Showing posts with label astrophysics. Show all posts
Showing posts with label astrophysics. Show all posts
Sunday, 10 February 2013
Saturday, 10 March 2012
Flares between old flames
How often do we look up at the sun and think about it as a great, big ball of hydrogen and helium swirling around a single point out of which emanates a huge gravitational force that holds them all together? How often are we curious enough to step beyond something that's everyday-material and look at it with the awareness that a much bigger picture exists?
Not very often, I'd suppose, because if all of us managed to look at the sun that way, many of Earth's and the universe's beauties would become explicable. And, at least in my opinion, that would only make them more beautiful.
[caption id="attachment_22709" align="aligncenter" width="512" caption="An ultraviolet image of the sun taken at the time of emission of the CME (NASA)"]
[/caption]
Last week, there was a great flurry of activity after our nearest star unleashed a massive coronal mass ejection (CME) that ranked in the 'X' compartment on the scale of flare strength. What's more, the flare was pointed directly at Earth, prompting astrophysicists to let loose warnings about electricity grids, satellite operations, GPS reception and communication networks being severely disrupted.
However, the stream of high-temperature high-energy particles belched by the sun - that's what makes a CME - didn't quite have the effect it should have had. When scientists started to ask why, they found a simple explanation: the magnetic field embedded in the ejection was oriented in such a way to the earth's own that it was fizzled out on contact.
[caption id="attachment_22710" align="aligncenter" width="545" caption="Streams of particles along the magnetic flux lines on the sun's surface are visible"]
[/caption]
The sun's magnetic field is extremely strong and, because of the star's high-temperature surface, such fields influence the formation and paths of charged particles that exist in a plasma state (the fourth state of matter). Sometimes, these particles are shot out in the form of a flare when magnetic energy stored in the sun's corona suddenly jumps a few orders of magnitude, accelerating the heavier ions to speeds near that of light. Needless to say, this process is also linked to a big jump in temperature.
More often than not, the radiation emitted during such a flare is across the electromagnetic spectrum and not quite just localized to the visible region. Because of this, most flares are observable only by special instruments and not the naked eye.
[caption id="attachment_22711" align="aligncenter" width="545" caption="An illustration of solar wind and its impact with Earth's magnetic field"]
[/caption]
Now, what causes this jump in magnetic activity? To understand that, observe the sun's core: at a temperature of 15,000,000 kelvin, it is the hottest place in the solar system. By comparison, the surface of the sun exists at a meagre 6,000 kelvin. Because of the temperature gradient between the two, there is a mass convection going on at all times: gases move from the hotter core to the cooler surface. However, they don't travel in a straight line. This is because of two mutually-acting reasons.
This energy conservation manifests itself in the gases in the convection current as well. Instead of moving straight - during which they're not conserving the star's angular momentum - they move out in a spiral. The speed at which they move out to a particular point is dependent mostly on the temperature gradient between the core and the surface at that point. Because of this uncertainty, gases at different parts of the sun's surface are moving at different velocities, as a result giving the sun a differential rotation: the speed of rotation at each solar latitude is different.
[caption id="attachment_22712" align="aligncenter" width="545" caption="Stars near the centre of the Milky Way galaxy take less time to orbit it than stars farther away. This difference in orbital periods gives rise to a spiral pattern much as differential rotation on the sun gives rise to spiral convection."]
[/caption]
Consequently: though the sun's magnetic field possesses an overall shape and size that is measurable and fairly fixed, it's local magnetic fields are the troublesome ones. For example (and this being a conveniently chosen example), when one band of convection is shearing against another band moving at different speeds, a zone of high mechanical and thermodynamic stress is created.
When this stress no longer becomes bearable, a "wound" is punctured on the sun's surface. This creates a no-convection region that limits the amount of energy coming in from the core to the wound, cooling it. As the temperature falls, so does visibility, and a sunspot appears on the surface.
CMEs and flare activity are particularly energetic around sunspots because there, the magnetic field is very strong and oriented in such a way that it connects the sun's corona to its interior. In fact, at a sunspot, the component of the magnetic field perpendicular to the sun's surface is more pronounced than the other, inclined, component, providing a sort of rails on which charged particles can be accelerated and shot out.
[youtube http://www.youtube.com/watch?v=uecMk8ZZ1uE]
The rate of formation of sunspots affects solar storm activity, and this rate is dependent on whether the sun is in its solar maximum or solar minimum. During solar maximum, which lasts for a period of 11 years on average, the magnetic field at the solar equator is rotating slightly faster than that at the solar poles, producing enough heliomagnetic stress to influence the formation of hundreds of sunspots. Needless to say, solar storms can get really vicious when our star is in its solar maximum or is in the process of entering it - like now. The solar minimum, on the other hand, lasts for about 12 months, seeing decreased sunspot activity.
When such storms come in contact with the Earth's magnetic field, which they don't often do because they're pointed in other directions, they're called geomagnetic storms. Yes, this results in the disruption of our communication network, but it also gifts us the auroras that are a treat to watch. The storm that hit us a few days ago as a result of the massive 'X' class CME last weak fared poorly, being relegated to the 'G' class.
When the charged and heated solar wind reaches Earth, the particles come in contact with the geomagnetic field, transferring a bulk of their energy to it and increasing the movement of plasma through the magnetosphere. Some of this energy transferred manifests as increased electric currents in the ionosphere, which is what disrupts our communication.
[caption id="attachment_22713" align="aligncenter" width="519" caption="The magnetosphere engulfs all these layers in a bullet shaped envelope and extends far out into space, almost as much as 127,000 km to 160,000 km in the direction away from the sun."]
[/caption]
However, the principle effect of the currents is increase the magnetic force in Earth's magnetosphere, pushing the boundary between the layer and the malevolent solar wind out, as if into space. A geomagnetic storm may last from a few minutes to a few days.
The auroras they create, however, last for only a few hours each time. During the geomagnetic storm, there is an immigration of particles from the magnetosphere and the ionosphere to the atmospheric thermosphere. Here, the incidence of oxygen and nitrogen atoms is relatively higher than it is at the ground and collision rates are sparse enough to admit ionization of their atoms.
