CLASSICAL MOTION OF QUANTUM OBJECTS 

In classical mechanics, objects move along clear, predictable paths, while in quantum mechanics, events are inherently probabilistic, and well defined paths lose their meaning. Despite these differences, classical motion concepts can sometimes provide insights into quantum behaviour.
This work starts by referring to some foundational topics and then analyses approach events in three distinct two-part systems: classical, mixed, and quantum. For separation events, the analysis is mainly focussed on quantum systems, with brief reference to mixed systems. The main focus is on Bohr’s correspondence principle and the gradual transition between classical and quantum behaviour, with particular emphasis on the hydrogen atom, the simplest two part quantum system.
A central assumption is that charged objects radiate photons when moving with changing accelerations. This radiation is considered when exploring how specific events evolve between the classical and quantum realms, revealing details overlooked due to simplifying assumptions used in conventional models.
The analysis suggest that a subtle change might occur as particles transition between states, potentially linked to electromagnetic mass, where a portion of a particle’s mass arises from its electromagnetic field. For example, when a hydrogen atom transitions from an excited state to the ground state, the reduction in the systems potential energy might be attributable to energy withdrawn from the rest masses of the particles.
Any rest mass rest mass change would be minuscule-approximately three parts per hundred million between the near-ionised and ground state. Nonetheless, this variation could be significant when compared to the current precision of mass measurements, which is on the order of three parts per ten billion. However, these high-precision measurements are conducted using devices like Penning traps where the electron and proton are tested separately and not in situ as parts of the atom. Consequently such small variations may not yet be observable in conventional experimental setups, but could be meaningful in the context of particle interactions within a field.
To explore these ideas further this work introduces a model of how mass may change gradually through radiation interactions, with the potential for discrete mass decreases in annihilation events. While such mass changes are subtle, annihilation events could involve more substantial changes, challenging the traditional view of annihilation as instantaneous and hinting at a more gradual transition.
The analysis here is primarily qualitative, applying established mathematics to real physical events, to highlight limitations in existing models. By offering fresh perspectives on long-standing topics, this study invites further exploration of these grounded ideas.
PART 1. SINGLE PARTICLE SYSTEMS
There can be disadvantages of analysing events in terms of single particles. Two examples are given:
Reduced Mass Concept
In conventional models of the hydrogen atom, the concept of reduced mass simplifies the analysis of the two-body system by effectively reducing it to a one-body system. This approach treats the proton as a stationary point charge, with the electron interacting within its electric field. However, this simplification overlooks the intricate details of the interaction between both particles. In this work the reduced mass approximation is not used, to allow a more detailed exploration of the dynamic interaction between the proton and electron. This reveals subtleties which are missed in more conventional models.
Radiation from Accelerating Charged Objects
An ongoing question in physics is whether an accelerating charged object necessarily emits radiation. The prevailing view is that it does, but there remains debate over whether both uniform and non-uniform acceleration cause radiation, or if only one does.
To accelerate, the object must be part of a system containing at least one other object to conserve momentum. This was overlooked by Larmor and later by Lienard and Wiechart who examined radiation from a single charged particle moving with uniform acceleration, without accounting for interactions with other charges. Describing radiation as the result of a single accelerating charge may be an over simplification.
In this work, we will consider simple real systems of two charged parts. Evidence will be presented that the radiation from each part is influenced by the presence of the other part, indicating that conventional equations may not fully capture the behaviour of real world systems.
PART 2. POTENTIAL ENERGY
Quantum electrodynamics (QED) and quantum field theory (QFT) offer sophisticated frameworks for understanding energy interactions at a fundamental level. However, in this section, we begin to explore the concept of potential energy from a perspective that initially draws on classical ideas. It’s possible the conclusions reached can be incorporated into the QED or QFT frameworks:
We don’t know if potential energy has an absolute value in systems of charged objects, but we can calculate how the potential energy changes when the separation between the objects changes. To make these calculations two arbitrary conventions are made: one for separation distance and the other for the potential energy at that distance. The most logical and widely used conventions are to set the separation at infinity and the potential energy at zero. Using these conventions, when oppositely charged objects are infinitely far apart, the systems potential energy is defined as zero. As the objects come closer together, the potential energy becomes increasingly negative. While this concept is straightforward for two-part systems, it becomes more complex when dealing with systems of more than two parts.
In this work, we explore the possibility that potential energy has not only relative values but also absolute values and specific locations within a system. Consider a chemical energy source such as a litre of petrol. We can say that the energy exists within the petrol itself, residing in both the motion (kinetic energy) of the particles and the potential energy of the fields that connect them.
But can we further pinpoint the location of potential energy within individual particles? While each particle has kinetic energy due to its motion, could it also have localised potential energy based on its position in the system?
This exploration leads us to question whether potential energy, traditionally viewed as a property of the system as a whole, might be distributed among the interacting parts. For example, in a two part system one part might have some of the potential energy with the second part having the rest of it. This idea challenges conventional wisdom and opens up new possibilities for how we think about energy in multi-particle systems.
Richard Feynman wrote:
“There is definite experimental evidence of the existence of electromagnetic inertia – there is evidence that some of the mass of charged particles is electromagnetic in origin”.
The Feynman lectures on Physics (volume two 28.3)
PART 3. FIELDS IN CLASSICAL MECHANICS
While (QFT) and (QED) provide robust frameworks for understanding the quantum nature of fields, this section examines fields from a classical perspective. By stepping back to classical fields, we aim to reconsider some of the assumptions about how fields exist and interact in space, particularly in the absence of observable interactions.
Many of us are first introduced to the concept of fields as children when we use iron filings to visualize magnetic field lines. These early experiments often lead to the assumption that a magnet sets up a field that permeates the space around it. This, in turn, gives rise to a broader assumption that all fields exist everywhere in space. However, these assumptions warrant closer examination. Consider a point near a magnet where there is nothing present to interact with it. If there is no interaction at this point, does it still make sense to claim that a magnetic field exists there? Or is it more reasonable to assume that fields, such as magnetic fields, only exist where there are interactions?
Proponents of quantum field theory argue that there are no truly “empty” spaces and that all of space is occupied by fields. If fields are purely mathematical constructs, this claim might not be controversial. However, if we consider fields to be real, physical entities, then the assertion becomes more complicated: are there truly no places in the universe that are empty, even temporarily? Where is the experimental evidence that supports or challenges the idea that fields exist in places where no interaction occurs?
To frame this discussion, let’s consider a few key points about the nature of fields in classical systems:

