A Quantum Description of Investiture

[idanstark42 he/him]

I started reading the cosmere on the first year of my degree in physics and sociology, and after reading most of it (reading Edgedancer now, and missing Shadows of Silence and SP4), I looked at some of the spoiler streams and saw that someone asked about E=mc^2, and Brandon said that he didn't develop the math for this, since it would be to restricting, and that there were some problems, like how a sphere can emit light without losing energy. So, being a young eager physics student, I sat down and found solutions, for the sphere and for the restriction issue. Then... I developed these solutions. I found why Investiture acts at times like matter and at times like energy, how it causes effects in the Physical Realm, and what, assuming the solutions are turn, must be the structure of the Spiritual and Cognitive Realms. This allowed me to formulate a quantum description for Investiture and a General Relativity description for Realmatic Theory (which I think still needs some work).

Anyway, I wanted to share this, so I wrote a paper called "A Quantum Description of Invesisutre". It's presumebly written in world, so no scientific names are there, though there are a lot of scientific terms. I used one side of the alethi caligrapher's script for some of the equations. Please tell me what you think,

 

A Quantum Description of Investiture.pdf

[idanstark42 he/him]

Did anyone get a chance to read this? I would love some feedback

[Frustration]

5 hours ago, idanstark42 said:

Did anyone get a chance to read this? I would love some feedback

Sorry I've been meaning to but just haven't had the time.

Brandon is working on this with his team so it might be worth it to send him a copy.

[DrPhysics he/him]

I haven't made it all the way through yet, but in the end of section one, Example 1.1, you make this statement (and the math to match): "This Connection allows them to draw on a constant stream of Investiture, creating a constant Force."

Steelpush/pull behavior isn't described well with constant force. Instead, the amount of investiture used correlates better with the amount of power delivered to the object. For example, let's look at the scene in the first book where Vin pushes the coin into a wall and she goes flying backward. If she were exerting a constant force, thanks to Newton's third law, should would feel a constant force back and wouldn't be able to tell when the coin hit the wall. At constant power, the rapidly decreasing velocity that the coin experiences when it hits the wall creates a rapidly increasing force (Since P=Fv for moving objects), causing Vin to suddenly fly backward.

What level of degree did you get in physics? 

[Argenti he/him]

Oh god I'm really gonna need to learn Physics for Brandon

Edit:
I tried, I really tried, you lost me at page 3

Edited October 19, 2023 by Argenti

[Voidmaker he/him]

I'd love to give feedback, but I'm still in high school. I find it hard to comprehend the words, let alone all the formulas.... 

[idanstark42 he/him]

On 10/18/2023 at 10:19 PM, DrPhysics said:

Steelpush/pull behavior isn't described well with constant force. Instead, the amount of investiture used correlates better with the amount of power delivered to the object. For example, let's look at the scene in the first book where Vin pushes the coin into a wall and she goes flying backward. If she were exerting a constant force, thanks to Newton's third law, should would feel a constant force back and wouldn't be able to tell when the coin hit the wall. At constant power, the rapidly decreasing velocity that the coin experiences when it hits the wall creates a rapidly increasing force (Since P=Fv for moving objects), causing Vin to suddenly fly backward.

First of all, thank you for replying a serious idea! I've been waiting for someone to discuss this with!

You are right of course. There are a few great threads discussing this scene in particular making absolutly no physical sense, giving all sort of solutions (from the force being relaying on the mass of the percieved object, on the relative speed of the coinshot and the coin, and on the amount of purified metal).

Here are a few:

I regarded the force as constant, looking at the simple example of "coinshot pushing a coin with no disturbance", without adding any Heaviside Functions or other not-so-pretty changes to the system. In that particular case, without other forces being non-conservative, the allomantic force actually acts, by most accounts, as a regular inverse square force. I took the liberty of approximating it to a constant much like gravity is, but it probably really isn't very accurate in small distances.

I really did make a lot of assumptions and took the easy path in the first part, since it was just laying groundwork for chapter 2, which is the main part of the article. I would love to hear you opinion about it. What did you think about Investiture being Anyons in the Spiritual Realm?

BTW I am on the third year of my Physics & Sociology Bs.C. (bachelor's degree).

Thank you again for reading and writing back!

[idanstark42 he/him]

On 10/19/2023 at 6:25 PM, Argenti said:

I tried, I really tried, you lost me at page 3

If you have questions or want an explanation about anything, please write to me  The important part is the second chapter, I believe

[Alumínio he/him]

I haven't been able to follow all the reasoning behind your formulas yet, but I have a doubt.

In the case of the steelpush, in addition to using the person's weight, there is also their efficiency in using magic.

Brandon said that the strongest people in the magic system are like this because they use investiture more proficiently, that is, they waste less, and I don't think it's possible to calculate an ironpull or stellpush because of the character's own appearance and how much proficiency he has in his invested art.

But and you? Do you think there is a way to add this to the formula?

