Ideal Clock Research Articles

GAUGE INVARIANCE OF PARAMETRIZED SYSTEMS AND PATH INTEGRAL QUANTIZATION

Gauge invariance of systems whose Hamilton–Jacobi equation is separable is improved by adding surface terms to the action functional. The general form of these terms is given for some complete solutions of the Hamilton–Jacobi equation. The procedure is applied to the relativistic particle and toy universes, which are quantized by imposing canonical gauge conditions in the path integral; in the case of empty models, we first quantize the parametrized system called "ideal clock," and then we examine the possibility of obtaining the amplitude for the minisuperspaces by matching them with the ideal clock. The relation existing between the geometrical properties of the constraint surface and the variables identifying the quantum states in the path integral is discussed.

Comment on the Transition Amplitude for Toy Universe Models

The parametrized system called the “idealclock” is turned into an ordinary gauge system andquantized by means of a path integral in which canonicalgauges are admissible. Then the possibility of applying the results to obtain the transition amplitudefor empty minisuperspaces, and the restrictions arisingfrom the topology of the constraint surface, are studiedby matching the models with the ideal clock. A generalization to minisuperspaces with truedegrees of freedom is also discussed.

Digital ultrafast carrier recovery for interactive transmission systems

An ultrafast, all-digital method for phase synchronization and coherent carrier recovery is presented for time division multiple access (TDMA) and code division multiple access (CDMA) burst data communication systems. A new adaptive phase tracking (APT) method, presented and analyzed in this paper, uses a hard-limited IF signal in a feed forward configuration for carrier phase detection and recovery. A novel new technique of phase window filtering is presented as a means to combat noise induced phase errors, and improved the performance of a digital controlled phase shift oscillator by 7 dB. Experimental measurements show APT provides robust bit error rate (BER) performance within 1 dB of the theoretical binary phase shift keyed (BPSK) and tenths of dBs of an ideal hard wired clock. APT achieves acquisition within one- to four-bits-5 to 10 times faster than present requirements. A low power, low cost single chip fast carrier synchronization and demodulation solution for QPSK, GMSK and GSM compatible OQPSK and Feher's quadrature phase shift keyed (FQPSK) and binary phase shift keyed (FBPSK) systems are also presented.

Almost ideal clocks in quantum cosmology: a brief derivation of time

A formalism for quantizing time reparametrization invariant dynamics is considered and applied to systems which contain an `almost ideal clock'. Previously, this formalism was successfully applied to the Bianchi models and, while it contains no fundamental notion of `time' or `evolution', the approach does contain a notion of correlations. Using correlations with the almost ideal clock to introduce a notion of time, we derive the complete formalism of external time quantum mechanics. The explicit relation between the physical Hilbert space and the usual Hilbert space for a system with an external time is also derived and the limit of an ideal clock is found to be closely associated with the Klein - Gordon inner product and the Newton - Wigner formalism.

Extrinsic time in quantum cosmology

An extrinsic time is identified in most isotropic and homogeneous cosmological models by matching them with the ideal clock - a parametrized system whose only "degree of freedom" is time -. Once this matching is established, the cosmological models are quantized in the same way as the ideal clock. The space of solutions of the Wheeler-DeWitt equation is turned out into a Hilbert space by inserting a time dependent operator in the inner product, yielding a unitary theory equivalent to the phase space reduced theory.

The "Circadian Paradigm": A Test of Involvement of the Circadian System in the Photoperiodic Clock

