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1
Flowers, Jeff L., and Brian W. Petley. "Planck, units, and modern metrology." Annalen der Physik 17, no. 2-3 (February 22, 2008): 101–14. http://dx.doi.org/10.1002/andp.200710277.
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Kirakosyan, Khachatur A. "To the Content of Planck Units." Theoretical Physics 3, no. 2 (June 8, 2018): 33–37. http://dx.doi.org/10.22606/tp.2018.32002.
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Bunker, P. R., Ian M. Mills, and Per Jensen. "The Planck constant and its units." Journal of Quantitative Spectroscopy and Radiative Transfer 237 (November 2019): 106594. http://dx.doi.org/10.1016/j.jqsrt.2019.106594.
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Sharupov, Oleg. "PLANCK UNITS AND EXTENDED SPECIAL RELATIVITY." Respublica literaria, no. 1 (December 25, 2020): 65–67. http://dx.doi.org/10.47850/s.2020.1.18.
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The Planck length is an object of the relativistic quantum-gravitational theory, therefore, a more general and consistent direction of the special relativity extension, seems to be the use of the postulate of the relativistically invariant and limiting nature of all Planck units, that was introduced by V.V. Korukhov at the end of the 90s. One of the examples of the implementation of this postulate in its methodological meaning is the model of a vacuum-like medium, the physical properties of which are characterized by relativistically invariant values, which qualita-tively distinguishes it from the known types of matter –matter and field.
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Min, Brian B. K. "The photon element units and their relativistic properties." Physics Essays 33, no. 1 (March 5, 2020): 38–45. http://dx.doi.org/10.4006/0836-1398-33.1.38.
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A set of natural units is determined from the “photon element” model of light, the outcome of an extended Compton analysis. In terms of these units, the speed of light and the electrical and Boltzmann constants are, respectively, on the order of unity, but the Planck constant is ∼1027 or greater and gravitational constant ∼10−59 or greater. This makes the photon element units less convenient than the Planck units. With the mass unit that is only ∼10−43 of the Planck mass, however, the photon element units can correspond better to physical realities than the Planck units. For the spacetime, a photon element forms a set of unit base vectors, a natural basis that is Lorentz covariant. There an analysis shows that (1) of the above five universal constants all are Lorentz invariants except the gravitational constant, and (2) of the five natural units (time, length, mass, electrical charge, and temperature,) only the electrical charge is a Lorentz invariant.
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Stock, M. "The watt balance: determination of the Planck constant and redefinition of the kilogram." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1953 (October 28, 2011): 3936–53. http://dx.doi.org/10.1098/rsta.2011.0184.
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Since 1889, the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base unit of the SI, and it influences several other base units. This situation is no longer acceptable in a time of ever-increasing measurement precision. It is therefore planned to redefine the unit of mass by fixing the numerical value of the Planck constant. At the same time three other base units, the ampere, the kelvin and the mole, will be redefined. As a first step, the kilogram redefinition requires a highly accurate determination of the Planck constant in the present SI system, with a relative uncertainty of the order of 1 part in 10 8 . The most promising experiment for this purpose, and for the future realization of the kilogram, is the watt balance. It compares mechanical and electrical power and makes use of two macroscopic quantum effects, thus creating a relationship between a macroscopic mass and the Planck constant. In this paper, the operating principle of watt balance experiments is explained and the existing experiments are reviewed. An overview is given of all available experimental determinations of the Planck constant, and it is shown that further investigation is needed before the redefinition of the kilogram can take place. Independent of this requirement, a consensus has been reached on the form that future definitions of the SI base units will take.
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Iorio, Lorenzo. "Perspectives on Constraining a Cosmological Constant-Type Parameter with Pulsar Timing in the Galactic Center." Universe 4, no. 4 (March 26, 2018): 59. http://dx.doi.org/10.3390/universe4040059.
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Independent tests aiming to constrain the value of the cosmological constant Λ are usually difficult because of its extreme smallness ( Λ ≃ 1 × 10 - 52 m - 2 , or 2 . 89 × 10 - 122 in Planck units ) . Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the ≃ 10 - 43 – 10 - 44 m - 2 ( 5 – 1 × 10 - 113 in Planck units ) level, but they may turn out to be optimistic since Λ has not yet been explicitly modeled in the planetary data reductions. Accurate ( σ τ p ≃ 1 – 10 μ s ) timing of expected pulsars orbiting the Black Hole at the Galactic Center, preferably along highly eccentric and wide orbits, might, at least in principle, improve the planetary constraints by several orders of magnitude. By looking at the average time shift per orbit Δ δ τ ¯ p Λ , an S2-like orbital configuration with e = 0 . 8839 , P b = 16 yr would permit a preliminarily upper bound of the order of Λ ≲ 9 × 10 - 47 m - 2 ≲ 2 × 10 - 116 in Planck units if only σ τ p were to be considered. Our results can be easily extended to modified models of gravity using Λ -type parameters.
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SINGH, T. P. "NONCOMMUTATIVE GRAVITY, A "NO STRINGS ATTACHED" QUANTUM–CLASSICAL DUALITY, AND THE COSMOLOGICAL CONSTANT PUZZLE." International Journal of Modern Physics D 17, no. 13n14 (December 2008): 2593–98. http://dx.doi.org/10.1142/s0218271808014126.
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There ought to exist a reformulation of quantum mechanics which does not refer to an external classical space–time manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the "weakly quantum, strongly gravitational" dynamics of a relativistic particle whose mass is much greater than the Planck mass is dual to the "strongly quantum, weakly gravitational" dynamics of another particle whose mass is much less than the Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of the Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.
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Wang, Xijia. "New Discovery on Planck Units and Physical Dimension in Cosmic Continuum Theory." Journal of Modern Physics 09, no. 14 (2018): 2391–401. http://dx.doi.org/10.4236/jmp.2018.914153.
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KISELEV, V. V., and S. A. TIMOFEEV. "THE SURFACE DENSITY OF HOLOGRAPHIC ENTROPY." Modern Physics Letters A 25, no. 26 (August 30, 2010): 2223–30. http://dx.doi.org/10.1142/s0217732310033608.
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On the basis of postulates for the holographic description of gravity and the introduction of entropic force, for static sources we derive the universal law: the entropy of a holographic screen is equal to quarter of its area in the Planck system of units.
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Gaarder Haug, Espen. "The gravitational constant and the Planck units. A simplification of the quantum realm." Physics Essays 29, no. 4 (December 17, 2016): 558–61. http://dx.doi.org/10.4006/0836-1398-29.4.558.
