Arcadian Functor

New Format Blog

2010-04-10T13:01:00.000+12:00

Not sure if this will work out, but future posts should appear at Arcadian Pseudofunctor.

Women at Work

2010-04-10T09:35:00.002+12:00

Until the 1200s women in Europe often worked for a living, even for themselves, and played prominent roles in public life. It was the priests and noble women who learned to read, because noble men had to focus on fighting. The slow demise of women was undoubtedly heavily influenced by Christian thought, but as an institution the Church was not solely responsible for curbing their rights.
An early culprit was that fine new European institution, the University. Historically, many women had practised empirical medicine, but from 1271 the University of Paris insisted upon formal certification. By the early 1300s, women were being prosecuted for practicing medicine unlawfully. One example is Jacqueline Felicie de Alemania.
In Opera Muliebra, David Herlihy argues that women continued to be employed in many professions up until the population growth of the 1400s, after the great plague. In this century the power of the professional guilds was largely responsible for excluding women from apprenticeships.
The Church had tried to put women in their place for a millenium, without much success. The overriding factor in this story is that urban men wanted good work, once they had stopped fighting each other, and this was most easily achieved by excluding women, with excuses from Christian thought.

Dwarf Mysteries

2010-04-08T11:46:00.003+12:00

Universe Today reports on the discovery of a companion to the brown dwarf 2M J044144.

Astronomers say it is the right size for a planet, but they believe the object formed in less than 1 million years — the approximate age of the brown dwarf — and much faster than the predicted time it takes to build planets according to conventional theories.

Louise Riofrio predicted years ago that such planets would be found, because planets can form around tiny black holes. Thanks to Hubble and Gemini for these beautiful images.

M Theory Lesson 312

2010-04-06T17:11:00.005+12:00

Let us now take two quark matrices and multiply them together. Using the phase matrices (in terms of $12$-th roots) on the MUB side of the twisted Fourier transform, for anti-up and anti-down quarks, we find that the product is a positron in the dual braid space. This is a complementarity between quarks and leptons, taking full magic matrices to fun operators.

Quote of the Week

2010-04-05T18:36:00.001+12:00

Disgruntled, unemployed male postdoc:

Science has withstood the Catholic Church and its death threats. Science is not gonna go down to a bunch of feminists.

M Theory Lesson 311

2010-04-04T12:03:00.011+12:00

Under the correspondence between ribbon twists and roots of unity, as in there is a matching of particle ribbon diagrams to matrices, giving in particular Observe how two copies of each $1$-circulant set arise from the choice of crossings in the braid diagram. Complex conjugacy is a flip of crossings. Given these matrices, a twisted Fourier transform of the form $F C_{a} F^{\dagger} = DC_{b}$, for $D$ a phased diagonal, takes MUB type operators $C_{a}$ to particle circulants $C_{b}$. For example, Let us not forget the quarks! Quarks do not correspond to basis circulants, so under the inverse twisted transform they come from more general matrices. For example, the $C_a$ phases of an up quark are given by which is clearly not a MUB operator. Note, however, that this is a magic matrix, with all rows and columns summing to $- \pi / 6$.

M Theory Lesson 310

2010-04-03T10:54:00.017+13:00

Permutations may be represented by symmetric braids. A category theorist would usually draw a diagram like indicating that the braid crossing goes neither over nor under, and that one can slide strands across each other. It would be nicer if we could draw a braid like because this obviously untangles to the identity braid. However, the two crossings here are different, like in the law $(\sigma) \circ (- \sigma) = 1$, which is to say that $\sigma$ is a bit like the complex $i$, satisfying $i + i^{-1} = 0$. How about elements of $S_3$? The permutation $(231)$ cubes to the identity, as in the diagram where the crossings have been chosen so that no strand actually links with any other. Note that each $(231)$ section is a Bilson-Thompson braid. What fun! By assigning $n$-th roots of unity to each strand one obtains a fun operator, for $S_d$. The choice $n = d+1$ (see last time) gives a representation of $S_n$.

M Theory Lesson 309

2010-04-02T11:38:00.008+13:00

Recall that much of the tribimaximal mixing literature discusses small finite groups, such as $S_3$ and $A_4$. For example, Ernest Ma considers a $2 \times 2$ representation of the six element group given by the matrices where $\omega$ is the usual root of unity. This is an example of a fun set, with $d = 2$ and $n = 3$. In fact, it is the full such set under the condition that the non zero entries multiply to $1$. So special representations need no longer live in boring categories of vector spaces!

Meanwhile II

2010-04-02T10:01:00.002+13:00

So I've found a suitable proof reader for my book, am busy hunting down literary agents, and am making progress with exciting, although naturally temporary, alternative career options. Now if, and it is a big if, any of these avenues should land me in the UK again, where should I spend some time? Hmm. I wonder what Cambridge is like ...

Quote of the Day

2010-03-31T12:42:00.000+13:00

Courtesy of the small grocery shop near my place, which places a thought for the day on the chalkboard outside, no matter the weather:

The Emperor will not judge you by your medals and diplomas but by your scars.

Quantum Computation

2010-03-30T16:47:00.010+13:00

A well funded industry these days is research into the real world implementation of small sets of carefully chosen quantum operations, combinations of which are able to closely simulate any quantum computation. This is known as universal quantum computation, or UQC.

For example, in this paper by Kitaev and Bravyi, it is shown that the Clifford operations (which stabilise Pauli operators) along with certain magic states are sufficient for UQC. They assume that Clifford operations may be implemented ideally, and that the preparation of magic states is faulty. However, they first consider ideal magic states, such as
$|H \rangle = \textrm{cos} \frac{\pi}{8} |0 \rangle + \textrm{sin} \frac{\pi}{8} |1 \rangle$
$|T \rangle = \textrm{cos} \beta |0 \rangle + \omega \textrm{sin} \beta |1 \rangle$
where $\omega$ is a primitive eighth root of unity and $\textrm{cos} 2 \beta = \sqrt{3}^{-1}$. In particular, $| T \rangle$ may be used to implement a one qubit phase gate for the $12$-th root of unity. With the Clifford operations, this gate gives UQC.

The only Clifford generator that is not obviously a fun (field with one element) operation is the one qubit Hadamard gate (Fourier transform), but recall that (in MUB maths) this basis behaves like the zero of a finite field, or the standard choice of marked point for a fancy set! Now let's do UQC without complex numbers.

Meanwhile

2010-03-29T12:20:00.003+13:00

Well, it seems that no matter how hard you try, you just can't keep a good woman down: a second peer reviewed AIP paper was just accepted for publication; I have just finished a first draft of my scary book about life for women in Oxford; and I'm considering alternative careers (not really) that use my survival expertise.

Meanwhile, I'll get back to wondering which streets to haunt when I become homeless once again. Have a nice day.

M Theory Lesson 308

2010-03-27T16:12:00.014+13:00

Any elementary matrix, denoted $E_{ij}$, can be expressed as a Fourier transform of the democratic matrix. In the $3 \times 3$ case, the nine choices for $F$ give the $9$ elementary matrices. Thus any matrix at all may be expressed as a combination of such Fourier transforms. For example, the circulant permutation $(231)$ uses the three Fourier matrices that sum to A general $1$-circulant is therefore a combination of three transforms, each of this form. An alternative choice of phases for $(231)$ would have given us which is a bit more reminiscent of CKM symmetries. Since the tribimaximal mixing matrix may be expressed as a product $F_3 F_2$, one hopes that the CKM matrix is also easily written in terms of a natural transform.

Magic Motives II

2010-03-26T14:08:00.006+13:00

If sets and vector spaces are secretly the same thing, and spaces are built out of these new sets, then there should be one big category of spaces that has everything in it, including invariants!

