In the OSTI Collections: Interferometry
Dr. William N. Watson, Physicist
DOE Office of Scientific and Technical Information
- Electromagnetic waves (I)
- Other waves
- Electromagnetic waves (II): tests of quantum-gravity hypotheses
- Reports Available through OSTI's SciTech Connect
- Reports Available through OSTI's DOE PAGESBeta
- Reports Available through DOepatents
- Additional References
Physical waves of any type—whether water waves, sound waves, light waves, or any other type—have a pattern of “peaks” and “troughs” which is shaped by the waves’ source, the media they travel through, and the paths they take through them. While we can easily discern the pattern in waves whose peaks and troughs are widely separated (e.g., large ocean waves), even the existence of peaks and troughs can be hard to detect in very short waves (e.g., visible light). As it turns out, though, directing a train of waves so that it crosses paths with another wave train of the same type, or even a redirected portion of the same wave train, can cause the two interfering waves to reshape each other into a more easily measured pattern.[Wikipedia] Where peaks or troughs from each wave train meet, they reinforce each other and form bigger peaks or troughs. Where a peak from one train meets a trough from another, they cancel out so the combined wave has some intermediate amplitude. The waves’ interference thus produces a new pattern of peaks and troughs which may be more easily discerned. For example, the reinforcing and canceling peaks and troughs of two same-frequency light waves can appear as alternating lighter and darker regions in space. If light waves of different frequencies interfere, their mutual reinforcement and cancellation at any point in space can alternate over time.
Interferometers, as their name suggests, are devices for measuring waves that interfere with each other. Different types of interferometers are designed to make waves interfere in different ways, thus changing the wave pattern to reveal different features of the waves’ sources or the media that affect their transmission. Interferometers have been used to learn about various phenomena since at least 1856, when Jules Jamin[Wikipedia] used one to measure how gases at different pressures and temperatures made light slow down as it traveled through them[Wikipedia]. Interferometers are still being designed, built, and used today for various purposes. Several recent reports available through OSTI explain some of these purposes and the designs made to accomplish them.
Waves of visible light, and electromagnetic waves of other frequencies[Wikipedia], are among the waves most commonly analyzed with interferometers to measure other things, such as temperature. Temperature measurement by interferometry is discussed in a paper entitled “Development of metal-ceramic coaxial cable Fabry-Pérot interferometric sensors for high temperature monitoring”[DoE PAGES], which was published in the journal Sensors in 2015. New designs for coal-fired power plants achieve lower carbon-dioxide emissions with high power output by operating at high temperatures. The paper notes that “real-time monitoring of the process conditions and equipment physical states are highly desired for realizing intelligent operation to enhance the energy efficiency and safety assurance of the power plants”, and that temperature distribution over large equipment and transportation lines is one of the most important things to monitor. Remote temperature sensing can be done in many situations with pairs of wire made of different conducting materials (thermocouples[Wikipedia]), but these devices are not suitable for the high-temperature, high-pressure, erosive and corrosive portions of a power plant like gasifiers and combustors.
Fiber-optic interferometers have been considered as temperature sensors, but their brittleness, their small sizes, and their components’ deterioration by diffusion of their atoms across the components’ interfaces have made their use in coal-fired plants problematic. The authors thus describe a more rugged interferometer that, instead of using visible light and optical fibers, uses lower-frequency microwaves and corundum[Wikipedia] in a stainless-steel coaxial cable. As shown in Figure 1, microwaves propagating along the cable are partially reflected at air gaps between sections of corundum. The reflected waves interfere with each other in a pattern determined by the spacing of the air gaps, which changes as the cable expands or contracts in response to changing temperature. Thus when microwaves of different frequencies are sent along the cable, the reflected waves with the least cancellation due to interference will have particular frequencies that depend on the cable’s temperature. Two sensors, one with air gaps in the corundum on one side of the cable, the other with air gaps completely separating corundum sections across the cable, were tested at temperatures between 200°C and 500°C (approximately 473 K and 773 K) and found capable of tracking temperature changes of one degree.
