Anime Science 101

Welcome class, A Certain Magical Index and its sister series A Certain Scientific Railgun are filled with super powered individuals called espers.  Esper is short hand for a person with extra sensory perception, the ability to use a so called sixth sense.  This sense is information gained outside of the standard set of senses a person has.  In the case of the aforementioned series it includes people with a vast array of powers that can alter the physical world.  Many of these powers make physics their play thing, so just what is the strongest power in the raildex universe.
 
            Now remember I said strongest power and not the strongest user, so for the sake of this discussion we can assume that all of them are at level 5 regardless of their actual standing.  Also I am limiting this list to people who have measurable powers related to physics, so no magic, or ultimate haxs.
 
 
            The infamous accelerator has the ability to control the vectors of any object around him.  Now a vector is anything that has magnitude and direction.  An easy way to think of it is like this.
 
1- A car is moving 15 miles per hour- Not a vector
2- A car is moving 15 miles per hour due west- Vector
 
            So it might seem that Accelerator has the strongest power since he has basically made Newtons laws of motion his play thing.  It is due to this power that he is nearly impossible to beat in a fight.  One thing to keep in mind is that there are scalar properties.  Scalar properties are things that have magnitude, but no direction.  An example of a scalar property would be temperature.
 
 
            Dark matter is not referencing the theoretical dark matter than astrophysicists discuss, but the ability to create matter that did not previously exist.  Two of the main corner stones of physics would make this ability impossible under normal conditions.  The law of conservation of matter, and the law of conservation of energy.
 
            The law of conservation of matter states that matter cannot be created or destroyed, only changed into different forms.
            The law of conservation of energy states that energy cannot be created or destroyed, only changed into different forms.
 
            Despite this, it is not impossible to create new matter when you consider Albert Einstein’s famous theory of E = mc² matter can be created using large amounts of energy.  Let’s say for example Dark matter wants to make 1 kg cannon ball to fire at accelerator.
 
E = energy
m = mass
c = speed of light
 
E = mc²
E = 1kg x (3x10⁸ m/s)²
E = 1kg x 9x10¹⁶ m/s²
E = 9x10¹⁶ kg*m/s² (newtons)
 
For reference the force of attraction between the Earth and Moon is 1x10²⁰ Newtons
 
            So Dark Matter has basically made the law of conservation of matter, the law of conservation of energy, and mass equivalence his plaything.  He would be limited to fighting using the laws of motion so he would be unable to defeat accelerator.  He can however manipulate the universe by making large amounts of matter upsetting the fabric of space time such as creating black holes.
 
 
            The infamous railgun has the ability to manipulate electromagnetism, which is one of the four key forces of nature.  This force is based on the interaction between particles that have different charges either positive or negative.  These interactions create a variety of different effects including electricity, and magnetism.  This allows our favorite bug zapper to be a human taser, fire off lightening, attach to walls, and use her signature railgun.
 
            A railgun is a weapon that uses electrical currents to create a magnetic field.  The magnetic field then propels the projectile at high velocities towards the target.  The advantage of a railgun over a conventional firearm is that it can attain much higher velocities.  This allows for greater range and energy delivery to the target.
 
Railgun

 
Railgun
https://www.youtube.com/watch?v=nGWvbUungcg
 
            While railgun might be extremely effective against normal people her abilities will create vectors so she will be powerless against accelerator, but she would have some success against dark matter.  It would come down to her being able to take out dark matter before he can start to create a defense against her more powerful abilities.
 
 
            It took some real doing to figure out just what is going on with the meltdowner given the lack of information given in universe.  However, did manage to come up with a potential explanation using a lesser known (in terms of the general public) theory of quantum mechanics.  Quantum electrodynamics deals with the interaction of matter and light, specifically electrons, and photons (particles of light).  It allows them to calculate the following three things.
 
1- movement of photons
2- movement of electrons
3- emission of photons by electrons
 
            With the ability to manipulate these three items meltdown can create glowing balls of lights, electron beams, and lasers.  She is also able to create a solid shield of electrons, but quantum electrodynamics cannot explain this ability.  Thus there are still some unknowns when discussing meltdowners powers.  Given the nature of her powers they would be useless against accelerator due to her powers creating vectors and railgun due to the electrical nature of the electron beam attack.  Dark matter would be a tossup and if she can create lasers she would have a chance against railgun, due to lasers being non electrical in nature.
 
 
            While this power is normally held by a lower level esper, for the purposes of this discussion we are going to raise her to a level five.  Float dial is the ability to manipulate the buoyancy of an object and or the surroundings.  Now I will admit that at lower levels of power it does not look all that impressive, but we need to take a closer look at how the power works before dismissing it.
 
            Bouyancy is an upward force exerted on an object by the fluid it is currently located in.  Please remember that fluids encompass far more than water and other liquids, so air is technically a fluid even if we do not commonly think of it as one.
 

 
            While the above diagram does illustrate how buoyancy works it does not help to actually calculate the buoyancy of the object.  To do that we will need to use the formula’s below.
 
Buoyancy = weight of the dispersed fluid
 
            Now to calculate the weight of the dispersed fluid and for the sake of time we are going to skip a few steps
 
(Density/ density of the fluid) = weight of the object / weight of the dispersed fluid
 
            Now real quick for those of you who don’t know what density is.  It is the amount of matter per unit of volume.
 