[Argenti he/him]

2 hours ago, idanstark42 said:

If you have questions or want an explanation about anything, please write to me  The important part is the second chapter, I believe

I haven't taken a physics class at all sooo. All I know is F=MA XD

I'm a lost cause

[idanstark42 he/him]

53 minutes ago, Argenti said:

I'm a lost cause

Journey before destination my friend

Here's the basic idea, for non physicts to understand. Please ask if you have questions. The debate is the point:
part 1
Investiture causes forces in our world. Forces that can be quantified. I show one (very simplistic) example of this, making a lot of assumption to make life easier for me, since this is not the point of the article. The most important thing to take from here is that for Invested art to work you need both Investiture and Intent. Intent leads the Investiture to become energy, or matter. Not all uses of Investiture is allowed to anyone with Intent, you need other factors, that are discussed next.
part 2

This is the interesting part. The idea is to show that since Investiture is neither energy nor matter, it must be something else. A third kind of particle. The only one that is mathematically possible is one that is called Anyon, which is named as such since it can take any phase on the range from energy to matter (yes, that is a range. In our world only those two are possible, but some anyons in rare cases exist here two).

Anyons technically only live in two dimensions, and since Investiture lives in the Spiritual Realm, it leads us to understand that each soul is basically a two-dimensional sheet, like a piece of paper all tangled up within itself. The simplest example of such structure (called a manifold) is a sphere, like earth. Though the sphere is in 3d, we can walk on it as if it were 2d. Now start poking holes in it, connected different sides of the sphere to eachother, making knots and a complex web (spiritweb if you will), and you got a complex structure that could hold Investiture.

So, in summary so far, the spiritweb is a very copmlex 2d manifold that can contain Investiture. Investiture is a quantum particle (anyon) that lives within the spiritweb.

But here is the thing about quantum particles. They are quantized. This means that only very specific particles can exist. Which particles can exist is based on two things: the structure of the spiritweb, and the forces acting in it. The the move the Investiture, are the Invent as established in the first section. The structure makes up the Identity.

One last thing that can control the type of Investiture is the Connection to other sources of Investiture. If that specific type of Investiture never enters the Spiritweb, it cannot use it. Connections are a bit tricky mathematically, but let's just say that they are point where the spiritwebs collide with eachother, allowing the passage of Investiture, along with other things.

One final thing we establish here is vertical connections, which are actually the bonds between a spirit and a body. This is not a regular Connection as known so far in the cosmere, since it doesn't connect sould or spiritwebs. Instead it allows the passage of energy between realms, much like a perpendicularity, only not through bending the realms.

part 3

Since the Spiritual Realm is 2d and the physical realm is 3d, there is a gradient of realms, with fractional dimensions. This is pretty trippy to think about, and is closely related to fractals, but in essance, the Cognitive Realm is created as a shadow between the two realms by the perception field, which lives on the connection of the body and the spirit.

part 4

spoiler for sunlit man

Spoiler

black body radiation, discussed in the next section, is mentioned in the sunlit man, not as black body radiation, but as infrared radiation. Even though a lot of manifestations of black body radiation in our world and in the cosmere (including glowing lava, glowing hot metal, and of course, fire) are not infrared and are actually visible. Nevertheless, the phenomenon described is black body radiation as we know it, transferring heat in a vaccum. This shows us that black body radiation exists in the cosmere, and since it is a quantum effect, that the cosmere is based on quantum mecahnics.

This part is just meant to explain that a sphere radiating light without losing energy is easily explained, by comparing it to what's called black body radiation. This is a radiation where a body that has a temperature, emits in relation to the temperature it has. In the same sense, the Investiture that a body causes it to emit light to the surroundings. For the same reasons Elantrians glow, the mists glow sometimes, stromlight glows, perpendicularities glow, the Dor glows, and so on.

 

I think that's it. If you have questions about specific parts, or general ones, let me know. If I still overshot with my theories, I'm sorry, and if you still want to understand I will happily explain it in more details. My part time job is a physics teacher, so don't be disncouraged.

Edited October 22, 2023 by idanstark42

[Argenti he/him]

47 minutes ago, idanstark42 said:

Journey before destination my friend

Here's the basic idea, for non physicts to understand. Please ask if you have questions. The debate is the point:
part 1
Investiture causes forces in our world. Forces that can be quantified. I show one (very simplistic) example of this, making a lot of assumption to make life easier for me, since this is not the point of the article. The most important thing to take from here is that for Invested art to work you need both Investiture and Intent. Intent leads the Investiture to become energy, or matter. Not all uses of Investiture is allowed to anyone with Intent, you need other factors, that are discussed next.
part 2

This is the interesting part. The idea is to show that since Investiture is neither energy nor matter, it must be something else. A third kind of particle. The only one that is mathematically possible is one that is called Anyon, which is named as such since it can take any phase on the range from energy to matter (yes, that is a range. In our world only those two are possible, but some anyons in rare cases exist here two).

Anyons technically only live in two dimensions, and since Investiture lives in the Spiritual Realm, it leads us to understand that each soul is basically a two-dimensional sheet, like a piece of paper all tangled up within itself. The simplest example of such structure (called a manifold) is a sphere, like earth. Though the sphere is in 3d, we can walk on it as if it were 2d. Now start poking holes in it, connected different sides of the sphere to eachother, making knots and a complex web (spiritweb if you will), and you got a complex structure that could hold Investiture.

