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The Quantum Zeno Effect concerns the use of repeated measurement of a particle to prevent the time evolution of the wave function, and hence "freeze" it in the observed state.

A Stasis Field is a science fiction device that holds its contents in a timeless state.

Now, the question concerns the energy requirements of using the QZE to create a stasis field by repeated measurements of its contents.

Since we are acquiring information, which we then discard (because its not a reversible process) we must be using a minimum amount of energy to keep (say) one atom from evolving in time. Scale that up to a kilogram of material via Avogadro's Constant and we can calculate the minimum energy requirements.

Assuming room temperature, or thereabouts, anyone care to offer ballpark figures (correct to within a few orders of magnitude) of the power necessary?

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    $\begingroup$ The rate at which you need to measure a system can be enormous: physics.stackexchange.com/q/33232 Now someone needs to extrapolate to a macroscopic system and apply a little bit of quantum information theory. $\endgroup$ – user10851 Nov 27 '14 at 14:55
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It looks like this experiment is similar to what you're talking about:

Graduate students Airlia Shaffer, Yogesh Patil and Harry Cheung work in the Ultracold Lab of Mukund Vengalattore, assistant professor of physics.

http://news.cornell.edu/stories/2015/10/zeno-effect-verified-atoms-wont-move-while-you-watch

They have a billion atoms of Rubidium, cooled to near absolute zero, "frozen in time" by the Quantum Zeno Effect using a well-timed laser pulse. That's 1.41923×10^-16 kg, according to Wolfram Alpha.

I doubt the experiment scales with a macroscopic sample. But, just say you could do it with lasers, magically, using a similar setup that somehow scales linearly. You'd need 10 quadrillion times the laser energy they've got there. If their experiment uses, say, 1/1000th of a suburban home's electricity, you're looking at using the electricity that would power over a trillion homes, far more electricity than all of the homes on earth.

On the other hand, cryogenics is probably a much more energy-efficient way to "freeze time" for an object, especially a living thing. If you're not trying to keep your sample from undergoing radioactive decay, I'd go cryo!

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Since we are acquiring information, which we then discard (because its not a reversible process) we must be using a minimum amount of energy to keep (say) one atom from evolving in time.

I am not sure if I follow the language completely here (how is a measurement process equivalent to erasure of information?) but if I take it literally, then by Landauer's principle, you need at least $k_B T \log 2$ worth of energy for every bit of information you erase, and to answer the question we need to quantify how many bits we discard for each measurement cycle.

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