tag:blogger.com,1999:blog-22977686383711569522024-03-12T23:35:44.024-07:00 Hasan's Thoughts DissectedA blog about everything (and everything in between). Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.comBlogger140125tag:blogger.com,1999:blog-2297768638371156952.post-89200274983602354222015-09-12T23:48:00.000-07:002015-09-12T23:48:41.296-07:00Where do the laws of Nature come from? <div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd9pEG9awxkv6izLNklGiubhn0pxAmCqZ4oNNj3IIKA9VQYL9Q2ZvbvbLb5bGBEoui1RzjdwrJ7CpM2hUbWGhOocZOSiHEAAzo2bprLThH3SkbEp5OrPIHKQqQuYjRcxcp4WgI-GuATy3g/s1600/sm_DSC06394.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd9pEG9awxkv6izLNklGiubhn0pxAmCqZ4oNNj3IIKA9VQYL9Q2ZvbvbLb5bGBEoui1RzjdwrJ7CpM2hUbWGhOocZOSiHEAAzo2bprLThH3SkbEp5OrPIHKQqQuYjRcxcp4WgI-GuATy3g/s320/sm_DSC06394.jpg" width="320" /></a></div>
Einstein famously said that “The most incomprehensible thing about the world is that it is comprehensible.”<a href="http://books.google.com.au/books?id=cdxWNE7NY6QC&lpg=PP1&pg=PA628&redir_esc=y#v=onepage&q&f=false"> [1]</a> And that very discovery, that we inhabit a universe governed by unbreakable patterns or ‘laws’ is a triumph of the scientific enterprise. Unlike the laws of Australia or America, the laws of physics appear to be descriptions rather than rules; in such a light, what would it mean to say that nature “obeys” or follows the “laws” that we have written down in our textbooks?<br /><br />This brings us to the ontological/metaphysical status of these ‘laws’. Since humans are pattern seekers who cannot help but anthropomorphise their surroundings, the question arises as to whether these principles are actually ‘written into’ the structure of reality, have an objective existence of their own (Platonism) or are simply human inventions/generalisations. To paraphrase Stephen Hawking, what is it that breathes fire into the Equations?<a href="https://books.google.com.au/books?id=rjLTsncFKCgC&pg=PT427&dq=What+is+it+that+breathes+fire+into+the+equations+brief+history+of+time&hl=en&sa=X&ei=AP6sVN3qDsKMmwWCuIK4DQ&ved=0CCgQ6AEwAg#v=onepage&q=What%20is%20it%20that%20breathes%20fire%20into%20the%20equations%20brief%20history%20of%20time&f=false"> [2]</a> Where do the laws of physics “come from”?<br /><br />The concept of a ‘law’ owes its origins to geometry and theology. In geometry, laws describe the dynamics of bodies (like Euclid’s axioms and postulates) and it was God who employed them to govern their motions. However, as a naturalistic understanding of the world progressed, the role of God in governing the universe via such laws was largely abandoned (or made redundant). Nevertheless, this underlying metaphor of “governance” remained.<br /><br />Broadly speaking, there are two competing metaphysical accounts of laws of physics; the former is a prescriptive view while the latter is descriptive:<br /><br />1. The Governing View: the laws of physics are an intrinsic part of reality that govern and explain the evolution of physical systems. (Armstrong, Maudlin, Ellis, Vilenkin, Krauss)<br /><br />2. The Summarising View: the laws of physics are certain theorems of the scientifically best systematic summary of the motions of particles, fields, etc. throughout space/time (Mill, Ramsey, Lewis, Loewer, Carroll). Interestingly this view also presupposes a 4D block universe view, hence the laws never "began to exist" and do not need to be "put in" or created as an initial condition. <br /><br />Now that we have a metaphysical framework for understanding what the laws of Nature are/where they “come from” (namely the BSA approach), a further query arises: why do the laws of physics take the form they do? For example, why do opposite charges attract, while like charges repel? Why is there an inverse square law rather than an inverse cube law? And so on…<br /><br />The answer is surprisingly simple: symmetry.<br /><br />As Sean Carroll notes <a href="http://arxiv.org/pdf/hep-th/0512148v1.pdf">[4]</a><br /><br /><blockquote class="tr_bq">
<i>The dynamical laws of nature at the microscopic level (including general relativity and the Standard Model of particle physics) are tightly constrained in the form that they may take, largely by symmetry principles such as gauge invariance and Lorentz invariance. The specific values of the numerical parameters of these theories are in principle arbitrary, although on naturalness grounds we would expect mass/energy scales to be roughly comparable to each other. [emphasis added]</i></blockquote>
<br />To be continued…Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com1tag:blogger.com,1999:blog-2297768638371156952.post-58989661691885090342014-07-26T02:35:00.000-07:002014-07-27T17:07:59.661-07:00Welcome to my site...<a href="http://static.squarespace.com/static/505f74c284ae5d07533fa2a6/t/514cb2a8e4b00a487d4155c0/1363980969324/Recycled-Wood-Welcome-Sign.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" class="irc_mi" src="http://static.squarespace.com/static/505f74c284ae5d07533fa2a6/t/514cb2a8e4b00a487d4155c0/1363980969324/Recycled-Wood-Welcome-Sign.jpg" height="208" style="margin-top: 11px;" width="320" /></a>Welcome to <i><b>Hasan's Thoughts Dissected</b></i>. You will find a panoply of articles on a range of topics and questions concerning human existence, knowledge and empirical inquiry. Most posts are organised under the following major subcategories:<br />
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<b>Click links below to view posts...</b></div>
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<b><a href="http://hasansthoughts.blogspot.com.au/search/label/Evolution">Evolution:</a></b> Exploring the diversity and history of life on earth; the evidence for common ancestry, macroevolutionary transitions, phylogenetics and special topics such as the evolution of social behaviour.<br />
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<b><a href="http://hasansthoughts.blogspot.com.au/search/label/Origin%20of%20Life">Origin of Life:</a></b> Building together a unified view of prebiotic chemistry; open problems in abiogenesis research and models of the origin of life including (but not excluded to) the RNA world, Iron-Suplhur world, the origin of biological information and other big ideas<br />
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<b><a href="http://hasansthoughts.blogspot.com.au/search/label/Cosmology">Cosmology:</a></b> Probing the origins, evolution and large scale structure of the observable universe and beyond. Topics include the formation of structure, quantum gravity, general relativity, the cosmic microwave background, inflation and speculative theories of the universe.<br />
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<b><a href="http://hasansthoughts.blogspot.com.au/search/label/Theoretical%20Physics">Theoretical Physics: </a></b>An inquiry into the fundamental nature of small-scale and high-energy physics: includes quantum mechanics, quantum field theory, string theory, supersymmetry and beyond. Investigation of particles, forces, symmetries and field theories with experimental and phenomenological implications.<br />
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<b><a href="http://hasansthoughts.blogspot.com.au/search/label/Philosophy%20of%20Mind">Philosophy of Mind:</a></b> Controversies regarding consciousness and mental states: a discussion of major schools of thought, physicalism vs non-physicalism, the hard problem of qualia, elimitivism, behaviourism, functionalism and more.<br />
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<b><a href="http://hasansthoughts.blogspot.com.au/search/label/Philosophy%20of%20Religion">Philosophy of Religion:</a> </b>A critique of popular and scholarly arguments for the existence of God(s). Implications of the naturalism vs. theism debate and open problems in professional theology.<br />
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<b><a href="http://hasansthoughts.blogspot.com.au/search/label/Psychology" target="_blank">Psychology:</a> </b> An introduction to influential ideas in modern psychology and cognitive science; an encounter with major figures and thinkers. Review articles on mental development, intelligence, personality, sociology and mental disorders.<br />
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<b><a href="http://hasansthoughts.blogspot.com.au/search/label/Pseudoscience" target="_blank">Pseudoscience:</a> </b><b> </b>Debunking claims of creationists, the intelligent design community and popular hoaxes.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-57364988617370674732014-07-25T23:47:00.002-07:002014-07-26T02:33:59.555-07:00Common Ancestry: An Introduction<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
A central tenet of
evolutionary biology is the notion of common ancestry. The theory of descent
with modification ultimately connects all organisms to a single common
ancestor. Humans, butterflies, lettuce, and bacteria all trace their lineages
back to the same primordial stock. The crucial evidence for universal common
ancestry includes homology.<o:p></o:p></div>
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<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b>Why Common Ancestry
Matters</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPIGrFx3KKNWFHj6be7-IBBINTJPZAN4o02OgB9VkUyhjJA6kQ_xEnuVwixYyd8y2EgucxHrOYWEnjU3R0Kd4Cv7DyKzPWs0GQP-Gur73DtvFFf-yJsQmM6WWEaMsaf_rC_IWIZHL8iMa8/s1600/acrobatscreensnapz002.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPIGrFx3KKNWFHj6be7-IBBINTJPZAN4o02OgB9VkUyhjJA6kQ_xEnuVwixYyd8y2EgucxHrOYWEnjU3R0Kd4Cv7DyKzPWs0GQP-Gur73DtvFFf-yJsQmM6WWEaMsaf_rC_IWIZHL8iMa8/s1600/acrobatscreensnapz002.png" height="256" width="320" /></a>Common ancestry is
the conceptual foundation upon which all of modern biology, including
biomedical science, is built. Because we are descended from the same ancestral
lineage as monkeys, mice, baker’s yeast, and even bacteria, we share with these
organisms numerous homologies in the internal machinery of our cells. This is
why studies of other organisms can teach us about ourselves. <br />
Consider work on mice
and yeast by Kriston McGary and colleagues (2010) in the lab of Edward Marcotte. The researchers knew that because mice and yeast are derived from a
common ancestor, we find not only many of the same genes in both creatures, but
many of the same groups of genes working together to carry out biological
functions—what we might call gene teams. The scientists thus guessed that a
good place to look for genes associated with mammalian diseases would be on
mouse gene teams whose members are also teammates in yeast. Using a database of
genes known to occur in both mice and yeast, McGary and colleagues first identified
gene teams as sets of genes associated with a particular phenotype. In mice the
phenotype might be a disease. In yeast it might be sensitivity to a particular
drug. The researchers then looked for mouse and yeast gene teams with
overlapping membership.</div>
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<o:p></o:p></div>
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<a href="https://www.blogger.com/null" name="more"></a><br /></div>
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Among the pairs of
overlapping teams they found was a mouse team of eight genes known to be
involved in the development of blood vessels (angiogenesis) and a yeast team of
67 genes known to influence sensitivity to the drug lovastatin. These teams formed
a pair because of the five genes that belonged to both. The connection between
the two teams suggested that both might be larger than previously suspected,
and that more than just five genes might play for both. In particular, the 62
genes from the yeast lovastatin team not already known to belong to the mouse
angiogenesis team might, in fact, be members. Starting with this list of 62
candidates, the researchers conducted experiments in frogs revealing a role in
angiogenesis for at least five of the genes. Three more genes on the list
turned out to have been identified already as angiogenesis genes, but had not
been flagged as such in the researchers’ database. Eight hits in 62 tries is a
much higher success rate
than would have been expected had the researchers simply chosen genes at random
and tested their influence on angiogenesis. In other words, McGary and
colleagues used genetic data from yeast, an organism with neither blood nor
blood vessels, to identify genes in mammals that influence blood vessel growth.
Researchers in Marcotte’s lab have since exploited the overlap between the
yeast lovastatin team and the mouse angiogenesis team to identify an antifungal
drug as an angiogenesis inhibitor that may be useful</div>
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<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
in treating cancer
(Cha et al. 2012). That the theory of descent with modification is such a
powerful research tool indicates that it has a thing or two going for it.<o:p></o:p></div>
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<a name='more'></a><br /></div>
<b>Homology </b><br />
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As the fields of
comparative anatomy and comparative embryology developed in the early 1800s,
one of the most striking results to emerge was that fundamental similarities
underlie the obvious physical differences among species. Early researchers
called the phenomenon <b>homology</b>—literally, the study of likeness.
Richard Owen, Britain’s leading anatomist, defined homology as “the same organ
in different animals under every variety of form and function.”<o:p></o:p></div>
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<br /></div>
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<i><span style="color: #0066b4; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-AU;"><b>Structural Homology</b></span></i><o:p></o:p></div>
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A famous example of
homology comes from work by Owen and by Georges Cuvier, the founder of
comparative anatomy. They described extensive similarities among vertebrate
skeletons and organs. Referring to Owen and Cuvier’s work, Darwin (1859, p.
