Thursday, May 12, 2011
Ah, they're coming for me.
http://www.msnbc.msn.com/id/28548425/ns/technology_and_science-space/t/scientists-hear-mystery-boom-space/
Wednesday, April 20, 2011
Sunny Scorp Fishy Moon
Merely minor disabilities will affect you in your intellectual endeavors.
The worst that could happen would be an:
overly inquisitive
indecisive nature
that never seems to be satisfied.
However, you have within you the ability to avoid these psychological obstacles
And, I will.
The combination of your Sun sign and your Moon sign produces a person with terrific intuition and sense that ordinary people simply don't have. You are overly dramatic and frequently exaggerate problems. You are, likewise, able to capture the drama of your surroundings as well as the imagination of the public. Yours is an emotional profundity that lends a great deal of inspiration to your personality. You attack any problem with unswerving enthusiasm and devotion, always giving more that just a part of yourself to your causes or ideals. Here there is a blend of the emotional force, determination and will power of Scorpio with the sensitivity, impressionability and intuitive insight of Pisces. This produces a strongly emotional and somewhat psychic or receptive and impressionable nature. A studious and intellectual bend permits you to succeed, especially in literary or artistic endeavors. You are very creative, but your success may be more from a willingness to apply yourself than from pure talent. On the down side, you are anxious and worry too much. Positive thinking is essential for you to attain personal balance and peace of mind. There are unexpected depths in your nature and you succeed by concentrating your energies on definite objectives, avoiding the tendency to dispense emotional energies and intellectual power in overemphasis on romance, daydreaming or negative apprehensions or worries.
The worst that could happen would be an:
overly inquisitive
indecisive nature
that never seems to be satisfied.
However, you have within you the ability to avoid these psychological obstacles
And, I will.
The combination of your Sun sign and your Moon sign produces a person with terrific intuition and sense that ordinary people simply don't have. You are overly dramatic and frequently exaggerate problems. You are, likewise, able to capture the drama of your surroundings as well as the imagination of the public. Yours is an emotional profundity that lends a great deal of inspiration to your personality. You attack any problem with unswerving enthusiasm and devotion, always giving more that just a part of yourself to your causes or ideals. Here there is a blend of the emotional force, determination and will power of Scorpio with the sensitivity, impressionability and intuitive insight of Pisces. This produces a strongly emotional and somewhat psychic or receptive and impressionable nature. A studious and intellectual bend permits you to succeed, especially in literary or artistic endeavors. You are very creative, but your success may be more from a willingness to apply yourself than from pure talent. On the down side, you are anxious and worry too much. Positive thinking is essential for you to attain personal balance and peace of mind. There are unexpected depths in your nature and you succeed by concentrating your energies on definite objectives, avoiding the tendency to dispense emotional energies and intellectual power in overemphasis on romance, daydreaming or negative apprehensions or worries.
Tuesday, April 5, 2011
Monday, March 28, 2011
Koinophilia is a term used by biologist Johan Koeslag, meaning that when sexual creatures seek a mate, they prefer that mate not to have any unusual, peculiar or deviant features.
Natural selection results, over the course of generations, in beneficial (or "fit") features replacing their disadvantageous counterparts. Thus, natural selection causes beneficial features to become increasingly more common with each generation, while the disadvantageous features become increasingly rare. A sexual creature, therefore, wishing to mate with a fit partner, would be expected to avoid individuals sporting unusual features, while being especially attracted to those individuals displaying a predominance of common or average features. This is termed "koinophilia". It has, as an important side effect, that mates displaying mutant features (the result of a genetic mutation) are also avoided. This, in itself, is also advantageous, because the vast majority of mutations are disadvantageous. Because it is impossible to judge whether a new mutation is beneficial or not, koinophilic creatures will avoid them all with equal determination, even if this means avoiding the very occasional beneficial mutation. Thus, koinophilia, although not perfect or infallible in its ability to distinguish fit from unfit mates, remains, on average, a very good strategy when choosing a mate. It will be right far more often than it will be wrong. Even when it is wrong, a koinophilic choice always ensures that the offspring will inherit a suite of thoroughly tried and tested features.
According to Koeslag, koinophilia provides very simple and obvious explanations for such evolutionary puzzles as the process of speciation,[1] evolutionary stasis and punctuated equilibria,[1][2] sex and the affordability of males,[3][4] and the evolution of cooperation[5][6]. This mating strategy, was first referred to as koinophilia by Johan H. Koeslag[2], from the Greek, koinos, meaning "the usual" or "common", and philos, meaning "fondness" or "love". It was independently identified in humans by Judith Langlois,[7][8][9][10][11][12][13] who found that the average of two human faces was more attractive than either of the faces from which that average was derived. The more faces (of the same gender and age) that were used in the averaging process the more attractive and appealing the average face became.
In keeping with these theoretical considerations, one study on an isolated human population, as opposed to Western subjects, has suggested that preferences for averageness appear to be universal.[14] The isolated people preferred average faces from their own race, but did not show any preference for average faces of other races. This makes sense since they are not exposed to outside races and thus have no knowledge of what an average face from another race looks like. This suggests that it is averageness alone, that is making a face attractive rather than some other artifact that results from averaging techniques [14]. Many studies have confirmed that subjects find young average faces the most attractive.[7][14][15][16][17][18] However, Perrett et al.[15] found that both men and women considered that a face averaged from a set of attractive faces was more attractive than one averaged from a wide range of women's faces. When the differences between the first face and the second face were slightly exaggerated the new face was judged, on average, to be more attractive still. Although the three faces look remarkably similar, close examination of the photos in Perrett, May and Yoshikawa's paper[15] shows, in fact, that the exaggerated face looks younger than the average face (composed of women's faces aged 22–46 years). Since the same results were obtained with Japanese subjects, these findings are probably culture independent, and would indicate that people generally find youthful average female faces sexually the most attractive,[7] as expected.
A major evolutionary problem has been how the continuous process of evolution produces groups of individuals, labeled species, whose adult members look extraordinarily similar, and distinctively different from the members of other species. Lions and leopards are, for instance, both large carnivores inhabiting the same general environment, and hunting much the same prey, in much the same way, but they look extraordinarily different, and would not be confused one for the other even by the most unsophisticated observer[19]. There would seem to be no obvious evolutionary reason which suggests that lion-leopard intermediates are likely to be less successful hunters than either of the two distinct species that inhabit the African savanna today. Why then do they not exist? What evolutionary force drives these intermediate forms to extinction, leaving only highly uniform and distinctive lions on the one hand and highly uniform and distinctive leopards on the other?
Speciation poses a "2-dimensional" problem. The discontinuities in appearance between existing species represent the "horizontal dimension" of the problem. The succession of fossil species represent the "vertical dimension".This is, however, only one aspect of what is almost certainly a two-dimensional problem[20][21]. The "horizontal" dimension refers to the almost complete absence of transitional, or intermediate forms between present-day species (e.g. between lions, leopards, cheetahs and lynxes)[19][22][23][24][25]. The "vertical" dimension concerns the fossil record. Fossil species are frequently remarkably stable over extremely long periods of geological time, despite continental drift, major climate changes, and mass extinctions[26][27]. When a change in appearance or form does occur, it tends to be abrupt in geological terms, again producing phenotypic gaps (i.e. an absence of intermediate forms), but now between successive species, which then often co-exist for considerable periods of time. Thus the fossil record, though open to different interpretations, suggests that evolution occurs in bursts, interspersed by long periods of evolutionary stagnation (i.e. by means of punctuated equilibria[26]). Why this is so, has been one of evolution's great mysteries[27].
