Assuming time travelers are real, but only influenced events so far back enough that a smartphone they lost in the past didn't survive for archeologists to find, how far back are we speaking?
And what were the dominant terrestrial species at said time? Would there even be any? I have zero idea of what's the expected survival rate of an iPhone in the fossil record, but I like to imagine a giant sloth stepped on one once and we are none the wiser.
Alternative title:
"Assuming the timeline is stable and time travel is possible, but no evidence is ever found until its invention, what would be the earliest acceptable time period for time-travel tourism, and the latest cut-off point no one would be allowed to go to?"
If they dropped just one piece of future tech, the chances of any archaeologist ever finding it is infinitesimally small even if it could survive indefinitely. They haven't dug up every inch of the earth's surface. The stuff they find is the stuff that was common enough for them to have a decent chance of finding it.
I know you updated the post and what you're really interested in is any tech they dropped not surviving, but I wanted to point out that "cell phones" would be useless with the infrastructure. They would be better off bringing radios or Star Trek-like communicators which transmit directly from one to another.
I was actually thinking of tourists taking photos in the past with cameras, but I found that a smartphone would be more realistic.
Ah, yep. So more like they bring their multi-function communication / information / documentation / entertainment devices with them. Heck, they may even use those devices for the time-travel itself. And then when they get to the ancient past, they pay no attention to the scenery and just watch reruns.
No idea.
Hawking threw a party once to see if any time travellers would turn up.
They need to go back to when earth was very hot ball of molten metal. Anything more recent than that means there is a non zero chance that the smart phone or parts of it would remain intact. There is also a chance of turning into a fossil (the phone gets buried into some mud, the mud dries and turn into a rock, eventually the phone dissolve and disappear leaving behind its print in the rock
You could go check out Earth 1.0 before the collision that created the moon and melted the Earth in the process.
Can't tell precisely since there are conditions, that might conserve a piece of technology to the point that it's still going to be recovered and recognized as OOPART.
I guess that a million years or further is relatively safe bet, but even that isn't granted.
TIL; "Out of Place Artefact"
Do not mistake with OP ART.
Assuming the time line is stable I would say any time in before a global catastrophic event such as the K-T dinosaur extinction event since any meddling there will be likely erased by the destruction. The latest cut-off point should be when the first true humans appeared, around 2-6 million years ago.
However, how does your novel account for not disrupting the timeline? Is the model a parallel universe, i.e. going back in time creates a new reality branch? If such is the case, then there are ethical issues for the putative time traveller.