DrPhysics

Sorry I'm late to this thread, it's been a busy semester. I'm in this camp. I've tried running the numbers on a few things, and while general principles seem to hold, there just isn't enough detail and/or consistency to come up with any reasonable numbers. I don't know how much I can add to this conversation, but I will say that based on how we see lashings work, the "rods from God" thing could work, with one big caveat: we don't see anyone using any comparable amounts of stormlight in the stories, so there may be some unknown limits to lashings. Also, Investiture seems to be infinite in the sense that it collects itself again after being used so that you will never run out, but that doesn't mean that an infinite amount is available at any given time. Also, there are two rules of thumb you should use when discussing physics in the Cosmere (#1 I see referred to all the time and I see #2 frequently ignored): Cosmere physics matches our physics unless investiture is involved (I know there's a WOB on this, but I can't find it at the moment). Above all, physics relies on observations and describing how the world works. If something happens in the books, that's how the universe works, even if it contradicts what we'd expect based on our own physics. So, when I run into things like the energy released by Kaladin's flight post (barring bad physics - acceleration is zero at terminal velocity, among other errors) we have to compare the predictions to what actually happened. Releasing that much energy would leave at very least a superheated column of air behind Kaladin and create a thundering boom as he traveled. Since those things didn't happen, investiture can't work the way suggested in that post.

Yeah, many scenes don't work without some way for the allomancer to calibrate the strength of the push. I think I'm going to interpret the scenes where it talks about not controlling the strength to really mean that it's very difficult to go below some minimum strength, but then they can calibrate from that minimum up to flare (maximum). Your model is an interesting one. I like it. Some of these fine details we won't ever be able to solve without concrete data. Until then, one guess is just as good (scientifically speaking) as another.

I might be misunderstanding what you mean by distance and how it relates to alpha. Is it cognitive distance or a physical one? The math makes it look like a physical distance. If it represents a physical change in distance, a push would always move you away from an object, so slowing yourself to a stop while moving toward metal would be impossible. Only in the scene where Vin pushes herself as high as she can go then stops.

You didn't factor in how alpha depends on r. Unless you are assuming that alpha is constant. That would explain the sudden increase in force when the object being pushed hits something solid, but doesn't describe regular leaping through the air. I couldn't find an analytical solution, but I only fed it into Mathematica. If it has one, it isn't easy to find. Combining the forces to create this potential doesn't fix the first law problem, it just shifts the equilibrium point. To fix it, you'd need some sort of very strong damping, (proportional to the velocity) so that you have an overdamped system. But, that damping would also have to make sense with Wax speeding up bullets and Duralumin-enhanced jumping. Or we can use the copout that Vin pushing up on a coin to stop at the top has some cognitive realm-based damping because she was expecting to stop which isn't present in other examples of steelpushing.

How is that? See the Vin/door example in the very first post of this thread.

I just realized another hole in my model when answering a question on another thread. While metal seems to follow F=ma, there are several instances where powerful objects (like an allomatic grenade) or people behave as if their mass is much larger than it actually is. Well, back to the drawing board.

It is unusual, but not the only place where this oddity pops up. Sometimes the push/push back follows Newton's third law, (I push on something, it pushes back just as hard), and sometimes it doesn't. Another similar scene happens in Hero of Ages where Elend and a steel inquisitor both push on the same object and the inquisitor moves much more than Elend, (the inquisitor thought that they'd both be thrown back the same amount, like what would happen with Newton's third). The book purposely makes a point of highlighting the oddity, so my best guess is there is some sort of "push mass" that depends on the allomancer's strength or perception of their strength that makes them respond less strongly to pushes than they should. The same effect must be what is going on with the grenade.

Well, that makes it much harder for the physics to make sense, possibly to the level that we can't consider a push a force. I'll have to chew on this one for a while. Controlling power instead of directly controlling the force of the push would still explain the discontinuity, just not quite how I described it in the example.

Either that or he does it in really short jerks so that by the time he is moving he isn't pulling anymore.

It stores mass (otherwise you wouldn't change speed mid-air). The short version of momentum is that without outside forces, the value of mass times velocity doesn't change. So, if you decrease your mass (without pushing on the mass that you are losing), you will speed up. If iron feruchemy changed how hard gravity was pulling on you, instead of speeding up in mid-air, you'd keep going at the same speed, but you wouldn't fall as quickly. There are a few people who argue about whether or not iron feruchemy conserves momentum if you change reference frames (e.g. Wax is in the train, what does someone outside the train see), but all of those problems go away if you imagine that the mass that you store (or tap) changes its speed so that it is at rest with respect to whatever the allomancer considers at rest (e.g. in the train example, any stored (or tapped) mass is moving at the speed of the train).

