## Background

When in motion, the length of an object can change. The faster something travels, the shorter its length. This is known as length contraction.

Albert Einstein’s relativity equations predict a non-intuitive scenario, but length contraction is real and has been validated by experiments. It is hardly noticeable at low velocities, but at relativistic speeds closer to the speed of light, length contraction of an object is very apparent. The object will shrink in the direction of motion. But there has been no reasonable explanation about why it is happening, until now.

## Explanation

All particles are sending out-waves, including electrons and positrons that make up an atom’s nucleus. Where these out-waves collide and cancel are gaps where free electrons fit, within their orbitals, attracted by the positron. This was proven with detailed calculations of orbital distances using the Force Equation.

Below is an illustration of an atom and where the electron may reside, at a specific number of wavelengths from the atom’s core. Whether stationary or in motion, the electron is always at the specified distance measured in wavelengths.

In the stationary atom, the electron is fixed at a distance X. For the purpose of illustration only, this is locked in at eight wavelengths from the proton (actual wavelength count from the proton to the electron would greatly exceed eight cycles). In the atom in motion, the electron is still locked in at eight wavelengths, but now at a distance Y, which is shorter than X. In fact, the proton itself is also smaller. This is because the wavelengths are now compressed due to the Doppler effect for the particle in motion.

The atom has been compressed in the direction of motion. Furthermore, all atoms in the molecules that make up the object traveling at high speeds are subject to the same compression. Thus the length of the object is contracting – only on the axis in the direction of travel – because the Doppler effect shortens the wavelengths that bring the atoms of the molecules closer together. This is length contraction at relativistic speeds.

### Deriving Length Contraction

Length contraction can be derived from the Energy Wave Equation, where frequency (f) is used to replace wave speed and wavelength. Since atoms share electrons, each atom in the direction of motion equally contracts such that the length is shorter relative to its initial length at the standard frequency/wavelength seen when the atom is at rest. The equations below describe the length of the object as being the sum of the atoms and their wavelengths to its orbitals. The derivation of length contraction starts with the base energy wave equation and **concludes with a length contraction equation that matches Einstein’s relativity**.