Koinophilia could explain both the horizontal and vertical manifestations of speciation, and why it usually involves the entire external appearance of the creatures concerned.[1][2] If sexual creatures prefer mates sporting predominantly common features, and avoid mates with unusual, unfamiliar, fringe, or extreme attributes, then common features will tend to become more common still, and at a rate and to an extent that natural selection on its own is unlikely to achieve. Since koinophilia affects the entire external appearance, the members of an interbreeding group will soon all begin to look astoundingly alike, both with regard to important or essential features (e.g. the jaws, dentition, and claws of a lion) and trivial features (e.g. the black furry tuft at the tip of the lion’s tail, or the lion's “beard”) [28]. It is almost inevitable that each interbreeding group will, in this way, very quickly develop its own characteristic appearance. An individual from one group who wanders into another group will consequently be recognized as being different, and will, therefore, be discriminated against during the mating season. This koinophilia-induced reproductive isolation might thus be the first crucial step in the development of, ultimately, physiological, anatomical and behavioral barriers to hybridization, and thus, ultimately, full specieshood. Koinophilia will thereafter defend that species' appearance and behavior against invasion by unusual or unfamiliar forms (which might arise by immigration or mutation), and thus be a paradigm of punctuated equilibria (or the "vertical" aspect of the speciation problem.[1][2]), and stabilizing selection.
Cooperation is any group behavior that benefits the individuals more than if they were to act as independent agents. There is, however, a second, very important, corollary to cooperation: it can always be exploited by selfish individuals who benefit even more by not taking part in the group activity, yet reaping its benefits. For instance, a selfish individual who does not join the hunting pack and its incumbent dangers but nevertheless shares in the spoils has a fitness advantage over the other members of the pack. Thus, although a group of cooperative individuals is fitter than an equivalent group of selfish individuals, selfish individuals interspersed amongst a community of cooperators are always fitter than their hosts. This means they raise, on average, more offspring and grandoffspring than their hosts, and will therefore ultimately replace them.
If, however, the selfish individuals are ostracized, and rejected as mates, because of their deviant and unusual behavior, then their evolutionary advantage becomes an evolutionary liability. Cooperation in all of its very many forms then becomes evolutionarily stable.[5][6] Sociability, social conventions, ritualistic behavior, the expressions of the emotions, and other forms of communication between individuals, all essential ingredients for full cooperativity, can all be similarly evolutionarily stabilized by koinophilia.
Co-operation or co-operative behaviours are terms used to describe behaviours by organisms which are beneficial to other organisms, and are selected for on that basis.[1] Under this definition, altruism is a form of co-operation in which there is no direct benefit to the actor (the organism carrying out the behaviour).[1] Co-operative behaviour in which there is a direct benefit to the actor as well as the recipient can be termed "mutually beneficial".[1] There are several theories which help to explain why natural selection favours some types of co-operative behaviour. They are not mutually exclusive, however, and more than one of the theories discussed below may contribute to explaining a particular case of co-operative behaviour. Note: This article uses British English. Standard U.S. English drops the hyphen resulting in cooperation or cooperative.
One well accepted explanation for altruistic behaviour (that is, co-operative behaviour which lacks a direct benefit for the actor) is the theory of kin selection. This theory suggests that individuals act co-operatively in order to help others which are genetically similar. Genes for such co-operative behaviour are preserved, because they help to perpetuate their own existence. The classic example is the social insects, such as bees and ants. Worker insects never reproduce, but instead, they work to allow the (genetically similar) queen to reproduce.
The theory of reciprocity suggests that individuals carry out co-operative behaviours because they get something in return. In order for such behaviours to be favoured, there needs to be some perception of external physical markers that the other individual will recognise (otherwise, there is no selective pressure to maintain the behaviour). Much research about reciprocity as leading to co-operation has concentrated on the 'prisoner's dilemma' known from game theory.
One theory suggesting a mechanism that could lead to the evolution of co-operation is the "market effect" as suggested by Noe and Hammerstein.[2] The mechanism relies on the fact that in many situations there exists a trade-off between efficiency obtaining a desired resource and the amount of resources one can actively obtain. In that case, each partner in a system could benefit from specializing in producing one specific resource and obtaining the other resource by trade. When only two partners exist, each can specialize in one resource, and trade for the other. Trading for the resource requires co-operation with the other partner and includes a process of bidding and bargaining.
This mechanism can be relied to both within a species or social group and within species systems. It can also be applied to a multi-partner system, in which the owner of a resource has the power to choose its co-operation partner. This model can be applied in natural systems (examples exist in the world of apes, cleaner fish, and more). Easy for exemplifying, though, are systems from international trading. Arabic countries control vast amounts of oil, but seek technologies from western countries. These in turn are in need of Arab oil. The solution is co-operation by trade.
Multi-level selection theory suggests that selection operates on more than one level: for example, it may operate at an atomic and molecular level in cells, at the level of cells in the body, and then again at the whole organism level, and the community level, and the species level. Any level which is not competitive with others of the same level will be eliminated, even if the level below is highly competitive. A classic example is that of genes which prevent cancer. Cancer cells divide uncontrollably, and at the cellular level, they are very successful, because they are (in the short term) reproducing very well and out competing other cells in the body. However, at the whole organism level, cancer is often fatal, and so may prevent reproduction. Therefore, changes to the genome which prevent cancer (for example, by causing damaged cells to act co-operatively by destroying themselves) are favoured. Multi-level selection theory contends that similar effects can occur, for example, to cause individuals to co-operate to avoid behaviours which favour themselves short-term, but destroy the community (and their descendants) long term.
Natural selection results, over the course of generations, in beneficial (or "fit") features replacing their disadvantageous counterparts. Thus, natural selection causes beneficial features to become increasingly more common with each generation, while the disadvantageous features become increasingly rare. A sexual creature, therefore, wishing to mate with a fit partner, would be expected to avoid individuals sporting unusual features, while being especially attracted to those individuals displaying a predominance of common or average features. This is termed "koinophilia". It has, as an important side effect, that mates displaying mutant features (the result of a genetic mutation) are also avoided. This, in itself, is also advantageous, because the vast majority of mutations are disadvantageous. Because it is impossible to judge whether a new mutation is beneficial or not, koinophilic creatures will avoid them all with equal determination, even if this means avoiding the very occasional beneficial mutation. Thus, koinophilia, although not perfect or infallible in its ability to distinguish fit from unfit mates, remains, on average, a very good strategy when choosing a mate. It will be right far more often than it will be wrong. Even when it is wrong, a koinophilic choice always ensures that the offspring will inherit a suite of thoroughly tried and tested features.
According to Koeslag, koinophilia provides very simple and obvious explanations for such evolutionary puzzles as the process of speciation,[1] evolutionary stasis and punctuated equilibria,[1][2] sex and the affordability of males,[3][4] and the evolution of cooperation[5][6]. This mating strategy, was first referred to as koinophilia by Johan H. Koeslag[2], from the Greek, koinos, meaning "the usual" or "common", and philos, meaning "fondness" or "love". It was independently identified in humans by Judith Langlois,[7][8][9][10][11][12][13] who found that the average of two human faces was more attractive than either of the faces from which that average was derived. The more faces (of the same gender and age) that were used in the averaging process the more attractive and appealing the average face became.