Figure 1. Left: A coaxial cable with conducting core and outer surface, with solid insulating material between them periodically separated by air gaps. Microwaves propagating through the solid insulators are partially reflected at the gaps between them. If these reflected waves oscillate in step with each other, they will interfere constructively and the total reflected wave will be strong; if the individual reflected waves are out of step, they will destructively interfere and the total reflected wave will be weak. Whether the reflected waves are in or out of step depends on the waves’ frequency and the spacing of the air gaps. Expansion and contraction of the cable with temperature affects the gap spacing and thus which microwave frequencies are most strongly reflected, so a change in the reflected waves’ frequency spectrum indicates a change in the cable temperature, allowing the cable-microwave system to act as a temperature sensor. Middle: A schematic of two different air-gap arrangements. Right: Photos of both types of cable with the outer conductors removed. (From “Development of metal-ceramic coaxial cable Fabry-Pérot interferometric sensors for high temperature monitoring” [DoE PAGES], pp. 24916, 24917, and 24919.)
Another paper describes a way to use microwaves to noninvasively monitor phenomena of a quite different type. Both shock waves and chemical reaction fronts (including detonation fronts) can propagate through materials like fuels and explosives that release high amounts of chemical energy per unit mass. “Development of a Multi-Point Microwave Interferometry (MPMI) Method”[SciTech Connect] describes how part of a microwave beam sent through such an energetic material, and made to interfere with the rest of the beam sent past the material, would produce an interference pattern that depended on the form of any shock or reaction fronts within the material. The microwaves’ interference pattern would be determined from their effect on a crystal placed in their path. The crystal would, in turn, be probed by a laser beam whose polarization[Wikipedia] would be affected by the crystal’s condition, which depends on the interference pattern of the incident microwaves. A light detector would receive the affected laser light, plus the light from a second laser added to ensure that the detector was illuminated enough to function. Since the total laser intensity depends on the microwave interference pattern, which is shaped by shock and reaction propagations in the energetic material, the amount of laser light at the light detector would provide information about the form and velocity of any shock and reaction waves.
The report describes this design in the context of current state-of-the-art microwave interferometers and the construction and testing of devices with some (not all) of the intended capabilities. Limitations and technical challenges raised by the tests, and suggested design alterations, are also discussed.
Figure 2. “Development of a Multi-Point Microwave Interferometry (MPMI) Method”[SciTech Connect] to detect the form and velocity of shock waves or chemical reaction fronts in an energetic material (“Explosive”). The plan for this method is to split and recombine a microwave beam, whose resulting interference pattern would affect a crystal’s electrooptical properties. The effect on the crystal (“EO Crystal”) will determine how the crystal affects the polarization of a laser beam (Laser 1) sent into it. The beam reflected from the crystal is sent along with a second laser beam into a detector, so that what the detector reads depends on the form of the wave propagating in the energetic material. (From “Development of a Multi-Point Microwave Interferometry (MPMI) Method”[SciTech Connect], p. 26.)
Microwaves with higher frequency near one terahertz (one trillion cycles per second), which are also describable as lower-frequency infrared waves, are called for in a patent entitled “Interferometric millimeter wave and THz wave doppler radar”[DOepatents]. The invention is one that uses the Doppler effect[Wikipedia]—the change in frequency a wave undergoes when it originates or is reflected from a moving object—to detect an object’s motion. The reflected wave’s frequency change is detected by how its interference pattern with a reference wave is altered. In this invention, the reference wave is produced by reflection from a continually oscillating object, so its frequency also continually oscillates. The use of terahertz waves makes the invention sensitive to object displacements of less than one micrometer, which it wouldn’t be if it used lower-frequency microwaves in their place. Another advantage of using terahertz waves is that they’re less disruptive to the functioning of common electronic devices. Even smaller object displacements might be detected by using higher-frequency waves like visible light, but rough object surfaces tend to scatter those waves away from where they would interfere with the reference waves, and common materials that might lie between the object and the measuring device are opaque to those waves.
Figure 3. In the invention described in “Interferometric millimeter wave and THz wave doppler radar”[DOepatents], a source of continuous terahertz waves (“CW Source”) emits a beam that is split in two, one part going toward an oscillating mirror and the other toward an object whose motion or lack thereof is to be measured. The beams reflected from both have frequencies that depend on the reflecting objects’ motions. When the reflected beams are reunited at the beam splitter, their alternatingly constructive and destructive interference makes the reunited beam’s intensity fluctuate in a way that correspond to the measured object’s motion. (From “Interferometric millimeter wave and THz wave doppler radar”[DOepatents], sheet 1 of 13 (drawings).)
