Proper Interval Locality

UNDER CONSTRUCTION

Proper Interval locality is a theory that claims the definitive explanations for:-

1. The wave-particle duality of matter

2. How individual quantum entities are
self-interfering

3. How in Aspect's experiment, Bell's inequality can be violated without in turn violating the special theory of relativity. See Bell's theorem and Bell test experiments

The theory is self-consistent and explains how the seemingly contradictory elements found in the modern wisdom arise; notable, how in quantum mechanics, the unseen development of quantum entities fill the space bounded by an experimental set up; whilst, the observable effects of any individual interaction, with a detecting device, always occur at point location in space.

The theory derives it name from the prediction that spatially remote electromagnetically charged particles can interact directly; provided the proper interval separating them has zero magnitude. The theory thus precludes the possibility that light as mediated by a particle (The Photon). Clearly this theory has serious implications for the current "standard model" where force is mediated by vector bosons.

The theory also has major implications for the "Many Worlds Interpretation" of quantum mechanics since it predicts interference without the need to invoke the existence of parallel worlds.

(Theory is simple and elegant and uses the basic foundations of relativity and quantum mechanics, without having to introduce arbitrary elements such as the photon, compacted dimensions or parallel worlds)?

The theory argues that the our perception of space, the flow of time and how our view of the world is restricted to seeing it from a unique point in space, at any perceived moment in time, is not a result of the fundamental properties of world geometry but is facilitated by the group behaviour of quantum ensembles. It is the group behaviour of quantum ensembles that determines how we perceive the geometry of the world.

When Einstein named his 1905 paper on special relativity "On the electrodynamics of moving bodies" The moving bodies he refers can only be "observable" bodies formed from quantum ensembles (observable without materially altering their mean physical state.) It is the group behaviour of the quantum entities forming the observable bodies that defines their profile their position in space and physical characteristics.

Above all other considerations theoretical physics depends on the observer’s ability to fix events in space and time relative to four-fold reference grids. These imaginary grids are drawn over the observer’s perception of the physical world. The gauging of the reference frames depends on the use of calibrated clocks and rulers. For any given reference frame the clocks and rulers normally have a common velocity relative to the observer’s perception of the world, hence the imaginary grids are called inertial reference frames.

The clocks and rulers we use to define our reference grids are formed from ensembles of quantum entities. It is the group behaviour of these quantum ensembles that gives rulers their perceived constant profile in space and clocks their ability to provide us uniform measures of the passage of time. The perceived uniformity of the behaviour of clocks and rulers (when at rest relative to each other) allows us to compare the spatial profiles of different rulers and the time intervals measured by different clocks thus allowing us to standardise and calibrate our measurements of time and distance. Thus our imaginary reference grids are drawn up against hypothetical measurements using calibrated measures of length and time. The validity of the reference system being dependent on the uniformity of the group properties of quantum entities.

Thus it is the group behaviour of quantum entities that is providing us with our perception of the world and its geometry. It is this group behaviour that restricts observable events to occur at unique positions in space for any moment in the observer’s sense of time. It is this group behaviour that allows us to fix on observable event relative to our reference grids.

Study of motion of observable bodies forms the basis of classical mechanics; which can be divided into two main branches.

1. Where the relative velocity between the bodies and observers is low relative to the speed of light. The basis of Newtonian mechanics.

2. Where the relative velocity between bodies and between observers represents a significant proportion of the speed of light. In this case the measurements of time and distance between events will be significantly different for observers with instruments in different states of motion.
Basis of relativistic mechanics.

Basic property of the universe that supports classical mechanics is the group behaviour of quantum ensembles that gives the observer the ability to fix the location of observable bodies relative to his inertial reference frames.

The world as we see it, is as it is because of the way quantum ensembles behave. The way we perceive space and time, are able to fix events relative to our inertial reference frames and our ability to assign physical quantities to bodies all rely on the group behavior of quantum ensembles. But how do the individual components of matter fit into the scheme of things. We cannot observe individual quantum entities. We infer what we think we know about them by the how the affect observable bodies. (This of course includes the observer, who's observations of the world are seemingly facilitated by quantum entities interacting with his sensors.)

The idea of things having locality in the world is fundamental to our survival.

