# An original Conjecture on what Time is and how it works

#### Stan

Assumptions
1. Time acts at 90 degrees to space – an assumption that time can be regarded as a fourth dimension – sort of
2. 3d space could be the surface of a 4d Ball (a hypersphere) embedded in 4d space
3. Space is expanding (pretty much firmly established)

If we accept the idea of a universe that is spherical in its nature, and assumption 2 above, then the fourth dimension (time) points outwards from the origin of the universe the singularity (?). However, it is within 4d embedded space and is simply another spatial dimension that we experience as time.

Imagine an aquarium full of water. Floating within is a ball. The surface of the ball represents the 3d space of the universe. It expands. It inflates. At right angles to the surface then is time. The radial increase is the passage of time. The forward march of the present.
Note though that the direction at right angles to space is radial. On the opposing sides of the ball time has an opposite direction. Each apposing position appears to be negative relatively each to the other.

The embedding space is assumed Euclidean. No particular dimension can be identified as time. Time only becomes a reality as a movement of space – in our case a radial direction of a spherical structure. If the universe is a hypersphere. Time can only exist in our expanding universe consequent to our expanding 3d space, is the proposal made here. The expansion of space (the circumference) gives a radial increase. The radial increase is our experience of time.
Time then becomes simply a spatial measurement . It becomes a distance measured in Kilometres. The cessation of spatial expansion would then, halt time. If time halted would the universe still exist? In any event the macro universe only exists in the present – in our macro work and play.

Would the same be true of the micro Quantum world? Guessing I think it unlikely. More like the present passing over (interacting with) a quantum universe at the point of the present. That is the present acts to influence the Quantum structure which itself encompasses the past as well as the future – but that’s another story.
PS The Hubble Constant is accurately derived assuming the above. An age of 13.82 billion years (as a radius) for each passing second expands the circumference to give a Hubble Constant of a bit less than 71. Work the numbers yourself to confirm. Anyone at secondary school can 😊
NB Use 1 second is equivalent to 300,000 km (ish)

#### Onemetertwometer

BANNED
Assumptions
1. Time acts at 90 degrees to space – an assumption that time can be regarded as a fourth dimension – sort of
2. 3d space could be the surface of a 4d Ball (a hypersphere) embedded in 4d space
3. Space is expanding (pretty much firmly established)

If we accept the idea of a universe that is spherical in its nature, and assumption 2 above, then the fourth dimension (time) points outwards from the origin of the universe the singularity (?). However, it is within 4d embedded space and is simply another spatial dimension that we experience as time.

Imagine an aquarium full of water. Floating within is a ball. The surface of the ball represents the 3d space of the universe. It expands. It inflates. At right angles to the surface then is time. The radial increase is the passage of time. The forward march of the present.
Note though that the direction at right angles to space is radial. On the opposing sides of the ball time has an opposite direction. Each apposing position appears to be negative relatively each to the other.

The embedding space is assumed Euclidean. No particular dimension can be identified as time. Time only becomes a reality as a movement of space – in our case a radial direction of a spherical structure. If the universe is a hypersphere. Time can only exist in our expanding universe consequent to our expanding 3d space, is the proposal made here. The expansion of space (the circumference) gives a radial increase. The radial increase is our experience of time.
Time then becomes simply a spatial measurement . It becomes a distance measured in Kilometres. The cessation of spatial expansion would then, halt time. If time halted would the universe still exist? In any event the macro universe only exists in the present – in our macro work and play.

Would the same be true of the micro Quantum world? Guessing I think it unlikely. More like the present passing over (interacting with) a quantum universe at the point of the present. That is the present acts to influence the Quantum structure which itself encompasses the past as well as the future – but that’s another story.
PS The Hubble Constant is accurately derived assuming the above. An age of 13.82 billion years (as a radius) for each passing second expands the circumference to give a Hubble Constant of a bit less than 71. Work the numbers yourself to confirm. Anyone at secondary school can 😊
NB Use 1 second is equivalent to 300,000 km (ish)
I would argue that the passage of time is a figment of the imagination, as all units of space and time are derived from artificial constructs that are fundamentally imprecise and can not be considered objectively valid. The perception of the passage of time may be quantified in terms of evolutionary fitness, i.e. significant digits. In other words, the experience of time exists relative to the observational bandwidth of a given conscious agent. A conscious agent with evolved or constructed mechanisms for observing ultra high energy light relative to our experience, will perceive time on a relatively "faster" scale, just as a conscious agent perceiving ultra low energy light relative to our experience will perceive time on a relatively "slower" scale. But in reality, everything happens at once, and can only be objectively quantified given infinite precision, which is impossible in relative terms.

