Gravitational Insights from Less Than Ten Percent the Speed of Light
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Transcript of Gravitational Insights from Less Than Ten Percent the Speed of Light
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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
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Minimal uncertainties, assumptions and variables
Easy to directly observe and analyze
The Challenge: The relativistic effects are very small
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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
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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
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An elastic collision between two objects of the same mass
Energy Transfer Resulting in a
change of:
MassEnergyMomentumVelocity
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The Energy Transfer Fully Accounts for the Change In:
Energy Mass
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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
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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
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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
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...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
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...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
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• 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
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232/1)( xxxF
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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
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Three Scale Metrics emerge all of which are functions of X:
232Metric Distance xx
232
2Metric Time-Distance
xx
232
1Metric Rate
xx
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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
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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
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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
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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
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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.