1. Fields have measurable effects only at locations where there are interacting parts.
2. Any detector that senses a field is, by definition, an interacting part of the system.
3. The resultant field in any system is shaped by the presence of all interacting parts, both microscopic (such as electrons) and macroscopic (such as metal objects).
4. When an interacting part changes location, the field adjusts in the areas where other interacting parts are present.
   To summarise these points we can say that fields exert their influence where interacting parts exist, regardless of scale. Yet despite this observation, the widely accepted assumption remains that fields permeate all of space, even in regions without interactions. This brings us back to a fundamental question: do fields exist independently of interactions, or are they a construct that manifests only when there are parts to interact with?

PART 4. BASIC CONCEPTS
Mass, length and time are three of the basic concepts used in physics, but are these clearly defined as may be assumed? In particular, what exactly do we mean when we talk about mass?
Definitions in terms of “amount of matter” or “inertia” may have intuitive appeal, but they remain rather vague. We might attempt to define mass in relation to other concepts, such as force and acceleration, energy at zero momentum or in terms of quantum mechanical operators. However, these may require other definitions, leading to the risk of circular reasoning, where one definition depends on another.
To further complicate matters various labels have been attached to the concept of mass, including bare mass, inertial mass, gravitational mass and relativistic mass, a concept considered obsolete by a majority of the physics theorist community.
We have precise definitions of units of mass. For example, the kilogramme is defined with reference to Planck’s constant. Additionally, we have the expertise to measure some masses very accurately. For example, the electron mass can currently be measured to ten decimal places.
But the underlying question remains:
What exactly is mass?
For those grappling with this question, Eugene Hecht’s paper, “On Defining Mass” may offer valuable insights. (“The Physics Teacher” vol. 49, Issue 1, February 2011)
In an earlier publication titled “There is no Really Good Definition of Mass”, Hecht discusses the challenge of defining mass and writes:
“The mass of an object depends on where it is in relation to other entities with which it interacts. This effect cannot be ignored if we are to create a completely correct operational definition of mass.”
(The Physics Teacher, Vol. 44, January 2006)
We can summarise this part of the work by saying that in general, establishing clear definitions is important to ensure discussions address the same points and avoid misunderstanding.

PART 5. IS RELATIVISTIC MASS REAL?

