The XENON experiment was designed to detect particles of dark Matter, has it detected Dark Energy instead?

Two of the greatest mysteries in all of science concern the nature of Dark Matter and Dark Energy which combined are estimated to make up as much as 95% of the matter and energy in the Universe. Dark Matter was first proposed in the 1920s to explain the rotation curves of the galaxies, which when all of the visible matter is taken into account, do not appear to obey Newton’s law of gravity. Dark Matter, particles that only interact with other particles by their gravitational attraction, is supposed to account for this discrepancy. The particles predicted by theories of Dark Matter have been given the generic title of WIMPs, which stands for Weakly Interacting Massive Particles. Trouble is that no particles of a type that could be called Dark Matter have ever been discovered.

Today scientists really only understand about 5% of everything that makes up the Universe. About 25% is Dark Matter and fully 70% id Dark Energy. (Credit: NDTV Gadgets 360)
There are literally dozens of different candidate particles that could be Dark Matter but at least that means we have some idea of what it’s like, we can design experiments to check our guesses. We have hardly any idea about what Dark Energy is like. (Credit: Physics – APS.org)

Dark Energy on the other hand, was proposed in 1998 to account for the shocking discovery that the Universe was not only expanding, it was accelerating its expansion. Something was pushing the galaxies apart and for want of a better name it was called Dark Energy, although many physicists would rather refer to it as Dark Pressure. We know almost nothing else about it.

We do know that since 70% of the Universe is Dark Energy it will determine the eventual fate of the Universe. (Credit: NASA)

Since Dark Matter is supposed to be made up of WIMPs, particles something like those we’ve been studying for decades experimental physicists have put a good deal more effort into trying to detect them than Dark Energy, which as I said we know almost nothing about. One of the current experiments designed to detect WIMPs is the XENON series of detectors operating at the Gran Sasso National Labouratory in Italy. The Gran Sasso facility is one of number of High Energy Physics labouratories that have been constructed deep underground, often in old mines, in order to help shield them from the cosmic rays that rain down from outer space.

The layout of the Gran Sasso National Labouratory in Italy, one of the world’s leading centers for High Energy Physics. (Credit: Nature)

To date there have been three XENON detectors with a fourth just beginning operation, all are designed to provide two distinct signals whenever a WIMP ‘bumps’ against an atom of liquid Xenon. The liquid Xenon is contained within a ‘time projection chamber’, see image below. The liquid Xenon is kept at its boiling point, 165 Kelvin or -108 degrees Celsius, and there is a layer of gaseous Xenon at the top of the chamber. At both the top and bottom of the chamber are arrays of photomultiplier tubes (PMTs). There is also a high voltage electric field across the chamber, positive at the top, negative at the bottom.

Setup of the Xenon Experiments. When an unknown particle strikes am atom of liquid xenon light is first detected at the bottom array of Photo Multiplier Tubes (PMTs). released electrons then float upwards in the liquid because of a large electric voltage until they reach the surface and ionize xenon gas that is detected by the upper array of PMTs. (Credit: NI Group at UC San Diego)

When, and if a WIMP strikes an atom of liquid Xenon it knocks off an electron causing a spark of ultraviolet light at a wavelength of 178 nm in a process known as scintillation. This signal is picked up by the lower PMTs and is referred to as S1.

The electron then begins to drift upward at a known speed, the deeper the collision with the WIMP took place the longer it takes for the electron to reach the top. Once the electron reaches the top of the liquid layer it pops out into the gaseous Xenon where it accelerates rapidly knocking into atoms and ionizing them. This ionization releases more photons of light that are picked up by the upper PMTs as signal S2. The X-Y location of the original collision is determined by the location of the PMTs that picked up S2. The Z coordinate, the depth in the liquid Xenon where the collision occurred is calculated from the time difference between S1 and S2.

The original Xenon10 experiment was just a small, proof of concept model. (Credit: UCLA Physics and Astronomy)

The first detector to be installed at Gran Sasso contained 15kg of liquid xenon as was known as XENON10. This experiment was operated between October of 2006 and February of 2007 as a proof of concept model and an analysis of the data provided by 58 days of operation found no excess signals that could have been caused by a WIMP collision.

The second experiment, called XENON100, contained 165 kg of liquid xenon and was operated between 2008 and 2014. Over several data collecting runs the detector found no excess signals beyond that which would be expected by random background events.

