How to limit a magical physics power?

Question

I have a character that gains a "force" power that allows him to use his mind to manipulate physics such as levitate weights, warm a space, cool a space, stop objects and transmits things by pulling individual particles away.

The character is going to have his "force" slowly increase in power. I have been trying to find one physical unit that a highschoolers could measure that would allow all of the above feats along with others.

My question is what limit can I put on this character for his "force" output that could be transformed into any of the above feats? I'm looking for the SI unit that would best fit these feats.

Answer 1

Classically there are two ways to "justify" and/or limit magical powers:

1. the already mentioned conservation of energy, which means the magician uses his own energy to accomplish his feats. This amount of energy is rather limited in a real human being. in this framework magic would have the same effect of (e.g.) a pulley system which can make easier to lift heavy weights, but essentially doesn't change the "work" (joules) needed.
2. tap into some available mystical energy available (i.e.: "Mana" or "the Force"). in this case you can distinguish two sub-cases:
   1. the "Mana" is finite in a certain place (or internally to the sorcerer, perhaps in some specialized organ or in a "generator" or "storage" amuleth) and you can exhaust it (locally); when this happens you can no longer do your magic. Variation on the theme: mana becomes more and more difficult to "extract" when exhausting, it will regenerate over time or not, Is a single energy or several (e.g.: Elemental Mana).
   2. "Mana" is infinite, but the sorcerer has to use his/her own strength to "funnel" it, posing a practical (but moveable) limit to his/her powers. Something akin to a a fireman who doesn't really need to use his own energy to move the water pouring from his hydrant, but he has to wrestle it in position and use a lot of energy to keep it focused unto his target.

In general the energy expense is measured in Joules and the (maximum) rate in Watts (Joule/s). If you want to be "correct" you need to compute the amount of energy needed for each of the "feats" and take into account the side effects:

• if you want to accelerate something you have to give it some kinetic energy and keep track of the change in momentum (something must be accelerated in the reverse direction)
• if you want to cool down or heat-up something you are effectively transferring heat form something to something else (this takes energy, of course, Carnot limits theoretical efficiency) thus you will have two things changing temperature in the reverse direction, with the warming one getting more energy than what's subtracted from the cooling one.
• teleportation would need to accommodate for potential energy (difference in height) and momentum (we are moving fast due to Earth rotation/revolution, instantaneously teleporting something at antipodes would result in a nice ground-level meteor)
• etc. etc.

Answer 2

You could limit his power using the law of matter and energy conservation. Basically he draw his own energy to cast a spell (or if you want he can draw energy of other place/universe/dimention/etc but at a fixed rate [in joules, calories or newtons]).
This energy could be:

• Thermal Energy:
  • Each time he want to warm something he draw the heat of his body to the object.
    For example:
    • Water has a heat capacity of 1 cal/gr or 4.184 joules/gr.
    • Human body (warning articule in spanish) has a heat capacity of 0.83 cal/gr or 3,47272 j/gr.
  • This means that for each litre of water he heat 1°C he will losse (this human has a average weight of 70 kg) 0,017°C of his own heat.
  • Also for each litre of water he cold 1°C he gets 0.017°C.
• Kinetic Energy:
  • Each time he want to move an object he produce the physical effort in his own body.
  • For example keeping floating 1 kg (+9.8 m/s - gravity = 0 m/s) he need 9.8 Newtons per second.
    • Keep in mind that you can "transmutate" thermal energy into kinetic energy: 1 joule = 1 newton and 1 calorie = 4.184 newtons. Remember that calorie is no the same as Calorie (nutritional value): 1 Calorie = 1,000 calories or 1 Calorie = 4,184 newtons or joules. (With an average nutritional input of 2,000 Calories per day you can do much things...)
• Chemical Energy:
  • If your character is able to make chemical reactions (e.g: burn something) with his mind you can use this.
  • Also you can storage energy in chemicals instead of body temperature:
    • For example: each gramme of glucose in your body you can release 3.75 kcal/gr equal to 3,750 cal/gr or 15,690 joules or newton/gr (also know as 15.69 kN and 15.69 kJ).
    • Keep in mind that glucose need oxygen to release this energy. $\mathrm{C_6H_{12}O_6 \to 3CO_2 + 3CH_4}$
      