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Bordé, Christian J. "Base units of the SI, fundamental constants and modern quantum physics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1834 (August 4, 2005): 2177–201. http://dx.doi.org/10.1098/rsta.2005.1635.
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Over the past 40 years, a number of discoveries in quantum physics have completely transformed our vision of fundamental metrology. This revolution starts with the frequency stabilization of lasers using saturation spectroscopy and the redefinition of the metre by fixing the velocity of light c . Today, the trend is to redefine all SI base units from fundamental constants and we discuss strategies to achieve this goal. We first consider a kinematical frame, in which fundamental constants with a dimension, such as the speed of light c , the Planck constant h , the Boltzmann constant k B or the electron mass m e can be used to connect and redefine base units. The various interaction forces of nature are then introduced in a dynamical frame, where they are completely characterized by dimensionless coupling constants such as the fine structure constant α or its gravitational analogue α G . This point is discussed by rewriting the Maxwell and Dirac equations with new force fields and these coupling constants. We describe and stress the importance of various quantum effects leading to the advent of this new quantum metrology. In the second part of the paper, we present the status of the seven base units and the prospects of their possible redefinitions from fundamental constants in an experimental perspective. The two parts can be read independently and they point to these same conclusions concerning the redefinitions of base units. The concept of rest mass is directly related to the Compton frequency of a body, which is precisely what is measured by the watt balance. The conversion factor between mass and frequency is the Planck constant, which could therefore be fixed in a realistic and consistent new definition of the kilogram based on its Compton frequency. We discuss also how the Boltzmann constant could be better determined and fixed to replace the present definition of the kelvin.
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Gueorguiev, Vesselin, and Andre Maeder. "Revisiting the Cosmological Constant Problem within Quantum Cosmology." Universe 6, no. 8 (August 2, 2020): 108. http://dx.doi.org/10.3390/universe6080108.
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A new perspective on the Cosmological Constant Problem (CCP) is proposed and discussed within the multiverse approach of Quantum Cosmology. It is assumed that each member of the ensemble of universes has a characteristic scale a that can be used as integration variable in the partition function. An averaged characteristic scale of the ensemble is estimated by using only members that satisfy the Einstein field equations. The averaged characteristic scale is compatible with the Planck length when considering an ensemble of solutions to the Einstein field equations with an effective cosmological constant. The multiverse ensemble is split in Planck-seed universes with vacuum energy density of order one; thus, Λ˜≈8π in Planck units and a-derivable universes. For a-derivable universe with a characteristic scale of the order of the observed Universe a≈8×1060, the cosmological constant Λ=Λ˜/a2 is in the range 10−121–10−122, which is close in magnitude to the observed value 10−123. We point out that the smallness of Λ can be viewed to be natural if its value is associated with the entropy of the Universe. This approach to the CCP reconciles the Planck-scale huge vacuum energy–density predicted by QFT considerations, as valid for Planck-seed universes, with the observed small value of the cosmological constant as relevant to an a-derivable universe as observed.
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Aghanim, N., Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, et al. "Planck intermediate results." Astronomy & Astrophysics 607 (November 2017): A95. http://dx.doi.org/10.1051/0004-6361/201629504.
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The six parameters of the standard ΛCDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit values derived from WMAP data. These shifts are driven by features in the Planck temperature power spectrum at angular scales that had never before been measured to cosmic-variance level precision. We have investigated these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium τ, the baryon density ωb, the matter density ωm, the angular size of the sound horizon θ∗, the spectral index of the primordial power spectrum, ns, and Ase− 2τ (where As is the amplitude of the primordial power spectrum), we have examined the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment ℓ < 800 in the Planck temperature power spectrum) and an all angular-scale data set (ℓ < 2500Planck temperature power spectrum), each with a prior on τ of 0.07 ± 0.02. We find that the shifts, in units of the 1σ expected dispersion for each parameter, are { Δτ,ΔAse− 2τ,Δns,Δωm,Δωb,Δθ∗ } = { −1.7,−2.2,1.2,−2.0,1.1,0.9 }, with a χ2 value of 8.0. We find that this χ2 value is exceeded in 15% of our simulated data sets, and that a parameter deviates by more than 2.2σ in 9% of simulated data sets, meaning that the shifts are not unusually large. Comparing ℓ < 800 instead to ℓ> 800, or splitting at a different multipole, yields similar results. We examined the ℓ < 800 model residuals in the ℓ> 800 power spectrum data and find that the features there that drive these shifts are a set of oscillations across a broad range of angular scales. Although they partly appear similar to the effects of enhanced gravitational lensing, the shifts in ΛCDM parameters that arise in response to these features correspond to model spectrum changes that are predominantly due to non-lensing effects; the only exception is τ, which, at fixed Ase− 2τ, affects the ℓ> 800 temperature power spectrum solely through the associated change in As and the impact of that on the lensing potential power spectrum. We also ask, “what is it about the power spectrum at ℓ < 800 that leads to somewhat different best-fit parameters than come from the full ℓ range?” We find that if we discard the data at ℓ < 30, where there is a roughly 2σ downward fluctuation in power relative to the model that best fits the full ℓ range, the ℓ < 800 best-fit parameters shift significantly towards the ℓ < 2500 best-fit parameters. In contrast, including ℓ < 30, this previously noted “low-ℓ deficit” drives ns up and impacts parameters correlated with ns, such as ωm and H0. As expected, the ℓ < 30 data have a much greater impact on the ℓ < 800 best fit than on the ℓ < 2500 best fit. So although the shifts are not very significant, we find that they can be understood through the combined effects of an oscillatory-like set of high-ℓ residuals and the deficit in low-ℓ power, excursions consistent with sample variance that happen to map onto changes in cosmological parameters. Finally, we examine agreement between PlanckTT data and two other CMB data sets, namely the Planck lensing reconstruction and the TT power spectrum measured by the South Pole Telescope, again finding a lack of convincing evidence of any significant deviations in parameters, suggesting that current CMB data sets give an internally consistent picture of the ΛCDM model.
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KIM, Mun-Seog, Dong-Hun CHAE, and Kwang-Cheol LEE. "Quantum Metrology of Electrical Quantities and Mass." Physics and High Technology 30, no. 3 (March 31, 2021): 17–25. http://dx.doi.org/10.3938/phit.30.008.
