Phase shifting

Phase shifting, or phasing, is the process by which objects and materials can be placed out of phase from normal substances which can cause effects from invisibility to allowing objects to completely pass through each other.

In 2369 the crew of the USS Enterprise (NCC-1701) was accidentally put out of phase while testing a prototype cloaking device developed by Starfleet Intelligence based on a Romulan cloaking device stolen by the Enterprise previously. 
 * The final outcome of this incident has yet to be revealed awaiting publication of the continuation of the miniseries.

Phase shifting was key function in cloaking devices used by the Romulan Star Empire in the 2370s. The component responsible for phase shifting in the cloaks was the interphase generator.

By the year 2376, the Federation Science Service under the direction of Doctor Leah Brahms attempted to secretly study Romulan phase shift technology to develop an advanced suit which was capable of shifting out of phase. The objective of this study was produce an engineering tool that would allow engineers to work in hazardous areas of a starship, such as the Warp core, without any worry of radiation or other dangers.

While testing the prototype of the suit in that year Leah Brahms was protected from the effects of the Genesis wave by being out of phase. This stroke of good fortune for Brahms later allowed Federation and Romulan forces to deploy interphase generators on other planets in the path of the wave to protect populations by phase shifting them to safety out of the effects of the wave. 

Appendices

 * See also: Interphase cloaking device