Artificial light has transformed human society. It frees us from the darkness, and allows us to light our homes and communities. It has also made the night sky increasingly less dark, which poses a challenge to astronomers. And it’s gotten worse in recent years, thanks to an energy-saving light known as LEDs.

The earliest light bulbs (of Edison fame) were extremely inefficient. They produce incandescent light by electrically heating a thin wire of metal to the point that it emits light. But only a small fraction of the light emitted is visible. Most of it is infrared, which we feel as heat. The bulbs make much better heaters than lights, and for a time there were even toy ovens that used a light bulb to bake little cookies or muffins. Their big advantage was that they were cheap and reliable.

As energy costs rose, the quest for greater efficiency led to new types of light bulbs. The most popular were variations known as fluorescent lights. These involve a tube of low-pressure mercury gas. An electric current is passed through the gas, causing it to emit ultraviolet light. The interior of the tube is coated with a phosphorus powder that converts ultraviolet light to visible light. The efficiency of these lights made them ubiquitous in large lighting environments such as office buildings, but their greenish hue and flickering nature were often found irritating. What we really needed was a light that is highly efficient and emits a more sun-like light.

The latest answer to that challenge is the Light Emitting Diode, or LED. These are based on semiconductors. The same type of semiconductors used in computers and other electronic devices, except that they are built to emit light. They are highly efficient, but only emit light in a narrow color range. However by combining LEDs of different colors you can approximate the wide spectrum of colors produced by sunlight.

The spectra of different types of lights.

Early on LEDs were expensive, but even as costs came down they still failed to mimic sunlight well. That’s because there weren’t any good blue LEDs. Early LED lightbulbs were an odd yellowish-orange, since they didn’t emit much light in the blue spectrum. But in 1993 Shuji Nakamura developed an efficient blue LED. This was such a big breakthrough that he was awarded the 2014 Nobel prize in physics for his work. LED lightbulbs could now be produced that emit a more natural white light. But this breakthrough has had unintended consequences.

As the price of white-LED lights have dropped, they have become a favored choice for both interior and exterior lighting. For outdoor lighting in particular they have started to replace mercury vapor and sodium vapor lights. Their low cost and high efficiency has also resulted in a rise of exterior lighting. The white glow of LEDs has filled our communities and homes. But white-LED lights depend upon blue LEDs, and are brightest in the blue spectrum. And blue light pollution is bad for astronomy.

Low pressure sodium lights are often used in protected dark sky regions. Credit: Robert Ashworth

If you’ve ever wondered why the sky is blue, the answer comes from the fact that our atmosphere scatters blue light more than red. Sunlight comes in a rainbow of colors, but it is the blue that is scattered across the sky, giving it a blue hue. Since modern LED lights emit a lot of blue, it is scattered by the atmosphere, giving a diffuse blue glow at night. We don’t notice it with the naked eye, but for astronomers it is a constant glow of light pollution. As more lights are converted to LEDs, the astronomer’s sky becomes ever less dark.

There are ways to help astronomers, such as making sure lights are shielded to focus only at the ground, and using “warm” LEDs that don’t emit strongly in the blue. In particularly sensitive areas, one of the best solutions is to use low-pressure sodium light for exterior lighting. You can recognize these by their distinct yellow-orange glow. That’s because they emit light at at very narrow range of colors, which makes it easy for astronomers to filter out.

Given all the advantages, we aren’t likely to give up artificial lighting. But sometimes we have to balance the desire for a brilliant night with the desire to see the stars.

The post How Saving Energy Can Hurt Astronomy appeared first on One Universe at a Time.

As we prepare for the Great American Eclipse, you might have your eclipse glasses ready. If not, another great way to view the eclipse is with a pinhole camera. They are extremely easy to make, and you just need a cardboard box, some tin foil, scissors, tape and a toothpick. 

Two holes are cut into the box. One for the pinhole, and one for viewing. The pinhole should be placed on the short side of the box. Credit: Brian Koberlein

The basic idea is to allow light to shine through a small opening. The hole acts as the lens of your camera. It doesn’t focus the light like a regular camera does, but since the hole is small it creates an image of your light source (like the Sun). Since light travels in a straight line, light coming from the left of the hole will reach the inside of the box slightly to the right. Light from the right will travel through the hole and to the right, and so on. As a result and image will appear on the inside of the box.

