To make a very short answer, this sounds very much to the (probably very western) problem of "when a tree falls in the forest and there's nobody around, does it make noise?". Have a look at it on wikipedia.
Being very scientific minded, I would assume that makes very little difference between the twins, as "I" am the only reference for any measurement, so each twin can assume what s-he sees as "the truth". But that is only my opinion
https://www.psychologytoday.com/blog/brain-food/201405/the-beneficial-mischief-neurosurgery
Perception is a mental process. It's just can be based on physical things. When the tree falls, there are the properties for a noise to be noticed but without a perceiver there is no noise. It's a Schrödinger's cat event.