Equestria's Science

by Sapidus3

On the Fundamental Nature of Magic

Hello everypony and thank you for all coming to listen to me today.

My name is Twilight Sparkle and I will be presenting on my research into the very nature of Equestria which was conducted under the guidance of my mentor, Princess Celestia.

First, we will begin by listing off some basic things that we know for fact.

1. Magic is a force that acts at a distance; it does not require contact.
2. A unicorn's horn is somehow involved in the unicorns ability to use magic.
3. The 'color' of magic can vary from pony to pony.
4. In at least some cases, using magic to lift things seems to apply a reactive response force (I submit to you when I met a unicorn named Trixie. I needed to dig my hooves into the ground to lift and ursa minor).
5. In some cases there does not seem to be a response force (The unicorn filly recently born to the Cake family was able to levitate itself. It's possible that this is some type of anti-gravity or mass-manipulation, but that seems unlikely). This seems, at first, to be a violation of one of the basic laws of motion.

I will make three fundamental assumptions.

1. We can, in fact, explain all aspects of magic within a logical and self consistent mathematical framework.
2. We can accomplish the above while remaining consistent with our current understanding of physics.
3. In order for assumption 1 and 2 to be true, we will need to formulate our theory of magic with physics as our inspiration.

To begin with, let us take one of the most fundamental spells that all unicorns learn while still just a foal: telekinesis.

Telekinesis is the ability to move objects without touching them through the power of one's mind by utilizing magic. Ordinarily the object being moved is enveloped in a glow of magic the same color as the unicorns horn. Telekinesis is able to move an object in all three spacial directions and affect rotation.

What makes telekinesis so odd, and difficult to understand, is that every other physical force that acts at a distance is either a attractive or repulsive force. Telekinesis seems to have much more freedom in its directionality.

It is at this point that I will be relying on assumption 3. All forces that are capable of acting at a distance are actually forces between fundamental 'charges.' In the case of electromagnetism, this is either an attractive or repulsive between positive and negative electric charges. In the case of gravity, it is an attractive force between positive 'charges' of mass. While some ponies have also theorized negative mass matter, because it is pure conjecture, we will be ignoring that for the sake of this discussion.

Obviously telekinesis is not just repulsive or attractive. It can also move objects perpendicular to the vector between the two objects.

For those of you who are unfamiliar with the term vector, imagine a vector is an arrow. When I refer to the vector between the two objects, I am talking about an arrow pointing from one to another. I recommend doing further reading on the subject. The human resource wikipedia can be of great help for beginners. In fact, if at any point I use a term that you do not understand, I recommend that you look it up as to avoid being lost. I will do my best to accommodate you, but I do want to avoid getting bogged down in the basics.

We also have the fact that most objects do not seem to be constantly affecting each other magically. In the case of telekinesis, it is only when a unicorn actively uses the magic that anything happens. A unicorn may be able to levitate two boxes, but the boxes will not levitate one another.

Therefore I posit that there must exist two types of magical charge.

1. Inactive magical charge. This will in no way interact with other inactive magical charges, but will respond to magical fields. However, it will not create a magical field of its own. The magnitude of inactive charge in an object will affect how easy the object is to affect with magic. Therefore we can also refer to inactive charge as magical conductivity.

2. Active magical charge. Active magical charge will exert a force on inactive magical charges. Active magical charge is the source of magical fields.

This right here explains fact 2 of magic, the importance of a unicorns horn. There are two likely explanations at this point of the role the horn plays in magic

1. The horn is like an active magical charge battery. The exterior surface of the horn acts as type of reverse faraday cage. A faraday cage is a construction which can protect whatever is inside from external electric fields. When the unicorn wishes to perform magic, some component of the pony's biology 'breaks' the cage allowing the internal magical field to escape from the confines of the horn. This would allow for the magical field to be directed in a specific direction. Further exploration of this possibility will need to wait for a later talk.

2. Accelerating inactive magical charge results in a magical field. Spirals in the horn conduct this charge, resulting in the generation in a field. This is the same basic way in which an electromagnet works. Once again, further investigation of this will wait for later.

While we will need to hold off on any definitive decision regarding the importance of a unicorn's horn, we nonetheless have established two reasonable possibilities.

We still have not explained the directionality of telekinesis, only its selectivity.

Because telekinesis is beyond a simple attractive and repulsive force, active magical charge, at least, must be more complicated than we have so far presumed.

Let us assume that active magical charge is composed of three components, an X, Y, and Z component. These components compose an 'active magical charge vector.' However, these components are dependent on the directionality of the main magic vector. The direction the telekinetic force applies will then be the cross product between the active magical charge vector and the unit vector along the direction between the unicorn and object the unicorn is levitating.

You may wish to read that one more time to make sure you have it.