Once an atom is ionized, it's said to be in the excited state, and returns to the ground state either by gaining or by losing an electron. The jump from excited to ground states is characterized by a loss of energy that shows up as green, red or blue light as a curtain in the night sky, usually in the latitudinal region between 3° and 6°.
[caption id="attachment_22706" align="aligncenter" width="545" caption="Images of auroras. The image on the second row and first coloumn is an incidence of aurora australis."]
[/caption]
CMEs and flares are not the only reasons a geomagnetic storm may occur. For example, there is a solar proton storm, which causes the acceleration of protons emitted by the sun to near-light speeds either by increased heliomagnetic activity or by the shock of CME-release. There are also geomagnetically induced currents that are caused by variations in interplanetary space weather or by changes in the dynamo action of Earth's core.
Such is the relationship between the gorgeous Sun and our home planet, one that extends far beyond the telltale gravitational pull, one that is from core to core. Now that the sun is entering a period of solar maximum, geomagnetic activity will be on the rise, and with that, stronger greener, redder and bluer auroras, annoying signal and network disruptions, and grander flares, coronal mass ejections, and heliomagnetic activity that let us admire the Sun for what it is and understand the solar system better.
Not very often, I'd suppose, because if all of us managed to look at the sun that way, many of Earth's and the universe's beauties would become explicable. And, at least in my opinion, that would only make them more beautiful.
[caption id="attachment_22709" align="aligncenter" width="512" caption="An ultraviolet image of the sun taken at the time of emission of the CME (NASA)"]
[/caption]Last week, there was a great flurry of activity after our nearest star unleashed a massive coronal mass ejection (CME) that ranked in the 'X' compartment on the scale of flare strength. What's more, the flare was pointed directly at Earth, prompting astrophysicists to let loose warnings about electricity grids, satellite operations, GPS reception and communication networks being severely disrupted.
However, the stream of high-temperature high-energy particles belched by the sun - that's what makes a CME - didn't quite have the effect it should have had. When scientists started to ask why, they found a simple explanation: the magnetic field embedded in the ejection was oriented in such a way to the earth's own that it was fizzled out on contact.
[caption id="attachment_22710" align="aligncenter" width="545" caption="Streams of particles along the magnetic flux lines on the sun's surface are visible"]
[/caption]The sun's magnetic field is extremely strong and, because of the star's high-temperature surface, such fields influence the formation and paths of charged particles that exist in a plasma state (the fourth state of matter). Sometimes, these particles are shot out in the form of a flare when magnetic energy stored in the sun's corona suddenly jumps a few orders of magnitude, accelerating the heavier ions to speeds near that of light. Needless to say, this process is also linked to a big jump in temperature.
More often than not, the radiation emitted during such a flare is across the electromagnetic spectrum and not quite just localized to the visible region. Because of this, most flares are observable only by special instruments and not the naked eye.
[caption id="attachment_22711" align="aligncenter" width="545" caption="An illustration of solar wind and its impact with Earth's magnetic field"]
[/caption]Now, what causes this jump in magnetic activity? To understand that, observe the sun's core: at a temperature of 15,000,000 kelvin, it is the hottest place in the solar system. By comparison, the surface of the sun exists at a meagre 6,000 kelvin. Because of the temperature gradient between the two, there is a mass convection going on at all times: gases move from the hotter core to the cooler surface. However, they don't travel in a straight line. This is because of two mutually-acting reasons.
- When stars are formed, they have an accretion process during which they suck in gases from around them because of the steadily building gravitational force, and to conserve momenta, they're made to go around. Therefore, stars are born spinning.
- They do have the option to stop, but that would violate the law of conservation of energy. To keep from misbehaving like that, they conserve their angular momentum by keeping themselves revolving about an axis.
This energy conservation manifests itself in the gases in the convection current as well. Instead of moving straight - during which they're not conserving the star's angular momentum - they move out in a spiral. The speed at which they move out to a particular point is dependent mostly on the temperature gradient between the core and the surface at that point. Because of this uncertainty, gases at different parts of the sun's surface are moving at different velocities, as a result giving the sun a differential rotation: the speed of rotation at each solar latitude is different.
[caption id="attachment_22712" align="aligncenter" width="545" caption="Stars near the centre of the Milky Way galaxy take less time to orbit it than stars farther away. This difference in orbital periods gives rise to a spiral pattern much as differential rotation on the sun gives rise to spiral convection."]
[/caption]Consequently: though the sun's magnetic field possesses an overall shape and size that is measurable and fairly fixed, it's local magnetic fields are the troublesome ones. For example (and this being a conveniently chosen example), when one band of convection is shearing against another band moving at different speeds, a zone of high mechanical and thermodynamic stress is created.
When this stress no longer becomes bearable, a "wound" is punctured on the sun's surface. This creates a no-convection region that limits the amount of energy coming in from the core to the wound, cooling it. As the temperature falls, so does visibility, and a sunspot appears on the surface.
CMEs and flare activity are particularly energetic around sunspots because there, the magnetic field is very strong and oriented in such a way that it connects the sun's corona to its interior. In fact, at a sunspot, the component of the magnetic field perpendicular to the sun's surface is more pronounced than the other, inclined, component, providing a sort of rails on which charged particles can be accelerated and shot out.
[youtube http://www.youtube.com/watch?v=uecMk8ZZ1uE]
The rate of formation of sunspots affects solar storm activity, and this rate is dependent on whether the sun is in its solar maximum or solar minimum. During solar maximum, which lasts for a period of 11 years on average, the magnetic field at the solar equator is rotating slightly faster than that at the solar poles, producing enough heliomagnetic stress to influence the formation of hundreds of sunspots. Needless to say, solar storms can get really vicious when our star is in its solar maximum or is in the process of entering it - like now. The solar minimum, on the other hand, lasts for about 12 months, seeing decreased sunspot activity.
When such storms come in contact with the Earth's magnetic field, which they don't often do because they're pointed in other directions, they're called geomagnetic storms. Yes, this results in the disruption of our communication network, but it also gifts us the auroras that are a treat to watch. The storm that hit us a few days ago as a result of the massive 'X' class CME last weak fared poorly, being relegated to the 'G' class.
