# Virtual rigid body in Special Relativity

Mischievous but non-trivial:

Can I use a virtual rigid body in a thought experiment? For instance four equidistant rockets in tetrahedral formation, variously accelerating in such a way that every pair agrees the distance between them doesn't change. The connecting rods are optional.

Depending on the nature of the experiment, yes. Strictly speaking you don't need any physical bodies to be present in order to model and calculate relativistic effects, just sets of coordinates. For example, SR says that the distance between two specified points fixed in one reference frame will be shorter when transformed to become the distance between the corresponding points in another reference frame in which they are moving. If you wished, the vertices of your tetrahedron could simply be four sets of coordinates with nothing physically present.

Of course, having rockets can make it easier to visualise.

• Depending on the nature of the experiment? Suppose the rockets spin it around an axis of symmetry … Do I have three points of a rigid spinning disk and a point on the axis?
– DrC
Sep 28, 2019 at 12:57
• You do. Again there is no need for rockets. You can simply imagine three points rotating points on a circular path on a plane and one fixed point on a line normal to the plane through the centre of the circle. Sep 28, 2019 at 15:39
• Thanks - so what do you think is the problem with clocks on the rotating disk?
– DrC
Sep 28, 2019 at 22:10
• @DrC Sorry, I don't understand- what problem? Sep 29, 2019 at 6:09
• I think the problem is calculating the correct rate of other rotating clock as seen from any one rotating clock. Surely every rotating clock must see every other rotating clock at the same radius advancing at the same rate.
– DrC
Sep 30, 2019 at 13:34