One of the most common misconceptions in planning and scheduling is that float somehow determines the ‘critical path’. For the PMI-SP exam and any serious consideration of the definition of the ‘critical path’, float is not the right answer.
Associating zero float with the critical path is correct if, and only if, there are no constraints placed on the schedule. As soon as you introduce a contract completion date the critical path may finish before the contract requirement and have positive float or after the contracted completion date and have negative float (and knowing by how much is important to managing both the schedule and the work).
Then add in the common contractual issues of delayed access to areas of work (available on or after a specified date), and mandated interim handovers of part of the deliverables and float goes all over the place. These issues were considered at length when we were writing of the Guide to Good Practice in the Management of Time in Complex Projects.
The description of the critical path developed for The Guide is:
Critical Path = the longest sequence of activities from commencement to completion of a key date, section, or completion of the works as a whole. In relation to each, it is that sequence of activities, which will take the longest to complete or, put another way, the sequence of activities, which will determine the earliest possible finish date. Hence, it is timely commencement and completion of those activities on that path, which will secure completion of the key date, section, or the works as a whole on time.
This description was condensed to a definition in ISO 21500 Guide to Project Management (2012), as:
Critical Path: sequence of activities that determine the earliest possible completion date for the project or phase.
This ‘Standard Definition’ does not preclude the possibility of several ‘completions’ within the one project to account for interim handovers required under a contract. It allows for the possibility of the critical path starting at the beginning of the schedule or at some interim point where an external dependency allows the ‘critical’ work to start. Additionally, the sequence of activities may be determined logically (through links or dependencies) or through the sequential movement of resources. The definition is both concise and unambiguous. For more see: http://www.mosaicprojects.com.au/WhitePapers/WP1043_Critical_Path.pdf
You need to get with the game – people who want to ignore the current international standard definition will become increasingly marginalised as the various national standards move into alignment with ISO.