The use of interfering laser beams to test a physical effect produced by other interfering laser beams is described in a report of an undergraduate research project entitled “Validating Laser-Induced Birefringence Theory with Plasma Interferometry”[SciTech Connect]. Initially, an intense laser beam is used to turn some helium gas into a plasma by separating electrons from many of the atoms in it. A second, weaker laser beam crosses paths with the first and interferes with it. Had the beams interfered in vacuum, a particular interference pattern would result, but the first beam’s polarization and the plasma it generates constitute a medium through which different components of the second beam travel at different speeds: the component of the second beam with the same polarization as the first travels more slowly than the component whose polarization is perpendicular to the first, resulting in a different interference pattern in which the second beam’s polarization changes as it moves through the plasma. This effect could be useful. There are practical optical devices (waveplates) made of materials through which differently polarized light beams travel at different speeds, but the solid materials that most waveplates are made of generally don’t hold up well at high plasma temperatures. Waveplates that are themselves made of plasma, though, would naturally withstand plasma conditions and thus allow plasma features that affect the polarization of light to be measured.
Calculations indicated that the difference in propagation speeds for differently-polarized light waves in plasma should depend on the density and temperature of the plasma’s free electrons. The research project involved checking these calculations by sending a third laser beam partly through and partly around the helium plasma waveplate, and then letting both parts interfere with each other. The change in the waveplate-crossing wave’s oscillation relative to that of the waveplate-avoiding wave affects their interference pattern in a way that also depends on the density of electrons removed from the plasma’s atoms. This test, plus other experiments, generally corroborate the calculations of how the first two beams’ interference pattern depends on the plasma electron density, though some discrepancies suggest that one or more parameters of the plasma or lasers were different from what was intended or expected.
Figure 4. Schematic diagram of horizontally polarized[Wikipedia] laser beam a0 that “pumps” enough energy into helium atoms to separate electrons from them, turning the helium gas into a plasma through which other horizontally polarized light beams will travel more slowly than other vertically polarized beams. The less intense “probe” laser beam a1, entering the plasma with an intermediate linear polarization indicated by green arrows (bottom left), becomes more elliptically polarized as its vertical and horizontal components travel at different speeds (top right). The way this effect depends on the density and temperature of free electrons in the plasma was confirmed in part by interferometric measurements of two other laser beams, not illustrated here, one of which ran through the plasma while the other did not. (From “Validating Laser-Induced Birefringence Theory with Plasma Interferometry”[SciTech Connect], p. 20.)
Measuring things by how they shape waves’ interference patterns isn’t restricted to the interferometry of electromagnetic waves. Any kind of wave can be used. While the report just discussed involved measuring plasma parameters with laser beams, a recent patent describes how measuring interferences in plasma waves[Wikipedia] can detect the presence of terahertz electromagnetic waves. “Two-path plasmonic interferometer with integrated detector”[DOepatents] isn’t limited to this, however; the same device can also be used to analyze samples placed on it by the changes they induce in the plasma waves’ interference pattern.
As in other terahertz-wave detectors, the terahertz electromagnetic waves interact with electrons in a nanometers-thick layer to generate plasma waves, but the small area of the layer in most such detectors makes the plasma waves hard to detect unless the detector is kept very cold. The interferometer described in the patent avoids the need for cryogenic operation by using a larger-area, high-quality layer of graphene[Wikipedia], on which a row of three electrical contacts is placed. When appropriate voltages are applied to the contacts and the device is exposed to terahertz waves, plasma waves originate at the end contacts and interfere at the middle one, thus acting as a terahertz-wave detector. Placing a material sample on the device above the path of one of the plasma waves changes that wave and thus its pattern of interference with the other plasma wave. The interference pattern will also change as the contact voltages are varied, in a manner that depends on the composition of the sample, so the interferometer can also function as a material analyzer.
On a much larger scale, interferometry of a quite different type of wave may help us characterize an important feature of an environmentally significant substance. Ongoing tests of the concept are reported in “Permafrost Active Layer Seismic Interferometry Experiment (PALSIE).”[SciTech Connect] Where so-called permafrost[Wikipedia] exists, its thickness varies seasonally as warmer weather partially thaws it and colder weather refreezes it. One concern is whether the cycle is stable. Permafrost traps large quantities of carbon compounds, so thawing permafrost releases more of those compounds directly into the atmosphere, or makes them accessible to microbes that metabolize them into carbon dioxide, which they release into the air. Since carbon compounds in the atmosphere trap heat, releasing more of them reduces the effect of winter cooling, perhaps enough to keep the permafrost from completely refreezing. This could result in an eventual runaway release of carbon compounds from permafrost and warming of the environment.
