Incertitude relations from QFT

[TeTeC]

Hello,

There are no incertitude relations in QFT. On the other hand, these incertainty relations do exist in non-relativistic QM. How can we reconcile these two facts ? Is it possible to "derive" uncertainty relations from QFT by "taking the non-relativistic limit" ?

Thanks !

 

[Bob_for_short]

In QED there is, for example, the number-of-photons/wave-phase uncertainty, and some others.

 

[Entropia]

First of all, it is important to clarify that uncertainty relations in quantum mechanics (QM) and incertitude relations in quantum field theory (QFT) are two different concepts. In QM, uncertainty relations refer to the limitations on the simultaneous measurement of two non-commuting observables, such as position and momentum. In QFT, incertitude relations refer to the inherent uncertainty in the values of fields and particles due to the quantum nature of the theory.

It is true that there are no incertitude relations in QFT, as the theory already incorporates the principles of quantum mechanics. In fact, QFT is a more fundamental theory than QM, as it encompasses and extends the concepts of QM to include relativistic effects. Therefore, QFT does not need to derive uncertainty relations, as they are already inherent in the theory.

The concept of taking the non-relativistic limit in QFT to derive uncertainty relations is not applicable. This is because the non-relativistic limit is a mathematical approximation used to simplify the equations of QFT in certain scenarios, such as low energy or non-relativistic systems. It does not change the fundamental principles of QFT or introduce new concepts such as uncertainty relations.

In conclusion, while uncertainty relations and incertitude relations may seem similar, they are based on different principles and cannot be reconciled. QFT already encompasses the principles of QM and does not need to derive uncertainty relations. Therefore, it is important to understand and distinguish between these two concepts in order to fully understand the complexities of quantum theory.