Abstract: The Standard Model falls short in providing explanation for particle-wave duality and other non-causal phenomena at quantum scale, due to forcing all fundamental elements to be particles. Through these notes, I propose a new model to provide a more consistent interpretation for the phenomena by defining four kinds of spaces in which the particles exist and interact, producing the results observed as particle-wave duality and other quantum phenomena.

The spaces: The four spaces are Material Space (MS), Velocity Space(VS), Frequency Space (FS) and Wave Space (WS). MS is the space that is perceived by us humans. VS and FS are used as stepping stones to understand WS. WS is the space where particles originate.

Oscillation: An oscillation is a magnitude that varies such that the variation is also an oscillation whose variation is the first oscillation.

Time, variation, difference: Time is the relation or mediation between a magnitude and its variation as another magnitude. A variation is a change in a magnitude with time. A difference is a relation across multiple things, while variation relates to same thing.

Magnitudes do not vary along spatial dimensions, though they can have different spatial locations and be different from each other.

Particles, bonds, objects: A particle is a set of oscillations sharing the same location in the material space (MS). A bond is the opposition between two oscillations that belong to different particles. An object in MS is a composition of bonds that has a boundary defining its inner and outer regions.

Material space (MS): This is the three-dimensional physical space that humans perceive. Objects in MS have properties such as location and speed relative to their containing objects. Objects can collide with others when they try to occupy a non-vacant location in this space. All the material existence and properties of objects in MS are relative.

Velocity space (VS): Velocity space is the variation space for MS with the linear movements of objects in MS as magnitudes. Points in VS represent the movement of points in the material space (MS). All points in MS which have relative speed among them as zero and direction of relative speed as same, are mapped to a single point in VS, irrespective of distances between those points in MS.

These points with zero relative speed and same direction in MS are called a swarm. The distance between two different points in VS indicates the relative speed between two swarms in MS. Each swarm in MS belongs to a different plane of excitation.

Molecules of gas in a container form a sphere in VS, due to their movement in all directions. The size of the sphere indicates the temperature of the gas (relative speeds of molecules).

Frequency Space (FS): Points in the frequency space represent the oscillations of points in the material space (MS). That is, all points in MS which have same frequency and same axial direction, are mapped to a single point in FS, irrespective of distances between those points in MS.

Wave space (WS): Wave space represents the space in which the oscillations move and collide with each other, similar to MS in which the linearly moving particles move and collide with each other due to MS locations being occupied. All objects which appear to be spinning or oscillating in MS have a relative movement or speed in WS.

Frequency space (FS) is a variation space for WS with oscillations as the varying magnitudes. Points in the FS represent the relative oscillations of points in the wave space (WS). All points in WS which have relative frequency among them as zero and direction of axis as same, are mapped to a single point in FS.

Collisions in MS and WS: Collisions in one space will appear as swaps or rearrangement of locations in its differential space.

Consider two billiards balls in MS having relative speed between them and about to collide. These two balls are represented by two points in FS with a distance between them. When the collision occurs in MS, the points in FS either swap their locations if the movements in MS are collinear, or rearrange their locations such a way that distance between them is unchanged (relative speed is preserved).

Particles do not collide in MS, as they exist only WS. Collisions in WS occur due to laws of WS in terms of occupancy of same WS location by two oscillating particles. Particles move and collide according to the laws of WS. This movement does not have a quality called direction as known in MS.

Consider two chairs A and B. A is occupied and B is vacant. How fast can the vacancy at B move to A? Let the occupant get up, move towards B and occupy it. Then the vacancy from B has spread to both the chairs instantly while the occupant started moving and then it collapsed to A instantly. The overall speed of the vacancy can be arbitrarily increased by having several chairs and all occupants move at the same time to the next chair.

The movement of occupants is the wave (movement of oscillation in WS) and the state is the oscillation itself. What we have observed here is a collision of states in WS, observed as a swap event in MS.

Existence of particles and matter: Particles exist only in WS because they are pure oscillations. Bonds between particles exist in MS, in the form of relations between the oscillations. A particle has no absolute existence in MS that can be described through its states or properties. All the states or properties belong to its bonds or relations shared with other particles. However, existence of the particle in WS arises due to its own magnitudes and time which are absolute.

Bonds reflect synchronization in oscillations (particles), thus forming the matter. Non-synchronization in oscillations of MS neighborhoods create regions of matter with boundaries and create material objects in MS.

Oscillations in WS are the root of existence, leading to various forms of existences in different spaces. If an object in MS is composed of particles that are not related to each other, then the object doesn’t e exist in MS due to lack of relations across particles.