434) wrote:<o:p></o:p></div>
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<br /></div>
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<i>What could be more
curious than that the hand of a man, formed for grasping, that of a mole for
digging, the leg of the horse, the paddle of the porpoise, and the wing of the
bat, should all be constructed on the same pattern, and should include the same
bones, in the same relative positions?<o:p></o:p></i></div>
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<br /></div>
<div style="text-align: right;">
</div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEm9tYxlz9HUUZNqGKdTEcKX7v5g3bmYypiE8QUKznS1ZzkGH1vSjYruDeT792K5xXoA2Wcj4IG6mKqrP2hNPvpu7PcZ-6D2R0MtJua6sE-jVivWuAcOZavitPlXVXn_zDI_agyWj5ExK1/s1600/123.PNG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEm9tYxlz9HUUZNqGKdTEcKX7v5g3bmYypiE8QUKznS1ZzkGH1vSjYruDeT792K5xXoA2Wcj4IG6mKqrP2hNPvpu7PcZ-6D2R0MtJua6sE-jVivWuAcOZavitPlXVXn_zDI_agyWj5ExK1/s1600/123.PNG" height="216" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Figure 1</b></td></tr>
</tbody></table>
His point was that
the underlying design of these vertebrate forelimbs is similar, even though
their function and appearance are different.This makes the similarity in design
among vertebrate forelimbs different from, say, that between a shark and a
whale .Both shark and whale have a <o:p></o:p></div>
streamlined shape, short fins or flippers
for steering, and a strong tail for propulsion. These similarities in form make
sense in view of their function: fast movement in water. Human engineers use
the same features in watercraft. In contrast, the internal similarity between
forelimbs with radically different functions seems arbitrary. Would an engineer
design tools for grasping, digging, running, swimming, and flying using the
same structural elements in the same arrangement? Darwin himself (1862)
analyzed the anatomy of orchid flowers (Figure 2) and showed that, despite their diversity
in shape and in the pollinators they attract, they are constructed from the
same set of component pieces. Like vertebrate forelimbs, the flowers have the
same parts in the same relative positions.<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgq1FXkiX-WUPLOc-07iCqAtKUAGLl-LaADvCWcTe7oV5WD-ry2dpNerzTgP_4OAoGMAkJOjnVbT5MRcjY6R_XRsGgFK0S-mqieuSlHW92Ln9TimheFEA1Zr4_gXR8wBvwnW4rh2LDFc5zF/s1600/orchids.PNG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgq1FXkiX-WUPLOc-07iCqAtKUAGLl-LaADvCWcTe7oV5WD-ry2dpNerzTgP_4OAoGMAkJOjnVbT5MRcjY6R_XRsGgFK0S-mqieuSlHW92Ln9TimheFEA1Zr4_gXR8wBvwnW4rh2LDFc5zF/s1600/orchids.PNG" height="200" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Figure 2</b></td></tr>
</tbody></table>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
What causes these
similarities in construction despite differences in form and function? Darwin
argued that descent from a common ancestor is the most logical explanation. He
argued that the orchids in Figure are similar because they share a common
ancestor. Likewise, the tetrapods in Figure 1 have similar forelimbs because
they are descended from a single lineage, from which they inherited the
fundamental design of their appendages.<o:p></o:p></div>
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<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #0066b4; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-AU;"><b><br /></b></span></i></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="color: #0066b4; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-AU;"><b>Using Homology to
Test the Hypothesis of Common Ancestry</b></span></i><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
We can use homologous
traits shared among species to test Darwin’s hypothesis of common ancestry. We
will show the logic using evolutionary novelties shared among imaginary snail
species derived with modification from a single lineage. shows the evolutionary
history. The common ancestor is the lineage of squat-shelled blue snails at far
left. This lineage underwent speciation (1). One of the daughter lineages
persisted to the present with no further changes in its shell (2). The other
lineage evolved elongated shells (3). The lineage with elongated shells
underwent speciation (4). One daughter lineage evolved bands on its shell (5),
then persisted to the present with no further changes (6). The other daughter
evolved pink shells (7), then split (8). One daughter lineage evolved
high-spired shells (9). The other persisted with no further changes (10). The
high-spired lineage split (11). One daughter lineage persisted with no further
changes (12). The other evolved spikes on its shell (13), then persisted with no
further changes (14). These events yielded the five extant species at far
right. shows the novel shell traits shared by the four species that exhibit them.
Note that these traits are shared in a nested pattern. The species with spikes is
nested within the set of species with high spires. The set of species with high
spires is nested within the set of species with pink shells. And the set of
species with pink shells is nested within the set of species with elongated
shells</div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2mZQM1NIOIC_jsurkBOushmoHdKyo9P2bKlLW_WNgE824o8P3u8vjs9bfjin73x3pvFSjcg2EsAMzxWTybdVftwOYfEjRwxElP56wVHRzWqXipsOByS2mDe3cQWV0S-TkjNiL6IPzgNzr/s1600/123455.PNG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2mZQM1NIOIC_jsurkBOushmoHdKyo9P2bKlLW_WNgE824o8P3u8vjs9bfjin73x3pvFSjcg2EsAMzxWTybdVftwOYfEjRwxElP56wVHRzWqXipsOByS2mDe3cQWV0S-TkjNiL6IPzgNzr/s1600/123455.PNG" height="322" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Figure 3</b></td></tr>
</tbody></table>
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<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
Our hypothetical
snails demonstrate that the theory of descent with modification from common
ancestors makes a prediction. Extant organisms should share nested sets of
novel traits. And, indeed, they do. For example, humans are nested within the
apes—a group of species that have large brains and no tails. The apes, in turn,
are nested within the primates—which have grasping hands, and feet, with flat
nails instead of claws. The primates are nested within the mammals—defined by
hair and feeding milk to their young. The mammals are nested within the
tetrapods, the tetrapods within the vertebrates, and so on. The nested pattern
of traits shared among extant species thus confirms a prediction of Darwin’s
theory. But we can go further. Look again at Figure 3 and compare part (b)
to part (a). Notice that the most deeply nested sets are defined by traits,
such as spikes, that evolved relatively late. If we start with one of these
sets and work our way out across the progressively larger sets that enclose it,
we encounter additional traits that evolved ever earlier in time. Spikes were
preceded by high spires. High spires, in turn, were preceded by pink shells.
And pink shells were preceded by elongated shells. Even if we had only the five
extant species and did not know their evolutionary history, we could still use
the nesting of the traits they share to predict the order in
which the traits should appear in the fossil record. We could then check the
fossil record to see if our prediction is correct. Mark Norell and Michael
Novacek (1992) performed such tests on two dozengroups of vertebrates.
Representative results appear in. In six cases, such as the duck-billed dinosaurs,
there was no significant correlation between the predicted order in which
traits arose versus the actual order. However, in the other 18
cases, including the reptiles and the elephants and kin, the correlation was
significant or strongly so.</div>
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<o:p></o:p></div>
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<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
More sophisticated
methods of assessing the correspondence between traitbased reconstructions of
evolutionary history versus the order traits appear in the fossil record have
since been developed (see Wills et al. 2008). The correspondence is generally
high, at least for well-studied groups of organisms that fossilize readily.
This pattern is consistent with descent from common ancestors.<o:p></o:p></div>
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<br /></div>
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<i><span style="color: #0066b4; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-AU;"><b>Molecular Homology</b><o:p></o:p></span></i></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkcTWXeec6vH5oWxXc0DmON7wR6LMTb-DEJyfUYoaS9k9sTBfNzhocvEmgi_-pb6AwuFKaTP25daCwLNSkuXCMSn8pShD1e-LZj78JOKeLz-mlk5HDRg0hwDiHcSYA7iG0uyWmZqntIKFU/s1600/processed.PNG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkcTWXeec6vH5oWxXc0DmON7wR6LMTb-DEJyfUYoaS9k9sTBfNzhocvEmgi_-pb6AwuFKaTP25daCwLNSkuXCMSn8pShD1e-LZj78JOKeLz-mlk5HDRg0hwDiHcSYA7iG0uyWmZqntIKFU/s1600/processed.PNG" height="267" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Figure 4</b></td></tr>
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Curious similarities
unrelated to functional need appear at the molecular level as well. Consider a
genetic flaw on chromosome 17 in humans. Shared flaws are especially useful in
distinguishing between special creation versus descent from a common ancestor.
The reason is familiar to any instructor who has caught a student cheating on
an exam. If A sat next to B and wrote identical correct answers, it tells us
little. But if A sat next to B and wrote identical wrong answers, our suspicions
rise. Likewise, shared flaws in organisms suggest common ancestry. The flaw on
chromosome 17 sits near the gene for a protein called peripheral myelin
protein-22, or PMP-22. The gene is flanked on both sides by identical sequences
of DNA, called the CMT1A repeats <span style="color: #f36664;"><b>Figure 4a</b></span>. This situation arose when the distal repeat,
which contains part of the gene for a protein called COX10, was duplicated and
inserted on the other side of the PMP-22 gene (Reiter et al. 1997). The
presence of the proximal CMT1A repeat has to be considered a genetic flaw
because it occasionally lines up with the distal repeat during meiosis,
resulting in unequal crossing over (Figure 2.28b; Lopes et al. 1998). Among the
products are a chromosome with two copies of PMP-22 and a chromosome that is
missing the PMP-22 gene altogether. If either of these abnormal chromosomes participates in a
fertilization, the resulting zygote is predisposed to neurological disease (Figure 2.28c). Individuals with three
copies of PMP-22 suffer
from
Charcot-Marie-Tooth disease type 1A. Individuals with only one copy of PMP-22 suffer from hereditary neuropathy with liability
to pressive palsies.
Motivated by the
hypothesis that humans share a more recent common ancestor with the chimpanzees than either humans or chimps do with
any other
species, Marcel
Keller and colleagues (1999) examined the chromosomes of common chimpanzees, bonobos (also known as pygmy
chimpanzees), gorillas,
orangutans, and
several other primates. Both common chimps and bonobos share with us the paired CMT1A repeats that can induce unequal
crossing over. The proximal repeat is absent, however, in gorillas, orangutans,
and all other species the researchers examined. This result is difficult to
explain under the view that humans and chimpanzees were separately created. But
it makes sense under the hypothesis that humans are a sister species to the two
chimpanzees. All three species inherited the proximal repeat from a recent
common ancestor, just as three of the snail species in Figure 3 inherited
pink shells.</div>
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<i><span style="color: #0066b4; mso-bidi-font-family: Frutiger-Italic;"><b>A Predictive Test of
Common Ancestry Using Molecular Homologies</b><o:p></o:p></span></i></div>
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Our second example of molecular homology concerns another
kind of genetic quirk that might be considered a flaw: <b>processed pseudogenes</b>. Before we explain what
processed pseudogenes are, note that most genes in the human genome consist of
small coding bits, or <b>exons</b>, separated by noncoding intervening sequences, or <b>introns</b>. After a gene is transcribed
into messenger RNA, the introns have to be spliced out before the message can
be translated into protein. Note also that the human genome is littered with <b>retrotransposons</b>, retroviruslike genetic
elements that jump from place to place in the genome via transcription to RNA,
reverse transcription to DNA, and insertion at a new site (see Luning Prak and
Kazazian 2000). Some of the retrotransposons in our genome are active and
encode functional reverse transcriptase. Now we can explain that processed
pseudogenes are nonfunctional copies of normal genes that originate when
processed mRNAs are accidentally reverse transcribed to DNA by reverse
transcriptase, then inserted back into the genome<o:p></o:p></div>
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<i><span style="color: #0066b4; mso-bidi-font-family: Frutiger-Italic;"><b>Universal Molecular
Homologies</b><o:p></o:p></span></i></div>
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<tr><td class="tr-caption" style="text-align: center;"><b>Universal Triplet Code</b></td></tr>
</tbody></table>
The molecular homologies we have discussed so far have been
confined to small numbers of species. Advances in molecular genetics have
revealed, however, many fundamental similarities among organisms. Prominent
among them is the genetic code. With minor exceptions (Knight et al. 2001), all
organisms studied to date use the same nucleotide triplets, or codons, to
specify the same amino acids to be incorporated into proteins. This is why
genetic engineers can, for example, take the gene for green fluorescent protein
from a jellyfish, transfer it into the fertilized eggs of a monkey, and get
green fluorescent baby monkeys (Yang et al. 2008). Like the forelimbs in Figure 1, the genetic code appears highly evolved (Judson and Haydon 1999). The pattern
of codon assignments to amino acids reduces ill effects of point mutations and
translation errors (Freeland et al. 2003) and facilitates rapid evolution of proteins by selection
(Zhu and Freeland 2006). Also like the forelimbs, however, many details of the
code have clearly arisen as a result of something other than functional
necessity. An enormous number of alternative codes are theoretically possible,
some of which would work better than the real one (Koonin and Novozhilov 2009;
Kurnaz et al. 2010). Furthermore, having a unique genetic code might offer
distinct advantages. For example, if humans used a different genetic code from
chimpanzees, we would not have been susceptible to the chimpanzee virus that
jumped to humans and became HIV. When the virus attempted to
replicate inside human cells, its proteins would have been garbled during
translation.If alternative genetic codes are possible, and if using them
would be advantageous, then why do virtually all organisms use the same one?