A long-standing and yet open question is whether the circadian system is involved in photoperiodism. A limited set of protocols were credited with the ability of answering this question. The most widely used are the so-called "resonance experiments". Recent models, however, showed how the working of a non-circadian photoperiodic clock (hourglass) could go with a positive result in resonance experiments, thus giving a strong indication of the unreliability of this test. This paper showed how inferring a series of logical consequences from two properties of circadian system made it possible to describe the behaviour of an ideal circadian photoperiodic clock when submitted to regimes derived from a resonance protocol. This design was dubbed "Circadian paradigm" (CP). Comparing the predicted circadian behaviour with that of a concrete photoperiodic system provided a test of circadian involvement. Application of the CP to an insect species, Pieris brassicae, which gave a positive response to classical resonance experiments, yielded evidence that the inset clock was an hourglass and that the observed circadian modulation could readily be attributed to an inhibitory action of the circadian system on the output of the clock, as proposed by recent models. Another issue was that short- and long-night responses were likely to result from different mechanisms. The CP thus appeared as a theoretical tool fitted to decide whether the circadian system is part of a photoperiodic clock working. The results, which reinforced the grounds for discarding resonance as a circadian test, besides supported some of the theoretical properties of recent models.

Digital burst mode clock recovery technique for fiber-optic systems

We present a clock recovery technique for burst mode systems that performs the functions of clock phase recovery, burst synchronization (to determine the first data bit in the burst), and timing alarm generation (to maintain bursts within their designated time slots). The method is based on the use of a correlation algorithm in which the incoming preamble containing a '0 1 0' bit sequence is sampled with multiple clock phases and correlated with stored, time delayed versions of the same sequence. The method was implemented in a 0.7 /spl mu/m CMOS Application Specific Integrated Circuit (ASIC). Measurements of the phase tracking characteristics over the frequency range of 38 to 90 MHz are presented. Bit error rate measurements made using the device in a burst mode fiber-optic receiver operating at 51.84 Mb/s were also performed, where it was found that the device performed well and was able to perform clock extraction with a penalty of approximately 2 dB with respect to an ideal clock extraction system. >

Quantum kinematics of spacetime. II. A model quantum cosmology with real clocks.

Nonrelativistic model quantum cosmologies are studied in which the basic time variable is the position of a clock indicator and the time parameter of the Schr\"odinger equation is an unobservable label. Familiar Schr\"odinger-Heisenberg quantum mechanics emerges if the clock is ideal---arbitrarily accurate for arbitrarily long times. More realistically, however, the usual formulation emerges only as an approximation appropriate to states of this model universe in which part of the system functions approximately as an ideal clock. It is suggested that the quantum kinematics of spacetime theories such as general relativity may be analogous to those of this model. In particular it is suggested that our familiar notion of time in quantum mechanics is not an inevitable property of a general quantum framework but an approximate feature of specific initial conditions.

A new class of ideal clocks

We have found a new class of ideal clocks within general relativity. They are self-gravitating systems such as rotating stars, rotating black holes, and binary star systems. The gravitational red shift of the observed period of rotation of such clocks in a given, weak external gravitational field is shown to be the same as that of an ideal atomic clock. Because the clocks have structure and dynamics determined by gravitational interactions, the full nonlinear machinery of general relativity must be used. This result is important for the binary pulsar PSR 1913+16, where the gravitational red shift of the pulsar's frequency caused by the companion's gravitational field is an observable effect.

Adjustability as a requirement of ideal clocks

A coordinate frame is considered as an arrangement of clocks that meet certain criteria of synchronization. Einstein's ideal clock is compared with the behavior required for clocks to maintain synchrony in the group of coordinate frames that leaves Maxwell's equations invariant. The required clock rates differ from the rate of Einstein's clock. An ideal adjustable clock is defined as an Einstein clock augmented by variable “gearing” that can offset its rate. Ongoing adjustment of these clocks enables them to meet all synchronization criteria in the group of coordinate frames. The need for adjustment is due to the well known invariance of Maxwell's equations under a group of coordinate transformations larger than the Lorentz group, and has nothing to do with imperfections in clocks. It is shown that the adjustments needed by ideal adjustable clocks to maintain synchrony can be measurably separated from additional adjustments that may be needed to compensate for random imperfections. The necessity for adjustment brings with it the necessity for ongoing measurement of the light signals whose exchange defines synchronization. Implications are discussed, both for the interpretation of Maxwell's equations and for the role of measuring instruments.

