Index: src/wp-admin/includes/dashboard.php
===================================================================
--- src/wp-admin/includes/dashboard.php	(revision 43380)
+++ src/wp-admin/includes/dashboard.php	(working copy)
@@ -37,7 +37,7 @@
 
 	// PHP Version.
 	$response = wp_check_php_version();
-	if ( $response && isset( $response['is_acceptable'] ) && ! $response['is_acceptable'] && current_user_can( 'upgrade_php' ) ) {
+	if ( $response && isset( $response['is_acceptable'] ) && ! $response['is_acceptable'] && current_user_can( 'update_php' ) ) {
 		add_filter( 'postbox_classes_dashboard_dashboard_php_nag', 'dashboard_php_nag_class' );
 		wp_add_dashboard_widget( 'dashboard_php_nag', __( 'PHP Update Required' ), 'wp_dashboard_php_nag' );
 	}
Index: src/wp-includes/capabilities.php
===================================================================
--- src/wp-includes/capabilities.php	(revision 43380)
+++ src/wp-includes/capabilities.php	(working copy)
@@ -554,7 +554,7 @@
 				$caps[] = 'manage_options';
 			}
 			break;
-		case 'upgrade_php':
+		case 'update_php':
 			if ( is_multisite() && ! is_super_admin( $user_id ) ) {
 				$caps[] = 'do_not_allow';
 			} else {
Index: tests/phpunit/tests/user/capabilities.php
===================================================================
--- tests/phpunit/tests/user/capabilities.php	(revision 43380)
+++ tests/phpunit/tests/user/capabilities.php	(working copy)
@@ -217,77 +217,77 @@
 
 	final private function _getSingleSiteMetaCaps() {
 		return array(
-			'create_sites'           => array(),
-			'delete_sites'           => array(),
-			'manage_network'         => array(),
-			'manage_sites'           => array(),
-			'manage_network_users'   => array(),
-			'manage_network_plugins' => array(),
-			'manage_network_themes'  => array(),
-			'manage_network_options' => array(),
-			'delete_site'            => array(),
-			'upgrade_network'        => array(),
-
-			'setup_network'          => array( 'administrator' ),
-			'upload_plugins'         => array( 'administrator' ),
-			'upload_themes'          => array( 'administrator' ),
-			'customize'              => array( 'administrator' ),
-			'add_users'              => array( 'administrator' ),
-			'install_languages'      => array( 'administrator' ),
-			'update_languages'       => array( 'administrator' ),
-			'deactivate_plugins'     => array( 'administrator' ),
-			'upgrade_php'            => array( 'administrator' ),
+			'create_sites'                => array(),
+			'delete_sites'                => array(),
+			'manage_network'              => array(),
+			'manage_sites'                => array(),
+			'manage_network_users'        => array(),
+			'manage_network_plugins'      => array(),
+			'manage_network_themes'       => array(),
+			'manage_network_options'      => array(),
+			'delete_site'                 => array(),
+			'upgrade_network'             => array(),
+
+			'setup_network'               => array( 'administrator' ),
+			'upload_plugins'              => array( 'administrator' ),
+			'upload_themes'               => array( 'administrator' ),
+			'customize'                   => array( 'administrator' ),
+			'add_users'                   => array( 'administrator' ),
+			'install_languages'           => array( 'administrator' ),
+			'update_languages'            => array( 'administrator' ),
+			'deactivate_plugins'          => array( 'administrator' ),
+			'update_php'                  => array( 'administrator' ),
 			'export_others_personal_data' => array( 'administrator' ),
 			'erase_others_personal_data'  => array( 'administrator' ),
 			'manage_privacy_options'      => array( 'administrator' ),
 
