The Summer Hill Journal Of New Physics

The Lorentz Factor Goes Out Of Scope

It's a matter of Point Of View

There is a little-known limit in the Lorentz Factor equation. This limit comes from (1- v² / c²).

The Lorentz equation covers 90 degrees of rotation. It is the view from an object moving at less than the speed of light (Point of View A below). This means that v=c is just outside the ability of the equation to produce reliable results.

The factor is good from 0 degrees up to, but not including, 90 degrees (PoV A). To cover 90 degrees down to, but not including 0 degrees, would require a -90 degree shift in our point of view (PoV B). Similarly to cover 90 degrees up to, but not including 180 degrees, (PoV C) would require a +90 degree shift in our point of view.

A                         B                         C

Figure 1: Point of View

If 0 degrees is v=0 then v=1 is at the start of the 91^st degree, not at the end of the 90^th degree (note the ordinal use of zero). We can rotate our view 90 degrees to get a reliable result for v=c (Point of View B). When we rotate our view 90 degrees to see things from a photons point of view, the result returns one (unity) for v=1 and null for v=0.

Conventional View versus Predicted

The usual graph we see of the Lorentz factor is shown for in Figure 1 below, with its Type 1 infinity alongside the Type 2 infinity at the right of the chart. On the right is the predicted version if zero is treated as null (arrow).

It is a quirk of nature that the Type 1 infinity sits alongside the Type 2 infinity, making the two seem to be a seamless continuum when using the { 0 } view of zero.

Figure 2: Conventional View of the Lorentz Factor		Figure 3: Predicted Lorentz Factor

Rotating Triangle View

One way to view this result of the Lorentz factor is to consider the v²/c² ratio as a triangle. As we compare the sides 'a' and 'b' in the series of triangles below, the ratio a/b becomes ever larger as the triangle changes, but then the result disappears as 'b' becomes 0. I.e. when the shape ceases to be a triangle and becomes a line then the result is null, not infinity.

Figure 4: Lorentz Factor Viewed As A Triangle

This result of null is correct in that it tells us that there is no result. The reason? Because v=c is a boundary condition. If the Lorentz factor is a rotation through 90 degrees from 0 up to, but not including, 90 degrees, then we have rotated our triangle through 90 degrees and we are now viewing it "edge-on". Regardless of how large the triangle may be, or what shape, edge-on it has zero dimensions.

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