In keeping with these theoretical considerations, one study on an isolated human population, as opposed to Western subjects, has suggested that preferences for averageness appear to be universal.[14] The isolated people preferred average faces from their own race, but did not show any preference for average faces of other races. This makes sense since they are not exposed to outside races and thus have no knowledge of what an average face from another race looks like. This suggests that it is averageness alone, that is making a face attractive rather than some other artifact that results from averaging techniques [14]. Many studies have confirmed that subjects find young average faces the most attractive.[7][14][15][16][17][18] However, Perrett et al.[15] found that both men and women considered that a face averaged from a set of attractive faces was more attractive than one averaged from a wide range of women's faces. When the differences between the first face and the second face were slightly exaggerated the new face was judged, on average, to be more attractive still. Although the three faces look remarkably similar, close examination of the photos in Perrett, May and Yoshikawa's paper[15] shows, in fact, that the exaggerated face looks younger than the average face (composed of women's faces aged 22–46 years). Since the same results were obtained with Japanese subjects, these findings are probably culture independent, and would indicate that people generally find youthful average female faces sexually the most attractive,[7] as expected.
A major evolutionary problem has been how the continuous process of evolution produces groups of individuals, labeled species, whose adult members look extraordinarily similar, and distinctively different from the members of other species. Lions and leopards are, for instance, both large carnivores inhabiting the same general environment, and hunting much the same prey, in much the same way, but they look extraordinarily different, and would not be confused one for the other even by the most unsophisticated observer[19]. There would seem to be no obvious evolutionary reason which suggests that lion-leopard intermediates are likely to be less successful hunters than either of the two distinct species that inhabit the African savanna today. Why then do they not exist? What evolutionary force drives these intermediate forms to extinction, leaving only highly uniform and distinctive lions on the one hand and highly uniform and distinctive leopards on the other?
Koinophilia could explain both the horizontal and vertical manifestations of speciation, and why it usually involves the entire external appearance of the creatures concerned.[1][2] If sexual creatures prefer mates sporting predominantly common features, and avoid mates with unusual, unfamiliar, fringe, or extreme attributes, then common features will tend to become more common still, and at a rate and to an extent that natural selection on its own is unlikely to achieve. Since koinophilia affects the entire external appearance, the members of an interbreeding group will soon all begin to look astoundingly alike, both with regard to important or essential features (e.g. the jaws, dentition, and claws of a lion) and trivial features (e.g. the black furry tuft at the tip of the lion’s tail, or the lion's “beard”) [28]. It is almost inevitable that each interbreeding group will, in this way, very quickly develop its own characteristic appearance. An individual from one group who wanders into another group will consequently be recognized as being different, and will, therefore, be discriminated against during the mating season. This koinophilia-induced reproductive isolation might thus be the first crucial step in the development of, ultimately, physiological, anatomical and behavioral barriers to hybridization, and thus, ultimately, full specieshood. Koinophilia will thereafter defend that species' appearance and behavior against invasion by unusual or unfamiliar forms (which might arise by immigration or mutation), and thus be a paradigm of punctuated equilibria (or the "vertical" aspect of the speciation problem.[1][2]), and stabilizing selection.
Cooperation is any group behavior that benefits the individuals more than if they were to act as independent agents. There is, however, a second, very important, corollary to cooperation: it can always be exploited by selfish individuals who benefit even more by not taking part in the group activity, yet reaping its benefits. For instance, a selfish individual who does not join the hunting pack and its incumbent dangers but nevertheless shares in the spoils has a fitness advantage over the other members of the pack. Thus, although a group of cooperative individuals is fitter than an equivalent group of selfish individuals, selfish individuals interspersed amongst a community of cooperators are always fitter than their hosts. This means they raise, on average, more offspring and grandoffspring than their hosts, and will therefore ultimately replace them.
If, however, the selfish individuals are ostracized, and rejected as mates, because of their deviant and unusual behavior, then their evolutionary advantage becomes an evolutionary liability. Cooperation in all of its very many forms then becomes evolutionarily stable.[5][6] Sociability, social conventions, ritualistic behavior, the expressions of the emotions, and other forms of communication between individuals, all essential ingredients for full cooperativity, can all be similarly evolutionarily stabilized by koinophilia.
Co-operation or co-operative behaviours are terms used to describe behaviours by organisms which are beneficial to other organisms, and are selected for on that basis.[1] Under this definition, altruism is a form of co-operation in which there is no direct benefit to the actor (the organism carrying out the behaviour).[1] Co-operative behaviour in which there is a direct benefit to the actor as well as the recipient can be termed "mutually beneficial".[1] There are several theories which help to explain why natural selection favours some types of co-operative behaviour. They are not mutually exclusive, however, and more than one of the theories discussed below may contribute to explaining a particular case of co-operative behaviour. Note: This article uses British English. Standard U.S. English drops the hyphen resulting in cooperation or cooperative.
One well accepted explanation for altruistic behaviour (that is, co-operative behaviour which lacks a direct benefit for the actor) is the theory of kin selection. This theory suggests that individuals act co-operatively in order to help others which are genetically similar. Genes for such co-operative behaviour are preserved, because they help to perpetuate their own existence. The classic example is the social insects, such as bees and ants. Worker insects never reproduce, but instead, they work to allow the (genetically similar) queen to reproduce.
The theory of reciprocity suggests that individuals carry out co-operative behaviours because they get something in return. In order for such behaviours to be favoured, there needs to be some perception of external physical markers that the other individual will recognise (otherwise, there is no selective pressure to maintain the behaviour). Much research about reciprocity as leading to co-operation has concentrated on the 'prisoner's dilemma' known from game theory.
One theory suggesting a mechanism that could lead to the evolution of co-operation is the "market effect" as suggested by Noe and Hammerstein.[2] The mechanism relies on the fact that in many situations there exists a trade-off between efficiency obtaining a desired resource and the amount of resources one can actively obtain. In that case, each partner in a system could benefit from specializing in producing one specific resource and obtaining the other resource by trade. When only two partners exist, each can specialize in one resource, and trade for the other. Trading for the resource requires co-operation with the other partner and includes a process of bidding and bargaining.
This mechanism can be relied to both within a species or social group and within species systems. It can also be applied to a multi-partner system, in which the owner of a resource has the power to choose its co-operation partner. This model can be applied in natural systems (examples exist in the world of apes, cleaner fish, and more). Easy for exemplifying, though, are systems from international trading. Arabic countries control vast amounts of oil, but seek technologies from western countries. These in turn are in need of Arab oil. The solution is co-operation by trade.
Multi-level selection theory suggests that selection operates on more than one level: for example, it may operate at an atomic and molecular level in cells, at the level of cells in the body, and then again at the whole organism level, and the community level, and the species level. Any level which is not competitive with others of the same level will be eliminated, even if the level below is highly competitive. A classic example is that of genes which prevent cancer. Cancer cells divide uncontrollably, and at the cellular level, they are very successful, because they are (in the short term) reproducing very well and out competing other cells in the body. However, at the whole organism level, cancer is often fatal, and so may prevent reproduction. Therefore, changes to the genome which prevent cancer (for example, by causing damaged cells to act co-operatively by destroying themselves) are favoured. Multi-level selection theory contends that similar effects can occur, for example, to cause individuals to co-operate to avoid behaviours which favour themselves short-term, but destroy the community (and their descendants) long term.
