Allomantic Iron and Steel are Energy Neutral

[Kurkistan]

EDIT: I'm kind of wrong. And stupid, also. Momentum is conserved, not energy. I got a bit too big for my britches so far as what "energy" meant. If you read the rest like I'm arguing for conservation of momentum, then it sounds much smarter (and also is probably true).

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I've failed to hijack two different threads using a series of posts about my pet theory that Iron/Steel Allomancy do not introduce any energy into the world, and that the power gained from the "End-Positive" aspect of Allomancy for these powers can be chalked up to avoiding the entropy normally present in transfers of energy. I decided to just go the whole nine yards and create a separate thread, since my dastardly plans have so far failed me. Enjoy.

I was going to re-cast my arguments, but it turns out that I'm already pretty darned eloquent, so I'll just copy-paste from the above links and edit out unnecessary tidbits: :P/>/>

Initial Argument:

I have always understood Steelpushes and Ironpulls to be straight action-reaction events between the Allomancer and the target, exactly the same as if they had physically pushed/pulled on that target. In fact, as far as I've seen, they are actually preserve the energy of the Allomancer-target system. Therefore, it would function in space identically to a system where astronauts have exceptionally long arms that can only grip non-aluminum-alloyed metal.

My mental model is such that Allomancers imparts some measure of their inertia to their target, that inertia either heading in the exact direction of the target (from the center of gravity of the Allomancer) for a Push or in the exact opposite direction of the target for a Pull. The duration (proportional to the strength) of the Push/Pull determines the amount of inertia imparted.

When the object is anchored such that it cannot move, the Allomancer simply keeps imparting their inertia up to and including the point where he/she can actually perceive the effects. They can achieve special effects with anchors because the object in question remains "in range" of the Allomancer, and can serve as an "interia-sink" as far as the frame of reference of the Allomancer goes. Similar to the space-walk example, this is the same effect that you could see with someone who had infinitely long arms in a world without anchors.

To Illustrate:

50 Kg Coinshot/Lurcher, situated to East of target

5 Kg target, unanchored, at rest relative to the Allomancer

Coinshot:

To impart 10 Km/hr of West velocity to the target, the Coinshot will impart 1 Km/hr of East velocity to themselves.

To impart 20 Km/hr of West velocity to the target, the Coinshot will impart 2 Km/hr of East velocity to themselves.

Lurcher:

To impart 10 Km/hr of East velocity to the target, the Coinshot will impart 2 Km/hr of West velocity to themselves.

etc.

Illustration of why Pushing coins results in no perceptible loss of inertia for the Allomancer:

A U.S. Quarter weighs 5.670 g, while a 110 pound person weighs 50 Kg, aka 50,000 g. 5.67/50000 = 0.0001134 = %0.01134.

If you accelerate a Quarter to 1,225.044 Km/hr (speed of sound at sea level on Earth), you will create an opposite reaction of 1,225.044 Km/hr * .0001134 on the Allomancer. That's 0.13891999 Km/hr of velocity for the Allomancer. I'm pretty sure that an Allomancer could just not notice that, and/or lean slightly against it.

Explanation for apparent gains in energy using Pushes/Pulls

Looking at this again, you can actually generate power for all intents and purposes as long as you consider changes in Scadrial's inertia to be externalities, and simply look at the Allomancer-target system. You can simply dump the inertia from the opposite reaction into the planet and have what looks like a perpetual motion machine going fairly easily.

TL;DR: Pushes and Pulls are more than just "heavier than you, you move; lighter than you, it moves." Some interesting things can happen here, especially in SPACE!

Edited March 5, 2013 by Kurkistan

[Satsuoni]

Um.. I fail to see how that is not an energy positive reaction. In your examples, the system before has 0 total kinetic energy, and after the push/pull has 50*1+5*10 joules of kinetic energy. In case of astronauts with long arms, that energy would come from chemical energy in their muscles. In case of Push/pull it would come from external source (Preservation). So, Energy is gained.

