If it’s true, both parts must be true, including the part that says “this statement is false”. As this part is describing the WHOLE statement, if it’s true, the whole statement is false. As this is contradictory, the whole statement cannot be true. Therefore, the statement is false.
In order to be false, ONLY ONE PART of the statement must be false. Now that we know the statement is false, the part that says “this statement is false” is obviously true. Therefore, the second part of the statement, “time travel is NOT possible” must be false.
Therefore, time travel is possible.
