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I'm reading A Universe From Nothing by Lawrence M. Krauss, and I encountered a paragraph that I found confusing:

The source of the infinity is easy to describe. When we consider all possible virtual particles that can appear, the Heisenberg Uncertainty Principle implies that particles carrying ever more energy can appear spontaneously out of nothing as long as they then disappear in ever-shorter times. In principles, particles can therefore carry almost infinite energy as long as they disappear in almost infinitesimally short times.

  1. I don't understand what this means by ever-shorter times. How can something disappear faster than it appears if it appears in an instant?
  2. I was under the impression that there are no physical phenomena which are infinite (indeed, such a phenomenon would be impossible to measure) -- this paragraph seems to be suggesting otherwise?
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    $\begingroup$ The paragraph has no rigorous meaning in physics, it is popscience at its best/worst. For the possible correct interpretations of a "energy-time uncertainty relation", see this question. $\endgroup$ – ACuriousMind Jan 10 '17 at 15:15
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  1. The text is making reference to and misapplying the Heisenberg uncertainty principle. In its incorrect but often quoted form, this principle implies that $$ \Delta E\Delta t\ge \hbar $$ which supposedly means that $\Delta E$ can be arbitrarily large as long as $\Delta t$ is correspondingly small. This is in fact an incorrect application of the Heinsenberg principle on several different levels. For one thing, virtual particles do not pop in and out of existence; see Do virtual particles actually physically exist? and What actually are virtual particles?. Also, $\Delta t$ is not the life-time of these "particles"; see What is Δt in the time-energy uncertainty principle?.

  2. Your impression is essentially correct. The paragraph is plain wrong, or at best very misleading. Don't expect pop-science to be precise.

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