Equestrian Cosmology and Supernatural Physics

Facts

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 ability to use magic.

3. The 'color' of magic can vary from pony to pony.

4. In some cases, using magic to lift things seems to apply a reactive response force (Twilight Sparkle needed to dig her hooves into the ground to lift and Ursa Minor).

5. In other scenarios, 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 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 unicorn’s horn. Telekinesis is able to move an object in all three spatial 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 an attractive or repulsive force. Telekinesis seems to have much more freedom in its directionality.

We will now 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. Negative mass matter is another theory, due to its pure conjecture, but 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.

Vectors

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 be 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.

And now onto fact 2: the importance of a unicorn’s horn. There are two possible 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 later.

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 made 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 it is levitating.

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, but here we are multiplying two different types of charges together).

The effect of the distance, at worst, results in the magical force decreasing as the inverse of the distance squared. However, this assumes the magical field is beaming off in all directions and that the field lines are decreasing in density. A capable 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 later.

In practice, 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 object's angular size decreases with distance, a unicorn will be able to use his or her magic more efficiently at greater distances.

Chapter Summary

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)

Key:

F- The force between the objects (a vector)

S- The sparkles constant, a number that I have yet to measure X, Y, Z; letters that represent the X, Y, and Z components of an active magical charge

Xhat, Yhat, Zhat- Directions in the x, y, and z direction

Rhat- the direction between the two objects

C- The magical conductivity (inactive magical charge) of an object

R- The distance between the objects

A- A parameter between 2 and 0 based on the 'tightness' and focus of the magical field.

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