DrPhysics

Other fun tidbit: The scene where Kelsier and Vin both push on a coin and flatten it gives us one place where we can quantify the forces involved. The coin is made out of copper (2.7 grams of it if the collectible version can be considered canon, but the weight doesn't come into play when calculating the forces). The force is strong enough to flatten the coin and break the small aspen tree that Vin was pushing against. Using the compressive strength of copper and combining that with the shear strength of aspen, Both Vin and Kelsier would have been exerting a force of 12 tons (24,000 lbs or 105,000 N), which a human could easily survive without negative long-term consequences (though it would be impossible to breath in). Edit: Made a math mistake (squared a diameter instead of a radius) The force should be 3 tons, 6,000lbs, or 26,000 N

That still assumes that the storing process conserves the momentum of whatever is stored. Momentum is only conserved when there are no external forces. You are converting mass into investiture and then investiture back into mass. Whatever that process involves, the end result is that mass leaving acts as if it is at rest with respect to whatever the feruchemist considers at rest, and mass entering the physical realm is also at rest with respect to whatever the feruchemist considers at rest. It doesn't matter when they stored it or what happens to the storage in between. It's the tapping/storing mechanism that changes the momentum of the tapped/stored mass. We can tell that they aren't storing mass directly in their ironminds, otherwise, their ironminds would gain as much weight as they have stored. My best guess is they are storing the small amount of investiture needed to pull/deposit investiture as mass directly from the spiritual realm where things like distance and speed don't really make sense to talk about.

That is real-world physics. It doesn't come from the books.

I opened one here, and added some notes about my steelpush rules (self-plagiarized from Reddit). If we end up with more to talk about with the quantum parts, we can return to this one.

