Photon and Radio Wave Distinction

Your question touches on several deep and fascinating aspects of quantum mechanics, electromagnetic waves, and the distinction between photons and classical electromagnetic waves. Let’s break it down into several key points and explore your ideas systematically:

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1. Quantum Entanglement and Electromagnetic Waves

Quantum Entanglement of Photons

• Quantum entanglement occurs when two or more particles (such as photons) share quantum states such that a measurement on one instantaneously determines the state of the other, even if they are separated spatially. This is commonly observed in processes like parametric down-conversion (PDC), where a single photon is split into two entangled lower-energy photons.
• In the case of PDC, the energy, momentum, polarization, and other properties of the two photons are correlated because they originate from the same parent photon. This entanglement suggests that the original parent photon carried the quantum information that was subsequently distributed between the two resulting photons.

Internal Structure of a Single Photon

• A photon is often described as a quantum of the electromagnetic field, and its quantum state is localized in space and time. However, the photon is not typically regarded as having “internal parts” that are entangled or bound. Instead, the entire photon is treated as a single quantum entity.
• In quantum electrodynamics (QED), photons are quantized excitations of the electromagnetic field, and their properties, such as energy ($E=h\nu$), momentum, and polarization, are described by the quantum wavefunction. While the photon is wave-like, the concept of “internal entanglement” between parts of the photon is not standard in quantum theory.

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2. Coherence and Structure in Electromagnetic Waves

Short-Pulse Photons vs. Long Electromagnetic Waves

• A photon is often associated with a short, localized pulse of electromagnetic energy. In contrast, a classical electromagnetic (EM) wave, such as a radio wave, can extend over vast distances and is typically represented as a coherent oscillation of the electric and magnetic fields.
• The distinction between a short photon pulse and a long EM wave lies in their coherence and spatial extent:
  • A photon is quantized and exhibits particle-like behavior, even though it has a wavefunction describing its spatial and temporal distribution.
  • A radio wave is a classical, macroscopic wave. It is not inherently quantized unless you examine it at the quantum level, where it can be described as a collection of many photons.

Coherence and “Bound Structure”

• Coherence refers to the phase relationship between different parts of the wave. In classical EM waves, coherence ensures that the electric and magnetic fields oscillate in a predictable, synchronized manner across space and time.
  • For example, electromagnetic fields exhibit a well-defined phase relationship in a laser beam or a highly coherent radio wave, giving the wave a “structured” behavior.
  • However, this coherence is not the same as quantum entanglement. Coherence in classical waves is a macroscopic phenomenon, while entanglement is a quantum phenomenon involving correlations between distinct quantum systems.
• A radio wave can be thought of as a superposition of many coherent photons, but it is not necessarily “bound” in the same way that a single photon might carry its energy and momentum as an indivisible quantum entity.

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3. Quantum Description of Long Waves (Radio Waves)

• When analyzed at the quantum level, a long radio wave is composed of many low-energy photons. Each photon has energy $E=h\nu$, where $\nu$ is the wave’s frequency. For a typical radio wave, the energy of each photon is extremely small because the frequency is much lower than that of visible light.
• If the radio wave is coherent (e.g., produced by a well-aligned transmitter), the photons that make up the wave can also be in a coherent quantum state. This is described by a coherent state in quantum optics, where the electromagnetic field behaves like a classical wave but has quantum properties.
• Importantly, the photons in a coherent radio wave are not necessarily entangled with each other. They are independent quanta of the electromagnetic field, and their coherence arises from the macroscopic properties of the wave, not from quantum entanglement.

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4. Can a Long Wave Have a “Bound Structure”?

Photons and EM Wave Structure

• A photon is a discrete quantum excitation of the electromagnetic field, and its energy is concentrated in a localized region of space and time. Its “structure” is dictated by its quantum wavefunction, which can describe properties like polarization, spatial distribution, and temporal duration.
• A long EM wave, such as a radio wave, does not have the same discrete “bound” structure as a photon. Instead, it is typically described as a classical wave unless you analyze it at the quantum level, where it is treated as a collection of many photons.

Does the Coherence of a Radio Wave Imply a Bound Structure?

• The coherence of a radio wave can give it a certain “order” or “structure” at the macroscopic level, but this is not the same as the quantum binding or entanglement seen in photons.
• While the wave’s electric and magnetic fields are synchronized, this coherence is a property of the entire wave and does not imply that the wave is “bound” in the sense of a single quantum entity.

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5. Implications for Quantum Mechanics and Classical Electromagnetism

Your suggestion that a long EM wave might have a coherent or “bound” structure similar to a photon is interesting, but the distinction between classical and quantum descriptions is crucial:

• A photon is a quantum particle with well-defined energy, momentum, and polarization that exhibits wave-particle duality.
• A classical EM wave is a macroscopic phenomenon that, when analyzed at the quantum level, can be described as a superposition of many photons.

Key Distinction:

• A photon is inherently quantized and indivisible, while a long classical EM wave is not a single quantum entity and does not exhibit the same “bound” structure as a photon. The coherence of a radio wave arises from the classical synchronization of the fields, not from quantum entanglement or binding.

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6. Final Thoughts

Your reasoning is thought-provoking, and you are correct to explore the similarities and differences between photons and long electromagnetic waves. While a photon can be thought of as a localized “pulse” of the electromagnetic field with quantum properties, a long radio wave is a classical phenomenon unless analyzed at the quantum level. At that level, the wave is described as a coherent state composed of many independent photons, but these photons are not entangled or “bound” in the same way as the components of a single photon.

In summary:

• A long radio wave does not exhibit the quantum binding or entanglement that might be associated with a single photon or a pair of entangled photons.
• The coherence of a radio wave is a classical property and does not imply quantum binding.
• The distinction between classical waves and quantum photons reflects the broader divide between macroscopic and quantum descriptions of electromagnetic phenomena.