So, in summary so far, the spiritweb is a very copmlex 2d manifold that can contain Investiture. Investiture is a quantum particle (anyon) that lives within the spiritweb.

But here is the thing about quantum particles. They are quantized. This means that only very specific particles can exist. Which particles can exist is based on two things: the structure of the spiritweb, and the forces acting in it. The the move the Investiture, are the Invent as established in the first section. The structure makes up the Identity.

One last thing that can control the type of Investiture is the Connection to other sources of Investiture. If that specific type of Investiture never enters the Spiritweb, it cannot use it. Connections are a bit tricky mathematically, but let's just say that they are point where the spiritwebs collide with eachother, allowing the passage of Investiture, along with other things.

One final thing we establish here is vertical connections, which are actually the bonds between a spirit and a body. This is not a regular Connection as known so far in the cosmere, since it doesn't connect sould or spiritwebs. Instead it allows the passage of energy between realms, much like a perpendicularity, only not through bending the realms.

part 3

Since the Spiritual Realm is 2d and the physical realm is 3d, there is a gradient of realms, with fractional dimensions. This is pretty trippy to think about, and is closely related to fractals, but in essance, the Cognitive Realm is created as a shadow between the two realms by the perception field, which lives on the connection of the body and the spirit.

part 4

spoiler for sunlit man

  Hide contents

black body radiation, discussed in the next section, is mentioned in the sunlit man, not as black body radiation, but as infrared radiation. Even though a lot of manifestations of black body radiation in our world and in the cosmere (including glowing lava, glowing hot metal, and of course, fire) are not infrared and are actually visible. Nevertheless, the phenomenon described is black body radiation as we know it, transferring heat in a vaccum. This shows us that black body radiation exists in the cosmere, and since it is a quantum effect, that the cosmere is based on quantum mecahnics.

This part is just meant to explain that a sphere radiating light without losing energy is easily explained, by comparing it to what's called black body radiation. This is a radiation where a body that has a temperature, emits in relation to the temperature it has. In the same sense, the Investiture that a body causes it to emit light to the surroundings. For the same reasons Elantrians glow, the mists glow sometimes, stromlight glows, perpendicularities glow, the Dor glows, and so on.

 

I think that's it. If you have questions about specific parts, or general ones, let me know. If I still overshot with my theories, I'm sorry, and if you still want to understand I will happily explain it in more details. My part time job is a physics teacher, so don't be disncouraged.

Hasn't the spiritual been described as a singularity? 

[idanstark42 he/him]

5 hours ago, Argenti said:

Hasn't the spiritual been described as a singularity? 

Yes! That's the great part!

The spiritual realm is a singularity in space and time, but in order to contain any sort of data, or more specifically, energy, it must retain a mathematical structure that can be viewed as its own manifestation of a spacetime. That is not the same space and time as that of the Physical Realm, but rather a different set, working on its own. The meaning of space and time there is... fuzzy, but here are a few things I noticed:

1. The space there might not be 3 dimensional, maybe it's 6 or 21 or infinity dimensions. The important part the is that the manifolds in that space are two dimensional, so that they can contain anyons.

2. Time in our world is called Loretzian. This means that the theory of special relativity applies. While this is probably the case in the Physical Realm, this might not be the case in the Spiritual Realm. If this is indeed not the case, time can be viewed as just another dimension of space, no different then why it the other ones, and there is no meaning to the direction of time there.

3. Connections are based on two Spiritwebs sharing a slight touch where they go together for a very small area before splitting back. This is the most meaningful concept I could find for this space. Somehow generalizing this concept will get us to what this space is.

Perhaps the space of Ideals, each axis representing a different Ideal. Then when they Spiritwebs touch it's because that specific part of them share exactly that same combination of amounts from each Ideal. Maybe.

That was a great question! Thank you for taking interest!

Edited October 23, 2023 by idanstark42
I wasn't clear enough and had typos

[Argenti he/him]

6 hours ago, idanstark42 said:

Yes! That's the great part!

The spiritual realm is a singularity in space and time, but in order to contain any sort of data, or more specifically, energy, it must retain a mathematical structure that can be viewed as its own manifestation of a spacetime. That is not the same space and time as that of the Physical Realm, but rather a different set, working on its own. The meaning of space and time there is... fuzzy, but here are a few things I noticed:

1. The space there might not be 3 dimensional, maybe it's 6 or 21 or infinity dimensions. The important part the is that the manifolds in that space are two dimensional, so that they can contain anyons.

2. Time in our world is called Loretzian. This means that the theory of special relativity applies. While this is probably the case in the Physical Realm, this might not be the case in the Spiritual Realm. If this is indeed not the case, time can be viewed as just another dimension of space, no different then why it the other ones, and there is no meaning to the direction of time there.

3. Connections are based on two Spiritwebs sharing a slight touch where they go together for a very small area before splitting back. This is the most meaningful concept I could find for this space. Somehow generalizing this concept will get us to what this space is.

Perhaps the space of Ideals, each axis representing a different Ideal. Then when they Spiritwebs touch it's because that specific part of them share exactly that same combination of amounts from each Ideal. Maybe.

That was a great question! Thank you for taking interest!