The latest experiment to complete its data collection run is known as the XENON1T and contains 3.2 tonnes of ultra-pure liquid xenon. This detector began operation in 2014 and gathered 278.8 days of data before being taken off line in order to make space for its successor. During its time in operation the XENON1T experiment recorded 285 events, 53 more events than were theoretically expected by random collisions with radioactive particles. These 53 signals are the first evidence for possible Dark Matter particles, specifically a type of theoretical particle known as an axion.

The Xenon1T experiment was much larger and was the first to give signals that could have been caused by unknown particles. (Credit: Science.Perdue.edu)

But a new theory suggests that the 53 events could be the sign of something even more exotic, particles of Dark Energy. In a paper written by astrophysicists at Cambridge University’s Kavli Institute for Cosmology and published in the journal Physical Review D the signals detected by XENON1T could have been caused by a hypothetical particle that screens the short range effects of Dark Energy and which the researchers have christened ‘Chameleons’. The idea is that; while Dark Energy is dominant over a distance scale of the entire Universe, at smaller scales, say within our galaxy, it is almost imperceptible, so some form of screening is necessary. The Chameleon particles would provide that screening.

Results from existing experiments already restrain the effective mass of any ‘Chameleon’ particles that could be Dark Energy. (Credit: Phys.org)

According to Doctor Sunny Vagnozzi, first author on the paper, “Our chameleon screening shuts down the production of Dark Energy particles in very dense objects…It also allows us to decouple what happens in the local, very dense Universe from what happens on the largest scales, where the density is extremely low.”

This whole idea of screening Dark Energy on the local scale while allowing it to have full effect at the cosmic scale is very new and so far without any observational data to back it up. So the question of just what are those 53 excess events detected by XENON1T, Dark Matter, Dark Energy or just some contamination inside the containment vessel will have to wait.

The Standard Model of Elementary Particles is nice and simple, it is also incomplete. Just what else there is in the Universe is the big question. (Credit: Quantum Diaries)
the XENONnT experiment is now completed and has begun taking data. (Credit: Pegasus WMS)

The XENONnT experiment, with 8 tonnes of Xenon gas, came on line just a year ago and is collecting data even now. Perhaps we’ll have the answer in a very few years.

Type 1 Supernovas, how do they differ from Type 2 Supernovas and how that makes them important to our understanding of the size and evolution of the Universe?

In my post of just two weeks ago, January 4th 2020, I talked about the possibility that the Red Giant star Betelgeuse might be about to explode as a Type 2 Supernova (SN2). At the end of that post I made an offhand remark about writing a post about Type 1 Supernovas (SN1) in order to clarify the difference between the two types. Well I recently came across a couple of papers concerning SN1s so I decided that now was as good a time as any to fulfill my promise.

The constellation of Orion. Betelgeuse has been acting strangely. Is it about to go Nova? (Credit: Sky and Telescope)

First of all I suppose I should start by describing how an astronomer distinguishes one type of supernova from the other when they observe one. They do this by breaking up the light from the Supernova into its spectral lines that show the elements giving off the light. In SN1s the spectral lines of hydrogen will be completely absent while in SN2s the spectra will indicate a fair amount of hydrogen. Other observational differences have been seen in a few individual Supernovas, ones near enough to observe additional details, but the presence or absence of Hydrogen is the consistent difference. Everything else is really just theory.

The Hydrogen absorption spectra. Seeing these lines in the light from a Supernova means that it is a Type 2 while the absence of these lines makes it a Type 1. (Credit: Slide Player)

So let’s examine the theories, SN2s first. As I discussed in my post about Betelgeuse, SN2s begin as stars that are ten times or more as massive as our Sun. Such stars race through their nuclear fuel very quickly, millions instead of billions of years. As the star begins to run out of its fuel it puffs up into a red giant like Betelgeuse is now. When that fuel is completely used up the star’s core collapses because of gravity but that collapse triggers an explosion of the star’s outer layers as a Supernova. Since the outermost layers of the star still possess some hydrogen, that element’s spectral lines are seen in the Supernova’s light letting astronomers know that it is an SN2.