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The new International System of Units (SI) became effective on 20 May 2019. In the new SI, the complete system of units can be traced to seven fixed values of the fundamental constants, not to seven base units as in the old system. Electrical metrology has two important quantum mechanical foundations. Here, we introduce the basics and the metrological applications of the Josephson effect and the quantum Hall effect, which play key roles in linking electrical quantities to the fundamental constants, including the Planck constant h, the elementary charge e, and the transition frequency of cesium 133 ΔνCs. Finally, we discuss the redefinition of the kilogram as one of the important examples of electrical metrology based on quantum physics.
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Sanchez, Carlos. "Realizing the Kilogram from the Planck Constant: The Kibble Balance and the Electrical Units." IEEE Instrumentation & Measurement Magazine 24, no. 3 (May 2021): 5–10. http://dx.doi.org/10.1109/mim.2021.9436095.
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Valdés, Joaquín. "Explaining to different audiences the new definition and experimental realizations of the kilogram." Journal of Sensors and Sensor Systems 10, no. 1 (January 21, 2021): 1–4. http://dx.doi.org/10.5194/jsss-10-1-2021.
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Abstract. Different options were discussed before reaching the final agreement on the new definitions of the SI units, effective from 20 May 2019, especially with regard to the kilogram, now defined in terms of the numerical value of the Planck constant (h). Replacing the artefact definition of the kilogram with a new one based on the mass of a particle, or the atomic mass constant (mu), would have been preferable for ease of understanding, among other reasons. In this paper we discuss some limitations of teaching to different audiences what a kilogram is in the redefined International System of Units (SI), including realizations of the new definition.
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CARNEIRO, SAULO. "FROM DE SITTER TO DE SITTER: A NON-SINGULAR INFLATIONARY UNIVERSE DRIVEN BY VACUUM." International Journal of Modern Physics D 15, no. 12 (December 2006): 2241–47. http://dx.doi.org/10.1142/s0218271806009510.
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A semi-classical analysis of vacuum energy in the expanding space–time suggests that the cosmological term decays with time, with a concomitant matter production. For early times we find, in Planck units, Λ ≈ H4, where H is the Hubble parameter. The corresponding cosmological solution has no initial singularity, existing since an infinite past. During an infinitely long period we have a quasi-de Sitter, inflationary universe, with H ≈ 1. However, at a given time, the expansion undertakes a phase transition, with H and Λ decreasing to nearly zero in a few Planck times, producing a huge amount of radiation. On the other hand, the late-time scenario is similar to the standard model, with the radiation phase followed by a dust era, which tends asymptotically to a de Sitter universe, with vacuum dominating again.
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Żenczykowski, Piotr. "MOND and natural scales of distance and mass." Modern Physics Letters A 34, no. 37 (December 6, 2019): 1950306. http://dx.doi.org/10.1142/s0217732319503061.
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We describe a MOND-related approach to natural scales of distance and mass, viewing it as a logical step following Planck’s modification of the Stoney system of units. The MOND-induced scales are not based on the strength of any physical interaction (electromagnetic, gravitational, or otherwise). Instead, they are specified by three physical constants of a general nature that define the scales of action, speed, and acceleration, i.e. [Formula: see text] — the Planck constant, [Formula: see text] — the speed of light and [Formula: see text] — the MOND acceleration constant. When the gravitational constant [Formula: see text] is added, two further distance scales (apart from the size of the Universe) appear: the Planck scale and a nanometer scale that fits the typical borderline between the classical and the quantum descriptions.
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CARNEIRO, SAULO. "ON THE VACUUM ENTROPY AND THE COSMOLOGICAL CONSTANT." International Journal of Modern Physics D 12, no. 09 (October 2003): 1669–73. http://dx.doi.org/10.1142/s0218271803004158.
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It is generally accepted that the entropy of an asymptotically de Sitter universe is bounded by the area, in Planck units, of the de Sitter horizon. Based on an analysis of the entropy associated to the vacuum quantum fluctuations, we suggest that the existence of such a holographic bound constitutes a possible explanation for the observed value of the cosmological constant, theoretically justifying a relation proposed 35 years ago by Zel'dovich.
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Wright, Jason T. "Planck frequencies as Schelling points in SETI." International Journal of Astrobiology 19, no. 6 (September 7, 2020): 446–55. http://dx.doi.org/10.1017/s1473550420000221.
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AbstractIn SETI, when searching for ‘beacons’ – transmissions intended for us and meant to get our attention – one must guess the appropriate frequency to search by considering what frequencies would be universally obvious to other species. This is a well-known concept in game theory, where such solutions to a non-communicative cooperative game (such as a mutual search) are called ‘Schelling points’. It is noteworthy, therefore, that when developing his eponymous units, Planck called them ‘natural’ because they ‘remain meaningful for all times and also for extraterrestrial and non-human cultures’. Here, I apply Planck's suggestion in the context of Schelling points in SETI with a ‘Planck Frequency Comb’, constructed by multiplying the Planck energy by integer powers of the fine structure constant. This comb includes a small number of frequencies in regions of the electromagnetic spectrum where laser and radio SETI typically operates. Searches might proceed and individual teeth in the comb, or at many teeth at once, across the electromagnetic spectrum. Indeed, the latter strategy can be additionally justified by the transmitter's desire to signal at many frequencies at once, to improve the chances that the receiver will guess one of them correctly. There are many arbitrary and anthropocentric choices in this comb's construction, and indeed one can construct several different frequency combs with only minor and arbitrary modifications. This suggests that it may be fruitful to search for signals arriving in frequency combs of arbitrary spacing. And even though the frequencies suggested here are only debatably ‘better’ than others proposed, the addition of the Planck Frequency Comb to the list of ‘magic frequencies’ can only help searches for extraterrestrial beacons.
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Walker, Martin. "SU(2) × SU(2) Algebras and the Lorentz Group O(3,3)." Symmetry 12, no. 5 (May 15, 2020): 817. http://dx.doi.org/10.3390/sym12050817.
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The Lie algebra of the Lorentz group O(3,3) admits two types of SU(2) × SU(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved quantity due to invariance under temporal rotations are investigated and found to be the same units of measure as the Planck constant. The breaking of time reversal symmetry is considered and found to affect the chiral properties of a temporal SU(2) × SU(2) algebra. Finally, the symmetry between algebras is explored and pairs of algebras are found to be related by SU(2) × U(1) symmetry, while a group of three algebras are related by SO(4) symmetry.
