This post relates to a previous post *here*.

The Michelson-Morley experiment is a famous “null” result that has been understood as leading to the Lorentz transformation. However, an elementary error has persisted so that the null result is fully consistent with classical physics. Let us look at it in detail:

The Michelson-Morley paper of 1887 [*Amer. Jour. Sci*.-*Third Series*, Vol. XXXIV, No. 203.–Nov., 1887] explains it using the above figures:

Let

sa, fig. 1, be a ray of light which is partly reflected inab, and partly transmitted inac, being returned by the mirrorsbandc, alongbaandca.bais partly transmitted alongad, andcais partly reflected alongad. If then the pathsabandacare equal, the two rays interfere alongad. Suppose now, the ether being at rest, that the whole apparatus moves in the directionsc, with the velocity of the earth in its orbit, the directions and distances traversed by the rays will be altered thus:— The raysais reflected alongab, fig. 2; the anglebab, being equal to the aberration =a, is returned alongba_{1}, (aba_{1}=2a), and goes to the focus of the telescope, whose direction is unaltered. The transmitted ray goes alongac, is returned alongca_{1}, and is reflected ata_{1}, makingca_{1}eequal 90—a, and therefore still coinciding with the first ray. It may be remarked that the raysba_{1}andca_{1}, do not now meet exactly in the same pointa_{1}, though the difference is of the second order; this does not affect the validity of the reasoning. Let it now be required to find the difference in the two pathsaba_{1}, andaca_{1}.Let

V= velocity of light.

v = velocity of the earth in its orbit,

D= distanceaborac, fig. 1.

T= time light occupies to pass fromatoc.

T_{1}= time light occupies to return fromctoa_{1}(fig. 2.)

The paper then goes on to give values for *T* and *T*_{1} incorrectly as

The correct values are as follows:

First, it is important to note that *distance* is the independent variable and *time* is the independent variable, since the distances are fixed at the outset, such that “the paths *ab* and *ac* are equal”. Second, this entails that pace and lenticity rather than speed and velocity should be used, since they have distance in the denominator. This is algebraically equivalent to using inverse speed and velocity (velocity with inverse magnitude).

Thus instead of the addition and subtraction of *velocities*, one should use the addition and subtraction of *lenticities*, or equivalently, the addition and subtraction of inverse velocities. Then the correct values for *T* and *T*_{1} are

This leads to

So the elapsed time and the pace (or speed) of light are independent of the earth in its orbit according to classical physics.