<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message\nnews:cfi8eo\\$r8v\\$1@pegasus.csx.cam.ac. uk...\n> In article <411BC7C1.5010508@univie.ac.at>,\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n> |>\n> |> Wikipedia says at http://en.wikipedia.org/wiki/Tachyon\n> |> the following:\n> |>\n> |> \'\'In the language of the theory of special relativity,\n> |> a tachyon is a particle with space-like four-momentum.\n> |> If its energy and momentum are real, its rest mass is imaginary.\'\'\n> |>\n> |> This is the meaning in technical terms, as I claimed.\n> |> In science fiction (which is also mentioned in W., the\n> |> terminology may be broader, but this is irrelevant for\n> |> science.\n>\n> Not quite. The English language is defined by its users, and\n> specialists ignore that at their peril. My point is that not\n> that the hypothesised particles don\'t have both properties (the\n> do), but that tying the word to its secondary aspect is creating\n> a hostage to fortune.\n>\n> This would become serious only if someone hypothesised a particle\n> with only one of those properties, of course.\n>\n\nI have never heard of the word tachyon, in science fiction or otherwise, as\nreferring to a particle that only travels faster than light through a\nmedium, and not faster than C.\n\nHere are the first matches that come up for tachyons on Google\n\nhttp://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html\n\nhttp://scienceworld.wolfram.com/physics/Tachyon.html\n\nhttp://users.primushost.com/~ewall/\n\nhttp://www.physics.gmu.edu/~e-physics/bob/tachyons.htm\n\nIf you read those, they all define tachyons as particles that travel faster\nthan C (although I didn\'t read them all very carefully, I did note that\nfact).\n\nIt\'s good to remember that C does not change when light travels through a\nmedium, although the speed of light does, so when a particle travels faster\nthan light through a medium, it is not travelling faster than C.\n\nIn any event, the users of the word "tachyon" are, and should be,\nphysicists, since they made it up to describe a specific idea. If we start\nusing it to mean other things, it makes physics very hard to do.\n\nAlso worthy of noting is what we calculate mass to be if a particle travels\nfaster than c.\n\nwe know that\nE^2 - p^2c^2 = m^2c^4\n\nand\n\np = m*gamma*v = m*v/sqr(1-v^2/c^2) = m*u*c/sqr(1 - u^2), where u = v/c\nif v>c then p^2 < 0\n\nnow with just a little work, we can show that\n\nE^2 - m^2*u^2*c^4/(1 - u^2) = m^2*c^4\nE^2*(1-u^2) - m^2*u^2c^4 = m^2*(1-u^2)*c^4\nE^2*(1-u^2) = m^2*c^4*(1-u^2 + u^2) = m^2*c^4\nE^2 = m^2*c^4/(1-u^2)\nE = m*c^2/sqr(1 - u^2)\n\nso, if m is real\n\nE = m*c^2/(i*k), where k is some positive real number and i is the square\nroot of -1. This means that E is imaginary.\nIf we want E to be real, m must equal some real number times i.\n\nIf the real number we label m, then\n\nE = m*i*c^2/(i*k), and E = m*c^2.\n\nso, if we want E to be real, the mass must be imaginary.\n\nAnd that is why if the energy and momentum of a tachyon are real, it\'s mass\nmust be imaginary, popular usage or not.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
news:cfi8eo$r8v$1@pegasus.csx.cam.ac.uk...
> In article <411BC7C1.5010508@univie.ac.at>,
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
> |>
> |> Wikipedia says at http://en.wikipedia.org/wiki/Tachyon
> |> the following:
> |>
> |> ''In the language of the theory of special relativity,
> |> a tachyon is a particle with space-like four-momentum.
> |> If its energy and momentum are real, its rest mass is imaginary.''
> |>
> |> This is the meaning in technical terms, as I claimed.
> |> In science fiction (which is also mentioned in W., the
> |> terminology may be broader, but this is irrelevant for
> |> science.
>
> Not quite. The English language is defined by its users, and
> specialists ignore that at their peril. My point is that not
> that the hypothesised particles don't have both properties (the
> do), but that tying the word to its secondary aspect is creating
> a hostage to fortune.
>
> This would become serious only if someone hypothesised a particle
> with only one of those properties, of course.
>
I have never heard of the word tachyon, in science fiction or otherwise, as
referring to a particle that only travels faster than light through a
medium, and not faster than C.
Here are the first matches that come up for tachyons on Google
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html
http://scienceworld.wolfram.com/physics/Tachyon.html
http://users.primushost.com/~ewall/
http://www.physics.gmu.edu/~e-physics/bob/tachyons.htm
If you read those, they all define tachyons as particles that travel faster
than C (although I didn't read them all very carefully, I did note that
fact).
It's good to remember that C does not change when light travels through a
medium, although the speed of light does, so when a particle travels faster
than light through a medium, it is not travelling faster than C.
In any event, the users of the word "tachyon" are, and should be,
physicists, since they made it up to describe a specific idea. If we start
using it to mean other things, it makes physics very hard to do.
Also worthy of noting is what we calculate mass to be if a particle travels
faster than c.
we know that
E^2 - p^{2c}^2 = m^{2c}^4
and
p = m*\gamma*v = m*v/sqr(1-v^2/c^2) = m*u*c/sqr(1 - u^2),[/itex] where u = v/c
if v>c then [itex]p^2 <
now with just a little work, we can show that
E^2 - m^2*u^2*c^4/(1 - u^2) = m^2*c^4E^2*(1-u^2) - m^2*u^{2c}^4 = m^2*(1-u^2)*c^4E^2*(1-u^2) = m^2*c^4*(1-u^2 + u^2) = m^2*c^4E^2 = m^2*c^4/(1-u^2)E = m*c^2/sqr(1 - u^2)
so, if m is real
E = m*c^2/(i*k), where k is some positive real number and i is the square
root of -1. This means that E is imaginary.
If we want E to be real, m must equal some real number times i.
If the real number we label m, then
E = m*i*c^2/(i*k), and E = m*c^2.
so, if we want E to be real, the mass must be imaginary.
And that is why if the energy and momentum of a tachyon are real, it's mass
must be imaginary, popular usage or not.