Schematic of a pinhole camera. Credit: Wikipedia

Pinhole cameras are an ancient technology. They were known by the Chinese since 500 BCE. Arabic astronomer Ibn al-Haytham first used one to view an eclipses around 1000 CE. The first modern cameras were also based upon pinhole cameras. They aren’t used as much today because of a major drawback. The sharpness of your image depends upon the size of your pinhole. The smaller the hole, the sharper the image. But a smaller hole also means the image is more dim. For everyday images this means a camera would need a long exposure time to get a decent image. Modern lens cameras create brighter images. But for a solar eclipse the pinhole cameras are perfect. The Sun is so bright that you need a much dimmer image to see it.

An image of the Sun and nearby clouds as seen through a pinhole camera. Credit: Brian Koberlein

To make a pinhole camera, any size box will do, but a larger box will work best. You’ll need to cut at least one square hole on the short side of the box. You then tape tin foil over the hole, and use a toothpick to poke a small hole in the foil. When you face the pinhole side of your box toward the Sun, the image will appear on the far side of the interior. To see your image you need a viewing hole. If your box is big enough you can cut it on the same side as your pinhole, but for smaller boxes you can cut it on an adjacent side. Some folks use big boxes and cut a hole in the bottom so kids can place the whole box on their heads. Any way works, as long as you don’t block the light coming through the pinhole.

You should build your box before the day of the eclipse, just to make sure it works well. It’s a great project for kids, and a way to teach them a little about optics before the main event. Regardless of your design, stay safe and have fun on eclipse day!

The post How To Build A Pinhole Camera, And Why It Works appeared first on One Universe at a Time.

If you play Scrabble, you might know syzygy as a great high-point word, but in astronomy it is the term used to describe three celestial bodies in a line. It’s derived from the Ancient Greek word meaning, “yoked together.” 

Astronomer Katie Mack’s famous twitter pun.

Nowadays syzygy is often used more broadly to denote an interesting arrangements of planets, such as when three planets appear to cluster together, but the original meaning leads to interesting arrangements on its own. The Moon is in syzygy with the Earth and Sun every full moon and new moon, since that is when the three bodies are roughly in a line. But usually the Moon is a bit above or below the Earth-Sun line due to the orientation of the Moon’s orbit. However when the Moon’s orbit comes into line with the Earth and Sun, then a lunar or solar eclipse can occur. Solar eclipses aren’t more rare, but they can only be seen along a narrow path on Earth due to the Moon’s smaller size.

When the inner planets Mercury and Venus are between the Earth and Sun, they can transit the Sun. As with the Moon, Mercury and Venus usually enter syzygy a bit above or below the Sun, so transits are rare. Although we usually only think of transits seen from Earth, others can occur, such as the transit of Phobos as seen from Mars. The outer planets can’t be seen to transit the Sun from Earth, but enter opposition when they are in syzygy. At such a time a planet is high in the sky around midnight, and is as close to Earth as it can be, making for excellent viewing conditions.

There are also times when the Earth, Moon and a planet are in syzygy, which can lead to an occultation. In this case the Moon passes in front of the planet, hiding the planet from view for a time. Capturing an occultation is high on the list for many amateur astronomers.

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Our Sun is adrift among the stars. As our home star moves through the galaxy, so to do the other stars. This means that the apparent positions of the stars change over time. Because of the great distances of stars this shift is minuscule and difficult to measure. For years we have only been able to measure the motion of a few close stars. But that’s beginning to change. 

From 1989 to 1993, the Hipparcos spacecraft made high precision measurements of more than 100,000 stars, cataloging their positions and distances, as well as a measure of their proper motion across the sky. This data was compiled in the Hipparcos Catalog in 1997. A less precise catalog of more than 2 million stars, known as the Tycho catalog was also published. While the accuracy of the Hipparcos data for some stellar clusters has been debated, it has proved to be quite accurate for most stars.

Then in 2013 the Gaia spacecraft was launched, with the goal of measuring the position and motion of more than a billion stars. In 2014 the Gaia team published its initial data, including measurements of more than 2 million Hipparcos stars. This gave us the opportunity to see just how far these stars had moved over the course of 25 years.

Fortunately the data from both Hipparcos and Gaia are freely available. So the United States Naval Observatory (USNO) analyzed the data to calculate both the location and motion of these 2 million stars, giving the most accurate proper motions thus far. They then went one step further, and compared the positions of these 2 millions stars with the positions of million that had been measured by the USNO in 1998 and 2004, and were able to determine the proper motions of millions more stars. A new catalog containing this data will be released soon.