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Gupta, Rajendra P. "Varying Physical Constants, Astrometric Anomalies, Redshift and Hubble Units." Galaxies 7, no. 2 (May 14, 2019): 55. http://dx.doi.org/10.3390/galaxies7020055.
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We have developed a cosmological model by allowing the speed of light c, gravitational constant G and cosmological constant Λ in the Einstein filed equation to vary in time, and solved them for Robertson-Walker metric. Assuming the universe is flat and matter dominant at present, we obtain a simple model that can fit the supernovae 1a data with a single parameter almost as well as the standard ΛCDM model with two parameters, and which has the predictive capability superior to the latter. The model, together with the null results for the variation of G from the analysis of lunar laser ranging data determines that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH0. This variation of G and c is all what is needed to account for the Pioneer anomaly, the anomalous secular increase of the moon eccentricity, and the anomalous secular increase of the astronomical unit. We also show that the Planck’s constant ħ increases as dħ/dt = 1.8ħH0 and the ratio D of any Hubble unit to the corresponding Planck unit increases as dD/dt = 1.5DH0. We have shown that it is essential to consider the variation of all the physical constants that may be involved directly or indirectly in a measurement rather than only the one whose variation is of interest.
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Davis, R. S. "The role of the international prototype of the kilogram after redefinition of the International System of Units." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1953 (October 28, 2011): 3975–92. http://dx.doi.org/10.1098/rsta.2011.0181.
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Since 1889, the international prototype of the kilogram has served to define the unit of mass in what is now known as the International System of Units (SI). This definition, which continues to serve mass metrology well, is an anachronism for twenty-first century physics. Indeed, the kilogram will no doubt be redefined in terms of a physical constant, such as the Planck constant. As a practical matter, linking the quantum world to the macroscopic world of mass metrology has, and remains, challenging although great progress has been made. The international prototype or, more likely, a modern ensemble of reference standards, may yet have a role to play for some time after redefinition, as described in this paper.
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Wang, Jin. "New SI and precision measurements: an interview with Tianchu Li." National Science Review 7, no. 12 (February 25, 2020): 1837–40. http://dx.doi.org/10.1093/nsr/nwz211.
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Abstract On 13–16 November 2018, the 26th General Conference of Weights and Measures (CGPM) was held in Paris. The conference adopted Resolution A on ‘Revision of the International System of Units (SI).’ According to Resolution A: four of the SI basic units, namely kilograms, amps, kelvin and mole, are defined by the Planck constant h, the basic charge constant e, the Boltzmann constant k and the Avogadro constant NA, respectively. This establishes the basic quantities and units in SI on a series of constants. The new SI was officially launched on 20 May 2019. This is the most significant change and a milestone in the history of metrology since the Metre Convention was signed in 20 May 1875. Professor Tianchu Li, an academician of the Chinese Academy of Engineering, has been working on time and frequency standards for 37 years. In this interview, Prof. Li reviews the quantization and constant evolutions of the second and meter, and introduces the redefinitions of ampere, kelvin, kilogram and mole, and their significance for precision measurements.
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Mills, Ian M., Peter J. Mohr, Terry J. Quinn, Barry N. Taylor, and Edwin R. Williams. "Adapting the International System of Units to the twenty-first century." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1953 (October 28, 2011): 3907–24. http://dx.doi.org/10.1098/rsta.2011.0180.
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We review the proposal of the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), currently being considered by the General Conference on Weights and Measures (Conférences Générales des Poids et Mesures, CGPM), to revise the International System of Units (Le Système International d'Unitès, SI). The proposal includes new definitions for four of the seven base units of the SI, and a new form of words to present the definitions of all the units. The objective of the proposed changes is to adopt definitions referenced to constants of nature, taken in the widest sense, so that the definitions may be based on what are believed to be true invariants. In particular, whereas in the current SI the kilogram, ampere, kelvin and mole are linked to exact numerical values of the mass of the international prototype of the kilogram, the magnetic constant (permeability of vacuum), the triple-point temperature of water and the molar mass of carbon-12, respectively, in the new SI these units are linked to exact numerical values of the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant, respectively. The new wording used expresses the definitions in a simple and unambiguous manner without the need for the distinction between base and derived units. The importance of relations among the fundamental constants to the definitions, and the importance of establishing a mise en pratique for the realization of each definition, are also discussed.
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THOMAS, MATTHIEU. "Kilogram and new SI definitions." High Temperatures-High Pressures 48, no. 3 (2020): 193–205. http://dx.doi.org/10.32908/hthp.v48.789.
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The seven base units of the SI will be defined on May 20, 2019 by reference to fixed and exact values of defining constants. In particular, the kilogram will be defined from the Planck constant h, allowing weaknesses of the previous artefact definition to be lift up. The Kibble balance is one of the methods to realize a macroscopic mass from h: LNE has developed such a balance which is described. This balance has allowed LNE to contribute to the latest adjustment of the h value, and will be used to realize the mass unit in France.
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Kaptay, G. "On the five base quantities of nature and SI (The International System of Units)." Journal of Mining and Metallurgy, Section B: Metallurgy 47, no. 2 (2011): 241–46. http://dx.doi.org/10.2298/jmmb110620015k.
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It is shown here that five base quantities (and the corresponding five base units) of nature are sufficient to define all derived quantities (and their units) and to describe all natural phenomena. The base quantities (and their base units) are: length (m), mass (kg), time (s), temperature (K) and electric charge (C). The amount of substance (mole) is not taken as a base quantity of nature and the Avogadro constant is not considered as a fundamental constant of nature, as they are both based on an arbitrary definition (due to the arbitrary value of 0.012 kg for the mass of 1 mole of C-12 isotope). Therefore, the amount of substance (mole) is moved from the list of base quantities to the category of the supplementary units (to be re-created after its abrogation in 1995). Based on its definition, the luminous intensity (cd) is not a base quantity (unit), therefore it is moved to the list of derived quantities (units). The ampere and coulomb are exchanged by places in the list of base and derived units, as ampere is a speed of coulombs (but SI defines meter, not its speed as a base unit). The five base quantities are re-defined in this paper by connecting them to five fundamental constants of nature (the most accurately known frequency of the hydrogen atom, the speed of light, the Planck constant, the Boltzmann constant and the elementary charge) with their numerical values fixed in accordance with their CODATA 2006 values (to be improved by further experiments).
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Ballantine, Kyle E., John F. Donegan, and Paul R. Eastham. "There are many ways to spin a photon: Half-quantization of a total optical angular momentum." Science Advances 2, no. 4 (April 2016): e1501748. http://dx.doi.org/10.1126/sciadv.1501748.