[ulyssessword]

I fail to see how steel and iron Allomancy are energy neutral. One simple example of steel Allomancy introducing energy into a system is shooting a coin into the air. As it is now at a higher altitude, it has more potential energy, which could not have come from any source other than Allomancy.

As for maintaining conservation of momentum (note: inertia is different from momentum), I agree completely. As far as I know, iron Feruchemy is the only thing that breaks that particular physical law.

EDIT: ninja'd

Edited December 20, 2011 by ulyssessword

[Satsuoni]

I fail to see how steel and iron Allomancy are energy neutral. One simple example of steel Allomancy introducing energy into a system is shooting a coin into the air. As it is now at a higher altitude, it has more potential energy, which could not have come from any source other than Allomancy.

As for maintaining conservation of momentum (note: inertia is different from momentum), I agree completely. As far as I know, iron Feruchemy is the only thing that breaks that particular physical law.

EDIT: ninja'd

I had a theory that explains conservation of Momentum, too. Simply put, momentum is only saved if there is no external energy input, and in case of Iron Feruchemy, mass becomes energy.

[name_here]

External Physical Allomancy seems to be a straight-up action-reaction pair system, but if you model the planet as a closed system which does not include Preservation it violates conservation of energy. But not momentum.

[Deus Ex Biotica]

Agreed. Even as you describe, the energy to push on those things has to come from somewhere, even if it still follows the laws of motion. I expect that if a Thug shoves you, "for every action there is an equal and opposite reaction" still applies.

Even a very strong person is unlikely to be able to perform constant chin-ups for hours, but that is exactly what Mistborn do when they travel with Pushes and Pulls - repeatedly lift their own weight by exerting forces on objects which they cannot move, and using the reaction to propel themselves, occasionally resting in a semi-controlled fall. And Mistborn never even describe the process as being tiring.

Sure, it could be their use of Pewter... except that Wax doesn't find it tiring, either. And Kelsier, at least, was cautious enough to not burn Pewter constantly, though Vin wasn't.

-- Deus Ex Biotica

[ReaderAt2046]

Even a very strong person is unlikely to be able to perform constant chin-ups for hours, but that is exactly what Mistborn do when they travel with Pushes and Pulls - repeatedly lift their own weight by exerting forces on objects which they cannot move, and using the reaction to propel themselves, occasionally resting in a semi-controlled fall. And Mistborn never even describe the process as being tiring.

Sure, it could be their use of Pewter... except that Wax doesn't find it tiring, either. And Kelsier, at least, was cautious enough to not burn Pewter constantly, though Vin wasn't.

-- Deus Ex Biotica

I think you're missing something here. The energy the Mistborn are using comes from the iron or steel. The allomancer isn't tired by Steelpushing any more than we are tired when driving a car.

[ReaderAt2046]

I agree with the idea that Iron and Steel generate equal force on both objects, though.

[Deus Ex Biotica]

I think you're missing something here. The energy the Mistborn are using comes from the iron or steel. The allomancer isn't tired by Steelpushing any more than we are tired when driving a car.

Exactly. The energy comes from the Iron/Steel, or rather, from Preservation. Thus, these Arts must still be End-Positive.

[Kurkistan]

Um.. I fail to see how that is not an energy positive reaction. In your examples, the system before has 0 total kinetic energy, and after the push/pull has 50*1+5*10 joules of kinetic energy. In case of astronauts with long arms, that energy would come from chemical energy in their muscles. In case of Push/pull it would come from external source (Preservation). So, Energy is gained.

Wikipedia definition of kinetic energy: "The speed, and thus the kinetic energy of a single object is frame-dependent (relative): it can take any non-negative value, by choosing a suitable inertial frame of reference." In this case, you are choosing the frame of reference of the Allomancer, where the only thing with kinetic energy in the Allomancer-target system is the target. This is an inaccurate representation, though, since in reality the Allomancer has also gained energy.

On a planet-based frame of reference, where the Allomancer-target system had 0 kinetic energy before the Push/Pull, we will see that the negative kinetic energy gained by the Allomancer (if "positive" is the direction that the target is relative to the Allomancer) when that Allomancer Pushes on a target completely offsets the positive kinetic energy of the target after the Push. Same for a Pull, only reversed.

