The Principle of Proper Interval Locality

Proper Interval Locality.

Proper Interval Locality is a system of mechanics that replaces the vector boson with zero proper arc length mediation of the interactions between charged quantum entities.
Proper interval locality identifies the relationship between relativity and quantum mechanics that eliminates the contradictions existing between the two theories.

The new mechanics modifies the principle of local causes such that “what happens at an event E1 can directly influence what happens at an event E2; E1 to being spatially remote from E2; provided the length of the proper interval along the arc separating the two events has zero magnitude.”

Two spatially separated events are said to be properly local if they are separated by a proper interval of zero length. The physical states at spatially separated events that have proper interval locality may directly mutually interact.

Thus according to proper interval locality mechanics the physical world possesses two forms of locality: -

1. Spatial locality; where what happens at one position in space responds directly only to conditions in its immediate vicinity; as in the principle of local causes.
2. Proper Interval Locality; where what happens at one position responds to conditions at spatially remote positions that are connected to the former by zero arc length paths.

Additionally proper interval locality recognises the world possesses two classes of objects: -

1. Bodies; these are large quantum ensemble whose group behaviour, makes it possible for them to be observed. They can be assigned a unique position in space relative to an inertial reference frame and assigned physical values such as momentum. The group behaviour of the ensemble forming a body presents to the observer the qualities of locality and physical reality. (A body can be assigned both position and momentum.) Bodies include measuring devices; clocks, rods making the perceived structure of space-time dependent on the group behaviour of large quantum ensemble! Since the observer views the physical world from a recognised time and place he also must be classed as a body. It is appropriate for the general study of the motion of bodies to use spatial locality as the mediator of causation.
Locality of a body relative to an inertial reference frame is not regarded as a fundamental property of the body but an acquired characteristic, (acquired through the interactions of the large number of quantum entities of which the body is constituted).

2. Quantum entities: these cannot be observed and their existence can only be inferred from their apparent influence on the behaviour of bodies (detectors). The principle of proper interval locality precludes events relating to quantum entities possessing unique set of coordinates relative to our four dimensional grid systems. A quantum event is projected onto our reference grids as a light cone. The light cone emanating from a quantum event is known as the primary light cone. Each event on the primary light cone acts as a source for the radiation of secondary light cones and secondary light cones act as sources for tertiary cones and so on ad infinitum. Thus quantum entities behave as if events in their history occur over the whole of space-time; distributed as an infinite succession of light cones. The probability of detecting a quantum entity at a given point in its history will be distributed throughout the entirety of space-time with the highest likelihood of occurrence if the detector is close to the apex of the primary light cone associated with the quantum entity at that point in its history. In studying the behaviour of the interactions of quantum entities and their observable effects on bodies then it is appropriate to use proper interval locality as the mediator of causation.

Notes.
1. The capacity for a quantum entity to interact with another entity is time dependent; this modifies the spatial probability distribution of the likelihood of detection and is fundamental to the development of the wave function relative to inertial reference frames. The inherent probabilistic nature of interactions governed by proper interval locality mechanics provides an explanation for the born rule.

2. The development of secondary light cones is necessary to explain the interference of light and matter.

3. When a detector at a given point responds to the existence of a quantum entity this does not uniquely indicate the location of the quantum entity. The detection event occurs at the perceived position of the detector, the locality of the quantum entity remains distributed throughout space-time.

4. Any two events in space-time are always connected by paths of zero interval arc length.

The benefits of proper interval mechanics.

The benefits of proper interval locality mechanics compared the idea that force is mediated by particles are: -
1. The relationship between relativity and quantum mechanics is established.
2. Because the vector bosons are eliminated the model of physical reality is simpler.(Infinitely Simpler?)
3. The observations of the behaviour of light and matter that suggest their wave particle duality are fully predicted by proper interval locality mechanics.
4. The model is self consistent since the contradictions between relativity and quantum mechanics are removed.
5. The Born rule is explained
6. The interference of matter and light is explained without invoking a many worlds model of physical reality.
7. Electromagnetism does not require the introduction of compacted higher dimensions.
8. The violation of Bell’s inequality is predicted without compromising the relativistic mechanics of moving bodies.
9. Proper interval locality can support quantum electrodynamics without violating the laws of conservation. The virtual photon being directly replaced by zero arc length mediation of the force between spatially remote entities. The energy forming the interacting field quanta of a charged entity being absorbed from remote quantum entities.
10. Since proper interval locality does not demand the existence of vector bosons then the requirement for the Higg’s boson also seems redundant. The problem of mass is reduced to how the change in the motion of the quantum entities is gauged when interactions occur. On this point it is worth noting that proper interval locality appears to demand all quantum entities be in constant interaction with the rest of the universe.

