# Maxwellian field vs many-body wave mechanics

• Swamp Thing
In summary, Maxwellian field and many-body wave mechanics are two approaches used to describe the behavior of particles in a physical system. While Maxwellian field theory is based on classical electromagnetism and describes particles as moving through a continuous electromagnetic field, many-body wave mechanics is a quantum mechanical approach that describes particles as discrete wave-like entities. Both approaches have their own strengths and limitations, with Maxwellian field theory being more accurate for macroscopic systems and many-body wave mechanics being more accurate for microscopic systems. They can also be used together, such as in quantum electrodynamics, and have various real-life applications including in electrical and electronic devices, quantum computing, and material science. The ease of understanding between the two approaches is subjective and depends on the
Swamp Thing
In some descriptions of the Hanbury Brown and Twiss experiment, I read that the correlation results can be derived from classical wave theory, and that you only need quantum theory to explain it at the level of individual clusters of photons.

So if one knows the value of the Maxwellian field at every point within the experiment zone, can one recover the quantum description of the experiment, e.g. can one say what percentage of the photons are individual particles and what percentage are entangled pairs, and what the phase relations are between their respective waves etc etc?

Thank you for bringing up this interesting topic. The Hanbury Brown and Twiss experiment is a classic example of a phenomenon that can be explained both by classical wave theory and quantum theory. In this experiment, the correlation results can indeed be derived from classical wave theory, but it is important to note that this only holds true for a large number of photons. At the level of individual clusters of photons, quantum theory is needed to fully explain the results.

To answer your question, if one knows the value of the Maxwellian field at every point within the experiment zone, it is possible to recover some aspects of the quantum description of the experiment. For example, one could determine the percentage of photons that are individual particles and the percentage that are entangled pairs. However, determining the phase relations between their respective waves would require a more detailed understanding of the quantum behavior of the photons.

It is important to note that even with a complete knowledge of the classical wave field, there are still limitations to what can be determined about the quantum behavior of the photons. This is because the quantum behavior of particles is inherently probabilistic, and even with a complete knowledge of the classical wave field, there will always be some uncertainty in the exact behavior of individual particles.

In summary, while classical wave theory can provide some insights into the Hanbury Brown and Twiss experiment, a full understanding of the quantum behavior of the photons requires the use of quantum theory. I hope this helps to clarify the relationship between classical and quantum explanations of this experiment.

## 1. What is the difference between Maxwellian field and many-body wave mechanics?

Maxwellian field and many-body wave mechanics are two different approaches used to describe the behavior of particles in a physical system. Maxwellian field theory is based on classical electromagnetism and describes particles as moving through a continuous electromagnetic field. Many-body wave mechanics, on the other hand, is a quantum mechanical approach that describes particles as discrete wave-like entities.

## 2. Which approach is more accurate in describing physical systems?

Both approaches have their strengths and limitations. Maxwellian field theory is more accurate in describing macroscopic systems, while many-body wave mechanics is more accurate in describing microscopic systems. Ultimately, the most accurate description of a physical system depends on the scale and complexity of the system being studied.

## 3. Can Maxwellian field theory and many-body wave mechanics be used together?

Yes, in some cases, these two approaches can be combined to provide a more comprehensive description of a physical system. For example, the electric and magnetic fields described by Maxwell's equations can be quantized and described using many-body wave mechanics. This is known as quantum electrodynamics (QED) and is used to describe the behavior of particles at the atomic and subatomic level.

## 4. Are there any real-life applications of Maxwellian field theory and many-body wave mechanics?

Yes, both approaches have numerous real-life applications. Maxwellian field theory is used in the design of electrical and electronic devices, such as motors, generators, and communications systems. Many-body wave mechanics is used in fields such as quantum computing, material science, and nuclear physics.

## 5. Which approach is easier to understand?

This is subjective and depends on the individual's background and level of understanding. However, many-body wave mechanics is generally considered more mathematically complex and requires a basic understanding of quantum mechanics. Maxwellian field theory, on the other hand, is based on classical physics and may be easier for some individuals to understand.

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