Understanding the nature of time remains a key unsolved problem in science. Newton in the Principia asserted an absolute universal time that {it `flows equably}. Hamilton then proposed a mathematical unification of space and time within the framework
of the quaternions that ultimately lead to the famous Minkowski formulation in 1908 using four-vectors. The Minkowski framework is found to provide a versatile formalism for describing the relationship between space and time in accordance with relativistic principles, but nevertheless fails to provide deeper insights into the physical origin of time and its properties. In this paper we begin with a recognition of the fundamental role played by three-dimensional space in physics that we model using the Clifford algebra multivector. From this geometrical foundation we are then able to identify a plausible origin for our concept of time. This geometrical perspective also allows us to make a key topological distinction between time and space, with time being a point-like quantity. The multivector then allows a generalized unification of time and space within a Minkowski-like description.
There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations a
nd vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one of the primary goals of nineteenth century science was to suitably describe vectors in three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Cliffords multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.
The four dimensional spacetime continuum, as originally conceived by Minkowski, has become the default framework for describing physical laws. Due to its fundamental importance, there have been various attempts to find the origin of this structure fr
om more elementary principles. In this paper, we show how the Minkowski spacetime structure arises naturally from the geometrical properties of three dimensional space when modelled by Clifford geometric algebra of three dimensions $ Cell(Re^3) $. We find that a time-like dimension along with the three spatial dimensions, arise naturally, as well as four additional degrees of freedom that we identify with spin. Within this expanded eight-dimensional arena of spacetime, we find a generalisation of the invariant interval and the Lorentz transformations, with standard results returned as special cases. The value of this geometric approach is shown by the emergence of a fixed speed for light, the laws of special relativity and the form of Maxwells equations, without recourse to any physical arguments.
The hidden sector photon is a weakly interacting hypothetical particle with sub-eV mass that kinetically mixes with the photon. We describe a microwave frequency light shining through a wall experiment where a cryogenic resonant microwave cavity is u
sed to try and detect photons that have passed through an impenetrable barrier, a process only possible via mixing with hidden sector photons. For a hidden sector photon mass of 53 $mu$eV we limit the hidden photon kinetic mixing parameter $chi < 1.7times10^{-7}$, which is an order of magnitude lower than previous bounds derived from cavity experiments in the same mass range. In addition, we use the cryogenic detector cavity to place new limits on the kinetic mixing parameter for hidden sector photons as a form of cold dark matter.
We describe the use of digital phase noise test sets at frequencies well beyond the sampling rate of their analog-to-digital converters. The technique proposed involves the transfer of phase fluctuations from an arbitrary high carrier frequency to wi
thin the operating frequency range of the digital instrument. The validity of the proposed technique has been proven via comparison with conventional methods. Digital noise measurements eliminate the need for calibration and improve consistency of experimental results. Mechanisms limiting the resolution of spectral measurements are also discussed.
Dielectric resonators are key components for many microwave and millimetre wave applications, including high-Q filters and frequency-determining elements for precision frequency synthesis. These often depend on the quality of the dielectric material.
The commonly used material for building the best cryogenic microwave oscillators is sapphire. However sapphire is becoming a limiting factor for higher frequencies design. It is then important to find new candidates that can fulfil the requirements for millimetre wave low noise oscillators at room and cryogenic temperatures. These clocks are used as a reference in many fields, like modern telecommunication systems, radio astronomy (VLBI), and precision measurements at the quantum limit. High-resolution measurements were made of the temperature-dependence of the electromagnetic properties of a polycrystalline diamond disk at temperatures between 35 K and 330 K at microwave to sub-millimetre wave frequencies. The cryogenic measurements were made using a TE01{delta} dielectric mode resonator placed inside a vacuum chamber connected to a single-stage pulse-tube cryocooler. The high frequency characterization was performed at room temperature using a combination of a quasi-optical two-lens transmission setup, a Fabry-Perot cavity and a whispering gallery mode resonator excited with waveguides. Our CVD diamond sample exhibits a decreasing loss tangent with increasing frequencies. We compare the results with well known crystals. This comparison makes clear that polycrystalline diamond could be an important material to generate stable frequencies at millimetre waves.
The phase noise and frequency stability measurements of 1 GHz, 100 MHz, and 10 MHz signals are presented which have been synthesized from microwave cryogenic sapphire oscillators using ultra-low-vibration pulse-tube cryocooler technology. We present
the measured data using independent cryogenic oscillators for the 100 MHz and 10 MHz synthesized signals, whereas previously we only estimated the expected results based on residual phase noise measurements, when only one cryogenic oscillator was available. In addition we present the design of a 1 GHz synthesizer using a Crystek voltage controlled oscillator phase locked to 1 GHz output derived from a cryogenic sapphire oscillator.
The digital signal processing has greatly simplified the process of phase noise measurements, especially in oscillators, but its applications are largely confined to the frequencies below 400 MHz. We propose a novel transpose frequency technique, whi
ch extends the frequency range of digital noise measurements to the microwave domain and beyond. We discuss two basic variations of the proposed noise measurement technique, one of which enables characterization of phase fluctuations added to the passing signal by the particular microwave component, for example by an amplifier, while another one is intended for measurements of phase fluctuations of the incoming signal itself.
Two nominally identical ultra-stable cryogenic microwave oscillators are compared. Each incorporates a dielectric-sapphire resonator cooled to near 6 K in an ultra-low vibration cryostat using a low-vibration pulse-tube cryocooler. The phase noise fo
r a single oscillator is measured at -105 dBc/Hz at 1 Hz offset on the 11.2 GHz carrier. The oscillator fractional frequency stability is characterized in terms of Allan deviation by 5.3 x 10^-16 tau^-1/2 + 9 x 10^-17 for integration times 0.1 s < tau < 1000 s and is limited by a flicker frequency noise floor below 1 x 10^-16. This result is better than any other microwave source even those generated from an optical comb phase-locked to a room temperature ultra-stable optical cavity.
The Hubble law, determined from the distance modulii and redshifts of galaxies, for the past 80 years, has been used as strong evidence for an expanding universe. This claim is reviewed in light of the claimed lack of necessary evidence for time dila
tion in quasar and gamma-ray burst luminosity variations and other lines of evidence. It is concluded that the observations could be used to describe either a static universe (where the Hubble law results from some as-yet-unknown mechanism) or an expanding universe described by the standard Lambda cold dark matter model. In the latter case, size evolution of galaxies is necessary for agreement with observations. Yet the simple non-expanding Euclidean universe fits most data with the least number of assumptions. From this review it is apparent that there are still many unanswered questions in cosmology and the title question of this paper is still far from being answered.