Darwin provided a logical answer a century before the genetic code was
deciphered: All organisms inherited their fundamental internal machinery from a
common ancestor.</div>
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Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-88622937598204538782013-12-05T23:20:00.002-08:002013-12-05T23:22:13.596-08:00Instantons- Topology of the Vacuum <div class="separator" style="clear: both; text-align: center;">
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<a href="http://blogs.uslhc.us/wp-content/uploads/2010/05/thooft.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" class="irc_mut" height="294" id="irc_mi" src="http://blogs.uslhc.us/wp-content/uploads/2010/05/thooft.png" style="margin-top: 0px;" width="320" /></a>In the beginning was the vacuum. And nature abhorred the vacuum, filling it with topology. The surprising connection between quantum field theory (QFT) and topology yields the instanton, a cousin of the magnetic monopole; a soliton. The <i>U(1) problem </i>in QCD; where strange, up and down quarks of identical mass give the Lagrangian an extra U(3) symmetry, a product of SU(3)xU(1). Removing all mass from the quarks generates an additional copy of U(3). The Eightfold Way of strongly interacting particles and the mesons generated from the spontaneous breaking make up the pair of SU(3) groups. Conservation of baryon number is indicated by one U(1) segment, but the last additional U(1) group necessitates particles that don't even exist; nonetheless the chiral symmetry is spontaneously broken; but how? The solution is the insanton. But what topological features make instantons relevant to the QCD vacuum? Imagine a topologist mowing her lawn with an electric mower; she subsequently faces complications as she tries to move the power-cord around trees and shrubs. An intuitive analogy for homotopy. She then gives each tree a 'winding number' of 1 for one circuit around the tree, 2 for two circuits, etc. Topologically, both a short or wide path around a tree shrub are equivalent to each other; hence they are homotopic as they can be deformed into one another without the need for cutting. But if she then moves the mower in a circular fashion back to her initial starting position, the paths might look as though nothing has changed but they have a subtle difference; one wind around a tree. An analogous example of how the non-trivial topology of a vacuum can have physical effects is the Aharanov-Bohm effect. If you split an electron in a way that it passes both ways around a solenoid carrying current and subsequently recombines, the outcome is an interference pattern which changes. Thus, the topology of a vacuum without a magnetic field is equivalent to a punctured plane (the puncture made by the solenoid). Now we can pump an extra gauge invariant term (the instanton) into the Lagrangian, in QCD this is essentially a gluonic entity; a ripple in a gluon field. If you take the initial and final field strengths, in the middle is a local region where there is some positive energy; this is the instanton. Instantons have a 'topological charge' which explains their stability, much like an A4 sheet of paper taped at both ends to a coffee table with a single 180 degree twist induced before the ends are secured. This part of the sheet will remain twisted until someone cuts the strip of tape, this is just like the topological charge.<br />
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In QFT, the initial and final state is the vacuum. We can envision an instanton as a sort of path that correlates or links initial and final states (that have different topological winding numbers) and since those winding numbers can be infinite in extent, the vacuum not only becomes a state of lowest energy but also an aggregation of an infinite number of apparently homogeneous yet topologically different vacua. The lawn-mowing analogy is helpful as the power-lead leading over the tops of trees and shrubs act as barriers to movement of the electric lawn-mower. In field theory, this is equivalent to an energy barrier, instantons surpass this barrier via quantum tunnelling (linking one distinct topological state to another, measured by the θ-parameter. But how do instantons solve the <i>U(1) problem</i>? We could just invoke a respectable particle to account for the symmetry breaking like the η meson; but it's a Goldstone boson and the particle with the next mass up is too heavy. Instantons, like goldilocks, give just the right symmetry disturbance. A massless spiral of gluons and inverts right-handed quarks to left-handed ones. Such an inversion of handedness breaks the chiral symmetry and deals with the additional U(1) symmetry without the need for particles.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-71661308724833539492013-10-12T23:44:00.000-07:002013-10-13T04:24:31.985-07:00Networks- Physics of the Web<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_2x-XVj7gNozCrJnVVVzxX7opHESMEeIwMLe1HRaHau4uH5xc3Yw7SmJvO_T12S1juK2t5764_fDJldu6MN6tMlZ3WZuBLhfzKFZdo0y3OIo_04VkHDZUiV3yjmqv0REDgJNXVhUgXzNV/s1600/network+theory.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_2x-XVj7gNozCrJnVVVzxX7opHESMEeIwMLe1HRaHau4uH5xc3Yw7SmJvO_T12S1juK2t5764_fDJldu6MN6tMlZ3WZuBLhfzKFZdo0y3OIo_04VkHDZUiV3yjmqv0REDgJNXVhUgXzNV/s320/network+theory.PNG" width="320" /></a></div>
The Web remains an untamed beast. Ever since its inception, routers and lines are added continuously without bounds in an uncontrolled and decentralised manner; the every embodiment of digital anarchy. But is this network of networks inherently random? Nope. But how them do you get order to emerge from the entropy of millions of links and nodes? Let's examine the Internet and the web in the light of network theory and statistical mechanics.The most fundamental qualitative feature of any network is its degree distribution. The degree of a node is the amount of edges connected to it. Much of the Internet is an aggregation of low degree nodes with some few high degree hubs. An intriguing pattern arises with degree distribution of the Internet at large; it follows roughly a straight line when plotted against a logarithmic scale, essentially implying that the # p(k) of nodes with a degree k obeys a power law p(k)xk^-a. The present value of a for the Internet is around 2.2. But if edges of a network were arbitrarily placed between nodes, the resultant degrees would obey a Poisson distribution (in which a majority of nodes have degrees fairly close to the mean value and a total lack of high degree hubs), much like the Erdős-Renyi random graph. So the fact that the Internet follows a power-law makes it far from random and hence 'scale-free'. Citation networks, where edges represent citations of one paper to another and nodes symbolise the papers themselves, are also scale-free. So why do the Web and Internet both have an affinity and indeed a tendency to form similar scale-free networks? Conventional graph theory makes the assumption that the amount of nodes in a network is static and that links are randomly distributed. Such assumptions fail given that the Internet continually evolves with new routers the the Web with new pages, also the fact that actual networks feature 'preferential attachment' (nodes have a high probability of forming connections with another nodes that have many links).Let's imagine that some nodes in a network are abruptly removed or disappear. 3% of Internet routers are destined to fail at any given time, so what percentage of nodes would need to be removed so as to affect network performance? We can perform one test by removing nodes uniformly and at random and another test by deliberately removing the nodes with the highest degree. It turns out that for a scale-free network, random node removal has little to no effect whereas targeting hubs can be destructive.<br />
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The concept of 'six degrees of separation', proposed by Stanley Milgram, suggests that anyone in the world can be connected to anyone else by a chain of five or six acquaintances. Does the Internet follow this trend seen in social networks (small separation of nodes and high degrees of clustering)? Since we don't have a complete copy of the entire web, even search engine cover only around 16%, we can use a small finite sample of it to make an inference about the whole. Using 'finite size scaling', you can quantify the mean shortest distance between two nodes (numbers of clicks to get from a page to another page). Given there are around 1 billion nodes that make up the Web, this bring the 'small world' effect to 19 'clicks of separation'. Not all pairs of nodes can be internconnected given that the Web is not a directed network; a link leading from one page to another does not mean an inverse link exists, hence such a path of 19 clicks is not guaranteed.In most complex networks, nodes undergo competition for links. We can model this by giving each node a 'fitness factor' which quantifies its ability to compete, subsequently energy levels can be assigned to each node to produce a Bose gas (its lowest energy level representing the fittest node). The Bose gas evolves with time, adding new energy levels; such corresponds to the addition of novel nodes in the network. Two different outcomes can arise depending on the distribution of energy level selection: (1) 'fit get rich': as the energy level increases, particle level decreases (2) Bose-Einstein Condensation: the fittest node gains a large percentage of all links and manifests itself as a highly populated lowest energy level. Perhaps the Web is just another Bose-Einstein condensate?Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-84461289464525195912013-10-03T02:04:00.002-07:002013-10-03T02:04:13.523-07:00Homology- A Unified Definition <a href="http://www.nature.com/ncomms/journal/v3/n12/images/ncomms2272-f4.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="272" id="irc_mi" src="http://www.nature.com/ncomms/journal/v3/n12/images/ncomms2272-f4.jpg" style="margin-top: 0px;" width="320" /></a>Homology is 'a word ripe for burning'. But how should it be defined? Superficially, it's often identified as similarity in morphology reflecting a common evolutionary origin; but can we give a more rigorous approach? Like 'species', the many definitions of homology fall into two basic forms: developmental and taxic. The developmental approach is based on ontogeny, and two characters are homologous if they have an identical set of developmental constraints. The taxic definition is based on cladistics and identifies a homologues as a synapomorphy (a trait that characterises a monophyly). Some complications arise with structural homology, for instance, the wings or bats and birds can be considered convergent as they are differently arranged (and lack common ancestry); but they can be considered homologous at the level or the organism (because they evolved from the same pattern or vertebrate forelimb traceable to a common ancestor). Circular reasoning also arises with structural homology in that it is used to build a phylogeny and that phylogeny is subsequently used to infer homology (notice the circularity); a phylogeny must be initially constructed based on evidence before homology is proposed. What about evo-devo? This is also unhelpful for a working definition of homology, different pathways of development can converge on the same adult form, such as the methods of gastrulation and the many routes of developmental regeneration in the hydroid <i>Tubularia</i>. Even the embryonic developmental origin is unuseful as it relies on the subsequent interactions between cells and fails to give a conserved adult morphology. Molecular markers such as genes succumb to hierarchical disconnect (whereby homologous characters produce non-homologous traits). A classic example is the gene PAX6 in eye development which is found and transcribed in species as diverse as insects, humans, squids and even primitive eyed nemertines and platyhelminths.<br />
<br />
Experiments involving grafting of <i>Drosophila</i> PAX6 into <i>Drosophila </i>limbs or wings can place eyes in incorrect positions; when mice PAX6 is inserted into <i>Drosophila</i>, it is expressed as mouse-like. These grafting tests indicate that the adjustability for change does not lie in the genes as in the regulatory network of genes that code for expression. The need by to redefine homology at different hierarchical levels is also indicated in other characters. For a long time, arthropod compound eyes had been thought to have evolved rather independently of the vertebrate simple eye; now this seems improbable given the immense similarity between cephalopod and vertebrate eyes (commonly attributed to convergence). In essence, the gene starting eye formation is homologous but it's expression is not necessarily homologous. Hierarchical disconnect in the form of nonhomologous traits causing homologous characters is also noted. With the exception of urodele amphibians, all tetrapods develop tissue between their primordial digits and later undergo apoptosis. But in newts and salamanders, there is no need for apoptosis and digits take a separate developmental pathway. The evolutionary hypothesis is that salamanders and newts (or one of their ancestral species) lost the ability of apoptosis between digits and differential growth is a derived process. Novel genes exchanged for older ones can also cause the same homologous morphology (co-option of genes during evolution for very distinct functions).Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-16685789566971246012013-09-28T01:53:00.001-07:002013-09-28T01:58:03.575-07:00Relativistic Chemistry- Why Mercury is Liquid<div class="separator" style="clear: both; text-align: center;">
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Mercury is a periodic anomaly. It's liquid at room temperature, but why? Traditionally, the answer has always been its low melting point, but how? The marriage of quantum chemistry and relativity allows us to demystify many deviations of the periodic table, let's begin by comparing some of its next-door neighbours. Au and Hg are similar and distinct in many ways: with melting points of 1,064 °C and -38.83 °C densities of 19.32 and 19.30 g·cm−3 respectively. Their entropies of fusion are quite similar as opposed to their enthalpies. And regarding their crystalline structures: Au, Ag and Cu are cubic while Zn and Cd are hexagonal; Hg is rhombohedrally distorted Finally, Hg is a poor conductor with weak metal-metal bonding as opposed to Au, despite their similar electron configurations. Looking beyond the rare earth elements, some surprising periodic deviations arise; Hf and Zr have an uncanny resemblance. To explain this phenomenon, the lanthanide contraction is invoked. This involves the filling of the 4f orbital (unlike s, p or d electrons, here the electrons poorly shield the nuclear charge). As we move along the rare earths, 14 protons are added and the lesser penetration of the 4f orbitals means they are partially shielded by the 14 4f electrons; causing the electron cloud to contract. But other questions remain unanswered by the lanthanide contraction: <b>1. </b>why is Ag coloured gold? why not silver? <b>2.</b>what is the reason for the high electron affinity of Au? One may be tempted to introduce the idea of an inert 6s pair, but this fails to address the liquid nature of mercury. Relativity dictates that the mass of an object increases with its velocity, hence we can derive 3 main relativistic effects relevant to Hg and Au.<br>
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Firstly, the p3/2 orbital contracts to a lesser degree as opposed to the s1/2 and p1/2 orbitals (which contract a lot). Secondly, such causes an outward augmenting of the d and f orbitals (in relation to the s and p orbitals). And thirdly, the relativistic splitting of the p, d and f orbital energies manifests itself as spin-orbit coupling. These 3 effects cause the energy gap (difference) between the 5d5/2 and 6s1/2 orbitals to shrink. More importantly, we may explain away the colours of Au and Ag; the colour of Au is caused by the absorption of blue light causing 5d electrons to be excited to the 6s level, however silver appears colourless when it absorbs UV. The relativistically contracted 6s orbital in Hg is filled and hence, unlike Au, the 2 6s electrons don't play that much a role in metal-metal bonding, which is why it is liquid at room temperature.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-61621650375979929722013-09-08T00:00:00.002-07:002013-09-08T00:00:26.960-07:00Universal Common Ancestry- A Test<div class="separator" style="clear: both; text-align: center;">