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The angular momentum of light plays an important role in many areas, from optical trapping to quantum information. In the usual three-dimensional setting, the angular momentum quantum numbers of the photon are integers, in units of the Planck constantħ. We show that, in reduced dimensions, photons can have a half-integer total angular momentum. We identify a new form of total angular momentum, carried by beams of light, comprising an unequal mixture of spin and orbital contributions. We demonstrate the half-integer quantization of this total angular momentum using noise measurements. We conclude that for light, as is known for electrons, reduced dimensionality allows new forms of quantization.
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MAGLIARO, ELENA, and CLAUDIO PERINI. "REGGE GRAVITY FROM SPINFOAMS." International Journal of Modern Physics D 22, no. 02 (February 2013): 1350001. http://dx.doi.org/10.1142/s0218271813500016.
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We consider spinfoam quantum gravity in the flipped limit, which is the double scaling limit γ → 0, j → ∞ with γj = const. , where γ is the Immirzi parameter, j is the spin and γj gives the physical area in Planck units. In this regime the amplitude for a 2-complex becomes effectively an integral over Regge-like metrics and seems to enforce Einstein equations in the semiclassical regime. The Immirzi parameter must be considered as dynamical in the sense that it runs to zero when the fine structure of the foam is averaged. In addition to quantum corrections which vanish for ℏ → 0, we find new corrections due to the discreteness of geometric spectra.
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Hart, Luke, and Jens Chluba. "Updated fundamental constant constraints from Planck 2018 data and possible relations to the Hubble tension." Monthly Notices of the Royal Astronomical Society 493, no. 3 (February 11, 2020): 3255–63. http://dx.doi.org/10.1093/mnras/staa412.
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ABSTRACT We present updated constraints on the variation of the fine structure constant, αEM, and effective electron rest mass, me, during the cosmological recombination era. These two fundamental constants directly affect the ionization history at redshift z ≃ 1100 and, thus, modify the temperature and polarization anisotropies of the cosmic microwave background (CMB) measured precisely with Planck . The constraints on αEM tighten slightly due to improved Planck 2018 polarization data but otherwise remain similar to previous CMB analysis. However, a comparison with the 2015 constraints reveals a mildly discordant behaviour for me, which from CMB data alone is found below its local value. Adding baryon acoustic oscillation data brings me back to the fiducial value, $m_{\rm e}=(1.0078\pm 0.0067)\, m_{\rm e,0}$, and also drives the Hubble parameter to H0 = 69.1 ± 1.2(in units of ${\rm km \, s^{-1} \, Mpc^{-1} }$). Further adding supernova data yields $m_{\rm e}=(1.0190\pm 0.0055)\, m_{\rm e,0}$ with H0 = 71.24 ± 0.96. We perform several comparative analyses using the latest cosmological recombination calculations to further understand the various effects. Our results indicate that a single-parameter extension allowing a slightly increased value of me (≃3.5σ above me, 0) could play a role in the Hubble tension.
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AMELINO-CAMELIA, GIOVANNI, NICCOLÒ LORET, GIANLUCA MANDANICI, and FLAVIO MERCATI. "UV AND IR QUANTUM-SPACETIME EFFECTS FOR THE CHANDRASEKHAR MODEL." International Journal of Modern Physics D 21, no. 06 (June 2012): 1250052. http://dx.doi.org/10.1142/s0218271812500526.
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We modify the Chandrasekhar model of white dwarfs by introducing some of the momentum-space features which have been considered in the quantum-gravity literature. We find that when the new effects are confined to high energies, one only finds significant corrections to the Chandrasekhar model in regimes where the model anyway lacks any contact with observations. But these high-energy effects could play an important role in cases where ultra-high densities are present, even when the relevant star is still gigantic in Planck-length units. If the effects are not confined to high energies, as a result of "ultraviolet/infrared mixing", there could be significant implications for white dwarfs whose mass is roughly half the mass of the Sun, some of which are described in the literature as "strange white dwarfs".
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DUAN, YISHI, GUOHONG YANG, and YING JIANG. "THE QUANTIZATION AND PRODUCTION OF THE SPACE–TIME DEFECTS IN THE EARLY UNIVERSE." International Journal of Modern Physics A 13, no. 12 (May 10, 1998): 2001–12. http://dx.doi.org/10.1142/s0217751x98000883.
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In Riemann–Cartan manifold U4, a new topological invariant is obtained by means of the torsion tensor. In order to describe the space–time defects (which appear in the early universe due to torsion) in an invariant form, the new topological invariant is introduced to measure the size of defects and it is interpreted as the dislocation flux in internal space. By the use of the so-called ϕ mapping method and the gauge potential decomposition, the dislocation flux is quantized in units of the Planck length. The quantum numbers are determined by the Hopf indices and the Brouwer degrees. Furthermore, the dynamic form of the dislocations is studied by defining an identically conserved current. Based on the implicit function theorem, the production of the defects at the limit points is detailed.
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Nicolaus, Arnold, Horst Bettin, Michael Borys, Ulrich Kuetgens, and Axel Pramann. "Revision of the SI: The Determination of the Avogadro Constant as the Base for the Kilogram." Key Engineering Materials 613 (May 2014): 3–10. http://dx.doi.org/10.4028/www.scientific.net/kem.613.3.
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At least four units of the International System of Units (SI) are on the way to a new definition. Especially for the unit of mass, the kilogram, a rigorous change is considered. Instead of the current definition, a 1kg-artifact in form of a Pt-Ir-cylinder, the intended formulation relates the unit of mass to a fundamental constant. In detail this requires in a first step a measurement of the chosen fundamental constant with contemporary lowest uncertainty and best reproducibility. The constant will then be fixed to that value. As an example the metre is related to the fixed constant speed of light.For the kg there are considered two ways: one is a watt balance, which determines the mass in units of the Planck constant, h. While at present the watt balances show a heterogeneous appearance, the second class of experiment the determination of the Avogadro constant, NA, which measures the mass in terms of the number of elementary entities has reached a considerable level of uncertainty and reproducibility. The fundament of the new determination of the Avogadro constant is a highly enriched 28Si crystal. The different working groups of the Avogadro team determine molar mass and lattice parameter of the crystal, and mass and volume of two precision spheres made from different positions, but of the same crystal. All measurements are carried out for both spheres and all measurement quantities are determined at least from two independent working groups, usually of different countries.