For instance, a vector space of dimension $n$ over a finite field may be represented by all $n$-tuplets of MUB operators representing the field. Now these tuplets are just collections of arrows in the category of fancy sets. A triplet of $3 \times 3$ matrices with cubed roots of unity would act on a $27$ element set, via Cartesian product. The collection of all finite dimensional vector spaces over $F_3$ would live in the set subcategory made up of Cartesian powers of the three element set.

Similarly, spaces for the two element field $F_2$ may occupy powers of the two element set, usually denoted by $\Omega$ in the ordinary topos. This suggests that a power set monad for fancy sets might have something to do with invariant functors for $F_2$ (or even $2$-adic numbers). How cool would that be? The world of motives would then return to Grothendieck's dream.

So Few

2010-03-25T10:12:00.003+13:00

Thanks to FSP for mentioning the Breaking Through Barriers website. Their new report on the problems faced by women in science contains basic suggestions on what science departments can do to improve the situation, including:

Teach professors about stereotype threat and the benefits of a growth mindset.
Take proactive steps to support women.
Ensure mentoring for all faculty.
Learn about your own implicit bias.
Take steps to correct for your biases.
Create clear criteria for success and transparency.
Raise awareness about bias against women.

Job Hunting

2010-03-25T09:29:00.011+13:00

There is one Kiwi government source of science funding for which I am still eligible to apply. Other countries have similar funding processes. However, in order to apply for such grants I require a host institution. The Kiwi universities don't even reply to my emails, and neither do most of the foreign ones. Occasionally I receive a polite rejection. Fellowship applications are ongoing, although now clearly pointless. Harvard sent me an amusing rejection email, but most places don't bother. With so few jobs, one doubts that anybody bothers to read the Job Wanted ads.

Winter is fast approaching. Should I take up a cleaning job or a mountain job? They each have their advantages and disadvantages. Both would require me to move yet again. Neither would give me much opportunity to do research. The standard of living here is not high, for the working class. The average person spends 40% of their income on rent, and food prices are now international. Even with a full time job, my expert budgeting skills would come in handy.

What are the alternatives? In the local news today, health law expert Jonathan Coates said the Bill of Rights Act and common law were clear about a person's right to starve themselves to death, even if other people didn't like it. I guess effective hunger strikes are a real possibility here.

In the past, disgruntled antipodeans would simply leave, never to return. This is becoming more difficult these days, with emigration to Europe or the States requiring either a job offer or tonnes of dosh. Well, at least the sky here is still blue.

Magic Motives

2010-03-23T13:11:00.022+13:00

The most fashionable of all phrases amongst real mathematicians studying QFT, occasionally mentioned here, are the words motivic cohomology. This is supposed to be the mother of all cohomology theories. But what is cohomology anyway?

As a basic concept, cohomology relies on the logic of ordinary sets, particularly the difference between unions and disjoint unions. The latter type of union keeps track of which set each element actually came from, so it tends to double count intersections. In the category Set, disjoint union is a coproduct. Ordinary unions are a little less natural, but intersections are pullbacks of subset monics.

Universality is a basic categorical concept. A cohomology theory usually assumes a standard set of axioms for a cohomology functor $H^{*}$ from some category of (commutative) spaces (which we want invariants for) to a category of groups (where invariants live). The existence of group inverses is related to the arbitrariness of path directions in a commutative space. A universal cohomology theory is supposed be about an elusive category of motives.

But thinking of the field with one element, what happens if we have sets with funny actions, instead of just sets? Are our spaces necessarily commutative? Perhaps the underlying logic of intersection and union should be modified to properly account for the geometry of the absolute point. This might require drawing higher dimensional limit diagrams, or looking at higher dimensional target categories, not necessarily groupoids. Fortunately, some really smart people are now thinking about noncommutative motives, but it may take a while for us poor physicists to see what is going on.

M Theory Lesson 307

2010-03-22T10:46:00.005+13:00

Such Hermitian matrices provide a basis for all $3 \times 3$ Hermitian $1$-circulants in the form Since the eigenvalues of each basis matrix take the values $(1,1,-1)$, the eigenvalues of the sum are of the form
$\lambda_1 = \alpha + \beta - \gamma$
$\lambda_2 = \alpha - \beta + \gamma$
$\lambda_3 = - \alpha + \beta + \gamma$
providing an alternative characterisation of mass triplets, replacing Brannen's $v$, $s$ and $\theta = 2/9$ with
$v = \alpha + \beta + \gamma$
$s = \frac{2 \gamma}{1.10265678}$
Note that when the Hermitian matrix is corrected by the appropriate phased diagonals, it arises as the Fourier transform of a circulant with only three non zero entries, representing the mass triplet. This Hermitian basis is only slightly different from the one derived by Brannen in his recent paper on generations.

M Theory Lesson 306

2010-03-21T14:22:00.019+13:00

The (wreath) product used in the theory of the field with one element is between the symmetric group $S_d$ and $d$ copies of the $n$-th roots of unity. For $\mu$ the primitive $n$-th root, an element of the product group is usually written like and the multiplication is given by semidirect product
$(g_1 , \pi_1) \circ (g_2 , \pi_2) = (g_1 \cdot (\pi_1 g_2) , \pi_1 \pi_2)$ otherwise known as a 2-group composition. For this particular group, the semidirect product is given by ordinary matrix multiplication The examples assume that $d = 3$, but $n$ is fairly arbitrary. How does the three dimensional Fourier transform act on such phased circulants? We may decompose the result into a diagonal and a $1$-circulant, as in Consider the case where $\mu^a = \mu^c$, reducing the circulant to where the diagonalisation of the ordinary $1$-circulant permutation is clear, if $\mu^a = \mu^b$. In order to be Hermitian, it is clear that the phases must satisfy $\mu^a = \pm 1$ and $\mu^b = \pm 1$. For example, when $(\mu^a , \mu^b)=(1,-1)$ then the two real eigenvalues for this operator are given by
$\lambda = \frac{1}{3} (1 - 4 \textrm{cos}(\frac{2 \pi k}{3})) \in -1, 1$
which are the values of $\mu^i$ as square roots of unity. Note that the Hermitian condition can only be satisfied here if at least two of the roots are the same, so this is the general situation for such phased operators. The natural generalisation is to replace $S_d$ with the braid group on $d$ strands, labelling strands with roots of unity.

Quote of the Month

2010-03-20T17:31:00.001+13:00

From Zuska:

You are not supposed to notice sexist behavior, and everything in our society is carefully designed to help you understand and accept it as natural and just the way things are and evolution and the battle of the sexes and God's will and girls like pink and boys love trucks and men are better at spatial hoo hah and women are so verbal and boys will be boys and act like a lady and don't be a slut and men can't help themselves and blah blah blah. If you should, by some amazing effort of will and education, manage to pull the curtain aside, there will be a great show of smoke and fire and booming voices declaiming from a huge green glaring disembodied head "pay no attention to that patriarchy behind the curtain!" Because, well, you might notice that it's a humbug.

Quirky Quasars II

2010-03-19T19:34:00.010+13:00

The Arp heresy is the hypothesis of intrinsic redshift for quasars, which are believed to be ejected from galaxies. An alternative, using a simple redshift-distance relation, is to drop the assumption that classical geometry holds for the triangle shown. That is, we assume that the galaxy (at low $z$) is fairly close to us and that the quasar (at high $z$) is very far away. But we do not assume that the distance between the galaxy and the quasar is determined by the pink curve. In fact, the observed filaments connecting quasars and galaxies suggest that the two objects are close together. From the perspective of Earth, it looks like the filament matter travels through cosmic time. If quasars are busy creating galaxies in the early universe, perhaps they are also creating their futures!

Cycles of Time

2010-03-19T17:18:00.013+13:00

Penrose's new book, Cycles of Time, is due out soon. This discusses his own thermodynamic cosmology, in which there are slowly decaying masses and information loss. Wrong for sure, but a step in the right direction.