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<a href="http://www.embl.fr/aboutus/communication_outreach/media_relations/2005/050701_hinxton/press1jul05pic.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" id="irc_mi" src="http://www.embl.fr/aboutus/communication_outreach/media_relations/2005/050701_hinxton/press1jul05pic.jpg" style="margin-top: 0px;" width="296" /></a>Are Americans, Archaea, Amoeba and bacteria all genetically related? The notion of a 'universal common ancestor' (UCA) is central to evolutionary biology. Much of the traditional arguments have been confined to 'local' common ancestry (of particular phyla) as opposed to the totality of life; let's overcome this assumption and test the hypothesis using probability theory and phylogenetics. The problem of UCA has been compounded by horizontal gene transfer (transduction, transformation and conjugation) where early genetic material passed on between entirely different species is thought by some to challenge the 'tree of life' pattern by creating reticulated lineages. The qualitative evidence for UCA spans the congruence of biogeography and phylogeny; the mutual agreement between the fossil record and phylogeny, the nested hierarchy of forms and the correspondence between morphology and molecular genetics. Such arguments boil down to 2 premises: (1) the nearly-universal nature of the genetic code and (2) critical similarities on molecular level (L-amino acids, fundamental polymers, metabolic intermediates). Since these arguments are merely qualitative, they do not rule out conclusively, the possibility of multiple independent ancestors. We can examine UCA quantitatively by model selection theory (without the presumption that sequence similarity implies a genealogical relationship) and a set of highly-conserved proteins. Also, we can model our test on Bayesian and likelihoodist probability (as opposed to the classical frequentist null hypotheses). Keep in mind that sequence similarity is the most likely consequence of common ancestry but this alone is not enough to support homology (similarity may be due to convergence). It is the nested, hierarchical relationship between sequences that necessitates the inference of common ancestry (because some similar sequences produce a conflicting phylogenetic structure which forces the conclusion of uncommon descent).<br />
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So are the three superkingdoms of life (archaea, bacteria, eukarya) united by a common ancestor? <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3314578/" target="_blank">Douglas Theobald </a>recently performed a test where 23 conserved amino-acids across the three domains had evolutionary networks (or trees) build around their sequences. Then contrasting the probability values for a range of ancestry hypotheses. But does this imply that life originated only once around 3.5 BYA? Not at all! It just implies that one of the primordial (original) forms of life has extant descendants; however it is possible for life to arisen more than once but the whole conclusion necessitates that all life has at least once common ancestor: a last universal common ancestor (LUCA). A problem however is that a phylogenetic tree can be build on virtually any set of data; we need to demonstrate an agreement between trees for the exact set of data spanning different datasets. And this agreement can also be explained in terms of other biological processes so the Akaike Information Criterion (AIC) may be applied to compare and contrast a range of hypotheses.So what signature feature of sequence data allows us to give qualitative evidence for UCA? In a nut-shell, the site-specific relationships in the amino-acids across a range of species; such relationships fade away as we go back in time through a lineage and species converge back (but with enough data, the progressive accumulation of relationships becomes statistically significant). On the other hand, if a pair of extant species have absolutely distinct origins, the relationships between the site-specific amino acid correlations (in the two species) disappear.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-52913479657017585842013-09-06T04:35:00.002-07:002013-09-10T00:09:59.915-07:00Graphene- One Carbon Thick <div id="irc_mimg">
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This carbon flatland is one wonder material. Graphene is a two-dimensional sheet of crystalline carbon just one atom thick; it is the 'mother' of all carbon-based structures: the graphite in pencils, carbon nanotubes and even buckminsterfullerene. The behaviour of electrons in the honey comb lattice as massless Dirac fermions gives graphene its unique properties. One signature effect of graphene is its distinct Hall effect, in the original Hall effect, an electric current (in the presence of a transverse magnetic field) causes a decrease in potential perpendicular to both the current and magnetic field. Near absolute zero, the Hall resistivity (ratio of decrease in potential to current flowing) in a 2-D electron gas becomes discrete (or quantised), taking integer values h/ne^2. But in graphene, a Berry phase means that the Hall resistivity is only quantised as odd integers (π), hence if you spin the wave-function of the Dirac fermions in graphene (about a circle), there is no symmetry and the state ends up in a different phase then what it began with. Moreover, the quantum Hall effect in graphene can occur at room temp. and can distinguish between layers (due to cyclotron energy of electrons). Graphene could give insight into relativistic effects on the bench-top, since the velocity of light for Dirac fermions is 300 times less in graphene, it should have a larger value for its fine structure constant (around 2). Zitterbewegung (the jerky motion that arises when its impossible to locate the wave function of a relativistic particle) is yet another frontier for graphene, the path of a relativistic electron jitters when it interacts with a positron. This type of motion occurs too quickly to be observed directly in materials like solids but when Dirac fermions are restricted to graphene sheets, they can be interpreted as mixing of states. <br />
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The Klein paradox in QED is when a potential barrier allows relativistic particles to move through freely, yet the probability that an electron tunnels through decreases at an exponential rate with the height of the barrier. Paradoxical enough, the probability for relativistic particles increases with barrier height (since a potential barrier that acts to repel electrons will also attract positrons). Chiral symmetry breaking may also be illuminated by graphene; in graphene the right and left-handed fermions behave the same unlike neutrinos which are strictly left-handed. But graphene is too conductive and to lower its conductivity we can take advantage of carbon's adaptability. In diamonds, each carbon is bound to four others (involving all electrons) in contrast to graphene, where one electron is left over (making it a good conductor). The most basic way of achieving this is to add a hydrogen (just like conversion of ethane to ethane) to make graphene into graphane. The σ-electrons that bind carbon atoms in graphene make a band structure with an energy gap between the final occupied and vacant states. But the delocalised π-electrons cause fully occupied and vacant bands to touch one another. In graphane, the π-electrons are strongly attached to hydrogen atoms, making an energy gap between the lowest vacant band and the highest occupied band. Bizarrely, annealing causes the hydrogen to disperse leaving the graphene backbone whole. Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-26802653858425240362013-08-25T02:22:00.000-07:002013-08-28T03:58:20.366-07:00Topological Insulators- The New Physics <div class="separator" style="clear: both; text-align: center;">
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We have all heard of conductors and insulators. And indeed some of us are more familiar with magnets and semiconductors or even superconductors; they are all manifestations of electronic band structure. But what about the topological insulator? They conduct on the outside but insulate on the inside, much like a plastic wire wrapped with a metallic layer. Weird enough, they create a 'spin-current', where the conducted electrons themselves into spin-down electrons moving in one direction and spin-up moving in the other. Such a topological insulator is an exotic state resulting from quantum mechanics: the spin-orbit interaction and invariance (symmetry) under time reversal. What's more, the topological insulator has topologically protected surface state which is free of impairment of impurities. So how can we understand this 'new' physics? The insulating state has a conductivity of exactly zero around a temperature of absolute zero due to the energy gap segregating the vacant and occupied electron states. The quantum Hall state (QHS) near absolute zero has a quantised Hall conductance (ratio of current to voltage orthogonal to flow of current), unlike other materials like ferromagnet which have order arising from a broken symmetry, topologically ordered states are made distinct by wound up quantum states of electrons (and this protects the surface state). The QHS (the most basic topologically ordered state) happens when electrons trapped to a 2-D interface in between a pair of semiconductors encounters a strong magnetic field. This field causes the electrons to 'feel' an orthogonal Lorentz force, making them move around in circles (like electrons confined to an atom). Quantum mechanics substitutes these circular movements with discrete energies, causing a energy gap to segregate the vacant and occupied states like in an insulator.<br />
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However, at the boundary of the interface, the electron's circular motion can rebound off the edge, creating so called 'skipping orbits'. At the quantum scale, such skipping orbits create electronic states that spread across the boundary in a one-way manner with energies that are not discrete; this state can conduct owing to the lack of an energy gap. In addition, the flow in one-direction creates perfect electric transport (electrons have no other option but to move forward because there are no backward-motion modes). Dispationless transport emerges because the electrons don't scatter and hence no energy or work is lost (it also explains the discrete transport). But topological insulators happen without a magnetic field, unlike the quantum hall effect; the job of the magnetic field is taken over by spin-orbit coupling (interplay between orbital motion of electrons via space and the electron's spin). Relativistic electrons arise in atoms with high atomic numbers and thus produce strong spin-orbit forces; so any particle will experience a strong spin-momentum reliant force that plays the part of the magnetic field (when spin changes, its direction changes). Such a comparison between a spin-reliant magnetic field and spin-orbit coupling allows us to introduce the most basic 2-D topological insulator; the quantum Hall <i>spin </i>state. This happens when both the spin-up and spin-down electrons experience equal but opposite 'magnetic fields'.<br />
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Just as in a regular insulator, there exists an energy gap but there are edge states where the spin-up and spin-down electrons propagate in opposition to another. Time-reversal invariance exchanges both the direction of spin and propagation; hence swapping the two oppositely-propagating modes. But the 3-D topological insulator can't be explained by a spin-dependant magnetic field. The surface state of 3-D topological insulators promotes the movement of electrons in any direction, but the direction of electronic motion decides the spin direction. The relation between momentum and energy has a Dirac cone structure like in graphene.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-26719785370176677382013-08-21T06:02:00.001-07:002013-08-21T15:12:13.253-07:00Gravitational Waves- Einstein's Final Straw <div class="separator" style="clear: both; text-align: center;">
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Like ripples through a rubber sheet, they squeeze and stretch spacetime and move outwards at the speed of light. Gravitational waves are still up for grabs. An exotic prediction of general relativity yet to be observed yet having profound implications for cosmology and astrophysics. If we picture a star in a relativistic orbit around a supermassive black hole, it may continue so for thousands of years but never forever. Neglecting even drag due to gas, the orbit would lose energy gradually until the star spiralled into the hole; the reason for this plunge is the emission of gravitational radiation. We know that if the shape or size of an object is altered, so is the gravity surrounding it; Newton realised the sphere was an exception since the gravitational field outside it is invariant (remains the same) if it merely expands or contracts. Changes in the gravitational field can't spread out instantly because this would imply a conveyance of information about the shape and size of an object at superluminal speeds (which is forbidden by relativity). If the sun were to somehow alter its shape and the gravitational field around it, 8 minutes would elapse for the effect to be 'felt' on the earth and at very large distances, this is evident as radiation (a wave of changing gravity) moving away from its source. This is analogous to the manner in which fluctuations in an electric field produces electromagnetic waves (a rotating bar with a charged ends produces an electric field unlike which is different from when the bar is end-on or sideways-on). But there are two main distinctions to be made between gravitational and electromagnetic waves. Firstly, gravitational waves are especially weak (except if very large masses are involved). Diatomic molecules are great emitters of electromagnetic radiation but terrible at transmitting gravitational waves. Because there is no such thing as negative mass (negative gravitational charge) to neutralise (or cancel out) positive ones (like in electricity), on large scales, gravity competes with electromagnetism. This lack of negative gravitational charge gives gravity an advantage over electromagnetism but it implies a deep paradox: it weakens the strength of an object to make gravitational radiation. Which brings us to the second difference between gravitational and electromagnetic waves:<br />
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The most productive (i.e. efficient) way of making electromagnetic radiation is for the 'centre of electric charge' to stagger or wobble in relation to the centre of mass. Dipole radiation is an example of this, where the ends of a spinning bar are positively charged on one end while negative on the other. But the Equivalence Principle (which dictates that gravitation is indistinguishable from acceleration, much like how a rising elevator makes you feel heavier while a descending one makes you feel lighter) also mentions that everything exerts a gravitational force equal to its inertial mass, hence at all points in spacetime, all bodies experience the same gravitational acceleration. Translating into english: this implies that the 'centre of gravitational charge' is really just the centre of mass and since the former can't wobble relative to the latter, dipole gravitational radiation can't exist. We compare gravitational radiation to the spinning bar by envisaging it possesses positive charges at both ends so that 'the centre of charge' remains set (fixed) at the centre and thus, low amounts of radiation are produced owing the existence of a quadrupole moment (it's only quantity that changes: it describes the distribution of shape and charge). Due to gravitational radiation, binary systems loses energy and their orbital period shrinks progressively, causing the component stars to coalesce; when two black holes meet, their even horizons combine into a larger one and in accordance with the 'no hair theorems', returns to a state described by the Kerr Metric (hole has mass and spin). </div>
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But the detection of such gravitational radiation (or waves) is causing a stir, it is Einstein's final straw. Any object in the way of a gravitational wave would experience a tidal gravitational force that acts transverse (perpendicular) to the direction in which the wave moved outward. If you interrupt a gravitational wave some sort of circular hoop head-on, it will eventually be contorted into an ellipse. In Louisiana, the LIGO detector uses laser interferometry, where a laser beam is divided and reflected off mirrors which are connected to two masses (kilometers away) in a perpendicular fashion (an L shape). If a gravitational wave were to arrive, it would cause two lengths, X and Y to change. To be continued...</div>
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Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-32936754836990843732013-08-18T03:34:00.001-07:002013-08-18T03:36:56.532-07:00Y Chromosome- An Evolutionary Curiosity <div class="separator" style="clear: both; text-align: center;">