Any guesses on F-Iron?

[idanstark42 he/him]

4 hours ago, Argenti said:

Any guesses on F-Iron?

Do you mean Iron Ferochemy? Because if so,I think that Iron allows to store the Connection to the Higgs Field, allowing more out less mass to be attributed to the axi

[Argenti he/him]

15 minutes ago, idanstark42 said:

Do you mean Iron Ferochemy? Because if so,I think that Iron allows to store the Connection to the Higgs Field, allowing more out less mass to be attributed to the axi

Thats more or less Guess I had too. 

[DrPhysics he/him]

22 hours ago, idanstark42 said:

I really did make a lot of assumptions and took the easy path in the first part, since it was just laying groundwork for chapter 2, which is the main part of the article. I would love to hear you opinion about it. What did you think about Investiture being Anyons in the Spiritual Realm?

I think that it is a cool connection to make, but in the end we just don't have enough information to classify the particles. 

The point of building a good model is to be able to make predictions, and I don't see there being much predictive power here.

I'm also noticing that those two staements above come across much more harshly written down than what I intended. What you have is good work and correct physics.

I'd recommend:

1. keeping this and revising part 2 when you have more quantum under your belt. 
2. Work on developing your classical model a bit more.

I've been through many of the discussions on steelpushing physics around here (and even wrote some about it on reddit, but I don't have enough posts to link.)

Here's a brief summary of what we do know:

1. Direction and strength act much like field forces and follow inverse square law. The product on top depends on the strength of the allomancer and how much metal there is.
   1. Also, skilled allomancers can learn to push with only part of themselves and/or on only part of the object, but forces still follow field lines
2. Inside objects, steelpushes/pulls add like pressure forces, not like field forces (which explains the coin that is held up between Vin and Kelsier, then smashed).
3. The strength of the burn (e.g. lightly burning metals vs flaring them) correlates to the power delivered to the object, but with a base metabolic rate (e.g. it takes some investiture to exert a force, even if no work is done). 
   1. Allomancers can't directly perceive the amount of force they apply, but can feel what it does to their bodies.

[idanstark42 he/him]

On 10/23/2023 at 10:42 PM, DrPhysics said:

I think that it is a cool connection to make, but in the end we just don't have enough information to classify the particles. 

My line of thought was this:
What we know is that they sometimes follow Pauli's principle (Dor, godmetals, stormlight, etc.), and sometimes not (Lashings, Steelpush/Ironpull, Awakening). According to that logic, they must sometimes be bosonic and sometimes fermionic. I thought about having two (or more) quantum fields that are considered "Investiture", and then the different "colors" of Investiture, i.e. the different Shards, being the different fields in this alternative standard model. Then I read that Brandon said that this devision of Shards is not the only one that was possible, and so I went away from that idea.

On 10/23/2023 at 10:42 PM, DrPhysics said:

The point of building a good model is to be able to make predictions, and I don't see there being much predictive power here.

I do believe that there is a lot to be tested here. Spoilers for about everything in the next part (RoW, The Sunlit Man, Warbreaker)

Spoiler

We could try to find Investiture with non-integer phase. We could test the correlation between amount of Investiture (measured in BEU) vs the amount of light emitted from a sphere in every frequency. Maybe compare these findings to the spectroscopy of godmetals. I'm sure that there are more things that I have not considered. This requires creating a measure of Connection strength, of Intent and Preception. This I do not have yet. Maybe that should be the next step, but I am taking your advice (next section).

I did see that one of the things Brandon said that any scientific theory with to much predictive power would overrride his ability to play with things, but he already introduced efficiency in The Sunlit Man, which was the same solution I had in mind.

 

On 10/23/2023 at 10:42 PM, DrPhysics said:

I'm also noticing that those two staements above come across much more harshly written down than what I intended. What you have is good work and correct physics.

Thank you  I think you did great and I'm sorry too if I came to strong, I just really wanted to hear what someone who understands thinks about the part that I did the most work on. I had to learn a bit past my level to create some of this, and since the semester here is being delayed (I'm in Israel, and things are not great here to say the least), I decided that on my off time I would continue to learn into next year's and try and build an understanding towards QFT. Just learned about path integrals and continuing next to the WKB approximation (I know my order is a bit funky, I'm trying to make a sense of things without much guidance right now).

Anyway, thank you for you input and advice, I do have a lot more learning to do, but it's nice to know I'm not totally off here

On 10/23/2023 at 10:42 PM, DrPhysics said:

I'd recommend:

1. keeping this and revising part 2 when you have more quantum under your belt. 
2. Work on developing your classical model a bit more.

Yes. You are definitly right. I want to continue and develop in these directions. Specifially, beyond my regular studies (mentioned above), I want to look into anyons (which are not part of the curriculum) for part 2, and spaces with non-integer dimensions for part 3.