This started as a discussion with @idanstark42 about quantum mechanics and investiture, then changed enough that we thought we should start a new thread. Also, I wrote up a lot of my notes for this in a reddit post, but with the way things are going over there I don't want to leave that as a primary source, so I'm copying the relevant bits over here. I also want to acknowledge this thread where the topic has been discussed before. Much of my model came about by addressing the oddities brought up there. Copied content: Physical Rules of a Steelpush This section is formatted so that the general rule is the high-level bullet point and any lower-level bullet points are an attempt to briefly explain the relevant physics. While steelpushes are related to electromagnetic forces, they can't simply be caused by an allomancer creating and manipulating electromagnetic fields with their bodies. Generally speaking, metals are attracted to anything that creates electric or magnetic fields, so it would be impossible to push on metals. There are some metals (called diamagnetic metals, like silver and copper) that they could push on, but the forces involved would be much smaller than anything we see in the books. An allomancer couldn't target specific metals to push/pull on. Manipulating your charge, for example, would make the allomancer pull on all metals surrounding them. The "Strength" of a push is limited by two factors: a maximum pushing force and the Power (energy per time) that an allomancer can produce by burning metals. The books do not give enough details to quantify (turn into equations) the relationship between these two limits. Allomancers (at least those that have described pushing/pulling on metals) either only feel the power of their push OR can't tell the difference between pushing with maximum force or maximum power. My best guess is that they can feel how quickly they are burning the metal and rely on the third law push-back to feel how hard they are actually pushing. The maximum force behaves similarly to how gravity and electrostatic forces do in our universe. They both depend on how much force causing stuff (mass for gravity, charge for electromagnetism) the interacting objects have as well as the distance between the objects. In the case of a steelpush, that limit is the allomatic strength of the individual and how much metal they are pushing on. The power delivered to an object is equal to the force applied to an object multiplied by its velocity in the direction of the force (e.g. if an object is moving north-west and being pushed to the north, only the northward part of its velocity counts). If you "push" two objects using the same amount of power but one is moving faster than the other, the force you apply to the fast one will be smaller than the force you apply to the slow one. Metals are still used up even if the push doesn't generate actual power (e.g. if the object doesn't move), similar to how our body would burn energy if we pushed on a wall without moving it. It takes energy to keep our muscles tense, but we don't deliver any power to the wall unless it starts moving. The direction of the force follows field lines like gravitational and electrostatic forces in our universe, but allomancers can manipulate how hard they push on each field line (sometimes without knowing it) and how much of their "self" they are using to push. Field line example: every single piece of the earth pulls on every single piece of you, but when you add up all of those little pulls they act like one big force at your center of mass that points to the center of the earth. If the earth could decide to pull a little more with one side than the other (or completely stop pulling with one side of the planet), you'd get a gravity force that pulled you down and to the side instead of straight down. That line from your center to the center of the earth would be like the blue lines that an allomancer sees. Skilled allomancers appear to be able to subdivide that further. Once you were more than a few body lengths away from an allomancer you wouldn't be able to see a significant difference in force direction from say a pull towards an allomancers hand vs a pull towards their center, but it does allow for tricks like an allomancer pulling a coin from their belt directly to their hand. When two (or more) pushes occupy the same space, they add like pressure forces, not like field forces. If you have two gravitational bodies pulling on you equally, every single part of your body (down to the atomic level) gets pulled on equally and the force is effectively zero everywhere in your body. You would feel weightless, rather than feeling like you had two people pulling you apart. (This ignores tidal forces where a tiny piece of your body that is closer to one planet will get pulled on very slightly harder than the other planet. You either have to be the size of a planet or near a black hole before you could feel a difference.) When pressure is exerted on an object, the force changes gradually from one side of the object to the other, with the result that an object caught between two pushes would feel smashed. Likewise, an object caught between two pulls would be ripped apart. These rules are based on what we see in the books. They operate much like how a push from our muscles operates. However, with how important perception (cognitive realm) is to magic in the Cosmere, a very skilled allomancer might be able to start perceiving the forces more like our electromagnetic forces and could do things like push/pull on non-metal objects or lift very heavy metal objects without being crushed, or even feeling any pressure at all (though they would still need an anchor). Additional Rules Based on Discussion (Edits added later, for more details read the discussion) Investiture and/or connection (in both individuals and objects) acts like extra mass in how objects respond to allomatic pushes/pulls but not regular forces The more mass you have, the more force it takes to accelerate you. The more investiture you have, the less you respond to allomatic pushes and pulls. Examples: Elend and a steel inquisitor (both about the same size) both push on the same piece of metal. The steel inquisitor expects them both to be pushed back about the same amount, but Elend (as a very powerful mistborn) hardly moves and the inquisitor goes flying off. Wayne throws a charged "push" grenade into a group of armed people. The grenade rolls in just fine, but the weapons all go flying off. Since the grenade contains ettmetal/harmonium, it is very invested and acts like it has a very large mass in response to the pushes acting back on it (otherwise the grenade would just fly off). However, it is still easy for Wayne to pick up and throw, so it can't be that it suddenly gains lots of actual mass There is a minimum push strength which is hard to go below. Vin and Kelsier both talk about how hard it is to fine-tune a push. For example, they both stop themselves from falling with a series of short pushes rather than one sustained weaker push. It is unknown what limits this push (force or power). There just isn't enough detail to conclude which. It may have something to do with what the allomancer expects will happen. Example: early in her training, Vin pushes up on a coin to see how high she can go. Eventually she slows to a stop, and then hangs there. If a strength of a push was only limited by distance (or power), her momentum would carry her much higher than where the force was equal to her weight, then continue to bob up and down centered on the point where her weight and push were equal, like a mass dangling from a spring. Since she slows to a stop and then hangs there, the slowing tells us that her push is actually less than her weight, then suddenly becomes equal to her weight at the stopping point. (There are a few posts discussing possible explanations for this.) Examples that I've seen discussed and how this model explains them How does the coin stay up when Vin and Kelsier are both pushing on it (I've also seen this as "does allomancy have friction"). If allomatic pushes were only center to center, when Vin and Kelsier both push on the same coin directly between them it would drop straight to the ground (there is no force holding it up). I've also seen this scene explained with an "if the coin was slightly higher then their centers, then they could hold it up", but that position would be very unstable and any small twitches would send it shooting off in any direction as long as it stayed equidistant from Vin and Kelsier. The coin would stay easily if they subconsciously pushed more on the top than the bottom. This is something we do all the time with our feet to keep from falling over when standing. We just make tiny adjustments in how we are pushing. To explain it in the Vin and Kelsier case, you could just imagine the coin being replaced by four lumps of metal held together by sticks to form a plus sign. If it starts to fall, the allomancers can push harder on the top than they do on the bottom and it will start to rise slightly. Whenever it starts drifting to the left, pushing a little bit harder on the right would recenter it. Having the forces add like pressure also explains why the coin was flattened in the push. Other scenes explained by this differential pushing: Any time an allomancer balances on a single coin (especially Zane's ability to re-orient himself in the air) and Kelsier's ability to start an object rotating during one of his fights with an inquisitor. **Lost metal spoiler -** Vin recoiling when her coin hits a building, also why allomancers don't leap by pushing on coins in the air. These scenes can both be explained with a power-limited push and by the fact that allomancers can't feel the difference between the force of a push and the power it uses. In the first Mistborn Vin gently pushes a coin out of Kelsier's fingers and is later thrown back when the coin hits a building. If she was controlling the force of her push, she wouldn't have felt any different when the coin hit the building. According to Newton's third law, the coin pushes on Vin just as hard as she pushes on it regardless of whether or not it has hit a building. But, if Vin was pushing so that the force felt the same, the coin would continue requiring more and more power to maintain the same force as it sped up. When the coin rapidly stopped by hitting the building, that power would go very quickly from pushing the coin to pushing Vin, whose much smaller velocity would result in a much bigger force. Technically, an allomancer could jump off a ten-story building and push on a coin with enough force to stay at the same height (they would just need to push with a force equal to their weight). But, that coin would hit the ground in a few hundredths of a second (ten times faster than human reaction time), and the sudden acceleration that would come from them maintaining the power needed to hover would kill them instantly. They wouldn't have time to pull back the power. It's something that would be possible, but allomancers would very quickly learn not to do it. For fun, I ran the numbers on what would happen if you dropped a coin from the top of the empire state building and used it to hold yourself up. The time it would take to get from the top of the building to the ground would still be significantly less than even world-record human reaction times and the accelerations due to the coin impacting the ground would be large enough to completely liquefy the allomancer. They wouldn't just break bones. Their bones would be crushed into dust.