We’ve long known the stars moved over time, but we are now able to determine this motion accurately for millions of stars. This will help us understand not only the dynamics and evolution of our Milky Way galaxy, it could also provide clues to things like dark matter.

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When news of the TRAPPIST-1 system blazed across headlines, one of the common questions I got was what the planets really looked like. After all, if we can discover planets around other stars, we surely must be able to see them. But we can’t. In some ways can barely see the star. But this demonstrates how what we actually observe (and what data is important to astronomers) is very different from the common perception of what astronomers observe. 

The apparent sizes are accurate, but the surface features are pure fiction.

Part of this misconception comes from the way we tell the story of astronomy. When articles came out talking about seven Earth-sized worlds, there were plenty of pictures of the planets as rich worlds with complex surface features. These artistic imaginings make for great images, but they are just imagined possibilities. We don’t know anything about the surface features of these planets, because we can’t even see the planets. But we don’t have to observe planets directly to know that they are there.

The TRAPPIST planets, like most exoplanets, were discovered using a technique known as the transit method. Basically we measure the brightness of a star over time, and watch for little dips in brightness. You can see a graph of these measurements in the image above, which shows 500 hours of data gathered from the Spitzer space telescope. Every dot on the graph is a brightness measurement. You can see how most of the time it seems to fluctuate randomly along a common average, but every now and then it dips in brightness for a bit. That dip occurs when one of the planets passes in front of the star, blocking some of the light.

Animation showing the actual brightness variation of the few pixels of light from TRAPPIST-1.

If you look on the vertical scale, you’ll notice that the variation in brightness is actually quite small. It only dips in brightness by about 1% when a planet passes by. This is actually pretty large for an exoplanet, and is due to the fact that TRAPPIST-1 is a small star, only about the size of Jupiter (though 80 times more massive), so the planets block about 1% of the light. This is why we need to make sensitive measurements of a star to detect exoplanets.

But even this graph is a bit misleading. We don’t just point a telescope at the star and measure “brightness.” What the telescope actually does is focus the image of a star on a digital camera detector known as a CCD. Each pixel of the detector measures the amount of light it gathers as a number, where a higher number means more light struck the pixel. TRAPPIST-1 is a small, faint, 18th-magnitude star, so even on a good telescope its light only strikes a few pixels at a time. You can see an animation of its actual image here. If you want to know what the TRAPPIST-1 system looks like from Earth, that’s it.

Technically we don’t even see that. Since the CCD pixels just produce a number, what we really have are an array of numbers for each observation we make. The pixel numbers for each observation are then combined to create an overall brightness measurement. From that we analyze the dips in brightness to calculate the orbits, sizes, and masses of the planets. It’s complex work, which is what makes exoplanet discoveries so amazing.

Now certain skeptics might argue that since we don’t have images of the planets, we don’t really know they exist. But that goes back to the misconception about astronomy. While there are lots of great astronomical images, astronomy is really about data. Even when we gather images, our focus is not about making them pretty, but about making them useful. That’s why, for example, most astronomical images are black and white rather than color, and why we observe things at a range of wavelengths to see different features.

So while astronomy can discover entire solar systems, and those distant worlds would undoubtedly be wondrous to behold, that’s not what we really see.

The post What We Really See appeared first on One Universe at a Time.

Green is an interesting color in astronomy. Our eyes are more sensitive to green than any other color, and so it is a color that is often seen in the night sky. There are green comets, the momentary green brilliance of a meteor, the faint green glow of northern aurora, and even a green glow to some distant galaxies. These objects can have other colors as well, but green is a common color of the night sky. 

While all these objects can share a common color, the mechanism behind their greenish glow can vary widely. Comets, for example take on a green hue because of the gas tail that forms as they approach the Sun. Most of the gas consists of hydrogen, but other compounds such as cyanide (CN₂) and carbon (C₂) can be contained in the tail as well. These molecules emit light at green wavelengths, and can be bright enough to be seen with the naked eye. In fact, cyanide (specifically cyanogen) was the first in Halley’s comet in 1910, and even led to a baseless panic that Earth might be poisoned by Halley’s tail.

The green glow of comet Lovejoy. Credit: Paul Stewart.

