astrophysics – One Universe at a Time https://briankoberlein.com Brian Koberlein Thu, 21 Feb 2019 22:09:36 +0000 en-US hourly 1 https://wordpress.org/?v=5.1 Winter Wonderland https://briankoberlein.com/2016/12/27/winter-wonderland/ https://briankoberlein.com/2016/12/27/winter-wonderland/#comments Tue, 27 Dec 2016 12:00:37 +0000 https://briankoberlein.com/?p=6388

Many are dreaming of a White Christmas. Here's why you should thank astrophysics if you get one.

The post Winter Wonderland appeared first on One Universe at a Time.

]]>

It’s winter in the northern hemisphere. That fact, combined with the arctic blast that’s reddening many cheeks in North America, means that many of us will enjoy a white Christmas. Since it’s a time to be thankful, here’s five reasons you should thank astrophysics for this year’s Winter wonderland. 

  1. Axial Tilt
    Earth’s axis is tilted about 23 degrees relative to its orbital plane. As the Earth orbits the Sun, the northern hemisphere is tilted toward the Sun for about half the year, and tilted away from the Sun for half the year. When it’s tilted away from the Sun, the sunlight that reaches us is at a lower angle, meaning there’s less energy and heat reaching the Earth’s surface. That, combined with the fact that the Sun is visible for fewer hours in the day means the northern hemisphere enters a period of cold winter. Of course, for the southern hemisphere it’s reversed, meaning it’s a summer Christmas for those down under.
  2. Elemental Abundance
    The most abundant element in the Universe is hydrogen, making up about 74% of cosmic matter by mass. Helium comes in second, making up about 24%. These two elements are so common because they were the elements formed soon after the big bang. Other elements of the periodic table are formed through astrophysical processes such as fusion in the heart of a star. This is true of the third most common element, oxygen, which makes up only 1% of the elemental mass in our galaxy. Helium is a noble gas, and doesn’t combine with other elements to form molecules, which leaves only hydrogen and oxygen. One of the most readily formed molecules from these two elements is H2O, which is the primary ingredient of snow. Water is so common in the Universe because it’s formed from the two most common molecule-forming elements.
  3. Heavy Bombardment
    Although water is common, it can evaporate away from a small, warm planet that forms close to its star. This is why Venus and Mars are so dry. We often think of Earth as a watery world, but it actually has less water than many moons of the outer solar system. We’re still not entirely sure how Earth came to have much more water than its planetary cousins, but one popular idea is that water was brought to Earth by asteroids and comets that bombarded our world during its youth.
  4. Dalton Solar Minimum
    When you think of the winter season, you might think of Charles Dickens, whose stories such as A Christmas Carol have become a holiday staple. Dickens often wrote of a wintery Britain covered in snow, which may have helped drive the nostalgia we have for a snowy holiday. But interestingly, Britain doesn’t often have a snow-covered Christmas. In the 1900s, it was a white Christmas only seven times. But things were very different in the early 1800s, when Dickens was a child. Six of his first nine Christmas holidays were snowy. This period also corresponds to the Dalton solar minimum, which is a period between 1796 to 1820 when sunspot activity was unusually low. There’s some evidence to show that solar minima are correlated with colder temperatures on Earth. For example, the Maunder minimum spanning 1645 to 1715 is associated with the “little ice age” of Europe. It might just be a coincidence, but sunspot activity could be the source of Dickens’ holiday nostalgia.
  5. Global Warming
    Although it is more properly called global climate change, the warming of Earth in recent decades could be the reason why it’s so cold in the northeast. It might seem paradoxical, but our cold temperatures are caused by the polar vortex dipping farther into North America than it usually does. The polar vortex is bounded by the jet stream, which typically moves in a smooth circle around the Earth. In recent years the jet stream has had a more wavy flow, and this may be driven by record warm temperatures at the north pole. As the arctic ice continues to melt and polar temperatures rise, the polar vortex can be pushed southward more often. It’s too soon to tell if this shift in the polar vortex is driven by climate change, but it is a possibility.

