I live in a timeline where time travel has not yet been invented. Even if someone invents it in the future and travels to the past to the party, that'd create an alternate timeline where the party is attended and civilization leaps bounds ahead in glorious post-scarcity, magical socialism fashion.
But nooooo since the timeline was forked at that point, no matter how many people do, in fact, attend the party, I'm stuck in the "strand" of the timeline when no one ever did because time travel has not been invented.
There's different ideas on how time travel "could" work and one of them is the timeline-split notion upon which you base your idea. In that vain it's solid.
Other ideas are that time travel always results in a loop or that its perhaps only possible under very specific circumstances (ie you can't pick an arbitrary location or time to travel to nor to travel from).
My hunch is that even if time travel were possible there's simply no practical experiment to tell whether you are in a split timeline (and if so how it differs from others), aka it's outside of the realm of scientific // logical inquiry.
If y'all like exploration of time travel go watch the show Travelers some time. It has some interesting premises in that regard.
There is also the Paycheck method. There is no travel you can only observe by looking through a special "time telescope." Maybe plenty of people observed the party, they just weren't able to physically attend.
First I ever hear of the Paycheck method honestly, at least under that name. Reminds me of a short story about the government keeping a secret "chronoscope" machine and the efforts of the MC to democratize that knowledge.
There is also the harry potter version, any time travel is woven into the only timeline. The past is "edited" to always have included the events time travel.
This can be considered similar to the branching method; where the original branch without the events of the time travel simply ends; only the "new" branch continues.
However, IF, your theory is accurate, then you are the prime instance of you. All time travel alternatives are just YOU in another scenario, not different versions of each other, they are all YOU.
Depends on how you see it. It could also be that for some reason or another even with backwards time travel no one shows up. And thus you avoid having a paradox
Or it could be like a time portal so once you build one you an travel back to any point it existed in but one to a point where it doesn't exist since you need time travel infrastructure
I mean, that for the most part makes sense. Although in that case, wouldn't it have been reported that "no one attended the party but the food and the snacks were somehow missing"?
That said. Unsure how exactly it went but I read somewhere that if you had the power of True Invisibility, that is being undetectable at any wavelength of light, then you'd basically be able to simulate negative mass, and from there to "time travel" it's kind of a straight line.