I told the RailEurope agent I wanted to travel from Interlaken in the morning, spend the day in Luzern, and then travel to Zurich in the evening. What he sent me is an open ticket from Interlaken to Zurich. Can I hop off the train in Luzern in the morning and hop back on a different train several hours later the same day and use the same ticket to complete my travel to Zurich?
you could have simply walked up to any ticket counter anywhere in Switzerland and bought that simple ticket probably for half the price AND not shipping costs. Does that mean you're staying in Interlaken, too? Hopefully that answer is no. Interlaken is NOT in the Swiss Alps, but just a gateway to them. 20 more minutes on the little train deposits you in one of the most beautiful areas in the world complete with hotels, B&Bs, grocery stores and restaurants.
Swiss train tickets are flat price, based on distance, no discount for advance purchase and all tickets are valid on all trains.
The fare from Interlaken Ost to Zürich HB is CHF 67.00, 2nd class single without discount card, via the quickest route, that is via Bern and Olten.
If you paid more than that you were ripped off.
Interlaken - Luzern - Zürich costs CHF 49.00. This is cheaper because it is shorter, but takes longer! Between Interlaken and Luzern it goes via the scenic Brünigbahn. Yes, you can get off en route.
Within Switzerland the cheapest option is always to buy from the ticket machine on the day.
Interlaken is in the Swiss Alps, more so than Luzern, which is just on the edge (with good views).
Check train times and prices on the Swiss Federal Railways website: www.sbb.ch