-			'edit_categories'        => array( 'administrator', 'editor' ),
-			'delete_categories'      => array( 'administrator', 'editor' ),
-			'manage_post_tags'       => array( 'administrator', 'editor' ),
-			'edit_post_tags'         => array( 'administrator', 'editor' ),
-			'delete_post_tags'       => array( 'administrator', 'editor' ),
-			'edit_css'               => array( 'administrator', 'editor' ),
+			'edit_categories'             => array( 'administrator', 'editor' ),
+			'delete_categories'           => array( 'administrator', 'editor' ),
+			'manage_post_tags'            => array( 'administrator', 'editor' ),
+			'edit_post_tags'              => array( 'administrator', 'editor' ),
+			'delete_post_tags'            => array( 'administrator', 'editor' ),
+			'edit_css'                    => array( 'administrator', 'editor' ),
 
-			'assign_categories'      => array( 'administrator', 'editor', 'author', 'contributor' ),
-			'assign_post_tags'       => array( 'administrator', 'editor', 'author', 'contributor' ),
+			'assign_categories'           => array( 'administrator', 'editor', 'author', 'contributor' ),
+			'assign_post_tags'            => array( 'administrator', 'editor', 'author', 'contributor' ),
 		);
 	}
 
 	final private function _getMultiSiteMetaCaps() {
 		return array(
-			'create_sites'           => array(),
-			'delete_sites'           => array(),
-			'manage_network'         => array(),
-			'manage_sites'           => array(),
-			'manage_network_users'   => array(),
-			'manage_network_plugins' => array(),
-			'manage_network_themes'  => array(),
-			'manage_network_options' => array(),
-			'setup_network'          => array(),
-			'upload_plugins'         => array(),
-			'upload_themes'          => array(),
-			'edit_css'               => array(),
-			'upgrade_network'        => array(),
-			'install_languages'      => array(),
-			'update_languages'       => array(),
-			'deactivate_plugins'     => array(),
-			'upgrade_php'            => array(),
+			'create_sites'                => array(),
+			'delete_sites'                => array(),
+			'manage_network'              => array(),
+			'manage_sites'                => array(),
+			'manage_network_users'        => array(),
+			'manage_network_plugins'      => array(),
+			'manage_network_themes'       => array(),
+			'manage_network_options'      => array(),
+			'setup_network'               => array(),
+			'upload_plugins'              => array(),
+			'upload_themes'               => array(),
+			'edit_css'                    => array(),
+			'upgrade_network'             => array(),
+			'install_languages'           => array(),
+			'update_languages'            => array(),
+			'deactivate_plugins'          => array(),
+			'update_php'                  => array(),
 			'export_others_personal_data' => array( '' ),
 			'erase_others_personal_data'  => array( '' ),
-			'manage_privacy_options'       => array(),
+			'manage_privacy_options'      => array(),
 
-			'customize'              => array( 'administrator' ),
-			'delete_site'            => array( 'administrator' ),
-			'add_users'              => array( 'administrator' ),
-
-			'edit_categories'        => array( 'administrator', 'editor' ),
-			'delete_categories'      => array( 'administrator', 'editor' ),
-			'manage_post_tags'       => array( 'administrator', 'editor' ),
-			'edit_post_tags'         => array( 'administrator', 'editor' ),
-			'delete_post_tags'       => array( 'administrator', 'editor' ),
+			'customize'                   => array( 'administrator' ),
+			'delete_site'                 => array( 'administrator' ),
+			'add_users'                   => array( 'administrator' ),
+
+			'edit_categories'             => array( 'administrator', 'editor' ),
+			'delete_categories'           => array( 'administrator', 'editor' ),
+			'manage_post_tags'            => array( 'administrator', 'editor' ),
+			'edit_post_tags'              => array( 'administrator', 'editor' ),
+			'delete_post_tags'            => array( 'administrator', 'editor' ),
 
-			'assign_categories'      => array( 'administrator', 'editor', 'author', 'contributor' ),
-			'assign_post_tags'       => array( 'administrator', 'editor', 'author', 'contributor' ),
+			'assign_categories'           => array( 'administrator', 'editor', 'author', 'contributor' ),
+			'assign_post_tags'            => array( 'administrator', 'editor', 'author', 'contributor' ),
 		);
 	}