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Introduction to the constants for nonexperts
Current advances: The fine-structure constant and quantum Hall effect The fine-structure constant The quantity
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where e is the elementary charge, ![]() ![]() ![]() ![]() Our view of the fine-structure constant has changed markedly since Sommerfeld introduced it over 80 years ago. We now consider According to quantum electrodynamics (QED), the relativistic quantum field theory of the interaction of charged particles and photons, an electron can emit virtual photons that can then emit virtual electron-positron pairs (e+, e-). The virtual positrons are attracted to the original or "bare" electron while the virtual electrons are repelled from it. The bare electron is therefore screened due to this polarization. The usual fine-structure constant As indicated above, the value of alpha from the quantum Hall effect (QHE) has corroborated the value from the electron magnetic moment anomaly ae. The QHE is characteristic of a completely quantized two-dimensional electron gas. Such a gas may be realized in a high-mobility semiconductor device such as a silicon metal-oxide-semiconductor field-effect transistor (MOSFET) or GaAsAlxGa1-x As heterojunction of standard Hall bar geometry in an applied magnetic flux density B of the order of 10 T and cooled to about 1 K. For a fixed current I (typically 10 µA to 50 µA) through the device, there are regions in the curve of Hall voltage UH versus gate voltage for a MOSFET, or of UH vs B for a heterojunction, where UH remains constant as either the gate voltage or B is varied. These regions of constant UH are termed quantum Hall plateaus. In the limit of zero dissipation (zero voltage drop) in the direction of current flow, the Hall voltage-to-current quotient UH(i)/I or Hall resistance RH(i) of the ith plateau, where i is an integer (we consider only the integral QHE), is quantized and given by The theory of the QHE predicts, and the experimentally observed universality of RH(i) = UH(i)/I = RK/i is consistent with the prediction, that RK = h/e2= µ0c/2 In practice, RK is measured in terms of a laboratory standard of resistance. Thus, the resistance of the standard must be determined in the SI unit ohm in a separate experiment using an apparatus known as a calculable cross capacitor in which the unknown resistance of a reference resistor is compared with the known impedance of the capacitor. The change in capacitance of such a capacitor, and hence its change in impedance, can be readily calculated since the change depends only on the position of a movable screen electrode whose displacement can be measured with a laser interferometer. In the NIST version of the experiment, the known 0.5 pF change in capacitance of the NIST calculable cross capacitor is used to measure the capacitances of 10 pF reference capacitors. These and a 10:1 bridge are then used in two stages to measure the capacitance of two 1000 pF capacitors, which are in turn used as two arms of a special frequency dependent bridge to measure the impedances of two 100 kiloohm resistors. The latter are then compared using a 100:1 bridge with a 1000 ohm transportable resistor, which in turn is compared using dc techniques with the resistance standard in terms of which RK has been measured. The ac-dc resistance difference of the 1000 ohm resistor is determined by means of a special 1000 ohm coaxial resistor of negligible ac-dc resistance difference. All ac measurements are carried out at a frequency of approximately 1592 Hz (2 The QHE has already yielded a value of
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