BTW, what did you think about parts 3 and 4? Tell me if I'm asking too much, but I would love to hear your opinions about the ideas:

1. That the Metric and Ryman Tensor of the Cognitive Realm are determined by a field of Perception

2. That the emission of light from a sphere is analogic to black body radiation

 

As for the classical mechanics model, and specifically the Steelpush/Ironpull conundrum, I though about something after you asked me, and tell me if it's rediculus (also we should probably discuss this on a different thread, but we'll see if this becomes a whole conversation):

The problem with Steelpush (and Ironpull, but let's focus on one), is the one you brought up, specifically we can look at three scenarios:

1. Pushing the coin against a wall/ground. The information of hitting the wall transfers somehow to the allomancer

2. Pushing the coin from two sides causes it not to move and creates stress inside the coin (as if pushing on it from the outside)

3. Pushing a coin against the ground when decending can cause a stop of the decent and even allow to hover.

Consider the following model:

The allomancer creates, at the moment it starts the steelpushing, something that acts like a spring between it and the coin (or another object, but let's say coin for terminology's sake). He then, if they steelpush, can only lengthen the spring, i.e. increasing its equilibrium length, or shorten it if they are ironpulling. The spring always starts with the rest length equals to the distance between them, and then gets more force the more the allomancer pushes. Keeping the spring active but not lengthening it, still requires a minimal flow of Investiture.

The force would grow as long as the object stays in place.

1. In the first case the information of the coin hitting the wall will propagate as a mechanical wave thorugh the spring back to the allomancer, and push him back an instandt r/v (r = the distance to the wall, v = the speed of the wave in the spring) after the hit.

2. The forces of the two springs pushing on both sides can cause stress to the coin, assuming they are not on the exact same point (maybe the spring actually pushed from the outside of the coin?)

3. Pushing against the ground includes creating a spring that will slowly slow the allomancer down until reaching equillibrium.

This model does answer the points you've made. The force goes along the field lines and the forces do become stresses inside the object. I have not touched the Investiture required, becuse I think I can think about this only after I do the math, and figure, for instance, how much work is being done here and if the force is really conervative in this instance.

I haven't gotten to doing the math for this yet, but I will tomorrow probably, and I'll post the results here. It's not the most elegantic model, but it seems like, at least qualitativly it works. What do you think?

All in all, it's fun to brainstorm theories. Thank you for engaing

[DrPhysics he/him]

18 hours ago, idanstark42 said:

Pushing the coin against a wall/ground. The information of hitting the wall transfers somehow to the allomancer

Pushing a coin against the ground when decending can cause a stop of the decent and even allow to hover.

Newton's third law works just fine for this, but making impacts a little springy would work. That's how it works with our muscles. We measure the sudden change in tension and adjust accordingly.

18 hours ago, idanstark42 said:

Pushing the coin from two sides causes it not to move and creates stress inside the coin (as if pushing on it from the outside)

The springs can explain the crushing, but not how it is held up in the air. The best explanation for that one is that the allomancers adjust the strength of the "field lines" that they are producing so that the ones pushing on the top of the coin are a little stronger than the ones on the bottom. This would also explain how Zane is able to reorient himself in midair while hovering above a single coin. The allomancer probably doesn't perceive it as strengthening/weakening different field lines, but it would explain what we see.

Edited October 25, 2023 by DrPhysics

[idanstark42 he/him]

18 hours ago, DrPhysics said:

The springs can explain the crushing, but not how it is held up in the air

Maybe it can, if we think about it like something hanging off a rope. The type needs a slight angle in order for its tension to act against gravity. It can be the same here. If the coin is slightly higher then the allomancers, their pushes would act against gravity.

That might not work if they start increasing the force, they should push the coin up, unless they also change the angle at the same time.

Do you think we should open this in another thread, about steelpushing? This really isn't about the quantum description anymore

Edited October 26, 2023 by idanstark42

[DrPhysics he/him]

4 hours ago, idanstark42 said:

Do you think we should open this in another thread, about steelpushing? This really isn't about the quantum description anymore

I opened one here, and added some notes about my steelpush rules (self-plagiarized from Reddit). If we end up with more to talk about with the quantum parts, we can return to this one.

[therunner he/him]

On 10/23/2023 at 1:48 AM, idanstark42 said:

This is the interesting part. The idea is to show that since Investiture is neither energy nor matter, it must be something else. A third kind of particle. The only one that is mathematically possible is one that is called Anyon, which is named as such since it can take any phase on the range from energy to matter (yes, that is a range. In our world only those two are possible, but some anyons in rare cases exist here two).

Correction, anyons are not a third kind of particle, nor is there any range of 'energy to matter'.

Anyons are simply particles that can have arbitrary spin, not just multiples of 1/2 like in 31 dimensional space-time (bosons and fermions). It has nothing to do with matter or energy. Strictly speaking, energy is simply a property of matter.

Quote

Anyons technically only live in two dimensions, and since Investiture lives in the Spiritual Realm, it leads us to understand that each soul is basically a two-dimensional sheet, like a piece of paper all tangled up within itself. The simplest example of such structure (called a manifold) is a sphere, like earth. Though the sphere is in 3d, we can walk on it as if it were 2d. Now start poking holes in it, connected different sides of the sphere to eachother, making knots and a complex web (spiritweb if you will), and you got a complex structure that could hold Investiture.

Spiritual Realm is not 2D as far as we can tell based on WoBs. If anything it is spaceless, but not timeless, so it would be 1D.