Entanglements between oscillations: Particle locations in WS do not map to locations in MS, similar to how locations in MS do not map to locations in VS. As a result, the distances in MS do not influence interactions between particles in WS. Such non-locality in MS reflected through instantaneous interactions between particles is known as entanglement.

Two kinds of entanglements are considered, through which particles can synchronize or swap their states with other particles — primary and secondary.

Primary entanglement is the well known quantum entanglement by which the particles can mutually synchronize their state instantly.

Secondary entanglement, being introduced in these notes, refers to a temporary entanglement between two particles (or two systems of particles) to facilitate a mutually balanced change (swap) to occur instantly.

Propagation of light: When a change occurs in an oscillation, the change is either absorbed into its attributes (amplitude, phase and frequency) or it is swapped with a lower oscillation from another particle. The swap occurs instantaneously through a temporary entanglement (secondary entanglement).

Linear WS movement occurs in a pre-swap phase which will correlate to a spherical expansion (ripple) in MS. The ripple carries information about the proposed swap event and facilitates selection of the target particle.

The spherical expansion (ripple) in MS during the pre-swap phase does not involve time. That is, it doesn’t hit the nearby targets earlier than the far away targets. If multiple paths can result in absorption, then an equal (random) probability decides the path, ensuring uniform distribution across all directions in MS and across multiple swaps.

Since the ripples propagate and collide in a time-less context resulting in a swap, there is no causal direction for this swap event. However, multiple such swaps might have an overall direction and order, such as a propagation of light, due to creation of causality when the chain ends in an absorption.

A single swap could involve multiple particles, rearranging their locations in FS, similar to a billiards ball hitting multiple balls in MS.

Light is a phenomenon in which two oscillations undergo a swap event through a secondary entanglement. There is nothing that is moving at the speed of light. Collisions in WS do not involve MS movement or MS speed.

There is no causal relation between the source and target. Destination particle is just as much the cause as the source particle is, for the light propagation. Reversing the direction, one can also say that the propagation starts at the destination, due to absorption of the oscillation. This is similar to how the electricity flow due to voltage difference doesn’t create a causal relation between the terminals of a battery.

Light is emitted from a source only because there is an absorption somewhere.

Speed of light: The observed speed of light arises from the time durations assigned to swap events by the causality in MS. Time duration for a swap event arises by conversion of the minimal path length in MS between the particles involved in the swap event, into time. Since the MS path length is not relative to any moving object in MS, it results in a perceived absolute speed for light.

Reflection and refraction of light: Reflection and refraction of light and the angles involved are to maintain minimality in time for the swap between the absorber and the source. If there is no absorption, then there is no reflection or refraction and no emission at source. A mirror will receive and reflect light only if there is an absorption of the reflected light by some material particles (or may be black holes).

Light from a source particle (from a single excitation) will reflect, during pre-swap phase, from all points on all mirrors that can be reached by its spherical expansion in MS (linear movement in WS). However, a specific mirror and a specific point on it is decided by a specific absorption (swap). It doesn’t use use other paths, if there is no absorption through those paths. Light doesn’t start or travel without a goal (absorption and minimality).

Interference of light: Interference pattern of light is the magnified view due to relative frequency of the oscillations caused by overlap of paths between multiple swaps. When a wire mesh with a hexagonal pattern moves across another mesh of same pattern, but with slightly smaller size of hexagons (or with a non-zero angle of overlap) it produces a magnified view of the hexagons. The magnified view is the relative frequency between the meshes or, how one mesh appears to the another.

Spatial extents in MS: Bonds between the particles require MS spatial distances to be maintained between the particles. This is a fundamental law in MS (exclusivity of particle locations). However, matter alone does not cause the space. Space (MS) arises from distances. Distances are caused by relative movements. Relative movements are caused by the translation of oscillations into linear movements. Oscillations are caused by the forces in WS.

MS space is composed of distances between the material objects. If the matter is finite, the space is finite too, as there are no distances beyond matter. A spatial direction MS can only exist, if a swap is possible in that direction. This makes direction to be discrete and aligned to distance between two MS objects. Also this makes the extent of MS space to be limited to distances between the MS objects.

Time in MS: Time is relation between a magnitude and its variation as another magnitude. It also serves as a link between the spaces (WS and MS etc), as they are related through variations. Observation of time duration and its flow direction is a result of conscious memory, at the observer, of multiple changes and their order. The time duration between two events is the number of changes that could be observed to happen between those two events.

World doesn’t move through time. There is no arrow of time. For a context which doesn’t have any locally observable changes or memory, it is not possible to be aware of time or its flow. Time flow is created by the order between multiple secondary entanglements, resulting in macro-scale causality.

