How did the Philadelphia Experiment and Montauk stories get tied to UFOs?

The short version is that the Philadelphia Experiment story grew from claims about a wartime naval invisibility test, while Montauk lore came later and added secret research, mind control, and time travel. The connections between them are part of the later mythology, not something established by reliable historical records.

They get discussed alongside UFOs because both stories offer a ready-made explanation for strange sightings: hidden technology, unusual experiments, and government secrecy. That makes for an intriguing story, but it is different from evidence that either project happened as described or drew UFOs to Earth.

A useful way to approach this is to separate the documented setting from the extraordinary claims. The Navy had ships and research facilities, and Montauk had a military installation. Those ordinary facts give the stories recognizable locations and institutions. They do not, by themselves, verify invisibility, teleportation, time travel, or contact with nonhuman craft.

When one legend borrows details from another, the shared ingredients can make them feel like parts of a single program. But a claimed link needs evidence of its own, such as credible contemporary records. I would treat the time-travel connection and the idea that Montauk increased UFO activity as speculation unless such evidence turns up.

They are compelling stories partly because they mix a little history with a lot of narrative. UFO discussions often welcome claims about secret experiments since they seem to connect sightings, military secrecy, and advanced technology. Once those ideas circulate together, the stories can reinforce each other even without independent evidence tying them together.

That does not mean you cannot enjoy the lore. I would just keep two questions separate: what can be checked in historical sources, and what belongs to later retellings or speculation.