Gravitation in 3D Spacetime

1. Gravitation in 3D Spacetime John R. Laubenstein IWPD Research Center Naperville, Illinois 630-428-9842 www.iwpd.org 2009 APS April Meeting Denver, Colorado May 5, 2009

2. Who We Are • Our team has been working together for over • 10 years, with our center becoming incorporated • in 2005 • Among our various activities, we explore • relationships between: • Observational data • Physical constants • Physical laws

3. 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

4. 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 and establishes • relationships that are consistent with observation

5. 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

6. 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 3D Spacetime • will be established that is equivalent to • 4-Vector Spacetime

7. 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

8. Flatlander • A series of events are depicted as a Worldline

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

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

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

12. 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

13. 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

14. 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

15. 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

16. 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

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

18. Flatlander3D vs. 2D

19. Flatlander3D vs. 2D

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

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

22. 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

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

24. The ISM Orientation (X) • The position of the timeline segment can change • relative to the (x,y) position coordinates (X) = 0.75

25. The ISM Orientation (X) • The position of the timeline segment can change • relative to the (x,y) position coordinates (X) = 1.0

26. The ISM Orientation (X) • The position of the timeline segment can change • relative to the (x,y) position coordinates (X) = 0.75

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

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

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

30. 3D Spacetime • 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?

31. Gravitation in 3D Spacetime • 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

32. Conditions of 3D Gravitation • The mass of the electron is normalized to the • electron charge: • From this, a fundamental quantum mass is • defined as: • The quantum values for mass, length and time are • different manifestations of the same fundamental • entity, dubbed the “energime” • From this, an argument may be made that matter • decays to free space • 3D Spacetime replaces the “points” of a 4D cooridate system with “segments” or “rings” • Matter decays to free space

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

34. The Nature of ISM Gravitation • Apply a factor of pi.

35. The Nature of ISM Gravitation • Time (Space from the decay of matter) emerges from • everywhere within the Initial Singularity

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

37. The Nature of ISM Gravitation

38. The Nature of ISM Gravitation

39. The Nature of ISM Gravitation

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

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

42. 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)

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

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

45. The Nature of ISM Gravitation

46. The Nature of ISM Gravitation

47. The Nature of ISM Gravitation

48. The Nature of ISM Gravitation Fundamental Unit Time Fundamental Unit Length

49. ISM Suggests a Linear Relationship between BEF and LEF • Velocity is typically determined by the • orthogonal relationship between 4-Velocity • and the observed 3-Velocity

50. ISM Suggests a Linear Relationship between BEF and LEF • If you attempt to subtract the 3-Velocity • from the 4-Velocity linearly, you will not get • the correct answer