Meteors are green for a completely different mechanism. As a meteor enters Earth’s atmosphere, it is heated to the point where its outer layer is vaporized. The metals in the meteor glow with particular colors. Green comes from nickel. The most common metallic meteors are iron-nickel, so green is a common color. This glow tends to be brightest when meteors hit the atmosphere at high speed. For example, fast moving Leonid meteors can often have a green glow.

Galaxies that glow green are known as green pea galaxies. They are compact, and have a strong green emission line from oxygen, making them look like a green pea. The oxygen surrounding the galaxies glows green when it is ionized by the galaxy’s starlight. In order for the oxygen to be bright enough to give the galaxy a green color, there has to be a lot of ionized oxygen, and thus a lot of ultraviolet light produced by young stars. So green pea galaxies are young galaxies where lots of stars are forming, and may have played a role in the reionization of the early universe.

The solar radiation spectrum. Credit: Robert A. Rohde (CC BY-SA 3.0)

Since we’re most sensitive to green light, why are there no green stars? They can be red, yellow, blue, and white, but not green. It all has to do with the way stars produce light, which is very different from other astronomical objects. Comets, meteors, and the gas around galaxies all give off color when particular atoms or molecules give of light. The electrons in these atoms jump from one energy state to another, emitting a particular wavelength of light. But the Sun and other stars produce light from internal heat. Rather than emitting specific colors, stars emit a range of colors known as a thermal blackbody. The brightest color of a star depends upon its temperature. For cooler stars, the brightest color is red, and thus a star appears reddish. Hotter stars are brightest in the blue range, and so appear blue. But a star that peaks in the green is also bright in red and blue. Thus we see red, green, and blue light from the star, which our eyes interpret as white.  Since a thermal blackbody can’t peak at green without being bright in the entire visible spectrum, a green star simply isn’t possible.

But since green is so common in the sky, its absence from the stars is not a big loss.

The post How Green Was My Meteor appeared first on One Universe at a Time.

On August 21 of 2017 the shadow of the Moon will trace a path across the United States. It’s a total solar eclipse that many will have the opportunity to observe. But whether you will observe totality or not depends on where you are. Astronomers have been able to predict the path of solar eclipses for millennia, but this new video demonstrates just how precise our predictions have become. 

The video combines lunar terrain data with that of the Earth’s terrain and the predicted positions of the Earth, Moon, and Sun. Data collected from a variety of sources and combined to create an extremely accurate prediction of the 2017 eclipse. Much of this data is publicly available, so you could do your own calculations as well.

If you have a chance to see this eclipse (or any solar eclipse) take it. We already know where you need to be to see it. The only other factor is to ensure a clear sky, but when we get within a few days of the eclipse we’ll have that prediction as well.

The post Wonderful Precision appeared first on One Universe at a Time.

Take a mass, any mass. Compress it into an ever smaller volume. As its density rises, the gravity near its surface with increase. Squeeze it into a small enough volume and the surface gravity will become so strong that nothing can escape, not even light. Squeeze anything into a small enough volume at it will become a black hole. The defining feature of a black hole is its event horizon, which defines the volume of no return. But the event horizon also marks a region where our basic understanding of physics breaks down. It is perhaps the greatest paradox of modern astrophysics.

The event horizon of a black hole is often defined as the point where the escape velocity becomes greater than the speed of light. It turns out the truth is a bit more subtle. Mass curves space around it, and for a black hole space is curved to the point where it basically folds into itself. The event horizon doesn’t mark an escape velocity, it marks a region that is isolated from the rest of the Universe until the end of time. The laws of physics conspire to keep you trapped, and you could no more escape a black hole than you could walk backwards in time.

However the existence of a one-way path to oblivion flies in the face of the most basic tenets of physics: phenomena should be predictable. If you throw a baseball in a particular direction at a particular speed, you can figure out where it’s going to land. Just determine the initial speed and direction of the ball, then use the laws of physics to predict what its motion will be. The ball doesn’t have any choice in the matter. Once it leaves your hand it will land in a particular spot. Its motion is determined by the physical laws of the universe. We can also work backwards. Knowing the speed and direction of the ball we can work out where it was in the past. If that’s true, then knowing something about the Universe now allows us to determine its past and future. But an event horizon breaks that rule. Once something crosses the event horizon, all you can possibly know about the object is its mass, charge and rotation. Was it a car or a spaceship? No idea. What path did it take to enter the black hole? No idea. All that information we’re supposed to know about the object, seems to simply disappear. This is known as the information paradox.

