# Antimatter to matter ratio

In Star Trek TNG "Coming of Age" (season 1) Mordock and Wesley discuss a tricky question on their Hyper Space Physics test, which is to calculate a matter to antimatter ratio under some circumstances:

Wesley: As soon as I realized it was a trick question, there was only one answer.

Mordock: Yes. There is only one "ratio" with matter-antimatter. One to one.

But in one of the following episodes, "Skin of Evil", leiutenant-commander Lynch says to computer (in order to run the warp engine):

Understood. Now. Prime matter/antimatter injectors. Set ratio at twenty-five to one...

So, how could both Wesley and Lynch be right?

• This is a good question. IIRC Lynch says that when re-initiating the reactor core. Perhaps it takes more matter to start the engines, but an equal ratio for nominal use? – Xantec Mar 22 '14 at 19:20
• A given mass of antimatter will annihilate (producing energy) with an equal mass of matter. If you mix 1 gram of antimatter with 25 grams of matter, you'll get 2 grams (times c**2) worth of energy with 24 grams of matter left over. That's the real-world physics of it; going beyond that requires knowing how warp engines work, which nobody does. – Keith Thompson Mar 22 '14 at 19:38
• Star Trek is infamous for having completely meaningless science and engineering terminology in its scripts, eg. "We have to tech the tech to the warp core, otherwise we're all doomed!" So expecting it to be consistent is basically futile. The show's creators have admitted as much: blastr.com/2009/10/ron_moore_calls_star_trek.php – Royal Canadian Bandit Mar 22 '14 at 19:47
• From a real-world physics perspective, adding extra matter to an antimatter/matter reaction would result in the extra matter becoming hotter and expanding. – Valorum Mar 22 '14 at 21:06

Per this excellent answer on Memory Alpha;

In the 2364 Starfleet Academy entrance exam, one of the questions dealt with intermix ratios:

"The matter and antimatter tanks on a Galaxy-class starship are nine-tenths depleted. Calculate the intermix ratio necessary to reach a starbase 100 light years away at warp factor 8."

This was a trick question as there was only one ratio with matter/antimatter: 1:1. (TNG: "Coming of Age")

In the same year, after the Shuttlecraft 13 crashed on Vagra II, the USS Enterprise-D was rushed to have warp drive operational. In the start-up sequence, prior to powering up the engine core and injecting reactants, the matter-antimatter injectors were primed to a ratio of 25:1. Minimal warp speeds were recommended, however Captain Jean-Luc Picard ordered warp 8. (TNG: "Skin of Evil")

Jadzia Dax ordered the intermix be manually set to 0.01, prior to the warp chamber initialization, on the USS Defiant after it had been damaged by a cascade virus. (DS9: "For the Uniform")

Several aspects of the intermix ratio are further explained in the Star Trek: The Next Generation Technical Manual (pages 61-62). According to the text, the 1:1 ratio applies when traveling at warp 8 or faster. When traveling at lower speeds the intermix ratio is different - a ratio of 25:1 is only used when the core is online in an idle state, prior to full startup. At warp 1 it is tuned to 10:1, gradually changing until it reaches 1:1 at warp 8.

This description tallies nicely with the real-world effects of adding extra matter to an antimatter/matter reaction since the extra matter would become hotter and expand as energy is input.

If the reaction chamber needs to be at a specific pressure before high levels of energy can be created, then adding extra matter (e.g. to "prime" the chamber) would be an excellent way to achieve this.