The relativistic mass equation has been a topic of considerable debate within the physics community. Central to this discussion is the relativistic energy equation which accounts for both the energy associated with an objects rest mass and its kinetic energy.
Energy due to rest mass = m0c2
Kinetic energy = moc2(γ – 1)
Here m0 is the rest mass which is assumed to be constant in all reference frames, c is the speed of light and γ is the gamma factor, a dimensionless quantity which depends on the speed of the body, it is equal to one when the body is at rest but increases with speed and approaches infinity as the speed of light is approached.
The total energy, E, is equal to the energy due to the rest mass plus the kinetic energy.
E = γm0c2
Dividing by c2 changes the units for example from Joules to Kilogrammes. We can write:
E = γm0
Both forms of the equation can represent energy or mass but by convention the first form is usually used for energy and the second for mass, but usually with a change of symbol the E being replaced by an m or an M. We can write:
M = γm0
The equation in this form is known as the mass variation equation and M is known as the relativistic mass.
The concept of relativistic mass has led to a divide amongst physicists. The majority reject it, one reason being that it can be misleading by suggesting that an objects intrinsic mass increase with speed. Instead they prefer to focus on rest mass and an objects energy and momentum. Conversely, some physicists still find the concept of relativistic mass useful in specific contexts, suggesting that it may provide insights that are not easily captured by rest mass alone.
Ultimately, the question remains: is relativistic mass a meaningful concept? Could it be that mass indeed changes with velocity, but in ways that challenge our current understanding? This question not only reflects the complexity of modern physics but also invites further exploration into the fundamental nature of mass itself.
There are numerous sources that address the concept of relativistic mass including a paper written by Lev B Okun, a well known critic of the concept:
(The Concept of Mass, Physics Today June 1989)
PART 6. ALL PHOTONS START FROM SOMEWHERE AND GO TO SOMEWHERE
Here we use the words light and photons as umbrella terms to cover all parts of the electromagnetic spectrum. But what exactly is light? This seemingly simple question opens a complex discussion that covers various models from particle to wave descriptions, each offering insights into the nature of light. The particle model describes light as discrete packets of energy called photons, while the wave model considers light as oscillating electromagnetic fields.
Most models agree that all light originates from sources where energy interactions result in its creation and emission. Similarly all light eventually reaches absorbers, where energy interactions result in its destruction or absorption. However, it’s possible that some light may never reach absorbers, raising the question of whether undetectable energy exists in the universe.
From a practical viewpoint it doesn’t matter what light is but it’s important to use the best model for the task at hand. Different models are suited to different tasks. For example, in geometrical optics we use the ray optics model and when working on diffraction and interference we use the wave model. Each model has its own domain of applicability.
A common assumption is that once emitted, each photon travels at the speed of light until it interacts with something, be it the eye, a scattering particle or an atom that absorbs the photon and then emits a copy of it. While this model makes intuitive sense, it has a significant limitation: photons do not interact in empty places. More precisely, interactions happen only at places that are suitably occupied by particles.
Any attempt at setting up a photon interaction at an empty place requires something suitable to be there rendering it non empty. It’s a catch twenty two situation. This limitation implies that although light may have certain intrinsic properties, other properties depend upon the system which light interacts with and is a part of. For example the speed of light in a vacuum may be an intrinsic property but the reflection of light from a surface is a property of the light and surface system, not a property of light separately or the surface separately.
The wave like and particle like behaviour of light might not be due to the properties of light alone, but best described as properties of the experimental arrangements of which light is a part. In some arrangements light can be modelled as having a wave nature and in others modelled as having a particle nature or a dual nature. Similarly, in quantum experiments involving entangled photons, the observed correlations do not necessarily reveal details of the photons alone. Rather they reveal details of the overall system which includes the photon emitters, the photons, the detectors and the measurement process.
PART 7. MOVING MAGNETS
There is an aspect of radio communication that has been known of since the pioneering days, which may merit further investigation. To investigate this we go back to basics by carrying out a simple experiment:
THE INCREDIBLE SHAKING MAGNET EXPERIMENT
• Apparatus. A Magnet.
• Method Shake the magnet.
The shaking magnet acts as a basic transmitter, as does a changing current in a piece of wire. These cause surrounding objects-like lumps of metal and circuit components to act as receivers by inducing current within them. These induction effects come under the heading of electromagnetic induction, a process that underlies the operation of things such as generators and transformers as well as some of the basic principles of radio transmission.
Transmitters induce responses in receivers regardless of the sophistication of their circuits. But something that is often glossed over is that it is a two way process and transmitters react to the presence of receivers. This mutual feedback is encapsulated in Faraday’s law particularly through the negative sign, which reflects Lenz’s law. This law can be considered as an expression of the conservation of energy, stating that that induced currents flow in directions which oppose the changes producing them. In other words the changes produced at a receiver result in a feedback to the transmitter causing it to undergo changes as well. Expressing it differently we can say that transmitters communicate to receivers and receivers communicate back to transmitters.
Such two way effects are well known and exploited, particularly within near-field regions. However, what’s particularly relevant is that these feedback effects may not be limited to the near-field only. They could extend into far-fields influencing systems over greater distances. For example in a system containing a transmitter and a receiver correlated currents in both circuits may alter the surrounding electromagnetic field and generate changing magnetic forces. In essence each circuit feels the presence of the other circuit. These observations challenge a commonly held assumption that electromagnetic wave sources function completely independently of their environments.
The Proximity Effect
The “Proximity Effect” is a proposed concept suggesting that the radiation and absorption of photons might be influenced by the separation between radiators and absorbers. It posits that when a radiator and absorber move closer, the probability of photon transfer between them increases, perhaps due to the enhancement of their resultant field. It’s assumed that this effect strengthens with decreasing separations and weakens with increasing separations, becoming negligible in many scenarios, but not necessarily reducing to zero. While this notion may seem intuitively plausible, it is not currently established as a proven phenomenon and should be explored further through theoretical and experimental studies.
PART 8. ARE ALL ELECTRONS IDENTICAL?

The claim that all electrons are identical is supported by current experimental data. Uncertainties in measurements of electron mass and charge are so extremely small that any variations, if they exist, would also be extremely small. However, the data is limited to specific environments such as Penning traps.
It’s conceivable that properties such as mass and charge depend on the structure of the environment and the electrons location within that environment. Any variations could become significant within extremely small particle separations or other regions of extremely high fields. In other words electron properties could be different in locations where there are very few reliable measurements available as of yet.
PART 9. CLASSICAL AND QUANTUM PATHS
Here we explore how approach events evolve in three distinct types of isolated bound system, each containing two oppositely charged objects. The events begin with the objects momentarily at rest in a vacuum and widely separated. In all cases, the Coulomb attraction causes the distance between the objects to decrease. However; the events end differently; in one system a mainly classical collision occurs, while in the other systems, one or more quantum mechanical interactions take place. In all cases kinetic energy is lost with some or all of it being radiated as photons to the surroundings.

