RESEARCH Revista Mexicana de F´ısica 62 (2016) 83–88 JANUARY-FEBRUARY 2016 Conversion of zero point energy into high-energy photons B.I. Ivlev Instituto de F´ısica, Universidad Autonoma´ de San Luis Potos´ı, San Luis Potos´ı, 78000 Mexico. Received 27 July 2015; accepted 5 November 2015 An unusual phenomenon, observed in experiments, is studied. X-ray laser bursts of keV energy are emitted from a metal where long-living states, resulting in population inversion, are totally unexpected. Anomalous electron-photon states are revealed to be formed inside the metal. These states are associated with narrow, 10¡11 cm, potential well created by the local reduction of zero point electromagnetic energy. In contrast to analogous van der Waals potential well, leading to attraction of two hydrogen atoms, the depth of the anomalous well is on the order of 1 MeV . The states in that well are long-living which results in population inversion and subsequent laser generation observed. The X-ray emission, occurring in transitions to lower levels, is due to the conversion of zero point electromagnetic energy. Keywords: Glow discharge; X-ray laser radiation. PACS: 79.20.Rf; 32.30.-r 1. Zero point electromagnetic energy bursts of the duration of 20 ¹s were generated approximately every 50 ¹s during 0.1 s after stopping the discharge. The concept of zero point energy was developed by A. Ein- Moreover, some collimated X-ray bursts have been seen stein and O. Stern in 1913. This energy depends on mutual up to 20 hours after switching off the discharge voltage. An positions of atoms or macroscopic objects in space resulting emission of separate photons by radioactive isotopes from the in interaction forces among them. The first calculation of cathode material is easy understandable. But here one deals this force between two atoms (van der Waals force) has been with strongly collimated X-ray laser bursts. So it was the done by F. London in 1928 [1]. As shown by H. Casimir in laser emission from “dead” sample, namely, which was acted 1948, van der Waals forces exist also between macroscopic by nothing during 20 hours. bodies [2, 3]. These results were expanded by E. Lifshitz in 1955 [4, 5]. The essential point is that above experiments were repeat- A significant problem is extraction of zero point energy edly performed for years and could be reproduced any time and conversion of it into a macroscopic form. It is possi- on demand. Indeed, the array of macroscopic laser bursts un- ble in reality and there is an example of this. Two hydrogen likely is an artifact. atoms, in the ground state each, are acted by the attractive It is hard, using a combination of known effects, to ex- van der Waals force which brings them together (until activa- plain phenomena observed. First, it is unclear how energy in- tion of covalent forces) from a large distance. In this process side the isolated and equilibrium solid is suddenly collected the sum of the atoms kinetic energy and zero point energy to get converted into the macroscopic laser burst. Second, of photons is conserved. Then the emission of the energy of even if this happens, a mechanism of creation of popula- 4.72 eV (H2 binding energy) by photons transfers the system tion inversion is unclear since electronic lifetimes in the keV to the ground state. As a result, zero point photon energy is regime are very short [12]. reduced by » 1 eV. In this case the vacuum energy is emitted Misinterpretation of experiments [12, 13] is possible by (“energy from nothing”). attributing the energy source to nuclear reactions. These reac- The macroscopic version of the above process was pro- tions are impossible here since energies of phonons (0.01 eV) posed in Ref. 6 and discussed in Ref. 7. See also Refs. 8 and electrons (1 eV) inside a solid are too low compared to to 10. MeV . It is not real to expect phonons in a solid to suddenly Apart from that, the mechanism of conversion of zero get collected into the MeV energy. point electromagnetic energy into high-energy photons (up to a few MeV) has been revealed in Ref. 11. This mechanism Below the conversion mechanism of zero point energy is based on anomalous electron-photon states. into high-energy photons [11] is shown to be likely the base of phenomena observed in Refs. 12 and 13. 