#### Stan

"I would argue that the passage of time is a figment of the imagination, as all units of space and time are derived from artificial constructs that are fundamentally imprecise and can not be considered objectively valid."

Time is defined very precisely in its relationship with space.
I suppose you could argue that space and time are both challenged in some possible theories. It is fashionable to suggest we are players in a computer program where the display only "comes to life" on the part on screen being played. Maybe you find that appealing.

As for my post I have tried to make it as close to standard theory as possible i.e. based on facts rather than.... whatever

#### Onemetertwometer

BANNED
Time is defined very precisely in its relationship with space.
I suppose you could argue that space and time are both challenged in some possible theories. It is fashionable to suggest we are players in a computer program where the display only "comes to life" on the part on screen being played. Maybe you find that appealing.

As for my post I have tried to make it as close to standard theory as possible i.e. based on facts rather than.... whatever
The problem is, standard theory is not based on facts. Science needs to learn to adjust its feelings to reality, not the other way around. This has nothing to do with theories that the Universe is a "procedurally generated computer game". This has everything to do with the demonstrably flawed assumption that Universal constants can be generated using relative terms.

#### Stan

The problem is, standard theory is not based on facts. Science needs to learn to adjust its feelings to reality, not the other way around.

I must admit I thought standard theory was based on fact - as best we can do. I do not understand what is meant by "Science needs to adjust its feelings". Maybe in a sentence or two you can tell me what reality might be - I cannot get a handle on where you are coming from. But I am new here. My problem.

#### Onemetertwometer

BANNED
I must admit I thought standard theory was based on fact - as best we can do. I do not understand what is meant by "Science needs to adjust its feelings". Maybe in a sentence or two you can tell me what reality might be - I cannot get a handle on where you are coming from. But I am new here. My problem.
Facts are invariably based on assumptions. Assumptions are invariably an artifice of informational constructs. Constructs are invariably a product of collective experience. Collective experience intrinsically defies definition. There has been an assumption underlying all physics, that the relative constructs of language and mathematics can be utilized in tandem to objectively describe universal constants. This is untrue. Any conceivable unit of space or time is infinitely divisible, and as such objectively inaccurate. It may be ascribed meaning relative to experience, but this is, in accordance with the nature of reality, a product of collective reason.

#### Hayseed

I disagree with that reasoning. Believe me, the constructs I use are not collective. Far from it. There is no relationship between space and time. Time is the duration of displacement, and comes along with length. Displacement does not require a change in position. Time and length are absolute. There is only one constant. You call it -e and +e. The constant of e not only sets all other measured values, it's the prime mover of all motion everywhere.

I believe physical reality to be very firm and very square.

Classical science did not fail. Space-time and the standard model most certainly have.

The explanation of light between frames is wrong. Because light is not a wave. It's intermittent(50%duty cycle) and functions within absolute time. And explains light's strange "Doppler effect" perfectly.

#### Stan

Facts are invariably based on assumptions. Assumptions are invariably an artifice of informational constructs. Constructs are invariably a product of collective experience. Collective experience intrinsically defies definition. There has been an assumption underlying all physics, that the relative constructs of language and mathematics can be utilized in tandem to objectively describe universal constants.

I see now where you are coming from and am inclined to agree. Thanks for explaining

#### Hayseed

What about absolute time and absolute length? Have you ever considered this?

Maybe an example might help. Have you ever considered what a crack in the curtain of nature, a simple reflection can reveal.

Let's acquire a laser pistol. We will set the pistol for a one foot long light beam. Now we shoot the pistol at a reflector at 45 degree angle.

A reflection is an instant event or act, with a duration. As soon as the front of the laser length hits the reflector, the reflection begins....at 45 degree out from reflector. And a foot long light length goes in, and a foot long light length comes out. Length in = length out.

And if that line length is moving at c, that line will have one nanosecond of duration. So it takes one nanosecond of interaction with the surface of the reflector. It takes one nanosecond for the line to go in, and the SAME nanosecond, to come out.

Now, instead of 45 degrees in, change that to 90 degrees in, or normal incidence in.....straight in, and straight out. Like a radar reflection from a plane. Or a mirror.