1. Pure Classical Systems
   In these systems, both objects are classical. Consider, two lumps of metal.
   Thought experiments, informed by observations from electrostatics and other areas of physics, suggest that in a pure classical system, the metals would move directly towards each other along classical paths. Momentum is conserved and the metals accelerate as potential energy gets converted to kinetic energy.
   It’s a well-established concept in physics that charged objects moving with changing accelerations emit electromagnetic radiation. Therefore, as the objects approach, they radiate electromagnetic waves, which can also be described as the radiation of photons.
   The event would end in a collision, governed mainly by classical mechanics. Energy will be lost through various processes including the generation of heat and sound. Some of the energy will be radiated as photons and this is best described by quantum mechanics.
2. Mixed Systems
   In these systems one object is classical and the other is quantum. Consider, for example, a lump of metal and an electron.
   Observations of certain real systems-such as X-ray tubes, mass spectrometers cathode ray tubes and particle accelerators-show that quantum objects, as well as classical objects can move along classical paths. This suggests that in a mixed system the electron would move along a classical path and the metal would as well, assuming its motion is considered and not ignored as being negligible. Momentum is conserved, and the objects would move with increasing accelerations as potential energy gets converted into kinetic energy. Due to their changing accelerations, the approaching objects would radiate photons.
   The event would end with a collision. A small part of the kinetic energy lost would be converted into X-ray radiation, mainly Bremsstrahlung radiation, but most would be converted to heat.
3. Pure Quantum Systems
   These systems contain two quantum objects. Consider, for example, an electron and a proton, in other words a hydrogen atom.
   Pure quantum systems are best described with quantum mechanics which typically does not account for classical paths. However, we can describe a sort of approach event by referring to concepts such as de-excitation transitions, expectation values and most probable positions.
   Imagine an excited hydrogen atom returning to its ground state via one or more de-excitation transitions. For each transition, a photon is emitted and the most probable separation between the particles gets smaller. This is a probabilistic reduction of separation and can be defined as a quantum approach event. In a similar way we can define quantum separation events and quantum paths.
   In the work that follows we will continue to focus on events involving oppositely charged parts that attract. For systems with like charges, similar principles apply, with the main difference being that the objects repel instead of attract.
   PART 10. COMMON FEATURES OF APPROACH EVENTS
   In classical and mixed systems, objects move along classical paths with changing accelerations while radiating photons. But can a bound proton and electron do the same?
   The answer is yes. Classical path lengths in real system are macroscopic, providing evidence that a bound proton and electron would start approaching classically if the initial separation between them is macroscopic. Further support for this comes from Bohr’s correspondence principle, which asserts that in the limit of large quantum numbers, the predictions of quantum mechanics must converge to those of classical mechanics.
   This principle is especially evident in the study of Rydberg atoms, which are atoms in highly excited states. Research has shown that in atoms of approximately 0.1mm in size, electrons can be manipulated into moving in near circular orbits which mimic the Bohr model of the atom. This suggests that as the size of the atom increases, the initial approach of the particles increasingly resembles classical behaviour. However, as the separation between particles decreases to microscopic levels, these approaches will transition into quantum behaviours.
   “Rydberg atoms form a valuable bridge between the microscopic world described by quantum mechanics and the macroscopic world ruled by Newton’s laws”. F Barry Dunning and Thomas C. Killian
   Rydberg Atoms: Giants of the Atomic World. Rice University E Book PART 11. REALMS OF PARTICLE SEPARATIONS
   To help with descriptions of approach and separation events we define different realms of particle separations.
   Classical Realm
   This is the range of macroscopic separations in which classical properties dominate. Objects moving in this realm move along deterministic classical paths.
   Quantum Realm
   This is the range of microscopic separations in which quantum properties dominate. Objects moving in this realm move in probabilistic quantum paths.
   Mesoscopic Realm
   This realm bridges the classical and quantum realms. In this realm there is a gradual transition of properties, with quantum properties becoming more dominant for reducing separations and classical properties more dominant for increasing separations.
   PART 12. THE HYDROGEN ATOM AND INFINITY
   In an idealised scenario, when a ground-state hydrogen atom absorbs energy equal to its ionisation energy, the proton and electron can, theoretically, separate infinitely. According to some interpretations of Coulomb’s law, they come to rest at an infinite separation where the force between them becomes zero. At this separation the system is in a state of unstable equilibrium, balanced between the bound and unbound states. It’s like a quantum superposition in that a slight disturbance can tip it one way or the other. However, in practical terms a perfectly ideal environment does not exist leading to a conceptual contradiction.
   Physical concepts involving infinities rarely conform to reality and often require the use of complex mathematics. To avoid this we can define infinity in terms of the relevant features of what can be observed and measured. In the context of this work an infinite separation can be defined as a separation beyond which further separation has negligible or immeasurable effects. In other words an infinite separation can have any value within a range which has a lower limit, which may increase with more precise data, but no upper limit.
   The relevance to this work is there is a finite probability of finding the electron at any distance from the proton, albeit the probability diminishes rapidly with distance. This enables us to carry out thought experiments in the knowledge that theory allows particle separations to move between the classical and quantum realms.
   PART 13. IS A GROUND STATE HYDROGEN ATOM LESS MASSIVE THAN THE COMBINED MASS OF THE PROTON AND ELECTRON?
   It’s commonly assumed that the mass of a ground state hydrogen atom is equal to the sum of the masses of the proton and electron minus the mass equivalent of the ionization energy. This relationship is expressed as follows:
   Mp +Me =Mg +Mi
   Mp = Mass of proton
   Me = Mass of electron
   Mg = Mass of ground state hydrogen atom
   Mi = Ionisation energy expressed in mass units
   Let the left side of the equation represent a highly excited state of the atom, where the proton and electron have negligible kinetic energies and are separated by a distance so large it can be considered infinite. In this system the particles are just barely bound and on the verge of becoming unbound and ionised. This state has potential energy, which remains the same even if the particles become unbound. Any change is negligible.
   Let the right side represents the low-energy ground state atom. If so the difference in mass between the two states equals the ionisation energy. The question can be rephrased as:
   Is the ground state hydrogen atom less massive than the atom in the highly excited, nearly ionised state?
   The answer is yes, in general, an atom’s mass increases with its energy state. Assuming the equation is correct it suggests that the potential energy of the nearly ionized atom is already accounted for within the masses of the proton and electron. If this is true, there is no need for an additional term for potential energy, as it’s contained within the particle masses.
   Key Points
4. Validating the equation would require precise measurements of the ground state atom’s mass independently, without relying on the equation itself.
5. As particles move from infinite separation to a separation equal to the Bohr radius, potential energy decreases by 2Mi. Transitioning to the ground state results in the emission of Mi, leaving the remaining kinetic energy as Mi
   Do the rest masses of particles actually vary based on their locations? Possibly, but further investigation is needed to clarify this.
   PART 14. HYDROGEN ATOM APPROACH EVENT THROUGH ALL THREE REALMS
   Consider again an approach event starting with a bound electron and proton in initial states of rest and separated by a macroscopic distance within the classical realm. At this stage the atom is in a highly excited state known as a Rydberg state. Let the event conclude by transitioning to the ground state with the particles separated by the Bohr radius. The event proceeds as follows:
   • The particles begin moving along classical paths, with increasing accelerations as potential energy is converted into kinetic energy. This acceleration results in the particles radiating photons.
   • As the separation decreases, the Coulomb force strengthens, causing the accelerations to increase and an increase in the power radiated as photons.
   • By extrapolation we predict that the trend of increasing radiated power with decreasing separation continues throughout the whole event. This prediction is supported by the principle of energy conservation and further validated, by classical electrodynamics in the classical realm, and the evolving expectation values in the quantum realm. The following notes provide a more detailed description of the classical to quantum changes as the event progresses.
   • As the separation between the particles enters the mesoscopic realm, properties gradually shift becoming less classical and exhibiting more quantum-like characteristics.
   • In the quantum realm, the reducing probabilistic separation can be described as a quantum approach.
   • The quantum changes can be linked to the classical realm through the use of expectation values, which evolve in accordance with the Ehrenfest theorem. For example, the expectation values of potential energy decrease as those of kinetic energy increase.
   • Here, we introduce the concept of “effective acceleration” which serves as a quantum analogy of classical acceleration. In the quantum realm, the effective acceleration continues to increase, as expressed in terms of the expectation values of position and momentum. Consequently, these increases lead to corresponding increases of radiation power.
   • Evidence suggests that the photons radiated during the event remain within the system of the atom. They should not be confused with the transition photons that transfer energy between the atom and the surroundings.
   • The event concludes when the atom reaches its ground state through one or more transitions, with each transition accompanied with the emission of a photon. If the initial separation of the particles is sufficiently large, the kinetic energy of the particles, prior to transition to the ground state, will be equal to twice the ionisation energy. Half of this will be retained by the atom as kinetic energy, while the other half is emitted to the surroundings as transition photons.

