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About teleportation in Star Trek

A friend once asked me about which of two methods was easier to teleport people. One consisted of "deconfiguring" and "reconfiguring" the person (as information, similar to Start Trek and the other in "creating a shortcut" between two places in space-time to pass to the person. Obviously, in both cases assuming that such things can be done.

Regarding the creation of the shortcut in space-time, I think I have not studied the equations of General Relativity to be able to do the math, although perhaps in Física Pasión give us these calculations.

The first of the alternatives consists of, basically, the representation of a person as information and its "deconfiguration" processing, transmission and processing of "reconfiguration". Since as humans we are made, mostly, of water we will assume a person of water for the calculations. We will also take as reference mass \(70\, \mbox {kg}\).

Some data that we will use are:

  • The molar mass of water is \(M_{H_2O}=18,01528\ \mbox{g/mol}\);

  • Avogradro number is \(N_A=6,022 \times 10^{23}/\mbox{mol}\).

Then, we have that the number of moles in a person is

\begin{equation*} m_\text{persona} = \frac{70\ \mbox{kg}\ \mbox{moles}} {18,015\times 10^{-3} \text{kg}} =3885,7\ \mbox{moles}\, , \end{equation*}

and the number of molecules is

\begin{equation*} N_\text{moleculas} = N_A m_\text{persona} = 2,34\times 10^{27}\ \mbox{moleculas}\, . \end{equation*}

Water has 12 vibrational and 6 translational modes, and furthermore 40 quantum electronic numbers. This add up to 58 degrees of freedom for each molecule. Thus, the total number of degrees of freedom is

\begin{equation*} N_{GDL} = 1,36\times 10^{29}\, . \end{equation*}

In 2011 there was a transmission record of 186 Gb/s, considering this rate the time it would take to transmit all data (assuming data represented as 32 bits real numbers) would take \(2,3 \times 10^{16}\ \mbox {s}\) or, equivalently, \(1.70 \times 10^{10}\) years (the estimated age of the universe is \(1.37 \times 10^{10}\) years).

If we wanted this to happen really fast, say in 1 millisecond, the transmission rate should be \(2.3 \times 10^{19}\) faster than the record they reached at CERN… something that is inconceivable for us today.


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