# HEP units

1. Aug 3, 2010

### Pengwuino

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 $$t=\frac{1}{m^2}$$. I figure theres 2 h-bars on top but that still leaves s^2. Can someone straighten me out here? Thanks!

2. Aug 3, 2010

### humanino

Assuming you remember the speed of light, the only other combination you need to remember is $\hbar c\approx$ 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 $E^2=p^2c^2+m^2c^4$)
So finally $\hbar$=1 gives you time and mass (or space and energy) with opposite dimensions :

t ~ $\hbar c$/m$c^2$
x~ct
E~pc
xp~$\hbar$
Et~$\hbar$

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
3. Aug 6, 2010

### nrqed

To add to what Humanino wrote: in natural units t=1/m. If you have seen t =1/m^2 it was a typo.

4. Aug 6, 2010

### Pengwuino

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 $$\frac{1}{m^2}$$. So there's some constants that I'm missing because the speaker was just showing us various proportionalitys

5. Aug 9, 2010

### kaksmet

Well, time is not proportional to $$\frac{1}{m^2}$$ but to $$\frac{1}{m}$$.