PART 15. HYDROGEN ATOM SEPARATION EVENT THROUGH ALL THREE REALMS

Consider a separation event involving the atom in its ground state with the particles separated by the Bohr radius and in an environment with extremely low pressure, where conditions allow particle separations to extend into the classical realm. This event is largely symmetrical to the approach event. It begins when a photon of energy equal to the ionisation energy enters the atom.

• Upon entering the atom, the photons energy is converted and added to the kinetic energy of the particles primarily to the electron. As a result the kinetic energy of the particles doubles and this initiates a separation event in which both particles emit photons.
• The initial part of the event can be described as a quantum separation event. This can be linked to the classical realm by describing it in terms of expectation values that evolve in accordance with the Ehrenfest theorem. Specifically, the expectation values of potential energy increase as the expectation values of kinetic energy decrease.
• The concept of “effective deceleration” also comes into play, serving as the quantum analogue of deceleration in classical physics. In this event the effective deceleration decreases, as can be defined in terms of expectation values of position and momentum, leading to corresponding decreases in radiation power.
• When the separation moves through the mesoscopic realm, the particle motions and photon emissions become increasingly more classical in nature, ultimately extending into the classical realm.
• The maximum separation is reached when both particles reach states of rest, within the classical realm, corresponding to a highly excited Rydberg state of the atom.
Separation events in classical and mixed systems are worth investigating. Photoelectric emission events serve as examples of separation events in mixed systems. These events are analogous to atomic separation events, such as ionisation or excitation, as both can be triggered by incident photons. In these cases, the photons must have enough energy to overcome the work functions of the systems they interact with.

PART 16. ALPHA PARTICLE PATHS
Alpha particle tracks in cloud chambers are a striking example of quantum particle moving in genuinely classical paths. Although the particles wave function is initially spherical, it soon follows a straight line path as described by classical mechanics. This shift from quantum to classical behaviour can be explained by the correspondence principle, as well as Nevill Mott’s analysis.
The emission of an alpha particle is a quantum event occurring at a microscopic scale, but as the particle moves away from its source and into the classical realm, its motion transitions to a predictable, classical path. This classical motion continues until the particle approaches and enters the microscopic scale of the detector.
In a cloud chamber, the alpha particle ionises molecules along its path, creating nuclei around which vapour condenses. These ionisation points form a linear trail of condensed droplets, showing that quantum particles can move along classical paths between quantum events like emission and detection. This is similar to how electrons move from cathode to target in an X-ray tube.
PART 17. THE RADIATION EXCHANGE MODEL
This section explores the consequences of radiated photons during approach and separation events of oppositely charged particles. We start with a brief recap:
• During an approach event, particles accelerate and emit photons as potential energy turns into kinetic energy. The event ends when the atom reaches its ground state by releasing transition photons into the surroundings.
• A separation event starts when an atom absorbs energy from an externally radiated transition photon. As the particles move apart, they slow down and emit photons, converting kinetic energy back into potential energy.
• Equations by Larmor, and by Lienard and Weichart, apply to one-part systems, not two-part bound systems of the type being analysed here.
• Changes associated with the radiation are probabilistic and discrete in the quantum realm, contrasting with the deterministic and smooth changes in the classical realm.
• The proximity effect posits that radiation is more likely to be exchanged between particles that are close together.
• The effects of changing fields and radiation transfer are felt at the locations of the particles, which can act as both photon absorbers as well as photon emitters. Photons can be described as moving from emitters to absorbers.

The key question is:

What happens to the photons radiated during approach and separation events?
If these photons were radiated to the surroundings, there would be energy losses from the system as the events proceed. These losses could theoretically be detected by measuring the emitted photons. However, while transition photons can be detected we have, not yet been able to detect photons emitted during non transition parts of events. This lack of detection may be due to the nature of the radiation: unlike the relatively large bursts associated with the transition photons, the photons radiated during non transition phases would be emitted in much smaller increments, making them more challenging to detect with current experimental precision.
Nonetheless, aside from any other possible forms of energy loss, there appears to be no evidence of energy loss specifically due to photons escaping during non-transition parts of events, suggesting that these photons remain within the system of the atom.