But there is nothing in our perception of physical reality that tells us for certain that individual quantum entities have a unique fixed location relative to our reference grids. Although the idea that individual quantum entities cannot possess a unique locality in the world runs contrary to the intuition that has sustained our survival and evolution for billions of years the evidence from quantum mechanics suggests its an idea we have to get use to.

Proper Interval Locality argues that the wave-particle duality of matter is an inevitable consequence of the structure of space-time demanded by relativity. For flat space-time there is a close relationship between the invariance of the laws of physics, the constancy of the speed of light in all inertial reference frames and the wave-particle duality of matter. The theory maintains that the explanation of the wave-particle duality of matter lies in understanding the nature of locality relative to our coordinate systems. In particular, it lies in the difference between the locality of observable bodies (quantum ensembles) and the hypothetical locality of quantum entities relative to our inertial reference frames.
Our methods for observing and measuring length and time using clocks and rulers enable us to fix events concerning observable bodies, in space and time relative to our four fold reference grids. Where the reference grids themselves are defined and gauged using clocks and rulers. Thus our ability to reference locality is dependent on clocks and rulers, in particular the invariance of their spatial and temporal profiles within a given inertial state. Since clocks and rulers are composed of countless individual quantum entities forming quantum ensemble then our ability to reference the locality of observable bodies is wholly dependent on the group behaviour of quantum ensembles.
The most fundamental elements of matter are not observable; we cannot measure their position in space.
Note
Observations of the position of a quantum object are often considered when discussing Heisenberg’s uncertainty principle. However this may refer, say, to a slit in a barrier. The narrower the slit then the more accurately we know its position; that is the position of the slit not the position of the position of the quantum entity. We can reduce the size of such a slit indefinitely and if the quantum entity appears to pass through the slit then the behaviour of the quantum object will be modified by the slit in accordance with Heisenberg’s Uncertainty principle. But a no time would we have been able to say the quantum entity was unique placed in the slit.

All information regarding quantum entities must be inferred from how we believe they affect observable bodies.
This is the sort of information that comes from experiments such as: -
Young's double slit experiment.
The photoelectric effect
The Compton Effect
The violation of Bell's inequality in Aspect's experiment.
But the results from these experiments seem to provide a logically contradictory view of the world, where matter behaves both like waves and particle and information seems o move around at super luminal speed thus seemingly defying the special theory of relativity.
Proper Interval Locality argues that these contradictions arise from our lack of understanding of how the locality of quantum entities are projected on to our inertial reference grids.
Proper Interval Locality argues that the wave-particle duality of matter is an inevitable consequence of the structure of space-time demanded by relativity. For flat space-time there is a close relationship between the invariance of the laws of physics, the constancy of the speed of light in all inertial reference frames and the wave-particle duality of matter. The theory maintains that the explanation of the wave-particle duality of matter lies in understanding the nature of locality relative to our coordinate systems. In particular, it lies in the difference between the locality of observable bodies (quantum ensembles) and the hypothetical locality of quantum entities relative to our inertial reference frames.
Our methods for observing and measuring length and time using clocks and rulers enable us to fix events concerning observable bodies, in space and time relative to our four fold reference grids. Where the reference grids themselves are defined and gauged using clocks and rulers. Thus our ability to reference locality is dependent on clocks and rulers, in particular the invariance of their spatial and temporal profiles within a given inertial state. Since clocks and rulers are composed of countless individual quantum entities forming quantum ensemble then our ability to reference the locality of observable bodies is wholly dependent on the group behaviour of quantum ensembles.
The most fundamental elements of matter are not observable; we cannot measure their position in space.
Note
Observations of the position of a quantum object are often considered when discussing Heisenberg’s uncertainty principle. However this may refer, say, to a slit in a barrier. The narrower the slit then the more accurately we know its position; that is the position of the slit not the position of the position of the quantum entity. We can reduce the size of such a slit indefinitely and if the quantum entity appears to pass through the slit then the behaviour of the quantum object will be modified by the slit in accordance with Heisenberg’s Uncertainty principle. But a no time would we have been able to say the quantum entity was unique placed in the slit.