Determining what is actually happening to the earth’s permafrost is the goal of the aforementioned seismic interferometry experiment. The permafrost’s thickness affects the speed of earth tremors propagating through it, and thus the way seismic waves interfere when they cross paths. Knowledge of seismic-wave amplitudes where permafrost is should therefore allow deduction of how the permafrost’s thickness varies with time at different places. Current methods for measuring permafrost thickness require digging through it, which requires periodic travel to where it exists and estimating its thickness between measurement points and measurement times. Seismic interferometers can be set up and left for continual monitoring, and the tremors they monitor are shaped by the entire volume of permafrost they pass through. Experiments in using data from just such a setup near Fairbanks, Alaska, are still in progress to test the method’s feasibility.
About two decades after light waves were discovered to have particle characteristics, individual particles of matter were found to have wave characteristics (such as interference). A number of recent reports deal with wave interferometry of electrons, neutrons, and even entire atoms.
The wave nature of electrons has long been put to work in electron microscopes. Any type of wave can resolve details about as small as the wavelength, which decreases as the kinetic energy of the wave’s associated particles increases. The particle beams that in an electron microscope resolve details smaller than 1% of an atomic width have much less kinetic energy than equivalent beams in a light microscope would have: the very energetic “light” waves of that wavelength are actually gamma rays that could damage many materials. Yet even electrons’ kinetic energy can be increased enough to damage samples if one tries using them the same way to view even finer details. Methods for getting more information out of weaker electron waves would allow higher-resolution electron microscopy of less robust objects. Simulations and a proof-of-principle experiment for one such method are reported in the Nature Communications paper “Efficient linear phase contrast in scanning transmission electron microscopy with matched illumination and detector interferometry”[DoE PAGES]. The method involves running portions of the electron wave through pieces of silicon nitride to retard them, so that on exiting the silicon nitride, their “peaks” and “troughs” will respectively align with the nodes between the “peaks” and “troughs” of the unimpeded wave portions. When the modified wave is sent through different portions of the sample afterwards, each portion deflects the electron wave pattern by a different amount. Electron detectors beyond the sample compare the phase pattern it receives with what it would be if the sample hadn’t been there. The resulting “interference” between the actual modified electron wave and what it would have been with no sample present reveals more detail about the sample than an electron wave whose phase hadn’t been modified by the silicon nitride would have shown. The report shows the difference with images of nanometer-scale gold particles taken with and without the silicon nitride phase modifier.
Figure 5. (a) Concentric rings of silicon nitride through which electron waves are sent in the electron microscope described in “Efficient linear phase contrast in scanning transmission electron microscopy with matched illumination and detector interferometry”[DoE PAGES]. Alternating portions retard the wave going through them so that neighboring sections are a quarter-cycle out of phase with each other. (b, c) Image of gold nanoparticles with (b) and without (c) the use of the silicon nitride device shown in (a). Scale bar in part (c) represents 2 nanometers. (“Efficient linear phase contrast in scanning transmission electron microscopy with matched illumination and detector interferometry”[DoE PAGES], p. 4.)
The electron microscopy system modifies its electron beam before its subsequent modification by the sample to be examined. A patent entitled “Phase-sensitive two-dimensional neutron shearing interferometer and Hartmann sensor”[DOepatents], on the other hand, describes an apparatus in which an examined sample interacts with a neutron beam first before the beam is partitioned into interfering portions. The resulting interference pattern of higher and lower neutron intensity depends on the grating characteristics and on how the sample affects the neutron beam. The interference technique is an adaptation of a method (shearing interferometry[Wikipedia]) used with light waves. Besides the interference technique, the patent also describes another kind of device (a Hartmann screen[Wikipedia]) to reroute portions of the beam after it goes through the sample to get information about the sample, but this rerouting doesn’t produce an interference pattern to be studied.