We proceed with the assumption that the radiated photons remain within the atom. This raises a fundamental question:
If the radiated photons remain within the atom where do they go?
The following reiterations may help in formulating an answer

1. Both particles can radiate photons and absorb them.
2. Photons move from emitters to absorbers.
3. If the proximity effect is real, photons are more likely to be exchanged between particles that are close together.
   Given these points, a logical answer is that the photons emitted by each particle move to the opposite particle. If correct this raises another question.
   What happens when the photons reach the opposite particle?
   The answer depends on whether the particles are separating or approaching.
   Particles separating
   • As the particles separate, energy radiated away as photons is derived from the reducing kinetic energy of the particles.
   • The photons emitted by each particle travel to the opposite particle, increasing its energy content and thereby increasing its mass which corresponds to a potential energy gain.
   • Because the electron initially holds the bulk of the kinetic energy, the proton gains the bulk of the potential energy (and mass increase)
   • To a good approximation, both particles have the same fractional increase of mass.
   • By considering the conservation of momentum we can estimate the change of mass on moving between the Bohr radius and the near ionised state. The fractional increase of mass(dm) of both particles is given by: dm = 2I / (Mp + Me) Mp = Mass of proton at Bohr radius Me = Mass of electron at Bohr radius I = Ionisation energy in mass units Calculations show that dm for the hydrogen atom is approximately equal to three parts per hundred million. This value will be smaller for all other atoms because of their smaller ionisation energy to atomic mass ratios.
   Particles Approaching
   • During the approach, each particle radiates its reducing potential energy (mass) as photons which move to the opposite particle.
   • Upon arrival these photons increase the kinetic energy of the receiving particle.
   • The event concludes when the atom transitions to its ground state.
   We conclude that between interactions with the surroundings, the total energy content of the system is the sum of the potential energy and kinetic energy carried by the particles, plus the energy of the photons which are in transit between the particles. This radiation exchange can be considered as the mechanism which brings about the conversions between potential and kinetic energy. There may be fluctuations in particle energies due to photon absorption and emission. This conclusion expresses a radiation exchange model.
   “If theory conforms to the facts, radiation conveys the inertia between the emitting and absorbing bodies”. A Einstein
   Does the Inertia of a Body Depend Upon its Energy Content? Annalen der Physik, 17, 1905
   PART 18. COMMON FEATURES OF RADIATION EXCHANGE EVENTS
   Events involving charged particles, which can be described in terms of the radiation exchange model, have the following common features.
   • Each particle is part of a system that includes at least one other interacting component.
   • This other component may be a particle of opposite charge or a macroscopic structure with an opposite charge.
   • The event involves movement between the two parts either moving closer together or further apart, resulting in energy transformations between potential and kinetic energy.
   • Due to the Coulomb force these parts move with varying accelerations, which lead to the emission of photons.
   • The radiation characteristics are predominantly classical in nature when considering larger particle separations, but they become more probabilistic in the quantum realm, where the rate of radiation is highest.
   These features are not exclusive to two-part systems alone: they can extend to certain more complex multi-part systems as well.
   In summary, during parts of events where there are changes between potential and kinetic energy, radiation is exchanged between the particles and remains within the system.
   PART 19. MIXED SYSTEM EVENTS
   There are several semi-classical systems within which the radiation exchange model can be applied. Here we mention three of particular relevance.
   • X-Ray TUBES
   Here we consider a basic X-Ray tube consisting of a thermionic cathode and a positively charged anode. If a single electron is released from the cathode, the resulting system can be viewed as analogous to the mixed semi-classical system. Here, the electron is the quantum part while the anode assembly represents the classical part. Due to the attraction between the two parts, they will move towards each other with increasing accelerations and eventually collide. (For reasons previously outlined, motion of the macroscopic part is taken into account, despite this normally being taken as negligible).
   There are different possible outcomes of this collision one being that the entire kinetic energy from the collision is converted into a single Bremmstrahlung photon which is then radiated to the surroundings. In this scenario, the event can be described as the conversion of potential energy into kinetic energy which is subsequently converted into photon energy, as a result of the collision. Empirical data shows that, in this particular outcome, the potential energy lost (eV) is equal to the kinetic energy gained, which in turn is equal to the energy of the photon (hf).
   e = electron charge
   V = potential difference between cathode and anode
   h = Planck’s constant
   f = frequency of photon
   This observation suggests that when the charges accelerate towards each other, with potential energy being converted to kinetic energy, there is no radiated energy lost to the surroundings. If there were losses, the energy of the photon (hf) would be smaller than the potential energy lost (eV).
   In normal operation an X-Ray tube emits a range of Bremmstrahlung photons along with any characteristic photons. The photon energy referred to corresponds to the highest possible energy photon in the Bremmstrahlung spectrum.
   • BASIC LINEAR ACCELERATORS (LINACS)
   Linacs are used to accelerate charged particles. They consist of a series of separated tube-shaped electrodes, arranged in a straight line within a vacuum tube. The tubes are connected to an alternating potential difference (p.d.) supply, causing the charge on each tube to switch between positive and negative at precisely timed intervals.
   When the first tube is positively charged, the particles are attracted toward it, converting potential energy into kinetic energy. The particles pass through the tube at constant speed, and by the time they emerge, the charge on that tube has switched to negative while the next tube in the line becomes positive.
   This process repeats as the particles continue to accelerate along the length of the Linac. The paths are approximately linear, with potential energy being converted into kinetic energy at each step. The transitions between the tubes, at the gaps, are key points where energy conversion happens in a stepwise fashion, allowing the particles to gain speed progressively.
   Each step during this event has the common features described in part seventeen therefore we would expect any radiation losses to the surroundings to be negligible. Empirical evidence suggests this is the case. However, radiation can be generated when the particles emerge from the Linac for example if they are smashed into targets.
   • BASIC CYCLOTRON
   A cyclotron is a particle accelerator that uses an alternating potential difference to accelerate charged particles, along with a magnetic field to control their motion. The cyclotron consists of two hollow, semicircular electrodes called “Dees” (because they are D-shaped) placed back-to-back in a vacuum chamber, with a gap between them.
   Charged particles start at the centre and are accelerated across the gap towards the positively charged Dee, converting potential energy into kinetic energy. Their motion inside the Dee is semi circular, being guided by the magnetic field. The magnetic field is not confined solely to the Dees; it extends across the gap as well. As a result, particles crossing the gap are influenced by both the electric and magnetic forces. This combined influence means that their paths in the gap are not perfectly circular or straight, instead they are more complex resulting in the whole path resembling a spiral of increasing size.
   There are two aspects of this process relevant to this work:
   Inside the Dees: Inside the Dees the particles move in curved paths. Their speed and energy remains constant, but their velocity changes direction continuously. This change in velocity (acceleration) leads to radiation losses due to the emission of electromagnetic radiation (photons). This phenomenon is well-documented and supported by empirical data.
   Crossing the Gap: There shouldn’t be radiation losses associated with the conversion of potential energy into kinetic energy, as given in part seventeen of this work. However, there are possible losses due to the curved trajectory in the gap.
   The Equivalence Principle
   According to the equivalence principle, a charged particle at rest in a gravitational field should radiate, but no radiation is detected, creating a paradox.
   Could the reason be that the event does not meet the criteria described in this work?
4. The particle is not part of an event in a system containing more than one charged part and where there can be conversions between kinetic energy and electrical potential energy. In these events radiation is emitted, but not to the surroundings.
5. The particle is not accelerating as a result of it changing direction.
   PART 20. DO REST MASSES REALLY CHANGE?
   The prevailing view is that they do not.
   The rest masses of electrons, protons and other particles are considered fundamental constants, and numerous high-precision experiments seem to have confirmed the constancies. However, certain scenarios, such as the excitation and de-excitation of the hydrogen atom, as discussed in this work, suggest that rest mass changes might occur. As yet, there is little to no data available on mass measurements during these specific events.
   Precise measurements of particle masses have been achieved with devices like Penning traps where the uncertainties are approximately three parts in ten to the ten. Such precision would be more than enough to confirm or refute the constancy of rest mass, but the major problem would be in measuring the masses at different particle separations, such as those between the near ionised state and the ground state.
   Another problem arises when considering composite particles like protons. Unlike electrons, which are considered fundamental particles, protons are composed of quarks with most of their mass coming from internal energy rather than the intrinsic mass of the quarks themselves. This raises the question: If the rest mass of the proton were to change would it alter its structure?
   The answer is it does happen. In addition to the miniscule changes predicted in this work, there can be major changes of structure, for electrons as well as protons. One notable example is annihilation events where particles undergo a complete transformation.
   PART 21. MODERN QUANTUM THEORY
   To explain electron interactions in fine detail, we would normally turn to quantum electrodynamics (QED) or quantum field theory (QFT). The descriptions provided by these highly successful theories match experimental results to a very high degree of precision.
   This work offers a novel perspective and can be regarded as a nascent theory with potential of further development and refinement. A major difference is that this work considers real photons, unlike the virtual photons in QED, and it predicts variable rest masses. If validated, such a prediction could have implications for interpreting energy variations within atomic systems. Despite its different perspective it may be advantageous to incorporate some of the ideas presented here into the more established theories.
   In the following sections we explore some of the consequences of the radiation exchange model introduced in this work.
   PART 22. THE BOHR ATOM