So there you have it. But whether your solstice holiday is wintery white or summery green, I wish you a joyful and peaceful season.

The post Winter Wonderland appeared first on One Universe at a Time.

]]>
https://briankoberlein.com/2016/12/27/winter-wonderland/feed/ 2
Ten Amazing Things Astrophysics Says About You https://briankoberlein.com/2016/03/18/ten-amazing-things-astrophysics-says-about-you/ https://briankoberlein.com/2016/03/18/ten-amazing-things-astrophysics-says-about-you/#comments Fri, 18 Mar 2016 11:00:50 +0000 https://briankoberlein.com/?p=5817

Astrophysics has some pretty amazing things to say about you.

The post Ten Amazing Things Astrophysics Says About You appeared first on One Universe at a Time.

]]>

1) You live on a rock
Your home is a roughly spherical rock that orbits a star at about 100,000 miles per hour. Most of the surface is covered with a layer of water to produce lakes and oceans, and surrounding it all is a layer of air so thin that if the Earth were the size of an apple the atmosphere would be thinner than the apple’s skin. That’s home, and so far it’s been home for every single human that has ever lived. 

2) You are made of stardust
Sure it’s a bit cliche, but that doesn’t make it any less amazing. The carbon, nitrogen and oxygen in your body was created in the heart of a star long before our solar system formed. The most common elements in your body are also the most common elements in the galaxy. As a result you embody the history of our solar system.

3) Part of you is as old as time
While the heavier elements in your body were created in the hearts of stars, the hydrogen in your body formed about three minutes after the big bang. But the protons in your body formed about a millionth of a second after the big bang. Some of the protons that formed in the earliest moment of the Universe are in your body today.

4) You are the center of the Universe
Often it’s said that the Universe has no center. The big bang didn’t begin a particular point as a great explosion. All of the Universe (even space and time) formed together, which means where you are right now was once at the heart of the big bang. So you really are at the center of the Universe. Of course the same can be said about any other point in the Universe.

5) You are moving at 360 kilometers per second
The Universe is filled with a sea of microwave energy known as the cosmic microwave background (CMB). It is the thermal remnant of the big bang. The wavelengths we see are almost the same in all direction, but interestingly one side of the Universe has slightly longer wavelengths than the other. This is because our solar system is moving through space, causing the CMB to be slightly redshifted behind us and blueshifted ahead of us. It turns out that we are moving through space at about 360 km/s, which is surprisingly fast.

6) You are bombarded by neutrinos
Neutrinos are created in the core of our Sun through nuclear fusion. They are also created in the cores of distant stars. Since neutrinos don’t interact strongly with other matter, they tend to stream through things without interacting. And there are billions upon billions of them. At any given moment there are about 100 billion solar neutrinos streaming through every centimeter of your body. At night they travel through the entire Earth to reach you.

7) You are hotter than the Sun
The Sun has a much higher temperature than you. Even its surface is nearly 6,000 Kelvin, compared to your measly 310 Kelvin. But per volume you generate more heat than the Sun. That’s a bit misleading, since you generate heat through most of your volume through chemical reactions, but the Sun only generates heat in its core through nuclear fusion. Still, it’s a cool fact.

8) Everything is attracted to you
The universal law of gravity states that every mass is attracted to every other mass. When you step on a scale in the morning, the weight you measure is not just your weight in the Earth’s gravitational field, it is also the Earth’s weight in your gravitational field. Gravitationally you are pulling every slightly on everything around you. Everything is gravitationally attracted to you, even though that attraction is usually too small to notice.

9) Your experience of time is unique
Contrary to popular belief there is no cosmic clock that determines time in the Universe. According to relativity, there is no universal “now.” Instead, what constitutes the present depends upon your particular position and motion, and anyone with a different position and motion experiences a slightly different rate of time. You have a “now” that is uniquely yours.

