The date is a system-wide parameter that is crucial for the system (not the user). It appears in filesystem timestamps, logging, daemon operation, scheduling and so on. Many programs break or may even corrupt your system if the date is not accurate. So in this sense, the time has to be continuously increasing and correct not only locally, but if any non-www networking is done, also globally. Even certificates stop working if there is too much time difference between client and server.
So in this sense, the system date/time is only one - the actual date/time (preferably in UTC, otherwise your laptop's filesystem may break when you switch timezones).
On the other hand, the timezone setting is just a translation layer from UTC to the date-time that is presented to the user. That can be changed (see the comment by X Tian). But I don't know if that is what you want - it can only set an integer (sometimes fractions of integers) number of hours, never more than a day. It's technically possible to construct a custom timezone to induce arbitrary delay, but it's an ugly hack.
All basic manipulation of time still deals with the unix time (an integer that ticks uniformly from 1/1/1970), so the locale (timezone & stuff) is usually only used for visual display of time, or some very specific uses in scripts that rely on this functionality. For instance, the
clock_gettime function that retrieves the system time, and then calls
localtime to translate into the current locale. The internal representation is always system time.
There may be special kernel modules to do that - or replacement libraries. You could create a corrupt library with adapted
clock_gettime function and make it visible to one user. I have no idea how would this affect your system. The filesystem manipulation and stuff like that is still handled by the kernel, so the essentials would work. However, scheduling, backup facilities and makefiles may not work correctly.
EDIT: maybe what you want is a virtual machine. That is then more isolated and if you wanted to change the time, you could. It's sometimes useful to circumvent time-triggered software failures.