Cosmere E=mc^2

[Elsecaller_17.5]

First, this isn't going to make much sense unless your caught up with the The Lost Metal Release chapters including today's. Second, I am a amateur physicist at best; I've completed a (singular) college physics class.

So Wax just invented nuclear bombs. Fun. But good old E=mc² isn't going to quite do that for us with investiture in the mix. Harmony has confirmed that we need to get an I in there somewhere. To my mind the I has to modify the m. c² is a constant and isn't going to be affected, energy is the output. The two simplest results would be

E = MI c²

or

E = M^I c²

I could also see E = MsubI C² allowing for a far more complicated relationship between M and I.

People who are smarter than me please tear this to pieces. I've put this in the cosmere spoiler area in case you want to involve RoW physics somehow.

Edited November 7, 2022 by Elsecaller_17.5

[offer]

There is both the regular matter-energy equivalent and another investiture-energy equivalence.

So the equation should be E = Mc^2 = I *k 

For some constant k.

[Elsecaller_17.5]

1 minute ago, offer said:

There is both the regular matter-energy equivalent and another investiture-energy equivalence.

So the equation should be E = Mc^2 = I *k 

For some constant k.

But what about invested matter. It seems that invested matter has more fundamental energy. Could it just be E = Mc^2+I and we need a way to quantity I?

[offer]

25 minutes ago, Elsecaller_17.5 said:

But what about invested matter. It seems that invested matter has more fundamental energy. Could it just be E = Mc^2+I and we need a way to quantity I?

Yes, exactly.

I think that it is like a spring that has more energy when it is compressed - there is still the Mc^2 term, but there is aditional term for the potential energy.

[Ixthos]

1 hour ago, Elsecaller_17.5 said:

First, this isn't going to make much sense unless your caught up with the The Lost Metal Release chapters including today's. Second, I am a amateur physicist at best; I've completed a (singular) college physics class.

So Wax just invented nuclear bombs. Fun. But good old E=mc² isn't going to quite do that for us with investiture in the mix. Harmony has confirmed that we need to get an I in there somewhere. To my mind the I has to modify the m. c² is a constant and isn't going to be affected, energy is the output. The two simplest results would be

E = MI c²

or

E = M^I c²

I could also see E = MsubI C² allowing for a far more complicated relationship between M and I.

People who are smarter than me please tear this to pieces. I've put this in the cosmere spoiler area in case you want to involve RoW physics somehow.

Interesting idea  however, E=m*c^2 (though from what I understand, that is only for the rest mass, and when dealing with moving objects the equation is a little bit longer, and I think it has a ^4 in it somewhere ...) is all about determining the amount of energy a chuck of matter has based on its mass - it is the relation between energy and matter. Rather, what you want is one other equation, say the equation that relates a given amount of energy to a certain amount of investiture, and from there one could then derive an equation for a relation between investiture and matter. The key point is that investiture, while it can become energy and / or matter, is not bound by a set amount within a given invested item - after all, if Wax were to full his ironminds the total mass of the Wax-ironmind system would go down, but the amount of investiture would go up. I don't think a full metalmind has any difference in weight to an empty one, thus there is no way to multiply the two, but rather one would have to add a "+ (energy-investiture relation)" into the mix.

So the equation would be (for a rest mass):

• E (energy of the item, say a metalmind) = m*c^2 (uninvested rest mass of the item) + "I*R" (I being the amount of investiture the item has, R being the energy-investiture relation)

With R as a constant, just as c^2 is a constant based on the constant c. It could be R is a more complex number, but related to some other cosmere constant.

Edited November 7, 2022 by Ixthos
Fixed equation, added quote, added more detail to reply

[Firesong]

I don't think that it is going to be as simple as just one formula, I think that the Investiture-Energy and Investiture-Mass relations are different than Energy-Mass. So, maybe it is indeed more like E = M(sub)i*c^2. At least that is how I interpreted it. With M_i being the mass of the God Metal. 

