1900: A physics genius wandering around Europe

Chapter 657 Quantum Electrodynamics! The End of Electromagnetic Interaction! The Beginning of Everything! Reaching the Pinnacle!

To everyone's astonishment, Liggiev presented the first perfect theory of quantum field theory: quantum electrodynamics.

In reality, the birth of quantum electrodynamics was not without its challenges.

In 1926, Heisenberg, Born, and Jordan were the first to consider the electromagnetic field as an infinite-dimensional harmonic oscillator.

This method was used by Heisenberg when he created matrix mechanics, but now it is being applied to electromagnetic fields.

However, when the three quantized the electromagnetic field, they discovered a problem:
"The interaction between electromagnetic fields and charged particles has not been taken into account."

As is well known, the concept of a field was proposed to describe the "direction and intensity of attraction".

If interactions cannot be calculated, then such quantization is meaningless.

You could even quantize time and consciousness through some means, making it a purely mathematical game with no physical meaning.

This is the first problem in quantum electrodynamics.

In 1927, Dirac brilliantly proposed the method of "canonical quantization".

The so-called canonical quantization refers to a mathematical method for quantizing classical theories or concepts.

The term "canonical" originally comes from classical physics and refers to "a specific structure" in a theory.

This structure is also preserved in quantum theory.

Take the field as an example.

In classical field theory, a field is a function of spacetime, describing the field intensity at every point in space.

In quantum mechanics, these fields are quantized and become operators acting on quantum states, which is equivalent to changing the mathematical form of the structure.

This process is called canonical quantization.

Canonical quantization, also known as "secondary quantization," means that it goes a step further than traditional quantization.

(To fully understand regular quantization requires a great deal of background knowledge, which I won't go into here.)
Dirac creatively proposed the generation and annihilation operators using canonical quantization.

In this way, the interaction between the quantized electromagnetic field and charged particles can be handled.

Ordinary quantum mechanics can only deal with systems where the particle number is conserved.

For example, a system with 6 electrons will still have 6 electrons after undergoing a series of changes.

Ordinary quantum mechanics can precisely describe the processes that a system undergoes.

But what if there are only 4 electrons left in the system?
At this point, quantum mechanics is powerless.

However, the operators proposed by Dirac can be explained.

The creation operator describes the process of particle creation, while the annihilation operator describes the process of particle disappearance.

As you can probably see, this is the annihilation of matter and antimatter.

With the addition of creation and annihilation operators, Dirac was finally able to describe the behavior of electromagnetic fields and charged particles.

For example, when energy is input into an electromagnetic field, it will generate a pair of photons (the antiphoton of a photon is itself).

When an electron and an antagonist meet, they annihilate each other into two photons.

In summary, this new theory can explain the quantum properties of electromagnetic interactions, such as photon emission and absorption, annihilation of charged particles, scattering between charged particles, and scattering between charged particles and photons.

Therefore, Dirac named it quantum electrodynamics.

But then a second problem arose.

Photons are produced by the excitation of electromagnetic fields, but how are physical particles, such as electrons, produced?

Dirac's quantum electrodynamics can only describe the annihilation of electrons and positrons, but not the creation of electrons.

Between 1928 and 1934, Wigner, Heisenberg, Pauli, Fermi, and others used the "anti-quirk" method to consider material particles as being excited by some corresponding field after quantization.

For example, electrons are generated by an electron field.

The mathematical description of the electron field uses Dirac's operator results.

In this way, with the help of the concept of quantum mechanics, physicists have finally unified electromagnetic waves and particles under the concept of "field".

The quantum field theory framework embodied in quantum electrodynamics caused a sensation!
It is a higher version of quantum mechanics, enabling physicists to have a deeper understanding of the world.

However, the good times did not last long.

Soon, it was discovered that quantum electrodynamics could not explain the two electromagnetic problems of the electron's anomalous magnetic moment and Lamb shift.

The theoretical predictions differed greatly from the experimental data.

Oppenheimer then found the theoretical reason.

Because in perturbation calculations, some unavoidable infinite divergence phenomena will occur in higher-order terms of quantum electrodynamics.

This is the third problem in quantum electrodynamics.

For a long time, no one was able to solve it.