Now some of you might point out that quantum mechanics isn’t deterministic like a baseball, so perhaps information isn’t conserved after all. But it turns out that quantum theory does conserve information, it simply conserves the probabilities of certain outcomes. Knowing the state of an object we can still predict what it’s likely to do next, and what it likely did in the past. But it’s possible that quantum theory might provide a way out of the information paradox. After all, Stephen Hawking showed that quantum theory allows matter to escape a black hole through Hawking radiation. If matter radiates from a black hole, perhaps it also allows information to escape the black hole.

Unfortunately quantum theory isn’t an easy fix. Hawking radiation as it is typically defined is completely random, so while matter and energy can escape a black hole, information can’t. Theoretically you can make Hawking radiation non-random, but doing so turns it into an intense firewall near the event horizon. This flies in the face of the principle of equivalence, which says that a small region of space near an event horizon shouldn’t be any different than a small region of space anywhere else. Thus trying to solve the information paradox gives rise to another problem known as the firewall paradox.

So how do we solve this problem? The short answer is we don’t know. Lots of very smart people have tried to crack this problem, and while there are some interesting ideas there is no definitive solution. To really address this issue will require a quantum theory of gravity, which we don’t yet have. There have been some arguments that the way around the paradox is to simply declare that black holes can’t exist, but now that we’ve detected gravitational waves we know they absolutely do exist.

There’s no easy way around these paradoxes, and until there is, event horizons will remain a clear marker of the great unknown.

Miss the beginning of this series? It all starts here.

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Earth is showered with cosmic rays. They are protons, electrons and atomic nuclei traveling at nearly the speed of light, and strike our atmosphere to create the most power particle collisions ever observed. As a particle approaches the speed of light, it’s energy increases exponentially, so it might seem that there is no upper limit to just how much energy cosmic rays can have. But it turns out there is a limit, at least in theory. 

The limit is imposed by the cosmic microwave background (CMB). This thermal remnant of the big bang fills the Universe with a sea of microwave photons, which is why we observe the CMB from all directions in space. But because of relativity, a cosmic ray moving at nearly the speed of light will observe this radiation greatly blue shifted. Instead of a sea of faint microwaves, these cosmic rays observe CMB photons as high energy gamma rays. Occasionally the cosmic ray will collide with a photon, producing particles such as pions and taking some of the energy from the cosmic ray. This will continue until the cosmic ray isn’t powerful enough to produce pion collisions. As a result, over the vast expanse of intergalactic space any really high energy cosmic ray will be lowered to this cutoff energy.

High energy protons collide with CMB photons, producing pions while losing energy. Credit: Wolfgang Bietenholz

This cutoff is known as the GZK limit, after Kenneth Greisen,Vadim Kuzmin, and Georgiy Zatsepin, who calculated the limit to be about 8 joules of energy (a proton traveling at 99.999998% of light speed), and that any cosmic ray traveling at least 160 million light years will have dropped below this limit. While that’s a huge amount of energy, there have been observations of cosmic rays with even higher energy. The highest energy cosmic ray had an energy of about 50 joules. So how is this possible?

The short answer is that we aren’t sure. High energy cosmic rays are more powerful than any particle accelerator we have, so these kinds of particles can’t be recreated in the lab. One possibility is that our measurement of high energy cosmic rays is somehow wrong. We don’t observe cosmic rays directly, but instead observe the shower of particles they create when striking our atmosphere. From this we infer its energy and composition. While that’s certainly a possibility, the observations we have seem pretty robust.

Another solution is that these cosmic rays are produced locally (in a cosmic sense). Most cosmic rays have traveled billions of light years before reaching us, but if a cosmic ray was produced less than 160 million light years away it could have more energy than the GZK limit. The problem with this idea is that there is no known source of high energy cosmic rays within 160 million light years, so this answer simply replaces the GZK paradox with the mystery of their origin. Another possibility is that the highest energy cosmic rays might be heavier nuclei. About 90% of cosmic rays are protons, and another 9% are alpha particles (helium nuclei), with the rest mostly electrons. It’s possible that a few cosmic rays are nuclei of heavier elements such as carbon, nitrogen, or even iron. Such heavy nuclei might be able to sustain their energy over greater cosmic distances, thus overcoming the GZK limit.

