# Questions in the quantum theory of radiation

• Abu Abdallah
In summary: A linear polarized field is a coherent linear combination of R and L fields, classically or QMly.I don't understand what you mean by "classically." Can you elaborate?3. In terms of QED, the photon is a point particle.The photon has a finite size and a point-like behavior.
Abu Abdallah
I have several questions in quantum optics or the quantum theory of radiaition. I begin by the following three questions:

How can a DC field ( static field) be constructed using photons ??

If the spin of photons is related to circular polarization of the constructing fields. How can linear polarized fields be constructed using photons.

What is the temporal and spatial exension of photons? The single photon number state makes the spatial extension of the photon bounded only by the dimensions of the cavity in which we quantize the field !

First of all, read the "size of the photon" thread earlier. Photons don't have a "size" since you cannot localize a photon.

I'm not sure what you mean by a DC field? A constant electric field is set up by a superposition of photons that yield that field. Write down a general linear superposition of photon number states, write down the electric field operator, and calculate what the coefficients have to be to yield that $$\langle \mathbf{E} \rangle$$ is a constant.

As for the spin of the photon, I think I'll punt on that one and let someone else explain, since I'm a little fuzzy myself about how photon spin works.

An electric field consists of photons with infinite wavelength.

Abu Abdallah said:
I have several questions in quantum optics or the quantum theory of radiaition. I begin by the following three questions:

How can a DC field ( static field) be constructed using photons ??

If the spin of photons is related to circular polarization of the constructing fields. How can linear polarized fields be constructed using photons.

What is the temporal and spatial exension of photons? The single photon number state makes the spatial extension of the photon bounded only by the dimensions of the cavity in which we quantize the field !
1. A DC field has no photons.
2. A linear polarized field is a coherent linear combination of R and L fields, classically or QMly.
3. In terms of QED, the photon is a point particle.
The spatial extension is of the wave function of the photon.

Meir Achuz said:
1. A DC field has no photons.

I disagree. Show me any EM field that contains photons. I will then redshift it as far as you please to render it DC. Do the photons disappear? Of course not! Their wavelength approaches infinity, that's all.

## 1. What is the quantum theory of radiation?

The quantum theory of radiation is a branch of quantum mechanics that studies the behavior and properties of electromagnetic radiation, such as light, at a subatomic level. It explains how particles of light, known as photons, interact with matter and how they are created and destroyed.

## 2. How does the quantum theory of radiation differ from classical theories of light?

Classical theories of light, such as Maxwell's equations, treat light as a continuous wave. In contrast, the quantum theory of radiation describes light as a collection of discrete packets of energy, or photons. It also takes into account the probabilistic nature of quantum mechanics, which allows for phenomena such as particle-wave duality and quantum entanglement.

## 3. What is the role of uncertainty in the quantum theory of radiation?

Uncertainty is a fundamental principle in quantum mechanics, and it plays a crucial role in the quantum theory of radiation. According to the Heisenberg uncertainty principle, it is impossible to know both the position and momentum of a particle, such as a photon, with absolute certainty. This uncertainty is reflected in the probabilistic nature of quantum mechanics and is essential for understanding the behavior of particles at the subatomic level.

## 4. What are the applications of the quantum theory of radiation?

The quantum theory of radiation has numerous practical applications in fields such as telecommunications, electronics, and medical imaging. For example, understanding how photons interact with matter has led to the development of technologies such as lasers, solar cells, and MRI machines. It also plays a crucial role in the development of quantum computing and quantum cryptography.

## 5. What is the relationship between the quantum theory of radiation and the theory of relativity?

The relationship between the quantum theory of radiation and the theory of relativity, specifically Einstein's theory of special relativity, is a topic of ongoing research and debate. While the two theories have been highly successful in their respective domains, they have not yet been fully reconciled. Some theories, such as quantum field theory, attempt to bridge the gap between the two theories, but a complete understanding of their relationship is still an active area of research.

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