Comparison with other interpretations of quantum mechanics.

The other interpretations of quantum mechanics can be reinterpreted in terms of proper interval mechanics.

For instance the many worlds interpretation can be replaced with the super positioning of many times of our own world. The atemporal handshake in the transactional interpretation is explained by interacting quantum entities being in immediate contact with each other even though relative to our inertial reference frames they appear to affect observations that are spatially and temporally remote from each other.
The existence of pilot wave in David Bohn’s mechanics is explained in proper interval locality by quantum events being projected over the whole of our four dimensional reference frames. The quantum entity must fill the entire universe and inherently contains the information about how it may interact.

With respect to Feynman´s path integral formulation, proper interval locality provides the mechanism for how relative to our inertial reference frames a particle may appear to travel over an infinite number of possible trajectories. These corresponding to the infinite number of zero proper interval arc lengths existing between any two events in space-time.

The future development of proper interval mechanics.

The proposed mechanism for the creation of the electromagnetic field suggests that the universe is driven by a great electromagnetic cycle where charged entities are constantly absorbing energy to form the electromagnetic field quanta which immediately** interact with other charged entities that in turn scatter the energy back into the universe. This scattered energy is reabsorbed by further charged entities to form the next generation of field quanta. In this manner the electromagnetic field is perpetuated.

This suggests that the fundamental forces of nature may all be described as components of this cycle.

* Here a quantum event is a point in the history of a quantum object relative to itself. The geometry of space-time is such that quantum event cannot be fixed by unique set of coordinates relative to an inertial reference frame.

** Relative to hypothetical observations along the path taken by the field quanta; relative to all other inertial reference frames quantum events radiate out as light cones and a false temporal delay is supposed as existing between the donation and absorption of quanta. It is this false sense of spatial and temporal separation between the emission and absorption of electromagnetic radiation that demands the idea that light is mediated by a particle! Note. The photoelectric effect and Compton scattering are equally well explained by proper interval locality

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This site is being updated to include general relativity! The original work on zero interval mediation of electromagnetism in flat space-time remains on the site. It includes how single "photons" are subject to self interference of quantum entities and how Bell's inequality can be violated without violating special relativity.

Zero proper interval arc length mediation of electromagnetism in Riemannian manifolds characterised by the restrictions imposed by the Einstein tensor.

Abstract

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Riemann geometry places no restrictions on the number of dimensions or the values of the components of the metric tensor. But the geometry of the physical world must have limitations. It is the role of the physicist to find the appropriate number of dimensions and value of the metric tensor to create a mathematical model that accurately reflects the behaviour of the physical world.

This site claims that the fundamental problem with modern physics is that it does not have the proper description of the mechanism for the mediation of the electromagnetic force
The apparent contradictions existing between relativity and quantum mechanics arise because of this short-coming. This site demonstrates that a single four dimensional universe can accommodate both gravity and electromagnetism. General relativity gives us the inertial motion of bodies in four dimensional Riemannian space-time (characterised by the restrictions imposed by the Einstein tensor), the bodies following the natural geometry along geodesic paths. When a force is applied to a body it will no longer follow its original geodesic path but will be redirected to into a new geodesic path. Our task is to understand how the cause of the change from one geodesic path to another is mediated. What is the geometric relationship between the effect, where the there is a change to the geodesic path of the body and state of the world which is “forcing” the change in the body’s inertial condition. Whatever, this relationship is; it must be consistent with the violation of Bell’s inequality; this is now an essential requirement for compatibility with quantum mechanics.

The holy grail of physics is to find the number of dimensions and metric values such that all the known forces of nature are included in our model. In such a model, objects follow geodesic paths; their motion only being determined by the local geometry of the neighbourhood in which it finds itself. However, this approach has only been successful in explaining motion in free space and gravitational fields. The link between pure geometry and physical geometry in relativity’s limited success being provided by the Einstein tensor!
There idea that all elementary forces can be explained by inertial motion along geodesic paths appears to run into many knotty problems and may not be achievable. However, this may not necessarily mean that there exists a deep rooted inconsistency between relativity and quantum mechanics, we argue here that such inconsistencies arise because of the way we interpret the nature of Riemannian geometry and its relationship to how we perceive locality and how we interpret the way forces are mediated. Let us briefly consider some of the problems that we must overcome to achieve an exhaustive solution to our description of the physical world.
1. We only perceive three spatial dimensions and one time dimension! If we are forced into a model with more than four dimensions we need to explain why the additional dimensions are beyond perception.
2. The movement of bodies in an electromagnetic field depends on the charge possessed by the bodies. The motion, therefore not only depends on the local geometry but on the characteristics of the body, making a purely geometric solution in terms of geodesic path seem improbable.
3. Any model must explain why individual quantum entities exhibit a form of self interference.
4. The solution must provide for the violation of Bell’s inequality.

