RelativityChallenge - Comparison (c) 2005

There are several similarities and differences between the models established by Einstein, Newton, and Bryant. The following table illustrates some of the differences for each with respect to their Fixed Point, Wave Front, and One-Half Oscillation equations.

Newton established the early model for fixed-point equations using one type of coordinate system.

Einstein extended Newton's model by adjusting it for light (actually, light waves) using one type of coordinate system.

This new model extends Einstein's by generalizing the wave behaviors, accounts for Complete and Incomplete Coordinate Systems, corrects the time equation, re-establishes the Newtonian equations for fixed-point transformations, and introduces equations for one-half oscillations.

Notes

The dimensions of the coordinate system are x', y, and z.

The coordinate system moves at velocity v.

The phenomena under observation (e.g., wave) moves at velocity w.

When v meets or exceeds w in an Incomplete Coordinate System, oscillations will not occur.

Adjustments

The equations for one-half oscillations can be adjusted as needed in the following ways:

Alpha can be used to normalize the equations to account for the behavior of the timekeeping mechanism. If time is kept external to the moving coordinate system, alpha will be 1.

When using the one-half oscillation equations, x' can be replaced by x-vt, if x and t are known or can be computed.

Mu is set to 1 (or possible values between 0 and 1) when performing calculations for Incomplete Coordinate Systems. Mu is set to 0 when performing calculations for a Complete Coordinate System.

Other Comparisons

The model of Complete and Incomplete Coordinate Systems define two types of coordinate systems. It associates the postulates with Complete Coordinate Systems, while associating the equations for one-half oscillations with Incomplete Coordinate Systems. Einstein's and Newton's model appear to assume only one type of coordinate system.

This model aligns with Maxwell's equations, aligns with Newton's equations, and aligns with the spirit of Einstein's findings for the postulates.

This model can be used to explain the behaviors of waves and particles. Newton's equations did not explain waves (e.g., electromagnetic force).

This model establishes that Electromagnetic Force travels through the ether, unlike Einstein's model that removes the ether.

This model, like Newton's model, does not have an upper limit to velocity.

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