All information regarding quantum entities must be inferred from how we believe they affect observable bodies.
This is the sort of information that comes from experiments such as: -
Young's Double-slit experiment.
The photoelectric effect
The Compton scattering
The violation of Bell's inequality in Aspect's experiment.
But the results from these experiments seem to provide a logically contradictory view of the world, where matter behaves both like waves and particle and information seems o move around at super luminal speed thus seemingly defying the special theory of relativity.
Proper Interval Locality argues that these contradictions arise from our lack of understanding of how the locality of quantum entities are projected on to our inertial reference grids.
Proper Interval Locality argues that the wave-particle duality of matter is an inevitable consequence of the structure of space-time demanded by relativity. For flat space-time there is a close relationship between the invariance of the laws of physics, the constancy of the speed of light in all inertial reference frames and the wave-particle duality of matter. The theory maintains that the explanation of the wave-particle duality of matter lies in understanding the nature of locality relative to our coordinate systems. In particular, it lies in the difference between the locality of observable bodies (quantum ensembles) and the hypothetical locality of quantum entities relative to our inertial reference frames.
Our methods for observing and measuring length and time using clocks and rulers enable us to fix events concerning observable bodies, in space and time relative to our four fold reference grids. Where the reference grids themselves are defined and gauged using clocks and rulers. Thus our ability to reference locality is dependent on clocks and rulers, in particular the invariance of their spatial and temporal profiles within a given inertial state. Since clocks and rulers are composed of countless individual quantum entities forming quantum ensemble then our ability to reference the locality of observable bodies is wholly dependent on the group behaviour of quantum ensembles.
The most fundamental elements of matter are not observable; we cannot measure their position in space.
Note
Observations of the position of a quantum object are often considered when discussing Heisenberg’s uncertainty principle. However this may refer, say, to a slit in a barrier. The narrower the slit then the more accurately we know its position; that is the position of the slit not the position of the position of the quantum entity. We can reduce the size of such a slit indefinitely and if the quantum entity appears to pass through the slit then the behaviour of the quantum object will be modified by the slit in accordance with Heisenberg’s Uncertainty principle. But a no time would we have been able to say the quantum entity was unique placed in the slit.

All information regarding quantum entities must be inferred from how we believe they affect observable bodies.
This is the sort of information that comes from experiments such as: -
Young's double slit experiment.
The photoelectric effect
The Compton Effect
The violation of Bell's inequality in Aspect's experiment.
But the results from these experiments seem to provide a logically contradictory view of the world, where matter behaves both like waves and particle and information seems o move around at super luminal speed thus seemingly defying the special theory of relativity.
Proper Interval Locality argues that these contradictions arise from our lack of understanding of how the locality of quantum entities are projected on to our inertial reference grids.
Proper Interval Locality argues that the wave-particle duality of matter is an inevitable consequence of the structure of space-time demanded by relativity. For flat space-time there is a close relationship between the invariance of the laws of physics, the constancy of the speed of light in all inertial reference frames and the wave-particle duality of matter. The theory maintains that the explanation of the wave-particle duality of matter lies in understanding the nature of locality relative to our coordinate systems. In particular, it lies in the difference between the locality of observable bodies (quantum ensembles) and the hypothetical locality of quantum entities relative to our inertial reference frames.
Our methods for observing and measuring length and time using clocks and rulers enable us to fix events concerning observable bodies, in space and time relative to our four fold reference grids. Where the reference grids themselves are defined and gauged using clocks and rulers. Thus our ability to reference locality is dependent on clocks and rulers, in particular the invariance of their spatial and temporal profiles within a given inertial state. Since clocks and rulers are composed of countless individual quantum entities forming quantum ensemble then our ability to reference the locality of observable bodies is wholly dependent on the group behaviour of quantum ensembles.
The most fundamental elements of matter are not observable; we cannot measure their position in space.
Note
Observations of the position of a quantum object are often considered when discussing Heisenberg’s uncertainty principle. However this may refer, say, to a slit in a barrier. The narrower the slit then the more accurately we know its position; that is the position of the slit not the position of the position of the quantum entity. We can reduce the size of such a slit indefinitely and if the quantum entity appears to pass through the slit then the behaviour of the quantum object will be modified by the slit in accordance with Heisenberg’s Uncertainty principle. But a no time would we have been able to say the quantum entity was unique placed in the slit.

