Quantum Control, Entanglement and Noise in the Seminal Bohr and Rosenfeld Paper on Electromagnetic Field Measurements

In the 1933 Bohr and Rosenfeld’s famous article on electromagnetic field measurements they did not consider the measurement of a magnetic component in a given space-time region, nor the measurement of two parallel magnetic components, nor the measurement of two non-parallel magnetic components, nor the parallel measurement of one magnetic and one electric component, nor the non-parallel measurement of one electric and one magnetic component, nor the non-parallel measurement of one magnetic and one electric component in two different space-time regions. This article covers the first one of these pending matters. QUANTUM ENTANGLEMENT AND QUANTUM CONTROL OF VACUUM FLUCTUATIONS (NOISE) IN MAGNETIC FIELD MEASUREMENTS From the uncertainty relations predicted by the formalism for the average components of the free quantum electromagnetic field [1] there are at least ten representative and different cases of measurement, from which the measurement cases considered by Bohr and Rosenfeld [2] were: (1) ) (I x E , (2) ) (I x E and ) (II x E , (3) ) (I x E and ) (II y E and (4) ) (I x E and ) (II x H . The measurement cases not considered [3] by Bohr and Rosenfeld are: (5) ) (I x H , (6) ) (I x H and ) (II x H , (7) ) (I x H and ) (II y H , (8) ) (I x H and ) (II x E , (9) ) (I x E and ) (II y H and (10) ) (I x H and ) (II y E . The case number (5) will be treated here. In 1951 Corinaldesi [4] discovered that Bohr and Rosenfeld [2] had made a mistake in the calculation of a critical field related to vacuum fluctuations. Continuing with which has been done before [5], we intend to show that Corinaldesi’s correction does not change the conclusions made by Bohr and Rosenfeld in the cases studied by them. We will show that Bohr and Rosenfeld’s conclusions also hold in the cases not considered by them. We will justify the subsequent studies based on Bohr and Rosenfeld’s pioneering article from a very different perspective to that used by Hnizdo [6] in the defense of Bohr and Rosenfeld’s work, which has been under attack from Compagno and Persico [7]. Bohr and Rosenfeld designated the square root of any of uncertainty relations above mentioned as a critical field ∆ Bohr-Rosenfeld = ∆ BR, for every electromagnetic field that may be considered, if the latter, being much greater than ∆ BR, was close to the classical description. Similarly, Bohr and Rosenfeld defined another critical quantity ∆ oBohr-Rosenfeld =∆ oBR, as the square root of the mean quadratic fluctuation of each quantity of electromagnetic field, when the number of photons