Lorentz invariance (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

87
1
1. The problem statement, all variables and given/known data

I have two four vectors v and w with [tex] v^{2} = m^{2} > 0, v_{0} > 0 [/tex] and [tex] w^{2} > m^{2}, w_{0} > 0 [/tex]. Now we consider a system with
[tex] w' = (w_{0}', \vec{0}) [/tex] and [tex] v' = (v_{0}', \vec{v} \, ') [/tex] and in addition we consider the quantity [tex] \lambda = \vert \vec{v}' \vert \, \sqrt{ w_{0}'^{2} - m^{2}} [/tex]. Now I should find a Lorentz invariant expression of [tex] \lambda [/tex] only using the invariants [tex]v^{2}, w^{2}, vw[/tex].

2. Relevant equations



3. The attempt at a solution

I think I've found a solution: [tex] t = \sqrt{\dfrac{(vw)^{2} - v^{2} w^{2}}{v^{2}} (v^{2} - w^{2})} [/tex].
But I'm not really sure if this "solution" is really Lorentz invariant (my problem is the square root). Could anyone confirm this solution or is there any mistake?
 

Avodyne

Science Advisor
1,384
81
The square root is OK as long as what you're taking the root of is positive. I didn't check your math, but the answer should look something like this.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top