10) There is only one of you
The Universe is mind-bogglingly huge. It’s estimated that there are 100 billion galaxies in the visible universe alone. That’s more than 10 galaxies for every man, woman and child on Earth. Those galaxies might have an average of about 100 billion stars. Around most of those stars might be tens of planets. Despite that vast diversity, the odds of your combination of DNA and your experiences coming together by chance is so astronomically tiny that there can only be one you in the entire cosmos.

The Universe is 93 billion light years across with billions upon billions of potentially habitable worlds, and yet there’s no one else quite like you.

The post Ten Amazing Things Astrophysics Says About You appeared first on One Universe at a Time.

]]>
https://briankoberlein.com/2016/03/18/ten-amazing-things-astrophysics-says-about-you/feed/ 2
How Does Gravity Escape a Black Hole? https://briankoberlein.com/2015/08/21/how-does-gravity-escape-a-black-hole/ https://briankoberlein.com/2015/08/21/how-does-gravity-escape-a-black-hole/#comments Fri, 21 Aug 2015 11:00:30 +0000 https://briankoberlein.com/?p=5116

Here's the deal: nothing can travel faster than light. A black hole traps everything including light. So how does gravity escape a black hole?

The post How Does Gravity Escape a Black Hole? appeared first on One Universe at a Time.

]]>

Here’s the deal: nothing can travel faster than light. A black hole traps everything including light. So how does gravity escape a black hole? It’s a great question, and a perfectly reasonable one given most people’s understanding of gravity. The answer is that gravity doesn’t work the way you probably think it does.

The most common way to think of gravity is as a force between two masses. For example, the Earth exerts a gravitational force on the Moon, and the Moon pulls back on the Earth in return. This “force model” of gravity is what Newton used to develop his law of universal gravity, which stood as the definite theory of gravity until the early 1900s, and is still used to this day. But built into this model of gravity are some assumptions that we can explore by playing the “what if?” game.

Suppose we had a universe with a single mass. Imagine empty space extending as far as you like, with a single mass in the center (which we’ll call Bob). Would such a mass have gravity? If gravity is a force of one object on another object, then the answer would be no. There’s no other mass for Bob to pull on, so there’s no gravitational force. If we add another mass to our universe (call this one Alice), then Bob and Alice would each exert a force on each other, and gravity would exist. But gravity would only exist between Bob and Alice, and nowhere else in our empty universe.

Earth and Moon with their effective gravitational fields. Credit: Hyperphysics

Earth and Moon with their effective gravitational fields. Credit: Hyperphysics

One of the problems with this force model is that it requires masses to exert forces on other masses across empty space. This “action at a distance” problem was resolved in part by Pierre-Simon Laplace in the early 1800s. His idea was that a mass must reach out to other masses with some kind of energy, which he called a field. Other masses would sense this field as a force acting upon them. So if we again imagine our Bob mass in a lonely universe, we would say that Bob has a gravitational field surrounding it, even if there were no other masses in the universe. This eliminates the need for action-at-a-distance, because when we put our Alice mass into the universe, it simply detects whatever gravitational field is at its location, and experiences a force. We know the gravitational field is due to Bob some distance away, but Alice simply knows there is a gravitational field at its location.

Both the force model and field model of Newtonian gravity give the same predictions, so experimentally there’s no real way to distinguish one from the other. However fields are often an easier concept to work with mathematically, and fields are also used to describe things like electricity and magnetism, so we generally think of Newtonian gravity as a field.

If the speed of gravity was finite, it would create gravitational waves.

If the speed of gravity was finite, it would create gravitational waves.

