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I've been thinking about the physics and realmatics of soulcasting. We have seen quite a bit of it on screen, but there are, of course, still mysteries. Going down the soulcasting rabbit-hole, I came across the following WoB:

https://wob.coppermind.net/events/105-17th-shard-forum-qa/#e1139

Quote

ReaderAt2046

Is Soulcasting mass-conservative (Soulcast a 1kg goblet, you get 1 kg of blood)?

Brandon Sanderson

In most circumstances, yes.

source

Unfortunately, this seems to disagree with the canonical description of soulcasting. I imagine Brandon said this because in general he likes to preserve the laws of physics. (In this case the conservation of mass.)

But how does mass conserving soulcasting contradict canonical soulcasting:

1) Soulcasting is shape preserving. We have seen this in every case where it is possible to see the shape of both the original object and the soulcast object. However, not only is it shape preserving, soulcasting also seems to be volume preserving. We have never seen a soulcast object, when soulcast into a denser material, shrink. This would be a very visible effect. It looks like marble has a density of about 2.7 g/mL. A human body has a density(if we include the air filled lungs) a little less than water, so let's call it 1 g/mL. If soulcasting conserved mass, a body soulcast to marble would shrink in volume by about 63%. This would cause a 6 ft. man to become a 4' 4" statue.

2) If soulcasting conserved mass, soulcasting to a lighter density material would cause catatrophic explosions. The analysis would be easier if she had soulcast it to air, but let us consider the example of Jasnah soulcasting the boulder to smoke. The smoke floated upward so it is less dense than the surrounding air. It looks like air at Standard temperature and pressure is about 1.3e-3 g/mL. If the boulder was 1m diameter sphere (This is being generous, it was likely much larger), it would have a mass of about 1.4 million grams of 1400 kg (using the density of marble as above). If soulcasting conserved mass, this would result in smoke that really wants to occupy about 1 million liters. To put that in D&D terms, that is 307 5ftx5ftx5ft cubes.

Upon being soulcast the smoke would initially be at a pressure of 770 atms. A rough estimate would put the resulting expansion of the smoke at the equivalent of 55 lbs of TNT. (This last figure is very detail dependent and it is possible that I made some mistakes in the calculation. To make the conversion to equivalent pounds of TNT, I referenced http://ftp.feq.ufu.br/Luis_Claudio/Segurança/Safety/GUIDELINES_Chemical_Process_Quantitative_Risk_Analysis/0720X_02e.pdf)

My conclusion? Soulcasting doesn't preserve mass, it preserves volume.

Breaking conservation of mass is always problematic if you want to have physics behave in any way like we are used to, but I have some realmatic thoughts about that that I will share soon. I think that you can avoid the troubles associated with non-conservation of mass in a realmatic way.

Edited by LiquidBlue
Changed the height of the statue. I originally calculated using a reduction in volume of 37%
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Generally the usage of soulcasting in Stormlight Archive preserves mass, with a few exception. While it's likely that Brandon has not done the full math on the specifics, the way it has acted in the series indicates this. As you indicated with Jasnah in WoK, soulcasting the stone boulder into smoke resulted in the same mass of smoke in the same volume. If it wasn't the same mass and just volume, then there would be no reason for the expansion which saw. Likewise, in WoR when the ardents soulcast a stone windbreak, the suction of air inwards was because of the lower density of air requiring a greater volume to make the volume of stone in the windbreak.

There are definitely some weird points of course, such as the formation of statues from people. It's possible then that either it's an exception as Brandon is possible, or they're just drawing extra mass from air. However, generally speaking the text does support Brandon's direct statement that it's a conservation of mass, loosely speaking.

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1 hour ago, Spoolofwhool said:

Generally the usage of soulcasting in Stormlight Archive preserves mass, with a few exception. While it's likely that Brandon has not done the full math on the specifics, the way it has acted in the series indicates this. As you indicated with Jasnah in WoK, soulcasting the stone boulder into smoke resulted in the same mass of smoke in the same volume. If it wasn't the same mass and just volume, then there would be no reason for the expansion which saw. Likewise, in WoR when the ardents soulcast a stone windbreak, the suction of air inwards was because of the lower density of air requiring a greater volume to make the volume of stone in the windbreak.

There are definitely some weird points of course, such as the formation of statues from people. It's possible then that either it's an exception as Brandon is possible, or they're just drawing extra mass from air. However, generally speaking the text does support Brandon's direct statement that it's a conservation of mass, loosely speaking.

Spoolofwhool, I'll have to disrespectfully disagree. If mass is conserved, then it is the exception and not the rule. Volume conservation seems to be the rule.

