Physics often relies on simplified models that work extremely well in practise, but which may sometimes hide deeper physical insights. I recently explored one such possibility in a formal paper which I hope to publish.
Here I will describe the main ideas in plain English. In particular, I ask whether treating photon exchange as something physically real, rather than merely mathematical, may shed new light on potential energy in bound systems.
This discussion focuses on bound systems of oppositely charged objects, particularly electron-based systems such as the hydrogen atom, the simplest two-body atomic system.
INTRODUCTION STRIPPING AWAY: STRIPPING AWAY THE SIMPLIFICATIONS
Much of physics relies on simplifying assumptions to make complex equations manageable. But what happens when we strip those assumptions away and look at basic physics from a completely literal standpoint?
Consider two oppositely charged bodies bound together-for example an electron and a proton-moving from an effectively infinite separation down to microscopic distances. When viewed in this way, some interesting and often neglected consequences begin to emerge.
We can explore this by looking at three distinct situations where two objects start at rest and move toward each other:
- Classical Systems: Both objects are macroscopic (for example, two charged spheres).
- Mixed Systems: One object is classical and the other is quantum (for example, a charged sphere and an electron).
- Quantum Systems: Both bodies are quantum particles (for example, the electron and proton in a hydrogen atom).
In the first two cases, the objects follow clear classical paths as they accelerate towards each other and eventually collide. Potential energy is converted into kinetic energy while total momentum remains zero. But as the separation becomes microscopic, the behaviour enters the quantum regime where photons are emitted into the surroundings.
THE BRIDGE BETWEEN CLASSICAL AND QUANTUM PATHS
Quantum mechanics does not usually refer to classical paths. Yet classical trajectories are observed every day in devices such as particle accelerators and mass spectrometers.
When we consider an electron-proton interaction, Bohr’s correspondence principle predicts a crossover between classical and quantum behaviour. The principle states that for sufficiently large quantum numbers, the predictions of quantum mechanics approach those of classical mechanics. In the present discussion, the principal quantum number is particularly relevant.
In other words, if the initial separation of a proton and an electron is large enough, their motion must initially resemble a classical approach.
We see experimental evidence of this transition in giant Rydberg atoms, where highly excited electrons display features resembling classical motion. Although there are practical limits to the size of atoms we can observe, there are no known theoretical limits.
This suggests that, an electron-proton approach event may begin in a largely classical manner before gradually transitioning into discrete quantum behaviour as the separation becomes microscopic.
CHALLENGING TWO MAJOR SIMPLIFICATIONS
Standard textbook treatments of two–body bound systems often rely on two important simplifications:
- Neglecting radiation during acceleration: Radiation emitted while charges accelerate toward each other before a collision, for example an electron approaching a target in an X-ray tube-is usually neglected.
- Treating the larger mass as fixed: The heavier body, for example a proton, is commonly treated as stationary while only the lighter body, for example an electron, is allowed to move, often using approximations such as the reduced mass principle.
If we avoid these simplifications, the system must instead be treated as a fully dynamic, two-body problem in which both bodies move, and interact throughout the entire approach.
Whether radiation is emitted during continuously changing acceleration remains a matter of debate, since the traditional Larmor and Liénard-Wiechert treatments were originally developed for single-particle systems rather than interacting pairs. However, if such radiation does occur, an interesting and physically meaningful mechanism begins to emerge.
THE MYSTERY OF THE INTERNAL PHOTONS
If accelerating charged particles radiate energy as they approach each other, an important question immediately arises:
Where does that energy go?
The simplest possibility is that the particles radiate directly to each other. In this picture, photons carry energy losses away from one particle and deliver them as energy gains to the other.
During separation events, kinetic energy is gradually reduced and transferred back into the particles as potential energy, appearing as tiny increases in rest mass. Because of the large mass difference, the electron acts as the dominant net radiator while the proton acts mainly as the absorber.
During approach events, the process reverses. The proton becomes the dominant net radiator and the electron the dominant net absorber. In effect, potential energy stored within the system is converted into kinetic energy.
An interesting consequence is that both particles undergo the same fractional change in mass, despite their enormous difference in size.
RETHINKING POTENTIAL ENERGY
This model suggests that what we traditionally call potential energy may correspond to a real and continuous physical process: the exchange of photons between bound particles.