All information regarding quantum entities must be inferred from how we believe they affect observable bodies.
This is the sort of information that comes from experiments such as: -
Young's double slit experiment.
The photoelectric effect
The Compton Effect
The violation of Bell's inequality in Aspect's experiment.
But the results from these experiments seem to provide a logically contradictory view of the world, where matter behaves both like waves and particle and information seems o move around at super luminal speed thus seemingly defying the special theory of relativity.
Proper Interval Locality argues that these contradictions arise from our lack of understanding of how the locality of quantum entities are projected on to our inertial reference grids.
Proper Interval Locality argues that the wave-particle duality of matter is an inevitable consequence of the structure of space-time demanded by relativity. For flat space-time there is a close relationship between the invariance of the laws of physics, the constancy of the speed of light in all inertial reference frames and the wave-particle duality of matter. The theory maintains that the explanation of the wave-particle duality of matter lies in understanding the nature of locality relative to our coordinate systems. In particular, it lies in the difference between the locality of observable bodies (quantum ensembles) and the hypothetical locality of quantum entities relative to our inertial reference frames.
Our methods for observing and measuring length and time using clocks and rulers enable us to fix events concerning observable bodies, in space and time relative to our four fold reference grids. Where the reference grids themselves are defined and gauged using clocks and rulers. Thus our ability to reference locality is dependent on clocks and rulers, in particular the invariance of their spatial and temporal profiles within a given inertial state. Since clocks and rulers are composed of countless individual quantum entities forming quantum ensemble then our ability to reference the locality of observable bodies is wholly dependent on the group behaviour of quantum ensembles.
The most fundamental elements of matter are not observable; we cannot measure their position in space.
Note
Observations of the position of a quantum object are often considered when discussing Heisenberg’s uncertainty principle. However this may refer, say, to a slit in a barrier. The narrower the slit then the more accurately we know its position; that is the position of the slit not the position of the position of the quantum entity. We can reduce the size of such a slit indefinitely and if the quantum entity appears to pass through the slit then the behaviour of the quantum object will be modified by the slit in accordance with Heisenberg’s Uncertainty principle. But a no time would we have been able to say the quantum entity was unique placed in the slit.

All information regarding quantum entities must be inferred from how we believe they affect observable bodies.
This is the sort of information that comes from experiments such as: -
Young's double slit experiment.
The photoelectric effect
The Compton Effect
The violation of Bell's inequality in Aspect's experiment.
But the results from these experiments seem to provide a logically contradictory view of the world, where matter behaves both like waves and particle and information seems o move around at super luminal speed thus seemingly defying the special theory of relativity.
Proper Interval Locality argues that these contradictions arise from our lack of understanding of how the locality of quantum entities are projected on to our inertial reference grids.

Our reasoning suggests that our perceived unique locality of events and our ability to assign paths to “moving bodies” relative to our reference grids is a product of observation. Observation, itself, being dependent on the group behavior of quantum ensembles that in turn is dependent on the behavior of individual quantum entities and their interactions all of which is occurs within the event arena of space-time.
We use space-time diagrams to represent the motion of observed and measured bodies relative to our inertial reference grids. The space-time diagram is essentially a Euclidian and is not a true reflection of the geometry of the world. The principle of proper interval locality argues that the wave-particle duality of matter and the associated contradictions in our understanding of physical reality originate from the difference between the perceived false geometry of the world and the true geometry experienced by quantum entities.

To understand how the wave particle duality of matter develops we must understand how events experienced by individual quantum entities are hypothetically projected on to our inertial reference frames. Remembering that our reference frames are imaginary grids drawn over our perception of space and time. They are a product of how we measure and represent length and time and do not reflect the true geometry of our world. What happens to quantum entities exists in the true natural geometry of the universe. It is how quantum events relate to our false reference geometry that is the key to understanding how we create a mathematical description of quantum entities that requires them to have characteristics of both particle and waves.

To gain this understanding we must turn to Initially to the Special relativity

The central postulates of the special theory of relativity are: -

1.All motion is relative and there is no privileged state of rest, the laws of physics being the same in all states of motion.