 

Also, yes, E=mc^2 is about rest mass. Full one is E^2 = (mc^2)^2 + (pc)^2. With p being momentum. M is specifically rest mass, therefore, it is not the whole m * (1/sqrt(1-(v^2 / c^2))) thing. 

Edited November 7, 2022 by Firesong

[18th Shard]

I think the relevant question here is whether adding Investiture to a metalmind makes it (even infinitesimally) more massive. I think it would. Adding energy (kinetic, potential, or thermal) to something increases its mass a little bit, and massive concentrations of Investiture, like a perpendicularity, can cause some time dilation. E^2=(mc^2)^2+(pc)^2 really is saying that any energy added to a system increases either its mass or momentum. Adding an Investiture term should really just describe the same thing.  In that case, I would think it would be something like: (E/c)^2+(I/k)^2=(mc)^2+p^2, where k is an arbitrary constant to get Investiture in compatible units at the right ratio. 

Edit: Or perhaps (E/c)^2=(mc)^2+p^2+(Ik)^2 + i^2, where I is passive Investiture and i is kinetic Investiture, analogous to rest mass and momentum. 

Edited November 8, 2022 by 18th Shard

[KaladinWorldsinger]

I have always felt that investiture is just spiritual energy or energy with emotions,thoughts and souls attached so should be very similar. Like

I=KE=Kmc^2

For some constant K

[+Child of Hodor]

On 11/7/2022 at 2:14 PM, Elsecaller_17.5 said:

First, this isn't going to make much sense unless your caught up with the The Lost Metal Release chapters including today's. Second, I am a amateur physicist at best; I've completed a (singular) college physics class.

So Wax just invented nuclear bombs. Fun. But good old E=mc² isn't going to quite do that for us with investiture in the mix. Harmony has confirmed that we need to get an I in there somewhere. To my mind the I has to modify the m. c² is a constant and isn't going to be affected, energy is the output. The two simplest results would be

E = MI c²

or

E = M^I c²

I could also see E = MsubI C² allowing for a far more complicated relationship between M and I.

People who are smarter than me please tear this to pieces. I've put this in the cosmere spoiler area in case you want to involve RoW physics somehow.

On 11/7/2022 at 2:26 PM, offer said:

There is both the regular matter-energy equivalent and another investiture-energy equivalence.

So the equation should be E = Mc^2 = I *k 

For some constant k.

When I read the lab scenes in the preview chapters my eyes kind of glazed over. "Another lab experiment scene with an explosion so soon after RoW?". But this thread is a lot of fun to read and makes me more interested in the magiscience. Thank you!

 

[Firesong]

On 11/7/2022 at 2:14 PM, Elsecaller_17.5 said:

First, this isn't going to make much sense unless your caught up with the The Lost Metal Release chapters including today's. Second, I am a amateur physicist at best; I've completed a (singular) college physics class.

So Wax just invented nuclear bombs. Fun. But good old E=mc² isn't going to quite do that for us with investiture in the mix. Harmony has confirmed that we need to get an I in there somewhere. To my mind the I has to modify the m. c² is a constant and isn't going to be affected, energy is the output. The two simplest results would be

E = MI c²

or

E = M^I c²

I could also see E = MsubI C² allowing for a far more complicated relationship between M and I.

People who are smarter than me please tear this to pieces. I've put this in the cosmere spoiler area in case you want to involve RoW physics somehow.

I doubt it is  M^Ic²  unless the I is greatly modified to be a very small number usually. Like, (1+ I0/k) or (1+(I0*k)) for a simple form, but might include like, more exponents or logarithms. Also, I0 means the pure amount of Investiture in it, before modification into the form it needs to be for M^Ic².

More likely, it is something more like E = Mc² + (investiture part), is more likely, I feel. Which separates them, multiplying them up individually and adding up the products. This is of course only using the calculation for a resting object. E² = (pc)² + (mc²)² Is the full one, which would become like, ((pc)² + (mc²)² ) + (investiture part), with the investiture part likely also modified to include the effects of momentum and variant mass. 

Also, how did you get the superscript?  doesn't work and can't find any settings on this site for it.  