The short answer: magic makes time go faster/slower (and yes, I know that answer is facetious). They break so many physical laws, that I can't make any good predictions or explain them any other way. Beyond redshift, you'd also have to worry about things like super fast air molecules crossing the boundary and heating the rest of the room (Wayne would just cook everthing). They also increase (or reduce for slow bubbles) the pull of gravity. The way gravitational forces work, if someone dropped something in a bubble, someone outside the bubble should meaure it falling at the same rate we'd expect in the regular room, and anyone in the bubble would see it fall much too slowly (and they'd be apparently much lighter), and we dont see that happening. We do have ways to slow down/speed up time, but there is no way to create something like a speed bubble using those principles (bending spacetime to that degree would shred everything that passes through the edge of the bubble and the energy released would kill everyone in the room, even after compensating for redshift). Therefore, since there is no real world physics that can even approximate speed bubbles, we're stuck with "magic makes time go faster/slower".

When constructing a physical model, you need a justification for each piece. So, we could talk about relative velocity and show that the bigger the relative velocity, the harder it is to push the thing, but that doesn't give us a reason. Saying that an allomancer is limited by the power they can produce (the rate they can convert investiture into energy), however, tells me that I'd expect the force to be proportional to 1/v, rather than 1/v^2 or exp(-v), all of which get weaker when you have a larger velocity. Those kinds of justifications are especially important if you don't have solid data to put a fit to. If we had a graph of Vin's speed over time and we saw that the fit was actually 1/v^2, then we'd have to figure out why that is, but until then, it's better to find physical, direct cause reasons for any models that you build. As another example, since the pushing applies to metals, we'd have to guess that it is at least somewhat related to electromagnetism, so I'd guess that we follow Coulomb-like forces and we'd expect the push to be proportional to 1/D^2. So what I was really trying to say is that any model I'd use would have the force proportional to 1/V and 1/D^2, unless I had a really good reason not to. Part of the problem is that pushes/pulls aren't as consistent over Era 1 as they are through Era 2. I think Sanderson was still developing his model, so we see lots of oddities in Era 1 that don't pop up as much in Era 2. For example, this scene from TFE: That wouldn't happen if we could describe pushes and pulls as a force exerted on the object that points directly at the allomancer. Instead, we'd see them curve and arc like we do when Vin travels with horseshoes in the next book. Era 1 was pretty bad with Newton's first and third law problems (like the example above), but in era 2, they are much more consistently applied. Does that mean the first law applies or doesn't? What about third law? At some point we need a little hand waving and justification, and it looks like we don't agree on which pieces to handwave away (and there's no reason that we should have to). For me, assuming those rules I posted above and that Allomancers have more unconscious control than they think that they do is how I'm able to justify most of the oddities that I run into. (Except for that Kelsier example. I can't think of any way to justify that other than Sanderson didn't understand inertia when he wrote it.)

I've introduced myself in other places, but I'm a physics professor who is also a big fan of Sanderson's works. There are a lot of in-depth physics discussions on various topics all over this forum. This isn't that. I wanted to start a thread for those who have simple questions about Cosmere (or other Sanderson works) physics, but without diving off the deep end. So, if you have a question but don't want to debate the proper way to model a steelpush (or if those threads just feel way too intimidating), ask it here and I'll do my best to answer. If we run into a topic that could use a more in-depth discussion, we can spin it off into a new thread and I'll edit this original post to include a brief summary and a link.