When the charged and heated solar wind reaches Earth, the particles come in contact with the geomagnetic field, transferring a bulk of their energy to it and increasing the movement of plasma through the magnetosphere. Some of this energy transferred manifests as increased electric currents in the ionosphere, which is what disrupts our communication.
[caption id="attachment_22713" align="aligncenter" width="519" caption="The magnetosphere engulfs all these layers in a bullet shaped envelope and extends far out into space, almost as much as 127,000 km to 160,000 km in the direction away from the sun."]
[/caption]However, the principle effect of the currents is increase the magnetic force in Earth's magnetosphere, pushing the boundary between the layer and the malevolent solar wind out, as if into space. A geomagnetic storm may last from a few minutes to a few days.
The auroras they create, however, last for only a few hours each time. During the geomagnetic storm, there is an immigration of particles from the magnetosphere and the ionosphere to the atmospheric thermosphere. Here, the incidence of oxygen and nitrogen atoms is relatively higher than it is at the ground and collision rates are sparse enough to admit ionization of their atoms.
Once an atom is ionized, it's said to be in the excited state, and returns to the ground state either by gaining or by losing an electron. The jump from excited to ground states is characterized by a loss of energy that shows up as green, red or blue light as a curtain in the night sky, usually in the latitudinal region between 3° and 6°.
[caption id="attachment_22706" align="aligncenter" width="545" caption="Images of auroras. The image on the second row and first coloumn is an incidence of aurora australis."]
[/caption]CMEs and flares are not the only reasons a geomagnetic storm may occur. For example, there is a solar proton storm, which causes the acceleration of protons emitted by the sun to near-light speeds either by increased heliomagnetic activity or by the shock of CME-release. There are also geomagnetically induced currents that are caused by variations in interplanetary space weather or by changes in the dynamo action of Earth's core.
Such is the relationship between the gorgeous Sun and our home planet, one that extends far beyond the telltale gravitational pull, one that is from core to core. Now that the sun is entering a period of solar maximum, geomagnetic activity will be on the rise, and with that, stronger greener, redder and bluer auroras, annoying signal and network disruptions, and grander flares, coronal mass ejections, and heliomagnetic activity that let us admire the Sun for what it is and understand the solar system better.
Sunday, 28 August 2011
Black holes and information theory
When you see a star in the night sky and think to yourself of its beauty, you're doing the following things.
One way or another, we're using up energy to receive information, process it and convert it into another form which we can use. In fact, even the information we receive is a form of energy. When you log in to access your Facebook account, the letters and numbers on the screen are digitized data, and that means they're a series of data modification pulses shipped in through hundreds of optical cables, electronic circuitry and wireless data transmission systems to appear on your screen. Every physical manifestation of intention and will, in this world, is the conversion of energy from one form into another.
Now, the law of conservation of energy states that the total amount of energy in this Universe is fixed and cannot ever be changed. In that case, shouldn't the amount of information we receive and generate be fixed? At any point of time, would it be possible to generate more information than this Universe can contain? And since this Universe seems equipped only to contain so much information, is it fair to consider either that humankind's capabilities are limited or that humankind will never have to worry about that limit because they won't get there?
Second: because of the nature of the origin of this Universe, it is assumed to be a constantly expanding volume of space, and so, the amount of information that the Universe can contain also increases with it. What is the rate of increase, then? A simple answer to this question can be arrived at by considering two concepts: the Kepler problem in general relativity and black holes.
A black hole is a singularity. A singularity is a point in space where the quantities used to measure space-time change in a way that is independent of the coordinate system. Imagine just having neatly pressed your new sheets, and then finding somewhere a small crease that you aren’t able to iron out, as if it wasn’t there at all when you last looked there, but now won’t go away however hard you try. That’s your black hole.
[caption id="attachment_20246" align="aligncenter" width="545" caption="Depiction of a black hole"]
[/caption]
A black hole is a point in space, whereas the large black spheres we imagine them to be are true if only because that is the region around which the black hole exerts its influence. This “sphere of influence” doesn’t have a definite boundary. For the sake of convenience, which physicists also see the need for from time to time, there’s the event horizon: a hypothetical sphere whose surface marks the point of no-return.
Because of there massive densities, black holes exert a gravitational force that is just as strong as they are dense. Now, the Standard Model of particle physics dictates that photons, the packets of energy that carry electromagnetic radiation like light, have no mass. The most important consequence of masslessness is non-conformance to the forces of gravity, and that means light should be able to pass through black holes with no reflection, refraction or absorption. However, that’s not the case; in fact, black holes swallow light completely and burp a small amount of heat out. This happens because, instead of bending rays of light into themselves, black holes distort the shape of the space-time continuum itself.
Now, imagine a long stretch of flat land parallel to the surface of which a missile is fired. The missile is such that it guides itself to stay 1m above the ground at all points of time. If, suddenly, a gorge opens beneath the missile, it dips down and continues to follow the surface. Light behaves like the missile when the ground is the space-time continuum, and the only known phenomenon capable of distorting the continuum like that is a black hole – the only difference is that a black hole wraps the continuum around itself.
Now, this distortion lends itself to a very useful technique with which to measure the rate of expansion of the Universe, a technique called gravitational lensing. Consider the animated image below.
Beams of light coming from the galaxy in the background are bent around the black hole. As a result of this bending, two consequences arise:
During lensing, the distance traveled by a beam increases while the net displacement doesn't change, thereby keeping the colours of the image intact but changing its brightness and dimensions. Therefore, the black hole behaves like a convex mirror or, more commonly, a fish-eye lens. Now, the Kepler problem in general relativity gives rise to the formula:
θ = (4GM / rc2)
Here, θ is the angle through which the light beam is deviated by the bending object (as depicted in the latest image), G is the universal gravitational constant, M is the mass of the bending object, r is the distance between the beams and the bender (between "missile" and "ground"), and c is the speed of light (note how the forces of gravity are not instantaneous but also travel at the speed of electromagnetic radiations).
Think of the space-time continuum as an elastic fabric and the various phenomena and objects as special designs on its surface. When, at a point, the weave is wrapped around a spherical object, the surface area at that point goes from being flat to being rounded, giving rise to a bulge that enlarges the image. In physical terms, the angular size of the image is said to have been increased.