But one other option is perhaps the most tantalizing. Since these cosmic rays have more energy than anything we can create in the lab, they are a test of really high energy particle physics. It’s possible that the GZK limit is simply invalid. It’s based upon our current understanding of the standard model, and if the standard model is wrong so could the GZK limit. The answer to the GZK paradox might be new physics we don’t yet understand.

The energy of the most powerful cosmic rays might just be too big to fail.

Next time: The event horizon of a black hole marks a one way trip to oblivion. It also seems to defy some of the most foundational ideas of physics. We look at the hottest paradox in physics tomorrow.

The post Too Big To Fail appeared first on One Universe at a Time.

Although the Sun seems ageless and never changing, it is a star like any other. It’s only a bit older than the Earth itself, and like every star it formed from the gas and dust of a stellar nursery. As we’ve come to understand stellar evolution, it has become clear that stars get warmer as they age. Billions of years ago, our Sun was about 70% as luminous as it is today. That means young Earth received less heat from the Sun than it does today. So much less heat that it wasn’t enough to sustain liquid water. But geologic evidence clearly shows that there were oceans of water in Earth’s youth. 

The luminosity of the Sun has changed over billions of years.

This is known as the faint young Sun paradox, and it remains a big challenge. Over the past few decades we’ve learned how atmospheric composition can drastically affect surface temperature on a planet. While Venus is warmer than Earth, it’s thick atmosphere makes it even hotter than Mercury. Mars, on the other hand once had liquid water on its surface due to a thicker atmosphere. But while Earth did have a thicker atmosphere in its past, that can’t fully account for young Earth’s oceans. It’s not just the amount of atmosphere, but its composition that plays a vital role in surface temperature. Greenhouse gases like methane and carbon dioxide are far more effective at trapping solar heat than other compounds. Measurements of Earth’s young atmosphere taken from air trapped in rocks show that methane and carbon dioxide levels weren’t high enough to maintain liquid water on Earth.

One possible solution to the problem is that Earth’s early atmosphere had high quantities of molecular hydrogen. Today our atmosphere has very little hydrogen. It’s so light that it can escape Earth’s atmosphere pretty easily. But it does so with the help of ultraviolet light. Since Earth’s young Sun was cooler it produced less ultraviolet light, making it more difficult for hydrogen to escape. Hydrogen is not a particularly strong greenhouse gas, but it can trap heat. As part of a thicker nitrogen atmosphere it might have been enough to maintain Earth’s early oceans. Other ideas propose that solar flares from our young Sun helped heat our atmosphere, or that tidal heating from a closer young Moon contributed to Earth’s warmth.

As it stands there is no definitive answer. So the faint Sun paradox remains a challenge, as it has since the dawn of time.

Next time: Cosmic rays are powerful. Too powerful, in fact. The discussion heats up tomorrow.

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The discovery of white dwarfs in the early 1900s was deeply perplexing for astronomers. From their temperature and brightness it was clear white dwarfs are roughly the size of Earth. Since some white dwarfs orbit other stars, we can also determine they are about as massive as the Sun. How is it possible for so much mass to be compressed within such a small volume without collapsing on itself? 

The most popular idea at the time supposed that under great pressure electrons would become free from atoms, producing a super dense plasma of free electrons and atomic nuclei. Since electrons are extraordinarily tiny, they would act like an ideal gas with the usual temperature and pressure relations. The “electron gas” of a white dwarf would therefore have enough pressure to keep the star from collapsing.

The Boomerang Nebula hovers just above absolute zero, with a temperature of just 1 K.

While that seems reasonable, Arthur Eddington noted it gave rise to a paradox involving thermodynamics. A fundamental law of thermodynamics states that nothing can be cooled below absolute zero. This applies to a gas of electrons as well. Since white dwarfs emit heat and light, over time they would cool. But Eddington noted that white dwarf matter only existed because it is under pressure. If you removed the pressure the material should expand back into regular atomic matter. So suppose you found a particularly cold white dwarf. The gas of electrons and nuclei would be above absolute zero, but it’s energy per mass would be less than that of regular matter at absolute zero. If you scooped up a bit of that white dwarf and remove the pressure, what would happen? Theoretically it should be colder than absolute zero, which isn’t possible.

