ChatGPT-4 on Quantum Mechanics

The following is a transcript of my exchange with ChatGPT-4 on 20.04.2024 on the question of how momentum is transferred in quantum physics. The specific question I sought to address was the apparent conflict between the requirement that the energy of a quantum must be a single unit and the spatial uncertainty of the “unmeasured” kinetic photon interactions.

(“I can’t believe I’m having this conversation!”)

Me:
Is it correct to say that a photon, when being reflected by a mirror, gives off some energy to the mirror?

ChatGPT:
When a photon is reflected by a mirror, it does interact with the mirror, but typically, it does not give off any energy to the mirror in a way that would change the photon’s energy. Here’s a breakdown of what happens:

Photon-Mirror Interaction: Photons are electromagnetic waves, and when they strike a mirror, they interact with the electrons in the material of the mirror. This interaction causes the electrons to oscillate at the frequency of the incoming electromagnetic wave (the photon).
Reflection Process: The oscillating electrons then re-emit the energy as a new electromagnetic wave — the reflected photon. Ideally, this process happens without any loss of energy if the mirror is perfect and the reflection is elastic (meaning no energy is transferred into other forms like heat).
Energy and Momentum: While the energy (and thus the frequency) of the photon remains the same, the photon does impart a very small momentum to the mirror when it reflects. According to the laws of conservation of momentum and energy, the mirror absorbs the momentum change of the photon, which involves a direction change but not an energy change. For a perfect mirror in ideal conditions, this transfer of momentum does not translate into a noticeable change in the energy of the photon or the mirror.
Practical Real-World Mirrors: In real-world situations, some energy can be lost due to imperfections in the mirror or non-ideal reflection conditions, where some of the photon’s energy might convert into heat or other forms of energy within the mirror material, particularly if the mirror absorbs some of the light rather than reflecting it perfectly. This can be observed with less efficient mirrors that get warm upon exposure to intense light.

So, in summary, in an ideal and theoretical setup, a photon does not lose energy to the mirror during reflection, retaining the same frequency before and after reflection. However, it does transfer a tiny amount of momentum to the mirror. In practical scenarios with non-ideal mirrors, there could be minor energy losses due to imperfections.

Are you sure the photon is re-emitted as a new electromagnetic wave in the process of reflection?

ChatGPT:
Yes, let me clarify that further: In the context of quantum electrodynamics (QED), which is the quantum field theory of electromagnetism, the process of reflection is indeed more nuanced than simply stating that photons are absorbed and then re-emitted by the atoms of the mirror.

In the QED view, photons are elementary particles that mediate electromagnetic forces, and when a photon interacts with a mirror, it can be thought of as interacting with the electrons in the atoms of the mirror. Here’s a more precise breakdown:

Photon-Electron Interaction: As a photon approaches a mirror, it interacts with the electrons in the mirror’s material. This interaction is governed by the electromagnetic force. The photons induce oscillations in the electron field, particularly affecting the electrons on the surface.
Quantum Amplitude: Each possible path the photon might take (including being absorbed, passing through, or reflecting off each electron it encounters) contributes to the overall quantum amplitude for the process. The rules of quantum mechanics govern how these contributions are added together.
Reflective Outcome: The dominant process that emerges from this sum of probabilities (in the case of a mirror designed to reflect light) is that the photon will reflect. However, this isn’t a matter of the photon being absorbed and then a new one being emitted in the classical sense. Instead, the reflection is a result of the collective interaction between the incoming photon and the electron field, leading to a photon emerging that appears to have “bounced off” the mirror.
Energy and Momentum Conservation: This interaction conserves energy and momentum. The frequency (and thus the energy) of the photon typically remains unchanged, indicating that the process is elastic. The photon’s momentum changes direction, which implies an interaction with the mirror, but without a net transfer of energy.

Thus, while it is often a useful simplification to describe reflection as absorption and re-emission, particularly in classical optics or simple explanations, the quantum description involves coherent scattering processes where the incident photon influences the electron field and a photon is scattered off that field. This scattered photon maintains the same quantum identity (in terms of energy and frequency) but changes direction. The mirror itself does not absorb and then emit a new photon in the way a fluorescent material might.