By calculating the value of θ, the distance between the galaxy and the black hole can be established. Over the course of, say, one year, the initial and final values of θ between two objects can be computed to give the distance by which they have been moved apart in that year. The perfect way to understand is the "raisin bread" model of the Universe. Consider a loaf of bread embedded with raisins. If the loaf is expanded, the number of raisins and the shape of the raisins do not change, but the distance between them changes proportionately.
With that, we are in a position to understand by how much the information-carrying capacity of the Universe changes as it itself becomes more voluminous. That leaves a third and last question to be answered, the question of information transfer.
Information transfer
In the process flowchart shown above, an idea is encapsulated by certain words that are then transmitted by an "information generation" controller (which is duty-bound to filter out noise and other such chaotic elements from the message). Next, the message is conveyed through a medium to an "information reception" controller (which is also duty-bound to filter out noise), and then the message is understood as an idea.
Now, while the message is being conveyed, certain errors and losses could creep in into the transmission process. For instance, because of the incapacity of the system itself, data loss and/or data corruption could occur. Further, if the right medium is not chosen for the most-efficient conveyance of the message, it might be understood differently, which is also a kind of data corruption. In order to avoid such possibilities, the message is sometimes amplified.
During amplification, two processes can be said to occur:
As such, the amplification and abridgment processes have to accompany the conveyance-medium-conveyance subsystem because they compensate for the shortcomings of the conveyances (just as if A lends money to B and B lends that amount to C, it is only B's responsibility to retrieve it from C and return it to A). That being said, let's move on to the idea of interstellar magnifiers.
Interstellar magnifiers
If human civilization were to spread out from Earth and distribute itself across other planets in other galaxies, communication between the various systems is bound to become a pain. In that case, suitably modified electromagnetic signals (such as light, RF waves, etc.) can be pulsed into the sky, aimed at objects with strong gravitational forces that would further amplify, or boost, them on their way. With the assistance of suitably positioned satellites, the broadcast information can then be "narrowcasted" down to the receiving stations on some planet.
[caption id="attachment_20245" align="aligncenter" width="350" caption="Cassini's gravity-assistance"]
[/caption]
A significant hindrance posed to this method of communication is a phenomenon called galactic extinction: when intercepted by a cloud of galactic dust, the waves are absorbed and scattered into space, the information becoming lost in the process. In order to minimize the amount scattered, polarized radiation may be considered.
The no-hair theorem
What happens when light, instead of bending around a black hole, enters into it? The answer to this question is a puzzler because of something called the no-hair theorem, which states that every black hole is characterized only by its mass, charge and angular momentum. That means that if my laptop flies into a black hole, no information about the laptop can be retrieved if the mass, charge and/or the angular momentum of the black hole is/are not changed! If you cannot open an invisible door floating around my room, and if I step inside the door someday, how will you find me?
If any mass enters a black hole and is swallowed, there should be a subsequent increase in the mass of the black hole. Astronomers observed that this didn't happen in the case of energy, which meant that just as the black hole consumed some energy, it must also have radiated some energy in order to maintain its overall state.
This radiation is called Hawking radiation (in honour of its discoverer), and later observations found that it lay in the thermal section of the electromagnetic spectrum, i.e. a black hole radiated heat more than anything else. And since the black hole radiated heat, it must slowly be losing energy and, at one point, must also completely evaporate without a trace left behind. Using equations available in the theory of relativity, it was found that smaller black holes evaporated faster than larger ones. In fact, a black hole with the mass of a car would evaporate in 10-88 seconds.
[caption id="attachment_20247" align="aligncenter" width="545" caption="Hawking radiation mechanism"]
[/caption]
After complete evaporation... what about my laptop? Ultimately, we have a paradox: if my laptop went into the black hole, which then burped out some heat in the form of Hawking radiation, then is the no-hair theorem violable? Because my laptop's mass has caused a change in the interior energy of the black hole, which shouldn't happen according to the theorem.
Is the information then lost forever? Not possible; if it is, then the law of conservation of energy stands violated. Does the information also evaporate during the evaporation of the black hole? Not possible; if it did, then Hawking radiation would become inexplicable. Does the information jump out during the last moments of evaporation? Not possible; if it did, then a smaller black hole must have held on to that information that didn't participate in the evaporation. Does the information slip into a baby universe that we can't interact with? If your imagination can understand the creation of such a universe, sure. Does the information get lost in the time dimension? Nah.
Where is the information, then?
- Deciding to look up at the night sky
- Firing a sequence of signals through the motor neurons in the central nerve system
- Powering up muscles and lifting bones
- Positioning your eye to receive optimal amounts of light
- Employing a photo-chemical reaction at the back of the retina
- Sending electric signals to the brain
- Evaluating the beauty by accessing your memory
- Understanding the beauty and feeling it by letting it manifest as a suitable configuration of muscle positions
One way or another, we're using up energy to receive information, process it and convert it into another form which we can use. In fact, even the information we receive is a form of energy. When you log in to access your Facebook account, the letters and numbers on the screen are digitized data, and that means they're a series of data modification pulses shipped in through hundreds of optical cables, electronic circuitry and wireless data transmission systems to appear on your screen. Every physical manifestation of intention and will, in this world, is the conversion of energy from one form into another.
Now, the law of conservation of energy states that the total amount of energy in this Universe is fixed and cannot ever be changed. In that case, shouldn't the amount of information we receive and generate be fixed? At any point of time, would it be possible to generate more information than this Universe can contain? And since this Universe seems equipped only to contain so much information, is it fair to consider either that humankind's capabilities are limited or that humankind will never have to worry about that limit because they won't get there?
Second: because of the nature of the origin of this Universe, it is assumed to be a constantly expanding volume of space, and so, the amount of information that the Universe can contain also increases with it. What is the rate of increase, then? A simple answer to this question can be arrived at by considering two concepts: the Kepler problem in general relativity and black holes.
A black hole is a singularity. A singularity is a point in space where the quantities used to measure space-time change in a way that is independent of the coordinate system. Imagine just having neatly pressed your new sheets, and then finding somewhere a small crease that you aren’t able to iron out, as if it wasn’t there at all when you last looked there, but now won’t go away however hard you try. That’s your black hole.