2. Glow discharge and X-ray bursts In papers [12,13] and references therein unusual results were reported on high-current glow discharge in various gases. At 3. Anomalous electron-photon states discharge voltage of (1-2) kV X-ray emission (up to 10 keV) from the metal cathode was registered. Both diffuse and col- In this section we study some aspects of the electron-photon limated X-ray emissions were observed. Collimated X-ray interaction. 84 B.I. IVLEV 3.1. Electron-photon system 3.2. Lamb shift Electron-photon interaction in quantum electrodynamics is When He¡ph 6= 0, for the potential U0(r) in Fig. 1 the mod- described by the part He¡ph [5]. One can apply multi- ified ground state energy Etot hardly differs from bare E by dimensional quantum mechanics to the electron-photons sys- the Lamb shift [5]. Analogously the inclusion of the electron- tem since photons are the infinite set of harmonic oscilla- photon interactions hardly influences the electron density in tors. This method was proposed in Ref. 14 and developed Fig. 1. in Ref. 15 and further publications. This is because of smallness of radiative corrections [5]. Due to the interaction with zero point electromagnetic os- When formally He¡ph = 0 the total energy is the sum cillations the electron “vibrates” [16, 17]. This idea was pro- Pof the electron energy E and the zero point photon energy ~!=2. The stationary state of the system with that total posed by W. Nernst in 1916. The mean electron displacement 2 2 energy is described by the wave function h~ui is zero but the mean squared displacement rT = hu i is finite. One can estimate for the electron in hydrogen atom [11, 16] Ã0 = Ãe(~r; z)Ãph ; (1) r 4e2 ~c where à is the multi-dimensional photon function. We sup- r ' r ln ' 0:81 £ 10¡11cm; (4) ph T c ¼~c e2 pose the part Ãe in (1) to be the usual electron wave function ¡11 of the ground state with the energy E in the potential U0(r). where rc = ~=(mc) ' 3:86 £ 10 cm is the Comp- 2 This is shown in Fig. 1 where ½0 = jÃej is the electron den- ton length. The electron, due to the uncertainty rT in its sity. As the first step, we consider the general problem in a positions, probes various parts of the electrostatic potential smooth axially symmetric potential and do not specify a par- and therefore electron energy levels become slightly shifted ticular physical situation. (Lamb shift [5]). The finite He¡ph turns the wave function (1) into exact one, Ã. In this case à (as Ã0) also corresponds to a station- 3.3. Singular electron density ary state of the total Hamiltonian with the certain total energy Etot. One can present Etot as Let us consider the potential U(r) which coincides with µ ¶ U0(r) at a < r, where a is the scale of the potential in the X ~! X ~! space. At r < a the potential U(r) exceeds U (r) as shown E = E(~r; z) + ¡ ; 0 tot (2) in Fig. 2. The energy E, the same as in Fig. 1, becomes below 2 2 0 the ground state energy in the modified potential. The corre- where the first term relates to the electron part which also in- sponding Ãe (coinciding with one in Fig. 1 at a < r) is no cludes He¡ph. The last term is zero point energy of photons more the eigenfunction since it has the singularity at r = 0 in absence of the electron. According to [14,15], the electron sketched in Fig. 2. This is a formally correct solution of the density problem at all r excepting r = 0 which is the singularity line 2 ½ = hjÃj iph (3) corresponds to the average on photon coordinates. At 2 He¡ph = 0 the density is ½ = jÃej . FIGURE 2. He¡ph = 0. Compared to Fig. 1, the potential U(r) is larger at r < a. Now E (the same as in Fig. 1) is below the ground FIGURE 1. He¡ph = 0. Ground state energy E of electron in the state energy. The electron density ½ is singular at r = 0 since 2 potential U0(r). The electron density is ½0 = jÃej . a is the spatial the related Ãe is not the electron eigenfunction for U(r). Dashed scale of the potential. curves correspond to Fig. 1 and at a < r U = U0 and ½ = ½0. Rev. Mex. Fis. 62 (2016) 83–88 CONVERSION OF ZERO POINT ENERGY INTO HIGH-ENERGY PHOTONS 85 (thread) of Ãe. The electron density ½ in Fig. 2 coincides with ½0 in Fig. 1 at a < r. To formally support the singular wave function (density) in Fig. 2 the potential should be singular U(r) »¡±(r). This is shown in Fig. 2. Let us look at Fig. 1. Inclusion of the electron-photon in- teraction just slightly modifies the ground state energy in the potential U0(r), which becomes Etot (Sec. 3.3). The related electron density is also close to ½0. The associated total wave function Ã, which produces that electron density according to (3), follows from the milti-dimensional Schrodiger¨ equa- tion (Sec.