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HEP units

  1. Aug 3, 2010 #1

    Pengwuino

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    I have a quick question about the units used in high energy physics. In natural units, c = h = 1, but I keep seeing time referenced as [tex]t=\frac{1}{m^2}[/tex]. I figure theres 2 h-bars on top but that still leaves s^2. Can someone straighten me out here? Thanks!
     
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  3. Aug 3, 2010 #2
    Assuming you remember the speed of light, the only other combination you need to remember is [itex]\hbar c\approx[/itex] 200 MeV fm
    (It's really 197.326 9631(49) according to PDG[/URL])

    With unit c=1 you get that space and time are really measured in the same unit, as well as energy and mass
    (and momentum, when restoring c just remember [itex]E^2=p^2c^2+m^2c^4[/itex])
    So finally [itex]\hbar[/itex]=1 gives you time and mass (or space and energy) with opposite dimensions :

    t ~ [itex]\hbar c[/itex]/m[itex]c^2[/itex]
    x~ct
    E~pc
    xp~[itex]\hbar[/itex]
    Et~[itex]\hbar[/itex]


    For instance an interaction which would be mediated by a pion (with mass 135-139 MeV/c[sup]2[/sup]) will act (with a Yukawa potential) over distances of the order of :
    200/140 ~ 1.5 fm (just about twice the usual definition of the size of the proton, quite good considering the handwaviness)

    The typical interaction time is also 1.5x10[sup]-9[/sup]/3x10[sup]8[/sup] ~ 5x10[sup]-18[/sup] s
     
    Last edited by a moderator: Apr 25, 2017
  4. Aug 6, 2010 #3

    nrqed

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    To add to what Humanino wrote: in natural units t=1/m. If you have seen t =1/m^2 it was a typo.
     
  5. Aug 6, 2010 #4

    Pengwuino

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    Sorry, I meant to change it but never got around to it. In the discussions I've been seeing it, the time was proportional to [tex]\frac{1}{m^2}[/tex]. So there's some constants that I'm missing because the speaker was just showing us various proportionalitys
     
  6. Aug 9, 2010 #5
    Well, time is not proportional to [tex]\frac{1}{m^2}[/tex] but to [tex]\frac{1}{m}[/tex].
     
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