[caption id="attachment_20246" align="aligncenter" width="545" caption="Depiction of a black hole"]
[/caption]A black hole is a point in space, whereas the large black spheres we imagine them to be are true if only because that is the region around which the black hole exerts its influence. This “sphere of influence” doesn’t have a definite boundary. For the sake of convenience, which physicists also see the need for from time to time, there’s the event horizon: a hypothetical sphere whose surface marks the point of no-return.
Because of there massive densities, black holes exert a gravitational force that is just as strong as they are dense. Now, the Standard Model of particle physics dictates that photons, the packets of energy that carry electromagnetic radiation like light, have no mass. The most important consequence of masslessness is non-conformance to the forces of gravity, and that means light should be able to pass through black holes with no reflection, refraction or absorption. However, that’s not the case; in fact, black holes swallow light completely and burp a small amount of heat out. This happens because, instead of bending rays of light into themselves, black holes distort the shape of the space-time continuum itself.
Now, imagine a long stretch of flat land parallel to the surface of which a missile is fired. The missile is such that it guides itself to stay 1m above the ground at all points of time. If, suddenly, a gorge opens beneath the missile, it dips down and continues to follow the surface. Light behaves like the missile when the ground is the space-time continuum, and the only known phenomenon capable of distorting the continuum like that is a black hole – the only difference is that a black hole wraps the continuum around itself.
Now, this distortion lends itself to a very useful technique with which to measure the rate of expansion of the Universe, a technique called gravitational lensing. Consider the animated image below.
Beams of light coming from the galaxy in the background are bent around the black hole. As a result of this bending, two consequences arise:
- Increase in the illumination and the size of the image
- Apparent change in the position of the source of the image (irrelevant for this discussion)
During lensing, the distance traveled by a beam increases while the net displacement doesn't change, thereby keeping the colours of the image intact but changing its brightness and dimensions. Therefore, the black hole behaves like a convex mirror or, more commonly, a fish-eye lens. Now, the Kepler problem in general relativity gives rise to the formula:
θ = (4GM / rc2)
Here, θ is the angle through which the light beam is deviated by the bending object (as depicted in the latest image), G is the universal gravitational constant, M is the mass of the bending object, r is the distance between the beams and the bender (between "missile" and "ground"), and c is the speed of light (note how the forces of gravity are not instantaneous but also travel at the speed of electromagnetic radiations).
Think of the space-time continuum as an elastic fabric and the various phenomena and objects as special designs on its surface. When, at a point, the weave is wrapped around a spherical object, the surface area at that point goes from being flat to being rounded, giving rise to a bulge that enlarges the image. In physical terms, the angular size of the image is said to have been increased.
By calculating the value of θ, the distance between the galaxy and the black hole can be established. Over the course of, say, one year, the initial and final values of θ between two objects can be computed to give the distance by which they have been moved apart in that year. The perfect way to understand is the "raisin bread" model of the Universe. Consider a loaf of bread embedded with raisins. If the loaf is expanded, the number of raisins and the shape of the raisins do not change, but the distance between them changes proportionately.
With that, we are in a position to understand by how much the information-carrying capacity of the Universe changes as it itself becomes more voluminous. That leaves a third and last question to be answered, the question of information transfer.
Information transfer
In the process flowchart shown above, an idea is encapsulated by certain words that are then transmitted by an "information generation" controller (which is duty-bound to filter out noise and other such chaotic elements from the message). Next, the message is conveyed through a medium to an "information reception" controller (which is also duty-bound to filter out noise), and then the message is understood as an idea.
Now, while the message is being conveyed, certain errors and losses could creep in into the transmission process. For instance, because of the incapacity of the system itself, data loss and/or data corruption could occur. Further, if the right medium is not chosen for the most-efficient conveyance of the message, it might be understood differently, which is also a kind of data corruption. In order to avoid such possibilities, the message is sometimes amplified.
During amplification, two processes can be said to occur:
- The information being carried is modified: it is made stronger in order to survive the journey
- An accompanying signal is sent to the receiver to inform it about the changes that have been made
As such, the amplification and abridgment processes have to accompany the conveyance-medium-conveyance subsystem because they compensate for the shortcomings of the conveyances (just as if A lends money to B and B lends that amount to C, it is only B's responsibility to retrieve it from C and return it to A). That being said, let's move on to the idea of interstellar magnifiers.
Interstellar magnifiers
If human civilization were to spread out from Earth and distribute itself across other planets in other galaxies, communication between the various systems is bound to become a pain. In that case, suitably modified electromagnetic signals (such as light, RF waves, etc.) can be pulsed into the sky, aimed at objects with strong gravitational forces that would further amplify, or boost, them on their way. With the assistance of suitably positioned satellites, the broadcast information can then be "narrowcasted" down to the receiving stations on some planet.
[caption id="attachment_20245" align="aligncenter" width="350" caption="Cassini's gravity-assistance"]
[/caption]A significant hindrance posed to this method of communication is a phenomenon called galactic extinction: when intercepted by a cloud of galactic dust, the waves are absorbed and scattered into space, the information becoming lost in the process. In order to minimize the amount scattered, polarized radiation may be considered.
The no-hair theorem
What happens when light, instead of bending around a black hole, enters into it? The answer to this question is a puzzler because of something called the no-hair theorem, which states that every black hole is characterized only by its mass, charge and angular momentum. That means that if my laptop flies into a black hole, no information about the laptop can be retrieved if the mass, charge and/or the angular momentum of the black hole is/are not changed! If you cannot open an invisible door floating around my room, and if I step inside the door someday, how will you find me?
If any mass enters a black hole and is swallowed, there should be a subsequent increase in the mass of the black hole. Astronomers observed that this didn't happen in the case of energy, which meant that just as the black hole consumed some energy, it must also have radiated some energy in order to maintain its overall state.
This radiation is called Hawking radiation (in honour of its discoverer), and later observations found that it lay in the thermal section of the electromagnetic spectrum, i.e. a black hole radiated heat more than anything else. And since the black hole radiated heat, it must slowly be losing energy and, at one point, must also completely evaporate without a trace left behind. Using equations available in the theory of relativity, it was found that smaller black holes evaporated faster than larger ones. In fact, a black hole with the mass of a car would evaporate in 10-88 seconds.
