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Absolute Zero in Casimir Vacuum Original Research Papers Fundamental Journals Open Access Journals International Journal of Fundamental Physical Sciences (IJFPS) ISSN: 2231-8186 IJFPS, Vol 10 , No 1, pp 01- 04 March, 2020 Xingwu Xu DOI: 10.14331/ijfps.2020.330133 Absolute zero in Casimir vacuum Xingwu Xu Research Institute of Hefei Gotion High-tech Power Energy Co, Ltd 599 Daihe Road, Hefei, Anhui 230012, P. R. China E-mail addresses: [email protected] Received Dec 2019 Received in revised: Feb 2020 Published: March 2020 ABSTRACT Casimir vacuum has many peculiar properties, e.g. the speed of light can exceed c. This paper investigated the behavior of gas molecules in Casimir vacuum. Analysis and calculation indicate that we can get a new absolute zero in Casimir vacuum. This is due to the Hamiltonian, which equals the kinetic energy of the ensemble of gas molecules that is reduced in Casimir vacuum; therefore, the gas constant R is changed. This conclusion has great significance for the research of the vacuum properties. Keywords: Casimir vacuum, Absolute zero ©2020 The Authors. Published by Fundamental Journals. This is an open access article under the CC BY-NC https://creativecommons.org/licenses/by-nc/4.0/ https://doi.org/10.14331/ijfps.2020.330133 INTRODUCTION 푛 (0) = 1 (2) Casimir vacuum has many peculiar properties. For example, ‖ Scharnhorst found that the speed 푐⊥ of light normal to the 11π2 α2 Casimir parallel mirrors could exceed 푐 = 1 (Barton, 1990; n (0) = 1– (3) ⊥ (90)2 (mL)4 Scharnhorst, 1990). In fact, the vacuum structure has been modified in Casimir vacuum. The propagation of light depends Where L is the distance of two plates. Therefore, 푛 (0) < 1, on the structure of the vacuum (Scharnhorst, 1990). The main ⊥ and the propagation velocity (c/n⊥) of light perpendicular to factor is that the refractive index (n) in Casimir vacuum is the mirrors will be faster than c. This conclusion does not changed, contradict the special theory of relativity (Scharnhorst, 1998). 44훼2 This research stimulated a broader interest in the study of the 푛(0) = 1 − 푘휌 푘 = (1) 135푚4 properties of vacuum. The question raised in this paper is: Will Casimir vacuum affect the value of absolute zero? Where 휌 is the vacuum energy density, 훼 is the fine structure constant, m is the electron mass. The results of Scharnhost’s calculation are, https://doi.org/10.14331/ijfps.2020.330133 ISSN: 2231-8186/ ©2020 The Authors. Published by Fundamental Journals This is an open access article under the CC BY-NC https://creativecommons.org/licenses/by-nc/4.0/ 1 IJFPS, Vol 10 , No 1, pp 01-04, March, 2020 Xingwu Xu THE INTERACTION BETWEEN MOLECULES OR Where HA is the atomic Hamiltonian, HF is the free field ATOMS AND THE VACUUM FIELD Hamiltonian, and HAF is the atom-field interaction Hamiltonian. Now, we consider an ensemble of gas molecules This issue is related to the reaction between molecules or in Casimir vacuum. The total kinetic energy of gas molecules atoms of gas and the vacuum field. The molecules or atoms is, moving in the ordinary vacuum will change their momentum 퐸푘푛−푠푦푠 = ∑ 퐻 (9) due to the reaction between molecules or atoms and the vacuum. Bercegol and Lehoucq (2015) state that there is a In fact, the Casimir vacuum is a space where some k modes braking torque in a rotating pair of atoms when reacting with (longer wavelength) are excluded, as shown in Fig. 1 (Chown, quantum vacuum, which decreases the kinetic energy and the 1990). angular momentum of the atoms. Recently, Sonnleitner found that an excited two-level atom moving through a vacuum sees a tiny friction force (Sonnleitner, Trautmann, & Barnett, 2017). The friction force arises from the interaction between atoms and the vacuum field. The interaction can be described by the so-called “Rontgen term (HAF)” (Wilkens, 1994). 