Now, during the one nanosecond of in, let's move the reflector, towards the light beam. This will shorten the interaction time. So instead of getting one foot out, now the length out will be a little shorter................because of the reduced interaction time.

If we move the reflector away from beam, during reflection, we will get a longer line out.

We can shorten....or lengthen, that beam, with the movement of the reflector, during the act of reflection.

Now, instead of using a laser beam, use one wavelength of light. It's much shorter, but the timing and mechanics still work the same way.

The important thing to note about this reflection....and moving reflections that give a shift in duration(frequency shift)........is that this function......requires absolute time and absolute length. No matter the location of the emitted light, the location of reflector, or where the reflection goes and ends up.

Reflection....and instant act, with a duration. Instant actions are common.....in nature.

With a little more study, one will realize that emission is an instant act also. Only instead of having a duration, emission propagates a duration....a chuck of EM disturbance with a duration. Light(EM radiation) is chunky. It is a strobe, not a wave.

#### Hayseed

Light has velocity, direction, frequency, momentum, energy, density, and an orientation of that density.

And all these properties can be turned in an instant to a new direction. With just one instant turn.

Amazing.

So, if reflection is instant, emission could be instant. If, and I believe it does, if light is intermittent and not a wave, then the special theory of relativity is not necessary to explain our measurements.

Light can be explained with absolute time and length......if it has an instant emission duration, and a strobe propagation. A duty cycle propagation. The so called frequency of light, only appears at the absorber. Due to absorber inertia. Or reactance.

Something to chew on.

#### Hartmann352

Let me offer some recent advances in optical atomic clocks and optical time transfer which have enabled new possibilities in precision time keeping for both tests of fundamental physics and advanced timing applications for orbital use and beyond.

A high stability laser link would connect the relative time, range, and velocity of the orbiting spacecraft to earthbound stations. The primary goal for this mission would be to test the gravitational redshift, a classical test of general relativity, with a sensitivity 30,000 times beyond current limits. Additional science objectives include other tests of relativity, enhanced searches for dark matter and drifts in fundamental constants, and establishing a high accuracy international time/geodesic reference.

In general relativity (GR), the tick rate of time is no longer universal, but slows in the presence of massive bodies. With further advances in clock accuracies and stabilities, measurements of time on the surface of the earth will soon be limited by the instability of time itself due to gravitational fluctuations, for example from tides and seismic noise. A straightforward solution is to locate one or more clocks in orbits around the Earth, thereby avoiding Earth’s tidal motion/gravitational noise and reducing the sensitivity to Earth’s gravity for medium-Earth (MEO) and high Earth (HEO) orbits.

Such an orbiting platform provides a low-noise environment that can enable atomic clocks to perform at the nineteenth digit and beyond. As a result, anticipated improvements in clock performance could be used in a variety of applications, including dramatically advancing tests of fundamental physics. There is a strong synergy between the technology and the underlying measurements of optical atomic lattice clocks and the atom interferometers being proposed for gravitational wave (GW) observations at mid-band frequencies, complementary to the eLISA and LIGO observatories.

These motivations have led to a number of international projects on orbiting clocks. A laser- cooled microwave clock, CACES, operated on the Chinese Tiangong-2 space station (Liu et al. 2018) and the ESA project ACES with a cold atom clock is scheduled to launch in the coming years (Cacciapuoti et al. 2020; Savalle et al. 2019a). For over a decade the European Space Agency, or ESA, has been developing optical clocks for space as part of their INTEGRAL Science Operations Centre, or ISOC, program (Schiller et al. 2012). The German Aerospace Center (DLR) is developing a combined Iodine clock and frequency comb for the ISS (COMPASSO), and the Chinese Space Agency aims to demonstrate an optical lattice clock in orbit on their next generation space station (Klotz). In contrast to the more modest clocks/links used in these projects, we propose below a mission that aims to deploy an optical clock and link with state-of-the-art performance in a modulated spacetime/gravity environment that will yield an ultra-sensitive space-time probe for fundamental physics with uncertainties reduced dramatically below current limits.