One of the main criticisms of the Bohr model of the atom is that, according to classical electromagnetic theory, an accelerating electron should continuously lose energy to the surroundings by emitting radiation and as a result would spiral into the nucleus, leading to the collapse of the atom.
However, the radiation exchange model offers a different prediction. In this model, both the electron and proton radiate energy, but they don’t lose this to the surroundings, because they radiate to each other. This internal energy exchange keeps the energy within the system, and as a result, the atom remains stable.
The motion of the particles can be compared to that of a binary star system, where two stars orbit around their common centre of mass. Similarly, the electron and proton in this model orbit around their shared centre of mass due to the mutual radiation they exchange.
While this work is not intended to either promote or reject the Bohr atom model, it remains a significant concept, especially from a historical standpoint, as it laid the groundwork for the development of modern atomic theory.
Part 23. PAIR PRODUCTION AND PARTICLE ANNIHILATION
Pair production is a fundamental process in quantum physics, where a high energy photon interacts near a nucleus and transforms into a particle-antiparticle pair. We will consider the most commonly observed example which is the creation of an electron and its anti particle, the positron. For this to occur, the photon must have energy greater than the combined rest mass energy of the electron and positron, which is 1.022MeV. Higher energy results in the particles gaining extra kinetic energy causing them to separate by greater distances. In high-energy experiments, these separations can extend into the classical realm of particle separations.
Now, let us consider the approach of the bound electron and positron, starting with an initial separation in the classical realm. While this event is similar to previously described interactions, the symmetrical structure of the system leads to a different outcome.
• Both particles start to move towards each other along classical paths in line with the correspondence principle
• As they accelerate, they radiate photons as potential energy is converted into kinetic energy.
• Each particle gains kinetic energy by absorbing photons radiated due to the reducing mass (potential energy) of the opposite particle.
• The energy gains balance the energy losses so that, on average, the total energy of each particle remains constant, as their masses decrease and kinetic energies increase.
• There may be fluctuations in the energy of the particles due to photon emission and absorption.
• As the particles approach each other through the classical and mesoscopic realms the changes in energy and mass are exceedingly small remaining minimal and gradual throughout these realms. However, within the quantum realm, the transformation becomes more rapid, eventually resulting in the particle masses reducing to zero and the speed of light being reached.
• This final stage represents the end point of an ongoing event, where two particles, initially possessing mass and energy, are transformed into two photons, each with energy but no mass.
Annihilation events involving composite particles, such as protons and anti-protons, are more complex due to their internal quark structure. These events involve quark-anti quark annihilation, producing not only photons but also a wide range of particles, including gluons, pions and kaons. The production of only photons is extremely rare.
PART 24. THE RELATIVISTIC ENERGY EQUATION
It’s interesting to note that in interactions involving a larger mass body and an electron, it can be predicted that the larger mass body loses energy while speeding up but gains energy while slowing down. Using the radiation exchange model, we examine whether these results contradict the energy variation equation’s predictions. Specifically we consider the electrons motion in two systems each containing a positive part as well as the electron.
The energy variation equation can be written as follows;
M/m = γ
m = mass of electron, M =mass of larger mass body, γ = Gamma Factor. It will be assumed the equation is correct and any non standard ways of interpreting it should be considered.
Writing the equation as shown, highlights that it’s not necessarily just M that changes it’s the ratio M/m that changes. There are two extreme ways of interpreting the changes and each one applies to an extreme type of system structure.
Extreme Interpretations and Corresponding Extreme Structures
Interpretation 1: At one extreme, M changes whilst m remains constant. This is the standard interpretation and applies to an asymmetrical structure where the second object has a near infinite mass relative to the electron.
Interpretation 2: At the opposite extreme, M remains constant while m changes. This applies to a symmetrical structure where the second object has the same mass as the electron, making it a positron.
Between the extreme interpretations there is a range of intermediate interpretations, where M and m both change, each one corresponding to a structure between the asymmetrical and symmetrical extremes.
Since constant rest mass is widely accepted interpretation one is prevalent. However, for m to stay constant the system must be asymmetrical, with an infinite mass for the second object so that it remains stationary.
Perfectly asymmetrical structures are idealisations but are approximated in systems where the second mass is large enough to render its motion to be negligible. (Although this motion of the larger mass in two part systems can often be ignored there are situations where taking it into account can provide new insights, as demonstrated in this work).
Interpretation two and its corresponding symmetrical structure, appears to be overlooked when relativistic changes due to motion are considered. Here M remains constant due to the symmetry of approach and separation events. During these events each particle absorbs energy from the opposite particle at the same rate it radiates energy to that particle.
In summary, as M/m approaches infinity, interpretation number one is approached and as M/m approaches one, interpretation number two is approached.
Despite everything the standard interpretation persists and this is largely due to the simplifying assumptions used in the derivation of the equation:
• It’s assumed that m is constant
• The derivation focuses on an electron moving in an electric field ignoring the necessity for the electron to be part of a system containing at least one other component, to conserve momentum.
• It disregards the electrons charge which contributes to the overall field in which the parts move.
• The derivation doesn’t seem to recognise the electron as being one part of a system, within which the relevant events involve radiation exchanges
Had the derivation considered a more general two-part system the standard interpretation would still hold, but only exactly if the mass of the second part is infinite. Interestingly, in practically all intermediate systems the second part can usually be considered as having infinite mass so, overall it’s a very successful equation with a wide domain of applicability. But it has an even wider domain relating to different system structures and this has been overlooked.

