual cosmere, but it was one of the cosmere magics originally. So when you read Dragonsteel (we’ll probably release it sometime around the Words of Radiance leatherbound Kickstarter, would be my guess), you can read about people seeing… in cosmere terms, they’re called “axi.” Or “an axon,” rather than atoms. You can see people playing with that. And I even think there are rumors in the books of people playing with those to the point that they make enormous explosions that cause wastelands. Because you do something a little wrong, and suddenly you’re splitting some atoms, and that can be very bad. That can have ramifications.

Waterstones RoW Release Event (Nov. 18, 2020)

1 hour ago, Heilven said:

Oh and on thermodynamics I am completely fine with breaking thermodynamics. Magic as a method of breaking the laws of thermodynamics is normal, and I think the laws of thermodynamics are broken in almost every cosmere book. The laws of thermodynamics are more like guidelines anyway, they are backed in experimentation and probability, not facts of the universe.

So fine with breaking laws of thermodynamics but not fine with breaking conservation of energy? That's totally like me!