DrPhysics

@ChaosI'm going to call you out on this one (I'm a physics professor). If that's your justification, then volume of a sphere would be 1/6 tau r^3, not 2/3 tau r^3 Area integrals don't need to be symmetric with path integrals. (Please note tone of joking/sarcasm) And solutions to the wave equation are much more satisfying to write as sin(n pi x/L). Who would want sin(n tau x/(2L))? That's a whole other constant I need to track through separation of variables. Also, if we use tau for 2pi, what am I going to call torque, time constants, and shear stress?

I have been summoned! So, @alder24 is correct. The higgs field only accounts for a tiny fraction of the mass of all matter (electrons and quarks) but most mass is from binding energy. What he didn't talk about was what would happen if we adjusted the Higgs field strength. Here's a very important fact: electron orbitals and the size of protons and neutrons depend greatly on their wavelengths, which are also inversely proportional to their mass. If you double the higgs field, you double the electron mass, cutting its wavelength in half, which also cuts its obit in half. Since they are closer to the atoms, binding energies get much much higher, the repulsion forces between nuclei wouldn't let two atoms get that close, chemistry as we know it collapses, and organic molecules all fall apart. Oh, and doubling the higgs field would only effect the mass of the electrons and quarks, which only accounts for about 1% of the mass of a person. So, by increasing your weight by 1% through the Higgs field, you would most likely cause every single molecule in your body to fall apart. Our best explanation for storing mass is simply somehow the magic changes your interactions with the world so that you have effectively a higher/lower total mass, without changing your molecular density or how those molecules behave. That, and any mass you store/tap is considered to be at rest with respect to whatever you perceive "at rest" to be (otherwise the momentum stuff doesn't work). ETA: I've been thinking about this more over the past few days and have a few corrections - some bonds would fall apart (covalent becoming ionic), others would get much stronger, but that sudden increase would generate a lot of heat energy as all the atoms snap closer together, which would easily be enough to boil the fluids in your body. So, not every molecule would fall apart. Some would literally cook you to death. And that's ignoring whatever would happen with complicated proteins like hemoglobin that are designed to lightly bind oxygen so it can be easily removed when delivered to the right location...

That is true at long ranges, but there are several instances where it appears that allomancers are pushing/pulling with only part of their body. I mentioned a few in the post that @Treamayne linked, but I'll not list them here because I don't know what level of spoilers we are at. This will not be the only time you see that contradiction. As far as breaking the glass goes, the best I could find was this paper that shot BB's at sheets of glass, and observed the breakage pattern. They found that if you had an impact energy of around 3-4 J would give glass failure at a level where the BB went through (for reference, a .22 rifle would have a 40 J impact energy). They used double-strength window glass, which would probably be comparable with a well made glass vial. We couldn't produce tempered glass for anything except curiosities (like Prince Rupert's Drop) until the late 1800's, so they wouldn't have had the tech available in the Last Empire either. Since neither metal nor glass has much give, impact energy will be a better predictor for shattering than anything using PSI (Only the front most part of the bead would touch the glass before shattering it, so using the entire cross-section of a sphere would be a bad predictor). So, 3-4 J does mean a velocity of around 130 m/s for the BBs, which sounds insanely fast, but it doesn't have enough energy to do much to you. A 1 cm diameter steel ball bearing would only have to travel at 45 m/s to shatter the glass, which matches your 90+ mph calculation, but it would still only have 3-4 J of impact energy, which is equivalent to a baseball going about 16 mph. But, we have two other things to consider: (1) these speeds would be the speed of the bead relative to the glass, which would be slower than the speed of the bead towards Vin and (2) that assumes that the bead doesn't lose any energy or speed on impacting the glass, which is impossible. Doing the exact calculation for speed involves many more assumptions (thickness of the glass, speed of the vial away from Vin, cross-sectional area of the bullet, which matters if you are going through, but not for whether or not the glass breaks, ect.) than I feel comfortable assigning an exact number to, but some back of the envolope calculations suggest that the bead should lose somewhere between 25%-75% of its enery, which works out to be 45%-85% of its speed.