Monday, March 7, 2011
Vole Love
Hmm... This is interesting.
http://loveatbrown.com/2010/04/02/vasopressin-a-vole-story/
Friggen cute bastards.
http://www.vivo.colostate.edu/hbooks/pathphys/endocrine/hypopit/adh.html
http://loveatbrown.com/2010/04/02/vasopressin-a-vole-story/
http://www.vivo.colostate.edu/hbooks/pathphys/endocrine/hypopit/adh.html
Sunday, March 6, 2011
Neutrinos make me hawt.
The neutrino and its friends
Neutrinos are one of the fundamental particles which make up the universe. They are also one of the least understood.Neutrinos are similar to the more familiar electron, with one crucial difference: neutrinos do not carry electric charge. Because neutrinos are electrically neutral, they are not affected by the electromagnetic forces which act on electrons. Neutrinos are affected only by a "weak" sub-atomic force of much shorter range than electromagnetism, and are therefore able to pass through great distances in matter without being affected by it. If neutrinos have mass, they also interact gravitationally with other massive particles, but gravity is by far the weakest of the four known forces.
Three types of neutrinos are known; there is strong evidence that no additional neutrinos exist, unless their properties are unexpectedly very different from the known types. Each type or "flavor" of neutrino is related to a charged particle (which gives the corresponding neutrino its name). Hence, the "electron neutrino" is associated with the electron, and two other neutrinos are associated with heavier versions of the electron called the muon and the tau (elementary particles are frequently labelled with Greek letters, to confuse the layman). The table below lists the known types of neutrinos (and their electrically charged partners).
Hawking Radiation
Why does Hawking radiation contains other particles?
'Thermal' does not mean only photons... What it means that you have a probability distribution for the energy of the particles, of the form of
Black holes radiate every kind of particle because all quantum fields behave in a similar way near the event horizon -- and why wouldn't they.
'Thermal' does not mean only photons... What it means that you have a probability distribution for the energy of the particles, of the form of
Black holes radiate every kind of particle because all quantum fields behave in a similar way near the event horizon -- and why wouldn't they.
The Stefan-Boltzmann constant can be expressed purely in terms of kB, h and c, so that makes me think that there is nothing special about photons or electromagnetism here. If you look at the Feynman diagram for vacuum fluctuations to produce a pair of photons, there is no electron involved, and no vertex at which an electron's world-line enters, so I think it makes sense that the rate of radiation is independent of e. Many of the other possibilities wouldn't seem to lead to any observable effects. For instance, electron-positron pairs could contribute, but there's no way you could observe them at a distance, because the positrons would annihilate with electrons before they could cross interstellar distances. I think E would have to be the mass-energy of the particle here, not just its kinetic energy. So unless the black hole is extremely small and hot, exp(E/T) should be extremely large for a particle of any significant mass. So the probability of emitting a neutron, etc., would be negligible except maybe for a black hole that was in its final burst of radiation. If I'm thinking straight this morning, I think the link between the basic thermodynamic expression 1/(exp(E/T)-1) for bosons and the standard blackbody curve requires counting the states of the photon field. For other types of bosons, e.g., bosons with mass or different spin, you'd have different statistics. In particular, you're not going to get emission that goes down to E=0 if the particle has nonzero rest mass, since E>=m. For fermions, you're going to get Fermi-Dirac statistics, with 1/(exp(E/T)+1). Neutrinos seems like the most reasonable candidate for something interesting. But the temperature of a solar-mass black hole is so low that I would expect the rate of emission of neutrinos to be essentially zero, since they do have nonzero rest mass. | |
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Wednesday, March 2, 2011
Walks
Yesterday, I decided to walk home from school. Which I just found to be over three miles. Yay!
On my walk, I was wondering if it's wrong to be pessimistic sometimes. I find myself to be a downer on occasion. However, when I think about being absolutely positive all the time, I get sick to my stomach. I feel that people that are always positive have no ability to empathize and are not logical. I decided being fifty-fifty is okay might still be bleak, but it could be worse.
On my walk, I was wondering if it's wrong to be pessimistic sometimes. I find myself to be a downer on occasion. However, when I think about being absolutely positive all the time, I get sick to my stomach. I feel that people that are always positive have no ability to empathize and are not logical. I decided being fifty-fifty is okay might still be bleak, but it could be worse.
I hate seeing one shoe on the ground.
I feel like this person was kidnapped and this is their last trace.
Ooo Scawy.
I love the pretty view of the city. Hod.
You know what else I love?
BUNGALOWS!!
Avocados for a dollar a piece. Mmmm... <3
Monday, February 28, 2011
I could run so far so fast away from this place.
Get me out of here.
I want to feel like I'm in the right place again....
http://www.youtube.com/watch?v=vwG7_hmVfJk
I want to feel like I'm in the right place again....
http://www.youtube.com/watch?v=vwG7_hmVfJk
Wednesday, February 23, 2011
Rawr
"Everything that happens is followed by something else which depends on it by causal necessity. Likewise, everything that happens is preceded by something with which it is causally connected. For nothing exists or has come into being in the cosmos without a cause. The universe will be disrupted and disintegrate into pieces and cease to be a unity functioning as a single system, if any uncaused movement is introduced into it." - Chrysippus
I don't enjoy when philosophers use fallacies.
I don't enjoy when philosophers use fallacies.
Sunday, February 13, 2011
Doing the Damn Thing.
Quotes of the day:
"Weakness of attitude becomes weakness of character."
and
"A person starts to live when he can live outside himself."
-Albert Einstein
Widdle Bio:
Albert Einstein was born at Ulm, in Württemberg, Germany, on March 14, 1879. Six weeks later the family moved to Munich, where he later on began his schooling at the Luitpold Gymnasium. Later, they moved to Italy and Albert continued his education at Aarau, Switzerland and in 1896 he entered the Swiss Federal Polytechnic School in Zurich to be trained as a teacher in physics and mathematics. In 1901, the year he gained his diploma, he acquired Swiss citizenship and, as he was unable to find a teaching post, he accepted a position as technical assistant in the Swiss Patent Office. In 1905 he obtained his doctor's degree.
During his stay at the Patent Office, and in his spare time, he produced much of his remarkable work and in 1908 he was appointed Privatdozent in Berne. In 1909 he became Professor Extraordinary at Zurich, in 1911 Professor of Theoretical Physics at Prague, returning to Zurich in the following year to fill a similar post. In 1914 he was appointed Director of the Kaiser Wilhelm Physical Institute and Professor in the University of Berlin. He became a German citizen in 1914 and remained in Berlin until 1933 when he renounced his citizenship for political reasons and emigrated to America to take the position of Professor of Theoretical Physics at Princeton*. He became a United States citizen in 1940 and retired from his post in 1945.
After World War II, Einstein was a leading figure in the World Government Movement, he was offered the Presidency of the State of Israel, which he declined, and he collaborated with Dr. Chaim Weizmann in establishing the Hebrew University of Jerusalem.
Einstein always appeared to have a clear view of the problems of physics and the determination to solve them. He had a strategy of his own and was able to visualize the main stages on the way to his goal. He regarded his major achievements as mere stepping-stones for the next advance.
At the start of his scientific work, Einstein realized the inadequacies of Newtonian mechanics and his special theory of relativity stemmed from an attempt to reconcile the laws of mechanics with the laws of the electromagnetic field. He dealt with classical problems of statistical mechanics and problems in which they were merged with quantum theory: this led to an explanation of the Brownian movement of molecules. He investigated the thermal properties of light with a low radiation density and his observations laid the foundation of the photon theory of light.
