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In QFT, we can work with functionals of fields ##\Psi[\phi(x)]=\langle \phi | \Psi \rangle## that give us the probability amplitude for the field to be ## \phi(x) ##. It seems to me that the Born rule we get here i.e. ##P(\phi(x))=|\Psi[\phi(x)]|^2=|\langle \phi | \Psi \rangle|^2## is not of much use in QFT because It seems to me we can't actually have an experiment that tells us what is the field in the whole spacetime let alone having an ensemble of...spacetimes?...that we can check the probability that the above Born rule gives us. Can anyone explain about this?
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