Considering a state-of-the-art optical atomic clock in an eccentric orbit around Earth, which provides a relatively large variation of the gravitational potential, to achieve multiple fundamental science goals. A single orbiting clock can be connected with earthbound clocks through high performance optical links to enable high stability earth/space clock comparisons. The modulation of the gravitational potential in turn modulates the frequency of the space clock with an accurately known period. This modulation is measured through the optical link, which enables evaluation of gravitational frequency shifts at uncertainty levels below the absolute accuracy of the clocks being compared and makes it easier to separate gravitational effects from possible systematic drifts in the clocks and the links. As a result, the space clock system, with a planned fractional frequency instability of 1 × 10−16τ−1/2 and fractional inaccuracy of 1x10-18, will enable a measurement of the gravitational redshift with a sensitivity 30,000 times higher than previously achieved. We note that variations of such experiments with optical clocks in space have been proposed, e.g. (Altschul et al. 2015; Litvinov & Pilipenko 2021).

A clock orbiting in space near Earth will also enable tests of local Lorentz invariance and searches for hypothetical ultralight fields. Taken together, these measurements will contribute significantly to our understanding of the basic framework of the universe and will help constrain or support new theories of spacetime/gravity that attempt to explain physical phenomena (dark energy, dark matter, quantum gravity) not presently accounted for in existing theories. Moreover, a space-based clock will provide an ultimate timing/geodesic reference frame that is freed from the noisy gravitational environment of the earth’s surface that is expected to contribute significantly to clock uncertainty budgets in the 10-19 decade. Such an orbiting reference could be used to connect widely separated earthbound optical atomic clocks to create a global network to perform fundamental physics tests at unprecedented levels, such as dark-matter induced variation of fundamental constants, searches for gravity-atom orientation coupling, and searches for new physics field emission from black-hole mergers, in addition to using the GR shift for geodesy and static gravity measurements. Finally, this proposed mission, FOCOS (Fundamental physics with an Optical Clock Orbiting in Space), will lay the groundwork for subsequent missions with the longer-term goal of using space-based constellations of optical clocks to search for dark matter e.g., (Roberts et al. 2017), and to observe mid-band gravity waves (Ebisuzaki et al. 2019; Kolkowitz et al. 2016; National Research Council 2011; Turyshev et al. 2007), including potentially using asteroids as test masses (Graham 2021).

Phenomenologically, tests of General Relativity, or GR, address three different aspects of EEP:
1. (i) Universality of Free Fall (UFF), i.e., acceleration is independent of body composition, which is also referred to as the Weak Equivalence Principle. The recent MICROSCOPE experiment took advantage of the quiet gravitational environment of space to compare the differential acceleration of two test masses made from different materials, with agreement at the 1 x 10−14 level (Bergé et al. 2018), which surpassed the long-standing UFF measurement precision set by the ground pendulum experiments (Schlamminger et al. 2008) and the lunar laser ranging experiments (Murphy et al. 2012; Williams, Turyshev & Boggs 2004).
2. (ii) LocalLorentzInvariance(LLI)-non-gravitationalphysicallawsareindependent of velocity and orientation of the inertial reference frame. The tests of LLI are analyzed in the context of a phenomenological framework known as the Standard Model Extension (SME) (Colladay & Kostelecký 1998). The minimal SME Lagrangian contains every possible combination of the standard model fields that are not term-by-term Lorentz invariant, but maintains gauge invariance, energy– momentum conservation, and Lorentz invariance of the total action. The SME provides a valuable framework to compare the constraints from very different experiments for the same SME coefficients. We note that SME allows for separate violation of LLI by all particles, which makes it compelling to stringently verify LLI in different systems. Atomic physics tests of LLI have been carried out with atomic clocks and high-precision dysprosium spectroscopy, magnetometers, electromagnetic cavities, and quantum-information-trapped-ion technologies
(Safronova et al. 2018). Atomic physics LLI tests set some of the highest bounds
on the SME coefficients in the photon, electron, neutron, and proton sectors.
Optical atomic clocks (Yb+) produced the most stringent limits, of the order of
10−21, on Lorentz symmetry violation parameters for electron (Sanner et al, 2019).
The anisotropy of the speed of light has been constrained by Michelson-Morley- type experiments. In the SME framework, this is an effect of Lorentz violation in the photon sector, which can also be probed with atomic physics experiments (as it affects the Coulomb interaction). The most recent LLI violation bounds for all sectors are listed in the 2021 edition of the Data Tables for Lorentz and CPT Violation (Kostelecky & Russell 2008).

