The amicus brief in support of DOJ’s cert petition in Jones is here. The brief doesn’t really have much to do with GPS surveillance, but it’s interesting that it advocates a rejection of privacy as a Fourth Amendment guide and a return to property as a guide — including back to the common law “mere evidence” rule, by which the government cannot get a warrant to obtain mere evidence. If I understand the brief, then, the amici are not arguing that a warrant should be required for GPS surveillance: Rather, they are arguing that GPS surveillance should never be allowed even if the police have probable cause and a warrant.
For what it’s worth, I actually don’t think the Fourth Amendment has really changed much on the specific issue of whether its rights track privacy or property interests. Scholars often to say that the Fourth Amendment used to protect property, but that in 1967 it dropped property and instead embraced privacy. That’s the narrative Justice Brennan pitched in his majority opinion in Warden v. Hayden. But it strikes me as quite wrong. The Fourth Amendment has always tracked a complex mixture of both property and privacy interests, from the first Fourth Amendment cases onwards. I wrote about some of that in part 1 of this article, and I hope to get to the other half of the argument in a future essay.