Question about Natural Units in High Energy Physics

Click For Summary

Discussion Overview

The discussion revolves around the use of natural units in high energy physics, specifically addressing the relationship between time and mass. Participants explore the implications of setting constants such as the speed of light and Planck's constant to unity, and how this affects the dimensional analysis of time in relation to mass.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the expression for time as t=\frac{1}{m^2} in natural units, suggesting confusion over the dimensional analysis involved.
  • Another participant provides context by discussing the relationship between mass, energy, space, and time in natural units, indicating that time should be proportional to \frac{1}{m} instead.
  • Some participants note that there may have been a typo in the expression for time, clarifying that it should be t=1/m rather than t=1/m^2.
  • There is acknowledgment of missing constants in discussions where time was referenced as proportional to \frac{1}{m^2}, indicating a lack of clarity in those presentations.

Areas of Agreement / Disagreement

Participants express differing views on the correct expression for time in natural units, with some asserting that t=1/m is the accurate representation while others reference t=1/m^2 as a potential typo. The discussion remains unresolved regarding the correct interpretation.

Contextual Notes

There are indications of missing constants and potential typos in the expressions discussed, which may affect the clarity of the arguments presented.

Pengwuino
Gold Member
Messages
5,112
Reaction score
20
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 there's 2 h-bars on top but that still leaves s^2. Can someone straighten me out here? Thanks!
 
Physics news on Phys.org
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 [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:
Pengwuino said:
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 there's 2 h-bars on top but that still leaves s^2. Can someone straighten me out here? Thanks!

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

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
 
Pengwuino said:
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

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

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 11 ·
Replies
11
Views
10K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 22 ·
Replies
22
Views
14K
  • · Replies 20 ·
Replies
20
Views
3K
  • · Replies 28 ·
Replies
28
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 8 ·
Replies
8
Views
4K