(iii) Local Position Invariance (LPI) - non-gravitational physical laws are independent of location in time and space of a freely falling reference frame. Tests of LPI include searching for deviations from the predicted frequency shifts due to the gravitational redshift and changes in the values of fundamental constants as a function of position or time. These experiments often employ atomic clocks and have a sensitivity proportional to clock performance. The most sensitive redshift test, performed with the orbiting Galileo clocks, set a fractional redshift constraint at < 3 × 10−5 (Delva et al. 2018; Herrmann et al. 2018). Local position invariance also refers to position in time. If LPI is satisfied, the fundamental constants of non- gravitational physics should be constants in time. Earth-based atomic clock tests have put the most stringent limits on drifts of the fine structure constant and μ, the proton-electron mass ratio, at 1.0(1.1)×10−18/year and -8(36)×10−18/year, respectively (Lange et al. 2021).
(iii) Local Position Invariance (LPI) - non-gravitational physical laws are independent of location in time and space of a freely falling reference frame. Tests of LPI include searching for deviations from the predicted frequency shifts due to the gravitational redshift and changes in the values of fundamental constants as a function of position or time. These experiments often employ atomic clocks and have a sensitivity proportional to clock performance. The most sensitive redshift test, performed with the orbiting Galileo clocks, set a fractional redshift constraint at < 3 × 10−5 (Delva et al. 2018; Herrmann et al. 2018). Local position invariance also refers to position in time. If LPI is satisfied, the fundamental constants of non- gravitational physics should be constants in time. Earth-based atomic clock tests have put the most stringent limits on drifts of the fine structure constant and μ, the proton-electron mass ratio, at 1.0(1.1)×10−18/year and -8(36)×10−18/year, respectively (Lange et al. 2021).

Connecting clocks world-wide would also enable new applications in fundamental and applied science. For instance, an interesting theme in fundamental physics research is that our fundamental constants may not be constant throughout space or in time (Dirac 1938; Martins 2017). Such an inconstancy violates Lorentz Position Invariance and the Universality of Free Fall; indeed, many extension theories predict such a violation. The most sensitive tests to date have compared atomic spectra, either between Earth and quasar-absorption spectra in high-redshift gas clouds, or between atomic clocks. While some astronomical spectral comparisons have hinted at possible variations (Webb et al. 2011), ground based measurements have shown no present-day variations in αFS, the fine structure constant, or μ, the proton-electron mass ratios, at the 10−18/year level (Lange et al. 2021). So far, such ground-based tests have been limited to comparisons between clocks in the same laboratory or those connected by direct fiber links. Connections via FOCOS (Fundamental physics with an Optical Clock Orbiting in Space) links would enable fundamental tests between larger numbers of high-performance clocks and provide checks for non-null results, as well as enabling new tests between remotely located systems with larger differential sensitivities to drifts.

The FOCOS mission takes advantage of the large variation in gravitational potential in an eccentric Earth orbit. A modulation of the gravitational potential modulates the clock’s frequency, as compared to an earthbound clock, with an accurately known period. This modulation offers two principal metrology benefits: (i) it enables the possibility to take advantage of the stability of the clocks to evaluate gravitational effects at levels beyond the clocks’ accuracies, and (ii) it helps to separate gravitational effects from possible drifts in the clocks and link hardware. While this eccentric orbit, and the resulting modulation of the gravitational potential, is required to meet the primary scientific objectives (tests of the gravitational redshift and Lorentz invariance), a circular orbit in MEO is more natural for other scientific objectives, which rely on connecting the FOCOS clock to ground-based clocks around the earth. For example, future state-of-the-art space-time references may benefit from smaller eccentricities, to reduce the variations of relativistic corrections throughout the orbit. Satellite visibility, which sets the duration and frequency of optical links with ground stations that have high performance optical clocks is an important priority for an international space-time reference.

Mission Schematic: a high-performance optical atomic clock is placed in one of several possible highly eccentric orbits around Earth to modulate the gravitational potential for a sensitive measurement of the gravitational redshift and other relativistic corrections. In addition, a clock in this orbit can serve as an international space-time reference. (a) The orbits (to scale) have an 8-hour period, where the peak elevations of the perigee and apogee are 30 degrees when viewed from 40 N. A tilt of the orbit’s minor axis (orange, red, and blue) provides better visibility in both hemispheres. (b) The spaceborne clock’s frequency (purple) will vary throughout the orbit because of the summed contributions of the gravitational red shift (magenta) and time dilation (blue-green). This frequency shift, and the corresponding difference in elapsed time, compared to the ground clock, will be measured via low-noise, free space laser links. The black dashed curve is Earth’s redshift on the surface, and the colored dashed curves are the corresponding time averages over an orbit. Here we plot the lowest order corrections, and significantly more detailed relativistic calculations are required to realize the accuracy goals of this mission, for example as in (Blanchet et al. 2001).