Is it then correct to say that when light is not reflected, but we “see” an object the light shines on, there is the process of absorbing and re-emitting photons, whereby the re-emitted photons are of a specific (longer) wavelength than the incoming light, and the rest of the energy is converted to heat?

ChatGPT:
Yes, that’s a correct description of how we perceive objects that light shines on, when the light is not simply reflected but absorbed and re-emitted. This process is fundamental to how we see color and understand the interaction of light with materials. Here’s a more detailed explanation:

Absorption: When light hits an object, the photons can be absorbed by the atoms or molecules of the material. The energy from the photons is taken up by the electrons in these atoms or molecules, which move to higher energy states (excited states).
Re-emission: Not all of this absorbed energy stays within the atom or molecule. Often, the electron will return to a lower energy state after a brief period, and this transition back to a lower state results in the emission of a photon. The energy (and thus the wavelength) of this emitted photon is usually different from that of the absorbed photon. This difference corresponds to the energy difference between the electron’s excited state and its new state.
Wavelength and Color: The specific wavelengths that are re-emitted depend on the material’s properties. Different materials have different characteristic energy levels for their electrons, so they absorb and re-emit different wavelengths of light. This is why objects have different colors; the color we see is the light that is not absorbed but re-emitted. For example, a leaf appears green because chlorophyll absorbs blue and red light efficiently but reflects and re-emits green light.
Conversion to Heat: The rest of the energy that is not re-emitted as photons can be converted into other forms of energy, typically heat. This happens through non-radiative processes where the energy is transferred to other motion within the molecules, such as vibrational or rotational motion, which eventually dissipates as heat.

So, in summary, when light illuminates an object and is not merely reflected but absorbed and re-emitted, the object absorbs some wavelengths of light and re-emits others. The wavelengths that are re-emitted determine the color of the object as perceived by our eyes, and any energy not re-emitted as light contributes to heating the object.

Back to the reflection of light. The solar sail concept is based on the reflection: photons pass on some momentum to the solar sail that reflects, not absorbs and re-emits light?

ChatGPT:
Yes, that’s exactly right. The concept of solar sails in space propulsion is based on the momentum transfer from photons to the sail upon reflection. Here’s how this works:

Photon Momentum: Although photons have no rest mass, they do carry momentum, which is related to their wavelength. The formula for the momentum of a photon is \(p=\frac{h}{\lambda}\), where \(h\) is Planck’s constant and \(λ\) is the wavelength of the photon.
Momentum Transfer: When photons strike the surface of a solar sail, they reflect off it. In reflecting, each photon imparts momentum to the sail. Since the direction of the photon changes upon reflection, the change in momentum associated with this direction change is transferred to the sail. This transfer of momentum exerts a force on the sail.
Force from Light Pressure: Each individual photon contributes a very small amount of momentum, but a large number of photons striking the sail continuously results in a significant cumulative force. Over time, this force, though initially small, can accelerate the solar sail to high speeds. This principle allows for propulsion without the need for fuel, which is highly beneficial for long-duration space missions.
Efficiency in Reflection: For maximum efficiency, the solar sail is designed to reflect as much of the incident light as possible, rather than absorbing it. Absorption would convert the light energy into heat rather than utilizing it for propulsion. Reflective materials ensure that the light’s momentum is more effectively used for pushing the sail.

The effectiveness of a solar sail is enhanced by using materials that have high reflectivity and by optimizing the angle of the sail relative to the incoming light to maximize the momentum transfer. This makes solar sails a promising technology for propelling spacecraft without the need for carrying conventional fuel.

When a photon reflects off a solar sail, all of its momentum/energy must be in one place, i.e. it interacts with the sail at a specific location? At the same time, that point of impact is undefined in terms of QED, as well as in terms of the wave function. What is your take on this?