Density = mass/ volume
 
            Thus the higher the density the more stuff that is packed into an area.  Now if you look at the first diagram you can see that it is the density of the object and the density of the fluid that plays a large role in determining the buoyancy of an object in a particular situation.  So what the float dial is really doing is manipulating the density of the object.
 

 
            There are two ways to change the density of an object, change its mass or change its volume.  As we can see in the picture above the robot float dial is holding is not any bigger or smaller so, what she is actually doing is changing its mass.  Specifically, she is lowering the mass in order to be able to hold it over her head.  In universe she only seen raising buoyancy by lowering the density of the object by reducing the mass.  Now imagine if she was a level 5 she could theoretically begin to raise the mass of any object, changing its weight.  Taken to the extreme she could use the increased density to cause explosions via nuclear fusion, but the backlash to her would be rather extreme.
 
            This is all well and good but how would she rank against the other powers.  Well she could increase accelerators mass, but it wouldn’t do any good as he can simply change gravity as it is a vector property making her powers less effective on him.  Dark matter, railgun, and meltdowner have no direct defense against their powers, and float dial lacks the range that the others have, so it would come down to who can use their powers in a more creative way.
 
 
            This particular power is stated to be the manipulation of quantum particles.  These particles are in fact subatomic particles.  The particles that make up the proton, neutron, and electron, that are taught in high school chemistry classes around the world.  Over the past century 13 have been discovered and 3 more have been theorized to exist.  The cannon material on the synchrotron power actually makes our job a bit easier as it is stated to be the manipulation of gravitrons.
 
            Gravitrons are the theoretical particles that mediates the force of gravity, thus a synchrotron user could in essence manipulate the force of gravity.  This would give the user a wide range of powers beyond the simply making a person heavier or lighter, similar to the float dial.  Additionally, he or she would be able to make a nuclear explosion by using gravity to compress matter to the point of inducing fusion.  Unlike float dial, the synchrotron would be able to use gravity to protect him or herself from the backlash of the explosion.
 
            Sadly, still no take down of accelerator due to his being able to reflect the radiation and energy released by any explosion synchrotron can release.  He can also reverse the effects of any gravity manipulation placed on him.  The only chance synchrotron has is to roast acceleration using the temperature of the explosion.  However, accelerator could cancel out the explosion by trying to neutralize the gravity needed to make it.  Dark matter, railgun, and float dial could make a shield against the explosion using their powers to absorb, or redirect the energy and radiation released by the explosion.  They would still be vulnerable to the heat.  Sadly, meltdowner probably can’t do much of anything to stop it.  The best case for everyone except accelerator is to attack first given the time it would take to set up the explosion, or before synchrotron can manipulate the gravity.
 
 
            Initially thermal hand is the weakest out of all of the powers on the list, but remember we are boosting her to a level five.  Thermal hand is the ability to conserve the temperature of any object she touches as long as it doesn’t hurt her hand forcing her to let go.  Temperature is the measure of the thermal energy, and particle kinetic energy of particles.  On a basic level what temperature measures is how much a particle is moving and the higher the temperature the more the particle is moving.  We can see this in the picture below.
 

 
            Given the expansion of powers the other espers get as they level up we can assume that thermal hand will gain the ability to increase or decrease the temperature of objects and her surroundings.  In essence she will make the laws of thermodynamics her plaything.  These laws deal with the energy in systems.
 
0- If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.
1- The internal energy of an isolated system is constant.
2- Heat cannot spontaneously flow from a colder location to a hotter location.
3-As a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.
 
            Thermal hand lacks the ability to blow up a city block like many of the other powers on this list but she is not defenseless.  Imagine if you will accelerator, dark matter, or railgun launching a projectile at her but she is surrounded by a wall of heat that incinerates the projectile, before it hits her.  Also this heat barrier would prevent them from being able to touch her.  Meltdowner’s electron beams can be blocked if thermal hand creates a barrier at absolute zero a temperature so cold that the motion of all particles would stop and fall apart.  This would cause the electron beam to fall apart.  She has no defense against float dial and synchrotron except for cooling the matter they might use to make explosions below the temperature needed for fusion.
 
            I know it seems like she is fairly useless as almost every other esper has a way to damage her in some way.  Her one advantage is the ability to take down the so far untouchable accelerator.  She can take down accelerator as temperature is a scalar property, which means he will be unable to defend against it.  Her method of attack would be to increase or decrease the temperature around accelerator until her is rendered unconscious.  True accelerator could manipulate vectors to stay warm or cool off, but these would become useless after a certain point as long as the temperature in the surrounding area continues to change.
 
 
            Accelerator- beats everyone except thermal hand
            Dark matter- beats meltdowner, float dial, and synchroton, and loses to accelerator, railgun and thermal hand.
            Railgun- beats dark matter, meltdowner, float dial, synchrotron, and thermal hand, and loses to accelerator.
            Meltdowner- dark matter, beats float dial, synchrotron, thermal hand and loses to accelerator and railgun.
            Float dial- beats thermal hand, and loses to everyone else due to the time it takes for her powers to work.
            Synchrotron- beats thermal hand loses to everyone else due to the time it takes for her power to work.
            Thermal hand- loses to everyone except accelerator and dark matter as long as she has time for her powers to get up to speed.