The Principle of 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 interactions 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

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.

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

Part 1 On the electrodynamics of special relatvity

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.