A recent interview also mentions another upcoming book by Penrose, entitled Fashion, Faith and Fantasy in the New Physics. Faith questions the idea that quantum mechanics is the final word on the universe, Fantasy is the standard cosmology and Fashion is being a stringer. Some, such as Woit, would argue that being a stringer is no longer the fashion, but they still seem to have most of the jobs.

Meanwhile, kneemo provides the link to Strings 2010 in Texas. My broadband limitations will not allow me to watch seminars online, so please comment if there is anything interesting here, or elsewhere.

Quirky Quasars

2010-03-17T13:51:00.020+13:00

The 2009 paper by David Elbaz, Quasar induced galaxy formation: a new paradigm?, discusses the theory that supermassive black holes are responsible for galaxy formation.

The team looked at the quasar HE0450-2958 from Chile and noticed that a jet of matter from the black hole pointed exactly in the direction of a star forming region in a nearby galaxy. As Louise would ask: if galaxies are formed this way, even early in cosmic time, then where did all the black holes come from? New Scientist calls this the 64000 dollar question. Goodbye LCDM.

Note that this is a neat opposite of the Arp theory, where galaxies eject quasars. It would explain why the local galaxy M33 is missing its central black hole: the black hole has not yet arrived in the centre. That is, the black holes can create galaxies from nearby gas clouds and only later migrate into the galactic centres. The quasar jets can contain so much matter that they might create a whole galaxy out of nowhere!

Ribbon Review

2010-03-16T09:18:00.012+13:00

Why you should love the Field with One element

In the theory of $F$, matrices are no longer interpreted as linear operators for complex number Hilbert spaces. If we can do quantum mechanics without ordinary vector spaces, using special sets instead, then we can consider the $n \times n$ quantum operators as a reduction of the larger set representing the braid group $B_n$.

For example, the two strand group $B_2$ consists of the unknot, the unlink, a series of Hopf links and the series of $(2,q)$ torus knots. These knot diagrams look like twisted ribbons. Recall that a tripling of such ribbons, using six strands, was used in the Bilson-Thompson particle scheme, as shown.

Prime Evil Cats

2010-03-15T12:27:00.029+13:00

Category theorists are fond of replacing the counting numbers by sets, in the category Set. The trouble is that prime numbers don't make a lot of sense for ordinary sets. If I buy 3 oranges and 5 apples, I can add them by putting them all in the same fruit bowl. On the other hand, what is special about three oranges, as opposed to four or six? The category Set does have Cartesian product, but there is nothing special about sets with a prime number of elements.

The simplest object for which the primes define a space of some kind are the integers, as a special object in the category of rings. But as Kapranov and Smirnov point out in their paper, this space has dimension greater than zero, with respect to any reasonable topology. Where are the points?

This question leads to a study of the field with one element. Recall that ordinary sets are like vector spaces for this field $F$, but sets can also come with extra structure. In particular (for an extension $F(n)$ of the magical field $F$) one has pointed sets and actions by roots of unity. Now sets are usually acted on by permutations, so we want mixtures of permutations and roots of unity, which is what MUBs were about!

The correct actions for $F(n)$ are given by the wreath product of permutations $S_{d}$ and roots of unity. That is, $d \times d$ matrices with only one non zero element in each row and column, with every element an $n$-th root of unity. When $n$ is prime, and when $n$ corresponds with $d$, we get nice MUB type operators.

Unfortunately, although quantum mechanics is suddenly a whole lot closer to arithmetic, it is still not clear why quantum $3$-oranges are so much better than quantum $4$-oranges, except that $n$-oranges had better be built from prime ones.

M Theory Lesson 305

2010-03-14T12:13:00.005+13:00

Since the g-vector is obtained from the h-vector using differences, it may also be expressed as a square matrix. For $d = 3$ this is so for the $d=3$ associahedron, we obtain using the Narayana numbers directly.

M Theory Lesson 304

2010-03-13T09:22:00.015+13:00

The special $M$ matrices map the h-vector to the face vector as follows. First turn an h-vector into a g-vector by taking differences of entries. For example, $(1,3,1)$ will become $(1,2)$, because we imagine a dummy zero to the left of the h-vector. The vectors are shortened, because it is unnecessary to include the information that there is one cell for the polytope in the highest dimension. In dimension $d$, the $M$ matrix is defined by which leads to the odd convention of writing, for $d = 3$, The pentagon formula is given by which shows that a pentagon has $5$ vertices and $5$ edges. Our favourite associahedron in dimension $3$ is described by These $M$ matrices work for any polytopes. Another example is the cyclohedron face vector, given by Note that the usual description of the $M_d$ matrices does not define them as square matrices, but square matrices work fine.

Galaxies and Quasars

2010-03-12T14:36:00.024+13:00

Supernova Condensate reports on a mystery with our neighbouring galaxy M33. A member of the Local Group, M33 appears to be missing its large, central black hole! More precisely, an upper limit on the central mass of $3000$ solar masses is obtained.

In his book Quasars, Redshifts and Controversies, Halton Arp discusses quasars associated with M33. Figure 8.12 shows a line of high redshift quasars lying between M33 and M31, the Andromeda galaxy. There is also a concentration of low redshift quasars near M33.

Note that Andromeda has a possible binary black hole system at its core. The quasar data suggests a strong interaction between M33 and M31. This lends support to the unpopular idea that the central black holes, or lack thereof, of such galaxy pairs are not independent. A possible relation between high $z$ quasars and AGNs is discussed here.

M Theory Lesson 303

2010-03-12T10:26:00.014+13:00

Recall that the counting in BCFW recursion hinges on the Catalan and Narayana numbers.

The Narayana numbers may be obtained from the associahedra via its dual simplicial complex, as shown by Fomin and Reading. This Pascal type algorithm computes the so called h-vector of a complex from the face vector. For example, for our favourite associahedron in dimension 3, the face vector is $(1,9,21,14)$, since there are $14$ vertices, $21$ edges and so on. Write these numbers along the diagonal left edge of a Pascal triangle, with ones along the bottom. The h-vector is obtained by taking differences of the entries to the left and below. So the number $8 = 9 - 1$ will be filled in to the right of the original entry $9$. Completing this process until the triangle is filled results in the h-vector on the right hand edge. In this case, we obtain $(1,6,6,1)$, which counts the allowed trees for the 7 gluon scattering amplitudes.

Now the g-theorem fully characterises h-vectors for polytopes. The face vector may be expressed in the form $gM$ (the McMullen correspondence), where $M$ is a certain matrix. In a recent paper it is shown that all minors of $M$ are nonnegative numbers.

Cubes Galore

2010-03-11T11:09:00.011+13:00

When multiplying $2 \times 2$ matrices, a pair of rows gives two multiplications and then an addition. By analogy, a cubic product on three operations would take a pair of faces, with the nonassociative product on these faces followed by the final addition. This gives which easily generalises to the $n \times n$ case. Alternatively, with one type of product a natural ternary product on three cubes $A$, $B$ and $C$ is given by
$(A,B,C)_{ijk} = \sum_{pqr} A_{ipq} B_{pjr} C_{qrk}$

Programming

2010-03-09T09:28:00.001+13:00

LOL

M Theory Lesson 302

2010-03-08T15:55:00.007+13:00

Assuming now that all matrix entries and scalars are complex numbers, let us consider a mass circulant $M$ in the form for two parameters $r$ and $\theta$. Under the nonassociative exponential product, $M$ acts on the right of the democratic matrix as a scaling, as in whereas its left action is of the form So when $\lambda = r = 1$, the special scale free value of $\theta$ results in a familiar choice for $M$, namely where $\omega$ is a sixth root of unity. Note that a zero element in a left hand factor results in a totally zero matrix, so the nonassociative product has many zero divisors.

