By mathematical definition, any activity with a TF of 0 is a critical activity. This is logical, since TF is the float available to an activity before it starts impacting the finish date of the project. By application of this principle, the chain of all critical activities will run straight through start-finish, thereby equaling the project’s duration. In other words, a project of 30 days duration must ha…ve a critical path equaling 30 days in length.
It is possible the critical path may be less (or more) than 30 days in which case the network governed project finish date will also be earlier (or later) than the available 30 days. However, we are not considering exceptional scenarios here although universally in all such cases the total run of the critical path would equal project duration.
When a schedule is first made, and as is evident from the above discussion, the critical path will be the (longest) path running through the schedule, from start till the end. (** This makes for an interesting discussion; Whether the critical path is the longest path or the shortest?; Please refer an earlier post for the same).
So far so good. At this point, critical path equals longest path.
Suppose for the entire month nothing is started and no progress is made at all. At the end of the month when the network is recalculated, the longest path would still be the same (and the critical path as well). However, computing TF and applying contractual project finish date for the backward pass, many of the earlier non-critical activities will have varying levels of TF reduction; some will even become zero or negative (in this example all would be negative). Irrespective of this mathematical result, not all ‘critical’ activities will affect project finish. As determined earlier, tt would still be the activities on the longest path (which will all surely be negative TF). This is the difference between critical ‘activities’ and the longest path.
Extending the explanation a little further, with changing progress scenarios, the critical activities (various critical paths) will change over time, however, it will always be the (remaining) longest path (or critical path # 1) which would govern project finish.