Since Wax speeds up when storing "weight" in the air, he is most definitely storing mass. If he was sitting how gravity attracted him, you wouldn't see the speed up. You're right. So far, everything suggests that information/investiture/etc is bound by the speed of light within the realm it travels in. Span reads share a connection that is separated by the physical realm. Aons connect through the spiritual realm, so the effective distance between them is zero. I imagine one of the ways around the Elsecalling portal that he talks about would be to cross the much shorter distance in the cognitive realm at the speed of light, popping out faster than light would have traveled in the physical realm. Another would be to enter the spiritual realm and pop out somewhere else.

Physicist here. This rule works well for an RPG since it is simple to calculate and follow, but it doesn't work as a way to estimate force because the object moves at a constant speed, which just means that all of the resistive forces (like friction) balance out with the force from the attractor, giving a total force of zero. And calculating all of the resistive forces would be a nightmare for something like water. (Is it flowing across the ground? Is it in a sliding bucket? If so, what is the bucket made out of? etc.) Everything we've seen in the books so far makes it looks like attractors work by exerting a long-range pulling force like gravity or static electricity, just attuned to a single substance. In Words of Radiance, we see one draw water out of the air, and another that collects smoke from a fire. In a fluid, that would result in a small, pressure-like force. Pulling water out of air is easy, because air is just a loose collection of molecules. Pull on the water a little bit, it will just drift towards the attractor without having much impact on the air around it (you'd see a little bit of air drug along through collisions, but not enough that you'd expect to be able to feel a wind). Pulling air out of water is much harder because the air is actually dissolved in the water, and there are intermolecular forces bonding (albeit weakly) to the water molecules, so if you start dragging the air out, you also exert a significant force on the water, pulling it in with the air. Using a repeller to create a pocket of air around you is incredibly difficult. Because fluids can rearrange themselves, if you create a bubble around yourself under water, you don't just have to push away the water immediately around you; you have to push away hard enough to lift all of the water above you as well. (Think about trying to lift a stack of books. Technically, you only puch on the bottom book, but that push has to be strong enough to lift the rest of the books in the stack too.) To put that into perspective, if you have a repeller attuned to air that can push hard enough to create a perfect vacuum around itself (which is much stronger than anything we see in the books), and you changed it so it could push water just as hard, your bubble would completely collapse by the time you reached 10 m below the surface. Water is very, very heavy.

Yes, this should work. The downward lashings would be comparable to having a strong anchor, but the forward motion would keep you closer to the coin allowing you to push harder, longer. However, there are two big caveats to this. One, you would up the coin's knock back, but you wouldn't speed it up very much (see this discussion: The coin is already moving so fast they there just isn't much time to push on it. However, once it slams into a target, it will still have all that force left behind it. The other consideration: you don't want to miss. Hitting a solid object with a coin would hurt. (Remember Vin getting knocked back by the door?) This suggests that allomancers push with a constant power, rather than a constant force, and having all that extra power in the coin would slam into you, and it would not be fun. If it helps, here's a thread I wrote a while ago that summarizes everything we know about pushing physics, and it might help with some of your theorizing:

Since many of the others in this thread have stated that they aren't physics people, I thought I'd start by saying I am one. I'm a Professor with a PhD that has been teaching physics for over a decade. The biggest problem is that gravity can only pull. Gravitational lashings work (sort of, with some problems) by changing the direction of the connection to the planet. You're always still attracted; direction just gets funny. And here's the important part of that: it breaks Newton's third law. The planet would still be attracted to the person, even as the person was falling away from it. If pushing worked by doing gravity but backwards, we'd still have that weird force flipping element, and having a chunk of metal slam into something wouldn't throw you backwards; it would pull you towards it. Eddy currents don't work, either. Creating eddy currents large enough to make metal attracted/repelled as described in the books would make it very hot (some of Wax's heavy pushes would have started fires) and would make the metal that was being pushed/pulled an electromagnet strong enough that we should have seen it attracting other ferromagnetic materials. I did a post a while ago summarizing everything we know about steelpushes (link), though I didn't do much to address how they work. The way they describe being able to see atoms (as was mentioned previously) and how it affects metals more than other materials suggests that it is electromagnetic in nature (the gravitational signature from individual atoms would blur too much to see them), but there are no electromagnetic processes in our universe that could make metal behave that way without some very obvious side effects (like eddy current superheating metals that are pushed hard, or magnetized metals acting like magnets), so the only explanation we have is "Cosmere magic via a mechanism that we don't understand yet", which isn't very satisfying. Sorry.