I set up a simple Euler's method code in Python. There isn't an analytical solution that can include both power delivered and drag force. Newton's third law and statics. If I push with 140 N, 140 N pushes back on me. An average (70 kg, 1.7m tall, chest height at 1.3m, 0.5 m stance) person, without bracing, will fall over if pushed by a force larger than 140 N at chest height. Most of the time that we see coinshots pushing coins, they are pushing multiple coins and aren't bracing. 140 N gives the net force they could exert without bracing against something behind them. Kelsier says that is it hard, (Exact quote, while training Vin early on: “Varying the strength with which you Push or Pull is difficult, but possible. It’s better to just fall a bit, then Push to slow yourself. Let go and fall some more, then Push again. If you get the rhythm right, you’ll reach the ground just fine.”), but we have to remember that he is not a physicist, and "strength" does not necessarily mean the same thing as force. Also, when he does say it, he's talking to a brand new Mistborn just starting with her powers. My best guess is that conscious control is hard, but we modulate our strength all the time in unconscious ways. Therefore, any model that tries to describe pushing as an allomancer simply setting some "force of push" is bound to fail. That would be like trying to model our muscles based on tension in our biceps. We don't think about how hard we are flexing our bicep to move our arm or lift a thing, we're thinking about what kind of path our arm takes as we lift (or fail to lift) the thing that we are trying to move. We can find some limits (human bicep will tear if it exceeds a certain tension), but those limits don't let us model every single motion. I misunderstood your notation. It makes sense now. Sorry. I agree, but I think it makes more physical sense to model the force based on Power (which is proportional to Velocity (P=FV)) and Distance. Power would reflect how quickly the allomancer can convert Investiture into kinetic energy. The faster they can make that conversion, the more powerful they are. Whereas, there is no good physical model that would suggest why velocity alone would matter.

I've never made that argument. Only that that was a scene where we could approximate a force. Then it must be much less than 1 MW. Why isn't that possible? We can use the colt single action army revolver for a stand in. Those would fire a .45 caliber, 16 gram bullet at about 300 m/s. At that speed, drag alone is about 1 kw. 10 kW of a push would have the bullet moving at 350 m/s at 10 meters from the gun, 400 m/s at 25 meters. That's a big increase without much power. (And the push averages to about 30 N) Pushing a coin at that constant power does get it up to 500 m/s, but that involves very large initial forces that would knock an allomancer down. An average person (70 kg, 1.7m) in a good stance could take a 140 N force without being knocked over. If you run the numbers limiting a maximum force to 140 N and a maximum power to 10 kW, you get coins that hit fast but still subsonic speeds (260 m/s) at 10 meters, which fits what we see in Era 1. Also, thanks for finding that WOB. Now I know what my next deep dive topic will be: what flying with lashings would really feel like.

I'd have to find the exact WOB, but he says that in the Cosmere matter, energy, and investiture are all equivalent, but doesn't want to put an exact E=mc^2 equation together because it would limit the storytelling.

Air resistance is proportional to speed, and while you can have big forces at high speeds, as you slow down they get weaker and will take a very long time to slow you to a "stop" (technically, air drag can never truly stop you). Also, your model seems to be relying on a "force of motion" (i.e. when force is zero, you stop). That isn't the case. We also treat gravity as if it pulls on the center of mass, but in reality, it pulls on every single piece of us. The behavior of steelpushes suggests that they follow similar rules (see rule #3 in the original post). I went looking for examples, and I couldn't find where it's talked about. Do you remember where this happens? They could for a very short time, but wouldn't be able to maintain the acceleration (see rule #2, the push is limited by both a maximum strength and power delivered).

Couldn't you just apply the inefficiency constant to the process of storing/removing mass from the spiritual realm? So maybe priming the pump was a bad analogy. Instead, imagine it like an electrical relay. We use a little bit of investiture to open access, but keeping the access open uses up the stored investiture. Really, the point I was trying to make was that if you literally stored all of the mass in the metalmind as investiture, you would see a large increase in the mass of the metalmind. If it follows an E=mc^2 like relationship as Brandon has said, then the metalmind's weight would increase just as much as the mass you stored, and storing mass would have no meaning. You'd still be just as heavy, it's just that some mass would be in the metal, and the rest would be in your body. Something else must be going on, and as far as what that something else is, your guess is as good as mine.

In order for the velocity to reach zero, the push must already be less than gravity in order forher to slow down. Therefore, she has to push with less force, and then increase it. I'm have a hard time following your notation here does f(distance) mean force as a function of distance? or does it mean force times distance? And how is g different from G?

It does if you give the added/stored mass a velocity that puts it at rest with respect to whatever the feruchemist views as "at rest".

Not nearly as much as you'd think. There are two main components to drag (1) friction between the air and the object and (2) pushing the air out of the way. For a human shaped object, number 2 is almost always bigger than number 1. You'd see an appreciable drop in wind resistance if you were moving in the face forward, superman flying type pose, but if you were in an upright running position getting rid of friction would only drop wind resistance by about 10%.

