The opening chapters set up the possibility of voyaging through time. While most of his friends are skeptical, the Time Traveller believes his Time Machine will work. And then...it does! (It's not so much a "fall" into another world, though, as a very conscious jump.)
The Time Traveller is largely confused by the beautiful world he finds. He really drives these two qualities (confusion and beauty) home – for instance, the speech of the Eloi is beautiful but he can't understand it. What could be better for an explorer than a beautiful, mysterious world? (Imagine if he had gone to an ugly, straightforward world – not very interesting, right?)
Exploring the future seems like fun as long as you know you can leave anytime you want. Once the Time Machine goes missing, the Time Traveller, to use the technical term, freaks out. He can't find the Time Machine anywhere, which must be very…what's the word?...frustrating. The future world becomes increasingly alarming. First he startles some animal while running through the trees (even though he's told us that there aren't any large animals left in the future). Then he sees some ghost-like shapes running with some object (and that's after he's woken up from a dream of being touched by soft hands). Then he sees a Morlock climb down a well.
Here's our checklist for the perfect nightmare: you're in a small, dark space, you can't see or move, and you're surrounded by groping monsters that want to eat you. That's what the Time Traveller faces when he goes to investigate the Morlocks' home underground. For a pretty good (but not perfect) nightmare, we'd trade in the claustrophobic underground space for a forest fire. That's what the Time Traveller faces on his way back from the Palace of Green Porcelain.
In The Time Machine, the "Thrilling Escape" stage is probably when the Time Traveller thrillingly escapes from the Morlocks. But then he also goes through a few more thrills. First he sees the inhuman inheritors of the earth, the butterfly and crab monsters. (The Eloi and the Morlocks weren't really humans either, but they were clearly our descendants.) Then he goes on to see a nearly lifeless, silent beach. Only after all these thrills does the Time Traveller return home to share his wisdom. As usually happens when one tries to share wisdom, no one listens. The Time Traveller has had this profound experience, but everyone else just thinks it's a fun story. Then the Time Traveller disappears. It kind of sounds like we might still be in the nightmare stage.