Gravitational Insights from Less Than Ten Percent the Speed of Light

Kandi M. CockreamIWPD Research Center

Midwest Relativity MeetingUniversity of Notre Dame

October 25, 2008

Minimal uncertainties, assumptions and variables

Easy to directly observe and analyze

The Challenge: The relativistic effects are very small

Motion at less than 10% the speed of light is still part of the relativistic spectrum

Observations at the lowest relativistic levels may be helpful in the unification of GR and QT

General Relativity

Quantum Theory

Energy is conserved: Total mass prior to interaction = mass after absorption

Momentum is NOT conserved: p of free energy is less than p of object moving with v << c

An elastic collision between two objects of the same mass

Energy Transfer Resulting in a

change of:

MassEnergyMomentumVelocity

The Energy Transfer Fully Accounts for the Change In:

Energy Mass

The Energy Transfer DOES NOT Account for the:

• The magnitude of the momentum change for both objects

• The anticipated velocity of the objects based upon the momentum of the transferred energy

Energy and Momentum are linked by Velocity

But . . . Velocity alone does not fully account for the relationship

An additional factor, ranging from 1 at c to ½ at v << c must be incorporated

This suggest the possibility of a Scaling Effect between the Anticipated Velocity and the Observed Velocity

The scalar acts between like units (velocity) The value of this scalar can be quantitatively defined based upon Relativistic Kinetic Energy

...8

3

2

1 2422 cvmvmcmE

• Relativistic Kinetic Energy is approximated by the Binomial Expression:

• With our standard equation for Kinetic Energy at v << c outlined in red

...8

3

2

1 2422 cvmvmcmE

Kinetic Energy can be exactly expressed as:

2vXmE t

Select an exact velocity and invariant mass Relativistic Mass is known from the Lorentz transformation Energy is exactly known (Relativistic Mass – Invariant Mass) Therefore, X is exactly known

• X has significance in a number of applications involving energy, force and momentum

• Specifically, the relationship between Apparent Velocity and Observed Velocity is a function of X:

2vXmE t

232)( xxxF

232/1)( xxxF

232/1)( xxxF

Provides an exact relationship between the Observed Velocity and the Anticipated Velocity across the entire velocity spectrum

Larger Relativistic EffectsSmall

Relativistic Effects

Three Scale Metrics emerge all of which are functions of X:

232Metric Distance xx

232

2Metric Time-Distance

xx

232

1Metric Rate

xx

Distance Metric: Defines a grid representing the local observers concept of distance

Distance -Time Metric: Defines a circle that changes inversely with the Distance Metric

Rate Metric: Defines the rate at which the Distance -Time Metric changes as measured by the Distance Metric

Distance Metric: Defines a grid representing the local observers concept of distance

Distance -Time Metric: Defines a circle that changes inversely with the Distance Metric

Rate Metric: Defines the rate at which the Distance -Time Metric changes as measured by the Distance Metric

Two-dimensional space grid

The intersect of cosmic scale circles cutting through the 2D space grid

The Distance-Time Metric expands as the Distance Metric decreases

232 xx

232

2

xx

232

1

xx

At the beginning:

• All three scale metrics were unified

• With time, the metrics diverge as the value of X decreases

Distance Metric = 1Distance-Time Metric/2pi = 1Rate Metric = c = 1

Mass decomposes to Free Space via a fundamental quanta defined by Scale Metrics

In the beginning, there was only mass and no space

At the end, there will be only space and no mass

At 14.2 billion years there is both mass and space in a universe whose expansion rate is observed to be accelerating

As the universe expands, the Scaling Effects resulting from the diverging values of the Scale Metrics are not exactly the same everywhere

The is due to a slightly uneven distribution of mass within the universe

This results in a “warping” of the Distance Metric and the Distance-Time Metric

A benefit of this approach is that IWPD Gravitation does not break down at the Planck Scale.