The chemical energy in someone's muscles is "the entropy normally present in transfers of energy" which I said that Allomancy is replacing in this case. It doesn't truly add any energy to the system, and is simply wasted.

I fail to see how steel and iron Allomancy are energy neutral. One simple example of steel Allomancy introducing energy into a system is shooting a coin into the air. As it is now at a higher altitude, it has more potential energy, which could not have come from any source other than Allomancy. As for maintaining conservation of momentum (note: inertia is different from momentum), I agree completely. As far as I know, iron Feruchemy is the only thing that breaks that particular physical law.EDIT: ninja'd

As I noted in my "Explanation for apparent gains in energy using Pushes/Pulls," you do not gain energy when considering the entire system, including Scadrial. The reaction energy is dumped off into the ground, which is slightly disinclined to move most of the time.

I may well have ventured slightly too far into the realm of cool-sounding in my use of "inertia" instead of the more easily understood "momentum". Despite this, my understanding is that inertia is essentially the same as momentum, just looked at from the frame of reference of the inertia-laden object instead of the planet.

I had a theory that explains conservation of Momentum, too. Simply put, momentum is only saved if there is no external energy input, and in case of Iron Feruchemy, mass becomes energy.

Yeah, Iron Feruchemy just cheats. It's a dirty cheater. It adds and subtracts mass, and therefore inertia/momentum, to the Allomancer willy-nilly, so we do see a gain in energy.

External Physical Allomancy seems to be a straight-up action-reaction pair system, but if you model the planet as a closed system which does not include Preservation it violates conservation of energy. But not momentum.

I agree with the idea that Iron and Steel generate equal force on both objects, though.

Unless my physics teacher did me a graver disservice than I was aware of, Conservation of Energy and Conservation of Momentum are exactly the same thing. Momentum, i.e. kinetic energy, is simply another, specific form of energy. If you conserve momentum, then you're conserving energy. When we see imperfect transfers of momentum, such as in inelastic collisions, the "lost" kinetic energy is transformed into another type of energy. At least that's my understanding coming into this.

Stolen from a random website:

What these laws say is that if there are no net forces on a system, then that system will have the same momentum, p = mv, at all times. In addition, if there are no external or internal forces acting in or on a system, then the energy of that system will remain constant. Newton's First Law is hidden in these conservation laws. Newton's First Law states that bodies at rest will remain at rest as long as no forces act upon them, and bodies in motion will remain in motion as long as no forces act upon them. As one can see, Newton's First Law is a statement about conservation of momentum and energy. Things stay the same, as long as they are left alone.

Edited December 20, 2011 by Kurkistan

[Satsuoni]

Ok, my mistake. The energy is 50*1/2+5*100/2, frame of reference - Center of mass of Allomancer/Object, in space.

Wikipedia definition of kinetic energy: "The speed, and thus the kinetic energy of a single object is frame-dependent (relative): it can take any non-negative value, by choosing a suitable inertial frame of reference." In this case, you are choosing the frame of reference of the Allomancer, where the only thing with kinetic energy in the Allomancer-target system is the target. This is an inaccurate representation, though, since in reality the Allomancer has also gained energy.

On a planet-based frame of reference, where the Allomancer-target system had 0 kinetic energy before the Push/Pull, we will see that the negative kinetic energy gained by the Allomancer (if "positive" is the direction that the target is relative to the Allomancer) when that Allomancer Pushes on a target completely offsets the positive kinetic energy of the target after the Push. Same for a Pull, only reversed.

Negative kinetic energy does not exist for positive mass. Energy uses squared velocity, which, for non-complex numbers is always positive.

Unless my physics teacher did me a graver disservice than I was aware of, Conservation of Energy and Conservation of Momentum are exactly the same thing. Momentum, i.e. kinetic energy, is simply another, specific form of energy. If you conserve momentum, then you're conserving energy. When we see imperfect transfers of momentum, such as in inelastic collisions, the "lost" kinetic energy is transformed into another type of energy. At least that's my understanding coming into this.