M Theory Lesson 301

2010-03-05T17:33:00.020+13:00

Some time ago we looked at a nonassociative product for matrices with ordinary commutative number entries, using exponentiation and multiplication. For $3 \times 3$ circulants this product takes the form Consider a Koide mass matrix with two real parameters, $r = e^x$ and $\theta$. This may now be expressed in the form which puts the mass gap between distinct eigenvalues into a simple complex number, $x \pm i \theta$. Note that any base may replace $e$ here, so long as logarithms are taken in that base. Scalar multiplication of the left hand matrix by $\lambda$ results in a rescaling of $\lambda^{2x}$, so for the special value of $x = 1/2$ this nonassociative product preserves scale. Scalar multiplication on the right would not be permitted.

Women in Physics

2010-03-05T13:38:00.007+13:00

Dear patronising male physicists

Snippets of overheard gossip are easily answered online. So for the record: I have never slept with any bosses, supervisors, collaborators, students or support staff. Moreover, the next time I happen to mention the work of another female physicist, you might consider not taking this as an invitation to discuss her sex life with me. I fail to see how this topic of conversation could have any relevance to data obtained at the LHC experiments. Neither does telling me that she has no brain add to the professional discussion.

Many of you, over the years, have pointed out that my continuing effort with job applications is a complete waste of everybody's time. Believe me, I know that. But each one of those hundreds of applications is accompanied by an Equal Opportunity form, which will end up on the desk of a hard working statistician, and like good little scientists, we know that the numbers don't lie, don't we?

Fortunately, due to the excellent Academic Jobs website, I now have a job wanted page with an expiry date close to my 60th birthday. So the next time you think of giving me advice about how to get on in the world, ask yourself what you know. The J. Math. Phys. paper has finally appeared in the online journal. Apologies to those who do not have access to this site. This means that you will have to find new excuses to be rude to me, but I am sure that your imagination is up to it.

Since cities are expensive and noisy, at present I am living in a village with one shop, two restaurants and a small community hall. I might be wrong, but I strongly suspect that activities at the community hall do not include discussions of Koide formulae or motivic cohomology. Now I will let you return to pretending not to read my blog, since I have a very limited budget for internet time.

Have a nice day
Kea

FFP10 Day 3

2009-11-27T13:09:00.003+13:00

The three days of the conference passed quickly, and it seems that most people have already left Perth. I arrived early on the last day, in order to spend time with the lorakeets, kookaburras, ducklings and galahs.

Links: The Halton Arp website has interesting quasar information, as discussed by C. Fulton. The conference proceedings will be published early next year, and you can now play spot the physicist on the conference photo.

FFP10 Day 2

2009-11-26T12:35:00.003+13:00

On Day 2 of FFP10, John Hartnett spoke about an alternative cosmology that does not require gravitational waves.

In a later, split session on alternative cosmologies, we heard from Robin Booth, who has a concrete prediction for the recently launched Planck: the photon noise for the CMB should be 40 times that predicted by the standard cosmology. Perhaps more on the quasars later.

So by the time it came to the conference dinner, in the extravagant University Club, all participants seemed quite comfortable telling jokes about how many string theorists it takes to change a light bulb.

FFP10 Day 1

2009-11-25T12:32:00.007+13:00

FFP10 has a variety of interesting badge wearing participants, including Apoxyomenos. However, as a statue, Apoxyomenos has difficulty taking a seat in the air conditioned lecture hall.

Professor 't Hooft began the proceedings with his lecture on Gravity and the Quantum. First he discussed a concept of classical black hole complementarity for internal and external observers: the former seeing objects behind the horizon, but no Hawking radiation, and the latter observing Hawking radiation. In principle, these observers should see the same physics. The proposal of so called extreme complementarity sets up a perfect time reversal symmetry between the causal structures for internal and external observers. These assumptions allow for a conformal factor relating two observations, and the suggestion that generators of scale transformations have a non local character. The second part of his talk discussed cellular automata as deterministic systems with a quantum mechanical description. That is, acceptable hidden variables in a theory of dynamics of states.

Huw Price thankfully managed to avoid multiverses in the first half of his talk on Time's Arrow and Eddington's Challenge, starting with a clear explanation of the distinction between dynamic and block views of Time (although the potential use of both together was not, as usual, considered). The most notable proponents of the latter view, in relatively modern times, include Einstein and Boltzmann. On the dynamical side we have Eddington, who, in 1928, said:

Events give ... no indication that they undergo what has been described as the formality of taking place.

Eddington supposedly coined the concept of the changing world as becoming, but that sounds rather like Hegel to me. Unfortunately, from this point on, the multiverse takes over as an attempt to address the challenge of Time's Arrow ... by creating universes that restore the overall symmetry.

From Perth

2009-11-23T19:49:00.003+13:00

Carl and I are now happily settled at UWA, enjoying Perth's notoriously perfect weather. We are only a 5 minute walk from beaches on the Swan river. The FFP10 fun starts tomorrow.

Mt John News VI

2009-11-14T07:19:00.002+13:00

Weather permitting, today's plan involves a pleasant wander up the Hopkins valley with a few astronomers. Tomorrow I head for Christchurch, and Monday for Australia. Put a prawn on the barbie for me ...

Mt John News V

2009-11-08T09:25:00.002+13:00

I'm now up to roughly 21 complete postdoc job applications for the year end! Employers looking for a hard working, mature, friendly, intelligent, categorical M theorist will have to get in quick!

Supernovae Seminar

2009-11-07T09:43:00.002+13:00

Next Thursday, the astronomer Robert P. Kirschner visits the South Island to talk about supernovae observations, without necessarily committing to the Dark Force.

Supernova samples are now large enough that systematic errors dominate over statistical uncertainties, so better understanding, not just a larger sample, is required to make progress on this question. New observations carried out at near-infrared wavelengths promise to reduce these errors and lead to a more certain knowledge of the nature of dark energy.

Mt John News IV

2009-11-06T09:50:00.002+13:00

Without realising it, I submitted a paper some months ago to a respectable journal that uses blind refereeing. As far as I know, this is the first time I have sent a paper for blind review. Yesterday I was told that, with minor changes, the paper was accepted for publication. For the first time in my life, I found that the referee's report was constructive and polite. The world indeed works in mysterious ways.

Mt John News III

2009-11-02T10:15:00.002+13:00

Now that most physics jobs require three references from professionals who are familiar with one's work, I am struggling to apply for anything. As far as I can tell, only two current applications of mine are complete. Thanks all the same to those who have helped. On my return from Australia in December, I have lined up a mountain job for the Christmas and New Year period: warden of French Ridge hut. Those of you who have visited this spot will appreciate the inevitability of an improvement in my fitness. This midsummer, I will fall asleep to the sounds of rumbling icefalls.

Quote of the Month

2009-11-01T17:49:00.004+13:00

In the 1975 book by Maurice Pope on the history of decipherment (of Egyptian hieroglyphs, cuneiform and Linear B) there is a quote by the esteemed Professor Hyde, from 1700:

Travellers' graffiti ... a monument of ill writing and inexpert sculpture ... late, insignificant and scarcely worth the trouble of solving.

This was his assessment of the great Achaemenid tombs of Naqsh-e Rustam, which he visited. They date back as far as 1000BC. Having stood beneath these tombs once myself, I can testify that only a fool would think them insignificant to the age of decipherment. With three parallel texts, the tombs were a key element in the eventual decipherment of Old Persian cuneiform, and this in turn led to an understanding of other, far more ancient forms of writing, back to the evolution of writing from symbols and accounting systems in the dawn of history.

Anyone can be wrong.

LHC Era Begins

2009-10-29T10:00:00.002+13:00

As the LHC begins operations, real tests were run on the beam through LHCb. The LHCb RICH detector has also seen its first particle from cosmic rays, as the two rings shown here.

