Diamond Enthusiast

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Is it possible? Yep
However I doubt it would be like Star Trek, with just a transporter being able to pinpoint and rearrange the molecules back into the correct order.
There are two methods that come to mind:
1. To disassemble the body and convert all the matter into energy, send that along with a detailed map of the body to another location, convert the energy back into matter and then reassemble as per the map.
This method is, well, energy expensive. Converting matter to energy and energy to matter requires a lot more energy than it is worth.
Method 2 is more promising:
Map the body, send the map to another station, that station holds all the key elements, and assembles the atoms in their proper places. Signals station one when complete so station one can disassemble the body to its respective atoms.
In this case we are making a copy, the original material is not used or sent to the receiving station.
These are your Star Trek variety kinds of transporters.
There are also the possibilities of Worm Holes (Einstein/Rosen bridges) and there may also be trans-dimensional crossings. In these cases the universe moves and not the body (relatively speaking)
What is needed? For Options 1 and 2 a powerful enough computer and a sensor array that can map the position of every single atom in the object to be transported in a split second.
A means to send a pure signal over a distance to where there will be Zero change in the map (or so close to zero that no one can tell the difference).
A means to move atoms and place them precisely in a 3D space in a split second, and also to take them apart without an explosion.
For option 1 a really, really big source or energy. For option 2 A really Big source of energy.
For the last two options all we need is a way to open a portal to X dimension, or to create a wormhole that connects point A to point B.
Some would say that this has been done before, while others say it requires a lot of mass and energy. For those who said its already been done, they placed the date of this near or around 1950 and according to them all that was needed was a big naval ship generator.
I say that though it is possible it is not really practical for every day applications or global distances (even interplanetary distances the expense would be daunting).
However, for long range interstellar distances, this may be the way to go at some future date. But, it would require the sending of a receiving station via the slow road, have it set up at your destination then start transporting. Here the economics of time = money pay off. The worm-hole or trans-dimensional portal would nearly instantaneously transport a person stepping around the Light Speed barrier.
Options 1 and 2 would still take years - since signals travel at the speed of light - Unless one starts thinking along the lines of tachyons (particles reputed to travel faster than light) for your signal medium.
Mind we still do not know if Gravity is a particle (gravaton) or a wave form (like radiation) We have not unlocked all the secrets of electo/magnetic force, weak force and nuclear force either. Further, we still are lacking a Grand Unified theory which brings everything together - That suggests that we missed something in all of our physics - we missed a connection there, one which may hold the key to teleportation at pennies a teleport.
With what we know of physics we can theorize methods to travel not only through space, but through time as well. All in theory, but all thought provoking and giving hints to possibilities which no man has dared dream before.
Cheers
David
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