2. The speed of light is the same for all all observers regardless of their state of motion.

Given these postulates then the values of sets of coordinates for a given event when measured in different inertial frames are related by the Lorentz transformation. Pil argues that there is a close and fundamental relationship between the fundamental postluates of relativity, the Lorentz transformation and the development of the wave particle duality of matter. It further argues that the form of space-time demanded by the postulates of special relativity and the Lorentz transformation actually preclude the possibility of assigning unique sets of coordinatesto describe the location of an event in the history of a quantum object. That is there is not a one to one correspondence between how a quantum entity experiences an event in the "true" geometry of space-time and how that event is hypothetically projected on to our inertial reference grids. The Lorentz transformation holds the key to understanding how quantum events are projected on to our inertial reference grids and hence a deeper understanding of how quantum objects behave relative to our coordinate systems.

To achieve this understanding we need to look to the relationship between the sets of coordinates assigned to events and the apparent proper interval separating them.

Hermann Minkowski showed that for any two events with, respectively, assigned coordinates (X₁ , Y₁ , Z₁ , T₁) and (X₂ , Y₂ , Z₂ , T₂) then assuming the Lorentz transformation the proper interval between the two events is: -

ΔS = ((X₂ -X₁) + (Y₂-Y₁) + (Z₂-Z₁) - c (T₂-T₁) )

This equation is known as the Minkowski Metric and is said to have a metric signature of (3, 1).

This signature creates the interesting property that pairs of events that are spatially separated from each other can be separated by an interval that has zero magnitude providing the square of the temporal element is equal to minus the sum of the squares of the spatial elements.

ΔS = 0

If
((X₂ -X₁) + (Y₂-Y₁) + (Z₂-Z₁) = c (T₂-T₁) )

If we fix one of the events P (X₁, Y₁, Z₁, T₁) then all other events (X, Y, Z, T) that fulfill the requirement form a cone relative to our inertial reference grids. In relativity theory this cone is called a light cone. In the standard theory the future light cone represents all events that can be reached by a light pulse from P and the past light cone represents all events that can send a light pulse to P.

In proper interval locality the light cone represents all events that are properly local to event P or properly contiguous with event P. This idea has major implications for how theoretically the locality of quantum entities relates to our inertial reference grids.

Contrary to Einstein assertion that causality is governed by the Principle of locality, our new interpretation suggests that what happens at a given event in space-time cannot be independent of what is going on elsewhere in the universe. An event at the apex of a light cone cannot be independent of the states of the world elsewhere on the light cone. Each event on the light cone is contiguous with the apex of the cone. The state of the world at the apex of the cone can influence events anywhere on the cone and the state of the world at any point on the light cone can influence what happens at the apex. Proper interval locality interprets this as events at a fundamental level do not have a unique location relative to our inertia reference frames. A distinction is drawn up between observable locality, observed events can be assigned unique locality relative to our inertial frames of reference; whilst the unobservable events involving the fundamental states of the universe do not possess unique locality but are projected onto our inertial reference frames as light cones.

Events involving quantum entities are projected onto our reference grids as light cones. A quantum event involving an electron or an atom cannot have an exact location on our reference grids. The way we have developed our measuring and referencing systems precludes the possibility of quantum entities having unique locality relative to our space-time constructs.

Thus the locality of an event involving a quantum object is primarily projected onto our inertial reference frames as a light cone. This we shall call the primary conical projection of the quantum object. However every event on the primary light cone cannot be independent of what happens elsewhere in the universe thus each event on the primary conical projection acts a source for the projection of further light cones thus creating an infinite progression of light cones that eventually cause the quantum event to be projected over space-time in its entirety. However, any effect on observable events caused by the presence of the quantum object are much more likely to occur in the vicinity of the apex of the primary conical projection than in observed locations that are spatially or temporally remote from the apex.

Relative to our inertial reference frames quantum events ( a unique moments in the history of a quantum object not a quantum interaction between quantum objects) unlike observable events do not have unique sets of coordinates, instead hypothetically they are projected on to our space-time construct as light cones. The apex of such a light cone is, according to the theory, is called the proper interval locality of the quantum event; the light cone is the primary projection of the event. All sets of coordinates on the primary conical projection of the quantum event project further light cones; resulting in an infinite succession of conical projections that cause the physical presence of the quantum object to fill the entire space-time arena, as referenced by our grid system. It is this infinite succession of projections that is responsible for quantum objects interfering with themselves.

