Uncertainty Principle and Super-Radiance

Associate Professor Hasegawa Yuji of the Vienna University of Technology and Professor Masaaki Ozawa of Nagoya University and other scholars published empirical results against Heisenberg's uncertainty principle on January 15, 2012.They got a measurement result with a smaller error than the Heisenberg uncertainty principle, which proved the measurement advocated by the Heisenberg uncertainty principle.This article follows the method I used to study super-radiation and connects the uncertainty principle with the super-radiation effect. I found that under the super-radiation effect, the measurement limit of the uncertainty principle can be smaller.

2 relativistic quantum tunneling process. When trying to understand whether this result is an artifact of the step potential used by Klein, Sauter found that the nature of the process has nothing to do with the details of the barrier, although the probability of propagation decreases with decreasing slope. This phenomenon was first called "Klein's Paradox" by Sauter in 1931.
Further research conducted by Hong De in 1941 now deals with charged scalar fields and the Klein-Gordon equation, and the results show that when the potential is strong enough, the step potential produces a pair of charged particles.
Hunde tried-but failed-to get the same result for fermions. It is worth noting that this result can be regarded as a precursor to the results of Schwinger and Hawking's modern quantum field theory. The latter shows that spontaneous pairs are possible in the presence of strong electromagnetic fields and gravitational fields of bosons and fermions. .
In fact, we already know today that the resolution of the "old" Klein paradox is due to the formation of particleantiparticle pairs at the barrier, which explains the unattenuated transmission part.
In 1972, Press and Teukolsky [15] proposed that It is possible to add a mirror to the outside of a black hole to make a black hole bomb (according to the current explanation, this is a scattering process involving classical mechanics and quantum mechanics [1,3,9,10,13,14,16]).
When a bosonic wave is impinging upon a rotating black hole, the wave reflected by the event horizon will be amplified if the wave frequency ω lies in the following superradiant regime [11,12,15,17,18] where m is azimuthal number of the bosonic wave mode, Ω H is the angular velocity of black hole horizon.This amplification is superradiant scattering. Therefore, through the superradiation process, the rotational energy of the black hole can be extracted. If there is a mirror between the black hole's horizon and infinite space, the amplified wave will scatter back and forth and grow exponentially, which will cause the black hole's superradiation to become unstable.

Associate Professor Hasegawa Yuji of the Vienna University of Technology and Professor Masaaki Ozawa of Nagoya
University and other scholars published empirical results against Heisenberg's uncertainty principle on January 15, 2012 [8]. They used two instruments to measure the spin angle of neutrons and calculated them, and they got a measurement result with a smaller error than the Heisenberg uncertainty principle, which proved the measurement advocated by the Heisenberg uncertainty principle. The limit is wrong. However, the uncertainty principle is still correct, because this is the inherent quantum nature of the particle. This article follows the method I used to study superradiation and connects the uncertainty principle with the superradiation effect. I found that under the superradiation effect, the measurement limit of the uncertainty principle can be smaller.

II. THE SUPERRADIATION EFFECT OF BOSON SCATTERING
We get the Klein-Gordon equation Electronic copy available at: https://ssrn.com/abstract=3683008 where we defined Φ ;µ ≡ (∂ µ − ieA µ )Φ and e is the charge of the scalar field.We get A µ = {A 0 (x), 0},and eA 0 (x)can be equal to µ(where µ is the mass).
With Φ = e −iωt f (x), which is determined by the ordinary differential equation We see that particles coming from −∞ and scattering off the potential with reflection and transmission amplitudes R and T respectively. With these boundary conditions, the solution to behaves asymptotically as where k = ±(ω − eV ).
To define the sign of ω and k we must look at the wave's group velocity. We require ∂ω/∂k > 0, so that they travel from the left to the right in the x-direction and we take ω > 0.
The reflection coefficient and transmission coefficient depend on the specific shape of the potential A 0 . However one can easily show that the Wronskian between two independent solutions,f 1 andf 2 , of is conserved. From the equation on the other hand, if f is a solution then its complex conjugate f * is another linearly independent solution. We find|R| 2 = |I| 2 − ω−eV