You don't need to know more physics. If you see something (a particle fe) disappear, and reappear somewhere else then a possible explanation is that it got ther

You don't need to know more physics. If you see something (a particle fe) disappear, and reappear somewhere else then a possible explanation is that it got there via another dimension. So if you eliminate all other possible explanations, the only remaining one is that there must be more dimensions. However, since things appearing and disappearing does not happen on macroscopic scale, the dimensions must be small.