When the boulder was soulcast, it results in a wind, but can be explained simply by having a bubble of lighter than air material surrounded by a denser gas, you will observe convective movement. It does not however result in an explosion of the equivalent of 55 lbs of TNT, as it would if mass were conserved.

It seems like ever other example of soulcasting also is volume preserving, or at least there is no indication that it is not. Another good example are the men in the alley. The man soulcast to crystal is not remarkably smaller, but instead appears as he did in life. The men soulcast to smoke did not produce the explosions I previously discussed, and we didn't get a man's mass worth a fire exploding out of the alley. (If we use .3 kg/m^3 as the density of flame, and assume the thug has 100 kg. the mass preserving soulcasting would produce over 300 cubic meters of flame).

The only real evidence of mass conserving soulcasting is the inrushing air during creation of stone structures from air, but this is also a special case where the object being soulcast wasn't already a specific shape or volume. It is also special because it is soulcasting only a part of what is otherwise a continuous whole (a technique that we haven't seen before), and it is not clear what would comprise the cognitive aspect of the atmosphere. 

Edited by LiquidBlue
typo: ally -> alley
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Respectfully disagree all you want, but Brandon has stated how he feels the magic works and has attempted to portray it the best that he can. He doesn't have a high-level science background and most definitely isn't a physicist by any stretch so it's likely that most of the nuances that you are presenting here weren't kept in mind when he wrote those scenes. If you do feel like those scenes inadequately present what he has stated is happening, perhaps contact Peter his assistant with suggestions for better to portray it. You do make good points and it would be nice to have a better tie-in to science since that is what Brandon has expressed wanting.

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Yeah I think Brandon is intending that conservation of mass happens most of the time, but that he misses some instances because he's not a physicist.  Peter is the science nerd on the team.

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Solid to solid seems to preserve volume. Varied states seem to preserve mass. It may not be the level of explosion outward that should result in proper physics, but the Boulder to smoke was far more than just convective motion. It was an explosion outward that ruined paintings and needed the entire hallway to be scrubbed clean.

If it were merely volume, you'd have had a boulder shaped cloud of smoke that would have cleared quickly and covered far less area.

Brandon's math is definitely off, if he bothered with it at all, but there is definitely more smoke than could fill the Boulder shape from volume alone. 

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A bunch of us on the Discord did the math on the boulder, and got a lot less pressure than you indicated.

We calculated the pressure produced by that much TNT in the volume of the boulder (assuming the boulder was around 0.5 m^3), and got 8.368 GPa, which is orders of magnitude greater than our calculation.

 

Spoiler

Givens: PV = nRT

Density of granite = 26.91 kg/m^3

Approximate molar mass of smoke = 58 g/mol (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2004JD005628)

Room temperature = 293K

ideal gas constant (R) = 8.3144598 kg * m2 / (s^2 * K * mol)

 

P(smoke) = (moles) * R * (T of stone)/(V of stone)
mass of stone = (V of stone) * (Density of stone)

assuming stone is granite for simplicity

mass of stone = V * 26.91 kg/m^3
assuming mass of smoke is equal:
moles of smoke = mass of smoke / molar mass of smoke


P(smoke) = (moles) * R * (T of stone)/(V of stone)

P = (V * density / molar mass) * R * T of stone / V
P = density * R * Temperature / molar mass

assuming room temperature, this gives us a number

26.91kg/m^3 * (8.3144598 kg * m2 / (s^2 * K * mol)) * 293 K / (58 g/mol)

1.13 MPa, or about 160 PSI

 

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Because Pedantry is the Second Rule of 17th Shard Discord :D

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1 hour ago, WireSegal said:

A bunch of us on the Discord did the math on the boulder, and got a lot less pressure than you indicated.

We calculated the pressure produced by that much TNT in the volume of the boulder (assuming the boulder was around 0.5 m^3), and got 8.368 GPa, which is orders of magnitude greater than our calculation.

 

  Reveal hidden contents

Givens: PV = nRT

Density of granite = 26.91 kg/m^3

Approximate molar mass of smoke = 58 g/mol (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2004JD005628)

Room temperature = 293K

ideal gas constant (R) = 8.3144598 kg * m2 / (s^2 * K * mol)

 

P(smoke) = (moles) * R * (T of stone)/(V of stone)
mass of stone = (V of stone) * (Density of stone)

assuming stone is granite for simplicity

mass of stone = V * 26.91 kg/m^3
assuming mass of smoke is equal:
moles of smoke = mass of smoke / molar mass of smoke


P(smoke) = (moles) * R * (T of stone)/(V of stone)

P = (V * density / molar mass) * R * T of stone / V
P = density * R * Temperature / molar mass

assuming room temperature, this gives us a number

26.91kg/m^3 * (8.3144598 kg * m2 / (s^2 * K * mol)) * 293 K / (58 g/mol)

1.13 MPa, or about 160 PSI

 

Awesome! It's good to see the work. How did you estimate the TNT equivalent? I tried to avoid using a molecular theory since I wanted to avoid coming up with a molar mass for "smoke".

