When planing on visiting the USA, there are different steps one needs to take to fill the requirements for a visa-free entry.
The traveler needs to be a citizen of a member state of the Visa Waiver Program (VWP). Switzerland is one of 36 countries in the VWP, that are considered as developed countries with high-income economies.
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Secondly, the passport needs to meet the criteria required. The Swiss Government has changed the Swiss Passport 4 times in the last ten years. One can visit the USA without a visa if in possession of a "Passport 03" if issued before October 25th 2006, a "Passport 06" or the new "Passport 10". With a "Passport 03" issued later than October 26th 2006 and a "Provisional Passport", one needs to apply for a travel visa which would be a big administrative effort.
Fortunately, I possess an early "Passport 03" meaning I will not need a visa.
When not in need of a travel visa, the traveller nets to fill out an ESTA travel permit. With this ESTA form, one declares to not have illnesses or addictions, not to have any criminal intentions or not to plan on applying for a citizenship or a work visa. It is only since July 1st 2010 when the green form one had to fill out on the airplane disappeared. Since then, one needs to fill out the same ESTA form online at least 72 hours before departing. This form refers only to getting there, the actual permission of entering the country is still given by the local authorities at the airport.
Before take off the Airline sends all the personal data including passport number and address in the USA and so on to the local authorities. If all 4 criteria are met, one is allowed to enter the USA without a visa.