Mass, Density, and Investiture

[StanLemon]

So a while back on one of the Fullborn vs Radiant threads there was a lot of talk about mass and density and how F-Iron doesn't make sense. 

I threw out an equation off the cuff about how to ro rectify this

m=(p x V) x I 

m - mass

p - density

V - volume

I - Investiture 

There were a few issues with this as it was a quickly put together equation. But one of the arguments was that it implies Investiture changes mass and things like Nightblood were brought up that it isn't super heavy etc.

However this book does straight up say that high levels of Investiture seemingly does alter mass. Or at least acts as additional mass on spacetime.

A line from the book also caught my attention 

Quote

It created far more gravity than it should have for its size—so either it was incredibly dense or incredibly Invested.

The part I found interesting, which admittedly could be reading too much into the wording, is the implication that even though it has this mass like property it doesn't affect density.

This could explain some of the F-Iron weirdness in that the Investiture for Iron Feruchemy could be going toward just this property of Investiture thus explaining the mass/density contradiction partially. There are other issues but it could be a start

[Serack he/him]

Just some back of the envelope calculations based off of info from TSM and the Arcanum Unbound (roshar being ~0.7 of standard gravity), I've come up with the following rough values for Canticle.  Note, the numbers for earth that I used to get this (assuming standard gravity is earth's) resulted in a calculated density for earth that was off by about a factor of 1.5, compared to what the internet says is the average density of the Earth, so consider these very back of the envelope, on the scale of less than an order of magnitude.  

Mass (kg) =~2.7x10^21 (4/10,0000 that of the earth)

Density (kg/m^3) =~ 2x10^5 (~30x as dense as earth)

Note, this is about 10x as dense as Tungsten or Gold. 

The density is within the range of densities of white dwarfs provided by wikipedia (10^4 to 10^7), but the smallest of those has 0.17 the mass of the sun, or 100,000,000 as massive as Canticle (and is much larger in size than 200 miles in diameter).  Denser objects like Neutron Stars and stellar black holes are even heavier.  A Black hole with Canticle's mass would have a Schwarzschild radius way smaller than the earth's (0.88 cm) so that's probably not what is going on either.  

Conclusion:  Canticle is 10x as dense as pretty much anything we encounter on earth, but can't really be compared to any stellar objects because it has way too little mass.

 

Footnote:  mass was calculated using Newton's gravitational force equation assuming Canticle's force at the surface is ~0.7 that of earth's with a radius of 100 miles.  

Edited October 6, 2023 by Serack

[Firesong she/her]

On 10/6/2023 at 10:01 AM, Serack said:

Just some back of the envelope calculations based off of info from TSM and the Arcanum Unbound (roshar being ~0.7 of standard gravity), I've come up with the following rough values for Canticle.  Note, the numbers for earth that I used to get this (assuming standard gravity is earth's) resulted in a calculated density for earth that was off by about a factor of 1.5, compared to what the internet says is the average density of the Earth, so consider these very back of the envelope, on the scale of less than an order of magnitude.  

Mass (kg) =~2.7x10^21 (4/10,0000 that of the earth)

Density (kg/m^3) =~ 2x10^5 (~30x as dense as earth)

Note, this is about 10x as dense as Tungsten or Gold. 

The density is within the range of densities of white dwarfs provided by wikipedia (10^4 to 10^7), but the smallest of those has 0.17 the mass of the sun, or 100,000,000 as massive as Canticle (and is much larger in size than 200 miles in diameter).  Denser objects like Neutron Stars and stellar black holes are even heavier.  A Black hole with Canticle's mass would have a Schwarzschild radius way smaller than the earth's (0.88 cm) so that's probably not what is going on either.  

Conclusion:  Canticle is 10x as dense as pretty much anything we encounter on earth, but can't really be compared to any stellar objects because it has way too little mass.

 

Footnote:  mass was calculated using Newton's gravitational force equation assuming Canticle's force at the surface is ~0.7 that of earth's with a radius of 100 miles.  

I will say, they actively bring up that it is denser than any natural element. Also, I got a different number for the density. I got 152.57 g/cm3. Which is not in the range of White Dwarf Stars, which are around 1000 10^4 to 10^7 g/cm3. This is only 1.5257 * 10^2. Not White Dwarf levels, but still around 6.7539x the density of osmium. And due to the fact that the overall density is lowered due to the density of the silicate layer which is implied to be Earth-like, so around 3-4 g/cm3, so the actual density of the core would be higher than 152.57, but not by much. But we don't know the core sized compared to the planet, so we can't say with absolute certainty. 

I also got a total mass of 0.000446043 Earths, so a bit higher than what you got. 

My thought is that it isn't that Investiture acts like mass (though it can be converted into mass), but that it causes the same spacial distortions that are what define gravity. 

Spoiler

 Image of what gravity essentially is, it is a distortion of spacetime. If we go into the realm of fantasy, this doesn't necessarily have to be from just mass. But high amounts of Investiture could give an object an increased level of spaciotemporal distortion without increasing its mass. That, or it creates a Gravitation effect like the Gravitation Surge.