To get the magnitude of the force we must also multiply it by the magical conductivity (keeping in mind that we are being inspired by the electromagnetic force, ordinarily you multiply two charges together, here we are multiplying two different types of charges together).

What then is the affect of distance? At worst, the magical force decreases as the inverse of the distance squared. However, that assumes the magical field is beaming off in all directions and that the field lines are decreasing in density. A skilled unicorn can 'tighten' his or her magical field and reduce the exponent on the distance to a theoretical zero at maximum tightness. Of course this ignores the magical interference caused by intervening air which we will discuss in a later talk.

In practice, however, because objects are not of infinitesimal size, the unicorn will need to allow some widening of the magical field in order to encompass an object. Ironically, because an objects angular size decreases with distance, a skilled unicorn will be able to us his or her magic more efficiently at greater distances.

So what we have is

F = S*(((X*Xhat+Y*Yhat+Z*Zhat)of object 1 x Rhat) * C of object 2)+((X*Xhat+Y*Yhat+Z*Zhat)of object 2 x Rhat) * C of object 1))/(R^A)

Where:
F is the force between the objects (a vector)
S stands for Sparkles constant, a number that I have yet to measure
X, Y, Z, represent the the X, Y, and Z components of an active magical charge
Xhat, Yhat, Zhat, are directions in the x, y, and z direction
Rhat is the direction between the two objects
C is the magical conductivity (inactive magical charge) of an object
R is the distance between the objects
A is a parameter between 2 and 0 based on the 'tightness' and focus of the magical field.

Note, this formulation obeys Newton's law that all forces must have an equal and opposite force.

I will freely admit that this does not explain unicorn self levitation nor the visual glow of magic. It also does not explain how a unicorn could levitate something heavy without the response force breaking the unicorns neck. There are, however, exploitations too these two issues based on our current understanding. However, I would like us to take a break to allow for discussion.

Please feel free to ask any questions, bring up any problems, or share any formulations of your own.

Comments

[Dozy Dreamer]

This is impressive. I will return to analyse this properly when I have the time to give it the attention it deserves, but from skimming it , I can see no flaws in this theory. I will most definitely be watching this with great interest in the future.

[Taranasauruso_o]

Topics that I feel need explaining:

1. How is a pegasus able to lift itself with it's wings. According to our physics, it should be impossible for a pegasus to lift itself from the ground because of the comparison between it's wingsize/span and body weight.

2. How was the young pony, this 'Pound', able to lift himself up from the ground using only his magic? Did he expand his magical field around himself, or is it a specific form of magic?

3. Is it possible to construct things from nothing? E.g: Can you summon a book from nothing, and fill it with information? (What I believe would be an explination is: The unicorn, although able to do this, takes a part of their magic from within themselves and uses it to sustain the spell, rendering their magical reserves less.)

4. Is it possible to splice DNA of a specific type of pony with another (Hypothetically speaking, of course. No testing is needed)? If so, what can we estimate the results to be? Are we able to construct alicorns artificially?

5. Why and how does a unicorn's magic reserves refill whilst they are sleeping? In fact, while on the topic of magic reserves, why do the size of a unicorn's magic reserves differ from pony to pony?

6. Do all objects and ponies in Equestria contain magic, even minisqule amounts?

Well, if you have any solutions/speculations about these questions, please elaborate. I look forward to more of your work, good day miss Twilight Sparkle.

Written and spoken by
Bright Spark
Head chief and scientest for princess Celestia.

/me Hasn't read this but:
You're surely brave for delving into this I hope that your imagination/knowledge and writing skill is up to the challenge

[hahatimeforponies]

As an obsessive world builder interested in mathematical treatments of magic and overthought of the pony world in general, I approve. Some topics I feel could use discussion, and some of my suggested rationales for them:

1. The heritability of unicorn, pegasus and earth pony traits in Mendelian genetics, and what this means for alicorns.
2. Pegasus flight (possibly some innate, subconscious magic to do with water vapour, also explaining why clouds are solid to them?)
3. The biological basis of Cutie Marks.
4. The evolutionary history of ponies (the involvement of magic in pegasus flight and cutie marks would indicate that all ponies have some kind of tissue specifically there for magical interaction, possibly a rudimentary horn (if unicorns are ancestral, the horn would have been secondarily lost in pegasi and earth ponies, or if earth ponies are ancestral, the horn is more advanced in unicorns)?
5. The physiology of a unicorn's horn (possibly a concentration of the hypothetical tissue in #4 into an outward bone process from the skull (presumably cartilaginous and "floppy" at birth to prevent injury to the mother), innervated so that it can be consciously activated, sort of like an arcane muscle?)

Apologies if these are more biological than physical questions (and if there's more answer than question in there!), I'm a zoologist by training, so these are the questions that spring to mind first. I'd also like to commend your balls in posting the closest this website has to non-fiction.