Figure 6. Interference of overlapping portions of a neutron beam is used to provide information about an object (“Phase Object”, item 305) after the neutron beam has passed through the object. Portions of the neutron beam that get past the grating (item 400) spread out and interfere before reaching the neutron detector (item 360). The interference pattern of higher and lower neutron intensity that the detector registers depends on the grating characteristics and on how the sample affects the neutron beam. (From “Phase-sensitive two-dimensional neutron shearing interferometer and Hartmann sensor”[DOepatents].)
Two other patents describe devices that produce interference patterns in the atoms or molecules of a gas when the devices are rotated or accelerated in certain directions. Although atoms and molecules are much larger than neutrons or electrons, even their motion is associated with waves that can self-interfere, producing regions of space in which peaks and troughs of different wave portions can mutually reinforce or cancel out. The interferometers described in the patents expose gas molecules to laser pulses that split the waves associated with each molecule into two paths and then recombine them to produce interference. The phase of the recombined wave, which depends on the acceleration and rotation that the interferometer undergoes, determines how likely each gas molecule is to contain or not contain a certain amount of energy above the minimum amount that it can have, and thus the phase is reflected in the actual numbers of gas molecules that contain those energies. Those numbers determine how much an additional “probe” laser pulse is affected by the gas, so what happens to the probe pulse shows how much the interferometer was accelerated or rotated.
The two inventions largely differ in the way their gas particles are set in motion before being examined. In the “Light-pulse atom interferometric device”[DOepatents], all the gas particles configured by one set of laser pulses and measured by another are housed in a single vapor cell, the device using as many vapor cells as needed to determine the accelerations or rotations along or around particular axes. The “High data rate atom interferometric device”[DOepatents], on the other hand, has pairs of traps instead of single vapor cells, and shuttles gas particles between the cells in each pair. Both inventions take up less space than typical atom interferometers and take data frequently enough to make them practical for navigation on dynamic platforms.
Figure 7. Vapor cell (left) and pair of magnetooptical atom/molecule traps (right) used with accompanying laser beams in matter-wave interferometers to detect the interferometers’ accelerations and rotations. (From “Light-pulse atom interferometric device”[DOepatents] and “High data rate atom interferometric device”[DOepatents].)
As we saw above, electromagnetic-wave interferometers can measure various material entities. They have also shown us significant features of space and time. In the late 19th century, a visible-light interferometer demonstrated one aspect of how space and time are interrelated by showing the speed of light is independent of any motion of its source.[Wikipedia] More recently, the Laser Interferometer Gravitational-Wave Observatory (LIGO) demonstrated that waves of spacetime curvature (gravitational waves) not only exist, but can provide much information about events far across the universe that produce them[Wikipedia], such as the merging of black holes (themselves examples of extreme spacetime curvature). The interrelation of space and time and the existence of intrinsic curvature in spacetime are accounted for by Albert Einstein’s special and general theory of relativity.[Wikipedia]
As has long been appreciated, though, relativity theory does not account for any quantum-physical features of spacetime. If space and time were only a featureless “container” of quantum-physical material entities, the container’s own lack of such features might be unproblematic, but since spacetime is not featureless, and its curvature interacts with the matter it contains (thus producing gravity), a complete theory of spacetime would seem to necessarily be a quantum theory as well. Since distinctly quantum-physical phenomena generally appear in matter when waves associated with material particles are significantly curved over distances of one wavelength, and since wavelengths and black-hole sizes are both functions of mass, it is widely suspected that spacetime should manifest some quantum-physical features over tiny distances (about 1.6 x 10-35 meter[Wikipedia]) at which wavelengths and black-hole radii correspond to nearly the same mass. (This distance is so tiny that the width of a proton is about 100,000,000,000,000,000,000 times bigger.) Even with this expectation, though, all current attempts at a quantum theory of spacetime are informed less by any experimental data about quantum-physical features of spacetime than by the fact that such theories should not disagree with what experiment already tells us about physics in general.