Multiverse Mania

2009-10-26T13:46:00.006+13:00

Matti Pitkanen points out that any reasonable quantum cosmology involves a multiverse, in some sense. Unfortunately, the word multiverse is too widely used in the painfully ludicrous context of stringy landscapes and the Dark Force, and this classical geometry essentially defines its meaning. If AF ever lapses into some strange use of the word, without clarifying its meaning, then you have permission to swear in the comments section.

It is quite difficult to figure out which multiverse advocacy group is the most impossible to forgive. Certainly the so called theoretical physicists are high on the list. But are the philosophers any less guilty? At least the physicists have the excuse that they were never required to take courses in the history and philosophy of science and, in true 20th century camaraderie, were rewarded for playing the game and forgetting about the problems that they were actually supposed to solve.

A professional philosopher of physics, on the other hand, should be able to dismiss the objective, observer independent multiverse with three words that they learned in kindergarten: I am thinking, therefore I exist. Descartes, and many others, must be turning in their graves, to see science so debased.

ViXra Video

2009-10-25T09:10:00.002+13:00

Thanks to Phil Gibbs for his video on the String Wars. Make sure you watch it right to the end.

White Dwarfs

2009-10-24T13:29:00.008+13:00

A Kiwi astronomer has been telling me about his work on white dwarf stars, which are the end states of around 99% of all stars. In theory, white dwarfs cool quickly due to neutrino emission from the core in a photon decay process

$\gamma \mapsto \nu + \overline{\nu}$

from photons that acquire an effective mass due to the plasma medium. This mass depends on the core density of the star. One aims to measure cooling rates for such stars by observing changes in the periods of their pulsation.

A Mt John result focuses on the fairly stable pulsating hot dwarf star EC20058-5234, which is about $0.55$ the mass of the sun. This is the only known stable white dwarf of DBV type. For such a hot star, plasmon neutrino cooling should be far more important than photon emission from surface processes. However, constraints on plasmon neutrino emission for this star, in terms of period decay, currently lie around $10^{-13} s s^{-1}$.

Some authors have also considered novel cooling processes for white dwarfs, such as axion emission.

Mt John News II

2009-10-23T15:48:00.002+13:00

I seem to be spending rather a lot of time sending futile emails to U.S. institutions requesting support for postdoctoral fellowship applications. I am doing the same with Oxford. Meanwhile the stunning spring weather continues and I am enjoying the local walks.

The LHC Era

2009-10-21T14:15:00.010+13:00

My visit to the University of Warwick in September naturally made me regret my ignorance of the LHCb experiment. Very little time remains for theorists to get off their asses (yours truly included) and make some decent predictions.

The LHCb experiment will study bottom quark physics. It consists of a vertex detector, track reconstruction capabilities, and two Cherenkov detectors for velocity measurements and particle identification, which will separate pions and kaons.

In particular, LHCb will further study the beyond the standard model CDF result for the CP violation parameter $2 \beta_{s}$ in decays of the meson $B_{s}^{0}$. The definition of this parameter is

$2 \beta_{s} = 2 \textrm{arg} \frac{V_{ts} V_{tb}^{*}}{V_{cs} V_{cb}^{*}}$

in terms of the usual CKM matrix parameters. As CDF points out (cheers, Tommaso):

The presence of physics beyond the standard model could contribute additional processes and modify the magnitude
or the phase of the mixing amplitude.

The Standard Model predicts $2 \beta_{s} = 0.04$, in contrast to the observation that $2 \beta_{s}$ lies in the interval $[0.32,2.82]$, with $68%$ confidence. The D0 experiment also reports on this decay.

M Theory Lesson 300

2009-10-20T08:34:00.002+13:00

Last time we considered the relation between $\Omega_{B}$, the baryonic mass fraction, and two phases appearing in Carl Brannen's mass matrices. A more natural choice involves the angles

$\phi = \frac{1}{9 \pi}$
$\alpha = \frac{1}{24}$,

where $\alpha$ comes from the phase $\pi / 12$. The difference $( \alpha - \phi )$ appears in mass relations for neutrinos, charged leptons and hadrons. We now have

$24 \alpha - 27 \phi = \Omega_{B}$

where $24 \alpha = 1$, the total of baryonic and dark matter components. Both the numbers $24$ and $27$ have a multitude of interesting number theoretic properties which M theorists enjoy. For example, $27$ is the dimension of the octonionic exceptional Jordan algebra, which in terms of $3 \times 3$ Hermitian matrices has a $24$ dimensional component coming from three octonion elements. The number $24$ decomposes into $2^3 \cdot 3$, and in Brannen's path integrals the $3$ indexes particle generation number, and $2$ stands for the fermionic spin quantum number.

Motives in Tokyo

2009-10-19T13:18:00.001+13:00

Thanks to Motivic Stuff for pointing out a wonderful workshop in December in Tokyo: International Workshop on Motives.

Mt John News

2009-10-18T13:11:00.002+13:00

The snow has gone now and the weather alternates between the usual warm, clear skies and today's cold rain. I have been bathing for hours in the hot springs, eating the excellent local Japanese food, and walking with friends from Wanaka. We discussed my job options, for when I return from Australia in December. Cleaning is more appealing than waitressing, but in the sparsely populated countryside these jobs are less reliable.

One original suggestion was motivational speaker. Not bad, heh? Can you see me in a white shirt, grey suit and red tie? Earning big bucks? Yeah, right.

Meanwhile, back in the Mt John kitchen, a local astronomer assured me (entirely without prompting) that he appreciated the compelling evidence for large primordial black holes. The Milky Way black hole, which we have actually observed through the remarkable motion of orbiting objects, is far too massive to have evolved via standard theories of stellar and galactic evolution.

Major Meltdown

2009-10-15T18:19:00.005+13:00

Lest there be anyone remaining under the delusion that all is well in the world of physics ...

Today Woit discusses the predictable actions of the arxiv over the backward causation ~~joke~~ theory. This follows a jaw dropping plunge by Carroll, who was already swimming in the murky depths of the Multiverse*, into a confidant explanation of the plausibility of backward causation ideas given the non local nature of quantum gravity:

Because they are not actually crackpots, they even admit what they’re doing — in their own words, “Our model with an imaginary part of the action begins with a series of not completely convincing, but still suggestive, assumptions.”

Well, it must be all right then, mustn't it? Or is there perhaps another scent in the air? In the words of Alberich: you eternal revellers! Beware!

*The Multiverse: the bandwagon idea that quantum information theory has won the String Wars, but that mainstream theory will still be hunky dory with that.

Quote of the Month

2009-10-13T13:17:00.002+13:00

From Overbye's article in The New York Times:

In an unpublished essay, Dr. Nielson said of the theory, “Well, one could even almost say that we have a model for God.” It is their guess, he went on, “that He rather hates Higgs particles, and attempts to avoid them.”

This malign influence from the future, they argue, could explain why the United States Superconducting Supercollider, also designed to find the Higgs, was canceled in 1993 after billions of dollars had already been spent, an event so unlikely that Dr. Nielsen calls it an “anti-miracle.”

You might think that the appearance of this theory is further proof that people have had ample time — perhaps too much time — to think about what will come out of the collider...

M Theory Lesson 299

2009-10-11T08:14:00.002+13:00

Recall that in the charged lepton and neutrino mass matrices, there is a peculiar phase given by the fraction

$\phi = \frac{1}{9 \pi}$,

in contrast to the cubed root of unity, which corresponds to the rational fraction $\omega = 1/3$. We have seen these numbers before. Observe that

$\frac{1}{3} \omega - 3 \phi = \frac{1}{9} \frac{\pi - 3}{\pi} = \frac{1}{9} \Omega_{B}$,

where $\Omega_{B} = 0.0450703$ is the baryonic matter fraction, first computed by Louise Riofrio in her varying speed of light cosmology. In other words, to put it more simply,

$27 \phi = \Omega_{DM}$,

the dark matter fraction. One suspects that the factor of $27 = 3^3$ is due to the dimensionality of the information space required to describe the dark matter quantum numbers.

