Quaternion gravity

Looking down or looking up from below changes time and space measurements in opposite ways.

If one kid is at a different height in a gravity field to another, then time measurements get smaller while spatial ones get bigger. That is standard physics (general relativity, GR).

The Quaternion Gravity (QG) proposal says the space-times-time values are precisely the same. With general relativity, this space-times-time is not mentioned, but it is almost - but not quite - the same.

Note: the numbers are far too big.

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A brief explantion of this page.

For nerds

Special relativity could have been called "special equivalence" because it is the interval that all inertial observers agree upon forming an equivalence class. An equivalence class is a deep insights into how Nature works.

The quaternion gravity proposal postulates a new equivalence class: that different observers making measurements in different locations in a gravitational field will agree on the value for space-times-time. Some care is required to say this in a coordinate-independent way. All observers are free to pick their coordinate system. There then exists a norm-preserving rotation in space such that the space-times-time measurement of one observer is exactly equal to another.

But how precisely does the interval change? For a spherically symmetric, non-rotating, uncharged source, only one dimensionless ratio comes into play: GM/c²R. The requirement that the space-times-time term is equivalent means the the changes in the time term must be the mathematical inverse of the changes in space. To be consistent with Newton's law of gravity, the simplest functions would be (1 - 2 GM/c^{2 R) for
time, and 1/(1 - 2 GM/c}2 R) for space. To be consistent with weak field test of gravity, one more term must be added to both: (1 - 2 GM/c^{2 R + 2 (GM/c}2 R)^2) for time and its inverse for space. At this point, quaternion gravity disagrees with general relativity because such terms do not solve the Einstein field equations. Orbital systems are harmonic systems, suggesting that one use exponential of the dimensionless ratio.

e to the -z dt, e to the z dR sub i over c squared equals e to the -2 z dt
squared - e to the 2 z dR sub i squared, 2 dt dR sub i over c equals e to the -
2 G M c squared R dt squared - e to the 2 G M over c squared R dR sub i
squared, 2 dt dR sub i if z = G M over c squared R

The resulting exponential interval has the same form as the Rosen metric. The Rosen metric makes the same experimental predictions as the Schwarzschild metric for all weak field gravity tests to first order Parameterize Post-Newtonian (PPN) accuracy. At second order PPN accuracy, the exponential interval predicts 6% more bending of light around the Sun. We have yet to achieve the precision to decide this issue on experimental data.

Special relativity is not a field theory. It is a constraint on all field theories. The quaternion gravity proposal is also not a field theory. Quaternion gravity is a constraint on all field theories. As such, there is no need for a graviton. Quaternion gravity makes the search for quantum gravity moot.