But this raises another question. Suppose in our Bob and Alice universe we suddenly shift Bob’s position. How long will it take for Alice to recognize the change? In other words, if we change the position of Bob, at what speed does the change propagate through the gravitational field? When Laplace looked at this idea he found that changes in a gravitational field had to happen instantly. The “speed of gravity” would have to be infinite. For example, if gravity travelled at the speed of light, the Earth would try to orbit the point where the Sun was 8.3 minutes ago (the time it takes light to travel from the Sun to Earth). As a result, Earth’s orbit would become unstable over time.

At the time, the idea of gravity acting at infinite speed wasn’t seen as a problem. In fact it was used as an argument against alternative gravity ideas proposed at the time. But in the early 1900s Einstein developed his special theory of relativity, which (among other things) required that nothing could travel faster than light. If that’s the case, then there’s something wrong with our theory of gravity. By 1915 Einstein had developed a new model of gravity known as general relativity, which satisfied both Newton’s gravitational model and special relativity.

pulsardecay

Decay of a pulsar orbit compared to general relativity (dotted line).

According to theory, for example, when two large masses such as neutron stars orbit each other, they should produce gravitational waves that radiate away from them. These gravitational waves should travel at the speed of light. There have been experimental attempts to detect such gravitational waves, but they have been unsuccessful so far. We have, however, found indirect evidence of gravitational waves. By observing a binary pulsar, we have observed its orbit decay slightly over time. This orbital decay is due to the fact that gravitational waves carry energy away from the system. The rate of this decay matches the prediction of general relativity perfectly. Since this rate of decay depends crucially on the speed of gravitational waves, this is also indirect confirmation that gravitational waves move at the speed of light.

But if gravity moves at the speed of light, doesn’t that mean that planetary orbits should be unstable? Actually, no. When Laplace studied finite-speed gravity, he considered only the effect of the speed of gravity, which is what leads to his result, but in special and general relativity, the finite speed of light leads to other effects, such as time dilation due to relative motion, and the apparent change of mass due to relative motion. Mathematically these effects arise because of a property known as Poincaré invariance. Because of this invariance, the time delay of gravity and the velocity dependent effects of time and mass cancel out, so that effectively masses are attracted to where a mass is. This canceling effect means that for orbital motion it is as if gravity acts instantly.

But wait a minute, how can a gravitational field have a finite speed and act instantly at the same time? A gravitational field can’t, but in general relativity gravity is not an energy field.

The relative nature of now.

The relative nature of now.

Since long before Newton, it was generally assumed that objects and energy fields interacted in space at particular times. In this way, space and time can be seen as a background against which things happen. Space and time were seen as a cosmic grid against which anything could be measured. In developing special relativity, Einstein found that space and time couldn’t be an absolute background. In Newton’s view, two events seen to occur at the same time will be seen to be simultaneous for all observers. But Einstein found that the constancy of light required this concept of “now” to be relative. Different observers moving at different speeds will disagree on the order of events. Rather than a fixed background, space and time is a relation between events that depends upon where and when the observer is.

The distortion of space and time near Earth. Credit: Christopher Vitale

The distortion of space and time near Earth. Credit: Christopher Vitale

This principle carried forward into Einstein’s theory of gravity. In general relativity gravity is not an energy field. Instead, mass distorts the relations between space and time. If we go back to our earlier example, if we place mass Bob in an empty universe, the relations of space and time around it are distorted. When we place mass Alice nearby, the distortion of spacetime around it means that moves toward mass Bob. It looks as if Alice is being pulled toward Bob by a force, but it’s actually due to the fact that spacetime is distorted.

As physicist John Wheeler once said, “Spacetime tells matter how to move; matter tells spacetime how to curve.”

This is how gravity can seem to act instantly while gravitational waves seem to travel at the speed of light. Gravity isn’t something that travels through space and time. Gravity is space and time.

A black hole is an extreme distortion of space and time due to a very dense mass. Such a spacetime distortion can prevent light and matter from ever escaping. But the spacetime distortion is also gravity. It doesn’t need to escape the black hole, because it is the black hole.

That’s the thing about science. Sometimes a simple question will pull you toward an unexpected answer.