In this picture, pulling two attracting particles further apart slightly increases their combined mass, while allowing them to move together converts that stored energy back into kinetic energy.
For a hydrogen atom moving between its Bohr radius and complete separation, the predicted fractional mass change is extremely small, being twice the ionisation energy divided by the combined masses of the proton and electron.
Detecting such tiny changes directly would be extraordinarily difficult. To test this type of radiation-exchange model experimentally, future measurements would likely need to monitor atoms in situ as they move between ground and ionised states.
EINSTEIN, FEYNMAN, and ELECTROMAGNETIC INERTIA
The idea that mass may change through energy exchange is consistent with several well-established themes in physics. Albert Einstein famously showed that the inertia of a body depends directly on its energy content.
Richard Feynman also noted that experimental evidence suggests that part of the mass of a charged particle may be electromagnetic in origin.
If this is the case, then a radiation-exchange model may offer a possible physical mechanism underlying this form of electromagnetic inertia.
RESOLVING THE RELATIVITY CONTRADICTION
At first glance, a changing rest mass may appear to conflict with the familiar relativistic energy relation:
E = γEo
where the total energy (E) increases with the Lorentz factor (γ) while the rest mass energy (Eo) remains constant.
However, this standard treatment is usually applied under two important approximations: radiation losses are assumed to be negligible, and the mass ratio between the interacting bodies is extremely large, effectively infinite for mixed systems.
Ms/Me = ∞
Ms =mass of larger mass body for example a charged metal. Me = mass of smaller mass body for example an electron
Such a limit represents a highly asymmetrical idealised system in which one body effectively remains fixed while the other gains kinetic energy.
Particle accelerators approach this situation closely, but nature also contains more symmetrical systems.
At the opposite extreme, electron–positron annihilation involves equal masses. In this case, rest mass energy decreases as the particles are converted into gamma-ray photons.
Intermediate systems — such as the hydrogen atom — may then be viewed as lying between these two limiting cases.
BROADER IMPLICATIONS ACROSS PHYSICS
If a radiation-exchange model of this kind has physical validity, it may have implications for several broader areas of physics.
- Revisiting the Bohr atom problem: (a problem of historical interest perhaps)
Early atomic models faced a major difficulty: accelerating electrons should continuously radiate energy and eventually spiral into the nucleus. Within a radiation-exchange picture, stability might instead arise because the exchanged energy remains internal to the system mediating energy exchanges, rather than being continually lost to the external environment. The electron and proton would then behave more like a coupled two-body system orbiting a common centre of mass.
- Connections with the uncertainty principle:
As particle separation decreases, the travel distance for exchange photons also decreases, while the energy transfer per unit distance increases rapidly. This may provide an interesting physical perspective on the energy–time uncertainty relation and quantum fluctuations.
- The specific charge constant:
If particle mass changes slightly during energy exchange, it is conceivable that charge could vary proportionally. In that case, the specific charge — the charge-to-mass ratio — might represent a deeper invariant quantity.
- Particles and fields:
Rather than treating particles and fields as entirely separate concepts, this approach suggests they may be closely linked aspects of the same underlying process. Potential energy traditionally associated with the electric field could then be interpreted as energy temporarily distributed through particle masses and exchange photons in transit.
Between interactions with the external environment, the total energy of the system would consist of the particles’ kinetic and potential energy together with the energy carried by exchange photons moving between them.
- Bound and unbound acceleration systems:
This approach may point toward an important distinction between bound and unbound accelerating charges. Freely accelerating charged particles are generally expected to radiate energy into the surrounding environment. In tightly bound parts of systems, however the exchanged energy may remain internal to the system through direct photon exchange which mediates exchanges between potential and kinetic energy.
REFERENCES AND FURTHER READING
On electromagnetic inertia:
Richard Feynman, Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Volume II, Chapter 28.3. Addison–Wesley.
On Rydberg atoms:
Dunning, F. B. Giants on the Atomic Landscape. Rice University eBook.
On mass and energy:
Albert Einstein (1905). Does the Inertia of a Body Depend Upon Its Energy Content? Annalen der Physik, 17, 891–921.
CLASSICAL MOTION OF QUANTUM PARTICLES 