To get some new data that could tell us which quantum spacetime theories might be true, an electromagnetic-wave interferometer has been constructed at the Fermi National Accelerator Laboratory to detect quantum-physical effects corresponding to the aforementioned -meter length[FNAL]. A paper in the journal Classical and Quantum Gravity (“Interferometric Tests of Planckian Quantum Geometry Models”[DoE PAGES]) briefly discusses some of the different proposed extensions of general relativity theory, how data from different interferometer setups can be used to check some of these theories against reality, and even how data from the LIGO interferometers have already proven some of the theories incorrect. The Fermilab interferometer has a different design to address at least one class of theories whose predictions weren’t checkable with LIGO’s present configuration; the paper also discusses these theories and their implications for what should be observed in the Fermilab and other interferometers if they are true. A doctoral dissertation[SciTech Connect] by one of the participants in the Fermilab experiment gives a more detailed discussion, and shows how the early experimental results already rule out one of the theories. Other theories are to be checked by further experiments with similar instruments.[FNAL]
The significance of these initial laboratory observations is somewhat reminiscent of how astronomical observations informed another field of spacetime physics: cosmology. Before Einstein’s general relativity theory, cosmology was much more a field of speculation than a matter of physical science. Even afterward, though, when people began to realize what general relativity implied about the shape of spacetime as a whole, they had little data to determine what the actual form of the universe was—whether it was finite or infinite, or whether it was expanding, contracting, or static, and if it wasn’t static, whether the rate of expansion or contraction was increasing or decreasing, and by how much. Many new astronomical observations, some made with space probes and some involving huge amounts of data from ground-based telescopes, answered several of these questions: the universe is not only expanding, but the rate of expansion has long since begun to increase after an earlier period of slowing down, and should increase indefinitely under present influences. Fermilab’s new interferometer represents a new source of data that should help determine what kind of quantum-physical features, if any, exist in spacetime.
- Interference (wave propagation)
- Jules Jamin
- Jamin interferometer
- Electromagnetic radiation
- Polarization (waves): Polarization state
- Doppler effect
- Plasma oscillation
- Shearing interferometer
- Shack-Hartmann wavefront sensor
- Michelson-Morley experiment
- LIGO: Observations
- Theory of relativity
- Planck length
Reports available through OSTI’s SciTech Connect
- “Development of a Multi-Point Microwave Interferometry (MPMI) Method” [Metadata]
Sandia National Laboratories
- “Validating Laser-Induced Birefringence Theory with Plasma Interferometry” [Metadata]
Lawrence Livermore National Laboratory
- “Permafrost Active Layer Seismic Interferometry Experiment (PALSIE).” [Metadata]
Sandia National Laboratories
University of Florida
Boise State University
Bureau of Land Management
- “Testing a Model of Planck-Scale Quantum Geometry With Broadband Correlation of Colocated 40m Interferometers” (Dissertation) [Metadata]
University of Chicago
Reports available through DoE PAGESBeta
- “Development of metal-ceramic coaxial cable Fabry-Pérot interferometric sensors for high temperature monitoring” [Metadata]
University of Cincinnati
Sensors, Volume 15, pages 24914-24925
- “Efficient linear phase contrast in scanning transmission electron microscopy with matched illumination and detector interferometry” [Metadata]
Lawrence Berkeley National Laboratory
University of Oregon
Universität Ulm [English]
Nature Communications, Volume 7, article number 10719
- “Interferometric Tests of Planckian Quantum Geometry Models” [Metadata]
University of Chicago
Fermi National Accelerator Laboratory (Fermilab)
Classical and Quantum Gravity, Volume 33, Number 10, article number 105004
Patents available through DOepatents
- “Interferometric millimeter wave and THz wave doppler radar” [Metadata]
Assignee: UChicago Argonne, LLC
- “Two-path plasmonic interferometer with integrated detector” [Metadata]
Assignees: Sandia Corporation, Research Foundation of The City University of New York
- “Phase-sensitive two-dimensional neutron shearing interferometer and Hartmann sensor” [Metadata]
Assignee: Lawrence Livermore National Security, LLC
- Laser Interferometer Gravitational-Wave Observatory (LIGO)
Observatory that, using laser interferometers, first confirmed the existence of gravitational waves—waves of curvature in spacetime—and their usefulness for observing astrophysical events.
Interferometer at Fermi National Accelerator Laboratory (Fermilab) being used to check certain quantum-physical theories of spacetime curvature. The name “Holometer” refers to the theories’ relation to the “holographic principle”: the concept that “the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region”[Wikipedia]. See also the July 2002 Reviews of Modern Physics article “The holographic principle”[arXiv, APS], and the December 3, 2015 Fermilab news article “Holometer rules out first theory of space-time correlations”[FNAL].