 

But broadly speaking yes, Investiture should be a new kind of quantum field, that has at least 16 distinct charges. From that point of view we could try and guess that the symmetry group of U(4) which has 16 generators, and so could plausibly act as gauge group for Investiture field.

Though interestingly enough, once used by a specific person it gets locked to that person, which implies existence of some other charges that are basically infinite (since different people would have different Identities).

[idanstark42 he/him]

19 hours ago, therunner said:

Correction, anyons are not a third kind of particle, nor is there any range of 'energy to matter'.

Anyons are simply particles that can have arbitrary spin, not just multiples of 1/2 like in 31 dimensional space-time (bosons and fermions). It has nothing to do with matter or energy. Strictly speaking, energy is simply a property of matter.

Hi, thank you for commenting

What I call matter is of course Fermions, and what I call energy is Bosons. I used laymen terms for them, both for people to understand, and because the article is presumably written in world, and so Boz and Fermi do not exist there.

Of course both Fermions and Bosons can have both mass and energy, but since in QFT everything is energy, and different quantum fields that can contain it, I didn't see the need to expand on it.

The reason to call Fermions "matter particles" is obvious: they follow Pauli's principle, and thus create complex constructs. First atoms, then molecules, and so on. The reason to call Bosons, or specifically gauge Bosons, "energy particles" is easy to see as well. They are responsible for passing energy between Fermions, by gauging the basic forces.

The range I specified is the statistics range between BE and FD statistics, which has Fermions on one side, Bosons on the other, and the middle is filled with Anyons, with fractional statistics based on their phase. This isn't usually considered as a range between energy and matter, but I think this is, in laymen terms, a good explanation I think it what Anyons are. You have particles that create matter on one side, particles that PDF energy on the other, and I'm the middle you have a range of other particles, which address Anyons.

I hope this makes sense, if not please tell me. I'm trying to explain the logic in my mind as best as I can, but I am new at this (both writing in forums and writing in scientific terms outside of tests)

19 hours ago, therunner said:

Spiritual Realm is not 2D as far as we can tell based on WoBs. If anything it is spaceless, but not timeless, so it would be 1D.

If we assume that Investiture is a QF, and according to WoBs it comes from the Spiritual Realm, the Spiritual Realm must contain Remannian manifolds over which the QF is defined. Those manifolds, while they don't exist in the same spacetime as the one of the Physical Realm, need their own spacetime. Having additional dimensions that are perpendicular to those of the Physical Realm, allows the singularity that is defined by that WoBs.

Since when passing energy from the Investiture field to the QF in the Physical Realm we sometimes get Fermions and sometimes get Bosons, the Investiture QF should be able to create both. When asking what statistics they follows, we reach the answer "it depends", and so we must conclude that it is an Anyonic field (or that is Fermionic and energy is a complex particle, but I chose the simplest description).

This means that, in this model, those manifolds only need to have 2+1 dimensions. Which are, I want to emphasize, not the same as the Physical Realm 3+1 dimensions.

19 hours ago, therunner said:

But broadly speaking yes, Investiture should be a new kind of quantum field, that has at least 16 distinct charges. From that point of view we could try and guess that the symmetry group of U(4) which has 16 generators, and so could plausibly act as gauge group for Investiture field.

Though interestingly enough, once used by a specific person it gets locked to that person, which implies existence of some other charges that are basically infinite (since different people would have different Identities).

Actually, there is a WoB that states these 16 shards are not the only way Ado could have been shattered. Though the idea that U(4) is the symmetry group could still be viable.

As for Identity, I suggest in the article that identity is encoded in the homotopy of Spiritweb manifolds, and that color (the quality for "which of the 16 shards this Investiture is ñ belongs to") is actually the family of solutions for Schrodinger's equation meeting different Identities (homotopy dictating boundary conditions) and Intents (Intent acting as potential field over the manifold).

what do you think?

Edited October 28, 2023 by idanstark42

[therunner he/him]

2 hours ago, idanstark42 said:

Hi, thank you for commenting

What I call matter is of course Fermions, and what I call energy is Bosons. I used laymen terms for them, both for people to understand, and because the article is presumably written in world, and so Boz and Fermi do not exist there.

Of course both Fermions and Bosons can have both mass and energy, but since in QFT everything is energy, and different quantum fields that can contain it, I didn't see the need to expand on it.

The reason to call Fermions "matter particles" is obvious: they follow Pauli's principle, and thus create complex constructs. First atoms, then molecules, and so on. The reason to call Bosons, or specifically gauge Bosons, "energy particles" is easy to see as well. They are responsible for passing energy between Fermions, by gauging the basic forces.

The range I specified is the statistics range between BE and FD statistics, which has Fermions on one side, Bosons on the other, and the middle is filled with Anyons, with fractional statistics based on their phase. This isn't usually considered as a range between energy and matter, but I think this is, in laymen terms, a good explanation I think it what Anyons are. You have particles that create matter on one side, particles that PDF energy on the other, and I'm the middle you have a range of other particles, which address Anyons.