ChatGPT:
You’re right in noting that quantum electrodynamics (QED) and the principles of quantum mechanics introduce complexities into understanding exactly how photons interact with surfaces like a solar sail. The nature of light and photons at the quantum level can be quite different from classical descriptions, especially when we consider the exact location and impact of a single photon. Here’s a breakdown of these concepts:

Photon as a Particle and a Wave: In quantum mechanics, a photon is described both as a particle and a wave. This wave-particle duality means that while a photon can be thought of as a particle with momentum, its exact position and trajectory are not as well-defined as they would be in classical physics. Instead, they are described by a probability distribution known as a wave function.
Wave Function and Location: The wave function of a photon describes the probability of its presence at various locations. When we say a photon impacts a solar sail, we typically consider a region rather than a pinpoint location. The wave function of the photon is spread out over an area, and where exactly the photon interacts with the sail isn’t precisely defined until an interaction (like reflection) occurs. At the point of interaction, the wave function “collapses” to a more definite state, localizing the photon at the time of interaction.
Interaction in QED: Quantum electrodynamics gives a more detailed account by considering the photon’s interaction with the electron field of the solar sail. This interaction isn’t a simple single-point impact; instead, it involves complex exchanges and interference patterns governed by the quantum fields of both the photons and the material’s electrons. The process involves the entire electromagnetic field interacting with the quantum states of the electrons in the sail.
Momentum Transfer and Uncertainty: Even though the exact point of interaction is not perfectly defined in quantum terms, the overall effect — the transfer of momentum from the photon to the sail — still adheres to the laws of conservation of momentum and energy. This happens across the entire interface area where the photon field interacts with the sail, reflecting the collective effect of many such quantum interactions.
Practical Consideration in Engineering: In practical terms, especially in engineering applications like solar sails, these quantum uncertainties often average out over the vast number of photons and the macroscopic scale of the materials involved. The force exerted by the photons on the sail can be calculated with classical physics principles, using the cumulative effect of the momentum transfers, despite the underlying quantum mechanical complexities.

OK, all the photon’s momentum has to be in a single place in order to be transferred to the solar sail (or an ordinary mirror). We noted above that the wave function does not collapse in the process of reflection. To meet this requirement, the photon’s momentum must be distributed over the mirror? How do you reconcile this conflict?

ChatGPT:
You’ve touched on a deep and intricate aspect of quantum mechanics and quantum field theory, where the concepts of how particles like photons interact with surfaces challenge our classical understanding of physics. The interplay between the photon’s quantum nature, its wave function, and its interaction with a mirror or solar sail involves reconciling several quantum phenomena:

Quantum Superposition and Spread: Photons, being quantum objects, are described by wave functions that are spread out in space. This spread does not necessarily imply that the photon’s physical presence or effects are equally distributed across this spread, but rather that the probability of finding the photon upon measurement (or interaction, like reflection) is spread out.
Localization During Interaction: When a photon interacts with a mirror or solar sail, it’s not that the entire wave function collapses immediately upon contact. In a quantum field theory (QFT) description, the photon interacts with the electromagnetic fields and the electrons of the atoms composing the mirror or sail. These interactions are localized where the electromagnetic fields of the photon and the electrons effectively overlap. The point of effective interaction, where momentum is transferred, occurs within this localized region. However, the precise point can still be fuzzy in quantum terms.
Momentum Transfer and Uncertainty: The momentum of a photon is indeed transferred to the mirror or solar sail upon reflection. This occurs even though the exact location of the photon before interaction is uncertain. In quantum mechanics, uncertainties in position do not prevent definite interactions from taking place. The photon imparts momentum to the mirror or sail effectively and predictably, despite its wave function being spread out.
Averaging Over Many Photons: In practical terms, when considering devices like mirrors or solar sails, the effects of single photons are typically averaged over the collective behavior of many photons. Each photon interacts with the material, reflecting and transferring momentum in accordance with quantum mechanical probabilities. The cumulative effect of these interactions (each possibly at slightly different but overlapping locations) results in the macroscopic phenomena we observe, like the pushing of a solar sail.
Reconciliation in Quantum Field Theory: QFT helps bridge these phenomena by treating particles and fields not as isolated entities but as excitations in an underlying field. In this framework, the photon is an excitation of the electromagnetic field and its interaction with the mirror or sail involves exchanges mediated by this field. This model naturally accounts for the spread of the photon’s wave function and the localized interactions where momentum is transferred.

In conclusion, while the wave function of a photon is spread out and describes probabilities rather than certainties, the process of reflection at the quantum level involves localized interactions where momentum is indeed transferred effectively to a macroscopic object like a solar sail. This transfer is consistent with the laws of conservation of momentum and energy, and fits within the probabilistic nature of quantum mechanics, where specific outcomes (like reflection and momentum transfer) emerge from the interactions of fields rather than from the classical particle-like collisions.

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