Instead, I think that we can do a good job with pressure, volume, and air density.
 

Spoiler

P_c = pressure of the smoke when it is compressed within the volume of the boulder
P_e = pressure of the smoke at STP (1 atm)
V_c = volume of the smoke when it is compressed within the volume of the boulder (the volume of the boulder)
V_e = volume of the smoke at STP
d_stone = density of stone
d_smoke = density of smoke at STP
m = mass of the boulder

For convenience note the V_stone = V_c = m/d_stone, and that V_e = m/d_smoke.

P_e*V_e = P_c*V_c
=> P_c = P_e * (V_e/V_c)
=> P_c = (1 atm) * (m/d_smoke * d_stone/m) = (1 atm) * (d_stone/d_smoke)

I used for the density of the boulder 2.7 g/mL, and for smoke 1.3e-3 g/mL, giving a pressure for the compressed smoke, ~2000 atm. (Hmm... I claimed 770 atms before.)

Let's do a consistency check with your numbers. Density of the boulder is 26.91 kg/m^3 (Already we see a problem, the density of styrofoam is 45 kg/m^3), density of smoke (at STP) = 58 g/mol * 1/22.4 mol/L = 2.6 kg/m^3 => Pressure of compressed smoke is ~10.4 atm ~150 psi.

Okay, so we didn't get the same answer even using the same numbers, but I think the two methods are roughly consistent. (160 psi vs. 150 psi). The problem is, it seems like you were using the wrong density for the boulder. 

Although it is of lesser importance, I don't agree with your choice of the molar mass of smoke. In the scene, the smoke is shown to rise, so it must have a density less than air. (I used the density of air in my calculation.)

Edited by LiquidBlue
Should be 10.4 atm, not 14 atm.
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all that math is a bit beyond me but i am curious to know if the rock to smoke soulcasting that happened in oathbringer 

(not really a spoiler but to play it safe...)

Spoiler

which was underwater by the island of aimia 

 was mathematically accurate  so if someone were to go ahead and calculate that it would be appreciated : ) 

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I'm a bit late to this party, but I'd like to put in my 2 cents on the subject of the human to stone problem. I think there is a very simple explanation. With the windbreak, the ardents wanted it to be dense, so the air compressed and changed. With the boulder, gas naturally wanted to expand. With the human statue, Jasnah just wanted him to turn to stone. You guys keep focusing on the density, but if when she changed the guy to stone all of the atoms converted, it's entirely possible they kept the same or similar configuration. Maybe it did shrink a little because of the mass to energy to mass conversion, but if the atoms stayed spread out, then conversion of mass is kept while still having the statue be roughly the same size. Of course this would bring up the problem of the crystal being weak and cloudy probably. Eh, just some food for thought

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You underestimate the mass added by a few septillion particles.

thats the whole debate.

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Hi,


Sorry for trying to resurrect this thread. I just want to stimulate a little more discussion.

I really think that all of the canonical examples of soulcasting show that it is volume preserving and not mass preserving. Even the rock to smoke example shows this. The boulder was changed to smoke which then billowed out. This isn't a counter example, Jasnah either consciously or subconsciously soulcast the boulder to compressed smoke, but there was not nearly enough smoke to account for the entire boulder's mass.

So does soulcasting violate conservation of matter/energy? Maybe... probably... does it matter? It seems like soulcasting isn't rearranging the nucleons/atoms/molecules of the object, but simply replacing the substance of the object with a different essence.

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On 5/10/2018 at 9:24 AM, LiquidBlue said:

Hi,


Sorry for trying to resurrect this thread. I just want to stimulate a little more discussion.

I really think that all of the canonical examples of soulcasting show that it is volume preserving and not mass preserving. Even the rock to smoke example shows this. The boulder was changed to smoke which then billowed out. This isn't a counter example, Jasnah either consciously or subconsciously soulcast the boulder to compressed smoke, but there was not nearly enough smoke to account for the entire boulder's mass.

So does soulcasting violate conservation of matter/energy? Maybe... probably... does it matter? It seems like soulcasting isn't rearranging the nucleons/atoms/molecules of the object, but simply replacing the substance of the object with a different essence.