PART 25. SPECIFIC CHARGE

If particle masses do change, it’s reasonable to assume that their charges change as well, and in a way that their specific charges remain constant. We explore this idea, in the context of an electron-positron annihilation event, where both particles are initially at rest.

Let the electron and positron each have an initial mass M0 and charge Q0. These values represent their maximum masses and charges when the particles are far enough apart that their separation is effectively infinite.

As the particles move towards each other, their masses and charges decrease equally. Now, consider a point during their approach when their masses and charges have decreased to M and Q respectively and the kinetic energy gained by each, expressed in mass units, is denoted as MKE. At this stage, we can describe the relationship between mass and charge for each particle with the following equations;
Q0/M0 = Q/M M =M0 – MKE
These equations suggest that, for each particle, as M approaches zero, the charge Q also approaches zero. The motion continues until they reach the speed of light, which occurs when M and Q for each particle reaches zero and MKE reaches M0. At this point, the original rest mass M0 of each particle is entirely converted to the energy, of the photon it turns into. We can describe this by saying that as M and Q decrease and MKE increases, the electron and positron become less particle-like and more photon-like.
Intrinsic Properties
While mass and charge are regarded as intrinsic, fundamental properties of particles it might be worth considering specific charge as the more fundamental property. This perspective implies a proportional relationship between mass and charge during certain processes, such as annihilation.
Spin and Quantised States
Spin is another intrinsic property of particles, but unlike mass and charge, spin is quantised- it can only take specific, discrete values. During annihilation events, the spin states of the electron and positron are transferred to the resulting photons. One open question is whether this transfer happens instantaneously, or if it could be a continuous process, similar to the transition in mass and charge. This might be an interesting question area for further investigation.
Conservation Laws in Annihilation
In addition to the conservation of mass-energy charge and spin, other properties must also be conserved. These include properties like:
• Lepton number,
• Helicity
• Parity
While the ideas presented in this section involve a certain level of speculation, they build on established concepts and introduce potential avenues worth considering. The relationship between mass, charge, and specific charge, as well as the nature of spin transitions during annihilation, may offer insights that warrant further exploration. Although not fully substantiated at this stage, these ideas are presented to stimulate thought and discussion around the fundamental properties of particles.
PART 26. PARTICLE FIELD SYSTEMS
As far as particle field systems are concerned there are two main frameworks;

1. Particles are more fundamental than fields
   In this framework it’s assumed that each particle is accompanied by its own field and these fields interact, to produce a combined field in the surroundings. This is a classical view which simplifies calculations, which is one of its main strengths.
2. Fields are more fundamental than particle
   Here the assumption is that each type of particle corresponds to a unique field that exists everywhere. Particles are seen as concentrated types of field energy or discrete vibrations of the field. This is a more modern field-centric view favoured by many theoretical physicists.
   Here we propose a third scheme which is that particles and fields are complementary aspects of a unified entity. Particles can be seen as parts of fields and fields can be seen as parts of particles. The potential energy within electric fields is contained in the mass of the particles, and photons mediate the energy exchanges between them.
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