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The X and Y chromosomes are an odd couple. But the Y reads more like a rule-breaker of human genetics; most of it refuses to recombine, more than half of it consists of tandem repeats of satellite DNA and it's not a prerequisite for life (females don't have or need one). So why bother with a chromosome that tells us about 50% of the population (assuming a 1:1 sex ratio)? Since it passes directly from father to son, its sex-determining role means it is specific to males and haploid. It contains vast numbers of unique SNPs and has some notable exceptions such as 2 pseudoautosomal regions that do recombine with the X as well as euchromatin sequences (which are loosened during interphase). Largely escaping recombination, the Y can bequeath haplotypes which are passed down a robust phylogeny (changes only via mutation) and can be used to trace back the most recent matrilineal ancestor, Y-chromosomal Adam. A gene called SRY (sex-determining-region-Y), derived from SOX3, which transcribes a protein to activate the formation of the testes, such is the origin of the sex-determining role. We can infer that the sex chromosomes started off initially as a matched pair (due to the identical telomeric sequences at the tips, which can engage in recombination); during the course of meiosis (the process of gamete formation), the homologous chromosomes align and exchange segments, subsequently sending off a copy of an autosome and and a sex chromosome to each cell. Other indications that Y and X were once alike include the non-recombining sites on the Y, most genes in this region have corresponding duplicates on the X. What makes the Y-chromosome an evolutionary curiosity is that its profound lack of recombination it makes it more prone to accumulating mutations and then decay; something must have happened to cease the exchange of DNA between the X and Y. The Y forfeited its ability to exchange DNA with the Y in discrete stages; firstly, a strip of DNA flanking the SRY gene spreads down the chromosome. But only the Y decayed in response to the loss of X-Y chromosome recombination, in contrast to the X which in females undergoes recombination when a pair of copies meet during meiosis. So what then could explain away the interruption of recombination between the X and Y?<br />
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As the early Y tended to exchange segments, a portion of DNA experienced an inversion (effectively turning the sequence upside down) relative to the X and since a prerequisite for recombination is that analogous sequences are aligned, any inversion would prevent interaction between the two regions. Comparative genomics unveils that autosomal precursors of the X and Y were unbroken (intact) in reptilian species before the mammalian lineage began . But monotremes like platypi were among the earliest to speciate and have a SRY gene aged back to 300 million years. X-inactivation followed (in which female embryo cells arbitrarily shut down a majority of the genes in one of the 2 X-chromosomes) to compensate for the degeneration. If we reduce the whole human population to two people (one man and woman), together this couple carries four copies of each autosome and three X chromosomes and a single Y. The effective population size of the Y can be therefore predicted to be similar to that of haploid mtDNA, 1/3 that of any X and 1/4 that of any autosome. Hence, we can expect much lower rates of diversification in the Y than any other region of the nuclear genome. We can predict is to also be more subject to genetic drift (random changes in frequency of haplotypes) and such drift would act as a catalyst for the differentiation between aggregates of Y-chromosomes in different populations. <br />
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Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-80842866925025721122013-08-17T06:53:00.002-07:002013-08-17T06:58:09.331-07:00Molecular Clocks- Timing the Gene Pool <div class="separator" style="clear: both; text-align: center;">
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It certainly doesn't tick. And it has no hands either. But the molecular clock is more than a faceless clock. It is a fairly new technique, employing a relatively constant rate of evolution to date almost anything from the divergence of taxa or species to the appearance of a viral epidemic. But this tool is made possible by an incredibly simple observation: the range of difference of DNA between species is essentially a function of the time ever since their divergence. Though the practical applications may seem subtle, molecular clocks put the final nail in the coffin of claims that HIV was first propagated by tainted polio vaccines in the 1950's, made using SIV (simian immunodeficiency virus) by dating the strain back to the 1930's. Essentially, the modern molecular clock has shown that a given protein has a characteristic rate of molecular evolution while genes are different in their characteristic rates . And that molecular evolution <i>per se </i>better fits into a neutralist rather than selectionist view. Linus Pauling reported a range of constant rates of evolution for different proteins (histones are characteristically slow, cytochrome c is slightly quicker (yet slower than haemoglobin) and fibrinopetides are quicker overall). Motoo Kimura and Tomoko Ohta explained away this fairly constant characteristic rate for each protein by positing that most amino acids changes were effectively neutral, so the change has no influence on the overall fitness and as a result the rate of change was no under the effects of natural selection. So on average, beneficial mutations were predicted to be rare, deleterious ones would be quickly wiped out by natural selection and a large fraction of the amino acids changes are effectively neutral. The actual mutation rate of the neutral mutations would only shaped by the mutation rate (and would be fairly constant, taken that the base mutation rate remained unchanged). Such predicts that in a species, the long-term rate of neutral molecular evolution is equivalent to the neutral mutation rate in the individuals. But why do different proteins have different characteristic rates of evolutionary change? We may explain these variations in terms of the assumption that proteins differed in the proportion of amino acid positions that were neutral (so that altering an amino acid has zero selective effect) or constrained (so any mutation was probably deleterious).<br />
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Summing up, the greater proportion of neutral sites, the more rapid the rate of molecular evolution. So in accordance with the neutral theory, the rate of which genes evolve is determined by the overall rate of mutation and proportion of neutral sites. Darwin actually predicted two phenomena (rate of fixation of mutations and high level of polymorphisms), which may be accounted by the neutral theory. And the amount of divergence between genes tends to increase (with time) since their evolutionary separation. But molecular clocks themselves may vary either as a result of 'sloppiness' of the tick-rate or variation in the mutation rate; since the clock is probabilistic (ticks are irregular intervals which can be described by a Poisson distribution), but where did this variation stem from? An important source of variation comes from the influence of population size on the rate of fixation of mutation. Ohta expanded the neutral theory (with the nearly-neutral theory) by acknowledging the important role of effective population size; smaller populations are more severely influenced by fluctuations in allelic frequency, so genetic drift can vanquish selection for alleles with small selection coefficients. So in effect, the fixation of of nearly-neutral alleles of small selection effect is predicted to be the greatest in the smallest populations, if a population undergoes a decrease in population, this might coincide with an influx of fixation of nearly-neutral alleles, so population flux can increase the sloppiness of molecular clocks. Another application of molecular clocks can be made to the Hawaiian Islands, where the phylogeny of endemic birds and fruit flies is confirmed by molecular dates that follow a linear correlation between divergence and time in which DNA distance is compared against Island age. Since viruses leave behind no fossil record, we can also reassemble the history of viral outbreaks using viral lineages (viral molecular clock). In the case of endogenous retroviruses (ERVs), dates of origin can be fine tuned by comparing the pair of long terminal repeats (LTRs) that surround the genome. </div>
Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-87566243369672357322013-08-10T19:31:00.001-07:002013-08-10T19:33:32.584-07:00Homochirality- Left-Handed Life <div class="separator" style="clear: both; text-align: center;">
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Life is anything but ambidextrous. And the problem of life's origins is compounded by a basic configuration of amino acids and sugars. Amino acids are molecules consisting of both an amino group (NH2) and a carboxylic group (COOH); the alpha amino acids have the carbon atom in the centre attached to both groups. The infamous Miller-Urey experiment showed how at least 22 amino acids could be produced in a spark discharge tube simulating a prebiotic environment containing water (H2O), methane (CH4), ammonia (NH3), molecular hydrogen (H2) and very little oxygen (O2). But an anomaly arises when trying to reconcile such a result with the chirality of the amino acids; just as your left and right hand can't be translated into each other, they can in principle when you look at the mirror image of one hand. Hence, hands possess a mirror symmetry. Chirality can also be explained in terms of the direction of rotation of circularly polarised light, rightly-polarised and leftly-polarised light behave very differently when they pass via a medium consisting of molecules that have selected chirality. All amino acids naturally occurring on earth are left-handed (except glycine which is non-chiral) but the Miller-Urey experiment produced racemics (equal numbers of left and right handed amino acids), so how did the amino acids get left handed? Such homochirality is critical to protein function, if proteins made of L-amino acids had random incorporations of their D-enantiomers, they would have varying conformations. Sugars also possess homochirality, they are classified as D-sugars based on the arrangement of the chiral centre furthest away from the carbonyl group of the sugar; so sugars are essentially right handed. But why? The Murchison meteorite that landed in Australia in 1969 had five alpha-methyl amino acids and an excess of L-enantiomers; these translate as S-enantiomers (a configuration where the methyl group is attached where the hydrogen atom would normally be in the L-amino acids). So why such an excess? The discovery that our place in the interstellar neighbourhood contains more right-circularly polarised light than anywhere else in the universe hints many possible explanations for homochirality. Among them is processing by ultraviolet photons in outer space, such as their polarisation is highest when they pass via a dense nebulae to leave stars (allowing scattering) and would thereby destroy molecules of one chirality while preserving the others.<br />
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The weak interaction of beta decay is the only force with the potential of producing a chirality due its parity violation. Conservation of parity means that the mirror image of an object has to be identical as the object itself, hence the weak interaction could distort the balance between right and left-handed molecules. One way this could be achieved is by electrons produced via beta decay, which have antiparallel spins to the direction of motion (longitudinal polarisation); more energetic, relativistic electrons are entirely longitudinally polarised and would produce Bremsstrahlung photons which interact with molecules to cause chiral discrimination. A similar hypothesis involves amplification via catalytic reactions: an agent that could act as a catalyst for its own synthesis and an inhibitor for the synthesis of the chiral opposite. Imagine a left handed molecule L and a right handed molecule R (both are made of the constituents A and B); once synthesised they trigger 'autocatalysis' where they can drive the synthesis of new molecules of their identical handedness from A and B. Finally merging to form molecule B', which leads to the destruction of one R and one L molecule.<br />
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An approach from astrobiology involves the interplay between neutrinos, amino acids and supernovae. 14N (nitrogen-14) is a constituent common to all amino acids and has a non-zero spin. The recently described 'Buckingham effect' occurs when the interaction of a nuclear magnetic moment with the magnetic moment possessed by electrons (produced by the Faraday effect), would behave in a different manner in a right-handed molecule than in a left-handed molecule. So the non-zero spin of the 14N nucleus, coupled with a strong magnetic field could allow a mechanism for chiral discrimination. The SNAAP (Supernova Neutrino Amino Acid Processing) model proposes that supernovae produce carbon, nitrogen, oxygen and a racemic assortment of amino acids (which synthesise in supernova nebulae). Neutrinos from other supernovae, together with the magnetic field from a neutron star or black hole, make the racemic mixture enantiomeric by selectively destroying one type of chirality of 14N based molecules. Subsequently, chemical evolution quickly amplifies the enantiomers and more L-amino acids are produced as the galaxy is permeated with molecular clouds.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com5tag:blogger.com,1999:blog-2297768638371156952.post-79843927607245802342013-08-07T03:45:00.000-07:002013-08-07T03:45:11.494-07:00Nucleosynthesis- Making the Elements <a href="http://cococubed.asu.edu/images/net_bigbang/bigbang_network1_web.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" id="irc_mi" src="http://cococubed.asu.edu/images/net_bigbang/bigbang_network1_web.jpg" style="margin-top: 0px;" width="316" /></a>The recipe for the making of the elements reads like a cookbook. In the first 3 minutes following the universe's fiery birth, very little was produced during big bang nucleosynthesis (BBN) due to some nuclear anomalies; there are no stable mass-5 or mass-8 nuclides making it almost impossible make anything other than 2H, 3He, 4He and 7Li (which is difficult to produce in abundance). Let's see how the light elements were initially synthesised. Firstly, a neutron coalesces with 1H to produce a deutron (2H) and a gamma ray; the deutron acts as a bottleneck for the rest of fusion events. Since a free neutron is highly unstable (half life of ~10 min) it decays into a proton and electron antineutrino; so you end up with around half the neutrons you started off with (which get captured into nuclei). 3He is produced when a proton is captured onto a deutron, which is converted to 4He via either neutron capture or a reaction where the deutron tosses in its neutron to the 3He and gives up its proton. In the another set of reactions, neutron capture by a deutron to produce 3He (a triton) gets converted to a 4He via either proton capture or a reaction in which a deutron gives up its proton and frees a neutron. That's pretty much hat was produced during BBN, aside from the fact that 7Li was made in minuscule amounts via the combination of 4He and 3H (in lows baryon density) or through the fusion of 4He and 3He to produce 7Be which was then fused with an electron neutrino. However, WMAP data seems to agree with theoretical calculations of 2H and 4He but not for 7Li (the prediction for lithium is about three times higher than actually observed). The 'lithium problem' may be addressed by short-lived hypothetical particles called axions which bind to nuclei; assuming it was negatively charged, the axion would reduce the Coulomb barrier between particles as the universe cooled to a certain point, hence triggering a revival of nucleosynthesis. So now that hydrogen, helium and a little bit of lithium were produced via BBN, the rest of the elements from carbon to lead and even as far as thorium and uranium were synthesised by nuclear reactions in stars.<br />
