## Tachyons

As every sci-fi geek knows, matter may travel faster than the speed of light as long as its mass is imaginary (a multiple of √−1). A so-called tachyon would not overturn special relativity—and it would provide a handy way of resolving any conflicts in a given Star Trek plot.

• 14th Law of How to Write Star Trek: Whenever you’ve written yourself into a hole, instead of re-writing the show so that it’s better, simply make characters issue the word “tachyon” several times toward the end. Everything is magically resolved, returning all aspects of life to the way the show started with no long-term consequences for the characters—which by the way is a great lesson to teach to young adults—and then Spock or Data has an “a-ha!” moment wherein he throws around jargon to further justify the deus ex machina.

The only problem with tachyons, as any sci-fi geek can attest, is that “imaginary” mass is pure fiction! How could anything weigh an imaginary amount?

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Well, I’m not sure that tachyons do exist—although if someone wants to post some arXiv links to relevant papers that would be awesome—but, I will say that “imaginary mass” isn’t that ridiculous of a concept.

As Tristan Needham said in the best book about complex numbers ever, the “imaginary” descriptor only reflects the historical prejudice against √−1.

Do imaginary numbers exist? No. But neither do counting numbers. Numbers are linguistic entities that humans communicate with. Sort of like how trees, flowers, bushes, shrubs, brambles, and vines all exist in nature, but those classifications, concepts, words, groupings are human-language mental constructs. “Five” doesn’t “exist” per se, but mathematical models built with the-thing-that-satisfies-the-properties making five five, do wonderfully at prediction of physics experiments.

Anyway, imaginary numbers exist just as much as other numbers. Just like rational numbers, they’re generated by an operation that comes up as a matter of course in algebra. And algebra seems to have something to do with nature. God knows why. (ohh! which way did I mean it?!)

So I’m not saying imaginary mass exists, but here are some good ways to think about imaginary numbers.

• imaginary numbers are twisted numbers
• imaginary numbers are phase-shifted like a sine wave versus a cosine wave
• an imaginary current heats up a wire but does no useful work

If the mass of a particle is an imaginary number, then … that might help you make sense of tachyons.

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Nerdy side note: E=MC² is not the real equation to describe the conversion of energy into matter or vice-versa.

• E=MC² tells you how to convert stationary matter into energy.
• The real equation is E² = [mc²]² + [pc]².
• (p is momentum.)
• (Notice that the real equation is of the form A²+B²=C². i.e., Energy is the hypotenuse (C) to the triangle sides B=mc² and A=p•c)

You can casually start/interrupt conversations with this knowledge the next time you attend a kegger / black-tie affair. Doing so will win handsome glances from potential sex partners. Also, there is a 0% chance that anyone will think you’re an insufferable know-it-all.

41 notes

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4. starvlings said: Shouldn’t the equation be E² = (mc²)² + p²c²
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Tachyons As every sci-fi geek knows, matter may travel faster than the speed of light as long as its mass is imaginary...
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As every sci-fi geek knows, matter may travel faster than the speed of light as long as its mass is imaginary (a...
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easily one my favourite blogs,...science or just thinking in general
12. cellular-automaton said: thank you so much, everything you post is so thought inspiring and beautiful, your blog is easily my favourite math/science blog (and I follow quite a few of them)
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