1

For background, I am not very mathematically sophisticated with QFT, but have been trying to get a conceptual grounding. In his Biggest Ideas series, Sean Carroll discusses the idea that in QFT there is a superposition of any number of particles in any region of space.

This seems strange to me given that before QFT we were content with the laws of chemistry which rely on a stable number of electrons orbiting atoms. How can we make sense of these laws of chemistry if the number of electrons could really be any number at all if we were to look.

Jeff Bass
  • 749
  • 2
    The fact it can be any number at all doesn't mean that its uniform over those options. Clearly in order to have a somewhat sensible low-energy limit most atoms will be found with only a very small number of positron-electron fluctuations at any given time. – jacob1729 Dec 21 '20 at 15:06
  • @jacob1729 So it is just exceedingly likely that the number of particles in the universe will be observed to be on average essentially constant? – Jeff Bass Dec 21 '20 at 15:09
  • Are you thinking about the vacuum energy in quantum field theory? If so see Are vacuum fluctuations really happening all the time? – John Rennie Dec 21 '20 at 18:06
  • Do you have a link to that point in the series so we can understand the context of his statement? – kaylimekay Dec 21 '20 at 23:17
  • @kaylimekay Sure, it's in this video: https://www.youtube.com/watch?v=Dy1LNk_B6IE&t=3839s at the 1:00:10 mark. He says "even in the vacuum, when you look you can get any answer" which seems to imply that this is not only the case in the vacuum. – Jeff Bass Dec 21 '20 at 23:57
  • @JeffBass The vacuum state in a relativistic QFT is entangled with respect to location in a special way, and as a result we can (mathematically) create any other state just by acting on the vacuum with observables localized in any one arbitrarily small region of space. I didn't watch the video, but maybe that's what Carroll was alluding to. If so, then it's not just a matter of "looking" at the vacuum. It would require making practically-impossible measurements, so it's not issue for quantum chemistry. – Chiral Anomaly Dec 24 '20 at 15:35
  • @ChiralAnomaly Thanks for answering so many of my questions. What would be involved in these measurements of the vacuum? – Jeff Bass Dec 24 '20 at 18:45
  • @JeffBass The theorem only proves that it's possible without saying specifically how to do it. It's a consequence of the Reeh-Schlieder theorem, which is reviewed by Witten in Notes on Some Entanglement Properties of Quantum Field Theory (http://arxiv.org/abs/1803.04993). – Chiral Anomaly Dec 24 '20 at 20:36

0 Answers0