In his early days in Berlin, Einstein postulated that the correct interpretation of the special theory of relativity must also furnish a theory of gravitation and in 1916 he published his paper on the general theory of relativity. During this time he also contributed to the problems of the theory of radiation and statistical mechanics.
In the 1920's, Einstein embarked on the construction of unified field theories, although he continued to work on the probabilistic interpretation of quantum theory, and he persevered with this work in America. He contributed to statistical mechanics by his development of the quantum theory of a monatomic gas and he has also accomplished valuable work in connection with atomic transition probabilities and relativistic cosmology.
After his retirement he continued to work towards the unification of the basic concepts of physics, taking the opposite approach, geometrisation, to the majority of physicists.
Einstein's researches are, of course, well chronicled and his more important works include Special Theory of Relativity (1905), Relativity (English translations, 1920 and 1950), General Theory of Relativity (1916), Investigations on Theory of Brownian Movement (1926), and The Evolution of Physics (1938). Among his non-scientific works, About Zionism (1930), Why War? (1933), My Philosophy (1934), and Out of My Later Years (1950) are perhaps the most important.
Albert Einstein received honorary doctorate degrees in science, medicine and philosophy from many European and American universities. During the 1920's he lectured in Europe, America and the Far East and he was awarded Fellowships or Memberships of all the leading scientific academies throughout the world. He gained numerous awards in recognition of his work, including the Copley Medal of the Royal Society of London in 1925, and the Franklin Medal of the Franklin Institute in 1935.
Einstein's gifts inevitably resulted in his dwelling much in intellectual solitude and, for relaxation, music played an important part in his life. He married Mileva Maric in 1903 and they had a daughter and two sons; their marriage was dissolved in 1919 and in the same year he married his cousin, Elsa Löwenthal, who died in 1936. He died on April 18, 1955 at Princeton, New Jersey.
What does any of that mean?
Einstein's Special Theory of Relativity describes the motion of particles moving at close to the speed of light. In fact, it gives the correct laws of motion for any particle. This doesn't mean Newton was wrong, his equations are contained within the relativistic equations. Newton's "laws" provide a very good approximate form, valid when v is much less than c. For particles moving at slow speeds (very much less than the speed of light), the differences between Einstein's laws of motion and those derived by Newton are tiny. That's why relativity doesn't play a large role in everyday life. Einstein's theory supersedes Newton's, but Newton's theory provides a very good approximation for objects moving at everyday speeds.
Einstein's theory is now very well established as the correct description of motion of relativistic objects, that is those traveling at a significant fraction of the speed of light.
Because most of us have little experience with objects moving at speeds near the speed of light, Einstein's predictions may seem strange. However, many years of high energy physics experiments have thoroughly tested Einstein's theory and shown that it fits all results to date.
Note that this is quite different from the motion of ordinary, massive objects. If I am driving down the freeway at 50 miles per hour relative to the road, a car traveling in the same direction at 55 mph has a speed of only 5 mph relative to me, while a car coming in the opposite direction at 55 mph approaches me at a rate of 105 mph. Their speed relative to me depends on my motion as well as on theirs.
Einstein developed a theory of motion that could consistently contain both the same speed of light for any observer and the familiar addition of velocities described above for slow-moving objects. This is called the special theory of relativity, since it deals with the relative motions of objects.
Note that Einstein's General Theory of Relativity is a separate theory about a very different topic -- the effects of gravity.
Gamma(
The measurable effects of relativity are based on gamma. Gamma depends only on the speed of a particle and is always larger than 1. By definition:
For example, when an electron has traveled ten feet along the accelerator it has a speed of 0.99c, and the value of gamma at that speed is 7.09. When the electron reaches the end of the linac, its speed is 0.99999999995c where gamma equals 100,000.
What do these gamma values tell us about the relativistic effects detected at SLAC? Notice that when the speed of the object is very much less than the speed of light (v << c), gamma is approximately equal to 1. This is a non-relativistic situation (Newtonian).
Notice that this equation tells you that for any particle with a non-zero mass, the momentum gets larger and larger as the speed gets closer to the speed of light. Such a particle would have infinite momentum if it could reach the speed of light. Since it would take an infinite amount of force (or a finite force acting over an infinite amount of time) to accelerate a particle to infinite momentum, we are forced to conclude that a massive particle always travels at speeds less than the speed of light.
Some text books will introduce the definition m0 for the mass of an object at rest, calling this the "rest mass" and define the quantity (M = gamma m0) as the mass of the moving object. This makes Newton's definition of momentum still true provided you choose the correct mass. In particle physics, when we talk about mass we always mean mass of an object at rest and we write it as m and keep the factor of gamma explicit in the equations.
This tells us the energy corresponding to a mass m at rest. What this means is that when mass disappears, for example in a nuclear fission process, this amount of energy must appear in some other form. It also tells us the total energy of a particle of mass m sitting at rest.
Einstein also showed that the correct relativistic expression for the energy of a particle of mass m with momentum p is E2 = m2c4 + p2c2. This is a key equation for any real particle, giving the relationship between its energy (E), momentum ( p), and its rest mass (m).
If we substitute the equation for p into the equation for E above, with a little algebra, we get E = gamma mc2, so energy is gamma times rest energy. (Notice again that if we call the quantity M =gamma m the mass of the particle then E = Mc2 applies for any particle, but remember, particle physicists don't do that.)
Let's do a calculation. The rest energy of an electron is 0.511 MeV. As we saw earlier, when an electron has gone about 10 feet along the SLAC linac, it has a speed of 0.99c and a gamma of 7.09. Therefore, using the equation E = gamma x the rest energy, we can see that the electron's energy after ten feet of travel is 7.09 x 0.511 MeV = 3.62 MeV. At the end of the linac, where gamma = 100,000, the energy of the electron is 100,000 x 0.511 MeV = 51.1 GeV.
The energy E is the total energy of a freely moving particle. We can define it to be the rest energy plus kinetic energy (E = KE + mc2) which then defines a relativistic form for kinetic energy. Just as the equation for momentum has to be altered, so does the low-speed equation for kinetic energy (KE = (1/2)mv2). Let's make a guess based on what we saw for momentum and energy and say that relativistically KE = gamma(1/2)mv2. A good guess, perhaps, but it's wrong.
Now here is an exercise for the interested reader. Calculate the quantity KE = E - mc2 for the case of v very much smaller than c, and show that it is the usual expression for kinetic energy (1/2 mv2) plus corrections that are proportional to (v/c)2 and higher powers of (v/c). The complicated result of this exercise points out why it is not useful to separate the energy of a relativistic particle into a sum of two terms, so when particle physicists say "the energy of a moving particle" they mean the total energy, not the kinetic energy.
Another interesting fact about the expression that relates E and p above (E2 = m2c4 + p2c2), is that it is also true for the case where a particle has no mass (m=0). In this case, the particle always travels at a speed c, the speed of light. You can regard this equation as a definition of momentum for such a mass-less particle. Photons have kinetic energy and momentum, but no mass!
In fact Einstein's relationship tells us more, it says Energy and mass are interchangeable. Or, better said, rest mass is just one form of energy. For a compound object, the mass of the composite is not just the sum of the masses of the constituents but the sum of their energies, including kinetic, potential, and mass energy. The equation E=mc2 shows how to convert between energy units and mass units. Even a small mass corresponds to a significant amount of energy.