Magnetic forces are perpendicular to magnetic field lines (which would point directly at the zap metal if the magnet was pointed towards the zap metal), so the moving electricity would feel no force as they flowed towards the magnet. The problem here is that there is no physical mechanism that could explain what you want the zap metal to do (even piezoelectric materials), nor could we create one. It goes too strongly against the rules of the universe (aside: I'm a physics professor and teach this stuff pretty regularly). Learning is great, so keep digging. And before when I said "magic", I really meant phenomenon unexplained by physics. Many sci-fi stories (including some hard sci-fi) have no problem pulling the "unobtanium acts like x because it just does" card. I've just taken to calling that tech magic because it lacks and/or defies explanation. What you have is awesome. Let the rule of cool win and don't worry that it breaks the laws of the universe.

So, what @Seonid says about capacitors is true, but you run into a problem where the capacitors will only discharge from one plate to another and you wouldn't get a big arc like you are hoping for, instead you would end up with a tazer (which uses a capacitor). Lightning arcs because the ground acts as one plate and the clouds/atmosphere as another. You also can't just say it uses it's energy to build up a big store of charge. That would explain the arcing (the wack breaks the hold on the excess electrons so they can fly free) but if you built up a charge big enough, the zap metal would start to be strongly attracted to any neutrally charged or opposite charged objects (think rubbing a balloon on your head and sticking it to the wall, but hundreds to thousands of times stronger. At some point, you just need to say it's "magic". If you ground it too much in real world physics without physics expertise, you're going to alienate anyone who does have that expertise. Marvel's arc reactor is a great example of this. It's essentially a magic power source. Yes, it's supposedly based in technology, but they never dive into how it works and it becomes easy to suspend disbelief when you're presented with "this machine makes power because it does" compared to "this machine makes power because of some nonsense reason that doesn't make any sense". On the other hand, you have stories like Project Hail Mary, where he tries to describe the science behind everything and fails horribly. The story is amazing, but I almost couldn't finish it because every few pages I'd be screaming in my head "That's not how the universe works". I think you are in a good spot with this magic system. Make sure your devices function consistently (that they follow their own rules), and don't worry so much about the physical details of how they work because there isn't anything that would do what you describe without introducing many other problems.

That is correct. Just take the weight and multiply it by 1.2. That said, this only applies to lifting things. Something that rolls on good wheels would feel comparably hard to push on both planets.

No. This is one of the most common misconceptions and where I have to spend most of my time when I start energy and momentum with my students (note: I'm a physics professor with a PhD who has taught for over a decade). "System" is the system of objects you care about (i.e. The ones you are doing math with). It is not closed, unless you can prove or otherwise reasonably assume that it is. To say that we always have a closed system is both pedantic and useless. When sliding to a stop, I'm not going to worry about how that changes the rotation of the planet (which we can't ignore because running across the surface technically gives you angular momentum, not linear momentum). It's also not how physicists talk about/work with momentum and energy. This discussion has gotten off topic, so ifnyou have questions, we can open up another thread/engage somewhere else. If you want to continue arguing whether or not momentum is conserved, I'm not going to respond.

Maneuverability and deceleration are also accelerations and would not be affected by changing mass. You could make an argument where decreasing mass might help you slow down faster by reducing your terminal velocity and air resistance, but there's a trade-off with momentum temporarily speeding you up. It definitely won't help with turning, because drag forces only act in the direction opposite travel. The depictions we see are wrong with good old Newtonian gravity as well. It's unclear whether that was a mistake by Sanderson or done for audience expectations, but the g-force effects only apply when something resists the pull of gravity. Put a hole in the bottom of a water bottle and drop it. While in free-fall, no water will come out because there is no pressure build up due to the container holding up the water.

Any system that experiences an external force. Examples: sliding to a stop. Bouncing off a wall. Also, energy is only conserved in isolated systems. Sure, energy is conserved on a universal scale (barring dark energy), but do I really care for the system I'm trying to model?

It always depends on the system. One can be conserved, or both, or neither.

Yeah, using steel directly would work better than trying to improve managing mass.