The Type 2 Supernova SN1987a, before (r) and during (l) images. (Credit: “© Anglo-Australian Observatory” and (optionally) “Photograph by David Malin”)

SN1s could hardly be more different. For one thing a SN1 can only occur in a double star system. In addition one of the stars must have already gone completely through it’s energy production life span and is now a burnt out cinder known as a white dwarf. White dwarfs can be as massive as our Sun but are crushed down to the size of a planet like Earth. Because they are so dense, and under such immense gravitational force, the material of a white dwarf is not made up of normal atoms as here on Earth, with electrons orbiting around a nucleus. Instead the electrons are squeezed into their nuclei and all of the nuclei are pushed much closer together than in normal matter, because of this the spectra of a white dwarf shows no sign of the presence of hydrogen.

A white dwarf star can have the mass of our Sun but only be as large as our Earth! (Credit: Medium)

There’s another peculiarity about white dwarfs as well. White dwarfs can only be so massive, a value known as Chandrasekhar’s number, which is equal to about 1.4 times the mass of our Sun. Any heavier and the white dwarf will continue to collapse down into a neutron star or black hole. That collapse triggering its outer layers to explode as an SN1.

So where would an otherwise stable white dwarf star get the extra mass needed to make it exceed Chandrasekhar’s number and explode as a SN1? From its companion star that’s where, which is why SN1 only occur in binary star systems. Astronomers have in fact observed binary systems where a white dwarf’s intense gravity is pulling matter away from its companion, a situation that will eventually lead to a SN1.

A white dwarf star pulling material away from its companion. Eventually this dwarf will go Supernova. (Credit: www.cfa.harvard.edu)

And now astronomers Bradley E. Schaefer, Juhan Frank and Manos Chatzopoulos of the Department of Physic and Astronomy at Louisiana State University have used some very precise measurements of the faint star V Sagittae in the constellation Sagitta to actually predict that it will explode as a SN1 in or about the year 2083. In fact V Sagittae is already rapidly increasing in brightness, currently shining at 10x the brightness it did when it was first accurately measured back in 1907.

V Sigittae is currently too dim to be seen without a telescope but a new study predicts in 2083 it will be the brightest star in the sky, for a few weeks. (credit: Sky and Telescope)

This rapid increase is likely to continue over the next decades as the white dwarf devours its companion. Eventually the star, which currently cannot even be seen with the naked eye, will become as bright in our sky as the star Sirius, or perhaps even the planet Venus, but not for long. How accurate the prediction about when V Sagittae will go Nova remains to be seen but you can be certain that astronomers will be keeping a close eye upon it for many years to come.

Another interesting thing about SN1 is that since they only occur when a white dwarf’s mass goes above Chandrasekhar’s number then all SN1 should be pretty much the same. That is, each SN1 should release the same amount of energy. If that is true then a SN1 can be used as a ‘standard candle’ to accurately measure distances throughout the Universe.

You see the distance to an object in deep space is the most difficult thing there is to measure in astronomy. We have many theories about the Universe that cannot be either confirmed or falsified simply because we can’t measure distances accurately enough to really be certain we know exactly what is going on. But if we know precisely how much energy an object puts out no matter where it is in the Universe, like a SN1, then we can measure how bright it appears in our sky and a simple formula tells us how far away it is.

Using actual Luminosity (L in watts) and brightness (B in Watts /meter-squared) to find the distance to an astronomical object. (Credit: Ohio State University)

Astronomers did just that back in the 1990s, using SN1 to accurately measure the rate at which the Universe is expanding. It was those measurements that indicated that the expansion of the Universe was actually accelerating, that ‘Dark Energy’ was pushing the Universe apart faster. This was the first and still the best evidence for the existence of Dark Energy.

The original evidence for Dark Energy. Notice how the Type 1 Supernova measurements (Red balls) indicate that the Universe is expanding faster than the ‘Standard Model’. (Credit: University of Arizona)

Now a new study threatens to upend all of that. Astronomers from the Department of Astronomy at Yonsei University in South Korea along with the Korean Astronomy and Space Science Institute have made highly detailed measurements from 60 SN1 events and have found that the absolute luminosity of an SN1 changes with the age of the Universe at which time the SN1 occurred. In other words SN1 have evolved over time. In fact if the changes in luminosity with time described in the paper are taken into account then the acceleration of the Universe simply disappears, there’s no such thing as Dark Energy!