[caption id="attachment_20247" align="aligncenter" width="545" caption="Hawking radiation mechanism"]
[/caption]After complete evaporation... what about my laptop? Ultimately, we have a paradox: if my laptop went into the black hole, which then burped out some heat in the form of Hawking radiation, then is the no-hair theorem violable? Because my laptop's mass has caused a change in the interior energy of the black hole, which shouldn't happen according to the theorem.
Is the information then lost forever? Not possible; if it is, then the law of conservation of energy stands violated. Does the information also evaporate during the evaporation of the black hole? Not possible; if it did, then Hawking radiation would become inexplicable. Does the information jump out during the last moments of evaporation? Not possible; if it did, then a smaller black hole must have held on to that information that didn't participate in the evaporation. Does the information slip into a baby universe that we can't interact with? If your imagination can understand the creation of such a universe, sure. Does the information get lost in the time dimension? Nah.
Where is the information, then?
Black holes and information theory
When you see a star in the night sky and think to yourself of its beauty, you're doing the following things.
One way or another, we're using up energy to receive information, process it and convert it into another form which we can use. In fact, even the information we receive is a form of energy. When you log in to access your Facebook account, the letters and numbers on the screen are digitized data, and that means they're a series of data modification pulses shipped in through hundreds of optical cables, electronic circuitry and wireless data transmission systems to appear on your screen. Every physical manifestation of intention and will, in this world, is the conversion of energy from one form into another.
Now, the law of conservation of energy states that the total amount of energy in this Universe is fixed and cannot ever be changed. In that case, shouldn't the amount of information we receive and generate be fixed? At any point of time, would it be possible to generate more information than this Universe can contain? And since this Universe seems equipped only to contain so much information, is it fair to consider either that humankind's capabilities are limited or that humankind will never have to worry about that limit because they won't get there?
Second: because of the nature of the origin of this Universe, it is assumed to be a constantly expanding volume of space, and so, the amount of information that the Universe can contain also increases with it. What is the rate of increase, then? A simple answer to this question can be arrived at by considering two concepts: the Kepler problem in general relativity and black holes.
A black hole is a singularity. A singularity is a point in space where the quantities used to measure space-time change in a way that is independent of the coordinate system. Imagine just having neatly pressed your new sheets, and then finding somewhere a small crease that you aren’t able to iron out, as if it wasn’t there at all when you last looked there, but now won’t go away however hard you try. That’s your black hole.
[caption id="attachment_20246" align="aligncenter" width="545" caption="Depiction of a black hole"][/caption]
A black hole is a point in space, whereas the large black spheres we imagine them to be are true if only because that is the region around which the black hole exerts its influence. This “sphere of influence” doesn’t have a definite boundary. For the sake of convenience, which physicists also see the need for from time to time, there’s the event horizon: a hypothetical sphere whose surface marks the point of no-return.
Because of there massive densities, black holes exert a gravitational force that is just as strong as they are dense. Now, the Standard Model of particle physics dictates that photons, the packets of energy that carry electromagnetic radiation like light, have no mass. The most important consequence of masslessness is non-conformance to the forces of gravity, and that means light should be able to pass through black holes with no reflection, refraction or absorption. However, that’s not the case; in fact, black holes swallow light completely and burp a small amount of heat out. This happens because, instead of bending rays of light into themselves, black holes distort the shape of the space-time continuum itself.
Now, imagine a long stretch of flat land parallel to the surface of which a missile is fired. The missile is such that it guides itself to stay 1m above the ground at all points of time. If, suddenly, a gorge opens beneath the missile, it dips down and continues to follow the surface. Light behaves like the missile when the ground is the space-time continuum, and the only known phenomenon capable of distorting the continuum like that is a black hole – the only difference is that a black hole wraps the continuum around itself.
Now, this distortion lends itself to a very useful technique with which to measure the rate of expansion of the Universe, a technique called gravitational lensing. Consider the animated image below.
Beams of light coming from the galaxy in the background are bent around the black hole. As a result of this bending, two consequences arise:
During lensing, the distance traveled by a beam increases while the net displacement doesn't change, thereby keeping the colours of the image intact but changing its brightness and dimensions. Therefore, the black hole behaves like a convex mirror or, more commonly, a fish-eye lens. Now, the Kepler problem in general relativity gives rise to the formula:
θ = (4GM / rc2)
Here, θ is the angle through which the light beam is deviated by the bending object (as depicted in the latest image), G is the universal gravitational constant, M is the mass of the bending object, r is the distance between the beams and the bender (between "missile" and "ground"), and c is the speed of light (note how the forces of gravity are not instantaneous but also travel at the speed of electromagnetic radiations).
Think of the space-time continuum as an elastic fabric and the various phenomena and objects as special designs on its surface. When, at a point, the weave is wrapped around a spherical object, the surface area at that point goes from being flat to being rounded, giving rise to a bulge that enlarges the image. In physical terms, the angular size of the image is said to have been increased.
By calculating the value of θ, the distance between the galaxy and the black hole can be established. Over the course of, say, one year, the initial and final values of θ between two objects can be computed to give the distance by which they have been moved apart in that year. The perfect way to understand is the "raisin bread" model of the Universe. Consider a loaf of bread embedded with raisins. If the loaf is expanded, the number of raisins and the shape of the raisins do not change, but the distance between them changes proportionately.
With that, we are in a position to understand by how much the information-carrying capacity of the Universe changes as it itself becomes more voluminous. That leaves a third and last question to be answered, the question of information transfer.
Information transfer
In the process flowchart shown above, an idea is encapsulated by certain words that are then transmitted by an "information generation" controller (which is duty-bound to filter out noise and other such chaotic elements from the message). Next, the message is conveyed through a medium to an "information reception" controller (which is also duty-bound to filter out noise), and then the message is understood as an idea.