If the boulder example was volume preserving, it wouldn't have "billowed out" - it would have been sucked in due to the decrease in density.  

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How do we know soulcasting solids doesn't conserve mass? Maybe people soulcasted into statues are hollow. That would preserve the volume/shape while allowing for mass conservation.

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On 5/21/2018 at 0:46 PM, Scion of the Mists said:

If the boulder example was volume preserving, it wouldn't have "billowed out" - it would have been sucked in due to the decrease in density.  

Density doesn't have anything to do with it, only pressure. I've conceded that the soulcasting of the boulder wasn't just soulcasting to room pressure smoke since the outward flow was much too vigorous for that, but it wasn't nearly vigorous enough if mass was being conserved. I think that the boulder was soulcast to pressurized smoke, because that was the result people expected.

On 5/21/2018 at 2:25 PM, Knight Oblivion said:

How do we know soulcasting solids doesn't conserve mass? Maybe people soulcasted into statues are hollow. That would preserve the volume/shape while allowing for mass conservation.

I doubt that hollow structures is really the answer, but let's look at it.

What if we soulcast Dalinar Kholin into a nice (hallow) marble statue. I don't know how tall Dalinar is, or how much he weighs so let's use Hulk Hogan. He is about 200cm tall and 137 kgs.

Marble has a density of ~2700 kg/m^3. So a Dalinar mass of marble occupies .05 m^3. The surface area of the Dalinar statue is about 1.9 m^2, so a hollow, volume conserving statue would have a shell with a thickness of .05m^3/1.9m^2 = 0.026m = 2.6cm. Which doesn't seem too unreasonable, but the structural qualities of the soulcast material become important (both to support the shape of the object and support it against the vacuum in the void of the object.)

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51 minutes ago, LiquidBlue said:

Density doesn't have anything to do with it, only pressure. I've conceded that the soulcasting of the boulder wasn't just soulcasting to room pressure smoke since the outward flow was much too vigorous for that, but it wasn't nearly vigorous enough if mass was being conserved. I think that the boulder was soulcast to pressurized smoke, because that was the result people expected.

Oh, I missed that you specified compressed smoke.  I was assuming standard pressure, which would result in an implosion (same volume, less mass).  

I imagine that Brandon was intending it to be mass-preserving, but his math was off by a bunch.  That seems a simpler explanation than Jasnah intentionally Soulcasting the boulder into very compressed smoke.  There's not really any reason for her to do that.  

Any "violation" of mass/energy can be hand-waved away by the introduction of Investiture (because magic).  

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On 5/25/2018 at 3:10 PM, Scion of the Mists said:

 I was assuming standard pressure, which would result in an implosion (same volume, less mass).   

There is no implosion. Being at the same pressure means that there is no net force at the boundary.

On 5/25/2018 at 3:10 PM, Scion of the Mists said:

I imagine that Brandon was intending it to be mass-preserving, but his math was off by a bunch.  That seems a simpler explanation than Jasnah intentionally Soulcasting the boulder into very compressed smoke.  There's not really any reason for her to do that.  

She may have done it intentionally. But even if not, it might have been an unconscious thought. Shallen expected the volume of smoke to exceed the volume of the boulder because of conservation of mass, Jasnah might have had the same expectation. If Jasnah didn't do it consciously to feed into the expectations of the audience, she might have done it unconsciously because of her own expectations.

On 5/25/2018 at 3:10 PM, Scion of the Mists said:

Any "violation" of mass/energy can be hand-waved away by the introduction of Investiture (because magic).  

This was one of my thoughts when I first started to think about it... That the difference in mass can be explain by the conversion of investiture to mass. However, I don't think that it is so simple. This would mean that soulcasting to a dense material would require more investiture, likely much, much more. And doesn't explain what happens to the missing mass/energy/investiture when soulcasting to a less dense material.

My theory at the moment is that the investiture is acting as a catalyst allowing the change from one essence to another. Even though the soulcasting is done by speaking to the cognitive aspect of the object, I think that it is effecting a spiritual change... Instead of rearranging what is there, soulcasting is changing the essence of the object.

This I think is a good explanation. Mass/Energy conservation comes from the time invariance of physical laws; however, for realm, such as the spiritual realm, that doesn't experience time, I don't think that mass conservation should be expected to hold true. 

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perhaps both conversions (light\dense and dense\light) take the same amount of stormlight and the excess energy of the the denser materiel transforms back into stormlight to either help fuel the change or goes back into the gem? or not at all b\c e=mc2 isn't stormlight=mc2

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