Winewood. Um that was not proof. Just a story of a practical example of how the sense of time depends on "good" record keeping.
I think that time being a 4th dimension is flawed ( or at worst I don't understand what a dimension is).
If you want to invent a dimension as a part of a coordinate plane so you can solve a few motion problems fine, but that does not imply that time exist.
Colors don't exist but the concept helps people identify some objects.
I almost believe space exist, and time may be a coping mechanism to explain how the universe restructures things in that space before our eyes with out becoming static or broken. Time could be the first religion

.
Airspirit you can't travel in something that does not exist (if you believe that way). Thats like trying to make unobtainium. Once you make it, it is not unobtainium.