The variable variable syntax does not allow this.
Would it make sense in your case to do one of these things instead?
Use a variable as the array index:
$joe["where_you_going"] = "hey joe";
$something = "where_you_going";
print_r($joe[$something]);
Use a variable as the name of the array and another as the index:
$joe["where_you_going"] = "hey joe";
$something1 = "joe";
$something2 = "where_you_going";
print_r(${$something1}[$something2]);
Use eval to evaluate the whole expression:
$joe["where_you_going"] = "hey joe";
$something = '$joe["where_you_going"]';
print_r(eval("return {$something};"));