Exploiting radiocarbon dating for FTL communication

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[Mentors' note: This thread was split from https://www.physicsforums.com/threads/can-we-carbon-date-a-gas.981218/]

Empirical test:
If one wished to implement a controlled experiment of this sort, start with separating stocks of pure C12 and pure C14 with a mass spectrometer. Use the C12 to grow a diamond epitaxy layer on a silicon wafer covered in an addressable array of a billion MOSFETs (plus a few spares). Then use molecular beam epitaxy to plant a billion individual C14 atoms in the channels of those FETs. Passivate. Measure the switching speed of each transistor. Now wait a while. After 0.00057 years (~5 hours) one would expect to see ~50 FETs change their speed where the semiconductor C14 has become N14 (a Group V, or n-type dopant). Once a FET's speed has changed, it should stay changed (no spontaneous conversion back to C14). The catalogue of which transistors had been doped should grow monotonically at the predicted rate.

Now, if this can be worked, it gets interesting. Make two such wafers, but use entangled (how is a different discussion) pairs of C14 atoms to make wafers of entangled transistors. Separate the two wafers, sending one off into a different relativistic frame (say on a Breakthrough Starshot). That one should age slower. In such a distinct frame, what does Bell's Theorem predict about the result when it reads the distant FETs? Will the inverse decay behaviour happen locally at the remote timescale? Can this be used for a low-power FTL signaling mechanism?
 
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Can this be used for a low-power FTL signaling mechanism?
Leaving aside whether your method would work at all, no. You cannot use quantum entanglement to communicate faster than light. I can predict your measurements (to some extent) instantly, but I cannot control them. So I cannot modulate them and transfer information.
 
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Empirical test:
If one wished to implement a controlled experiment of this sort, start with separating stocks of pure C12 and pure C14 with a mass spectrometer. Use the C12 to grow a diamond epitaxy layer on a silicon wafer covered in an addressable array of a billion MOSFETs (plus a few spares). Then use molecular beam epitaxy to plant a billion individual C14 atoms in the channels of those FETs. Passivate. Measure the switching speed of each transistor. Now wait a while. After 0.00057 years (~5 hours) one would expect to see ~50 FETs change their speed where the semiconductor C14 has become N14 (a Group V, or n-type dopant). Once a FET's speed has changed, it should stay changed (no spontaneous conversion back to C14). The catalogue of which transistors had been doped should grow monotonically at the predicted rate.

Now, if this can be worked, it gets interesting. Make two such wafers, but use entangled (how is a different discussion) pairs of C14 atoms to make wafers of entangled transistors. Separate the two wafers, sending one off into a different relativistic frame (say on a Breakthrough Starshot). That one should age slower. In such a distinct frame, what does Bell's Theorem predict about the result when it reads the distant FETs? Will the inverse decay behaviour happen locally at the remote timescale? Can this be used for a low-power FTL signaling mechanism?

This is a tremendous confusion of ideas!

First, relativistic time dilation, to which you allude, is symmetrical. Both samples are ageing slower in the reference frame of the other.

Second, quantum entanglement results in two correlated sets of data. But, the observers have no control over the data, so cannot use the correlation to send a message.

Third, Bell's theorem predicts what would happen if entangled particles were governed by so-called hidden variables (as opposed to being entangled quantum mechanically). So, what Bell's theorem predicts is generally wrong!
 
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Well, there's only one observer, the terrestrial one. In the observed frame, the distant Starshot sample should age slower. Consider a simple binary message: If life is detected, measure the first half of memory. Otherwise measure the second half. In the terrestrial wafer, does the remote measurement change the decay rate in one half of the FETs compared to the other?
 
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Well, there's only one observer, the terrestrial one. In the observed frame, the distant Starshot sample should age slower. Consider a simple binary message: If life is detected, measure the first half of memory. Otherwise measure the second half. In the terrestrial wafer, does the remote measurement change the decay rate in one half of the FETs compared to the other?

You can't send a message by measuring something. Nothing changes in the terrestrial sample.
 
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If what I say below about factorizable states, commuting observables, and that ##|\rangle## bra-ket notation is unfamiliar to you, you might want to spend some quality time with Giancarlo Ghirardi's book "Sneaking a look at God's cards". It's no substitute for a serious college-level QM course, but it's much more layman-friendly.
All of this is a long-winded way of saying that what you're proposing won't work because quantum mechanics and entanglement don't work the way you're thinking.
Make two such wafers, but use entangled (how is a different discussion) pairs of C14 atoms to make wafers of entangled transistors.
Entangled on what observable? If the two particles are entangled, the wave function of the single quantum system consisting of two particles will have to be of the non-factorizable form ##|\alpha_1\rangle|\beta_2\rangle+|\beta_1\rangle|\alpha_2\rangle## where ##\alpha_i## and ##\beta_i## are the possible results of measuring some observable property of particle ##i##. So which observable are you thinking about, and is it physically possible to prepare such a state?
And whatever observable you're thinking about, it cannot be decayed/not-decayed, because that observable is measured as part of introducing the carbon atoms into their respective wafers.... and of course any measurement will collapse the entangled wave function into one of its two unentangled factorizable states, either ##|\alpha_1\rangle|\beta_2\rangle## or ##|\beta_1\rangle|\alpha_2\rangle##.
In such a distinct frame, what does Bell's Theorem predict about the result when it reads the distant FETs?
Nothing. Bell's theorem is about the correlations between measurements of non-commuting observables (such as spin or polarization on different axes) and here we have no non-commuting observables.
 
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