Several factors constrain the choice of orbits. To avoid drifts of systematic errors in the clock that would degrade the measurement of the redshift, we favor observing the satellite clock from the same ground location over multiple orbits at both apogee and then at perigee with a minimal gap in time between the two observations, as set by the orbit. A low perigee, which gives a large redshift modulation, limits the visibility at moderate latitudes, such as 40 N, if the apogee is to be visible at the range of a geostationary orbit. Only an 8-hour orbit satisfies these constraints; the satellite clock is observed at perigee, completes 1.5 orbits in 12 hours, and then is observable 12 hours later at apogee after the Earth has rotated 180 degrees. An elliptical 24-hour orbit is also possible, but the apogee range is then large, requiring larger apertures or higher optical powers for the laser link to Earth. A shorter, 18-hour orbit would allow the satellite to be observed at perigee and then 3 hours after apogee, when its range is less than that of a geostationary orbit, but only for a single orbit. An increase in the time gap between observing the perigee and apogee to 36 hours offers a number of solutions, as does 60 hours, but places unfavorably higher demands on the clock’s frequency stability. Another possibility is to observe the perigee and the apogee from independent ground stations. This would require chronometric leveling at the level of the accuracy goal for the redshift. We therefore arrive at a baseline orbit with a period of about 8 hours, and a perigee altitude of approximately 5,000 km. For a ground clock located in moderate northern latitudes, tilting the orbital plane so that the perigee is 9 degrees above the equatorial plane allows both the perigee and apogee to have a sufficiently high elevation angle, here taken as at least 20 degrees, for the laser link. As shown in Figure 5, for 40 degrees North, the maximum elevation angle for both perigee and apogee is 30 degrees. The visibility throughout the orbit in both hemispheres further increases if the minor axis of the orbit is significantly tilted with respect to the equatorial plane (e.g. blue and red orbits in Figure 4a and 5). This increased observation time would allow an improved comparison with theory as the frequency shift could be compared through a larger portion of the orbital path, rather than only near periapsis and apoapsis.

The spaceborne clock frequency varies (see Figure 4b) throughout the orbit, and through low- noise, free space laser links, comparisons can be made between the frequencies of the space and ground clocks. The resulting frequency difference tests the redshift of general relativity (red curve), as well as time dilation (blue curve), and higher order relativistic effects. See (Blanchet et al. 2001; Petit & Wolf 1994, 2005) for a more complete discussion of the frequency shifts, including some subtleties related to time and frequency transfer.

Satellite elevation near periapsis and apoapsis for the orbits in figure above. A tilt of the minor axis of the orbit above the equatorial plane increases the peak elevation and extends the observation time before periapsis. At moderate northern latitudes, a 30 min observation is achievable at periapsis and longer observation times are straightforward at apoapsis. The solid sections of the curves denote elevations above 20 degrees where a laser link from the ground could have a reasonable line-of-sight to the satellite, albeit with ~3 times larger contributions from atmospheric turbulence as compared to a vertical sight path.

See: https://arxiv.org/pdf/2112.10817.pdf

See: https://techport.nasa.gov/view/93691

See: https://www.innovations-report.com/...-accurate-optical-single-ion-clock-worldwide/

Today’s most accurate frequency standards are realized by optical atomic clocks, where an atomic reference (either a single trapped ion or a cloud of ultra-cold atoms) is used to stabilize a laser beam frequency. Laboratory setups have reached relative frequency accuracies below the 10-17 level, owed by the use of an optical transition frequency, a tremendous level of technical noise reduction and exquisite experimental control. There is an academic as well as industrial need for compact atomic clocks with good frequency stabilities: observatories, very-long baseline interferometry, particle accelerators, GPS, telecommunications, all require a stable frequency reference for timekeeping purposes. The current compact atomic clocks are liter-sized with a 10-12 at 1 s relative frequency stability, and the 10-13 level will soon be commercially available.

There will be a decided need for even more sensitive clocks in the future, and research needs to be undertaken towards this goal. In particular, fundamental physics tests, geodesic measurements, time and frequency distribution for satellite networks would directly benefit from compact clocks with improved frequency stabilities and fewer inherent fluctuational instabilities.
Hartmann352

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