Um,no. Momentum is mass multiplied by velocity, a vector. Energy is a scalar, and currently negative energy is just as theoretical as antigravity. Also, inelastic collisions, strangely enough, conserve momentum, but the energy goes from kinetic into heat.

Also, IMO, Iron Feruchemy does not cheat. It just uses full definition of system energy, which is kinetic (sum of m*v^2/2), plus potential (depends on charge/whatnot), plus mass at rest (m*c^2, relativistic). And it all transforms into mass in the end. So when momentum changes, Feruchemist just taps his mass energy.

Edited December 20, 2011 by Satsuoni

[Kurkistan]

Ok, my mistake. The energy is 50*1/2+5*100/2, frame of reference - Center of mass of Allomancer/Object, in space.

Negative kinetic energy does not exist for positive mass. Energy uses squared velocity, which, for non-complex numbers is always positive.

Ah, thank you for the correction: Positive kinetic energy which just so happens to be heading in the opposite direction. Am I wrong to say that that this is balanced?

[Satsuoni]

Ah, thank you for the correction: Positive kinetic energy which just so happens to be heading in the opposite direction. Am I wrong to say that that this is balanced?

Yes. Momentum is balanced, energy is gained.

[Kurkistan]

Yes. Momentum is balanced, energy is gained.

This may be my imperfect grasp of physics rearing its ugly head again, but doesn't the fact that two perfectly identical amounts of energy are heading in perfectly opposite directions mean that the energy of the system hasn't changed from when neither object had any momentum?

Edited December 20, 2011 by Kurkistan

[Satsuoni]

This may be my imperfect grasp of physics rearing its ugly head again, but doesn't the fact that two perfectly identical amounts of energy are heading in perfectly opposite directions mean that the energy of the system hasn't changed from when neither object had any momentum?

Kinetic energy has changed. Take for example, an explosion (bomb) - the total momentum of the system is 0, but energy goes from chemical to kinetic and heat, and then back to potential (deformation, heat, etc). Same thing here, only instead of explosives, Preservation is used. Direction has no bearing on energy value, only mass and squared velocity does.

Also, momentum, AFAIK, is preserved in all (or most) allomantic interactions.

Edited December 20, 2011 by Satsuoni

[Zas678]

The energy is balanced; but it must come from somewhere.

Your use of "End-Nuetral" implies the definition given by the writer in the Alloy of Law, which is Energy that comes from the person. But the writer says that Allomancy is End-positive, or that the energy is gained through the solution, through the Power of Creation. That's what Steel Allomancy is. The user "burns" Steel, allowing them to access the Power of Creation and "Push" on metals with a force equivalent to their weight. If the system was "End-Nuetral" than that energy to Push and Pull would come from an in-world process, such as food, light, or waffles.

The chemical energy in someone's muscles is "the entropy normally present in transfers of energy" which I said that Allomancy is replacing in this case. It doesn't truly add any energy to the system, and is simply wasted.

Quote from Brandon:

People ask about getting the power from metals and things, but that’s not actually how it works. The power’s not coming from metal. I talked a little about this before, but you are drawing power from some source, and the metal is actually just a gateway. It’s actually the molecular structure of the metal… what’s going on there, the pattern, the resonance of that metal works in the same way as an Aon does in Elantris. It filters the power.

[name_here]

In that situation, the momentum of the system is unchanged but the energy is increased.

[Kurkistan]

Kinetic energy has changed. Take for example, an explosion (bomb) - the total momentum of the system is 0, but energy goes from chemical to kinetic and heat, and then back to potential (deformation, heat, etc). Same thing here, only instead of explosives, Preservation is used. Direction has no bearing on energy value, only mass and squared velocity does.

Also, momentum, AFAIK, is preserved in all (or most) allomantic interactions.

Very well then.

*Throws in towel*

I acknowledge that Iron/Steel Allomancy, while preserving momentum, still introduce energy into the world. And that's all she wrote.