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This is a screenshot from Edward P Tyron's article "Is The Universe a Vaccum Fluctuation?"

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The explanation Energy-time uncertainty principle from Griffiths:

$Δt$ represents the amount of time it takes the expectation value of $Q$ to change by one standard daviation. $Δt$ depends entirely on what observable $(Q)$ you care to look at- the change might be rapid for one observable and slow for another. But if $ΔE$ is small, then the rate of change of all observables must be very gradual; or to put it the other way around, If any observable changes rapidly, the 'uncertainty' in the energy must be large.

Is the interpretation of Energy-time uncertainty principle different for relativistic quantum mechanics/QFT which this article is addressing? My confusion arises from a strong remark of Griffiths, it doesn't seem he intends to restrict his words only for non-relativistic QM.

"It is often said that the uncertainty principle means energy is not strictly conserved in quantum mechanics-that you're allowed to "borrow" energy $ΔE$, as long as you "pay it back" in a time $Δt ≈ h/(4πΔE) $; the greater the violation, the briefer the period over which it can occur. Now, there are many legitimate readings of the energy-time uncertainty principle, but this is not one of them. Nowhere does quantum mechanics license violation of energy conservation, and certainly no such authorization entered into derivation of Equation 3.76. But the uncertainty principle is extraordinarily robust: It can be misused without leading to seriously incorrect results, and as a consequence physicists are in the habit of applying it rather carelessly."

SURYABARTA SAHA
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    I don't understand what the question is. Could you please clarify what specific question you are asking? – d_b Apr 28 '23 at 04:58
  • Heisenberg Uncertainty Principle is really about the Fourier transform. It is not clear what the Energy-Time uncertainty principle means, and there is still a lot of arguing in the literature about it. It is particularly difficult because both energy and momentum are strictly conserved, and so such borrowing is not ok. – naturallyInconsistent Apr 28 '23 at 06:05
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    More on HUP for time & energy. – Qmechanic Apr 28 '23 at 06:39
  • Experimentally the energy time uncertainty simply means that whatever "shutter" mechanism we are using in our experiment will transfer energy to the system under measurement, i.e. we can sometimes measure more energy than the original system had. Who put it there? We did. This has been demonstrated at the single quantum level extremely nicely with femtosecond lasers. The energy was certainly not borrowed from the vacuum. It simply takes more energy to perform a short measurement than it takes for a long measurement. Only an infinitely long absorption process is energetically "for free". – FlatterMann Apr 28 '23 at 14:45
  • If you're just asking whether Tyron's interpretation is correct, that point is addressed by this question & answer instead. – Michael Seifert Nov 17 '23 at 12:43

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