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.

The post Beyond The Cold appeared first on One Universe at a Time.

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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Anyone practicing science needs to get comfortable with uncertainty. Often the questions raised lead to an answer that is simply “we don’t know.” But there are times when we are instead faced with a contradiction. One set of evidence and theoretical reasoning leads to a conclusion in contradiction with another set of evidence. Usually these contradictions resolve themselves pretty quickly, but there are times when these contradictions grow into a paradox. While some of the most famous astronomical paradoxes are now used to demonstrate where our reasoning went wrong, others still challenge us with no clear resolution. 

What makes paradoxes so powerful is that they force us to reconsider both the evidence and our reasoning. If the Universe is self consistent (and we assume that it is) then there must be a solution to the paradox. So this week we’ll look at five major astronomical paradoxes. A couple have been solved, but most challenge even the most cutting edge research.

1. To Infinity And Beyond – Olber’s paradox is perhaps the most famous example, but there are similar paradoxes involving gravity and thermodynamics. They all raise the same question: How can our Universe possibly be infinite?
2. Cold Equations – When a white dwarf cools over time, can it actually get colder than absolute zero?
3. Icy Sunrise – Our Sun was much cooler in its youth. So how is it that liquid water existed on a young Earth?
4. Bigger Bang – There is an upper limit to the amount of energy a cosmic ray can have. So why do we observe cosmic rays that have even more energy than that limit?
5. Over The Edge – The event horizon of a black hole is a point of no return. But if nothing can escape a black hole, isn’t the fundamental nature of physics violated?

We’ll start by confronting the assumption that even Einstein failed to challenge. In an infinite and ageless cosmos, how is it possible that the Universe is cold, dark and dominated by gravity? The paradox series starts next time.

The post Riddle Me This appeared first on One Universe at a Time.

This post was originally written for Universe Today.

Nature News has announced that there are no black holes.  This claim is made by none other than Stephen Hawking, so does this mean black holes are no more?  It depends on whether Hawking’s new idea is right, and on what you mean be a black hole.  The claim is based on a new paper by Hawking  that argues the event horizon of a black hole doesn’t exist.

The event horizon of a black hole is basically the point of no return when approaching a black hole.  In Einstein’s theory of general relativity, the event horizon is where space and time are so warped by gravity that you can never escape.  Cross the event horizon and you can only move inward, never outward.  The problem with a one-way event horizon is that it leads to what is known as the information paradox.

Professor Stephen Hawking during a zero-gravity flight. Image credit: Zero G.

The information paradox has its origin in thermodynamics, specifically the second law of thermodynamics.  In its simplest form it can be summarized as “heat flows from hot objects to cold objects”.  But the law is more useful when it is expressed in terms of entropy.  In this way it is stated as “the entropy of a system can never decrease.”  Many people interpret entropy as the level of disorder in a system, or the unusable part of a system.  That would mean things must always become less useful over time.  But entropy is really about the level of information you need to describe a system.  An ordered system (say, marbles evenly spaced in a grid) is easy to describe because the objects have simple relations to each other.  On the other hand, a disordered system (marbles randomly scattered) take more information to describe, because there isn’t a simple pattern to them.  So when the second law says that entropy can never decrease, it is say that the physical information of a system cannot decrease.  In other words, information cannot be destroyed.

The problem with event horizons is that you could toss an object (with a great deal of entropy) into a black hole, and the entropy would simply go away.  In other words, the entropy of the universe would get smaller, which would violate the second law of thermodynamics.  Of course this doesn’t take into account quantum effects, specifically what is known as Hawking radiation, which Stephen Hawking first proposed in 1974.

The original idea of Hawking radiation stems from the uncertainty principle in quantum theory.  In quantum theory there are limits to what can be known about an object.  For example, you cannot know an object’s exact energy.  Because of this uncertainty, the energy of a system can fluctuate spontaneously, so long as its average remains constant.  What Hawking demonstrated is that near the event horizon of a black hole pairs of particles can appear, where one particle becomes trapped within the event horizon (reducing the black holes mass slightly) while the other can escape as radiation (carrying away a bit of the black hole’s energy).

Hawking radiation near an event horizon. Credit: NAU.

Because these quantum particles appear in pairs, they are “entangled” (connected in a quantum way).  This doesn’t matter much, unless you want Hawking radiation to radiate the information contained within the black hole.  In Hawking’s original formulation, the particles appeared randomly, so the radiation emanating from the black hole was purely random.  Thus Hawking radiation would not allow you to recover any trapped information.

To allow Hawking radiation to carry information out of the black hole, the entangled connection between particle pairs must be broken at the event horizon, so that the escaping particle can instead be entangled with the information-carrying matter within the black hole.  This breaking of the original entanglement would make the escaping particles appear as an intense “firewall” at the surface of the event horizon.  This would mean that anything falling toward the black hole wouldn’t make it into the black hole.  Instead it would be vaporized by Hawking radiation when it reached the event horizon.  It would seem then that either the physical information of an object is lost when it falls into a black hole (information paradox) or objects are vaporized before entering a black hole (firewall paradox).

In this new paper, Hawking proposes a different approach.  He argues that rather than instead of gravity warping space and time into an event horizon, the quantum fluctuations of Hawking radiation create a layer turbulence in that region.  So instead of a sharp event horizon, a black hole would have an apparent horizon that looks like an event horizon, but allows information to leak out.  Hawking argues that the turbulence would be so great that the information leaving a black hole would be so scrambled that it is effectively irrecoverable.

If Stephen Hawking is right, then it could solve the information/firewall paradox that has plagued theoretical physics.  Black holes would still exist in the astrophysics sense (the one in the center of our galaxy isn’t going anywhere) but they would lack event horizons.  It should be stressed that Hawking’s paper hasn’t been peer reviewed, and it is a bit lacking on details.  It is more of a presentation of an idea rather than a detailed solution to the paradox.  Further research will be needed to determine if this idea is the solution we’ve been looking for.

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