[Diamond Sparkle]

I'm certainly enjoying this.

[Guardian Talon]

after reading the science notes in your other story i was wondering if something like this was out there. i was actually hoping for Derpy science, but if it's magic makes sense that it's Twilight.

i might be saying the same thing in a more round about way, but what if instead of a force having it's own independent vector. upon contact and energizing the target (this would explain why both source and target glow, once that is explained at all) the target could have it's own vectors. the same as how an otherwise nonmagnetic piece of iron can temporarily gain a magnetic field of it's own, even if it's actually just an extension of the source.
with the target having a wide angle repulsion to the ground and possibly graviton negation if other forms of magic are involved, a heavy target could be lifted without damage to objects underneath or the initial source bearing all the weight. some reactionary force would still be applied to the initial source, unless done with enough power and precision to have the target and it's secondary targets absorb all reactions

[NopeNopeNope]

Brilliant, how about explaining Pegasus weather control and celestial sun?

[Sapidus3]

137465

1 will eventually be addressed
2 and 5 will be the focus of the next chapters.
3 I had not thought about, but will.
4 I have seen treated very well elsewhere but may address.

137553
The cloud thing I have some ideas on, want to run some numbers first though.
3-4 are good.
5 will be touched on in the next chapter or two, and may be further explored later.

137655
I should have mentioned, but I am going with an occam's razor approach. Gravity negation would require pulling in either quantum gravity or some other mechanism that I feel would only complicate things. It may be simpler to understand on a conceptual level at first, but playing around with gravity brings a whole mess of issues with it, and ultimately I am hoping its not necessary.

138424
I actually have an explanation for Celestia's sun in the author notes to my other story (at the very least I worked out the math regarding how much energy it must consume and why the pegasi need to control the whether).

I will eventually try to rework it into something a bit more story generic and easily readable for this.

[treos]

138830 i was going to say this on your other story but it'd fit better here probably, i'm not entirely sure how as the details of really advanced science (like time/space physics sometimes) sometimes elude me but if anyone here has ever played Star Ocean: The Last Hope for xbox360 then they explain and show a lot of real advanced theoretical science in the game series. one of them happens to be faster than light travel, mind you it might apply more to spaceships but still, they have a good theory there.

might be able to find the stuff in a guide for the game or on a wiki somewhere (in the last 2 star ocean games they had a in-game dictionary with descriptions of technology, people, and various locations). i just hope noone ever does something incredibly stupid, like screwing around with a anti-matter generator >.> could destroy the planet easily.

after reading through all this, its definately got my attention (always liked research into various tech and, when possible, magic), tracking

[Nazidash]

In the case of foals, twilight says that Unicorns have very strong and random magic. Twilight seems to be one of the few ponies who can use magic for most anything, so how are foals able to and how does it narrow down when they age? For pegasi, how are their wings so strong when they are very young, without any real use?

[NeuPferdfurt]

Sorry, I can't really argue with the science: whatever my department is, it's definitely not physics.

I do however admire your efforts. In my stories, I simply assume a phlebotinum of ancient nano technology (with Equestria crawling with nanomachines left by a previous civilization) with probability generators. As such, unicorn magic would be the manipulation of nano machines (the "glow") who in return, among other things, manipulate the laws of nature, making a specific highly unlikely event likely to happen.

[Pentad]

After reading this first chapter and your description of the force involved in levitation, I can't help but find that you didn't completely explain motion in three dimensions with it. The cross product between a constant radial vector and a vector free to vary in three dimensions will only produce vectors in a plane perpendicular to the radial vector connecting the active magical charge and the inactive one. This happens because of the fact that the cross product of two vectors is always perpendicular to both of those vectors. Since one of those vectors is in the same direction along which, by definition, radial motion must occur, it is impossible for a force relying solely on the cross product of a radial vector and any n-dimensional vector to produce radial motion. Thus, as described, your equation for the force involved in levitation does not account for motion of a levitated object toward or away from the source of active magical charge.

This should be easy to fix however, since you could easily re-purpose the electromagnetic force or any other attractive/repulsive force top produce this radial motion. Personally I like to think about this as the active magical charge creating a separation of the inactive magical charge (which I am assuming is similar to how electrical charges in atoms are balanced) and thus creating an induced dipole in the previously inactive magical charge which can then undergo interaction with the active magical charge. This might also explain the glow around the horn and the object as large amounts of charge gathering in one area should produce the magical equivalent to sparks. However, if this is the case, then such effects should only occur in situations where the magical field applied to the object is sufficiently high enough to overcome the energy required to magically ionize air.

I can't wait to see more on this and other topics!

[d00mf1sh]

This is even more impressive than your author's notes from Equestria's Twilight. I'd love for you to update this. It's very interesting.