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Burinskii, Alexander. "Weakness of gravity as illusion which hides true path to unification of gravity with particle physics." International Journal of Modern Physics D 26, no. 12 (October 2017): 1743022. http://dx.doi.org/10.1142/s0218271817430222.
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Well known weakness of gravity in particle physics is an illusion caused by underestimation of the role of spin in gravity. Relativistic rotation is inseparable from spin, which for elementary particles is extremely high and exceeds mass on 20–22 orders (in units [Formula: see text]). Such a huge spin generates frame-dragging that distorts space much stronger than mass, and effective scale of gravitational interaction is shifted from Planck to Compton distances. We show that compatibility between gravity and quantum theory can be achieved without modifications of Einstein–Maxwell equations, by coupling to a supersymmetric Higgs model of symmetry breaking and forming a nonperturbative super-bag solution, which generates a gravity-free Compton zone necessary for consistent work of quantum theory. Super-bag is naturally upgraded to Wess–Zumino supersymmetric QED model, forming a bridge to perturbative formalism of conventional QED.
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MEDVED, A. J. M. "ON THE "UNIVERSAL" QUANTUM AREA SPECTRUM." Modern Physics Letters A 24, no. 32 (October 20, 2009): 2601–9. http://dx.doi.org/10.1142/s0217732309031922.
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There has been much debate about the form of the quantum area spectrum for a black hole horizon, with the evenly spaced conception of Bekenstein having featured prominently in the discourse. Here, we refine a very recently proposed method for calibrating the Bekenstein form of the spectrum. Our refined treatment predicts, as did its predecessor, a uniform spacing between adjacent spectral levels of 8π in Planck units — notably, an outcome that already has a pedigree as a proposed "universal" value for this intrinsically quantum-gravitational measure. Although the two approaches are somewhat similar in logic and quite agreeable in outcome, we argue that our version is conceptually more elegant and formally simpler than its precursor. Moreover, our rendition is able to circumvent a previously unnoticed technical issue and, as an added bonus, translates to generic theories of gravity in a very direct manner.
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Fischer, J. "Low uncertainty Boltzmann constant determinations and the kelvin redefinition." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2064 (March 28, 2016): 20150038. http://dx.doi.org/10.1098/rsta.2015.0038.
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At its 25th meeting, the General Conference on Weights and Measures (CGPM) approved Resolution 1 ‘On the future revision of the International System of Units, the SI’, which sets the path towards redefinition of four base units at the next CGPM in 2018. This constitutes a decisive advance towards the formal adoption of the new SI and its implementation. Kilogram, ampere, kelvin and mole will be defined in terms of fixed numerical values of the Planck constant, elementary charge, Boltzmann constant and Avogadro constant, respectively. The effect of the new definition of the kelvin referenced to the value of the Boltzmann constant k is that the kelvin is equal to the change of thermodynamic temperature T that results in a change of thermal energy kT by 1.380 65×10 −23 J. A value of the Boltzmann constant suitable for defining the kelvin is determined by fundamentally different primary thermometers such as acoustic gas thermometers, dielectric constant gas thermometers, noise thermometers and the Doppler broadening technique. Progress to date of the measurements and further perspectives are reported. Necessary conditions to be met before proceeding with changing the definition are given. The consequences of the new definition of the kelvin on temperature measurement are briefly outlined.
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Lee, Hyung Mok. "Dynamical Evolution of Globular Clusters with Mass Spectrum." Publications of the Astronomical Society of Australia 9, no. 1 (1991): 41–44. http://dx.doi.org/10.1017/s1323358000024838.
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AbstractWe present a series of numerical models describing the dynamical evolution of globular clusters with a mass spectrum, based on integration of the Fokker-Planck equation. We include three-body binary heating and a steady galactic tidal field. A wide range of initial mass functions is adopted and the evolution of the mass function is examined. The mass function begins to change appreciably during the post-collapse expansion phase due to the selective evaporation of low mass stars through the tidal boundary. One signature of highly evolved clusters is thus the significant flattening of the mass function. The age (in units of the half-mass relaxation time) increases very rapidly beyond about 100 signifying the final stage of cluster disruption. This appears to be consistent with the sharp cut-off of half-mass relaxation times at near 108 years for the Galactic globular clusters.
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Nicolini, Piero, and Euro Spallucci. "Holographic Screens in Ultraviolet Self-Complete Quantum Gravity." Advances in High Energy Physics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/805684.
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This paper studies the geometry and the thermodynamics of aholographic screenin the framework of the ultraviolet self-complete quantum gravity. To achieve this goal we construct a new static, neutral, nonrotating black hole metric, whose outer (event) horizon coincides with the surface of the screen. The spacetime admits an extremal configuration corresponding to the minimal holographic screen and having both mass and radius equalling the Planck units. We identify this object as the spacetime fundamental building block, whose interior is physically unaccessible and cannot be probed even during the Hawking evaporation terminal phase. In agreement with the holographic principle, relevant processes take place on the screen surface. The area quantization leads to a discrete mass spectrum. An analysis of the entropy shows that the minimal holographic screen can store only one byte of information, while in the thermodynamic limit the area law is corrected by a logarithmic term.
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Possolo, Antonio, Stephan Schlamminger, Sara Stoudt, Jon R. Pratt, and Carl J. Williams. "Evaluation of the accuracy, consistency, and stability of measurements of the Planck constant used in the redefinition of the international system of units." Metrologia 55, no. 1 (December 12, 2017): 29–37. http://dx.doi.org/10.1088/1681-7575/aa966c.
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Benck, Eric Carl, Corey Stambaugh, Edward Mulhern, Patrick Abbott, and Zeina Kubarych. "Progress on vacuum-to-air mass calibration system using magnetic suspension to disseminate the Planck-constant realized kilogram." ACTA IMEKO 6, no. 2 (July 21, 2017): 70. http://dx.doi.org/10.21014/acta_imeko.v6i2.406.
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<p><span style="font-size: small;">The kilogram is the unit of mass in the International System of units (SI) and has been defined as the mass of the International Prototype Kilogram (IPK) since 1889. </span><span style="font-size: small;">In the future, a new definition of the kilogram will be realized by fixing the value of the Planck constant.</span><span style="font-size: small;"> </span><span style="font-size: small;">The new definition of the unit of mass will occur in a vacuum environment by necessity, so the National Institute of Standards and Technology (NIST) is developing a mass calibration system in which a kilogram artefact in air can be directly compared with a kilogram realized in a vacuum environment.</span><span style="font-size: small;"> </span><span style="font-size: small;">This apparatus uses magnetic suspension to couple the kilogram in air to a high accuracy mass balance in vacuum.</span><span style="font-size: small;"> </span></p><p> </p>
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. "Editorial." High Temperatures-High Pressures 48, no. 3 (2020): 191. http://dx.doi.org/10.32908/hthp.v48.787.
