The value of a quantum field at a point in spacetime is not precisely determined.
I haven’t studied quantum physics but came across this. Please explain it to me in simple term what it physically means.
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A quantum field at a point relates to the probability of finding a particle at this point. However, according to the Heisenberg Uncertainty Principle, a particle does not have the exact position and exact momentum (and therefore energy) at the same time. The smaller the uncertainty is in the position, the larger the uncertainty is in the energy and momentum. For this reason, if we wanted to measure a particle at a point of spacetime, we would need an infinite amount of energy, which is impossible. Consequently the value of the quantum field at a point cannot be determined precisely.
The idea of quantum field values at points of spacetime is one of the problems with the standard quantum field theory. The mathematical representation of this problem is that a field at a point is not an operator in a Hilbert space, an infinite-dimensional functional space used to describe a state of the quantum system.