The post How Does Gravity Escape a Black Hole? appeared first on One Universe at a Time.

]]>
https://briankoberlein.com/2015/08/21/how-does-gravity-escape-a-black-hole/feed/ 48
How To Build A Star https://briankoberlein.com/2015/08/12/how-to-build-a-star/ https://briankoberlein.com/2015/08/12/how-to-build-a-star/#comments Wed, 12 Aug 2015 16:09:03 +0000 https://briankoberlein.com/?p=5085

Suppose you wanted to build a star. How would you go about making one?

The post How To Build A Star appeared first on One Universe at a Time.

]]>

Suppose you wanted to build a star. Perhaps you’re part of an advanced Kardashev Type 3 civilization, and you need to make a star for your third grade science project. How would you go about creating a star?

On a basic level, it’s quite simple to build a star. Simply gather a star’s worth of gas and dust, let it collapse together under its own weight, and given enough time a star will form. This is how stars form naturally. But since we might be graded on this project, it would be nice to have an idea of how much mass we might need, and what the size and temperature of the resulting star might be.

The answer depends quite a bit upon what material you use, and how the material behaves under different temperatures and pressures (what’s sometimes called its equation of state). Since the most common material in the universe is hydrogen, lets keep things simple and assume we’ll build our star out of pure hydrogen. Since hydrogen has a very simple equation of state, it’s an easy matter to calculate what will happen as we build our star.

Size of planets by mass.

Size of planets by mass.

When we start to gather hydrogen together, two things will start to happen. The first is that the gravitational attraction between the hydrogen atoms will start to collapse the gas under its own weight. The second is that the pressure of the hydrogen will push back against the weight. Given time the gas will reach hydrostatic equilibrium, where the pressure of the gas is equal its weight, at which point you have a stable ball of hydrogen. This by itself isn’t enough to make a star. If you gathered a Saturn’s mass worth of hydrogen, what you would have is a Saturn-sized planet, not a star. The obvious solution is to simply add more hydrogen, which would make your planet bigger and bigger. Eventually your ball of gas would grow to a Jupiter-sized planet, and you just keep adding more hydrogen.

Peak size for a Jupiter-type planet.

Peak size for a Jupiter-type planet.

But it turns out that something interesting happens when you keep adding more hydrogen to your planet. The more hydrogen you have, the more mass you have, and that means more weight. The gas is squeezed more strongly, and as a result it compresses. So if you double the mass of your Saturn-sized planet, you don’t get a planet twice as big as Saturn. You get a planet that is a bit bigger than Saturn, but with a higher density. For example, Jupiter is more than three times the mass of Saturn, but only about 15% larger in size. However Jupiter has an average density about twice that of Saturn.

As you keep adding more mass, your planet will get bigger up to about 3 Jupiter masses. At that point, the weight of your ball of hydrogen is so large that adding more actually makes the planet smaller. As a result, a planet 10 times the mass of Jupiter would be about the same size as Jupiter itself. This poses a real challenge for astronomers that study exoplanets. Just because a planet is Jupiter sized doesn’t mean it has a Jupiter mass. The same is true for smaller planets. A “super-Earth” planet a bit larger than Earth could be a rocky planet or a small Neptune-like planet depending upon what it’s made of.

Brown dwarfs vs stars. Credit: P. Marenfeld & NOAO/AURA/NSF

Brown dwarfs vs stars. Credit: P. Marenfeld & NOAO/AURA/NSF

Once your ball of hydrogen reaches about 15 Jupiter masses it enters the regime of brown dwarfs. Adding more mass continues to make it smaller, but by this point the temperature of its interior starts to play a significant role. Our simple model of hydrostatic equilibrium isn’t enough. The hydrogen in the center is being squeezed so strongly that it heats up significantly. So while a brown dwarf is roughly the same size as Jupiter, it can be more than 10 times hotter. Adding more mass continues to shrink the brown dwarf slightly, but there comes a point where the interior becomes so hot that it raises the pressure of the hydrogen faster than the added weight can squeeze. Just as there is a maximum size for a planet, there is a minimum size for a brown dwarf. That minimum size is about 80% that of Jupiter, at which point a brown dwarf has a temperature of about 2000 K. Such a brown dwarf would look like a small, dim star.