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Stellar nucleosynthesis begins with the initial stage of hydrogen burning, where hydrogen is converted to helium. In each of the 3 pp (proton-proton) chains 4 protons undergo fusion to form a 4He nucleus. In the pp-I branch, 6 protons actually go into the chain but only 2 remain in the final reaction with the 4He nucleus (so the net number of protons consumed is 4). The pp-II branch, the final reaction produces 2 4He nuclei, but one of them is put in to restart the chain (net number is 1). While the pp-III branch begins with 7Be (4He nucleus and 3 protons), so the proton that enters the chain makes one net 4He nucleus when 8Be decays. The CNO (carbon/nitrogen/oxygen) cycle is used for hydrogen burning in more massive stars and uses 12C as a catalyst. Next, the triple alpha and alpha processes of helium burning are rather simple; 2 4He are fused to form 8Be, 8Be is fused with 4He to produce 12C and 12C combines with 4He to make 16O. Hoyle discovered a resonance (an excited energy level) in the carbon nucleus of 7.7 MeV, to compensate for the instability of 8Be (which lives for 10^-16 secs). Subsequent nuclear reactions involve silicon burning following oxygen burning; the temperature is high enough so photons can interact with 28Si to make 24Mg and a 4He nucleus. Other photons can interact with 24Mg to make 20Ne and 4He nuclei, moreover, the light 4He nuclei can be captured by other 28Si to make 32S followed by 36Ar (very simplified); so nuclei around nickel and iron are products of silicon burning.<br />
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But the picture of nucleosynthesis is not complete without a mechanism for making the elements heavier than iron and nickel. Most of which are produced via the s-process (slow neutron capture) and r-process (rapid neutron capture); the s-process happens during helium burning and makes around half the nuclei heavier than iron. Such a process continues until it encounters the closed shells of the nucleons, which makes it difficult to capture an additional neutron. The s-process peaks in element abundance at barium, lead and strontium but the heaviest element made is 209Bi; attempt to add an another neutron and it undergoes beta decay to 210Po, releasing a 4He nucleus and ending up at 206Pb. The favoured site for the r-process is core-collapse supernovae, as a star cools, the seed nuclei form nuclides all the way up to uranium and plutonium and beyond.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-24394445298230494422013-07-31T05:03:00.000-07:002013-07-31T05:04:08.510-07:00Superfluidity- Going with the Flow <a href="http://www.physics.umd.edu/rgroups/amo/opticallattice.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="287" id="irc_mi" src="http://www.physics.umd.edu/rgroups/amo/opticallattice.jpg" style="margin-top: 0px;" width="320" /></a>Cool things happen when you cool liquid helium to 2.2 K. Below this temperature (lambda point), superfluidity takes over and viscosity decreases radically, resulting in a frictionless flow. Place it in a container and it will flow into a thin film up around its edges and flow through the pores of the walls. This anomaly is difficult to understand using classical fluid mechanics; Poiseuille's law dictates that the flow rate of a fluid corresponds to the difference across the capillary and to the fourth power of the capillary radius. But below the lambda point, the flow rate of supercooled liquid helium was not only high, it was both independent of both the capillary radius and pressure; evidently, this is not within the explanatory scope of classical theory. When cooling liquid helium (by pumping out its vapour), the liquid ceases to boil due to fact that the thermal conductivity of liquid helium has so sharply increases to maintain a homogeneous temperature. Let's start our exploration from the ground up: the reason liquid helium never solidifies no matter how cold you cool it is because the weak Van der Waals forces between the atoms are adequate enough to overpower the zero-point motion related with attempting to restrain a helium atom to a site on the lattice. The nature of the superfluid is therefore necessarily quantum mechanical. London suggested superfluidity as an expression of a Bose-Einstein condensate (BEC) but the issue is that BECs happen in ideal gases where particles have no interaction with each other whereas helium atoms attract weakly at a distance and repel strongly when close. Feynman's path integral approach lead to the realisation of two important yet subtle notions, firstly, helium atoms are bosons and this means that a Bose symmetry ensures the wave-function is not affected by any two helium atoms changing their configuration. And secondly, if an atom is moving slowly along its trajectory, the adjacent atoms would have to move slowly to get out of the way, this act of 'making room' increases the kinetic energy of the helium atoms that would add to the action. The overall effect is that we must change what we usually perceive as the mass of the helium atom, because when it moved, more than one atoms would have to make way (as mentioned), hence the trajectories that give the most 'sum over paths', there would be a particle with a somewhat increased mass. But what keeps a superfluid helium superfluid? Landau suggested that there are no more available low energy states near the coherent BEC state at low temperatures that any fluctuations could place the quantum fluid into. A classical fluid has viscosity (resistance to flow) because separate atoms bounce around other atoms and molecules and any debris in the container; these excitations alter the motion of the particles and dissipate energy from the fluid to the container, but if no more states are there to be filled (as in Landau's suggestion), particles can't alter their motion and persist to flow without dissipating energy. Feynman wanted to extrapolate this to a quantum mechanical regime, essentially because helium atoms repel each other at short distances, the ground state (lowest energy) of the liquid will be of a roughly uniform density. You can imagine each atom in the system as confined to a 'cage' formed by the surrounding atoms, thus in high densities, the cage enclosing the atom would be smaller. The Uncertainty principle teaches us that as a result of confining the atom to a smaller space, its energy is raised; so the ground state is achieved when all atoms are as far apart from each other as possible.<br />
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Imagine a ground state configuration with uniform density and envision that we can create a state that differs from it, but only over large regions, so any 'wiggles' in the wave-function will not be closely arranged (a requirement of the Uncertainty principle). Now taking one atom a distance away to a new position will leave the system invariant due to the Bose symmetry, so the wave-function does not represent atomic displacements. This can be interpreted as the biggest extra wiggles in the wave-function to describe a new state can't be larger than the average space between the individual atoms. Since wiggles of this magnitude conform to excited energy states, they are higher than the random thermal perturbations that could produce at 2.2 K or below. Therefore, this hints that fact that there are no low-hanging energy states above the ground state that could be readily accessed by particle motion, so as to act as a resistance to current flow. Like superconductivity, the 'superflow' would continue provided the total energy of the system was lower than the 'energy gap' between the ground state and the lowest-energy excited state. Tizsa proposed a 'two-fluid' model where at absolute zero, all of the liquid helium would enter the superfluid state and as fluid gained adequate heat, excitations would dissipate energy and the normal portion would permeate the whole volume. But what would happen to a container or bucket or superfluid if one spun it around? Due to the configuration of the ground state and the energy needed for excitations above it, the superfluid had to have no rotation. And what about making the entire fluid rotate by spinning its container? Feynman suggested that small regions on the order of several atoms would rotate around a pivot, these pivots or central regions would form so called vortex lines (which tangle and twist around each other). Such vortices don't need to extend from the container top to the bottom but may form rings; this also equates to the minimum energy of a roton (lowest-energy excitations) where the roton is a local domain moving at a different speed to the background fluid. And hence, for the quantum behaviour of the angular momentum to still apply, the fluid needs to flow back somewhere else again like a vortex.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-35685355114618762082013-07-27T18:14:00.000-07:002013-07-27T18:14:14.998-07:00Genome- The Code of Us <a href="http://www.sciencemuseum.org.uk/WhoAmI/FindOutMore/Yourgenes/Wheredidyourgenescomefrom/~/media/WhoAmI/FindOutMore/Epigenetics%20-%20beyond%20the%20human%20genome.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" id="irc_mi" src="http://www.sciencemuseum.org.uk/WhoAmI/FindOutMore/Yourgenes/Wheredidyourgenescomefrom/~/media/WhoAmI/FindOutMore/Epigenetics%20-%20beyond%20the%20human%20genome.JPG" style="margin-top: 0px;" width="320" /></a>The genome is like a page of printed music, the page is a material object but the notes and scores are coherent with realisations in space and time; in a range of ways but in a range of limited ways. Our species is one amongst many and the code of us is what the genome contains; in the beginning was the word and the word was with our genes. The typical inventory of a human genome contains both moderately repetitive and highly repetitive DNA, namely functional classes of dispersed gene families (e.g. globin, actin), tandem gene family arrays (ribosome, histone and tRNA genes). It also contains the highly repetitive minisatellites (most of the heterochromatin around centromeres), telomeres and microsatellites (distributed throughout genome). Components with unknown function or vestigiality include the long and short interspersed elements (LINEs and SINEs) as well as pseudogenes. Many of the variations between individual genomes come in the form of single-nucleotide polymorphisms (SNPs), which are single-base differences; such SNPs in recombination-poor areas such as mtDNA and Y-chromosomes tend to remain together and define a person's individual haplotype (co-inherited genetic polymorphisms). Another important haplotype is the major histocompatibility complex (MHC); in the genome MHC proteins, which are clustered on chromosome 6, are especially polymorphic and help the host to identify foreign proteins and activate innate immunity by T-cell receptors. Dynamic components of the genome (those that can move around in it) are found in all organisms: retrotransposons (class I) copy themselves through an RNA intermediary and comprise many degenerate retroviruses, transposons (class II) encode transposase which cuts and pastes it some place else in the sequence, they contain upside-down repeats at their ends which are targets of the cut and paste process. Interestingly, retroviruses (which use reverse transcriptase) is susceptible to errors in the transcription process and thus inactivates them and integrates them into the host genome, such endogenous retroviral insertions (ERVs) are specific to species and if two species share the same ERVs in identical mutation points, it is evidence of common ancestry. Other examples of shared mutations includes the pseudogene responsible for the silencing of the enzyme L-gulonolactone oxidase; which is involved in vitamin C synthesis, such is evidence for common descent between humans and other simians. Repeated copying of sections of the genome can produce large volumes of homologues such as the super-family of G-protein-coupled receptors (GPCRs), 700 of which are in the human genome. But what makes us different to chimpanzees is more subtle, differing in our sequences by around 13 Mb, we diverge in terms of transcription factors like FOXP2 (responsible for language). But this is a classic paradox, given that yeast can survive a sacrifice of 80% of their genes while the 13Mb (4%) variation between humans and chimpanzees cause profound change in the phenotype. Let's examine the progress made in genome sequencing: Sanger's method uses DNA polymerase to create a new strand of DNA; the polymerase needs a supply of nucleotide triphosphates and the enzyme adds to the growing primer strand, this leads to the polymerase chain reaction (PCR) which amplifies small quantities of DNA. The whole-genome shotgun approach involves sequencing random fragments of the DNA and putting them back in the right order again, such overcomes the tedious nature of making a map as the basis for the assembly of partial sequences.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-56379691208197669132013-07-23T03:40:00.002-07:002013-07-23T03:40:47.566-07:00Cold Fusion- A Modern Heresy <div class="separator" style="clear: both; text-align: center;">
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Fusion is a hot topic these days. The stakes are higher than ever for a source of sustainable energy and many still want a piece of the action. But like most feats, it's fallen on the wayside of fringe physics as a modern-day heresy. The basic idea is whether it may be possible to recreate the power of the sun (which undergoes fusion of atomic nuclei at 10^7 K) at or near room temperature. In 1989, Fleischmann and Pons claimed they could create such a process on earth at room temperature using a simple electrolysis cell experiment. Using heavy water (D2O), where hydrogen atoms have been replaced by hydrogen's heavier isotope, deuterium; they applied a palladium cathode as an electrode and passed a current via the water, allegedly causing large quantities of heat to be produced. Such a 'cold fusion' reaction is nothing short of miraculous: firstly, there is a positive charge produced by the nucleus of every deuterium atom, prohibiting the atoms from coming close enough to fuse (Coulomb barrier). The sun overcomes the Coulomb barrier by the enormous temperatures that sends atoms accelerating at great speeds and colliding to fuse and release energy; even more miraculous, the Fleischmann-Pons experiment didn't produce lethal doses of radiation, as often expected from fusion reactions. To explain away their phenomenon, it was proposed that neutrons were being exchanged between the atomic nuclei (and releasing heat in the process), others believed that deep within the lattice of palladium atoms, an exotic clustering of electron clouds allowed the deuterium nuclei to come close enough to fuse. Another proposal was that spontaneous fractures in the palladium cathode effectively fired the deuterons together. The experiment itself was quantitatively measured in terms of the current put in to the cell compared with loss of heat and temperature rise during the entire set-up; but was this really cold fusion? Apart from the lack of experimental reproducibility, a strong theoretical argument can be made as a final 'nail in the coffin' against the feasibility of cold fusion; Leggett and Bayem maintained that in calculating the maximum degree to which the Coulomb barrier can be lowered (presuming maximum entropy/equilibrium) in addition to the binding energies of electrons in both hydrogen and helium, one can also consider the affinity of the metallic lattice for an atom (the energy released when an atom is put in the crystal and permitted to occupy the lowest energy-state). Such nuclear parameters are well defined, except for the final one because there is no precise measurement of the affinity of palladium or titanium for helium, but it can be rest assured that the value must be small due to the fact that helium releases readily from such metals at room temperature. Other cold fusion scenarios such as a deuteron-metal apparatus in a transient state but under thermodynamic equilibrium are questionable in their efficacy.<br />
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Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-85347657522150392932013-07-17T04:50:00.000-07:002013-07-18T14:22:01.948-07:00Particle Creation- The Ultimate Free Lunch <div class="separator" style="clear: both; text-align: center;">