From Christchurch

2009-10-09T04:46:00.002+13:00

Now 4.50am in Christchurch and I'm wide awake. It turns out that Oxford University have yet again had difficulties making foreign salary payments, and they neglected to pay me last month. Fortunately, I pre-booked all buses and am heading to Mt John this morning. Heavy snow is expected.

Thank You Oxford

2009-10-04T22:03:00.002+13:00

On March 4 the Heathrow bus dropped me off on High St. Bleary eyed, I lifted my head and saw the plaque to Boyle on the stone wall beside me, and it made me smile. I dragged my broken suitcase across the cobblestones to the gate at Oriel, where they were not expecting me. But a few phone calls later, I found myself in a comfortable room right in the city, where I enjoyed my first night.

At first, with weariness and disbelief that I should find myself here at all, there was only the shock of a functioning city, with its crowds and its garbage, its generosity and corruption. My student room on Cowley Rd was noisy at night, and it was over three months before I finally settled at home in Norham Rd.

And then it was summer. I had discovered the quietest corners of the large college gardens, my favourite chapels, and my favourite walks in the countryside. I was taken to lunch and dinner at Jesus and Balliol colleges. There were wonderful mathematics workshops and endless lectures to attend. The physicists were friendly. What more could I ask for than this? I will not forget you.

One night an old man at the Sheldonian told me that, in recent years, the light had changed. He said that now when he looked at the Magdalen tower in the afternoon, it did not seem real. We looked across the street to Trinity, and it was a beautiful night.

Fare well, Oxford. How fortunate I am, to have seen your dreaming spires.

M Theory Lesson 298

2009-10-04T02:47:00.011+13:00

A product of two Markov type limits is one way of writing down a six parameter $3 \times 3$ matrix with distinct elements. For this matrix to be Hermitian, we require that $a' = \overline{a}$, $b' = \overline{b}$ and $c' = \overline{c}$, obtaining a six real parameter class of Hermitian matrices of the form $H = A A^{\dagger}$.

Note that a general complex transition matrix $M$, with fixed column sum, satisfies a Markov type rule: a column sum $S$ for $M$ goes to a sum $S^{2}$ for $M^{2}$. Thus for $S = 1$, the limiting operator still has the Markov property. For any such complex $M$, there is then associated a unique Hermitian matrix $A A^{\dagger}$, where $A$ is the long time limit. This process reduces the $6$ complex parameters of $M$ to $3$.

A Day Out

2009-10-01T21:01:00.001+13:00

Criminally decadent it may be, but since the probability of returning is so low, I could not resist ... tomorrow.

HEP South

2009-09-30T21:41:00.005+13:00

The next in a series of conferences that I intend to participate in is HEP in the LHC era. This is in Chile in January. It is a wonderful part of the world, which I highly recommend visiting.

One Wonders

2009-09-29T21:39:00.003+13:00

Wasted paper, I guess. One does wonder about the other worlds that some people live in. From the Government Office for Science:

Rigour, respect and responsibility: A universal ethical code for scientists

Rigour, honesty and integrity
*Act with skill and care in all scientific work. Maintain up to date skills and assist their development in others.
*Take steps to prevent corrupt practices and professional misconduct. Declare conflicts of interest.
*Be alert to the ways in which research derives from and affects the work of other people, and respect the rights and reputations of others.

Responsible communication: listening and informing
*Seek to discuss the issues that science raises for society. Listen to the aspirations and concerns of others.
*Do not knowingly mislead, or allow others to be misled, about scientific matters. Present and review scientific evidence, theory or interpretation honestly and accurately.

Publications

2009-09-28T21:12:00.006+13:00

For many years people told me that, without a PhD, nobody would take me seriously. For the last few years people have been telling me that, without published papers, nobody would take me seriously. At 42, I think I get the idea. I cannot even apply for physics jobs without reference letters from professional physicists, even though many people I know apply for (and get) physics jobs without ever having studied physics.

But now it seems that Carl Brannen is publishing papers on quantum gravity left, right and centre! In respectable journals! Will people keep telling me not to waste my time with such amateurs? Will they keep saying I should focus on doing respectable science? What does that mean, anyway?

October

2009-09-27T23:00:00.001+13:00

Organised and ready for the weeks ahead. A total of 5 tickets acquired ... from the bus station in Oxford to Mt Cook village in New Zealand.

Mars Ice

2009-09-26T03:34:00.002+12:00

An article in Science explains that new crater sites on Mars indicate more water on the planet than previously thought:

Thermal models of one site show that millimeters of sublimation occurred during this fading period, indicating clean ice rather than ice in soil pores.

This follows confirmation of large amounts of lunar water.

M Theory Lesson 297

2009-09-25T23:51:00.004+12:00

A Markov chain for a three state system has a $3 \times 3$ transition matrix, with entry $A_{ij}$ the probability that the system transitions from state $i$ to state $j$.

If the system is time symmetric, the matrix is both symmetric and magic, in that all rows and columns will sum to $1$. But for time asymmetric systems, it is only necessary that the columns sum to $1$. Matrix multiplication stands for one step in the Markov process. A typical long time convergence will result in a matrix of the form:

a a a
b b b
c c c

In fact, if all entries of $A^{k}$ (for some $k$) are strictly positive, then this always happens, and the limiting vector is called the steady state vector for the system.

Seminar Thursday

2009-09-22T20:02:00.001+12:00

It seems that there will be an interesting seminar on Thursday at the University of Warwick!

Conference II

2009-09-20T22:19:00.002+12:00

Hah! The security guards happily let me into St Annes, and the lovely conference organiser asked Joseph Silk whether I could be let in. He refused. Apparently the theatre is very full and there is simply no space.

Shall we test them? There are about 60 particiants. The lecture theatre seats 100 people. Now I am guessing that people will be keen on skipping some lectures tomorrow and the next day. Would any participants be willing to offer me their valuable seat for a lecture that they are not interested in attending?

Conference

2009-09-20T22:00:00.003+12:00

I just found out about a cosmology conference around the corner from my office! Hah, let's see if I can gatecrash this YACWNW ...

Quote of the Month

2009-09-20T00:15:00.002+12:00

Ben Barres gave a great seminar today, but his work is much better than his sister’s work.

Statement by faculty member after the unpublicised female-male sex change of a transgendered academic.

Tipping the Scales

2009-09-19T23:56:00.004+12:00

I grow very weary of phrases along the lines of: the structure of quantum spacetime at the Planck scale.

Frontiers of Physics

2009-09-18T01:42:00.005+12:00

Any physicists near Perth in November, who are looking for something to do, can meet Carl and me at the conference on Frontiers of Fundamental and Computational Physics at the University of Western Australia. We will both be speaking, and I am looking forward to the beach!

M Theory Lesson 296

2009-09-18T01:30:00.009+12:00

The binomial coefficent that underlies the Catalan numbers is the central one: for $p = 2$. Consider the analogue for $p = 3$. If my algebra is correct, this is given by the formula which is similar in spirit to a certain decomposition of the Catalan numbers.

Out on a Planck

2009-09-17T23:08:00.003+12:00

Today Planck reports its first results!

The First Light Survey was completed on 27 August, yielding maps of a strip of the sky, one for each of Planck’s nine frequencies. Each map is a ring about 15 degrees wide, stretching across the full sky. Preliminary analysis indicates that the quality of the data is excellent.

M Theory Lesson 295

2009-09-17T00:34:00.013+12:00

A while back we looked at ways of counting constrained paths that give, say, Motzkin or Schroeder numbers.

