When I was 11, my family and I travelled on a ferry to Spain that had a swimming pool. At the time, I thought it was quite possibly the most amazing invention at sea. I had a similar feeling two weeks ago, when I was given the opportunity to test out the sky-diving simulator while Quantum was docked in Southampton.

Yesterday, however, surpassed even that, as we rose up in the North Star and gazed down on the Statue of Liberty and the skyline of Manhattan.

This is of course exactly the reaction Royal Caribbean was aiming for with Quantum of the Seas. In its advertising, the cruise line says its latest addition is “part spaceship, part cruise ship” and will “wow you from bow to stern”. And the strapline says simply: “This changes everything”.

There were certainly plenty of raised eyebrows and impressed faces from the paying passengers I spoke with yesterday, as the ship left port in Cape Liberty, New Jersey. This admittedly may have been enhanced by the stunning Manhattan skyline, which sparkled in the night as we sailed up the Hudson and past the Statue of Liberty.

“As we sailed up the Hudson, I noticed one employee Skyping his family to show them the lights of Manhattan”

Later on, passengers seemed particularly impressed with the four complimentary restaurants onboard – part of the ship’s new “dynamic dining” concept, which has replaced the traditional dining rooms on the rest of the fleet – and with the bionic robots (which seemed to suffer a few malfunctions in Southampton) were busy entertaining guests with their cocktail making.

Quantum has been billed as the world’s first smartship, designed to offer the fastest satellite internet on a passenger ship in the world. Wifi seemed to slow and falter in certain areas of the ship, but as we left port it strengthened, and it seemed that Royal Caribbean’s promise to allow guests to remain connected at sea had been fulfilled.

As part of this commitment to boosting its technology, the line has also pledged to give each of its 40,000 ship-based employees a Windows tablet to help them to keep in touch with their loved ones. Last night as we sailed up the Hudson, I noticed one employee Skyping his family to show them the shimmering lights of Manhattan.

The chairman and chief executive of Royal Caribbean Cruises Ltd said yesterday that choosing a ship’s name was typically a “controversial process”, however when someone suggested the name Quantum for the company’s latest addition to the fleet, “the room fell quiet”.

“Everybody knew that we had the name, because you can’t say ‘quantum’, without thinking ‘leap’, and that’s what this ship is,” Richard Fain explained.

He is right. And with Quantum and sister ship Anthem of the Seas having been designed to target the much-coveted new-to-cruise market, it might just be the biggest leap the cruise industry has seen in a long time.