Simultaneity and retarded aging in special relativity

The conditions under which the key experimental concept of simultaneity can be retained in special relativity are considered, and an expression is derived for the degree to which it breaks down when time measurements in two different inertial frames are involved. The kinetic assumption that impulsive accelerations do not produce discontinuous changes in the reading of an ideal clock is introduced. From this assumption the discontinuous change that an impulsive acceleration makes to an observer's conventional interpretation of the simultaneous reading of a distant clock is determined. The twin paradox results from ignoring the presence of these interpretational discontinuities. A clear distinction can then be drawn between time dilatation (complementary between pairs of inertial frames) and retarded aging. Retarded aging curves are presented for the travelling twin of the twin paradox and for an observer moving uniformly in a circle. Finally an extended convention of simultaneity is given which provides an accelerated observer with a consistent ordering of distant events, and reduces to the conventional definition for observers in a given inertial frame.

Horizontal, Vertical and Regulator Control IC

The automatic frequency and phase control loop used for television horizontal-line synchronization is an ideal clock source for a vertical-countdown system. The frequency and phase stability of the properly applied line-derived clock results in improved interlace and eliminates the vertical-hold control. Line-synchronized signals are also presently used for the discrete generation of control signals for SCR or transistor-based power-supply regulators. Combining the horizontal, vertical, and regulator functions on a single monolithic IC takes advantage of their commonality and eliminates over 70 components in related circuits. Specifically, the deflection processor shown in Fig. 1 performs the following functions: a) generates horizontal and vertical drive signals which are phase-locked to the video-derived sync; b) generates the control signal for the receiver's voltage regulator; c) regulates the IC supply; d) controls the IC and receiver startup; e) corrects for VCR skew error; and f) preamplifies the vertical-scan signal.

Relativistic Time for Terrestrial Circumnavigations

Relative to a clock at rest on the Earth's surface, the time recorded by an ideal clock after a circumnavigation of the Earth depends not only on the speed and altitude but also on the direction of the circumnavigation and on the rotational speed of the Earth. Such a clock may run either fast or slow, depending on the direction and ground speed for the circumnavigation. This directional dependence should be perceptible with commercial jet speeds and cesium beam clocks.

Clock Sources for Synchronized Communication Systems

The ideal clock source will have start-stop capability, maintain known phase with respect to a start signal and combine high-frequency stability with voltage tuning to permit phase lock and Doppler correction. These properties define a clock source suitable for synchronized communication systems in which a remote unit must be started in synchronism with the signal received from a local unit. For some space applications clock stabilities of the order of one part in 107 may be required. The two approaches to the problem considered are the gated crystal oscillator and the gated divider chain. The first requires that a high Q crystal oscillator be turned on in essentially steady state with insignificant transients of amplitude and phase. In the second a continuously running crystal oscillator is gated into a series of count-down dividers to obtain the clock output. Both of these approaches will produce circuits that have the required properties.

Relativistic observations and the clock problem

Relativistic observational data are discussed, with the purpose of clarifying some aspects of the clock problem, usually called the « clock paradox » or « twin paradox ». Einstein’s position, that an ideal clock which moves in a closed curve with respect to an unaccelerated clock will indicate the passage of less time, is supported. It is pointed out that the sets of observational data of two observers who take the place of the clocks in the above situation will not be at all similar. Furthermore, the data of the accelerated observer, obtained by means of single Doppler shift and visual observational methods, will be highly implausible and inconsistent with data obtained by radar and double Doppler shift methods. Thus the accelerated observer will be under no temptation to consider himself in a situation equivalent with that of the unaccelerated observer, and should not be surprised to discover upon returning that he has aged less than the other observer. It is pointed out that the accelerated observer will see striking effects due to relativistic aberration which will not be seen by the other observer, but that neither observer will be able to see or photograph the Lorentz contraction. Only the special theory of relativity is necessary in these calculations, since no genuine gravitational fields, produced by massive bodies, are involved.