1 퐻 =– 퐝̂ ∙ 푬̂⊥(푹̂) − {푷̂ ∙ [푩̂(푹̂) × 풅̂] + [푩̂(푹̂) × 풅̂] ∙ 푷̂} 퐴퐹 2M (4) Here 풅̂ is the atomic dipole operator, 푷̂ and 푹̂ are the atomic center-of-mass canonical momentum and position operator, 푬̂⊥ is the electric field, and 푩̂ is the magnetic field: ̂⊥ ̂ i퐤∙퐑̂ † −i퐤∙퐑̂ 푬 (푹) = i ∑k,λ εk퐞퐤,훌 (âk,λe – âk,λe ) (5) ̂ ̂ i i퐤∙퐑̂ † −i퐤∙퐑̂ Fig 1. Casimir effect: The vacuum is full of virtual photons, but 푩(푹) = ∑k,λ εk(풏푘 × 퐞k,λ)(âk,λe – âk,λe ) c photons with wavelength (λ) more than twice the separation of (6) the plates are excluded from the space between them. Where εk = √ℏωk/(2ω0 V) is the electric field strength per photon in quantization volume 푉, 풏푘 = 풌/|풌| is a unit vector The Rontgen term is actually the friction term with negative in the direction of propagation, 풆푘,휆 is a polarization vector value. For the sum operation, if the value of term is positive, perpendicular to the mode propagating in a direction 푲 = the greater the number of terms, the greater the sum. † Conversely, if the value of term is negative, the larger the 퐤c/ωk (Sonnleitner et al., 2017), 푎̂푘,휆 and 푎̂푘,휆 denote the ′′ photon annihilation and creator operators of the 푘푡ℎ mode with number of terms, the smaller the sum. Now let us use 푘 for ′ the polarization λ (λ = 1, 2). In fact, the “Rontgen term” is a the number of modes (terms) in Casimir vacuum, and 푘 for negative energy dissipation term caused by the displacement the number of modes in the ordinary vacuum. From equations ′′ ′ current. The interaction mentioned above results in the (4)～(6), we know that for 푘 < 푘 (Fig. 1), we have decrease of the momentum of atoms. Because the kinetic ′′ ′ momentum 푝 = 푀푣 (푀: mass, 푣: velocity), the change of 퐻퐴퐹 > 퐻퐴퐹 (10) momentum will be (Sonnleitner et al., 2017). Equation (10) indicates that in Casimir vacuum, the mean 푝̇ = 푀푣̇ + 푀̇ 푣 (7) coupling energy between the ensemble of gas molecules and the field is lower than in ordinary vacuum. Therefore, we have The conclusion is that the velocities of atoms do not change; ′′ ′ the atom’s decay in momentum comes from the mass defect 퐸푘푛−푒푛푠 < 퐸푘푛−푒푛푠 (11) caused by the photon’s emission. Where 퐸푘푛−푒푛푠 denotes the kinetic energy of the ensemble of THE KINETIC ENERGY OF GAS MOLECULES IN gas molecules. From another viewpoint, one can divide the CASIMIR VACUUM kinetic energy of the gas ensemble into two parts-the self- energy of the gas molecules and the energy of the vacuum However, if we put the gas molecules in the Casimir vacuum, field. A coupling exists between the gas molecules and the the kinetic energy will change. For a two-level atom, the sum vacuum field; the total energy of gas molecules is the coupling of the center-of-mass kinetic energy is (Wilkens, 1994). effect of two parts of energies. Thus, 퐏̂2 H = + 퐻 + 퐻 + 퐻 (8) 퐸푘푛−푠푦푠 = 퐸푠푒푙푓 + 퐸푣푎푐 (12) 2M 퐴 퐹 퐴퐹 2 IJFPS, Vol 10 , No 1, pp 01-04, March, 2020 Xingwu Xu From (Bercegol & Lehoucq, 2015) we know that, In Casimir vacuum, the total average kinetic energy of gas molecules becomes 2 π 퐸푣푎푐 =– (13) 720L3 퐸̅퐶푎푠 = 퐸̅ + 퐸 = 1.5198105 × 10−2 J (23) 푘푛 푘푛 푣푎푐 Where L is the distance between two plates, ℎ = 푐 = 1. The average kinetic energy for a single molecule in Casimir Therefore, the kinetic energy of gas molecules in Casimir vacuum is vacuum is lower than that in an ordinary vacuum ̅퐶푎푠푖 2 ′′ 퐸푘푖푛 −21 ′′ π ′ 퐸̅ = = 5.655928 × 10 퐽 (24) 퐸 (= 퐸 – ) < 퐸 (= 퐸 ) (14) 푘푛 푛푁 푘푛−푒푛푠 푠푒푙푓 720L3 푘푛−푒푛푠 푠푒푙푓 퐴 Therefore, the new 푘퐵 is A NEW ABSOLUTE ZERO IN CASIMIR VACUUM ̅′′ 퐶푎푠 2 퐸푘푖푛 −23 푘퐵 = = 1.38042 × 10 (25) According to (Fischer et al., 2007), temperature is proportional 3 푇0 to the mean translational kinetic energy of atoms or molecules; it is just the well-known equation The new gas constant is 3 퐶푎푠 퐸̅ = 푘 T (15) 푅퐶푎푠 = 푘퐵 푁퐴 = 8.31289 (26) 푘푛 2 퐵 The absolute zero in Casimir vacuum is Where 퐸̅ can be considered same as 퐸 . Now, the 푘푛 푘푛−푒푛푠 paradox arises: in Casimir vacuum at absolute zero 푉0푃0 temperature, 퐸′′ < 퐸′ , which term will change- 푇퐶푎푠 = − = −273.20 K (27) 푘푛−푒푛푠 푘푛−푒푛푠 푅퐶푎푠푖 kB or T? We have two options: 1) T decreases or 2) kB decreases. ∆T = 푇퐶푎푠 − 푇퐾 = −273.20 − (−273.15) = −0.05 K 1) If we put the Casimir vacuum as well as the ensemble of gas molecules into absolute zero, the temperature in Casimir (28) vacuum will be less than absolute zero, The conclusion shows that the change of vacuum structure will 푇퐶푎푠 < 0 K (16) result in a new absolute zero temperature. It is possible that in another planet, where the vacuum structure is different from 2) If the kB decreases, according to the relation: earth, there will be a new absolute zero, which will obey the 푅 푘퐵 = (17) third law of thermodynamics there. 푁퐴 PROOF AND MEASUREMENT Where 푅 is the gas constant, 푁퐴 is the Avogadro constant, then R will decrease. Back to the gas law, As a “thought experiment”, the new absolute zero can be proved and measured by designing a design of Casimir 푃 푉 0 0 = 푅 (18) vacuum pump (Fig. 2). As illustrated in Fig.2, the “modern 푇0 Magdeburg hemispheres” consist of several hollow spheres. Where 0 here denotes the standard condition, 푃0 = 1.01325 × There are many Casimir slits in the shells.
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