At SLAC, and in any particle physics facility, we also see the reverse effect -- energy producing new matter. In the presence of charged particles a photon (which only has kinetic energy) can change into a massive particle and its matching massive antiparticle. The extra charged particle has to be there to absorb a little energy and more momentum, otherwise such a process could not conserve both energy and momentum. This process is one more confirmation of Einstein's special theory of relativity. It also is the process by which antimatter (for example the positrons accelerated at SLAC) is produced.
Lets look at an example of how this energy unit works. The rest mass of an electron is 9.11 x 10-31 kg. Using E = mc2 and a calculator we get:
So if you ask a high energy physicist what the mass of an electron is, you'll be told the answer in units of energy. You can blame Einstein for that!
Eagle-eyed readers will notice that if you solve E=mc2 for m, you get m=E/c2, so the unit of energy should be eV/c2. What happened to the c2? It's very simple, particle physicists choose units of length so that the speed of light = 1! How can we do that? Quite easily, as long as everyone understands the system. All we have to do is use a conversion factor to get back the "real" (i.e. everyday) units, if we want them.
Not only are mass and energy measured in eV, so is momentum. It makes life so much easier than dividing by c2 or c all the time.
There is more information available on units in relativistic physics.
Consider two observers, each in a space-ship laboratory containing clocks and meter sticks. The space ships are moving relative to each other at a speed close to the speed of light. Using Einstein's theory:
For example, let's look at a particle sometimes created at SLAC known as a tau. In the frame of reference where the tau particle is at rest, its lifetime is known to be approximately 3.05 x 10-13 s. To calculate how far it travels before decaying, we could try to use the familiar equation distance equals speed times time. It travels so close to the speed of light that we can use c = 3x108 m/sec for the speed of the particle. (As we will see below, the speed of light in a vacuum is the highest speed attainable.) If you do the calculation you find the distance traveled should be 9.15 x 10-5 meters.
Pause to think about that for a moment. This result is totally contradictory to everyday experience. If you are not puzzled by it, either you already know all about relativity or you have not been reading carefully.
What is the resolution of this apparent paradox? The answer lies in time dilation. In our laboratory, the tau particle is moving. The decay time of the tau can be seen as a moving clock. According to relativity, moving clocks tick more slowly than static clocks.
We use this fact to multiply the time of travel in the taus moving frame by gamma, this gives the time that we will measure. Then this time times c, the approximate speed of the tau, will give us the distance we expect a high energy tau to travel.
What is gamma in this case? It depends on the tau's energy. A typical SLAC tau particle has a gamma = 20. Therefore, we detect the tau to decay in an average distance of 20 x (9.15 x 10-5 m) = 1.8 x 10-3 m or approximately 1.8 millimeters. This is 20 times further than we expect it to go if we use classical rather than relativistic physics. (Of course, we actually observe a spread of decay times according to the exponential decay law and a corresponding spread of distances. In fact, we use the measured distribution of distances to find the tau half-life.)
Observations particles with a variety of velocities have shown that time dilation is a real effect. In fact the only reason cosmic ray muons ever reach the surface of the earth before decaying is the time dilation effect.
How far would an observer, sitting in the tau rest frame, see an observer in our laboratory frame move while the tau lives?
We just calculated that the tau would travel 1.8 mm in our frame of reference. Surely we would expect the observer in the tau frame to see us move the same distance relative to the tau particle. Not so says the tau-frame observer -- you only moved 1.8 mm/gamma = 0.09 mm relative to me. This is length contraction.
How long did the tau particle live according to the observer in the tau frame? We can rearrange d = v x t to read t = d/v. Here we use the same speed, Because the speed of the observer in the lab relative to the tau is just equal to (but in the opposite direction) of the speed of the tau relative to the observer in the lab, so we can use the same speed. So time = 0.09 x 10-3 m/(3 x 108)m/sec = 3.0 x 10-13 sec. This is the half-life of the tau as seen in its rest frame, just as it should be!
A great relativity website: http://webs.morningside.edu/slaven/physics/relativity/index.html
Conclusion:
I love this guy.
"Weakness of attitude becomes weakness of character."
and
"A person starts to live when he can live outside himself."
-Albert Einstein
Widdle Bio:
Albert Einstein was born at Ulm, in Württemberg, Germany, on March 14, 1879. Six weeks later the family moved to Munich, where he later on began his schooling at the Luitpold Gymnasium. Later, they moved to Italy and Albert continued his education at Aarau, Switzerland and in 1896 he entered the Swiss Federal Polytechnic School in Zurich to be trained as a teacher in physics and mathematics. In 1901, the year he gained his diploma, he acquired Swiss citizenship and, as he was unable to find a teaching post, he accepted a position as technical assistant in the Swiss Patent Office. In 1905 he obtained his doctor's degree.
During his stay at the Patent Office, and in his spare time, he produced much of his remarkable work and in 1908 he was appointed Privatdozent in Berne. In 1909 he became Professor Extraordinary at Zurich, in 1911 Professor of Theoretical Physics at Prague, returning to Zurich in the following year to fill a similar post. In 1914 he was appointed Director of the Kaiser Wilhelm Physical Institute and Professor in the University of Berlin. He became a German citizen in 1914 and remained in Berlin until 1933 when he renounced his citizenship for political reasons and emigrated to America to take the position of Professor of Theoretical Physics at Princeton*. He became a United States citizen in 1940 and retired from his post in 1945.
After World War II, Einstein was a leading figure in the World Government Movement, he was offered the Presidency of the State of Israel, which he declined, and he collaborated with Dr. Chaim Weizmann in establishing the Hebrew University of Jerusalem.
Einstein always appeared to have a clear view of the problems of physics and the determination to solve them. He had a strategy of his own and was able to visualize the main stages on the way to his goal. He regarded his major achievements as mere stepping-stones for the next advance.
At the start of his scientific work, Einstein realized the inadequacies of Newtonian mechanics and his special theory of relativity stemmed from an attempt to reconcile the laws of mechanics with the laws of the electromagnetic field. He dealt with classical problems of statistical mechanics and problems in which they were merged with quantum theory: this led to an explanation of the Brownian movement of molecules. He investigated the thermal properties of light with a low radiation density and his observations laid the foundation of the photon theory of light.
In his early days in Berlin, Einstein postulated that the correct interpretation of the special theory of relativity must also furnish a theory of gravitation and in 1916 he published his paper on the general theory of relativity. During this time he also contributed to the problems of the theory of radiation and statistical mechanics.
In the 1920's, Einstein embarked on the construction of unified field theories, although he continued to work on the probabilistic interpretation of quantum theory, and he persevered with this work in America. He contributed to statistical mechanics by his development of the quantum theory of a monatomic gas and he has also accomplished valuable work in connection with atomic transition probabilities and relativistic cosmology.
After his retirement he continued to work towards the unification of the basic concepts of physics, taking the opposite approach, geometrisation, to the majority of physicists.
Einstein's researches are, of course, well chronicled and his more important works include Special Theory of Relativity (1905), Relativity (English translations, 1920 and 1950), General Theory of Relativity (1916), Investigations on Theory of Brownian Movement (1926), and The Evolution of Physics (1938). Among his non-scientific works, About Zionism (1930), Why War? (1933), My Philosophy (1934), and Out of My Later Years (1950) are perhaps the most important.
Albert Einstein received honorary doctorate degrees in science, medicine and philosophy from many European and American universities. During the 1920's he lectured in Europe, America and the Far East and he was awarded Fellowships or Memberships of all the leading scientific academies throughout the world. He gained numerous awards in recognition of his work, including the Copley Medal of the Royal Society of London in 1925, and the Franklin Medal of the Franklin Institute in 1935.