Now, while the message is being conveyed, certain errors and losses could creep in into the transmission process. For instance, because of the incapacity of the system itself, data loss and/or data corruption could occur. Further, if the right medium is not chosen for the most-efficient conveyance of the message, it might be understood differently, which is also a kind of data corruption. In order to avoid such possibilities, the message is sometimes amplified.
During amplification, two processes can be said to occur:
As such, the amplification and abridgment processes have to accompany the conveyance-medium-conveyance subsystem because they compensate for the shortcomings of the conveyances (just as if A lends money to B and B lends that amount to C, it is only B's responsibility to retrieve it from C and return it to A). That being said, let's move on to the idea of interstellar magnifiers.
Interstellar magnifiers
If human civilization were to spread out from Earth and distribute itself across other planets in other galaxies, communication between the various systems is bound to become a pain. In that case, suitably modified electromagnetic signals (such as light, RF waves, etc.) can be pulsed into the sky, aimed at objects with strong gravitational forces that would further amplify, or boost, them on their way. With the assistance of suitably positioned satellites, the broadcast information can then be "narrowcasted" down to the receiving stations on some planet.
[caption id="attachment_20245" align="aligncenter" width="350" caption="Cassini's gravity-assistance"][/caption]
A significant hindrance posed to this method of communication is a phenomenon called galactic extinction: when intercepted by a cloud of galactic dust, the waves are absorbed and scattered into space, the information becoming lost in the process. In order to minimize the amount scattered, polarized radiation may be considered.
The no-hair theorem
What happens when light, instead of bending around a black hole, enters into it? The answer to this question is a puzzler because of something called the no-hair theorem, which states that every black hole is characterized only by its mass, charge and angular momentum. That means that if my laptop flies into a black hole, no information about the laptop can be retrieved if the mass, charge and/or the angular momentum of the black hole is/are not changed! If you cannot open an invisible door floating around my room, and if I step inside the door someday, how will you find me?
If any mass enters a black hole and is swallowed, there should be a subsequent increase in the mass of the black hole. Astronomers observed that this didn't happen in the case of energy, which meant that just as the black hole consumed some energy, it must also have radiated some energy in order to maintain its overall state.
This radiation is called Hawking radiation (in honour of its discoverer), and later observations found that it lay in the thermal section of the electromagnetic spectrum, i.e. a black hole radiated heat more than anything else. And since the black hole radiated heat, it must slowly be losing energy and, at one point, must also completely evaporate without a trace left behind. Using equations available in the theory of relativity, it was found that smaller black holes evaporated faster than larger ones. In fact, a black hole with the mass of a car would evaporate in 10-88 seconds.
[caption id="attachment_20247" align="aligncenter" width="545" caption="Hawking radiation mechanism"][/caption]
After complete evaporation... what about my laptop? Ultimately, we have a paradox: if my laptop went into the black hole, which then burped out some heat in the form of Hawking radiation, then is the no-hair theorem violable? Because my laptop's mass has caused a change in the interior energy of the black hole, which shouldn't happen according to the theorem.
Is the information then lost forever? Not possible; if it is, then the law of conservation of energy stands violated. Does the information also evaporate during the evaporation of the black hole? Not possible; if it did, then Hawking radiation would become inexplicable. Does the information jump out during the last moments of evaporation? Not possible; if it did, then a smaller black hole must have held on to that information that didn't participate in the evaporation. Does the information slip into a baby universe that we can't interact with? If your imagination can understand the creation of such a universe, sure. Does the information get lost in the time dimension? Nah.
Where is the information, then?
- Deciding to look up at the night sky
- Firing a sequence of signals through the motor neurons in the central nerve system
- Powering up muscles and lifting bones
- Positioning your eye to receive optimal amounts of light
- Employing a photo-chemical reaction at the back of the retina
- Sending electric signals to the brain
- Evaluating the beauty by accessing your memory
- Understanding the beauty and feeling it by letting it manifest as a suitable configuration of muscle positions
One way or another, we're using up energy to receive information, process it and convert it into another form which we can use. In fact, even the information we receive is a form of energy. When you log in to access your Facebook account, the letters and numbers on the screen are digitized data, and that means they're a series of data modification pulses shipped in through hundreds of optical cables, electronic circuitry and wireless data transmission systems to appear on your screen. Every physical manifestation of intention and will, in this world, is the conversion of energy from one form into another.
Now, the law of conservation of energy states that the total amount of energy in this Universe is fixed and cannot ever be changed. In that case, shouldn't the amount of information we receive and generate be fixed? At any point of time, would it be possible to generate more information than this Universe can contain? And since this Universe seems equipped only to contain so much information, is it fair to consider either that humankind's capabilities are limited or that humankind will never have to worry about that limit because they won't get there?
Second: because of the nature of the origin of this Universe, it is assumed to be a constantly expanding volume of space, and so, the amount of information that the Universe can contain also increases with it. What is the rate of increase, then? A simple answer to this question can be arrived at by considering two concepts: the Kepler problem in general relativity and black holes.
A black hole is a singularity. A singularity is a point in space where the quantities used to measure space-time change in a way that is independent of the coordinate system. Imagine just having neatly pressed your new sheets, and then finding somewhere a small crease that you aren’t able to iron out, as if it wasn’t there at all when you last looked there, but now won’t go away however hard you try. That’s your black hole.
[caption id="attachment_20246" align="aligncenter" width="545" caption="Depiction of a black hole"]
[/caption]A black hole is a point in space, whereas the large black spheres we imagine them to be are true if only because that is the region around which the black hole exerts its influence. This “sphere of influence” doesn’t have a definite boundary. For the sake of convenience, which physicists also see the need for from time to time, there’s the event horizon: a hypothetical sphere whose surface marks the point of no-return.
Because of there massive densities, black holes exert a gravitational force that is just as strong as they are dense. Now, the Standard Model of particle physics dictates that photons, the packets of energy that carry electromagnetic radiation like light, have no mass. The most important consequence of masslessness is non-conformance to the forces of gravity, and that means light should be able to pass through black holes with no reflection, refraction or absorption. However, that’s not the case; in fact, black holes swallow light completely and burp a small amount of heat out. This happens because, instead of bending rays of light into themselves, black holes distort the shape of the space-time continuum itself.