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Dear reader, This year is full of events, anniversaries and milestones. Not only does HTHP celebrate its 50th anniversary, but also the Periodic Table of Elements has its 150th birthday. In 1869 Dimitri Mendeleyev and Lothar Meyer discovered and presented this table. In order to commemorate this breakthrough, UNESCO has declared 2019 as the “International Year of the Periodic Table of Chemical Elements”. In addition, another important event takes place in May 2019. The Conférence Générale des Poids et Mesures will put into effect the new SI system of units on May 20, 2019, the “World Metrology Day”. The introduction of this new system marks a change in paradigm: the new system relates all units to fundamental constants, rather than artefacts. The most prominent example is the definition of the new kilogram, which is now linked to the Planck constant, h. Of course, all of this has an impact on thermophysical property measurements. Therefore, we have asked Dr. Matthieu Thomas from the Laboratoire National de Métrologie et d’Essais (LNE), France, to explain shortly how this new definition works and how it was implemented. Dr. Thomas is involved in the Kibble balance project of LNE, a key element in the realisation of the new kilogram. You find his article in this issue of HTHP. The editors thank Dr. Thomas for his cooperation; we hope you will enjoy reading his article as well as the rest of this issue.
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Hod, Shahar. "A proof of the weak gravity conjecture." International Journal of Modern Physics D 26, no. 12 (October 2017): 1742004. http://dx.doi.org/10.1142/s0218271817420044.
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The weak gravity conjecture suggests that, in a self-consistent theory of quantum gravity, the strength of gravity is bounded from above by the strengths of the various gauge forces in the theory. In particular, this intriguing conjecture asserts that in a theory describing a [Formula: see text] gauge field coupled consistently to gravity, there must exist a particle whose proper mass is bounded (in Planck units) by its charge: [Formula: see text]. This beautiful and remarkably compact conjecture has attracted the attention of physicists and mathematicians over the last decade. It should be emphasized, however, that despite the fact that there are numerous examples from field theory and string theory that support the conjecture, we still lack a general proof of its validity. In the present paper, we prove that the weak gravity conjecture (and, in particular, the mass–charge upper bound [Formula: see text]) can be inferred directly from Bekenstein’s generalized second law of thermodynamics, a law which is widely believed to reflect a fundamental aspect of the elusive theory of quantum gravity.
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HSU, STEPHEN D. H., and DAVID REEB. "MONSTERS, BLACK HOLES AND THE STATISTICAL MECHANICS OF GRAVITY." Modern Physics Letters A 24, no. 24 (August 10, 2009): 1875–87. http://dx.doi.org/10.1142/s0217732309031624.
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We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective, they are objects with large proper volume that can be glued on to an asymptotically flat space. At no point is the curvature or energy density required to be large in Planck units, and quantum gravitational effects are, in the conventional effective field theory framework, small everywhere. Since they can have more entropy than a black hole of equal mass, monsters are problematic for certain interpretations of black hole entropy and the AdS/CFT duality. In the second part of the paper we review recent developments in the foundations of statistical mechanics which make use of properties of high-dimensional (Hilbert) spaces. These results primarily depend on kinematics — essentially, the geometry of Hilbert space — and are relatively insensitive to dynamics. We discuss how this approach might be adopted as a basis for the statistical mechanics of gravity. Interestingly, monsters and other highly entropic configurations play an important role.
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Balázs, Csaba. "Free Scalar Fields in Finite Volume Are Holographic." Universe 5, no. 12 (December 4, 2019): 223. http://dx.doi.org/10.3390/universe5120223.
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This brief note presents a back-of-the-envelope calculation showing that the number of degrees of freedom of a free scalar field in expanding flat space equals the surface area of the Hubble volume in Planck units. The logic of the calculation is the following. The amount of energy in the Hubble volume scales with its linear size, consequently the volume can only contain a finite number of quantized field modes. Since the momentum of the lowest energy mode scales inversely with the linear size of the volume, the maximal number of such modes in the volume scales with its surface area. It is possible to show that when the number of field modes is saturated the modes are confined to the surface of the volume. Gravity only enters this calculation as a regulator, providing a finite volume that contains the field, the entire calculation is done in flat space. While this toy model is bound to be incomplete, it is potentially interesting because it reproduces the defining aspects of holography, and advocates a regularization of the quantum degrees of freedom based on Friedmann’s equation.
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DADHICH, NARESH. "ON THE MEASURE OF SPACETIME AND GRAVITY." International Journal of Modern Physics D 20, no. 14 (December 31, 2011): 2739–47. http://dx.doi.org/10.1142/s0218271811020573.
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By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time) that requires not only a universally constant invariant velocity but also an invariant length given by its constant curvature, Λ and spacetime is completely free of dynamics. Thus c and Λ are the only two true constants of the spacetime structure and no other physical constant could claim this degree of fundamentalness. When matter is introduced, the spacetime becomes inhomogeneous and dynamic, and its curvature then determines by the Bianchi differential identity, the equation of motion for the Einstein gravity. The homogeneity thus demands that the natural state of free spacetime is of constant curvature and the cosmological constant thus emerges as a clear prediction which seems to be borne out by the observations of accelerating expansion of the Universe. However it has no relation to the vacuum energy and it could be envisioned that in terms of the Planck area, the Universe measures 10120 units!
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Stávek, Jiří. "Spin Interpreted as the Angular Momentum Curvature, Electron g-factor Interpreted as the Ratio of Toroidal Torsion and Curvature, Unlocking of the Fixed Planck Constant h – New Tests for Old Physics." European Journal of Applied Physics 3, no. 1 (February 17, 2021): 61–66. http://dx.doi.org/10.24018/ejphysics.2021.3.1.50.