I hope this makes sense, if not please tell me. I'm trying to explain the logic in my mind as best as I can, but I am new at this (both writing in forums and writing in scientific terms outside of tests)

Ah, that does make sense.
I would recommend using the proper terminology (even if it requires additional explanations for laymens) instead of misusing terms like 'matter' and 'energy', as that just leads to pseudo-science propagating through population.

I would add that while at first glance yes, fermions are 'matter' particles and bosons are 'force' particles (more appropriate then energy particles I would say), even humble proton is a mixture of both fermions and bosons, and in fact most of its mass comes from gluons not fermions. In other systems, you have composite bosons that are actually bound pairs of fermions, so fermions can also act as 'force' carriers.
So ultimately, separating particles in such a way does not make proper sense.

2 hours ago, idanstark42 said:

If we assume that Investiture is a QF, and according to WoBs it comes from the Spiritual Realm, the Spiritual Realm must contain Remannian manifolds over which the QF is defined. Those manifolds, while they don't exist in the same spacetime as the one of the Physical Realm, need their own spacetime. Having additional dimensions that are perpendicular to those of the Physical Realm, allows the singularity that is defined by that WoBs.

Investiture does not come from SR, it is just mostly there. Since we see e.g. Stormlight in PR and CR, that means that Investiture field exists also in PR and CR.

Holistically, you should look at the entire construction of PR+CR+SR as the 'space-time' you want to model, and all quantum fields are over this compound entity. In such a constructions you would get something along the lines of ~{R^{3} x R^{3} X {0}} X R (with appropriate metric), where the first is PR, the second term is CR and the last is SR, with common time dimension (though theoretically you could have two time dimensions, one for PR+CR and one for SR).

2 hours ago, idanstark42 said:

Since when passing energy from the Investiture field to the QF in the Physical Realm we sometimes get Fermions and sometimes get Bosons, the Investiture QF should be able to create both. When asking what statistics they follows, we reach the answer "it depends", and so we must conclude that it is an Anyonic field (or that is Fermionic and energy is a complex particle, but I chose the simplest description).

The fact that Investiture can create both fermions and bosons does not imply that it must be anyon, just that it must interact with both fermionic fields and bosonic fields.

The fact that Investiture does seem to saturate would suggest that it is fermionic, however.

2 hours ago, idanstark42 said:

Actually, there is a WoB that states these 16 shards are not the only way Ado could have been shattered. Though the idea that U(4) is the symmetry group could still be viable.

That is okay, currently there are 16 Shards, so U(4) could be a way to describe it.

More in-depth answer would require some form of symmetry breaking of a greater symmetry group G, of which e.g. U(4) would be surviving subgroup. The particular combination of generators that would survive the symmetry breaking would then correspond to the 'Intents' of the created Shards, and symmetry breaking would correspond to breaking of Ado.

2 hours ago, idanstark42 said:

As for Identity, I suggest in the article that identity is encoded in the homotopy of Spiritweb manifolds, and that color (the quality for "which of the 16 shards this Investiture is ñ belongs to") is actually the family of solutions for Schrodinger's equation meeting different Identities (homotopy dictating boundary conditions) and Intents (Intent acting as potential field over the manifold).

I am not sure homotopy would be a good property to correspond to Identity. Remember that Identity can be stripped from the spiritweb, without heavily altering the spiritweb as a whole. That suggests that it is not some global property, but property that is constant over the spiritweb.

Edited October 28, 2023 by therunner

[idanstark42 he/him]

2 hours ago, therunner said:

So ultimately, separating particles in such a way does not make proper sense.

4 hours ago, idanstark42 said:

Well, I agree with you and I disagree with you.

It's obvious that both Bosons and Fermions exist in matter, since complex structures require both "objects" and forces that hold the together. And yes, most of the mass in the protons doesn't come from Fermions, but that is just because quarks have a ridiculously low mass compared to the strong interaction. I think the best way to understand what I mean is to regard this comparasion: Fermi gas is matter (white dwarves), while Bose gas is radiation (Black Body radiation for example). This is, of course, exluding complex particles. For this reason, I do think in order to understand what Bosons and Fermions are in daily terms, those names are a good descriptor.

But I do agree with you that we do not want to propegate the idea that matter is only built on Fermions or that radiation is only built on Bosons.

2 hours ago, therunner said:

Holistically, you should look at the entire construction of PR+CR+SR as the 'space-time' you want to model, and all quantum fields are over this compound entity. In such a constructions you would get something along the lines of ~{R^{3} x R^{3} X {0}} X R (with appropriate metric), where the first is PR, the second term is CR and the last is SR, with common time dimension (though theoretically you could have two time dimensions, one for PR+CR and one for SR).

4 hours ago, idanstark42 said:

Yes, I tried this method before reaching my current one. SR still needs some data structure to include data about each Spiritweb's Connections, Intent, Identity, Fortune and Investiture. The data structure in the article is the best one I could come up with, but I would love to start over with some extra help .

What I though was that if the dimensinos of each Realm are perpendicular to one another then due to simple superposition I could look at the them seperatly. Then I thought to take one step backwards and ask why must all of those dimensions have the same QFs? Why should there be photons in SR? How many dimensions does it really have? And If all those dimensions exist in all places and times as one (since according to WoB SR does not share PR and CR's time, giving some entitied the ability to look into the pas and the future), what are the dimensions of SR?