    • If you want to store energy into glucose you can do: $\mathrm{6CO_2 + 6H_2O \to C_6H_{12}O_6 + 6O_2}$

Lastly, you can also control the speed of his power, I mean: ¿Could your character in one second frezee 10 KL of water (internal heat +172,17°C) but don't die because he release all that energy into a powerful kinetic blast (10 kN = sufficient force to push some metres away a car or break a wall)?. You can control de rate of his power in joules per second (j/s) or calories per second (cal/s) or newtons per second (n/s).

Answer 3

In "hard magic" systems, magical output is typically limited by the energy source that sorcerer is using. It could be his own body heat, or the heat of target object, or some other energy source that is magically linked to the sorcerer.

If we go less scientific, we can talk about an invisible "magic well" where a sorcerer can store power, or "magic channel" that gives access to some kind of omnipresent energy. Putting limits on size of this "well" or "channel" puts restrictions on power of magic.

Answer 4

I'd suggest that there are three factors limiting your characters abilities, all of them can be measured with SI units if you want a scientific touch.

Energy (J)

The first and most obvious one is the amout of pure energy he can deliver by magical means. Can he levitate a truck on top a mountain (or an X-wing from a swamp), or just lift a scroll from someones pocket (or a lightsaber to his hand)?

This is important, if you want to keep the basic laws of physics. The "magical" energy must be drained from some source, either the mages own metabolism or channeled from an external source.

As your character exersices, he can direct more energy by magical means.

Effect (W)

Energy is one thing. How quickly you can apply it is another. A Watt is one Joule per second. Your character has always been able to warm an item, but while in his youth it took him forever to make a cup of water lukewarm, he can now make the dagger in your hand burning hot in an instant.

Focus (sr or m)

So you have magical powers. You have the force and the stamina. But can you control it? If you want to hurt (or kill) someone, must you resort to throwing his entire body against the wall with your magic, or are your powers focused enough so you just need to manipulate his nerve cells? Flashlight or laser? Shotgun or sniper rifle?

Answer 5

While this is quite admirable (placing realistic limits to magic), the real issue comes from finding the source of the energy to do so. Human beings are not particularly energetic in the larger scale of things, so unless magic involves making tiny and subtle changes, manipulation of physical objects, changing temperatures and the like will almost certainly result in the death of the magic user as they exceed the limits of their own bodies.

Tapping into external energy is also problematic, since you now need to have some sort of plausible means of doing so, not to mention a sort of channel to move the energy through, "insulation" so you don't get killed by overloads, and perhaps a magical equivalent of things like transformers, voltage regulators, surge arrestors and so on. At that point, I'll just be reaching for my trusty ACME device.....

Oh this will do nicely....

The alternative I might suggest isn't to actually go for direct physical manipulation, but explore the quantum multiverse. There is some finite (even if very tiny) probability that something you want is happening or exists, so a careful magician could be carefully tuning in to the multiverse and "seeking" the timeline where a particular rabbit is in a particular hat....

This is possibly as fraught with problems as physical manipulation of the universe, so beware.

Wait a sec, what is the probability of "that" happening?

Answer 6

ENTROPY (and energy)

it is nicely explained in the other answers how conservation of energy can be used to limit the mage's power. But that is an idea very widely (ab)used. In almost every modern magic-using story magic runs on some kind of energy source. And it is also incomplete.

Limited by energy only your mage could separate a compound liquid or gas to it's components, the results adding up to the same heat energy as before. This hard task would be trivial to him, using no energy. Or he could stop a train, magically transmitting its energy to some molecules of air, he himself doing zero work. You need some other metric to measure the "complexity" of the task. How much order must be created from disorder? Entropy, measured in joule per kelvin, is the quantity for this.

Make your magic respect the second law of thermodinamics too, allowing the mage to only create as much order as much disorder he creates at other places.