The paradox was finally solved in 1926 by R. H. Fowler. The problem, he argued, stemmed from treating electrons as classical objects like atoms. Electrons follow the rules of quantum theory. Because of the Pauli exclusion principle there is a limit to how closely they can be pushed together. A gas of electrons in a white dwarf therefore can’t cool below absolute zero because the laws of quantum mechanics don’t allow it. Within a few years Subrahmanyan Chandrasekhar expanded upon this idea to show that white dwarfs can never have more mass than about 1.4 Suns. This upper limit on size became known as the Chadrasekhar limit.

What began as a paradox of thermodynamics became the first demonstration of the quantum connection between the very large and the very small. It pointed us toward the direction of modern astronomy.

Next time: Stars get warmer as they age, which means there was a time when our Sun was too cool to liquify water on Earth. But the evidence is clear water existed on Earth for much longer. What gives? The paradox of the faint Sun heats up tomorrow.

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No matter what direction you look in the night sky, it looks basically the same. In astronomy terms we say the Universe is homogeneous and isotropic. Sure there are areas where galaxies cluster together, and other areas where galaxies are rare, but on average the distribution of stars is pretty even. Because of this, an early idea for the cosmos is that it is the same everywhere forever. It seems both ageless and infinite in expanse. But if that’s the case it raises a few troubling paradoxes. 

Olber argued the sky should be bright as the Sun. Credit: Wikipedia user Htkym

The first paradox is perhaps the most famous. Known as Olber’s paradox, it questions how an infinite ageless universe could be mostly dark. At first glance it might seem obvious. The more distant a star, the dimmer it appears, so stars very far away are simply too dim to be seen. But the apparent brightness of a star follows a specific relationship known as the inverse square law. A single star some distance away is as bright as four similar stars twice as distant, or nine three times farther away. But if stars are distributed fairly evenly, then there are four times the number of stars twice as far away, and nine times more that are three times away. So while stars appear dimmer with distance, there are more stars at greater distances. So an infinite ageless universe should have a sky as bright as the Sun.

Thermodynamics requires that your coffee and the Universe are getting cold.

On the other hand, Clausius’ paradox argues that the sky should be completely dark, with no stars in the sky at all. First postulated by Rudolf Clausius, the paradox is based upon thermodynamics. One of the basic laws of thermodynamics is that heat flows from hotter regions to colder regions until they equalize in temperature. In other words, your morning coffee will always cool down until it reaches room temperature. It will never spontaneously heat up by cooling the surrounding room slightly. According to thermodynamics, even the stars will eventually cool. In an ageless universe the stars should have faded long ago, and the vast cosmos should be a sea of completely uniform temperature. So why is the universe not cold and dark?

Even Einstein thought the Universe was static.

Of course you might argue that stars still shine because gravity causes clouds of gas and dust to collapse in on themselves. New stars are being formed all the time, so naturally the Universe won’t be completely dark. But this raises another paradox: why does gravity work at all? As with light, gravity obeys the inverse square law. An object some distance away pulls upon you gravitationally with a force four times larger than an object of the same mass twice as far away. With distance a gravitational force gets ever weaker, but it never completely goes away. In an infinite universe the amount of mass at a particular distance also follows the square law. For every gravitational pull in one direction, there will always be enough mass in the other direction to balance it out. This is known as Seeliger’s paradox, and it means that gravity shouldn’t be able to act on anything. Gravitational forces should always balance out, so stars shouldn’t form and planets shouldn’t orbit stars. And yet they do.

The solution to these paradoxes is pretty clear. The Universe is not ageless, nor is it stationary. We now know it is only about 13.8 billion years old, and ever expanding. Because of expansion and a finite age, the observable universe doesn’t extend to infinity, so Olber’s and Seeliger’s arguments don’t apply. Since the Universe is finite in age, Clausius’ argument is also invalid. It seems an obvious solution to us, but it’s an excellent example of how incorrect assumptions are difficult to overcome. Before Hubble’s observation of cosmic expansion, it seemed obvious that the Universe must be ageless and stationary. The idea that it might begin with a primordial fireball seems downright creationist in comparison. But in the end, evidence for the big bang became overwhelming, and the paradoxes of an infinite cosmos were finally solved.

Next time: Nothing can be colder than absolute zero, or can it? Consider an ancient cold white dwarf. It’s temperature is near absolute zero, but it’s matter is tightly squeezed by gravity. If you took a chuck of the white dwarf away, would that chunk expand and cool even further? Arthur Eddington wrestles with stellar thermodynamics in tomorrow’s post.

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