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I think the key conceptual hurdle is that the vacuum state is not nothing. Quantum field theory describes matter as excitations in quantum fields. These quantum fields are very strange things, and I don't know of any easy way to explain to a non-physicist what a quantum field is. The key thing is that the quantum fields fill all of spacetime. So a vacuum is ...


4

Let us look at the instantons of an ordinary pure Yang-Mills theory for gauge group $G$ in four Euclidean dimensions: An instanton is a local minimum of the action $$ S_{YM}[A] = \int \mathrm{tr}(F \wedge \star F)$$ which is, on $\mathbb{R}^4$, precisely given by the (anti-)self-dual solutions $F = \pm \star F$. For (anti-)self-dual solutions, ...


2

I can think of two reasons why we need a lower bound, one statistical, one inuititive. First, the intuitive: The annihiliation/creation operators represent adding/removing particles (or excitations, or whatever). The vacuum state as lowest energy state represents obviously the empty state from which no further particles can be removed. It is also clear (in ...


2

The article you quoted is really badly written. Instead of unnatural the correct world should have been "tuned" or something similar. The issue is related to the fact that we know that, if the fundamental constants of nature would have been slightly different, the universe would have been completely different. For instance, carbon would not be formed at ...


1

The example of unnaturalness you describe is the example of the mexican hat for the higgs mechanism ( if you look at this page up on the left you will see the mexican hat in the PHYSICS logo). As all should know this symmetry is naturally broken at our energy levels, as in this the example, which is correct, that the pencil sits precariously and can break ...


1

Second answer, what about the phenomenon of “Quantum Locking”? Right now it is being used to levitate superconductors over magnets, but I am sure you could exploit the phenomenon to transmit torque. Plus, you can put the superconductor on the vacuum side of the seal to keep it cold.


1

John Rennie's answer is good already, but I want to add a single point: These fluctuations are very very short. In quantum mechanics you've got Heisenbergs uncertainty principle, which is often stated as $$ \Delta x \cdot \Delta p \le \frac \hbar 2 $$ and which means, that for any quantum object (think of an electron or a positron created in such a vacuum ...



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