# Test bodies general relativity

I'm studying section 82 of the Landau & Lifshitz Field Theory vol.2 In this page it's written that the relative position of test bodies can't remain unchanged during time. And ok with this. But then on the footnote they write

Strictly speaking, the number of particles should be greater than four. Since we can construct a tetrahedron from any six line segments, we can always, by a suitable definition of the reference system, make a system of four particles from an invariant tetrahedron. A fortiori, we can fix the particles relative to one another in systems of three or two particles.

What does this mean?

• They are describing how to use the gauge freedom of coordinate choice to fix the relative positions of particles. – ACuriousMind Jun 4 '15 at 11:52
• I thought they meant you need to use enough particles to demonstrate how things work in 3+1 dimensions. If you only use two particles, one above the other, you will see how the tidal force pulls them apart as they descend over time. That demonstrates how things work in 1+1 dimensions, but doesn't give the whole picture. – John Duffield Jun 4 '15 at 12:48
• I don't understand why with 4 or less particles the relative positions doesn't change or how we can create a rigid/invariant tetrahedron. – Saladinos Jun 5 '15 at 10:11