What is the mass of a tachyon if moves faster than light? How can something is positive mass move faster light? How likely are tachyons to actually exist?
And from this site:
http://www.site.uottawa.ca:4321/astronomy/index.html#tachyon
Why is the mass negative when it is squared?
I googled for “imaginary mass” and found this - http://www.faqs.org/faqs/astronomy/faq/part4/section-12.html it looks quite helpful.
You may need to brush up on imaginary numbers (basically i is a number defined by i^2=-1).
Oh, and because no-one ever reads links, here’s what I remember:
Nothing with a positive rest mass can go faster than the speed of light (or at the speed of light). For a tachyon to have superluminal velocity it must have a negative mass.
As for imaginary number that is the only way us humans can define something squared that equals a negative number. Ordinary mathematics doesn’t allow for it.
-2[sup]2[/sup]= 4
ã4 = 2
Whoops! Math should be reversible but in this case we don’t get back to -2 but are left instead with a positive 2.
To me imaginary numbers always seemed like a mathematical fast one but if you search this message board you can find some excellent threads discussing its validity and usefulness.
That said finding a physical object with negative mass would keep physicists busy for years to come (although I bet they would be thrilled).
Dang…this message board doesn’t seem to allow the square root symbol. That box-a before the ‘4’ above was meant to be ‘square root’.
Yes tachyons (which having never being observed are strictly theoritical oddity only) have imaginery mass, which means their energy is a mutiple of i, the sq rt of minus 1.
Take the equation (where E is energy, m is mass, v is the speed of the object as a fraction of c, where c is the speed of light):
E = m*[1-(v/c)^2]^-1/2
but when v is greater than c, v/c > 1, therefore (v/c)^2 > 1, therefore 1-(v/c^2) is a negative number, therefore [1-(v/c)^2)^-1/2 is an imaginery number.
Tachyons, if they exist, have imaginary mass, not negative mass. However, if you had something with negative mass, you could use that to build a warp drive or the equivalent, to effectively transport normal matter at faster than the speed of light.
And in a sense, imaginary numbers are a “mathematical fast one”, but then, so are negative numbers and fractions. Different kinds of numbers are useful for different purposes, and if a set of numbers does what you need it to do, why sweat it?
MC just snuck in before me, so I’ll comment on what he said, too. A tachyon’s mass is imaginary, which is the m in his equation, but the rest of that is imaginary, also, so the total energy is real. In fact, the fact that the energy needs to be real is why the rest mass has to be imaginary.
It seems to me that this whole tachyon question should be recognized as a reductio ad absurdum - we assume it exists, then derive other properties that turn out to be nonsensical. In any other context, this alone would be proof that they don’t exist, but in the strange world of relativity, QM, and Calabi-Yau spaces, people have become too eager to accept nonsensical results.
So I guess I’ll jump in too - if they exist, would they be observable?
Which specific properties are nonsensical? Do you mean actually logically contradictory, or just stupid?
I’m out of touch, but the last I heard tachyons were still a theoretical possibility, even though (almost) everyone thinks they can’t exist… is there something new I should know?
Or are you referring to imaginary mass? OK, it sounds stupid, but it ends up working in the end. We could consider it a bit of mathematical fiction if tachyons actually turned up. In relativity, i often crops up in the time dimension, but that works fine.
Oh, forgot this. I suppose so - their relatavistic mass would be real if I understand correctly, so they’d interact like anything else.
And, according to my earlier link, they’d constantly give off cerenkov radiation (due to the doppler effect), the lack of which is evidence against their existance. But I’m not sure about this bit.
Chronos, MC? Anyone want to chip in?
As I’ve heard it said, in the world of particle physics, the rule seems to be, if something is mathematically capable of existing, it does exist. It’s the same reason some people believe in magnetic monopoles. 
My understanding of tachyons is that they are purported to have c as a lower velocity limit, in much the same way as a mass particle can approach but not reach c. (Imagine c being an asymptote around which our conventional physics are mirrored, with everything on the tachyon side being the imaginary component of the equations).
As was mentioned before, this does not imply negative mass, but rather imaginary mass, which could be either positive or negative. A particle with real negative mass would occur within the observable universe, on the real number side of the c asymptote.
-FK
It seems like this to me: Bob might have some apples. If he has some apples, then you can take the square of the number of apples, and add 7 to get zero.
Now I would say that Bob doesn’t have any apples, but the theoretical physicist would say that Bob has i*sqrt(7) apples. So I guess my answer to you is (B), just stupid.
What?
Sorry, I’m confused again. Are you saying that physicists are saying that you can have an imaginary number of apples, because I don’t think so (how would you square number of apples?), or that using imaginary numbers in real life in general is stupid (cf relativity or electricity) ?
Seriously, can you explain your post to me as if I was an idiot?