The new evidence that SN1 have evolved over the age of the Universe. Does this mean that Dark Energy doesn’t even exist? (Credit: Phys.org)

If this study is true it would undo much of the Astronomy of the last 30 years, but other astronomers have to review it first, check the data, make some more measurements to be certain. Whether or not SN1 can be used as a ‘standard candle’ is an important matter for Astronomers but regardless of the answer to that question they are still an awesome example of the many different objects in our Universe.

With the Dark Energy Spectroscopic Instrument (DESI) astronomers and physicists hope to learn something about the nature of the mysterious Dark Energy.

If you ask any astronomer or physicist what is the biggest, the most critical question, the biggest mystery in science today they will immediately reply, “What is dark Energy?” You see our observations tell us that the Universe is expanding while our theories of Gravity tell us that the expansion should be slowing down. But instead what we see is that the expansion of the Universe is accelerating. Something, some pressure is pushing the Universe ever farther apart and that ‘Dark Energy’ actually accounts for some 80-85% of all the energy in the Universe.

After the Big Bang Gravity should have caused the expansion of the Universe to at least slow down but instead something is causing to accelerate! Dark Energy! (Credit: NASA Science Mission Directorate)

The idea that we know so little about 80-85% of the Universe is more than just a bit embarrassing because since Dark Energy is the dominate part of the Universe it will obviously have the dominant effect to the eventual fate of the Universe. To understand why that is so I’m going to take a step back and review the history of the ‘Big Bang Model’ of the Universe.

One hundred years ago astronomers thought that the Universe was pretty static, neither expanding nor contracting. Physicists however didn’t like that picture because without something acting to keep the galaxies apart the force of gravity should pull everything together into a ‘Big Crunch’. Everybody was relieved therefore when the astronomer Carl Hubble found that the galaxies were in fact moving away from each other, the Universe was expanding.

The Famous image of Andromeda taken by Carl Hubble that allowed him to measure the distance and proving Andromeda was another Galaxy. (Credit: Space and Astronomy News Daily)

This was the start of the Big Bang Model where billions of years ago an incredibly dense, hot Universe expanded rapidly, cooled and then formed the galaxies we see today. The question then became whether gravity was strong enough to eventually bring the expansion to a halt, or had the Universe reached ‘escape velocity’ and the expansion would go on forever. In the first case once the Universe stopped expanding gravity would begin to cause it to contract leading to a Big Crunch. This was a known as a closed Universe. The alternative was an open Universe that would fly apart forever.

The difference between an open and closed Universe id the first expands forever while the second ends in a Big Crunch. (Credit: Astronomy Today)

The measurements needed to determine which model was correct were very difficult to make, so difficult in fact that it wasn’t until the 1990s that everyone was shocked to discover that the Universe was actually expanding faster. Something was pushing it apart and for lack of a better name that something was called Dark Energy. So we then had the biggest problem in science, what is Dark Energy?

The first thing that scientists would like to learn about Dark Energy is whether or not it is even a constant force or does it’s strength change with time? You see when Einstein formulated the equation of Gravity in his theory of general relativity, see equation below; he realized that mathematically the equation could have a constant added to it. Einstein gave that constant the symbol λ, and he calculated that the effect of that constant would look a lot like the Dark Energy we now see.

Einstein’s full equation for gravity with the cosmological constant lambda. The left hand side is the geometry of the Universe while the right hand side is the energy of the Universe. (Credit: WordPress.com)

Now if Dark Energy is just this ‘cosmological constant’ as Einstein pictured it then the expansion of the Universe will continue forever. If the strength of Dark Energy varies however, maybe even reverses itself to an attraction, then the ultimate fate of the Universe is still unknown.

However the measurements needed to determine whether the strength of Dark Energy varies with time are far more difficult to make than the measurements that discovered it in the first place. Still, astronomers have learned quite a bit in the last 25 years and advances in technology have made their instruments vastly more precise and sophisticated. It is with this improved technology that the Dark Energy Spectroscopic Instrument or DESI has been designed and constructed.

The setup of the Dark Energy Spectroscopic Instrument (DESI). New detectors and computer controlled fiber optics have been installed on the Mayall Telescope making it the most sensitive instrument for studying Dark Energy. (Credit: Spiedigitallibrary)

Retrofitted into the Mayall telescope at Kit Peak observatory outside of Tucson Arizona the DESI detector consists of a bundle of 5000 fiber optic cables, each with its own computer controlled positioning mechanism. The fiber optic cables lead to an array of 5000 spectrographs so that the combined telescope / detector will allow astronomers to accurately measure the position, magnitude and redshift of 5000 galaxies at a time. 