The Catalan number $C(n)$ counts the number of vertices on an associahedron polytope in dimension $n-3$, which is labelled by an $n$-gon. The generalised Catalan numbers $C(p,n)$ are given by

$C(p,n) = \frac{1}{n - 1} B(p (n - 2); (n - 2))$

for the binomial coefficient $B(n;k)$. The usual Catalan numbers are recovered when $p=2$. For example, $C(5) = 5$ gives the $5$ vertices of the pentagon in dimension $2$. The case $p=2$ is for binary trees. $C(p,n)$ is related to $p$-ary trees. For example, in lesson 284 we looked at the case $p=3$, which divides polygons into square pieces. The generalised Catalan number $C(p,n)$ is also used to count the number of paths on a lattice (from the origin) lying below the line of slope $p-1$.

The Blog Book

2009-09-16T20:38:00.002+12:00

Thanks to Lubos ... here is a cool site where you can automatically turn any blog into a book! Get your pdf copy of AF for a few dollars (unfortunately, I won't get paid). The latex won't compile, but the formatting is pretty good.

End/Start of Summer

2009-09-15T20:36:00.002+12:00

The last weeks in Oxford are looking eventful, with the new term now approaching. Who knows? Perhaps I will make the opera in London before I leave. Meanwhile, plans are being made for the beautiful southern summer in the mountains.

A Wedding

2009-09-12T23:55:00.003+12:00

Today is Let's Embarrass Jamie Vicary Day! On this stunning summer's day, the young Jamie gets married to the lovely Laura! Congratulations to them both.

M Theory Lesson 294

2009-09-11T00:22:00.004+12:00

Recall that the associahedra polytopes are labeled by chorded polygons. For example, the vertices and edges of the pentagon (the associahedron in the plane) are given as a five sided polygon with either one or two chords. In category theory, the edges of the associahedron may be directed. This can be achieved by choosing a root edge on the index polygon, which is the same as selecting a root for the dual tree. A natural source (target) for the full polytope is then given by the fully left (right) branching tree. But for many purposes, where the cyclic symmetry is relevant, we need not select a root edge.

Perpetual Summer

2009-09-09T20:05:00.002+12:00

With the changing seasons will come a return to the south. I may have lined up a waitressing job for the busy southern summer. Meanwhile, check out this new academic jobs site: provide the usual data, and apply for hundreds of jobs at once!

Quote of the Summer

2009-09-08T20:26:00.001+12:00

... so in philosophy, when we make use of false principles, we depart the farther from the knowledge of truth and wisdom exactly in proportion to the care with
which we cultivate them, and apply ourselves to the deduction of diverse consequences from them, thinking that we are philosophizing well, while we are only departing the farther from the truth; from which it must be inferred that they who have learned the least of all that has been hitherto distinguished by the name of philosophy are the most fitted for the apprehension of truth.

Rene Descartes

viXra Reading

2009-09-07T21:27:00.004+12:00

Some interesting recent papers from the viXra preprint archive:
On Information Geometry, by Chris Goddard
Solar System Dynamics, by A. L. Kholodenko
Study of Supernovae Dimming, by T. B. Andrews
Keplerian Polyhedral Models, by Tony Smith

Mass Gap Revisited

2009-09-07T03:02:00.006+12:00

In a theory with cosmologically varying masses, to some approximation there is no mass gap in the sense that a neutrino mass tends to zero in the early universe, at least from the point of view of a distant observer.

However, the standard model is only about local observations. And so as a matter of principle, given that we do not occupy the early universe, there must be a mass gap, given by the mass of the lightest neutrino, namely $0.00039$ eV.

In lecture 4B (you did watch it, right?) Arkani-Hamed discusses locality in terms of factorization for the coefficients of singularities that arise when internal lines in an old fashioned Feynman diagram go on-shell. This dictates how a proper four particle vertex with helicity labels should decompose into two three particle vertices. There are only two kinds of three particle vertex: (--+) and (-++).

It can be shown that factorization only allows two possible spin values, for a vertex with all legs having the same spin $s$. That is, either $s = 0$ or $s = 2$. Sound familiar? Spin $1$ Yang-Mills theory is OK if we mix spin values on the inputs. In that case, factorization says that the amplitudes must come from Lie group type structures. So the presence of Lie groups is derived from locality. They are not fundamental.

Varying Mass

2009-09-06T04:39:00.004+12:00

Recently we considered time varying mass in the Riofrio cosmology.

This is not a new idea. In the viXra article, Against the Tide: A Critical Review by Scientists of How Physics and Astronomy Get Done (188 pages), there is an article by Halton Arp which includes a discussion of the quasar NGC 7603:

Number 92 in my Atlas of Peculiar galaxies has a large companion on the end of a luminous arm. In 1971, a spectrum revealed that this companion had a 8000 km/sec higher redshift than the central, active Seyfert galaxy. This amount of excess redshift cannot be accomodated in the conventional picture where redshifts mean velocities in an expanding universe. They could not be at such different distances and be physically interacting.

When Fred Hoyle heard about this he came up from the Cal Tech campus to my Carnegie office and asked to see the original picture. In 1972 he gave the prestigious Russell Lecture at the Seattle meeting of the American Astronomical Society and outlined a theory whereby younger galaxies radiated intrinsically redshifted photons. His theory of growing particle masses was a more general solution to the conventional field equations but was physically a Machian (not Einsteinian theory). At the end of the lecture he said the NGC 7603 observation created a crisis in physics and we needed to cross over the bridge to a radically more general physics.

In 2002, an astro-ph paper, by M. Lopez-Corredoira and Carlos M. Gutierrez, described two even higher redshift objects sitting exactly on the filament connecting the two galaxies of the NGC 7603 system.

Amused

2009-09-05T22:55:00.005+12:00

An experienced traveller quickly gets used to the idiosyncracies of a new place. When a newly arrived Canadian researcher told me of her shock at being unable to open a bank account at a local bank which actually owed her money, I simply laughed (but then I did assure her that I knew it wasn't funny). When a few English colleagues failed to obtain cash from the ATMs in Waterloo, Canada, I merely shrugged my shoulders. When it took six months to obtain a health insurance number, I never gave it a thought.

But the train ticketing system is just plain hilarious. Many years ago, on my first visit to India, after several weeks of moving around by train I remember the great feeling of accomplishment when I finally understood how to find myself an appropriate seat. I have often been told that they inherited bureaucracy from the English, as indeed my country also did, but only now do I understand how true that is. Anyway, I booked and paid for a return trip to London online, and requested the tickets be sent to my home address (the alternative is to go to the station and stand in the line to use the only unbroken automatic ticket collection machine). The tickets arrived today. So how many ticket stubs am I issued for a simple return trip to London, which is only a few stops away? Eight. That's right, eight. Nine if you count for the extra one containing my address. That's because each trip has a minimum of two tickets: one ticket and one seat reservation. Then there is a ticket stub for the record of payment, a bit like a receipt but one also gets one of those. The remaining three tickets are indecipherable records of further details about both the booking and the payment.

But the tickets arrived promptly and the friendly postman handed them to me personally, bringing back distant memories from my childhood, when the same postman would come by our house every day.

M Theory Lesson 293

2009-09-05T02:17:00.006+12:00

Last time we considered chord flips on a square. Recall that a chorded square labels a point at the source or target of an associator edge.

A basic three leaf tree is what labels the associator edge. In other words, an associator edge is like two four point diagrams connected by a single three point diagram. This is backwards (or rather, Poincare dual) to the situation of interest in twistor QFT, which is where a four point vertex may factorize into pairs of three point vertices.

As it happens, there is such a thing as a dual square, where points become edges and edges points. In this context, roughly speaking, the square would be called a Hodges diagram. The vertices on a Hodges diagram stand for twistor variables in a massless field theory. Poincare duality is a simple enough idea, so massless particle physics really does see associahedra.

