## The Fallout of Michelson's Null Result

There was very little reaction to Michelson's Potsdam experiment. Hendrik Lorentz – another "king,"(whom we'll meet in a later lesson) this time of electromagnetic, pointed out a numerical mistake in Michelson's analysis but it didn't change the result: still zero.

<img align="left" src="../_images/relativity/lorentz.png" width=60% />

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<figcaption> Hendrik Lorentz, 1853-1928 </figcaption>

Hendrik Lorentz was the undisputed expert in the mathematics and physics of Maxwell's electromagnetism and extended it in a crucial way. Maxwell's equations describe the electric and magnetic fields due to extended charge distributions – "stuff" that you could hold in your hand.

Lorentz, however, was a firm believer in the atomistic picture and that the atoms included "electrons" which when they oscillated, radiated electromagnetic waves. (Notice, this was before our electron was discovered so Lorentz's "electrons" were not what we think of as electrons today...they were just hypothetical charged components of an atom.)  In 1887 he worked out the equations for the motions of his "electrons" and today we call these the Lorentz Force equations.  His theory required that the motions of the electrons be related to the stationary coordinate system defined by the ether and so he was interested in Michelson's 1881 Potsdam results since they were inconsistent with his theory. Indeed, he criticized Michelson's conclusions in which he postulated that the ether was dragged by the Earth, and so no speed would be detected in his apparatus.

In order to study the results, Lorentz built a model and calculated what the electric field would be like for a moving charge...like in the materials of Michelson's instrument...and what he found was that materials would actually shrink in size along the direction of the motion relative to the ether. *An actual mechanical change of size.* In our river analogy, my trip up and downstream would take longer than across but it could be brought to coincidence with your across-trip if my distance $L$ was shorter by

```{admonition} &nbsp; Pencils Out! 🖋 📓
:class: warning

$$
L_{me}=\frac{L_{you}}{\sqrt{1-\left({\frac{v_{boat}}{u_{river}}}\right)^2}}
$$
```

The Irish physicists George FitzGerald originally thought of this, but without a model to illustrate the shrinkage. While this is not the actual case, that square root factor will be a big part of our lives for the next few lessons!