The DESI instrument, black object upper right, installed on the Mayall telescope. (Credit: Popular Mechanics)

First light for the DESI instrument came in September of 2019 and the ambitious five-year observation program is now well underway. Once completed the DESI will have obtained the position and redshift of 35 million galaxies allowing scientists to produce a 3D model of a large section of the Universe. This model will then provide the data needed to answer the question of whether the strength of Dark Energy has varied with time.

And there are other instruments that will soon be coming online that will compliment the observations of DESI. The 4MOST telescope at the European Southern Observatory is similar to DESI while the Euclid space telescope will also be observing galactic redshift versus distance from orbit.

The Euclid space telescope will also study the nature of Dark Energy. (Credit: Wikipedia)

 Now it is true that DESI will only tell physicists how Dark Energy changes with time nevertheless that information will be enough to enable them to eliminate many of the competing theories about its nature. So the theorists are anxiously awaiting the results of DESI and its companions, hoping that they give them direction in their effort to describe the entire Universe.

We’ve learned a great deal in the last 100 years about the structure and evolution of our Universe. I’ve little doubt that the next 100 years will bring just as many exciting discoveries.

Here we go Again. A Recent Paper by a Group of Cosmologists raises doubts about the very Existence of Dark Energy.

We’ve all heard the old saying ‘Two steps forward, one step back’. Well, when it comes to Cosmology, the study of the Universe as a whole, it seems like we take a step forward, another sideways, close your eyes and spin, take two steps etc, etc, you get the idea. The Universe is so large, the measurements so difficult to make, the theories so complex that progress in cosmology has always been slow with many wrong turns. So hang on folks, today’s post is going to be a little trip with Alice into wonderland.

Today the best model we have for the basic nature of the Universe is that is consists of billions of Galaxies like our Milky Way. That the Universe is expanding, all those Galaxies are moving away from each other, and that the expansion is not being slowed by the gravity of the Galaxies. In fact the expansion is accelerating. This basic model is outlined in the image below.

Big Bang Model (Credit: NASA)

It was Carl Hubble, back in the 1920s and 30s who discovered that the Universe was made of Galaxies and that it was expanding. The acceleration of the Universal expansion was discovered in the 1990s by two groups of astronomers led by Saul Perlmutter and Adam Riess.

The cause of this acceleration was completely unknown and quickly given the name ‘Dark Energy’, although cosmologists prefer the name ‘Vacuum Pressure’. Today we know almost nothing about ‘Dark Energy’ and it ranks as one of the greatest mysteries in all of science.

Now a recent paper published by Lawrence H. Dam, Asta Heinesen and David L. Wiltshire of the University of Canterbury in New Zealand may be about to throw the whole science of cosmology into a state of confusion. According to Professor Dam and his colleagues there is no such thing as Dark Energy, it simply doesn’t exist. Cosmologists only think there’s Dark Energy because they’re trying to fit their measurements to an incorrect mathematical model of the Universe.

To understand what Professors Dam, Heinesen and Wiltshire are saying we need to talk a little bit about the mathematical ideas we use to describe the Universe and of course we start with Albert Einstein. When Einstein published his General Theory of Relativity, also known as his Theory of Gravity, it was quickly realized that since it was gravity that held the Universe together then Einstein’s Gravity theory was the best way in which to study the Universe. The full Einstein equation for gravity is shown below, it’s the lambda (L) symbol that relates to Dark Energy.

Einstein’s Field Equation

A trio of physicists named Alexander Friedman, Howard Robertson, and Arthur Walker used Einstein’s theory to develop an exact set of equations for a Universe where matter was spread smoothly (homogenous) and the same in every direction (isotropic). A mathematician named Georges Lemaitre later expanded the FRW model to include the expansion of the Universe thereby creating the ‘Big Bang Theory’, although technically it is referred to as the FLRW model.

Now remember the two assumptions of the FLRW model, that the matter in the Universe is smoothly distributed with no preferred direction, i.e. it is homogenous and isotropic. At first glance however the Universe sure doesn’t look smooth, it’s got the Galaxies, clusters of stars with a whole lot of empty space between them. However, the idea was that when you considered the whole Universe with tens of billions of Galaxies they would all spread out evenly.