There's mixed evidence on what happens. Wax often runs around at 3/4 weight because it makes him "lighter on his feet, quicker to react", but he also talks about how increasing his weight must increase his strength, because he doesn't crush himself and doesn't seem to have a hard time moving around at increased weight. So, it turns out that "the magic be weirder than that."

Newton's third law works just fine for this, but making impacts a little springy would work. That's how it works with our muscles. We measure the sudden change in tension and adjust accordingly. The springs can explain the crushing, but not how it is held up in the air. The best explanation for that one is that the allomancers adjust the strength of the "field lines" that they are producing so that the ones pushing on the top of the coin are a little stronger than the ones on the bottom. This would also explain how Zane is able to reorient himself in midair while hovering above a single coin. The allomancer probably doesn't perceive it as strengthening/weakening different field lines, but it would explain what we see.

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.

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.

They break it much more than that. At faster times, gravity should be weaker. There's a thermodynamic exchange at the border that keeps speed bubbles from superheated the room and slow bubbles from freezing it. There's an unknown process besides momentum exchange that causes objects to deflect at random directions instead of just reflecting like you'd expect. There's whatever was happening with Wayne's vision at the end of the lost metal that doesn't make any sense based on other bubble behaviors. And, There's the fact that you can't explain them using general relativity, because any spacetime bending that sharp would rip a hole in the universe that would destroy everything on the border, and create a series of microblackhole that would then evaporate and irradiate everything inside and outside the bubble. So, we're limited to "fancy magic speeds up/slows down time" Wax is my favorite character. Best representation of inattentive type adhd that I've ever seen.

Kelsier states the rule that way, but as we see more scenes with allomancy, it becomes apparent that the pushes follow Newton's third law: if you push on something it pushes back just as hard. Every time you push, both objects feel the force, the effect is just more apparent on the lighter object. If two things were the same mass, they would move away from eachother at the same rate. If you are already moving (like Vin falling), it takes a while for that force to slow you to a stop and turn you around, which is why Vin could crush the tower.

I've read all of the books. Here's my answers to some of those. Others, sadly, we just don't have enough information/examples to come up with a model. Also, I'm a big fan of the physics of superheroes. Too many books/blog posts/etc. just say "it can't work because Superman shouldn't be able to fly". I'm a much bigger fan of descriptive (vs proscriptive) physics models in stories. This is what we see, how can you make it work in the context of the world.

I'm new to the online community, but old to the fandom. I first heard about Brandon when a college roommate loaned me their copy of Elantris, selling it to me based on our shared love of Wheel of Time and telling me it was by this cool new author who had another book "mist something" coming out later that year. I'm a physics professor by profession and love applying real-world physics to the Comsere any chance that I get.

I think that it is a cool connection to make, but in the end we just don't have enough information to classify the particles. The point of building a good model is to be able to make predictions, and I don't see there being much predictive power here. I'm also noticing that those two staements above come across much more harshly written down than what I intended. What you have is good work and correct physics. I'd recommend: keeping this and revising part 2 when you have more quantum under your belt. Work on developing your classical model a bit more. I've been through many of the discussions on steelpushing physics around here (and even wrote some about it on reddit, but I don't have enough posts to link.) Here's a brief summary of what we do know: Direction and strength act much like field forces and follow inverse square law. The product on top depends on the strength of the allomancer and how much metal there is. Also, skilled allomancers can learn to push with only part of themselves and/or on only part of the object, but forces still follow field lines Inside objects, steelpushes/pulls add like pressure forces, not like field forces (which explains the coin that is held up between Vin and Kelsier, then smashed). The strength of the burn (e.g. lightly burning metals vs flaring them) correlates to the power delivered to the object, but with a base metabolic rate (e.g. it takes some investiture to exert a force, even if no work is done). Allomancers can't directly perceive the amount of force they apply, but can feel what it does to their bodies.

I haven't made it all the way through yet, but in the end of section one, Example 1.1, you make this statement (and the math to match): "This Connection allows them to draw on a constant stream of Investiture, creating a constant Force." Steelpush/pull behavior isn't described well with constant force. Instead, the amount of investiture used correlates better with the amount of power delivered to the object. For example, let's look at the scene in the first book where Vin pushes the coin into a wall and she goes flying backward. If she were exerting a constant force, thanks to Newton's third law, should would feel a constant force back and wouldn't be able to tell when the coin hit the wall. At constant power, the rapidly decreasing velocity that the coin experiences when it hits the wall creates a rapidly increasing force (Since P=Fv for moving objects), causing Vin to suddenly fly backward. What level of degree did you get in physics?