# What is 3-Force and 3-acceleration?

I can't seem to find any information related to the 3-Force or the 3-acceleration, only for the 4-force and 4-acceleration. Could someone explain the difference? The context is that I'm trying to derive an expression for the 3-force in terms of the 3-acceleration $\vec{a}$ and $\vec{\beta}$ using the relativistic expression for the momentum of a massive particle.

My guess is that 3-force and 3-acceleration just means the good ol' 3-dimensional force and acceleration from early physics classes, but then I'm not sure why someone would call this a 3-force and 3-acceleration. It just unnecessarily causes confusion.

• Your guess is right. The reason would be to avoid confusion with 4-variables if you are trying to talk about both at the same time. – mmesser314 May 7 '17 at 22:54
• I've never heard of force and acceleration being referenced that way but I would be sure that "3-force" and "3-acceleration" is exactly as you have stated and given by the 3-dimensional vector definition for both. – Rumplestillskin May 7 '17 at 22:55
• Thank you both!!! Yea, it's confusing as heck to say it like that!! – loltospoon May 7 '17 at 23:03
• 3-force and 3-acceleration are similar to the "good ol' 3-dimensional force and acceleration from early physics classes"... in the sense that they are spatial-components...but the way they transform according to special relativity is different from how they transform "from early physics classes" 3-acceleration: en.wikipedia.org/wiki/… 3-force: en.wikipedia.org/wiki/Four-force – robphy May 8 '17 at 0:28