More over, thinking about CR as an additional set of dimensions perpendicular to PR doesn't seem to describe it very well. There is a clear mapping between the two. I think looking at it as another set of fields over the same 3+1 D is probably more accurate.

I didn't yet have answers for that when writing the article, but I'm starting to think that if I could model SR as a spacetime, then that spacetime would be spanned by all possible Ideals. But this, too, is just a postulation.

2 hours ago, therunner said:

The fact that Investiture can create both fermions and bosons does not imply that it must be anyon, just that it must interact with both fermionic fields and bosonic fields.

I agree that Stormlight, Voidlight, Dor, Godmetals, all seem to be Fermionic manifestations of Investiture. We cannot ignore though, that Steelpushing/Ironpulling, Lashings, Awakening, those are also manifestation of Investiture. Not forces caused by its existance, like an electron causes electromagnetic waves, but the Investiture itself passes onto those forces, seemingly becoming the Bosons governing those interactions.

There are other ways to make this work, as you've said, but given all possible theories I still think that Investiture being Anyons is the simplest one. Here is why:

1. The limitation of particles being Fermions or Bosons comes to us only in 3+1 D and above. There is no guarantee that the manifold(s) in SR over which QF run are not 2+1 D (again, in SRs own dimensions and spacetime).

2. Having a QF that can transfer all of its energy and spin to a QF in PR, both to a Bosonic and a Fermionic Field, requires either an anyon, a bosons which can split or fermions which can merge. All three are possible, but removing our 3+1 D preception, Investiture being anyons is the simplest one.

The actual WoB about Investiture being in all three realms (at least the one quoted in The Coppermind) is this one:

Quote

Questioner (paraphrased)

What is the Realmatic composition of Investiture?

Brandon Sanderson (paraphrased)

Investure is intended to be the building blocks of the cosmere so I would say for the most part it transcends the different realms. Probably more of the Spiritual if anything but more accurately it transcends them.

Words of Radiance Houston signing (March 11, 2014)

I think this is the one you quote. This was one of the places where I started, of course (starting a theory about Investiture without reading existing knowledge is not very wise). I thought about this with connection to what I said about CR and PR not being actually different dimensions, while SR acting like the data there is stored in different dimensions. This made me think that the actual two objects of this universe are SR and PR, and CR is a result of something between them. I started a theory about PR existing because of a missing dimension in the mapping between them, but I don't really like it. I do still think that CR is a result of the other two, but that is a discussion for another time. For now, for simplicity, let's focus on SR and PR, like we did so far.

So I thought how can Investiture exist in two dimensions (at least one from SR and one from PR) at the same time? A vector sum of two perpendicular wave functions would not work, since the two would be independent. I needed a solution that says that wherever there is Investiture in one realm, there is Investiture in the other. My only way to model that was to simply say "there is Investiture in this Spiritweb (SR), and this Spiritweb is Connected to a position in PR".

So I said that the Spiritweb is a manifold, over which there is a QF for Investiture, and that Manifold has a point where it is tangent to PR, and so energy can pass from it to PR at that point in the PR spacetime. The fact that Investiture doesn't really "exist" in PR, in the sense that the QF that contains it is not over that spacetime, but over another one, tangent to it, does bother me, but again, I couldn't find a better solution, and this seems to work. Whereever there is Investiture in SR, there is Investiture in PR.

3 hours ago, therunner said:

I am not sure homotopy would be a good property to correspond to Identity. Remember that Identity can be stripped from the spiritweb, without heavily altering the spiritweb as a whole. That suggests that it is not some global property, but property that is constant over the spiritweb.

Yeah, this bothered me too. I thought about stripping Identity as injectly mapping (is this correct to say in english?) the Spiritweb into a plane, not removing any Connections or affecting any of the fields over it other then chaging the metric and Reimann Tensor. This results in the removal of all boundary conditions. In this sense, if you are still Connected to Preservation, you could still use pull on its Intent and use Feruchemy, but the stable excited states in your Spiritweb can pass into any Spiritweb, not only to yours.

This is a bit combersome. Maybe a better model would look at it as its own QF that creates potential in the other ones. Or maybe even really a simple "index" of the Spiritweb, without needing to go into any QM for this. It just seems like a very elegant solution. 

 

Again, thank you for engagin in this conversation! I love learning from this, and I feel like I do learn a lot.

Please let me know if you want to start this theory together from scratch, because I would love to try and see what we can come up with

3 hours ago, therunner said:

More in-depth answer would require some form of symmetry breaking of a greater symmetry group G, of which e.g. U(4) would be surviving subgroup. The particular combination of generators that would survive the symmetry breaking would then correspond to the 'Intents' of the created Shards, and symmetry breaking would correspond to breaking of Ado.

5 hours ago, idanstark42 said:

I forgot to respond to that. I do not yet have the group theory knowledge to do anything more then understand this, but I will study and get back to you.

This does seem like a really interesting option, perhaps with very cool implications. I would love to hear more about this. Specifically. what we can deduct about group G from this? Do you think we could find specific elements of U(4) that correspond with specific shards?