Attempts to resolve such problems; imagine world models with hidden dimensions, spooky non-local influences and multiple universes! Stuff treasured by science fiction writers! But perhaps alarm bells should be ringing; for often when solving problems this level of complexity and incompleteness indicates that at a fundamental level something is not correct. Possibly we are experiencing a situation that has a parallel in Ptolemaic cosmology! The Ptolemaic system suffered from the fact that a simple earth centred cosmology did not match observations of planetary motion. In a valiant effort to confirm the flawed geocentric model a complex system of “deferents”, “epicycles”, “epitrochoids” emerged which became increasingly more complex as observations became better.
The situation today mirrors the pre-Copernican cosmology where we arbitrarily adjust and enlarge the theory to make its predictions match the facts.

This site claims that the fundamental problem with modern physics is that it does not have the proper description of the mechanism for the mediation of the electromagnetic force
The apparent contradictions existing between relativity and quantum mechanics arise because of this short-coming. This site demonstrates that a single four dimensional universe can accommodate both gravity and electromagnetism. General relativity gives us the inertial motion of bodies in four dimensional Riemannian space-time (characterised by the restrictions imposed by the Einstein tensor), the bodies following the natural geometry along geodesic paths. When a force is applied to a body it will no longer follow its original geodesic path but will be redirected to into a new geodesic path. Our task is to understand how the cause of the change from one geodesic path to another is mediated. What is the geometric relationship between the effect, where the there is a change to the geodesic path of the body and state of the world which is “forcing” the change in the body’s inertial condition. Whatever, this relationship is; it must be consistent with the violation of Bell’s inequality this is now an essential requirement for compatibility with quantum mechanics.

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Locality in Riemann space

This site argues that Riemann space possesses two forms of locality: -
1. Coordinate difference locality.
This occurs when the all coordinate differences between pairs of events are identically zero. This corresponds to our normal common sense notion of locality, and will be the only locality in a Riemann space where all the components of the metric tensor are positive. In such spaces, bodies can only interact if some points on their profiles touch; for example the collision of billiard balls. The vector boson mediation of force as formulated in modern physics would be a suitable account of how quantum entities interact in these types of spaces.
2. Proper Interval Locality
Proper Interval Locality can only occur if components of the metric tensor are both positive and negative. This allows the arc length between pairs of events in the Riemann space to have zero length even though the intervals are spatially separated from each other. The existence of the zero arc length between spatially remote events creates a causal conduit allowing influences to pass between events.
The geometry of our world is characterised by metric tensors which always have both negative and positive components. We would therefore expect proper interval locality to play an important role in determining the physics of our world. It is this form of locality that is responsible for the counter intuitive and seemingly bizarre behaviour of quantum entities, for example the probabilistic expectation of observations resulting from quantum interactions, self interference of quantum entities and the violation of Bell’s inequality.

The original work now follows

(I will continue with the general theory as time permits. Please be patient if you want to know how Riemann manifolds are transformed into arenas fit for quantum mechanics.)

Part 1 On the electrodynamics of special relatvity

Image: Interaction

Main Index

Abstract

On the Electrodynamics of Special Relativity.

Newlocality 1 January 2005
proper.locality@Gmail.com

Based on the idea that the minus sign in the metric of space-time creates zero interval paths between spatially and temporally separated events, that permits energy to be directly exchanged between “non-local” quantum objects. This is proper interval locality. The “proper interval locality energy exchange process” is developed and predicts observable characteristics consistent with the energy exchange being quantitised and having associated wave-functions that control wherein space-time pairs of exchange events are likely to occur. The new process is applied to single slit and double slit experiments illustrating the development of uncertainty and interference effects. Finally Aspect’s experiment is analysed showing that the new interpretation of special relativity to be consistent with the timing of observed events. The paper concludes that proper interval locality interpretation could be used as the foundation for developing a self-consistent process for combining special relativity and quantum mechanics.