Gravitation in 3D Spacetime John R. Laubenstein IWPD Research Center Naperville, Illinois APS April Meeting Denver, Colorado May 5, 2009 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 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 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 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 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 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 A series of events are depicted as a Worldline A point tangent to the Worldline defines the 3-Velocity, which is normalized to a value of 1 The observed (2D) velocity is depicted by the blue vector that lies in the plane of the observable dimensions The orientation of the 3-Velocity vector can be determined from its angle ( ) relative to the 2D observable plane of the Flatlander world 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 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 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 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 A series of events are depicted as a Worldline As viewed from above, the three points may be seen plotted on the 2D plane A series of events are depicted as a Worldline A series of events are depicted as points embedded in time segments A series of events are depicted as a Worldline A series of events are depicted by ever-increasing time lines 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 position of the timeline segment can change relative to the (x,y) position coordinates (X) = 0.5 The position of the timeline segment can change relative to the (x,y) position coordinates (X) = 0.75 The position of the timeline segment can change relative to the (x,y) position coordinates (X) = 1.0 The position of the timeline segment can change relative to the (x,y) position coordinates (X) = 0.75 The position the timeline segment can change relative to the (x,y) coordinate (X) = 0.5 Both ( ) and (X) represent orientations They are related by the following expression: ANSWER: X has allowable values ranging from 0.5 to 1 (X) = 0.5 (X) = 1.0 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? 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 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 How do you determine the directionality of the time segment? Apply a factor of pi. Time (Space from the decay of matter) emerges from everywhere within the Initial Singularity Time progresses as a quantized entity defining quantized space The collective effort results in the creation of an overall flat Background Energime Field (BEF) Flat Background Energime Field (BEF) Perturbation due to local effects of a gravitating mass resulting in a Local Energime Field (LEF) Gravitation is an interaction between a local gravitating mass and the total mass-energy of the universe As time progresses, the initial singularity increases in size as the scaling metric changes. Fundamental Unit Time Fundamental Unit Length Velocity is typically determined by the orthogonal relationship between 4-Velocity and the observed 3-Velocity If you attempt to subtract the 3-Velocity from the 4-Velocity linearly, you will not get the correct answer If you attempt to subtract the 3-Velocity from the 4-Velocity linearly, you will not get the correct answer a b However, if you apply a scaling factor, you can achieve a linear relationship between 4- Velocity and 3-Velocity However, if you apply a scaling factor, you can achieve a linear relationship between 4- Velocity and 3-Velocity a b ANSWER: The ISM Scaling Metric (M), relative to the Fundamental Unit Length (L), defines the magnitude of the Scaling Factor required to make a = b. Fundamental Unit Time (T) Fundamental Unit Length (L) Scaling Factor = M/L ISM Scaling Metric (M) Fundamental Unit Time (T) Fundamental Unit Length (L) Scaling Factor = M/L ISM Scaling Metric (M) If a Worldline is due to gravitation, the challenge becomes to accurately describe the curvature of space and space-time to accurately depict the curve of the Worldline The simplest case (a uniform spherical non rotating mass with no charge) requires the Schwarzschild solution In the case of ISM, an object under the influence of gravitation must have a specific value of X The value of X and therefore the geometry of ISM space-time is defined by: Fundamental quantum mass: Electron mass: Proton mass: Age of the Universe: Redshift: Mass Density: Gravitation Constant (G): Plancks Constant (h): Coulombs Constant (k): Electron (mass and charge) : Fundamental Quantum (mass, length, time) : 1 All of the information in 4-Vector space-time can be captured in 3 spatial dimensions by incorporating: a quantized time segment (ring) with an orientation value (X) The relationship between time and (X) defines velocity ISM coordinates are consistent with a new formalism for gravitation ISM is supported by observational data A quantum theory of gravityPhysical explanation of the fine structure constant A university that is 14.2 billion years oldA new interpretation of objectivity and local causality An accelerating rate of expansionAbsolute definition of mass, distance and time Inflationary epoch falling naturally out of expansionA link between gravitation and electrostatic force A clear definition of the initial singularityA link between gravitation and strong nuclear force A physical definition of spaceDefined relationship between energy and momentum A physical definition of Cold Dark MatterExplanation of the effects of Special Relativity A physical explanation of Dark Energy4-Vectors expressed in a 3D ISM coordinate system