Launching an X application from a locally running Apache web server using PHP

Question

I have Apache and PHP running on my local Linux desktop. My PHP script launches "xcalc", and looks like this:

<?php
    shell_exec("xcalc");
?>

When I execute the PHP script using the PHP binary, I see xcalc running on the desktop. When I execute the same script through Apache, I see nothing happening on the screen. I can't figure out where it fails.

I changed Apache's User and Group to a regular user, just to make sure that all X settings are correct.