Force fields: A field is the medium for interaction between elements in a space through it’s variation space. It is the result of a variation in quantities such as direction, velocity, flow, charge, spin etc. It is the medium through which a variation in one quantity could result in variation or movement in another quantity or object.

For example, a change in direction of movement in MS results in moving across the discrete spatial directions, and results in producing a magnitude in a variation space.

Magnetic field arises due to time-varying change in number of swap events in an MS region. Centrifugal field arises due to time-varying direction in movement of objects, Gravitational field arises due to time-varying oscillations (spin, orbiting) in the bonds.

Curvature of space and time in MS: There is no curvature of space or time as none of them exist in a physical form that can be curved. Also a curvature is relative to some “flat-ness”. If the space is curved relative to some flat-ness, then that flat-ness is the space and it is not curved by definition.

However, a relative interpretation for the curvature can be extracted due to modifications in path and time for the swap events in the presence of force fields such as magnetism in particle accelerators. It is a relative interpretation because it exists only if the modifications in path and time are not considered.

Objects in MS: Objects are perceptions due to the conscious ability to perceive more than one kind of dimensionality. That is, for example, the ability to perceive both 3D and 2D. This causes to perceive a boundary of lesser dimension for objects of higher dimension. This gives rise to existence of objects through the differentiation between their inside and outside regions.

When a boundary of an object changes, it can not be determined whether the object still exists. For example, when a country splits into two, the old country ceases to exist. Thus existence of an object through time, is dependent on ignoring variations in its boundary.

Energy and matter in MS: Energy is a function of relative speeds and relative oscillations across MS objects and is represented by the square of distance between two points in VS and FS. Similar to speed, energy doesn’t belong to an MS object. Two MS objects with a non-zero distance between them in VS or FS, have a possibility of collision in MS or WS and rearrangement of the points in VS or FS respectively. The rearrangement of points in VS or FS is incorrectly called as energy transfer, because there is no receiver and sender. The rearrangement is a symmetric process.

However, the relative speeds and relative oscillations exist because there are differing spatial movements in MS and WS which arise from the absoluteness in WS.

Matter arises from the bonds between the particles due to synchrony and oppositeness in their oscillations. A system of gears in a running engine is an analogy of matter due to its synchronized oscillations. Just as the gears allow transmission of oscillations (spin), matter allows transmission of oscillations (heat or impact) through its bonds. Inertial mass is the resistance offered by the bonds against such transmission.

Organic processes such as photosynthesis are the processes of creating matter by creating new bonds. It requires creating synchronization by increasing the frequency of some parts. This increase in frequency is typically achieved by swap of the oscillations (light incidence).

When bonds are broken, it results in splitting the point in VS creating a relative distance there and some non-zero relative speed in MS. However, breaking the bonds would require creating asynchrony across the parts by changing their oscillation frequency, through heat or impact.

Order, numbers and comparison: Countability of numbers exists due to conscious ability to perceive time and changes. Counting requires time and order. However, quantitative order of objects is due to perception of whether an object can fit fully into inside region of other object and such arrangements of multiple objects. Numbers, as instants or points, have no quantitative comparison but have an order due to the perceived arrow of time. Any time instant is not larger or smaller than any other time instant, but they have an order.

Also, numbers do not have absolute magnitudes. Given two numbers, it may be possible to know their difference, but their absolute values are actually the differences relative to an imaginary absolute quantity called zero. It is imaginary because nothingness does not exist in MS.

Zero and nothingness: Zero serves to provide identity, multitude and distinguishability for magnitudes. For example, if the difference between two numbers is zero, then they are the same and single number (not different and multiple). Lack of zero causes lack of identity, multitude and distinguishability in WS.

The state of absence of something is indistinguishable from the state of absence of something else. That means the two different things lost their identity and distinguishability when their measure dropped to zero. Since objects do not loose their identity or multiplicity due to change in their measure, the zero measure or quantity is imaginary.

Causality created by absorption: Biological eyes, detectors in a double-slit experiment, photo synthesis and other absorbing processes act as oscillation sinks or stores, creating the causality and reality in MS by ending the secondary entanglement chains. Causality in MS is formed by a backwards trace after a chain of secondary entanglements results in absorption of the change by an oscillation.

Identity and multiplicity: Particles in WS have identities based on the oscillation differentiation in MS but not by their MS spatial locations. The particles with identical properties (oscillations) act as a single entity in WS while maintaining their multiplicity due to MS locations. This may reflect in measurements made on properties of particles. Though measurements are made on different particles in MS, they are being made on a single entity in WS and will result in random values.

Measurement: WS does not store information about oscillations. The information is stored in MS as an oppositeness between oscillations, but not as absolute quantities attributable to oscillations. As a result, measurements can only be made to reveal the relativeness between particles, but not any definitive properties of the particles.

