Donald Trump is mad at Twitter, Facebook, and other big technology companies, and in an Oval Office statement on Thursday, he pledged to do something about it.

“A small handful of social media monopolies controls a vast portion of all public and private communications in the United States,” he said. “They’ve had unchecked power to censor, restrict, edit, shape, hide, alter, virtually any form of communication between private citizens and large public audiences.”

After his comments, Trump signed an executive order designed to bring social media companies to heel. But Trump has a problem: US law doesn’t give the president much actual authority over technology companies. Indeed, the First Amendment arguably prohibits the federal government from second-guessing the editorial decisions of private companies like Facebook, Twitter, and Google.