Why Star Trek’s Transporter Will Never Be

As an engineer I totally love Start Trek, from Enterprise to Warp Drives to inspiring technologies such as cell phones and tablets. But certain technologies in the sci-fi-verse will never fracking be. One of them is the famed transporter of Star Trek.

Basically, there are 2 ways to teleport, one is by quantum entanglement, which is when 2 or more particles are in superposition, then they can be separated and any change in one will instantaneously happen on the other. We’ll save a discussion on this later. The other, is by converting matter to energy a la Einstein and modulating that energy to a data stream, then beaming that data down, to say, a habitable planet at which the data/energy stream is then converted back to matter where a hopeless red shirt suddenly appears.

At first glance, I always thought the two transporter ideas were theoretically possible, but after further scrutiny I realized there is no fracking way the latter could ever be achieved. Why? For us engineers , if we dig deep to the remote recesses of our ape brains, pass the depleted neurons due to binge drinking and sleep deprivation (from cramming for a test the night before) we remember that little thingy called the Shannon Limit! Oh yeah!

The Shannon Theorem essentially states there is a theoretical maximum data rate of a communication channel and quantitatively it looks like this:

data rate = B*log2(1+SNR).

What this means is that we can only beam down so much data per unit of time. There are other factors that affect data rate such as channel encoding, compression, modulation type, etc., but for simplicity we’ll ignore these for now.

So, assume we want to beam down to a habitable planet in this manner. We would be limited to the microwave, terahertz and certain atmospheric windows of far-infrared radiation of the electromagnetic spectrum because visible light and radiation above UV would be blocked if not at least severely attenuated, to use the engineering vernacular, by the atmosphere, fog, dust, smoke, clouds, etc. We can expect our transporter to work in various weather conditions.

Microwaves can pass through all of these, even buildings, so we can have the option to beam down our most revered tribbles to our grandmother’s kitchen. As a result, we are limited to frequencies below roughly 100 Terahertz or so (3 um in wavelength). Anything above would be in the near-infrared and or visible range and would be blocked by walls, etc. therefore rendering our beaming ability into buildings useless. If we include the microwave and terahertz wave bands, essentially we are limited to roughly 101 terahertz of bandwidth to beam all the info of a human body for reassembly on the planet surface. Bandwidth is the B in our equation above.

Now, how much data would it take to convert the human body into bits? Well, good question! I think we would have to know about the body on the molecular level to convert the body from matter to energy and then back again, at least to me that makes sense. From here on, I’m guesstimating but bear with me the exercise bears fruit.

Assume it would be possible to encode every molecule in a human body to its own 256 bit sequence. This sequence would tell the necessary info of the molecule such as chirality, location, composition, etc. and all the necessary info to reassemble the energy back into a human body. So, how much data are we talking about then? It comes out to be the # of molecules in your body multiplied by 256 bits. That’s a hell of a lot of data roughly, 256 * 10^25 bits or 64 yottabytes or 64 billion terabytes. The actual numbers aren’t important, what is, is that it will take a massive amount of data to convert the entire human body into a data stream for the teleporter to transport!

Now, assume our teleporter system is really powerful so we can transmit with a received SNR of 30 dB. Our equation now comes to:

Data rate = 101 * 10^12 * log2(1001) =~ 1010 terabytes per second

Due to the Shannon limit, and from the fact we want to beam through various atmospheres and into buildings our teleporter is limited to transporting ~1000 Tb per second. We now see the issue here. It would take an incredible long time to beam our 64 billion terabytes of data through a teleporter limited to somewhere around 1000 terabytes per second. Roughly around 2 years!! I don’t think the crew of Star Trek would want to wait that long! It would be far better just to take a shuttle down to the planet surface.

Now we roughed over a lot of the details but I feel the points have been strongly made even if we fudged around with the numbers. The basic points are that it will take an incredible amount of data to encode the entire human body onto a data stream. And second, we are bandwidth limited due to the physical restraints of what we are trying to accomplish. That is, beam through atmospheres and into buildings for instance. A teleporter of this type might be more practical for beaming from ship to ship in space, and not have to worry about atmospheric attenuation or beaming into a building, therefore greatly increasing the available bandwidth. And possibly reducing the teleportation time. So for now, we are dependent on some sort of quantum mechanical way of teleportation.