Until 1950, based on the work of his predecessors, Schwinger, Feynman, Tomonaga Shinichiro and others established a systematic method for eliminating the divergence of higher-order terms.

This is the famous "renormalization". (Feynman diagrams are a visual method for describing renormalization.)
After renormalization, quantum electrodynamics has achieved unimaginable precision in predicting the anomalous magnetic moment and Lamb shift of electrons.

At this point, quantum electrodynamics became an impeccable theory.

Quantum field theory has thus become the framework theory that can describe all microscopic phenomena.

However, this good fortune didn't last long.

Physicists then discovered that quantum field theory has two fatal problems:
First, Fermi theory, which describes the weak interaction, is non-renormalizable. That is, quantum field theory cannot effectively describe the weak force.

Second, strong interactions cannot be perturbed. That is, quantum field theory cannot effectively describe the strong force.

This gave the bigwigs at the time a real headache.

The core idea of ​​quantum field theory is that everything is a field.

The four fundamental forces each have their corresponding fields. We just perfectly solved the electromagnetic field problem, but now we're encountering problems with the weak and strong forces.

Quantum field theory is once again in crisis.

Things took a turn for the better when a peerless genius from China, Yang Zhenning, emerged out of nowhere.

In 1954, Yang Zhenning and Mills published the world-shaking "Yang-Mills equation".

This is a very powerful mathematical method, the core of which is: U(1) group, SU(2) group, SU(3) group.

Simply put, these three groups represent a transformation of the coordinate system.

However, this transformation does not occur in the traditional Euclidean coordinate system, but in a higher-dimensional coordinate system.

U(1) is a first-order transformation with only one parameter variable (so U is followed by a 1).

Therefore, U(1) can describe the photon that transmits electromagnetic interactions.

This is quantum electrodynamics.

SU(2) is a second-order transformation with a total of 4 parameter variables, but one of them is fixed, so only 3 parameters are independent.

Therefore, SU(2) can describe the three bosons (i.e., W+ boson/W- boson/Z boson) that transmit the weak interaction.

Combining the two, SU(2)×U(1), allows us to describe both photons and bosons simultaneously, unifying the electromagnetic force and the weak force.

This is the electroweak unification theory.

Similarly, SU(3) is a third-order transformation with a total of 9 parameter variables. After removing one fixed parameter variable, there are 8 independent parameter variables remaining.

Therefore, SU(3) can describe the eight gluons that transmit strong interactions.

This is quantum chromodynamics.

Finally, as long as SU(3)×SU(2)×U(1) can be unified, then the unification of the three forces will be achieved.

See? It's that simple.

Yang Zhenning's greatness lies in the mathematical framework he proposed.

Based on the Yang-Mills equations, Glashow and Salam independently proposed the electroweak unification theory between 1960 and 1964.

This is the so-called SU(2)×U(1). (Note: Before this, the parity non-conservation proposed by Yang Zhenning and Li Zhengdao was also an important theoretical basis for electroweak unification. So Professor Yang is indeed amazing.)
However, there is a problem with their theory.

That is, according to the Yang-Mills equations, these particles that transmit interactions should be massless.

However, except for photons and gluons which have no mass, bosons all have mass.

Theoretical predictions and actual results have become contradictory.

Then, in 1964, Yoichiro Nambu proposed the concept of "spontaneous symmetry breaking" in an attempt to explain this problem.

Building on his work, Higgs made the groundbreaking proposal of the "Higgs boson," which endows these particles with mass using a spontaneous symmetry breaking mechanism.

This is the famous "Higgs boson," also known as the "God particle."

Because of it, the universe has mass. (Note: The Higgs boson was discovered in 2012.)
In 1967, Weinberg introduced the Higgs mechanism into electroweak theory, giving bosons mass.

Thus, the electroweak unification theory was formally established, becoming a reliable theory like quantum electrodynamics.

Finally, physicists turned their attention to the strong interaction.

Gell-Mann and Zweig independently proposed the quark theory.

Then, in 1972, Gell-Mann proposed quantum chromodynamics to describe strong interactions, based on the Yang-Mills equations.

That is: SU(3).

However, it still has some problems that are troubling countless geniuses.

All of the above combined constitutes the Standard Model of particle physics.

And the starting point of this pinnacle theory is quantum electrodynamics.