Einstein's gifts inevitably resulted in his dwelling much in intellectual solitude and, for relaxation, music played an important part in his life. He married Mileva Maric in 1903 and they had a daughter and two sons; their marriage was dissolved in 1919 and in the same year he married his cousin, Elsa Löwenthal, who died in 1936. He died on April 18, 1955 at Princeton, New Jersey.
What does any of that mean?
Special Relativity
Newton's laws of motion give us a complete description of the behavior moving objects at low speeds. The laws are different at speeds reached by the particles at SLAC.Einstein's Special Theory of Relativity describes the motion of particles moving at close to the speed of light. In fact, it gives the correct laws of motion for any particle. This doesn't mean Newton was wrong, his equations are contained within the relativistic equations. Newton's "laws" provide a very good approximate form, valid when v is much less than c. For particles moving at slow speeds (very much less than the speed of light), the differences between Einstein's laws of motion and those derived by Newton are tiny. That's why relativity doesn't play a large role in everyday life. Einstein's theory supersedes Newton's, but Newton's theory provides a very good approximation for objects moving at everyday speeds.
Einstein's theory is now very well established as the correct description of motion of relativistic objects, that is those traveling at a significant fraction of the speed of light.
Because most of us have little experience with objects moving at speeds near the speed of light, Einstein's predictions may seem strange. However, many years of high energy physics experiments have thoroughly tested Einstein's theory and shown that it fits all results to date.
Theoretical Basis for Special Relativity
Einstein's theory of special relativity results from two statements -- the two basic postulates of special relativity:- The speed of light is the same for all observers, no matter what their relative speeds.
- The laws of physics are the same in any inertial (that is, non-accelerated) frame of reference. This means that the laws of physics observed by a hypothetical observer traveling with a relativistic particle must be the same as those observed by an observer who is stationary in the laboratory.
The Speed of Light is the same for all observers.
The first postulate -- the speed of light will be seen to be the same relative to any observer, independent of the motion of the observer -- is the crucial idea that led Einstein to formulate his theory. It means we can define a quantity c, the speed of light, which is a fundamental constant of nature.Note that this is quite different from the motion of ordinary, massive objects. If I am driving down the freeway at 50 miles per hour relative to the road, a car traveling in the same direction at 55 mph has a speed of only 5 mph relative to me, while a car coming in the opposite direction at 55 mph approaches me at a rate of 105 mph. Their speed relative to me depends on my motion as well as on theirs.
Physics is the same for all inertial observers.
This second postulate is really a basic though unspoken assumption in all of science -- the idea that we can formulate rules of nature which do not depend on our particular observing situation. This does not mean that things behave in the same way on the earth and in space, e.g. an observer at the surface of the earth is affected by the earth's gravity, but it does mean that the effect of a force on an object is the same independent of what causes the force and also of where the object is or what its speed is.Einstein developed a theory of motion that could consistently contain both the same speed of light for any observer and the familiar addition of velocities described above for slow-moving objects. This is called the special theory of relativity, since it deals with the relative motions of objects.
Note that Einstein's General Theory of Relativity is a separate theory about a very different topic -- the effects of gravity.
Relativistic Definitions
Physicists call particles with v/c comparable to 1 "relativistic" particles. Particles with v/c << 1 (very much less than one) are "non-relativistic." At SLAC, we are almost always dealing with relativistic particles. Below we catalogue some essential differences between the relativistic quantities the more familiar non-relativistic or low-speed approximate definitions and behaviors.Gamma(
)
The measurable effects of relativity are based on gamma. Gamma depends only on the speed of a particle and is always larger than 1. By definition: | c is the speed of light v is the speed of the object in question |
What do these gamma values tell us about the relativistic effects detected at SLAC? Notice that when the speed of the object is very much less than the speed of light (v << c), gamma is approximately equal to 1. This is a non-relativistic situation (Newtonian).
Momentum
For non-relativistic objects Newton defined momentum, given the symbol p, as the product of mass and velocity -- p = m v. When speed becomes relativistic, we have to modify this definition -- p = gamma (mv)Notice that this equation tells you that for any particle with a non-zero mass, the momentum gets larger and larger as the speed gets closer to the speed of light. Such a particle would have infinite momentum if it could reach the speed of light. Since it would take an infinite amount of force (or a finite force acting over an infinite amount of time) to accelerate a particle to infinite momentum, we are forced to conclude that a massive particle always travels at speeds less than the speed of light.
Some text books will introduce the definition m0 for the mass of an object at rest, calling this the "rest mass" and define the quantity (M = gamma m0) as the mass of the moving object. This makes Newton's definition of momentum still true provided you choose the correct mass. In particle physics, when we talk about mass we always mean mass of an object at rest and we write it as m and keep the factor of gamma explicit in the equations.
Energy
Probably the most famous scientific equation of all time, first derived by Einstein is the relationship E = mc2.This tells us the energy corresponding to a mass m at rest. What this means is that when mass disappears, for example in a nuclear fission process, this amount of energy must appear in some other form. It also tells us the total energy of a particle of mass m sitting at rest.
Einstein also showed that the correct relativistic expression for the energy of a particle of mass m with momentum p is E2 = m2c4 + p2c2. This is a key equation for any real particle, giving the relationship between its energy (E), momentum ( p), and its rest mass (m).
If we substitute the equation for p into the equation for E above, with a little algebra, we get E = gamma mc2, so energy is gamma times rest energy. (Notice again that if we call the quantity M =gamma m the mass of the particle then E = Mc2 applies for any particle, but remember, particle physicists don't do that.)
Let's do a calculation. The rest energy of an electron is 0.511 MeV. As we saw earlier, when an electron has gone about 10 feet along the SLAC linac, it has a speed of 0.99c and a gamma of 7.09. Therefore, using the equation E = gamma x the rest energy, we can see that the electron's energy after ten feet of travel is 7.09 x 0.511 MeV = 3.62 MeV. At the end of the linac, where gamma = 100,000, the energy of the electron is 100,000 x 0.511 MeV = 51.1 GeV.
The energy E is the total energy of a freely moving particle. We can define it to be the rest energy plus kinetic energy (E = KE + mc2) which then defines a relativistic form for kinetic energy. Just as the equation for momentum has to be altered, so does the low-speed equation for kinetic energy (KE = (1/2)mv2). Let's make a guess based on what we saw for momentum and energy and say that relativistically KE = gamma(1/2)mv2. A good guess, perhaps, but it's wrong.
Now here is an exercise for the interested reader. Calculate the quantity KE = E - mc2 for the case of v very much smaller than c, and show that it is the usual expression for kinetic energy (1/2 mv2) plus corrections that are proportional to (v/c)2 and higher powers of (v/c). The complicated result of this exercise points out why it is not useful to separate the energy of a relativistic particle into a sum of two terms, so when particle physicists say "the energy of a moving particle" they mean the total energy, not the kinetic energy.
Another interesting fact about the expression that relates E and p above (E2 = m2c4 + p2c2), is that it is also true for the case where a particle has no mass (m=0). In this case, the particle always travels at a speed c, the speed of light. You can regard this equation as a definition of momentum for such a mass-less particle. Photons have kinetic energy and momentum, but no mass!
In fact Einstein's relationship tells us more, it says Energy and mass are interchangeable. Or, better said, rest mass is just one form of energy. For a compound object, the mass of the composite is not just the sum of the masses of the constituents but the sum of their energies, including kinetic, potential, and mass energy. The equation E=mc2 shows how to convert between energy units and mass units. Even a small mass corresponds to a significant amount of energy.
