Expressing n dimensions as n-1

Expressing n dimensions as n-1 John R. Laubenstein IWPD Research Center Naperville, Illinois 630-428-9842 www.iwpd.org 2009 APS March Meeting Pittsburgh, Pennsylvania March 20, 2009

Presentation Goal • IWPD Scale Metrics (ISM) DOES NOT: • Claim to identify some past error or oversight that sets • the world right • Suggest that past achievements should be discarded for • some new vision of reality

Presentation Goal • IWPD Scale Metrics DOES: • Suggest an alternative description of space-time • Show that ISM is equivalent to 4-Vector space-time • (at least in terms of velocity) • Modify gravitation so that it can be described using ISM • Show that ISM makes predictions consistent with • observation

Adding to the Base of Knowlege • ISM quantitatively links Scale Metrics and 4-Vector • space-time through a mathematical relationship • Scale Metrics and 4-Vectors are shown to be • equivalent (at least for specific conditions) • Scale Metrics adds to the body of knowledge

Flatlander • Approach. We will conceptually develop ISM • using a two-dimensional flat manifold • Why?Because in our world we understand both • 3D and 2D Euclidean geometry • Verification. You can serve as the judge and jury • over the decisions made by the “Flatlanders” • Result.If successful, a model of n dimensions as • n-1 will result in describing 4-Vector space-time • using only three dimensions

Flatlander • When pondering a description for • space-time this individual decides • to plot time as an abstract orthogonal • dimension to the two dimensions of space known in • the Flatlander world • This requires three pieces of information • to identify an event • (x,y) coordinates for • position and a • (z) coordinate for time

Flatlander • A series of events are depicted as a Worldline

Flatlander • A point tangent to the Worldline defines • the 3-Velocity, which is normalized to a value of 1

Flatlander • The observed (2D) velocity is depicted by the blue • vector that lies in the plane of the observable • dimensions

Flatlander • The orientation of the 3-Velocity vector can be • determined from its angle ( ) relative to the 2D • observable plane of the Flatlander world

Flatlander • To describe the observed velocity of an object during • a specific event will require 4 pieces of information: • x,y: position coordinates • z: time coordinate • for the orientation of the 3-Velocity vector

Gravitation • If a Worldline is due to gravitation, the challenge • becomes to accurately describe the curvature of • space and spacetime to accurately depict the • curve of the Worldline • The simplest case (a uniform spherical non rotating mass • with no charge) requires the Schwarzschild solution

Initial Alternative Scenario Scenario • When pondering a description for space-time • this individual decided to plot time as an • abstract orthogonal dimension to the two • known dimensions of space in the Flatlander • world • This individual decides to • account for time within the • 2 observed dimensions by • plotting time – not as a point – but • as a segment representing the • passage of time

Initial Alternative Scenario Scenario • This approach also requires • three pieces of information • to identify an event • (x,y) coordinates for position • A line segment plotted on the x-y • plane to designate time • Three pieces of information are required • to identify an event • (x,y) coordinates for position and a • (z) coordinate for time

Initial Alternative ScenarioScenario • For an object at rest, its Worldline is • orthogonal to the x-y plane • For an object at rest, the • (x,y) ordered pair defines • a “point” at the center • of the time segment

Initial Alternative ScenarioScenario • As viewed from above, the • three points may be seen • “plotted” on the 2D plane • A series of events are depicted as a • Worldline

Initial AlternativeScenarioScenario • A series of events are • depicted by ever-increasing • time lines • A series of events are depicted as a • Worldline

Flatlander3D vs. 2D • A series of events are depicted as a Worldline

Flatlander3D vs. 2D

Flatlander3D vs. 2D • A series of events are depicted as points embedded • in time segments

Initial Alternative ScenarioScenario • The orientation of the • point relative to the • timeline is denoted as (X) • and is equivalent to the • value • The orientation of the 3-Velocity vector • can be determined from its angle ( ) • relative to the 2D observable plane of • the Flatlander world

The ISM Orientation (X) • The position of the timeline segment can change • relative to the (x,y) position coordinates (X) = 0.5

The ISM Orientation (X) • The position the timeline segment can change relative to the (x,y) coordinate (X) = 0.5

Initial Alternative ScenarioScenario • (x,y) position coordinates • segment coordinate for time • X: orientation • (x,y) position coordinates • z coordinate for time • coordinate for the orientation of the • worldline

What is the Relationship between θand X ? • Both ( ) and (X) represent orientations • They are related by the following expression:

Does (X) Have a Physical Meaning? • ANSWER: • X has allowable values ranging from 0.5 to 1 (X) = 1.0 (X) = 0.5

n Dimensions as n-1 • 2 + 1 dimensions in the Flatlander world can • be expressed in 2 dimensions with no • information lost • 4-Vector Space-Time may be expressed • within the 3 spatial dimensions we • experience • So What? Who Cares? Where is the • advantage of this?

Gravitation • When using ISM, time is not defined as orthogonal • to the spatial dimensions • A time segment with a defined point is equivalent to • the 4-Vector Worldline • The orientation of the point (X) is related to the • velocity of an object just as the slope of the • Worldline is related to velocity • Just as gravity influences the 4-Vector Worldline, • gravity must also be shown to influence the value • of X in ISM • Who c

The Nature of ISM Gravitation • How do you determine the • directionality of the time segment?

The Nature of ISM Gravitation • Apply a factor of pi. • The resulting “ring” defines a fundamental entity • dubbed as the “energime”

The Nature of ISM Gravitation • Time emerges from everywhere within the • Initial Singularity

The Nature of ISM Gravitation • Time progresses as a quantized entity defining • quantized space

The Nature of ISM Gravitation

The Nature of ISM Gravitation The collective effort results in the creation of an overall flat Background Energime Field (BEF)

The Nature of ISM Gravitation Flat Background Energime Field (BEF)

The Nature of ISM Gravitation Perturbation due to local effects of a gravitating mass resulting in a Local Energime Field (LEF) Flat Background Energime Field (BEF)

The Nature of ISM Gravitation Gravitation is an interaction between a local gravitating mass and the total mass-energy of the universe

The Nature of ISM Gravitation The more massive the gravitating entity, the stronger the gravitation effect

The Nature of ISM Gravitation The less massive the gravitating entity, the weaker the gravitational effect

The Nature of ISM Gravitation As time progresses, the initial singularity increases in size as the scaling metric changes.

The Nature of ISM Gravitation

The Nature of ISM Gravitation Fundamental Unit Time Fundamental Unit Length

Expressing n dimensions as n-1