Now, imagine a long stretch of flat land parallel to the surface of which a missile is fired. The missile is such that it guides itself to stay 1m above the ground at all points of time. If, suddenly, a gorge opens beneath the missile, it dips down and continues to follow the surface. Light behaves like the missile when the ground is the space-time continuum, and the only known phenomenon capable of distorting the continuum like that is a black hole – the only difference is that a black hole wraps the continuum around itself.
Now, this distortion lends itself to a very useful technique with which to measure the rate of expansion of the Universe, a technique called gravitational lensing. Consider the animated image below.
Beams of light coming from the galaxy in the background are bent around the black hole. As a result of this bending, two consequences arise:
- Increase in the illumination and the size of the image
- Apparent change in the position of the source of the image (irrelevant for this discussion)
During lensing, the distance traveled by a beam increases while the net displacement doesn't change, thereby keeping the colours of the image intact but changing its brightness and dimensions. Therefore, the black hole behaves like a convex mirror or, more commonly, a fish-eye lens. Now, the Kepler problem in general relativity gives rise to the formula:
θ = (4GM / rc2)
Here, θ is the angle through which the light beam is deviated by the bending object (as depicted in the latest image), G is the universal gravitational constant, M is the mass of the bending object, r is the distance between the beams and the bender (between "missile" and "ground"), and c is the speed of light (note how the forces of gravity are not instantaneous but also travel at the speed of electromagnetic radiations).
Think of the space-time continuum as an elastic fabric and the various phenomena and objects as special designs on its surface. When, at a point, the weave is wrapped around a spherical object, the surface area at that point goes from being flat to being rounded, giving rise to a bulge that enlarges the image. In physical terms, the angular size of the image is said to have been increased.
By calculating the value of θ, the distance between the galaxy and the black hole can be established. Over the course of, say, one year, the initial and final values of θ between two objects can be computed to give the distance by which they have been moved apart in that year. The perfect way to understand is the "raisin bread" model of the Universe. Consider a loaf of bread embedded with raisins. If the loaf is expanded, the number of raisins and the shape of the raisins do not change, but the distance between them changes proportionately.
With that, we are in a position to understand by how much the information-carrying capacity of the Universe changes as it itself becomes more voluminous. That leaves a third and last question to be answered, the question of information transfer.
Information transfer
In the process flowchart shown above, an idea is encapsulated by certain words that are then transmitted by an "information generation" controller (which is duty-bound to filter out noise and other such chaotic elements from the message). Next, the message is conveyed through a medium to an "information reception" controller (which is also duty-bound to filter out noise), and then the message is understood as an idea.
Now, while the message is being conveyed, certain errors and losses could creep in into the transmission process. For instance, because of the incapacity of the system itself, data loss and/or data corruption could occur. Further, if the right medium is not chosen for the most-efficient conveyance of the message, it might be understood differently, which is also a kind of data corruption. In order to avoid such possibilities, the message is sometimes amplified.
During amplification, two processes can be said to occur:
- The information being carried is modified: it is made stronger in order to survive the journey
- An accompanying signal is sent to the receiver to inform it about the changes that have been made
As such, the amplification and abridgment processes have to accompany the conveyance-medium-conveyance subsystem because they compensate for the shortcomings of the conveyances (just as if A lends money to B and B lends that amount to C, it is only B's responsibility to retrieve it from C and return it to A). That being said, let's move on to the idea of interstellar magnifiers.
Interstellar magnifiers
If human civilization were to spread out from Earth and distribute itself across other planets in other galaxies, communication between the various systems is bound to become a pain. In that case, suitably modified electromagnetic signals (such as light, RF waves, etc.) can be pulsed into the sky, aimed at objects with strong gravitational forces that would further amplify, or boost, them on their way. With the assistance of suitably positioned satellites, the broadcast information can then be "narrowcasted" down to the receiving stations on some planet.
[caption id="attachment_20245" align="aligncenter" width="350" caption="Cassini's gravity-assistance"]
[/caption]A significant hindrance posed to this method of communication is a phenomenon called galactic extinction: when intercepted by a cloud of galactic dust, the waves are absorbed and scattered into space, the information becoming lost in the process. In order to minimize the amount scattered, polarized radiation may be considered.
The no-hair theorem
What happens when light, instead of bending around a black hole, enters into it? The answer to this question is a puzzler because of something called the no-hair theorem, which states that every black hole is characterized only by its mass, charge and angular momentum. That means that if my laptop flies into a black hole, no information about the laptop can be retrieved if the mass, charge and/or the angular momentum of the black hole is/are not changed! If you cannot open an invisible door floating around my room, and if I step inside the door someday, how will you find me?
If any mass enters a black hole and is swallowed, there should be a subsequent increase in the mass of the black hole. Astronomers observed that this didn't happen in the case of energy, which meant that just as the black hole consumed some energy, it must also have radiated some energy in order to maintain its overall state.
This radiation is called Hawking radiation (in honour of its discoverer), and later observations found that it lay in the thermal section of the electromagnetic spectrum, i.e. a black hole radiated heat more than anything else. And since the black hole radiated heat, it must slowly be losing energy and, at one point, must also completely evaporate without a trace left behind. Using equations available in the theory of relativity, it was found that smaller black holes evaporated faster than larger ones. In fact, a black hole with the mass of a car would evaporate in 10-88 seconds.
[caption id="attachment_20247" align="aligncenter" width="545" caption="Hawking radiation mechanism"]
[/caption]After complete evaporation... what about my laptop? Ultimately, we have a paradox: if my laptop went into the black hole, which then burped out some heat in the form of Hawking radiation, then is the no-hair theorem violable? Because my laptop's mass has caused a change in the interior energy of the black hole, which shouldn't happen according to the theorem.
Is the information then lost forever? Not possible; if it is, then the law of conservation of energy stands violated. Does the information also evaporate during the evaporation of the black hole? Not possible; if it did, then Hawking radiation would become inexplicable. Does the information jump out during the last moments of evaporation? Not possible; if it did, then a smaller black hole must have held on to that information that didn't participate in the evaporation. Does the information slip into a baby universe that we can't interact with? If your imagination can understand the creation of such a universe, sure. Does the information get lost in the time dimension? Nah.
Where is the information, then?
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