The probability of two quantum objects interacting, assuming their quantum states are amenable, will depend on spatial separation of their respective event apexes. (inverse square law). Since the quantum objects do not have unique locations relative to our reference grids then neither do their interactions. Quantum interactions simply occur in space-time. However, quantum interactions sometimes produce observable effects, for instance the response of a photomultiplier. Any observable effects resulting from a quantum interaction must occur at a unique set of coordinates relative to our reference grids. In this case the observed effect occurs at the location of the photomultiplier.

An absorber quantum system, which is a constituent part (part of the photocathode) of the photomultiplier i.e. the word-line of its event apex is located within the Photomultiplier and follows the world-line of the photomultiplier. The absorber system interacts with some remote donor system, the excitation of the absorber system causes the release an electron through the photoelectric effect and a cascade occurs that creates sufficient electrons for a pulse to be generated at the anode and for an observable effect to be registered. Conventionally the pulse would signify the arrival of a photon at the photocathode. But proper interval locality says that the photon cannot exist and the observable event was initiated by the interaction of quantum systems via zero interval paths.
See The Wheeler-Feynman absorber theory

The Wave-Particle Duality of Matter and the Metric Signature of Space-Time.

The major difficulty with the metrics of relativity is the inertial reference grids cannot be properly graphically represented. In the conventional space-time diagram using rectilinear coordinates it is only the measures of distance and time that can be represented with direct proportionality. If relative to a given inertial frame two events (X₁ , Y₁ , Z₁ , T₁) and (X₂ , Y₂ , Z₂ , T₂) are separated by both distance and time then graphically the interval between them appears as : -

ΔS = ((X₂ -X₁) + (Y₂-Y₁) + (Z₂-Z₁) + c (T₂-T₁) ) , the Pythagorean metric of Eucldean geometry.

Compare this with the Minkowski metric, we see that in general the representation of the interval is elongated in the space-time diagram. In order to gain a better understanding of what is going on, the theory uses another form of representation called a proper interval diagram. In the proper interval diagram we choose (from a space-time diagram) a single set of coordinates (X₀ , Y₀ , Z₀ , T₀), from this event O we draw the gulf to any other event P proportionally to the proper interval separating it from O; rather that using the Pythagorean hypotenuse. In this new representation we find the axes compared with space-time diagram are unaffected by the transformation where as all other grid lines became curved and non-linear. Such that the light cone found in the space-time diagram whose apex is at event O, collapses entirely on the point O in the proper interval diagram.

But quantum entities are primarily projected onto space-time diagrams as light-cones but if we draw a proper interval diagram centred on the apex of the light-cone (relative to the space-time diagram) then relative to the proper interval diagram the quantum entity collapses to a point. In other words relative to the proper interval diagram an event on a quantum entity does not have unique location in space but is distributed through out space-time, but relative to the proper interval diagram the event has a unique location and the quantum entity takes on a particle like aspect.

These are the very characteristics that are contradictory in the standard theory. A wave being distributed in space; whereas a particle has a unique position in space. But in now seems our analysis of the demands of relativity on the character of space-time forces the fundamental elements of matter to have such qualities.
Relative to a space-time diagram based on a given inertial reference frame hypothetically the primary projection quantum event proceeds from past to present as an advanced wave once the wave passes through the event apex it spreads out as a retarded wave. In flat space-time these waves travel at the speed of light and extend indefinitely. It is interesting to consider what happens if the hypothesis of the big bang is correct and space-time collapses into a singularity at the moment of creation. In that case relative to our reference space-time the advanced wave begins its journey at the creation event. This implies that what happened at the creation is not independent of what is happening now?

Relative to the proper interval diagram based on the same inertial reference grid the light cone of a primary projection of a quantum event collapses into a singularity. Giving us a perspective that causes the quantum entity to look like a particle.

The theory of proper interval locality was developed to explain the interference of light and also to explain how Bell’s inequality can be violated without compromising the theory of relativity.

For more information regarding the Principle of Proper Interval Locality visit link Proper Interval Locality

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