Don't be. That's how we learn physics - try to use it to explain the world, and then fix our mistakes when we are wrong. No one learns physics by sitting and listening to a teacher. (We've been studying physics education for 50 years, and that is one consistent theme that pops up over and over again.) And in this thread, everyone got to the right place in the end. That's what really matters. Also, Newton's third law is really hit or miss in the first Mistborn trilogy. Based on interviews and Era 2, it's obvious that it is supposed to apply, but Newton's first and third laws are both really hard to wrap your head around and so there are lots of situations where one or both get broken unless you jump through some serious hoops to get them to work.

Looks like what I said didn't match up with what I meant. When I said G-Force was distributed all over the body, I meant that the force causing her acceleration should be distributed all over her body. When that happens, you don't get the same negative effects of G-Force (Though she would have felt it when pressed against the tree, and the book does talk about the pressure increasing). We feel the negative effects of G-Force when something is pushing against us on the outside (like in a cockpit). That creates a pressure differential, which then makes it hard to pump blood, get oxygen to the brain, etc. With field forces (and pushes seem to act like field forces unless there are multiple pushes in the same space), we don't get a pressure differential unless something is keeping us from accelerating with the field force. Example: Get a water bottle, poke a hole in the side, then unscrew the lid. You should get a stream of water coming out because the pressure inside the bottle at the bottom is higher than the air pressure outside of the bottle. Now drop the bottle. As it falls, the stream will stop because the pressure equalizes everywhere. So, If an Allomancer isn't bracing against an object (like a tree), they shouldn't feel a g-force. They would be limited by air resistance, but as long as the air resistance stays below 4 g's, they could have any acceleration and not experience G-LOC. (And if they are going face first, they could push until air resistance hits 40-50 g's (80 with pewter), though that might be fast enough you have to worry about heating). G-LOC and the negative effects of G-Forces are very dependent on both duration and direction. The 4-6 g's figure only applies vertical accelerations that last for a few seconds. You can withstand much higher g's for shorter times, and other directions. Here's a good graph, if you're curious. And I found the passage you are talking about: I can see two interpretations of that (and the exponential wouldn't fix either) 1) Brandon just got the science wrong. In the early books, he made a lot of mistakes with Newton's first law, and Peter didn't catch them. There are some pretty egregious examples all the way up through Starsight. They are better at it now. 2) Vin panics a bit when she asks herself "What happens if it disappears?" and either consciously or unconsciously backs off with her push. The reason why the exponential won't work is that it doesn't consider her inertia. With the exponential, she'd be at equilibrium at 30 m, but wouldn't come to a stop. She'd overshoot, fall, overshoot, fall, then repeat until she either changes how she is pushing or wind resistance lows her down over hours. Personally, I think #1 is boring, so I like explanation #2 better. We do similar things with our muscles all the time. We don't choose a force and go, instead, we make tiny adjustments to match the motion we want without thinking about it.

When you shove that much energy into a confined space (especially so that it can't move) it will bend spacetime and start acting like it has mass (or just change forms so that it has mass). Some of the other books suggest that investiture follows the same rules, even if we don't know the exact conversion rate. You're right. I had a longer edit that talked about how the investiture stored in the metal mind would probably be just enough for them to access the spiritual realm for the extra mass they are storing/tapping (like priming a pump, you need a little bit of water to start it, but the bulk of the water is pulled from the ground), and just felt like too long of an answer. The infinite energy supply referred to the amount of energy in the spiritual realm, and I didn't correct that when I cut out the extra. Oops.

It does take more work, even ignoring air resistance. Hopefully, you'll see my edit. The force is 1/4 the size of my original calculation. However, 210 g's actually is survivable, especially if it is distributed all over the body and only lasts a short time (as Vin starts moving, the force will decrease very rapidly and she stops pushing a moment later). Toss in that she was flaring pewter and that she was accelerated backward (the best direction for large g-forces) and the situation becomes even more survivable (Especially when you use the right force and she only feels around 50 g's). To calculate the force, I just took copper's compressive strength (70 MPa) and multiplied it by the surface area of the coin, which according to the replica is 2.2 cm in diameter (NOT radius, like I did the first time, oops). To check the reasonability, I found the shear strength of ash ( 6.0 MPa) and found the diameter of the tree it would need to take that force (6 in. or 15 cm diameter on the bad calculation, 3 inches or about 8 cm on the one I did the right way), and found that it was a plausible situation based on the tree type and the flattening of the coin.