I also direct you to the definition of “flight training” as per § 61.1(b)(6) which states: “Flight training means that training, other than ground training, received from an authorized instructor in flight in an aircraft.” (Emphasis added: “in flight in an aircraft”). Furthermore, § 61.51(h)(1) addresses logging of training time as “A person may log training time when that person receives training from an authorized instructor in an aircraft, flight simulator, or flight training device.”
However, time in a flight simulator or flight training device cannot be logged as “flight time” or as “PIC flight time” or as “SIC time” or as “night time” or as “daytime” or as “cross-country time” or as time in an “aircraft category, class, or type.” Time in a flight simulator or flight training device can only be logged in the columns noted as “Flight Simulator or Flight Training Device” time and “Dual Received” time. And in most logbooks, the person has to write in the notation “FS/FTD” as a heading on one of the extra columns. And in some logbooks they do have a column noted as “Synthetic Trainer.”