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The way physics explains Nature is to speak in terms of the consequences of a few very basic equations. The electromagnetic phenomena were explained within classical physics by Maxwell’s equations. Newtonian gravity and the rules of mechanics completed the classical picture. Assuming an atomic nature of substance, statistical physics allowed thermodynamics to be established from mechanics...
The cosmological parameters are well defined now, after the satellite WMAP has measured anisotropies in the cosmic microwave background with high accuracy. Adding to this the information from the Hubble diagram of type Ia supernovae, and from the analysis of the large scale galaxy distribution, we find that we live in a Universe that undergoes accelerated expansion. The energy densities reach...
A new era in fundamental physics began when pulsars were discovered in 1967. Soon it became clear that pulsars were useful tools for a wide variety of physical and astrophysical problems. Further applications became possible with the discovery of the first binary pulsar in 1974 and the discovery of millisecond pulsars in 1982. Ever since pulsars have been used as precise cosmic clocks, taking...
The problem of fundamental units is discussed in the context of achievements of both theoretical physics and modern metrology. On one hand, due to the fascinating accuracy of atomic clocks, the traditional macroscopic standards of metrology (second, metre, kilogram) are giving way to standards based on fundamental units of nature: velocity of light c and quantum of action h. On the other...
Our knowledge of the Universe depends on our ability to make measurements. Measurement is essentially a comparison process. In order to make comparisons valid for different positions in space and time a system of invariant units is required. The fundamental constants are a natural system of units in physics and have increasingly been used in practice to provide what is assumed to be an invariant,...
Time varying fundamental constants find a natural setting in the cosmology of extra space-time dimensions. Changes in the sizes of additional compact spatial dimensions manifest themselves as modifications of coupling strengths and masses in our effective low energy four-dimensional world. Those variations and their interconnection are best studied using the renormalization group equations...
Astrophysical indications that the fine structure constant has undergone a small time variation during the cosmological evolution are discussed within the framework of the standard model of the electroweak and strong interactions and of grand unification. A variation of the electromagnetic coupling constant could either be generated by a corresponding time variation of the unified coupling...
Two popular approaches towards a quantum theory of gravity are quantum general relativity and string theory (‘M-theory’). I review their essential ideas with special emphasis on the role of fundamental constants. A special section is devoted to Kaluza–Klein theories. Most of the ‘constants’ may have their origin in quantum fields of the fundamental theory and may be space- and time-dependent...
We present evidence for variations in the fine-structure constant from Keck/HIRES spectra of 143 quasar absorption systems over the redshift range 0.2 < zabs < 4.2. This includes 15 new systems, mostly at high-z (zabs > 1.8). Our most robust estimate is a weighted mean Δα/α = (–0.57 ± 0.11) × 10–5. We respond to recent criticisms of the many-multiplet...
Applied to three inhomogeneous samples of quasar absorption-line spectra, the many-multiplet method gives a shift in the value of the fine-structure constant of Δα/α = (–5.4±1.2)×10–6 in the redshift range 0.2 < z < 3.7 (Sydney group). The 1σ error claimed in these calculations is, however, much too small and cannot be maintained by current observations of quasars. We present...
The Oklo phenomenon, natural fission reactors which had taken place in Gabon about 2 billion years ago, provides one of the most stringent constraints on the possible time-variability of the fine-structure constant α. We first review briefly what it is and how reliable it is in constraining α. We then compare the result with a more recent result on the nonzero change of α obtained from the...
We describe two experimental tests of the Equivalence Principle that are based on frequency measurements between precision oscillators and/or highly accurate atomic frequency standards. Based on comparisons between the hyperfine frequencies of 87Rb and 133Cs in atomic fountains, the first experiment constrains the variability of fundamental constants. The second experiment is based on a comparison...
In 2003 we have measured the absolute frequency of the (1S, F=1, mF=± 1)→ (2S, F′=1, mF′=± 1) two-photon transition in atomic hydrogen. By comparison with the earlier measurement in 1999 we can set an upper limit on its variation of (–29± 57) Hz within 44 months. We have combined this result with recently published results...
An optical frequency standard (λ = 657 nm) based on cold and ultra-cold neutral Ca atoms is operated at PTB and its frequency has been measured with respect to the Cs hyperfine transition over eight years. Since measurements of this kind can be used to detect possible variations of fundamental constants, we present the status of the Ca optical frequency standard with emphasis to the systematic...
Optical transition frequencies of trapped laser-cooled ions have been measured so far with an uncertainty of 10–14 with reference to primary cesium clocks. Systematic frequency shifts in these systems should be controllable to significantly higher accuracy. We have performed comparisons between frequency standards based on two independently stored 171Yb+ ions. The present experimental results...
A single indium ion stored in a radio frequency trap and laser-cooled to a temperature below 1 mK can serve as an optical frequency standard of exceptionally high accuracy and stability. Probing the 5s2 1S0 - 5s5p 3P0 transition of 115In+ at λ = 237 nm with a natural linewidth of 0.8 Hz by a sub-Hertz linewidth laser can lead to...
Recent progress in precision control of pulse repetition rate and carrier-envelope phase of ultrafast lasers has established a strong connection between optical frequency metrology and ultrafast science. A wide range of applications has ensued, including measurement of absolute optical frequencies, precision laser spectroscopy, optical atomic clocks, and optical frequency synthesis in the...
The vibrational and rotational transition frequencies in molecules are functions of the electron-to-nucleon mass ratio. They can therefore be used for experiments searching for a time-dependence of the electron-to-proton and nucleon-to-nucleon mass ratios. We propose to to perform such tests with very high precision using ultracold molecular ions trapped in a radio-frequency trap and sympathetically...
This paper addresses the motivation, technology and recent results in the tests of the general theory of relativity in the solar system. We specifically discuss Lunar Laser Ranging (LLR), the only technique available to test the Strong Equivalence Principle (SEP) and presently the most accurate method to test for the constancy of the gravitational constant G. After almost 35 years since beginning...
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