Size vs mass for main sequence stars.

Size vs mass for main sequence stars.

But a true star is one in which nuclear fusion occurs in its core. A star’s light and heat isn’t due to gravitational contraction, but rather the creation of energy by fusing hydrogen into helium. This starts to occur when your ball of hydrogen reaches about 90 Jupiter masses, which coincidentally is about the same mass as a minimum-sized brown dwarf. Now that you’ve made a star, adding more hydrogen just makes it larger and hotter. Because stars fuse hydrogen in their core, their size and density changes over time. But if we only consider stable, main sequence stars, then there’s a simple relation between mass and size. So you can just decide how much hydrogen to use, and calculate the size of your star.

Of course this is just a simple hypothetical stars. Real stars aren’t made purely of hydrogen, and depending on their origin and age they can behave very differently than our simple star. The details will be left as a homework exercise for the reader.

The post How To Build A Star appeared first on One Universe at a Time.

]]>
https://briankoberlein.com/2015/08/12/how-to-build-a-star/feed/ 4
Achilles’ Heel https://briankoberlein.com/2014/07/06/achilles-heel/ https://briankoberlein.com/2014/07/06/achilles-heel/#comments Sun, 06 Jul 2014 14:01:47 +0000 https://briankoberlein.com/?p=3448

Achilles, so the story goes was a mighty Greek warrior. When he was born, his mother dipped him in the river Styx, rendering him invulnerable except for the heel by which he was held. It was that vulnerable heel that was Achilles' undoing, when Paris killed Achilles by shooting an arrow through the vulnerable heel. It's a story of how the mighty can be destroyed by a seemingly minor flaw. A cautionary tale, if you will.

The post Achilles’ Heel appeared first on One Universe at a Time.

]]>

Achilles, so the story goes was a mighty Greek warrior. When he was born, his mother dipped him in the river Styx, rendering him invulnerable except for the heel by which he was held. It was that vulnerable heel that was Achilles’ undoing, when Paris killed Achilles by shooting an arrow through the vulnerable heel. It’s a story of how the mighty can be destroyed by a seemingly minor flaw. A cautionary tale, if you will.

In science the same cautionary tale holds. Robust scientific theories are often so strongly supported by the evidence that they seem almost invulnerable, until some small unaccounted for phenomenon topples the reigning theory.  The failure of Newtonian gravity to account for the precession of Mercury allowed general relativity to redefine space and time. The inability of Maxwell’s wave description of light to account for things like the photoelectric effect led to the quantum revolution.  The unexpectedly low number of neutrinos coming from the Sun led to the discovery of neutrino mass.

We love to tell the story of fallen theories and their upstart replacements. It paints a picture of science as ever evolving and open to change. We don’t talk much of the vulnerable aspects of reigning scientific models. One of the criticisms of many fringe science proponents is that the “establishment” is unwilling to admit the weaknesses in their own models.  Science should be self critical, they argue, and not dogmatic.

So in that spirit, this week begins a new series.  We’ll look at the soft underbelly of standard cosmology and focus on five phenomena that modern astrophysics can’t fully explain.

Solar Corona – Hotter than we expect.

Dark Matter – Not for dwarf galaxies.

The Horizon Problem – Why so uniform?

Black Holes – A paradox wrapped in an enigma.

Supersymmetry – The perfect lie.

Each of these pose a challenge to modern astrophysics. Whether they will eventually succumb to standard models or whether they will overturn them is yet to be seen. We’ll look at problems without solutions, and questions without answers.

All this week.

The post Achilles’ Heel appeared first on One Universe at a Time.