Edited November 9, 2022 by Firesong

[AquaRegia]

I encourage everyone to keep in mind that Brandon is a storyteller, NOT a physicist.  I'm a science nerd too, and I get that it's fun to try to work out the rules; by all means, carry on!  But he has already admitted how his "science people" get headaches trying to work out how Cosmere FTL and time dilation will work. 

In the end I think the rules are going to be whatever works best for the stories, not what satisfies a rigorous mathematical relationship.

[18th Shard]

Quote

Questioner

Your magic systems are very structured, and specific rules that dominate them. But are there any universal laws that apply to all of the magic systems in the cosmere together?

Brandon Sanderson

Yes, there's several of them. Basically, the most important one and relevant to people who enjoy real physics is that I consider something called Investiture to be a third state of matter and energy. So, instead of e=mc^2, we have a third thing, Investiture, in there. And you can change Investiture to matter or to energy. And so, because of that, that law that you can do this, is where we see a lot of the cosmere magics living.

We also have a kind of rule that beings all exist, everything exists on three different levels. The Physical, the Spiritual, and the Cognitive. And, like we have DNA for our Physical self, we also have Mental DNA and Spiritual DNA, and all three influence one another. For instance, you couldn't test an Allomancer's blood and find the Allomancy gene, because it is in a different set of their DNA. You just have three sets. You could compose a test that could test it on the Spiritual Realm, but you're gonna have to use a different branch of physics to do that and determine who was an Allomancer. And so they all work on this kind of fundamental rules of: your Identity, your Connection, and being part of your soul, and the magics working through those things.

So there's some fundamental rules about this, about changing forms from energy to matter, and you having this Identity, Investiture, and Connection stored in your Spiritual DNA that are really relevant to everything.

ICon 2019 (Oct. 15, 2019)

Quote

Questioner

How much have you thought about the mathematical relationship between Investiture and energy/matter? Is there a cosmere E=mc^2?

Brandon Sanderson

I've thought about the concepts a lot. The numbers, I actually tried to get some mathematicians... There are some lovely folks, I'm like, can we come up with a standardization? And it kind of broke their brains, not because they aren't smart people, they're very smart people, but they're like, "Brandon, where do we even start? How much energy is being expended?" and this sort of thing. I would like to get a unit of measurement, how much Investiture equals how much energy, but at the same time, the work being done by the various magic systems, it's going to be too constrictive to put too much math on that, I feel like. I would like to. It is a much bigger project than you might imagine it being. How much energy is stored in a sphere? That's kind of where we started. A sphere stores Investiture, obviously some of that Investiture is being lost as energy, it is transferring energy as the sphere releases light. That is happening automatically, it's decaying and radiation is happening. How much is it therefore losing, how much could it do, how much of that can be transferred to doing work with a Lashing... All of this stuff, I have thought about way too much, and we have no answers for you yet because it is a really big project. Maybe we will someday, or maybe we'll just say, this is too big a project to even be able to mathematically quantify. I'm sure if you have suggestions, you can post thoughts on the subreddits, and perhaps that will get to the various arcanists who are helping me with this.

YouTube Spoiler Stream 4 (June 16, 2022)

 

[Leuthie]

By final era Mistborn (the one in space), there will be some rough calculations regarding Investiture to Energy to Matter and back. Until then, the idea that such conversions exist is enough to keep the magic systems in check.

I speculate that there will be three reversible equations: E=Mc^2, I = Mk and I = Ei, where k and i are constants defined by Cosmere rules and whose units work to convert the units of Mass and Energy to units of Investiture (Energy is Force times Distance which is equivalent to Mass times Velocity Squared, which is where the speed of light squared term comes from).

Quote

E = MI c²

or

E = M^I c²

These wouldn't work unless Investiture is unitless, which would be a copout in such a system. Investiture should have some unit of measure.

[NerdyAarakocra]

I think that it would be something like E=(M+I)C^2 or E=MC^2+IC^2

I suppose that it depends on how we quantify investiture.