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You can't get something from <i>nothing</i>, there is no simply no such thing as a free lunch. But considering the beginning of the universe, where did all the particles come from? Common sense tells us that some breach of natural law such as energy conservation (the total heat energy added to a system equals the increase in internal energy minus any work) was necessary for the universe to begin in maximum entropy and zero energy. Such intuition fails at the level of quantum mechanics and relativity where that matter may be 'created and destroyed' via E = mc2 and the Uncertainty principle permits 'accidental' violations of energy conservation to occur spontaneously. But such a state of <i>nothing</i> may not be compared with 'absolute nothingness' because the laws of physics are presupposed to exist beforehand. We live in a zero energy universe, where the negative contribution of the energy of the gravitational field cancels out the matter and energy to give a null value; so really it's just a case of nothing-for-nothing. The issue of particle creation is an example of that free lunch, revisiting some ideas from inflation and cosmology. The false vacuum that ignited inflation was very different from any typical expanding gas (that has positive pressure performing work on the external environment and reducing its internal energy if no heat is added); we can think of the false vacuum as a curved but empty space-time with a constant negative pressure performing work on itself and increasing its total internal energy via an adiabatic process as it inflates. This provides a starting point for the creation of elementary particles, the original inflationary model included an inflaton embedded in a stable field potential and quantum tunnelling as a mechanism for ceasing the exponential expansion. Since tunnelling ends inflation by bubble nucleation, bubbles emerged but sufficient collisions couldn't occur to distribute energy in a homogeneous fashion (the so called 'graceful exit problem'). This poses a big complication for particle creation due to the fact that energy (which is trapped in the bubble walls) can only be freed by the collision of many such bubbles; the graceful exit problem means that the bubbles remain in inhomogeneous clusters. However, this difficulty in early inflationary models was resolved by the concept of a 'slow-roll', whereby inflation is unstable and goes through a phase transition where fluctuations begin at the plateau of a field potential and roll gradually (universe inflates during this time) until it eventually becomes a true vacuum and inflation ends. But the universe becomes too cold after this exponential expansion for any particles or radiation to form so a theory of reheating is required; during this epoch the inflaton field slowly decayed and transferred energy to create particles. Firstly, coherent oscillations of a scalar field occurs and may last for some time if no rapid decays happen, thus the particle decay duration may be a lot longer than the Hubble time. Next, when the Hubble time (here the age of universe) reaches the decay time, the slow-case allows only fermionic decays to occur but when bosonic particles are produced, this allows parametric resonance (like a child swinging on a swing and momentarily standing and squatting to increase the magnitude of the oscillation) to take over. Such parametric resonance promotes a fairly rapid decay termed <i>preheating </i>differentiate it from the initial stage. Occupation numbers (quantities that determine degree to which a quantum state may be filled with particles) produced via parametric resonance are large so that bosons are formed far from maximum entropy (equilibrium); they also give a reason why preheating does not occur is the only decay pathway is fermionic in accordance with the Pauli exclusion principle. Finally, following the formation of high occupation numbers by parametric resonance, the reheating can continue normally according to normal conditions and bosons should interact and decay as well as achieve a state of maximum entropy (equilibrium).<br />
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Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-14476142581931207382013-07-12T05:37:00.004-07:002013-07-13T23:53:37.712-07:00Active Galaxies- Of Quasars and Kin<div class="separator" style="clear: both; text-align: center;">
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Something weird is going on in the centres of many galaxies. Often, intense of aggregates of 'blue' light with characteristics distinct from the radiation associated with stars or gas are produced. Galaxies possesing these centers are 'active galaxies' and their central sources are active galactic nuclei (AGN). The optical spectra of a typical galaxy is a composite of contributions from H II regions and stars; elliptical galaxies mirror the spectrum of a star while spiral galaxies are akin to both a star and H II region (partially ionised gas clouds). The optical spectrum of an active galaxy is a combination of the spectra of a typical galaxy and extra radiation that features strong emission lines. Since the common denominator of all active galaxies is an AGN, there are many such types of active galaxy; namely Seyferts, which are spiral galaxies containing very bright point nuclei which have brightness variation. Quasars look like far-way Seyferts with bright nuclei while radio galaxies are made distinctive by their massive radio lobes powered by relativistic jets. Blazars are just quasars that appear differently when observed from varying angles but have a stellar appearance and produce continuous spectra. The central question that concerns astrophysics is how a volume so small can generate such intense luminosities; the central engine of an AGN is thought to be driven by a supermassive black hole around which an accretion disk forms by falling material that converts gravitational energy to radiating heat. Jets are believed to to be discharged orthogonally to the accretion disk. Such a paradigm leads to a standard model of an AGN (pictured), summarised as an accreting supermassive black hole (central engine) encircled by a broad-line region contained inside a obscuring torus of infrared emitting dust and a narrow-line region. Unification is an emerging means of modelling AGN according to the viewers position relative to the axis of the accretion disk; one unification regime links so called Type 1 and Type 2 AGN depending on whether the observer has a clear view of the black hole (Type 1) or is prohibited from viewing it by an opaque dusty torus (Type 2). In Type 2 AGN, the observer can't see the source of ultraviolet radiation or even emission lines but only 'mirror images' of such properties on adjacent clouds of gas. Another unification regime is applicable to around a tenth of AGN that have intense jets (radio loud); an observer viewing along the axis of the jet will see a blazar while looking aside from the axis will make the AGN appear much less intense and would be discerned as either a radio-loud quasar or radio galaxy.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-22361597924612669742013-07-12T02:24:00.001-07:002013-07-13T23:47:35.868-07:00Structure Formation- Revisiting Dark Matter<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGv6vkP2iYHz1aiWac9BzVOGPOOiXIkcGngNFJpe6sKi8XB3GU2fW5T9BvOKyNKlXEaA53Lv7f5CeRX5ByjvsxVztYAsApbrKA8Y5WhHgL_5J3g9vC9sfnrgpQZxd3tR3egNoYkNKoHIBv/s1600/vorkinm.9cube.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGv6vkP2iYHz1aiWac9BzVOGPOOiXIkcGngNFJpe6sKi8XB3GU2fW5T9BvOKyNKlXEaA53Lv7f5CeRX5ByjvsxVztYAsApbrKA8Y5WhHgL_5J3g9vC9sfnrgpQZxd3tR3egNoYkNKoHIBv/s320/vorkinm.9cube.jpeg" width="320" /></a></div>
Looking up at the night sky and into our interstellar neighbourhood, we see matter clumped into galaxies, clusters and super-clusters. Quite distinct from the early universe, where the relatively low levels of anisotropies in the cosmic microwave background (CMB) serves as a cue to the smooth and sleek distribution of baryonic matter at recombination. The evolution of large scale structure is thought to have arisen from the gravitational instability and collapse of regions initially denser than usual; hence such regions expand slower than the average expansion of the universe. The minute perturbations layed down quantum mechanically produce relative density fluctuations and depends on the balance between two effects. Firstly, the self-gravitation of matter in the over-dense region which has a tendency to cause collapse and secondly, the maintenance of hydrostatic equilibrium that serves to prevent collapse. A key cosmological parameter is the Jeans mass which plays the role of a border or limit between these two effects, if a region exceeds the Jeans mass, it will collapse. Similarly, the horizon distance (at any moment in the chronology of the universe, the maximum interval a signal could transverse in the time that had passed up to that moment) plays a critical role in stability against collapse; an overdense region exceeding the horizon distance can't support itself. Something interesting happens at recombination, at about 3000K and 300,000 years after the big bang; the, Jeans mass falls sharply to about the mass of globular clusters and before recombination, the interaction of photons with free electrons contributed to the overall pressure. After the recombination epoch, when the electrons cease to interact with photons, the only protection against collapse comes from the internal pressure of gas. However, gravitational collapse with cold (non-relativistic) dark matter seems to have caused density fluctuations before recombination; the dominant influence on baryons is the gravitational attraction of regions which have acquired over-densities of cold dark matter. This means that baryons were drawn into those collapsing clouds of dark matter and kick-started galaxy formation; a hierarchical process (bottom-up) whereby cold dark matter drew condensations against the overall expansion of the universe into redshifts between the orders of 100 and 40. Cool gas was drawn into dark matter halos into well-defined disks to produce the first spiral galaxies, so this provides an intuitive reason why ellipticals have no young stars because only where gas can collect and coalesce can stellar formation proceed. After recombination, the decoupling of photons from baryons allowed them to travel unhindered, causing the universe to become transparent and ushing in a period of darkness (the dark ages). Such dark ages ceased 400 million years (reionisation) after with the inception of the maiden generations of galaxies and other objects (quasars and Pop. III stars) that emit UV radiation, forming the initial ionised portion of cosmic gas which exponentially increases until the complete ionisiation of hydrogen. This highlights a point where ionised gas became just as important as cold dark matter in structure formation. Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-39041482051845947672013-07-10T05:55:00.000-07:002013-07-12T21:15:04.205-07:00Magnetic Monopoles- Anomaly or Possibility?<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxMdDpEftYeUdeiZdytnOtbm9mkiThinFyFz_h0cYMCt4JGdwCKcwc-gYbV6TjNoFuO6joH9XRxmYtS7Ml15EAj3JKdRn-i0fslfQ8x7qIvlAsU0Kzxqq4PVHAWoOKP9TsSBJu7V5mRkte/s1600/magnetic-flux-transported-via-dirac-strings1.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="313" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxMdDpEftYeUdeiZdytnOtbm9mkiThinFyFz_h0cYMCt4JGdwCKcwc-gYbV6TjNoFuO6joH9XRxmYtS7Ml15EAj3JKdRn-i0fslfQ8x7qIvlAsU0Kzxqq4PVHAWoOKP9TsSBJu7V5mRkte/s320/magnetic-flux-transported-via-dirac-strings1.jpg" width="320" /></a></div>
Like poles repel and opposites attract. Such is an elementary rule of thumb and one of the basic properties of magnetism: a magnet always has two 'inseparable' poles, north and south. Yet there is no fundamental reason why this should be the case, why does a magnet always have 2 poles? Why can't the field lines of the magnetic field have a terminating end? Why can't a magnet have only one pole? Since electric field lines terminate as electric charges, it seems as though there are simply no magnetic charges. Case closed? Not quite. In classical electrodynamics, Maxwell's equations have an elegant symmetry; the electric-magnetic duality (ensuring the electric and magnetic fields behave identically). This symmetry appears broken because no magnetic charges have been found but the existence of monopoles would solve this anomaly and restore the elegant symmetry. In quantum mechanics, the forces of electromagnetism are quantified in terms of scalar and vector potentials as opposed to electric and magnetic fields and their introduction seems to break the duality. Because electromagnetism has an abelian U(1) symmetry, one can perform a gauge transformation using an unlimited number of potentials to give rise to the same fields; however the vector potential seems to prohibit magnetic charges due to the disappearance of the divergence of the curl of a vector field. Dirac devised a means to apply a vector potential to construct a monopole; a means similar to Faraday who used a long magnet contained in a mercury-filled vessel in such a manner that one of the poles was beneath the surface while the pole above acted as a monopole. The existence of monopoles can explain the quantisation of electric charge and hence Dirac envisaged a semi-infinite solenoid with an end that possessed a non-zero divergence (thus acted as the monopole) and Dirac strings (infinitely thin flux tubes that connect two monopoles). Moving onto GUTs, the Weinberg-Salam unification incorporates a U(1) x SU(2) symmetry which is broken by the Higgs field at low energies; a simpler equivalent is the Georgi-Glashow SO(3) model. 't Hooft and Polyakov found that a solution to such a model exists that incorporates both electric and magnetic charges; their topologically stable solution involves a Higgs field of stationary length with varying direction in each different direction. And for the field to be continuous, a point-like flaw in the origin of the field can't be a vacuum state; thus the origin of the field is a clump of energy corresponding to a massive particle (since the Higgs field disappears at the origin, the SO(3) symmetry is left unbroken. Interestingly, such a particle possesses magnetic charge because electromagnetism is made by oscillations around the Higgs field vector, one can quantify the magnetic field and the 't Hooft-Polyakov solution turns out to be a monopole. Even though monopoles haven't been directly observed, let alone discovered, they play an important role in modern physics; especially in explaining the phenomenon of quark confinement in QCD. At extremely low temperatures, materials become superconductors and allow current to flow without resistance but eject any magnetic flux (Meissner effect); if we could put a monopole-anti monopole pair into a superconductor, what would happen? Since any magnetic flux is ejected, a way to resolve this dilemma would be that an Abrikosov-Gorkov flux tube forms between the pair, hence the flux is restricted to this tube. And since the flux tube has a nonzero energy value, the quantity of energy needed to separate the pair increases in a linear fashion. Finally, monopoles are important is cosmology because GUTs predict they were produced in the early universe; the Kibble mechanism is likely candidate for how that happened. It proposes the universe contains domain walls with arbitrary yet uniform field direction and the Higgs field inserts itself continually between a pair of domains but the field disappears in the origin causing topological defects. But when two pairs of domain walls meet, a monopole can be made. Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-82059465548223328422013-07-07T22:15:00.001-07:002013-07-31T23:14:05.971-07:00Astrometry- The Cosmic Distance Ladder<a href="http://blogs.smithsonianmag.com/aroundthemall/files/2013/01/hires.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="256" id="irc_mi" src="http://blogs.smithsonianmag.com/aroundthemall/files/2013/01/hires.jpg" style="margin-top: 0px;" width="320" /></a><a 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" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a>Van Gogh's painting, 'The Starry Night', resembles not only the
Whirlpool galaxy but it proves its astronomical worth in a number of
ways. For starters, one can deduce it was painted in the predawn hours
due to the inclination of the moon to the horizon and that the brightest
of its 'stars' is in fact Venus, attesting to the fact that the planets
are usually the first to emerge in the evening. But what makes this
painting sacred is not what it shows but what it represents: astrometry.
Our obsession with the heavens means that we can measure distances with
greater rigour and precision, from gnomons and sundials to standard
candles and gravitational lensing; such are the rungs of the cosmic
distance ladder. The earth is the first rung of that ladder. Aristotle
and others provided the first indirect arguments that the earth is round
using the moon. He knew that lunar eclipses happned when the moon was
directly opposite the sun (opposite constellation of the Zodiac), so
eclipses happen because the moon falls into the earth's shadow. But in a
lunar eclipse, the shadow of the earth on the moon is always a circular
arc and since the only shape that produces such a shadow is the sphere
he inferred the earth was round. If the earth was circular yet flat like
a disk, the shadows would be elliptical. Similarly, Eratosthenes
calculated the radius of the earth to 40000 stadia. Having read of a
well in Syene that reflected the overhead sun at noon of the summer
solstice (June 21) because of its location on the tropic of cancer; he
used a gnomon (in Alexandria) to measure the deviation of the sun from
the vertical as 7 degrees. Knowing the distance from Alexandria to Syene
to some 5000 stadia, it was enough to compute the earth's radius.
