Demystifier
Science Advisor
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@A. Neumaier I also have a question.
Consider the following 3 hermitian scalar field operators (at the same time): ##\phi({\bf x})##, ##\pi({\bf x})\equiv\dot{\phi}({\bf x} )## and
$$A({\bf x})\equiv [ \phi({\bf x}) \pi({\bf x}) +\pi({\bf x}) \phi({\bf x}) ]/2$$
In the thermal interpretation, the corresponding expected values
$$\langle\phi({\bf x})\rangle , \;\; \langle\pi({\bf x})\rangle , \;\; \langle A({\bf x})\rangle$$
are all beables. But are all these beables equally fundamental?
If they are all equally fundamental, that there is an infinite number of fundamental beables at each point ##{\bf x}##, because there are also beables corresponding to products of an arbitrary number of field operators. Isn't it strange that there is an infinite number of fundamental beables?
Or if they are not all equally fundamental, then one would expect that only ## \langle\phi({\bf x})\rangle## and ##\langle\pi({\bf x})\rangle## are fundamental, while ##\langle A({\bf x})\rangle## is a function of ## \langle\phi({\bf x})\rangle## and ##\langle\pi({\bf x})\rangle##. But then how one would explain that
$$ \langle A({\bf x})\rangle \neq \langle\phi({\bf x})\rangle \langle\pi({\bf x})\rangle \; ?$$
Consider the following 3 hermitian scalar field operators (at the same time): ##\phi({\bf x})##, ##\pi({\bf x})\equiv\dot{\phi}({\bf x} )## and
$$A({\bf x})\equiv [ \phi({\bf x}) \pi({\bf x}) +\pi({\bf x}) \phi({\bf x}) ]/2$$
In the thermal interpretation, the corresponding expected values
$$\langle\phi({\bf x})\rangle , \;\; \langle\pi({\bf x})\rangle , \;\; \langle A({\bf x})\rangle$$
are all beables. But are all these beables equally fundamental?
If they are all equally fundamental, that there is an infinite number of fundamental beables at each point ##{\bf x}##, because there are also beables corresponding to products of an arbitrary number of field operators. Isn't it strange that there is an infinite number of fundamental beables?
Or if they are not all equally fundamental, then one would expect that only ## \langle\phi({\bf x})\rangle## and ##\langle\pi({\bf x})\rangle## are fundamental, while ##\langle A({\bf x})\rangle## is a function of ## \langle\phi({\bf x})\rangle## and ##\langle\pi({\bf x})\rangle##. But then how one would explain that
$$ \langle A({\bf x})\rangle \neq \langle\phi({\bf x})\rangle \langle\pi({\bf x})\rangle \; ?$$