That's category theory, folks. You can keep saying that category theory has nothing to do with physics. But Nature does not agree with you.

New Worlds

2009-09-02T20:34:00.005+12:00

The image below is taken from a paper by Ingrosso et al on the hunt for extrasolar planets in Andromeda. Yeah, no kidding. Here is the planet in the catalog, with a mass of $6.34 M_{J}$.

T Duality

2009-09-02T00:11:00.006+12:00

Now that String Theory has officially won the String Wars* (by changing its thinking radically enough to finally look like it is on the right track) it is worth making a simple point about T duality.

In modern physics, almost everything is measured in terms of energy. Distance is an inverse energy, temperature is an energy, and so on. For a basic black hole, the mass of a black hole goes like the inverse of a Hawking temperature. In other words, mass is somehow like an inverse energy, which is the distance scale of the black hole radius.

But mass is just an energy. So even without considering any kind of string theory at all, we should expect T duality to play an important role in gravity.

In a non local theory, however, it does no good to talk about a priori distance scales. At the fundamental level, black hole properties arise from considerations of, say, their information content. It is expected that a classical spacetime, with its notion of horizon scale, should only arise as a thermodynamic collection of such quantum states. So where is the T duality? It can only be in the mass quantum numbers. Distances are derived from the masses, but they are not inherently properties of the quantum states. This suggests that a rigorous T duality for Yang-Mills theory is closely related to the issue of a mass gap, because the limit of the Planck scale is replaced by a minimal, or dually maximal, mass.

*AF will still occasionally refer to string theorists as idiots, and the correct theory as M theory.

Planets Galore

2009-08-31T21:02:00.004+12:00

This is a lot of fun, so I downloaded the extrasolar data and found several systems with four or more known planets in them. Here are the plots of planet period vs $n$, as in $n = 1,2,3,4$.

Mighty Jupiter

2009-08-30T22:39:00.002+12:00

Today's random plot from the Interactive Extrasolar Planets Catalog.

Quote of the Week

2009-08-28T21:46:00.003+12:00

Scientists have discovered a planet that shouldn't exist. The finding, they say, could alter our understanding of orbital dynamics, a field considered pretty well settled since the time of astronomer Johannes Kepler 400 years ago.

So says an article about the discovery of the hot Jupiter Wasp-18b, by C. Hellier et al. Thanks, Lobo7922.

Twistor Buzz

2009-08-28T19:50:00.002+12:00

Lectures 4A and 4B are compulsory viewing. In the most deliciously outrageous display of presumption I have ever witnessed, Arkani-Hamed introduces twistor QFT to a group of beginning graduate students who have never even taken a course in old fashioned QFT. Moreover, he carefully explains to them why Feynman diagrams are redundant and quantum gravity has a better way of doing things. Wow. If I tried that, I'd be lynched.

Extra LIGO

2009-08-27T22:32:00.002+12:00

Recommended reading for today: from LIGO.

The Fermi Debate

2009-08-27T20:19:00.005+12:00

The Fermi debate appears to have convinced some people that any kind of variation in $c$ has been ruled out, or will soon be ruled out as more GRBs are observed.

But consider the Riofrio cosmology. If one must insist (sigh) on a classical picture of photons whizzing through an objective vacuum from GRB 090510 to us, then the Riofrio cosmology would say that all photons shift their speed in unison, as the cosmic epoch changes. They would all be measured locally at a speed $c$. This quantum cosmology is consistent with all known data.

The Loopie picture, on the other hand, defends its new position on the fence by pointing out that DSR breaks Lorentz symmetry through deformation, a supposedly subtle kind of symmetry (actually, it's pretty simple and there is no physical motivation for it). The linked paper begins with the line:

What is the fate of Lorentz symmetry at Planck scale?

There is a problem with this statement. Traditional string theorists make similar statements. The Riofrio cosmology does not impose a fixed scale on the non local theory of quantum gravity, which contains all possible values of $c$, $\hbar$ and $M_{\textrm{pl}}$. It is capable of recovering local Lorentz invariance precisely because it considers a fixed Planck scale an approximation.

Computing Masses

2009-08-26T01:44:00.008+12:00

In the Scholars International series yesterday there were three sessions (A, B, C) by Arkani-Hamed, nominally on Research Skills, but actually a grand overview (for beginning graduate students) of his current picture of physical reality.

For example, lecture B discusses the impossibility of precision local observables in quantum gravity, such as rest mass, using the following argument. Quantum mechanics gives us the limit of the uncertainty principle, which is to say that an infinite precision measurement of position requires an infinite amount of energy. On top of this, gravity tells us that the infinite apparatus required to measure a mass would confront the limits of Planck scale physics. With finite resources, infinite precision is clearly impossible.

What is wrong with this argument? Firstly, no one seriously denies that, in practice, finite resources are all we really have. This does not mean that there exists no theory capable of computing the rest masses to high precision, but this theory must circumvent the argument above. Observe that it was first demonstrated that quantum gravity could not be a local spacetime theory, and then we discussed experiments taking place in a classical spacetime. So logically, the argument cannot hold as it stands, once we have abandonned the local point of view, no matter how compelling it sounds.

The computation of rest masses is an important aspect of quantum gravity. It is true that the description of such observables should not impose a unique and universal spacetime. So in quantum gravity, when we measure the rest mass of a particle, we carry with us several strict experimental conditions that limit our capacity to draw resources from the apparently objective spacetime. An example:

Observer spacetime construction: our status as an observer living roughly $13.5$ billion years after the big bang, a cosmic epoch by which the varying $c$ cosmology sets a mass scale that limits our ability to probe vastly different scales (note that this does not imply that humans have a special status, only that they must be considered as observers with limitations).

One enjoyable feature of these excellent (albeit stringy) lectures was the stress on the interconnectedness of the outstanding problems, over all physical scales. Arkani-Hamed says, for instance, that a leap in our understanding of quantum mechanics, or any theory that supercedes it, must involve cosmology and other domains of physics. I wholeheartedly agree.

The Latest Battle

2009-08-25T00:36:00.002+12:00

I'm not much of a sport's fan, but I guess AF should have a link to this Fermi inspired fight:
Lubos vs the Loopies

Big Jupiters

2009-08-24T21:25:00.003+12:00

More really cool websites: the extrasolar planet encyclopaedia has an interactive tool for both extrasolar planet and star data. For example, I created this plot of star metallicity against planet period:

Ultra Deep

2009-08-23T02:42:00.006+12:00

Thanks to Gizmodo for the link to the zoomable Hubble Ultra Deep Field image. Galaxies in this remarkable image existed possibly as long ago as 400 million years after the Big Bang. Check out the 3D version.

Endangered

2009-08-21T23:52:00.002+12:00

The endangered kea. Thanks, Sara Rodgers.

Gravity Goose

2009-08-21T20:23:00.019+12:00

Recall that, at GRG18, the LIGO collaboration reported null results for GRB 070201, which was coincident with the spiral arms of the Andromeda galaxy. That is, if this burst was located in Andromeda, it could not have been generated by a compact binary under the usual theoretical assumptions, most notably the assumption that gravitons (if they exist, which I suspect not) travel at speed $c$.

Nature reports on LIGO's latest null results with the heading: Gravity waves 'around the corner'. You gotta love those quotation marks. The new paper, for those fortunate enough (including me, at present) to have access, is here. Part of the abstract reads:

Our result constrains the energy density of the stochastic gravitational wave background normalized by the critical energy density of the Universe, in the frequency band around $100$ Hz, to be < $6.9 \times 10^{-6}$ at $95$% confidence. The data rule out models of early Universe evolution with relatively large equation of state parameter, as well as cosmic (super)string models with relatively small string tension that are favoured in some string theory models.