Why are all fields in an interface implicitly static and final?

An interface is intended to specify an interaction contract, not implementation details. A developer should be able to use an implementation just by looking at the interface, and not have to look inside the class which implements it.

An interface does not allow you to create an instance of it, because you cannot specify constructors. So it cannot have instance state, although interface fields can define constants, which are implicitly static and final.

You cannot specify method bodies or initializer blocks in an interface, although since Java 8 you can specify default methods with bodies. This feature is intended to allow new methods to be added to existing interfaces without having to update all the implementations. But you still cannot execute such a method, without first creating an instance implementing the interface.

Aside: Note that you can implement an interface with an anonymous inner class:

interface Foo {
    String bar();
}

class FooBar {
    Foo anonymous = new Foo() {
         public String bar() {
             return "The Laundromat Café";
    };
}

You have to provide the full implementation of the interface for the anonymous inner class to compile.

new Foo() is initializing the anonymous inner class with its default constructor.

Reason for being final

Any implementations can change value of fields if they are not defined as final. Then they would become a part of the implementation. An interface is a pure specification without any implementation.

Reason for being static

If they are static, then they belong to the interface, and not the object, nor the run-time type of the object.

The fields must be static because they can't be abstract (like methods can). Because they can't be abstract, the implementers will not be able to logically provide the different implementation of the fields.

The fields must be final, I think, because the fields may be accessed by many different implementers allows they to be changeable might be problematic (as synchronization). Also to avoid it to be re-implemented (hidden).

Just my thought.

There are a couple of points glossed over here:

Just because fields in an interface are implicitly static final does not mean they must be compile-time constants, or even immutable. You can define e.g.

interface I {
  String TOKEN = SomeOtherClass.heavyComputation();
  JButton BAD_IDEA = new JButton("hello");
}

(Beware that doing this inside an annotation definition can confuse javac, relating to the fact that the above actually compiles to a static initializer.)

Also, the reason for this restriction is more stylistic than technical, and a lot of people would like to see it be relaxed.