The ancestor Newton really made a good start. In order to establish the theory of physics, he first developed calculus, which was the initial model of combining mathematics with physics. It is really unacceptable that three simple formulas can predict the motion of celestial bodies and explain the small balls on the slope.

The basic physical quantities of Newtonian mechanics are space coordinate X, time T, mass M and energy, which can be intuitively understood by normal people.

And calculus is intuitive. Think about how we use image thinking a lot when solving the problem of high mathematics. For example, we can understand differential as a small quantity and integral as a sum. Come to think of it, it's not much different from elementary mathematics.

Post-Newton period;

Statistical mechanics, Maxwell electromagnetism and analytical mechanics appeared after Newton. Although these theories are independent of Newtonian mechanics to some extent, they have no fundamental contradiction with Newtonian mechanics in the world view. Moreover, the mathematics needed by these theories is only elementary mathematics+calculus.

Among them, the basic physical quantities of electromagnetism are electric field and magnetic field, and statistical mechanics introduces entropy and heat, which is generally intuitive. However, analytical mechanics is subtle. Although the theoretical system is completely equivalent to Newtonian mechanics, Lagrange and Hamiltonian are basic physical quantities. The definitions of these two quantities are entirely based on mathematical considerations and are not intuitive. Facts have proved that these two brothers have played an extremely important role in modern physics.

Einstein's period:

Since Einstein came to this world, physics has been developing in the direction of transformation. . .

In Newton's time, physical intuition was the first thing, and then the needed mathematics was developed. In Einstein's time, on the contrary, some mathematicians used to play around.

During this period, things that were considered irrelevant to the real world were introduced into physics.

Special relativity tells us that time and space are equal, and switching inertial system is actually rotating four-dimensional space-time, which we can understand by analogy with three-dimensional rotation. Momentum, wave vector and electromagnetic field can find their corresponding four-dimensional covariant forms.

General relativity tells us that space-time is not flat, but twisted together. The reason why we feel flat is that there is nothing with particularly high density around us, so the bending effect of time and space is not obvious (of course, this is said on the premise that the bending of time and space caused by the earth is interpreted as gravity). Time and space have such a profound connection in physics for the first time! What really describes space-time is not Euclidean geometry, but Riemannian geometry (slapped Kant). Generally speaking, Einstein replaced normal people's understanding of naive in time and space with the language of differential manifold, and we found that what we intuitively take for granted is not necessarily true. But we can still use intuitive two-dimensional and three-dimensional space bending to understand the bending of four-dimensional space-time. In addition to emphasizing space-time geometry, relativity does not introduce more basic physical quantities than Newtonian mechanics.

Then let's talk about quantum mechanics. This guy is so counterintuitive.

1. It follows the concepts of Hamiltonian and generalized coordinates in analytical mechanics.

2. In Newtonian mechanics, coordinates and velocity are used to describe the state of a particle, while in quantum mechanics, particles are considered to have no definite coordinates and velocity, so the state of particles is characterized by wave function, and the modulus of wave function is the probability density distribution of particles.

3. Quantum mechanics does not think that physical quantities are numbers, but operators or linear transformations in linear algebra (Hermite's). Algebra was first mentioned in such a high position in physics.

4. The linear algebra it uses is not the linear algebra in the real number field of most undergraduates, but the linear algebra in the complex number field. Yes, the basic equation of quantum mechanics Schrodinger equation contains imaginary numbers! Think about it, when have you seen imaginary numbers in the basic equations of physical theory or in any engineering course before? Of course, Fourier transform doesn't count, because you have to change it back. . . How crazy it is that imaginary numbers that seem impossible to have physical meaning actually appear in basic equations.