I can currently imagine two possible (though currently only science fiction) methods for Teleportation, loosely defined as near-instantaneous relocation of matter from one place to another.
Method 1 – shortening the distance between the two places through some method such as a ‘wormhole’ or ‘sub-space doorway’ etc, and then stepping through this doorway. While no such technology exists, I think this is totally within the realm of Torah and belief in Hashem. For simplicity, and to hint at why I think it is compatible with Judaism, we can call this “Kevitzus Haderech”. Sound familiar??
Method 2 – Converting all matter on site A into purely digital or other ‘transmittable’ signals, waves, or particles, then transmitting them to site B and reconstructing them into their original form. I believe that this method is impossible according to Judaism and it’s tenets. Since a human consists of more than just physical particles, but also contains a Neshama (and maybe a Ruach too depending on how you define these terms,) once it is deconstructed, it is dead. It cannot be ‘reconstructed’ by a machine. Also, if that were possible, we would be able to save the electronic ‘digital image’ of the deconstructed person and then replicate it by reconstructing it more than once. We would be able to create people using something like a 3D printer, and call it ‘alive’! Of course, it would still be missing the Ruach and Neshama, so it can’t be alive. That was Frankenstein’s dilemma. You can call this one ‘Yesh MeAyin’!
See lightbrite? someone did think about this!