AngularJS - Why does $scope.$apply affect other scopes - angularjs

Question

In my AngularJS app, I have 2 controllers which are not nested. Calling the $scope.$apply method seems to affect the other sibling scope as well.
In the jsfiddle below, it seems that the ControllerOne's {{doubleMe(x)}} expression is evaluated whenever ControllerTwo updates the clock every second. This can be shown from the console message.
I can understand why that expression is evaluated whenever the text input (on the same scope) changes, but why would $scope.$apply on another scope cause that expression to be re-evaluated as well?
Note that I could have avoided $scope.$apply by using $timeout, but the outcome is observed.
<!-- HTML file -->
<div ng-app>
<h1>Root</h1>
<div ng-controller="ControllerOne">
<h2>Scope One</h2>
1 * 2 = {{doubleMe(1)}}<br/>
2 * 2 = {{doubleMe(2)}}<br/>
3 * 2 = {{doubleMe(3)}}<br/>
<input ng-model="text">
</div>
<div ng-controller="ControllerTwo">
<h2>Scope Two</h2>
{{clock.now | date:'yyyy-MM-dd HH:mm:ss'}}
</div>
</div>
// js file
function ControllerOne($scope) {
var counter=1;
$scope.doubleMe = function(input) {
console.log(counter++);
return input*2;
}
$scope.text = "Change Me";
}
function ControllerTwo($scope) {
$scope.clock = {
now: new Date()
};
var updateClock = function() {
$scope.clock.now = new Date()
};
setInterval(function() {
$scope.$apply(updateClock);
}, 1000);
}

Answer 1

as you can see $scope.$apply = $rootScope.$digest //+ some error handling and since $scope.$apply uses $rootScope it affects all its descendants.
so If you update a child scope, you can call $scope.$digest to dirty-check only that scope and its descendants and as a result you reduce the number of dirty-checks and increase your performance.
Example
I changed your code and added $digest.
setInterval(function() {
$scope.clock.now = new Date();
$scope.$digest();
}, 1000);
Live example:
http://jsfiddle.net/choroshin/JY5sb/4/

Answer 2

From the AngularJS docs in the source code
* # Pseudo-Code of `$apply()`
* <pre>
function $apply(expr) {
try {
return $eval(expr);
} catch (e) {
$exceptionHandler(e);
} finally {
$root.$digest();
}
}
* </pre>
Alex is correct that if you just want to have your changes reflected in the current scope and its children, scope.$digest() is the thing to use. However, AngularJS often discourages this since expressions often have side-effects that modify global objects like services which can in turn modify sibling scopes.