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We have proposed several new rules for the description of events in the microworld. We have newly defined the interpretation of the quantum spin as the angular momentum curvature and defined the geometry of helixes and toroidal helixes of quantum particles. Some new properties of quantum particles can be experimentally tested. Based on this concept we have defined the electron g-factor as the ratio of the toroidal torsion and curvature and events between the electron and its coupling photon. From this model we have extracted the values of the fine-structure constant α and the Planck constant h. The comparison of these values with the latest experimental data reveals some possible circular arguments in the experimental determination – the so-called SI barrier created by the fixing of the SI constants (SI – International System of Units). We propose on the one side to analyze those possible circular arguments and on the other side to continue to develop new generations of instruments for getting one or two more significant figures of those values h and c. The predictions of this classical model could be compared with the best predictions of QED (quantum electrodynamics) for the fine-structure constant α.
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Oakley, William. "A Review of Inconsistencies and Unfounded Assumptions in Physics Enables A Path Forward." International Journal of Cosmology, Astronomy and Astrophysics 2, no. 1 (December 18, 2020): 115–20. http://dx.doi.org/10.18689/ijcaa-1000124.
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It is widely recognized significant parts of leading-edge physics are at an impasse. Perhaps it is time to re-evaluate long-standing inconsistencies and assumptions that have become dogma but are erroneous and blocking progress. Newtonʼs gravitational constant GN is assumed a natural constant, having originated via Newtonʼs notion of gravity as radial force acting on mass in flat observer space. But Einstein showed gravity due to curved space time with “mass” dimensionally c2 remote from the observer energy domain. Dirac stated (elementary) particles are “no more than electromagnetic energy localized in observer space”. This suggests gravity is emergent at the particle scale by spacetime curved in three dimensions. But Newtonʼs assumed radial force is consistent only with spacetime curvature in the two dimensions orthogonal to the radial, so how can GN be fundamental? Do the different dimensionalities of Newtonʼs and Einsteinʼs theories relate to the Dark Matter issue? Describing the electron as a photon in a relativistic quantum loop localized by curved spacetime enables derivation of an expression for GN giving a value within the empirical uncertainty. The electron is posited as relativistic electromagnetic energy in dynamic equilibrium between circumferential metric tension at the Strong Force scale and radial electrostatic force, satisfying the Planck “Force Equality” premise. As historically long suspected GN contains a numerical factor of c4, derived from the cgs units, in which it was first measured, and a relativistic factor, α-4/3, which move the Planck scale into exact correspondence with the electron parameters. General Relativity is shown a fundamental femto-scale theory where the strong force in a metric curved at the particle scale is manifest in observer space reduced by the classical “Large Number” of 5.7x1044 and is evident as gravity. The expression obtained for GN is supported by deriving the MOND constant and the observed flat galactic star rotation velocity curves. Resolving identified erroneous assumptions and inconsistencies will significantly impact cosmology and particle physics and bring gravitational and electromagnetic unification closer.
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Nez, F., A. Antognini, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. Covita, A. Dax, et al. "Is the proton radius a player in the redefinition of the International System of Units?" Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1953 (October 28, 2011): 4064–77. http://dx.doi.org/10.1098/rsta.2011.0233.
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It is now recognized that the International System of Units (SI units) will be redefined in terms of fundamental constants, even if the date when this will occur is still under debate. Actually, the best estimate of fundamental constant values is given by a least-squares adjustment, carried out under the auspices of the Committee on Data for Science and Technology (CODATA) Task Group on Fundamental Constants. This adjustment provides a significant measure of the correctness and overall consistency of the basic theories and experimental methods of physics using the values of the constants obtained from widely differing experiments. The physical theories that underlie this adjustment are assumed to be valid, such as quantum electrodynamics (QED). Testing QED, one of the most precise theories is the aim of many accurate experiments. The calculations and the corresponding experiments can be carried out either on a boundless system, such as the electron magnetic moment anomaly, or on a bound system, such as atomic hydrogen. The value of fundamental constants can be deduced from the comparison of theory and experiment. For example, using QED calculations, the value of the fine structure constant given by the CODATA is mainly inferred from the measurement of the electron magnetic moment anomaly carried out by Gabrielse's group. (Hanneke et al. 2008 Phys. Rev. Lett. 100 , 120801) The value of the Rydberg constant is known from two-photon spectroscopy of hydrogen combined with accurate theoretical quantities. The Rydberg constant, determined by the comparison of theory and experiment using atomic hydrogen, is known with a relative uncertainty of 6.6×10 −12 . It is one of the most accurate fundamental constants to date. A careful analysis shows that knowledge of the electrical size of the proton is nowadays a limitation in this comparison. The aim of muonic hydrogen spectroscopy was to obtain an accurate value of the proton charge radius. However, the value deduced from this experiment contradicts other less accurate determinations. This problem is known as the proton radius puzzle. This new determination of the proton radius may affect the value of the Rydberg constant . This constant is related to many fundamental constants; in particular, links the two possible ways proposed for the redefinition of the kilogram, the Avogadro constant N A and the Planck constant h . However, the current relative uncertainty on the experimental determinations of N A or h is three orders of magnitude larger than the ‘possible’ shift of the Rydberg constant, which may be shown by the new value of the size of the proton radius determined from muonic hydrogen. The proton radius puzzle will not interfere in the redefinition of the kilogram. After a short introduction to the properties of the proton, we will describe the muonic hydrogen experiment. There is intense theoretical activity as a result of our observation. A brief summary of possible theoretical explanations at the date of writing of the paper will be given. The contribution of the proton radius puzzle to the redefinition of SI-based units will then be examined.
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Cukaric, Nemanja, and Milan Tadic. "Multiband model of the valence-band electronic structure in cylindrical GaAs nanowires." Chemical Industry 64, no. 3 (2010): 165–70. http://dx.doi.org/10.2298/hemind091221028c.
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We compute the hole states in the GaAs free-standing nanowires, and in the GaAs/(Al,Ga)As core-shell nanowires of type I-s, which are grown along the [100] direction. The hole states are extracted from the 4-band Luttinger-Kohn Hamiltonian, which explicitly takes into account mixing between the light and heavy holes. The axial aproximation is adopted, which allowed classification of states according to the total angular monentum (fz when expressed in units of the Planck constant). The envelope functions are expanded in Bessel functions of the first kind. The dispersion relations of the subbands E(kz) obtained by the devised method do not resemble parabolas, which is otherwise a feature of the dispersion relations of the conduction subbands. Furthermore, the energy levels of holes whose total orbital momentum is fz=1/2 are shown to cross for a free-standing wire. The low energy fz=1/2 states are found to anticross, but these anticrossings turn into crossings when the ratio of the inner and outer radius of the core-shell wire takes a certain value. The influence of the geometric parameters on the dispersion relations is considered for both free standing and core-shell nanowires.