Measurement is a swap of oscillations between the observed particle and a particle from the measuring device. The value measured corresponds to the relative difference between two entities involved.

First, the oscillation of the observed particle is altered (excited) by an incident light through a swap event before the observation is made. Then, the second swap event (observation itself) involves the swapping of the excited oscillation from the particle with the one from the device. As a result, the observed measurement relates to (s - p - d), where s is the incident oscillation, p is the oscillation absorbed by the particle and d is the oscillation at device before the observation was made. The values, at particle, before and after the observation are never known.

However, measurements across multiple particles, keeping s and d constant could provide relative values among the particles. For example, the color of an object imaged by a camera depends on the incident light, absorption of the object and sensors in the camera. However, since the incident light and camera sensors are the same across all the objects in an image, it is possible to get information about differences among the objects in the image, but not about objects themselves.

Particle-wave duality: Particles are not waves. They are groupings of oscillations in WS. Change in an oscillation might propagate as a wave if the change can’t be absorbed by the oscillation. The change wave selects a partner particle for participating in the transfer of the change through a swap event. Change propagation is a wave in a time-less context and the entities involved in the change are particles. There is no duality.

Double slit experiment: The pre-swap ripples from the source laser select particles at the detectors (or human eyes) where the absorption happens. There is nothing traveling at some speed, starting from the laser and hitting the detectors. Imbalanced absorptions by detectors cause lack of interference patterns on the screen.

There is no delayed erasure or time-lag between these swaps, as all the swaps are instantaneous in MS. The combination of source and target particles are decided by the pre-swap ripple that selects targets based on equal probability. Absorption of entangled particles (primary entanglement) occurs at same time for all the members of the primary entanglement.

Particle accelerations: Spatial particle accelerations do not occur in MS as particles neither exist nor move in MS. The magnetic fields in particle accelerators cause path modifications for pre-swap phase and time modifications for the swap.

Absoluteness and relativity in MS and WS: MS is a relativity space. Objects in MS do not possess any absolute measures such as mass, location, color, frequency, time, speed, energy, volume, boundary etc. Absoluteness for any measure in MS arises from an imaginary reference frame that is considered stationary and non-oscillating. Without such reference frame, all measures are relative and they belong to the relations between the objects, but not to the objects themselves.

WS is an absolute space, being the source for absolute linear speeds and oscillation frequencies. This is due to existence of a reference frame for each particle. The reference frame is particle itself.

Magnitude, absoluteness, symmetry, minimality as a goal, oppositeness, lack of identity or distinguishability, lack of cause and direction, periodicity, variation are the main features of WS. Cause, direction, zero, difference, distinguishable multitude, relativity, lack of goal or intent, dimensions are the main features of MS and serve to fulfil the minimality goal of WS.

Science though causality: Science has been progressing by studying causality (why a phenomenon occurs). But causality in MS obscures the goals of WS.

For example, a water molecule moves to minimize the overall resistance, for a given flow rate. Here the goal of minimality from WS is driving the causality in MS. Science makes studies about how interaction between adjacent molecules decides the direction of their movement in MS, which appears disconnected from the minimality goal.

Path taken by light has the goal of overall minimality in time across all the phenomena (emission or incidence) at source and destination. However, science studies the direction of path as caused by interaction of light with the medium through which light travels without an apparent goal.

Conclusions: Applications of science work because of their correctness in predicting the effect based on the cause, in most situations, by establishing an empirical relation between cause and effect. For example, by establishing the fact that the water flows in a slope direction, the empirical relation between the cause (slope) and effect (flow) can be utilized for many applications. Science might make the relation between the cause and effect to progress from “flow due to slope” to “pull due to gravity” and stop there, due to lack of further explanation. It also stops there due to lack of purpose in providing better explanation.

Causality was very well exploited by the classical mechanics and in interpreting the phenomenon of light and force fields, resulting in laws and formulae. Correctness of the current interpretations relating to EM radiation and particle interactions is relative to the rules of observation. These laws and formulae work because they were established after testing for their correctness in a causality reference frame which establishes causality as the primary criterion. But they fail in the contexts that defy the causality.

Quantum physics is unable to disconnect from the causality-based approach for its contexts which obey goals instead of causality. Consideration of force as particles (bosons) arise from the notions rooted in the causality, and leads progress in incorrect directions.

Science requires proof through establishing causality, which leads to reasoning. It looks for answers that say “that happens because of this equation”. Goals can’t be proved because they can not be extracted through causality, though inferences can be made. Thus, science can’t progress by giving precedence to causality over goals.

Dedication: I dedicate my these notes to my mother Chukkamma

Reddy Pagadala