- In the case of an atomic explosion, mass energy is released as kinetic energy of the resulting material, which has slightly less mass than the original material.
- In any particle decay process, some of the initial mass energy becomes kinetic energy of the products.
At SLAC, and in any particle physics facility, we also see the reverse effect -- energy producing new matter. In the presence of charged particles a photon (which only has kinetic energy) can change into a massive particle and its matching massive antiparticle. The extra charged particle has to be there to absorb a little energy and more momentum, otherwise such a process could not conserve both energy and momentum. This process is one more confirmation of Einstein's special theory of relativity. It also is the process by which antimatter (for example the positrons accelerated at SLAC) is produced.
Units of Mass, Energy, and Momentum
Instead of using kilograms to measure mass, physicists use a unit of energy -- the electron volt. It is the energy gained by one electron when it moves through a potential difference of one volt. By definition, one electron volt (eV) is equivalent to 1.6 x 10-19 joules.Lets look at an example of how this energy unit works. The rest mass of an electron is 9.11 x 10-31 kg. Using E = mc2 and a calculator we get:
E = 9.11 x 10-31 kg x (3 x 108 m/s)2 = 8.199 x 10-14 joules
This gives us the energy equivalent of one electron. So, whether we say we have 9.11 x 10-31 kg or 8.199 x 10-14 joules, we really talking about the same thing -- an electron. Physicists go one stage further and convert the joules to electron volts. This gives the mass of an electron as 0.511 MeV (about half a million eV). So if you ask a high energy physicist what the mass of an electron is, you'll be told the answer in units of energy. You can blame Einstein for that!
Eagle-eyed readers will notice that if you solve E=mc2 for m, you get m=E/c2, so the unit of energy should be eV/c2. What happened to the c2? It's very simple, particle physicists choose units of length so that the speed of light = 1! How can we do that? Quite easily, as long as everyone understands the system. All we have to do is use a conversion factor to get back the "real" (i.e. everyday) units, if we want them.
Not only are mass and energy measured in eV, so is momentum. It makes life so much easier than dividing by c2 or c all the time.
There is more information available on units in relativistic physics.
Peculiar Relativistic Effects
Length Contraction and Time Dilation
One of the strangest parts of special relativity is the conclusion that two observers who are moving relative to one another, will get different measurements of the length of a particular object or the time that passes between two events.Consider two observers, each in a space-ship laboratory containing clocks and meter sticks. The space ships are moving relative to each other at a speed close to the speed of light. Using Einstein's theory:
- Each observer will see the meter stick of the other as shorter than their own, by the same factor gamma (
- Each observer will see the clocks in the other laboratory as ticking more slowly than the clocks in his/her own, by a factor gamma. This is called time dilation.
Time Dilation for Particles
Particle processes have an intrinsic clock that determines the half-life of a decay process. However, the rate at which the clock ticks in a moving frame, as observed by a static observer, is slower than the rate of a static clock. Therefore, the half-life of a moving particles appears, to the static observer, to be increased by the factor gamma.For example, let's look at a particle sometimes created at SLAC known as a tau. In the frame of reference where the tau particle is at rest, its lifetime is known to be approximately 3.05 x 10-13 s. To calculate how far it travels before decaying, we could try to use the familiar equation distance equals speed times time. It travels so close to the speed of light that we can use c = 3x108 m/sec for the speed of the particle. (As we will see below, the speed of light in a vacuum is the highest speed attainable.) If you do the calculation you find the distance traveled should be 9.15 x 10-5 meters.
d = v t
d = (3 x 108 m/sec)( 3.05 x 10-13 s) = 9.15 x 10-5 m
Here comes the weird part - we measure the tau particle to travel further than this!Pause to think about that for a moment. This result is totally contradictory to everyday experience. If you are not puzzled by it, either you already know all about relativity or you have not been reading carefully.
What is the resolution of this apparent paradox? The answer lies in time dilation. In our laboratory, the tau particle is moving. The decay time of the tau can be seen as a moving clock. According to relativity, moving clocks tick more slowly than static clocks.
We use this fact to multiply the time of travel in the taus moving frame by gamma, this gives the time that we will measure. Then this time times c, the approximate speed of the tau, will give us the distance we expect a high energy tau to travel.
What is gamma in this case? It depends on the tau's energy. A typical SLAC tau particle has a gamma = 20. Therefore, we detect the tau to decay in an average distance of 20 x (9.15 x 10-5 m) = 1.8 x 10-3 m or approximately 1.8 millimeters. This is 20 times further than we expect it to go if we use classical rather than relativistic physics. (Of course, we actually observe a spread of decay times according to the exponential decay law and a corresponding spread of distances. In fact, we use the measured distribution of distances to find the tau half-life.)
Observations particles with a variety of velocities have shown that time dilation is a real effect. In fact the only reason cosmic ray muons ever reach the surface of the earth before decaying is the time dilation effect.
Length Contraction
Instead of analyzing the motion of the tau from our frame of reference, we could ask what the tau would see in its reference frame. Its half-life in its reference frame is 3.05 x 10-13 s. This does not change. The tau goes nowhere in this frame.How far would an observer, sitting in the tau rest frame, see an observer in our laboratory frame move while the tau lives?
We just calculated that the tau would travel 1.8 mm in our frame of reference. Surely we would expect the observer in the tau frame to see us move the same distance relative to the tau particle. Not so says the tau-frame observer -- you only moved 1.8 mm/gamma = 0.09 mm relative to me. This is length contraction.
How long did the tau particle live according to the observer in the tau frame? We can rearrange d = v x t to read t = d/v. Here we use the same speed, Because the speed of the observer in the lab relative to the tau is just equal to (but in the opposite direction) of the speed of the tau relative to the observer in the lab, so we can use the same speed. So time = 0.09 x 10-3 m/(3 x 108)m/sec = 3.0 x 10-13 sec. This is the half-life of the tau as seen in its rest frame, just as it should be!
A great relativity website: http://webs.morningside.edu/slaven/physics/relativity/index.html
Conclusion:
Attraction
This will be my first post, because it is the absolute most mind-blowing and odd thing about any of us.
Attraction: the force by which one object attracts another
wordnetweb.princeton.edu/perl/webwn
Why is this primarily a physical thing? Why haven't we seen through this yet?
It's like people that think puppy dogs are cute, but don't like dogs... Well, how was their cuteness effective in this situation?
None. Zip. Nada.
I want to be attracted to someone because what spills out of their mouth is something I long to hear.
End of story.
I don't want to be attracted to someone because they count calories and go to the gym.
I hope that they are healthy, so they feel good. Not fanatical about their physical appearance.
There's no fun in that.
So, why do I feel alone on board of the mind vs. matter ship?
Secondly, what kind of force (daddy issues would be my guess) would make it seem okay for girls to stand around half naked and have pictures taken of them?!?
Attraction: the force by which one object attracts another
wordnetweb.princeton.edu/perl/webwn
Why is this primarily a physical thing? Why haven't we seen through this yet?
It's like people that think puppy dogs are cute, but don't like dogs... Well, how was their cuteness effective in this situation?
None. Zip. Nada.
I want to be attracted to someone because what spills out of their mouth is something I long to hear.
End of story.
I don't want to be attracted to someone because they count calories and go to the gym.
I hope that they are healthy, so they feel good. Not fanatical about their physical appearance.
There's no fun in that.
So, why do I feel alone on board of the mind vs. matter ship?
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