It is the beginning of everything.

At this point, Ligvii's quantum electrodynamics, based on Dirac's work, incorporates particle fields.

It includes all the work of Heisenberg, Dirac, Pauli, Fermi, and others, leaving behind the problem of divergence of higher-order terms.

He even felt an impulse within him:
"Why not just develop the standard model as well?"

However, he could only think about it; it was impossible.

Those theories did not come out of thin air, but were built upon many high-energy particle experiments.

If he could write it without experimentation, he wouldn't be human, he'd be a god!
Moreover, Ridge-Wei's current status no longer requires the support of a standard model.

"Let's leave some soup for future generations."

Even so, the content of quantum electrodynamics alone was enough to amaze everyone present.

"Quantization of electromagnetic fields";
"Generate operators, annihilate operators";
"Electron field";
"Field stimulation";
"."

Do not!
It's not shocking!

It was more of a shock!

Everyone stared blankly at the various symbols on the blackboard, with only one question in their minds.

"Who am I? Where am I? Is the language on the blackboard alien?"

"Is this really physics, or mathematics?"

Of the more than one hundred people present, probably only Dirac could barely understand it.

Because his mathematical skills are the strongest besides Ridgway's.

The derivation of quantum electrodynamics is almost entirely a mathematical process, only interspersed with physical concepts.

Moreover, those operators are all original mathematical symbols that have never appeared before.

This shows how difficult it is to understand.

Hideki Ogawa and Shinichiro Tomonaga stared wide-eyed, their eyes bigger than saucers.

They both have only one thought in their minds right now.

If anyone dares to call them geniuses again, they'll definitely retaliate with insults:
"You are a genius, your whole family are geniuses."

As the strongest physics genius in the entire Sakura Clan, they weren't even qualified to understand Professor Li's theories.

"Where did you start not understanding?"

“I got it from Hamiltonian operators.”

"Why can it change like that?"

"What about you?"

"I don't understand it from the electron field excitation."

"Then you're a bit better than me."

Yoshio Nishina's lips twitched as he listened, feeling embarrassed because he hadn't understood anything from the beginning.

The content on the blackboard was beyond his comprehension.

That's the pinnacle of pure theory!
Hantaro Nagaoka took off his reading glasses and decided in his heart that he would never attend academic conferences again, so as not to embarrass himself.

Theoretical physics is now completely foreign to him.

Zhao Zhongyao looked horrified!
His pride was shattered in an instant.

Compared to the theories on the blackboard, his discovery of antimatter seemed rather insignificant.

Because Professor Li's quantum electrodynamics can perfectly describe the creation and annihilation of matter and antimatter.

It's like he only noticed an apple falling to the ground, while Professor Li proposed the law of universal gravitation.

That's roughly how big the difference is.

"This is the realm of God!"

Compton, Raman, Bose, and others were equally dumbfounded.

They never imagined that quantum field theory, which is based on quantum mechanics, would be so incredible!
Although they could not understand the derivation process, they knew the conclusion of the theory.

Photons are generated by the excitation of the ubiquitous electromagnetic field in the universe.

Electrons are generated by the excitation of the ubiquitous electron field in the universe.

Even all elementary particles are generated by the excitation of their corresponding fields.

This is the essence of "everything is a field"!

"Oh, God!"

"I can't imagine the shock that the theory of quantum electrodynamics will cause in the physics community when it is published!"

Bohr was overjoyed; he finally understood what his teacher meant when he said the trip was "worth it".

Fortunately, he came to China; otherwise, how could he have had the opportunity to witness the birth of quantum field theory firsthand!

Quantum → Quantum Theory → Quantum Mechanics → Quantum Field Theory!

Professor Bruce brought quantum mechanics to its true pinnacle.

Reaching the pinnacle!

"This is going to be exciting for the theoretical physics community."

At this moment, Li Qiwei looked at the shocked crowd and smiled slightly.

He suddenly looked at Dirac and asked:
"Dirac, did you understand?"

Dirac snapped out of his reverie and said:
"Professor, I understand about 80% of it."

Wow!
The whole audience was shocked!

An ordinary academic conference was made extraordinary by the presence of Professor Bruce.

No one could fully understand his report!

(End of this chapter)