How can PHP be used to initiate downloads from a different server without opening a new window?

To initiate downloads from a different server without opening a new window in PHP, you can use the `header()` function to send the appropriate HTTP headers to trigger the download. You can set the `Content-Disposition` header to `attachment` and provide the file name to prompt the browser to download the file. Additionally, you can use the `readfile()` function to read the file and output its contents to the browser.

<?php
$file_url = 'http://example.com/file.zip';
$file_name = 'file.zip';

header('Content-Description: File Transfer');
header('Content-Type: application/octet-stream');
header('Content-Disposition: attachment; filename="' . $file_name . '"');
header('Expires: 0');
header('Cache-Control: must-revalidate');
header('Pragma: public');
header('Content-Length: ' . filesize($file_url));

readfile($file_url);
exit;
?>