Except that they don’t. Another important astronomy project of the last twenty years has been the Sloan Digital Sky Survey (SDSS), an ambitious attempt to map the positions of nearly a million Galaxies and what the Sloan team has discovered is that the Universe actually looks more like Swiss cheese or soap bubbles with regions that are quite dense surrounding immense empty voids. The image below shows a sample of the results of the SDSS and clearly illustrates the ‘lumpiness’ of the Universe.

Results of Sloan Digital Sky Survey (Credit: SDSS)

So the basic assumptions of the FLRW model aren’t quiet right and Professors Dam, Heinesen and Wiltshire say that a new mathematical model, which they call the Timescape model, must be used instead. It’s in this mathematical model that the measurements made by Perlmutter and Riess fit without the need for anything like Dark Energy.

Now there’s a long way to go before the Timescape model is generally accepted, if it ever is. Chances are that this theory will not stand the test of close examination and Dark Energy will continue to be a mystery that needs to be solved. You never know though, every time we look further into the Universe it just seems to get stranger and stranger.

I realize that this post was rather long and heavy and dealt with some strange and difficult topics. However I hope that it wasn’t too abstract. The intersection between math and measurement is central to the advance of science and after all, we are taking about the basic structure of the Universe as a whole!

Does Dark Energy really Exist?

For the past twenty years the greatest mystery in all of Science has been the Nature of Dark Energy, a unknown force that is accelerating the expansion of the Universe and whose energy makes up more than three quarters of everything there is. Now a new study by Cosmologists J.T.Nielsen, A. Guffanti and S. Sarkar has called into question the very existence of Dark Energy.

To understand what is going on we have to go back to 1929 when astronomer Edwin Hubble discovered that the galaxies he was studying were all receding from our milky way and that the further a galaxy was the faster it was receding. This is Hubble’s law for the expansion of the Universe and the rate of expansion is called Hubble’s constant.

Almost immediately after Hubble’s announcement physicists and astronomers began to theorize what could have caused this expansion and so they developed the Big Bang Theory which was finally confirmed by A. Penzias and R. Wilson in 1965. But if the Big Bang Theory was true then the gravitational attraction of the galaxies should be slowing the rate of expansion, Hubble’s constant should not be truly constant. Cosmologists also theorized that there could be two basic solutions. One, the gravitational attraction was strong enough that eventually the expansion would come to a stop and the entire Universe would enter a Big Crunch phase. The other solution was that the expansion was so great that the Universe had achieved escape velocity and would expand forever.

It was to discover which of these two alternative Universes was true that two teams of astronomers, one led by S. Perlmutter and the other by A. Riess and B. Schmidt used Type Ia supernova to try to measure the deceleration of Hubble’s constant. In 1998 these two teams independently announced their findings that the expansion of the Universe was in fact accelerating, a discovery that shocked the world of science and led to Perlmutter, Riess and Schmidt being awarded the 2011 Nobel Prize in Physics.

The search was now on for the cause of this acceleration, an unknown force that was quickly named Dark Energy although cosmologists prefer to call it Dark Pressure. Literally hundreds of theoretical papers have been written over the past two decades speculating on the nature of Dark Energy but little more observational detail was provided by astronomers.

Now a new study, using data from more than ten times as many Type Ia supernovas as was available to Perlmutter, Riess and Schmidt has called into question the very existence of Dark Energy, asserting that the discovery was if fact only a statistical fluctuation. This new study by astronomers J.T. Nielsen, A. Guffanti and S. Sarkar uses data from 740 Type Ia supernovas and concludes that “we find, rather surprisingly, that the data are still quite consistent with a constant rate of expansion.”

This result is something of a shocker, have cosmologists spent the last 18 years chasing a phantom? Personally I’ll wait and see. There is other indirect evidence for Dark Energy in the Cosmic Microwave Background so Dark Energy isn’t gone just yet. In fact the new study found that the evidence for Dark Energy is at the three sigma level but scientists prefer five sigma so we are talking statistical weights of evidence.

Still this is yet another example of just how difficult it is to get real, precise details on the nature of our Universe. We have learned a great deal but that knowledge has required great effort, and just as often great patience. I’ll keep you informed.

I’m going to try a little experiment of my own and try to insert the actual article by Nielsen et al into this post. Enjoy.

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