Why are First-Principles Calculations considered a core method in theoretical physics?

Hello, that's a great and very representative question. I'll try to explain it in simple terms so you can grasp why this thing is so important in theoretical physics.

You can think of scientific research as having a few different approaches.

Approach 1: Empiricism, like an old Chinese doctor. This is like an old Chinese doctor diagnosing an illness. He relies on "inspection, listening, smelling, and palpation" (望闻问切) and ancestral remedies. For example, he might say: "For your symptoms, use Angelica sinensis with Astragalus membranaceus; it works well." If you ask him why, he might say: "It's experience; it's been used this way for hundreds of years, and it's effective." This method is common in physics, where we call it "phenomenological theory" or "empirical model." We observe a phenomenon, then fit a mathematical formula to the data. This formula is very useful and can predict results, but we don't fully understand the underlying principles behind it. It works, but it's a bit like "knowing what it is, but not why it is."

Approach 2: Pure Theory, like a mathematician. This approach starts purely from a few very basic axioms and hypotheses, using rigorous mathematics to deduce an entire theoretical system. For example, Einstein's General Relativity started from a few fundamental assumptions and derived the gravitational field equations. This method is incredibly elegant, but it's often the domain of geniuses, and sometimes it's too far removed from what we can verify in everyday life.

Now, here's the key.

First-principles calculation is like a "modern forensic scientist" + "super chef."

The term "First Principles" sounds very profound, but simply put, it means "starting from the most fundamental, most original laws, without adding any empirical assumptions."

In our field of studying atoms, molecules, and materials, these "most fundamental laws" are quantum mechanics. Quantum mechanics tells us that the world is composed of atomic nuclei and electrons, and how they interact with each other follows basic rules like the Schrödinger equation.

So, what does first-principles calculation do?

It's like an extremely rigorous forensic scientist facing a "crime scene" (e.g., a peculiar material). It won't guess. It will say: "Don't tell me about experience, and don't show me reference cases. Just tell me what basic elements are in this scene (e.g., what atoms, carbon atoms, iron atoms, etc.), how many protons and electrons each atom has. Just give me this raw information."

Then, it throws this information into a massive "simulator" (i.e., a supercomputer) and uses quantum mechanics, the sole "master code," to calculate how these atomic nuclei and electrons will organize themselves, what structures they will form, and what forces will arise between them.

After the calculation, it can predict all the properties of this material:

• How hard should it be? (Predicting hardness)
• Can it conduct electricity? Is it a conductor, semiconductor, or insulator? (Predicting electrical properties)
• What color is it? (Predicting optical properties)
• What will it become under high temperature and pressure? (e.g., what state is iron in the Earth's core?)

You see, throughout the entire process, besides telling the computer "there are a few carbon atoms here," we don't give it any "hints," such as "I guess it should be very hard" or "based on experience, it shouldn't conduct electricity." All results are derived purely from quantum mechanics.

So, why is it a core method in theoretical physics?

1. Powerful Predictive Capability (The Crystal Ball Power): This is its most amazing aspect. Traditional experiments are like "cooking a dish": you have to go into the kitchen, turn on the stove, put in all the ingredients, and only then do you know if the dish tastes good. First-principles calculation is like "perfectly simulating cooking in your mind": before you even enter the kitchen, you know what the dish will taste like with these ingredients and this heat. This means we can "invent" and "test" thousands of non-existent new materials on a computer, identify the most promising ones, and then synthesize them in the lab. For fields like new drug development, new energy materials (e.g., batteries, solar panels), and superconducting materials, this is revolutionary, saving astronomical experimental costs and time.

2. Profound Explanatory Power (The "Why" Power): It not only tells you "what it is" but also "why it is." For example, we all know that diamond is very hard and graphite is very soft, yet both are composed of carbon atoms. Why? First-principles calculation can clearly tell you how electrons in diamond "weld" carbon atoms together to form a strong three-dimensional network structure; while in graphite, electrons allow carbon atoms to form layers, with weak bonding between layers, making it easy to rub off. It allows us to understand the macroscopic properties of matter at the most fundamental electronic level.

3. Bridge Connecting Theory and Experiment: Theoretical physics can sometimes be too abstract, while experimental physics can sometimes be like "blind men touching an elephant." First-principles calculation acts as a bridge. Theorists propose a new theory, which can be simulated computationally to see what observable phenomena it would produce, guiding experimental physicists to conduct experiments. Conversely, if experimentalists discover a strange phenomenon that cannot be explained, they can use calculations to simulate it, to see if it's caused by some peculiar quantum effect, thereby helping theorists build new models. It has become the "common language" for dialogue between theory and experiment.

4. Exploring Extreme Conditions: Many experiments are impossible to perform. For example, we want to know what the core of Jupiter is like. The pressure and temperature there are unattainable in Earth labs. What do we do? Use first-principles calculation! We input data for hydrogen and helium atoms, set the extreme pressure and temperature of Jupiter's core, and the computer can tell you what magical states they will transform into (e.g., metallic hydrogen).

Of course, it's not omnipotent. This type of calculation is extremely computationally intensive; even for slightly larger systems, it requires national-level supercomputers to run for several months. Moreover, to complete calculations within a limited time, we still need to make some approximations. However, these approximations are based on physical theories, and their applicability and limitations are well understood.

To summarize:

First-principles calculation is core because it's a "God's-eye view" research method. It discards experience and guesswork, attempting to reconstruct and predict the behavior of the material world from the universe's most fundamental rules, through powerful computational capabilities. It can both guide us to create the future (design new materials) and help us understand the past (explain existing phenomena), serving as a powerful tool connecting pure theory and the real world.