Aristotle also argued the moon was a sphere (rather than a flat disk)
because the terminator (boundary of the sun's light on the moon) was
always an elliptical arc. The only shape with such a property is the
sphere, should the moon be a flat disk, no terminator wouldn't appear.
Aristarchus determined the distance from the earth to the moon as 60
earth radii (57-63 earth radii in actuality). He also computed radius of
the moon as 1/3 the radius of the earth. Aristarchus had knowledge of
lunar eclipses being caused by the moon passing through the earth's
shadow and since the earth's shadow is 2 earth radii wide (diameter) and
the maximum lunar eclipse lasted for 3 hours, it meant that it took 3
hours for the moon to cross 2 earth radii. And it also takes around 28
days for the moon to go around earth, sufficient to compute the moon's
radius. In addition, the radius of the moon in terms of distance to the
moon was determined by the time it takes to set (2 minutes) and the time
it take to make a full (apparent rotation) is roughly 24 hours. Next,
the Sun's radius was measured by Aristarchus by relying on the moon.
Having computed the radius of the moon as 1/180 the distance to the
moon, he knew that during a solar eclipse that the moon covered the sun
almost perfectly, using similar triangles, he inferred that radius of
the sun was also 1/180 the distance to the sun. But to determine the
distance to the sun, he knew that half moons happened when the moon
makes a right angle between the earth and sun, full moons occurred when
the moon was directly opposite the sun and new moons occurred when the
moon was between the earth and sun. This meant that half moons occur
slightly closer to new moons than to full moons. Simple trigonometry
could then be used to compute the distance to the sun at 20 times
further than the moon, but a time discrepancy of 1/2 hour meant that the
actual distance is 390 times the distance of the earth to moon. This
also lead to the conclusion that the Sun was enormously larger than the
earth and the first heliocentric proposal, later adapted by Copernicus. <br />
<br />
Continuing our trek up the cosmic distance ladder, the rung of the planets and speed of light is quite a story. The ancient astrologers realised that all the planets lie on the ecliptic (a plane) due to the fact that they only moved via the Zodiac (the set of 12 constellations around the Earth. Ptolemy produced inaccurate results due to his geocentric model while Copernicus made highly accurate conclusions, initially poring over the annals of the ancient Babylonians who knew that the synodic period of mars repeated itself every 780 days. The heliocentric model allowed Copernicus to calculate the actual angular velocity as 1/170 and knowing that the earth took 1 year to go around the sun he would subtract implied angular velocities to find that the sideral period of mars was 687 days.Copernicus determined the distance of mars from the sun to 1.5 AU (astronomical units) by assuming circular orbits and using measurements of mars' location in the Zodiac across various dates. Brahe made similar predictions but they deviated from the Copernican regime, Kepler maintained that this was so because the orbits were elliptical and not perfect circles as Copernicus has assumed. Kepler would attempt to compute the orbits of the earth and mars simultaneously and since Brahe's data only gave the direction of mars from the earth and not the distance, he would need to figure out the orbit of the earth using mars. Working under the assumption that mars was fixed and the earth was moving in an orbit, Kepler used triangulation to use Brahe's 687 day interval to compute the earth's orbit relative to any position of mars. Such allowed the more precise calculation of the AU by parallax (measuring the same object from two different locations on earth), especially during the transit of Venus across the sun in multiple places (including Cook's voyage). But the anomaly of the precession of Mercury (where the points of aphelion and perihelion progressively wind around one another in a circular manner) could not be reconciled with Newtonian mechanics, so general relativity was invoked.The first attempts at accurately measuring the speed of light (<i>c</i>) was by Rømer who measured <i>c </i>by observing Io, one of Jupiter's moons that made a complete orbit every 42.5 hours. Rømer noticed that when Jupiter was aligned with the Earth, the orbit advanced slightly but when it was opposed, it slowed and lagged by around 20 minutes. Huygens inferred that this was because of the extra distance (2 AU) that light had to travel from Jupiter, so light travels 2 AU in 20 minutes; hence the speed may be computed to 300,000 km/s.Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-24485480566141079912013-07-04T23:11:00.001-07:002014-10-03T20:29:39.518-07:00Entropy- Life and The Second Law<a href="http://image.funscrape.com/images/c/chick-8724.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="256" id="irc_mi" src="http://image.funscrape.com/images/c/chick-8724.jpg" style="margin-top: 0px;" width="320"></a>What do life, gravity and the second law of thermodynamics have in common? Entropy of course! The very ground rule that prohibits perpetual motion machines and one hundred percent energy efficiency is often dubbed 'the degeneracy principle'. But its implications for physics and biology are worth taking a peek. The loss of useful energy, which roughly equates to the degree of disorder or chaos present in a system is often equated as entropy; just like when a piston in a cylinder oscillates, its motion represents useful energy while the residual heat is disordered because it's the random motion of particles. The second law posits that in a closed or isolated system, the total entropy can't decrease nor will it rise indefinitely without limit, there is a state of 'maximum chaos' or maximum entropy that represents thermodynamic equilibrium. Once a system has reached that stage, it's a point of no return. Think of two bodies, one hot and one cold; heat moves from the hot body to the cold until they eventually both reach uniform temperature (equilibrium), so the initial state of heat can be considered as more organised, thus of lower entropy in contrast to the final state where heat has been chaotically dispersed to the maximum amount of molecules (heat always flows from hot to cold). <div><br></div><div>Coming to living systems, there is no contradiction to the second law just as a fridge allows heat to go from cold (the interior of the fridge) to hot (the kitchen); the fridge is an open system just like the living cell. So life can go on evolving, filtering deleterious mutations via natural selection and exporting the accumulated entropy as long as the environment can provide free energy. But unlike a state of equilibrium (maximum entropy), a state of disequilibrium is highly unstable and natural phenomena are constantly trying to increase the level of entropy to the maximum degree, but there are means to circumvent this natural tendency. Imagine a mixture of air and fuel vapour, such a mixture doesn't have maximum entropy but it would desire to ignite to release heat and increase entropy; such a system is incredibly stable yet incredibly fragile, thus it's an example of a 'metastable' state. Living systems rely on metastable sources of energy for usable energy and take advantage of enzymes and catalysis to circumvent potential obstacles to the release of such energy from inorganic systems.</div><div><br></div><div> The question of the origin of the biological information embedded upon DNA and the associated nucleic acids may be described via Shannon's information theory that proposes information as a form of 'negative entropy' while random noise and interference as the disorder itself; so the second law may be reformulated as an increase in entropy and a decrease in the information quantity of a system. But as mentioned, like fridges, living cells are not closed systems and so in principle, the information quantity of a cell can increase if the information present in the environment also increases (the source of biological information is the environment). Thus, processes such as metabolism, reproduction and locomotion which are central to life and continuity are based on the flow of information between the living system and the environment and exothermic heat (body heat) can be thought of as a means of releasing entropy. </div><div><br></div><div>But the very origin of information itself is still in question, if it spontaneously appeared one day, that would be tantamount to a reduction of the total entropy of the universe and thus a violation of the second law. So the information must have been there from the very beginning; but the cosmic microwave background (CMB) has an incredibly uniform spectrum which equates to a state of thermodynamic equilibrium, but that's a state of maximum entropy which equates to minimum information. How can that be so if the second law prohibits the total information quantity of the universe to increase with time? Where did the present 'extra' information come from? In other words, if the universe began in maximum entropy (equilibrium), how did it reach its current phase of disequilibrium? </div><div><br></div><div>The answer is surprisingly gravity!</div><div><br></div><div> If you put gas in a box and leave it there, it will reach a state of equilibrium but gas in interstellar space is subject to gravitational forces and gradually forms stars via accretion that release free energy or negative entropy. So just because the CMB is uniform, it doesn't mean the early universe was in a state of equilibrium. Hence, when the large scale structure of our universe was forming, the gravitational 'clumping' that caused star and galaxy formation resulted in an 'entropy gap' ∆S, a difference between the actual entropy (S<span style="font-size: xx-small;">act</span> = S<span style="font-size: xx-small;">max</span> + ∆S) and the maximum possible entropy, therefore stars like our sun are trying to fill this gap with their light. Therefore, all sources of negative entropy or free energy can be extrapolated back to the entropy gap that gravity created.</div>Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0tag:blogger.com,1999:blog-2297768638371156952.post-38494910892748246052013-07-02T01:47:00.004-07:002014-01-27T18:29:09.162-08:00Singularity Theorems- A Crash Course<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBFw9bJkB_m2fBLQRyYTyhH8LQSy8rHY4iRxaNTVTpXPbB7rUZY_ETr5sVzVOVQ4MfhDR9Qk38VNhn6KfmTIVS0yNrRnsd_EEnzWpEH0S2gdUibHIVnvoVANQoJOilwHqmXneyKoKDUg1g/s527/Singularity+theorems.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBFw9bJkB_m2fBLQRyYTyhH8LQSy8rHY4iRxaNTVTpXPbB7rUZY_ETr5sVzVOVQ4MfhDR9Qk38VNhn6KfmTIVS0yNrRnsd_EEnzWpEH0S2gdUibHIVnvoVANQoJOilwHqmXneyKoKDUg1g/s320/Singularity+theorems.PNG" height="289" width="320" /></a></div>
In high school, we learn to prove congruent triangles from first principles; similarly in cosmology, indirect yet powerful arguments can be made on the basis of little or no dynamics. A singularity in general relativity is characterised by 'geodesic incompleteness' where time-like and null geodesics can't be extended to the infinite past or future but terminate after a finite proper time boundary. The Friedman equations hold that in an increasingly homogeneous and isotropic universe (such as ours), there was once a time when distances between particles was zero. And since Einstein's field equations hold that a given distribution of energy and momentum is proportional to the geometric properties of spacetime (particularly its curvature), the initial zero volume causes the curvature to become infinite. Crucial to the understanding of the singularity is the notion of a geodesic, which is the worldline of the shortest path traced by a particle only subject to gravitation (the curvature of space time) and not any other force; because the worldline is shorter when not accelerated, a geodesic may also be defined as the worldline where the four acceleration is zero (in the language of special relativity). Like the moon orbiting around the earth, it is just tracing the shortest path via curved spacetime ie. a geodesic. A geodesic is to a sphere, what a straight line is to a flat surface; a straight line and a geodesic are both the shortest distance between two points, but unlike straight lines, geodesics are not infinite in length (they are closed and always circle back on themselves) and they are never parallel. On a globe, only the equator and lines of longitude are geodesics. If we follow the path of a particle back in time to the point of infinite density, the geodesic will terminate, and the particle will cease to exist and will not anymore be part of spacetime. Identifying unextendable geodesics is used to identify singularities in theorems. So if the universe is expanding, in fact, accelerating in its expansion, does it follow that we can extrapolate back to a point when all galaxies and clusters were packed into a single point? In the 1960s, it was thought that any form of matter would adhere to the strong energy condition (suggests a tendency for geodesics to merge to guarantee that gravity is attractive: <i>pc^2+3p>0 </i>) and because the universe is not entirely homogenous and isotropic as the Friedman-Robertson-Walker metric holds (it is only so on large scales), it is theoretically possible to avoid singularities if particles of mass miss each other when you trace their worldlines back in time (big bounce). Hawking and Penrose, assuming a strong energy condition (and causality conditions on global structure like no closed time-like curves to prevent time travel) proved that you can have geodesic incompleteness in a space-time that is not completely homogenous and isotropic, thus the presence of singularities is extremely generic even in black holes. But inflationary space-times don't abide by the strong energy condition and in fact violate it, so the Hawking-Penrose singularity theorems didn't apply to them.<br />
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The kinematic incompleteness theorem of Borde, Guth and Vilenkin proved that inflationary space-times are not past geodesically complete and this indicates under general relativity an initial singularity. They showed an integral going from <i>a(t) </i>distant past to now is bounded (only condition assumed is Hubble constant over zero) and is purely geometric, not assuming any dynamics such as energy conditions. The momentum of an object or test particle travelling on a geodesic is red-shifted in an expanding universe and extrapolating back into the past causes the geodesic to blue-shift, their theorem showed that the blue-shift reaches the velocity of light in a finite proper time (or affine parameter for photons) showing such a trajectory to be geodesically incomplete. Inflation is an exponential phase of de Sitter expansion, a full de Sitter space can't be past-eternal as it would experience a contracting phase preceding it that would cause tiny perturbations preventing the future expansion of the universe. Eternal inflation and cyclic models (which lead to thermal death) are both past geodesically incomplete and the emergent model (which assumes a closed and static universe in the asymptotic past) can collapse quantum mechanically, so they can’t be infinite into the past, even multidimensional brane models can't be extended indefinitely into the past. So its safe to say the universe had a beginning that is if you don't consider the <i>subtleties</i>...Hasan Mohammadhttp://www.blogger.com/profile/08872743961640358570noreply@blogger.com0