]]>
https://briankoberlein.com/2014/07/06/achilles-heel/feed/ 1
In the Hole https://briankoberlein.com/2014/02/09/hole/ https://briankoberlein.com/2014/02/09/hole/#comments Sun, 09 Feb 2014 12:00:03 +0000 https://briankoberlein.com/?p=1260

The idea of a white hole as an anti-black hole sometimes gets mentioned, but white holes aren't real. They are the result of taking the mathematics relativity beyond its usefulness.

The post In the Hole appeared first on One Universe at a Time.

]]>

Suppose you count down from five:  5, 4, 3, 2, 1, 0.  Then what?  You could just stop, or you could keep going -1, -2, -3 and so on.  Mathematically there is nothing to prevent you from counting down below zero.  Of course if you apply this idea to cupcakes, something changes when you reach zero.  If you start with five cupcakes and start giving them away, you eventually run out.  At that point you can’t give away any more.  In this case you can’t count down past zero.  Sure, you can hand out slips of paper with “I owe you a cupcake.” written on them, but it would be ridiculous to use the existence of negative numbers to claim that “negative cupcakes” exist and can be handed out to people.

A similar type of thing can occur  in physical models.  One example of this is the legendary “white hole” making the social media rounds of late.  The basic idea of a white hole is that it is some kind of anti-black hole.  Instead of capturing material and trapping it forever, a white hole spews material out.  So they would constantly be generating material around it.  There are even some speculations that black holes and white holes could be connected as a kind of wormhole.

All cool ideas, except for one problem.  White holes don’t exist.  I don’t mean they are hypothetical, but we don’t have evidence for them.  I really mean they don’t exist.  They are about as sensical as negative cupcakes.

The original idea of a white hole comes from the mathematics of general relativity.  One of the key features of general relativity is that you can represent the structure of space and time in all sorts of different coordinate systems.  This allows you to choose a coordinate system that makes your calculations easier, but it also means you have to be careful to recognize when you’re dealing with negative cupcakes.

In this coordinate system the edge is infinitely far away.  That doesn't mean you could walk beyond infinity. Credit: Claudio Rocchini

In this coordinate system the edge is infinitely far away. That doesn’t mean you could walk beyond infinity.
Credit: Claudio Rocchini

When describing a simple black hole, one useful coordinate system is known as Kruskal–Szekeres coordinates.  The coordinates are a good way to describe the spacetime around a simple black hole, but you can also extend them, just like you can count down to zero and keep going.  Mathematically there is nothing to prevent you from extending the coordinates.  When you do, you not only get a description of a black hole, you get a description of a white hole as a negative black hole.  But that doesn’t make white holes real, or even hypothetical.

You can see a similar example in the figure here.  It represents what is known as a hyperbolic coordinate system.  It is a way to represent an infinite surface, and it does it by representing close areas as large, and more distant areas as tiny.  Infinity is then represented as a finite area.  But just because you can represent an infinite surface this way doesn’t mean you could walk off its edge.

Mathematics is a powerful tool in astrophysics, but you need to be aware of what it actually represents.

The post In the Hole appeared first on One Universe at a Time.

]]>
https://briankoberlein.com/2014/02/09/hole/feed/ 1
Black Holes No More? Not Quite. https://briankoberlein.com/2014/01/30/black-holes-quite/ https://briankoberlein.com/2014/01/30/black-holes-quite/#respond Thu, 30 Jan 2014 21:56:33 +0000 https://briankoberlein.com/?p=1132

News has spread that Stephen Hawking has declared there are no black holes. That's not quite what Hawking said. Instead, Hawking proposes a radical new solution to the firewall paradox.

The post Black Holes No More? Not Quite. 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.

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.

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.

The post Black Holes No More? Not Quite. appeared first on One Universe at a Time.

]]>
https://briankoberlein.com/2014/01/30/black-holes-quite/feed/ 0