What are the fundamental operations of physics?

Question

So, I was going to ask this on physics forums but felt it would be to simplistic to ask it there compared to other, more informed questions.

I’m trying to create a magic system based on fundamental operations. Basically, with a fixed set of operations, a mage, or runeweaver on the setting, can make something change its state. For exapmle, putting a block at the center of a focus, a circle for example, the weaver would then, with a finite number of runes, each representing an operation, change the state of it from being solid to being pulverized, melted or even fissioned (probably killing the mage in nuclear blast, his problem not mine) or any other form of change observed in nature, gathering energy to do so from the environment.

So, my question is: Is there a fundamental set of such operations, something like transfers (transfer of mass, energy, momentum, etc.), that could represent most phenomena physics study? At least on the classical side?

I know I could go with pure handwavium for it, but I’m into sciency magic systems these days.

Answer 1

There is a single theory so fundamental everyone forgets about it and assumes it to be true.

The universe can be described by the same set of rules everywhere.

This is called "uniformitarianism" and is as much a philosophical theory as a scientific one.

200 years ago it was thought that mass would be conserved always. When Einstein did his $E=mc^2$ thing, it was to describe a way that mass could be transferred into energy. It is now assumed that this applies always (AFAIK).
For another example consider the speed of light. It is constant throughout the universe, right? Or even if it wasn't, surely someone will come up with some more fundamental rule that governs how it changes?

Even more esoteric things that require probabilistic descriptions fall into this category. As far as I understand, nearly all quantum theory is built on probabilities rather than direct relations. Saying something will occur $x\%$ of the time following formula $y$ is still a uniform universal rule.

You can some of derive fundamental physics from uniformatism. The fact that rules can be applied across space and time is what allows conservation of anything (mass, energy, momentum).

Thus the theory that the universe can be described through mathematical rules, and that these rules can be applied anywhere is the foundation of all science ever.

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For magic to not be a form of science, magic has to "break" uniformitarianism - otherwise it's just poorly understood science. As such the founding principle of all magic is:

The universe has things that cannot be described by a single set of rules

I can't even really conceive of something that follows this rule. You quickly hit the realm of paradoxes. What I would suggest for narrative purposes is to bind rules to people/entities instead of to the universe. The problem is that this requires a different magic system for every person. Consider:

• Person A uses spell B to evoke action C
• Person Z uses spell B to evoke action C
• Spell B is science - even if it requires extending to include mana, life force or whatever.

Or:

• Person A uses spell B to evoke action C
• Person Z uses spell B to evoke action K
• Spell B is somewhat science. It always has some externally measurable effect, even if the outcome is unpredictable.

The solution is:

• Person A uses spell B to evoke action C
• No-one else in the universe can use spell B to evoke action C. There must be no discernible rule governing the mapping between utterances required to evoke action C.
• It is possible there is no other method in the universe for action C to be performed other than by person A using spell B

This means that every magic school in existence is not "teaching spells" but instead has to teach some means of self-discovery. The problem is that every student will necessarily be completely different to the last, and the outcome is completely unpredictable. For some meditation will result in spawning fireballs. For others juggling crystal balls while whistling pop-goes-the-weasel will destroy the moon.

I wish your magic teachers good luck.

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As you can see, most fiction goes with the "magic is just poorly understood science" for the sake of simplicity.

Answer 2

1) The Law of Conservation of Mass

Matter can't be created or destroyed.

2) The Law of Conservation of Energy

Energy can't be created or destroyed, only transferred. In other words, energy can be converted to different forms: heat or work.

Exceptions to the Laws

These are the two primary principles of mass/energy. As a general rule, mass cannot be converted to energy, nor energy to mass. However, there are exceptions. The most obvious case is nuclear bombs. In the atom bomb (fusion) and the hydrogen bomb (fission), mass is converted into energy. Although converting energy to mass is more complex, there is evidence that it might exist on the microscopic level (think alpha/beta/gamma particles).

If you're looking for the basic rules of physics, this is pretty much the essence of it. Obviously, in a fantasy work there is much more room to test the boundaries of science and be flexible with the principles.

Answer 3

Let’s take the example of pulverising a block of matter: The difference between the block and the powder are bazillion molecular bonds that connect the powder grains to form the block. One might think of undoing one such molecular bond as a fundamental operation, but due to their sheer number I do not think they would satisfy you.

A bit more generally, the highest-level operations that anybody ever reasonably considered to be fundamental are collisions (and similar) of molecules. While we can decompose the molecular collisions into even finer physical interactions between elemental particles (making things even worse for you), we cannot do the opposite: There are no bigger physical units of matter that can be regarded as fundamental in any respect.

Now, physics does often consider transfers of things like momentum, energy, and so on in macroscopic collisions or similar. However, this is a mere simplification that summarises a lot of molecular interactions to easily describe the outcome with conservation laws. For example:

• When two billiard balls collide with each other, I can treat this as an instantaneous transfer of momentum and determine what happens after the collision. However, this point of view fails to describe the brief deformation and other complex stuff going on with the balls during the collision, in particular involving a lot of smaller transfers of momentum between molecules.

• When a chemical reaction happens in a well isolated liquid, I can regard this as a transfer of chemical energy to heat energy, with the latter heating up my entire liquid homogeneously if I wait long enough. Again, the transfer of energy is a simplification that allows me to determine the final state, but fails to describe the gradual spreading of heat through the liquid that happens on a small time scale.

Thus, if you want to stick to a small number of operations, I can suggest two things:

• Transfer single, particles at a very high speed. These can deposit a high amount of energy or momentum in a target. For example a single electron sufficiently close to the speed of light can hit somebody like a bullet.

• Transfer momentum or energy to entire macroscopic objects (or everything in a given volume). With other words, whatever you transfer gets evenly distributed over all molecules of the target. For example, a spell could deposit a certain amount of heat energy in a block of metal, making it hotter and possibly melting. In another example, when transferring momentum, you would push your block in some direction.

Obviously these suggestions are subject to limitations, e.g., neither would allow you to pulverise things, but I wouldn’t consider this a bad thing: Magic systems with clear limits are good.

Answer 4

Let's switch this up a bit. Instead of the fundamental operations, how about looking at what these operators are applied to?

The fundamental particles of the universe.

Bosons — named for Indian physicist Satyendra Nath Bose — are the conformists of the particle world, and photons their poster child. Technically speaking, they “show an enhanced probability to be in the same quantum state,” Wilczek says. “More colloquially,” he adds, “you might say they like to do the same thing.” Think of a laser beam: It’s made of countless photons all moving in the same direction, exhibiting the same color. They cooperate, in a sense.

Fermions — named for Italian physicist Enrico Fermi — on the other hand, are antisocial. They refuse to occupy the same quantum state, or, to extend the analogy, they don’t like to do the same thing. This is the essence of the Pauli exclusion principle, which finds its epitome in electrons. Because no two can exist in the same state, they are forced into the various shells around their atoms. This restricted arrangement produces all the elements in the periodic table, along with their dazzling chemical properties.

Therefore, it would seem that what you want are the fundamental operations that occur between these fundamental particles. It is those operations that completely determine what we perceive as 'reality'. How atoms are formed, how they come together as molecules, how they form into larger 'substances'. How they interact, hw they form how they behave.

Describing how these bosons interact and being able to manage these interactions, pretty much allows one to completely manipulate the universe any way one might want to.