The protests against Egyptian President Hosni Mubarak show little sign of relenting. The dismissal of the previous government, and swearing in of new ministers Monday did little to assuage those demanding Mubarak's ouster. There are calls for 1 million people to take to the streets of Cairo Tuesday. One report says demonstrators are giving the army until Friday to choose sides between the government and the people before protesters march on the presidential palace. Meanwhile, former International Atomic Energy Agency chief Mohammed El-Baradei may be making progress in his campaign to become the consensus candidate to lead a future Egyptian government. The Muslim Brotherhood has been content to lurk in the background throughout the weeklong uprising against Mubarak's government.
Progressive White House Babbler-in-Chief Gibbs opens door to MB in Egypt
BEIJING — In another era, China’s leaders might have been content to let discussion of the protests in Egypt float around among private citizens, then fizzle out.
Breaking wind is set to be made a crime in an African country.
The government of Malawi plan to punish persistent offenders 'who foul the air' in a bid to 'mould responsible and disciplined citizens.' But locals fear that pinning responsibility on the crime will be difficult - and may lead to miscarriages of justice as 'criminals' attempt to blame others for their offence. One Malawian told the website Africanews.com: 'My goodness. What happens in a public place where a group is gathered.
At the Daily Beast, Bruce Riedel has posted an essay called “Don’t fear Egypt’s Muslim Brotherhood,” the classic, conventional-wisdom response to the crisis in Egypt. The Muslim Brotherhood is just fine, he’d have you believe, no need to worry. After all, the Brothers have even renounced violence!
One might wonder how an organization can be thought to have renounced violence when it has inspired more jihadists than any other, and when its Palestinian branch, the Islamic Resistance Movement, is probably more familiar to you by the name Hamas — a terrorist organization committed by charter to the violent destruction of Israel. Indeed, in recent years, the Brotherhood (a.k.a., the Ikhwan) has enthusiastically praised jihad and even applauded — albeit in more muted tones — Osama bin Laden. None of that, though, is an obstacle for Mr. Riedel, a former CIA officer who is now a Brookings scholar and Obama administration national-security adviser. Following the template the progressive (and bipartisan) foreign-policy establishment has been sculpting for years, his “no worries” conclusion is woven from a laughably incomplete history of the Ikhwan.
By his account, Brotherhood founder Hassan al-Banna “preached a fundamentalist Islamism and advocated the creation of an Islamic Egypt, but he was also open to importing techniques of political organization and propaganda from Europe that rapidly made the Brotherhood a fixture in Egyptian politics.”
My 8yo runs in from playing outside. "Mom! We need something this big!" He holds out his hands. I have no idea what "something" is or why it has to be "this big."
"What for?"
"We're building something to help us catch a RACCOON!"
P.S. The most this trap is going to catch is a little boy's imagination! ;)
Metered Internet usage (also called "Usage-Based Billing") is coming to Canada, and it's going to cost Internet users. While an advance guard of Canadians are expressing creative outrage at the prospect of having to pay inflated prices for Internet use charged by the gigabyte, the consequences probably haven't set in for most consumers. Now, however, independent Canadian ISPs are publishing their revised data plans,and they aren't pretty.
Peter Sissons, a long-time as well as recent BBC anchor, just published his memoirs that present some details about the left-wing institutional bias in the BBC News and the political correctness that culminated with the global warming religion:
Friday, February 4, 2011 David Goldston Director of Government Affairs, U.S. Natural Resources Defense Council
Loving Science to Death: Problems at the Intersection of Science and Policy University of Colorado CIRES Auditorium | 4:00-5:00 p.m. (directions to CIRES)
Light reception to follow in the CIRES Atrium
Why is the use of science in policy so fraught with political and substantive danger? What can be done to improve the use of science in the policy process? Is the situation improving or getting worse? The talk will address these questions, drawing on a variety of past and current examples from environmental policy that David Goldston has been involved in on and off Capitol Hill.
About this series
The Cooperative Institute for Research in Environmental Sciences — CIRES — seeks to promote global perspectives by sponsoring distinguished speakers whose work crosses disciplinary boundaries. The Distinguished Lecture Series is designed to bring outstanding scientists, as well as historians of science, science policy makers, and science journalists, and others who take imaginative positions on environmental issues and can establish enduring connections after their departure. Participants' interests embrace those of the University departments and programs, and the National Oceanic and Atmospheric Administration labs affiliated with CIRES.
More stupid comments by the Harvard Professor on Canadian sabbatical. Where is he commenting on the Muslim Brotherhood, where was he during the last 30 years as Egypt operated as a brutal police state? Gee, we need to be clear about democracy!
Shouldn't that be our default position?
Jan 30, 2011
Canada needs to be clear to Egyptian authorities that a democratic government is the only acceptable outcome of the past week’s political unrest, Liberal Leader Michael Ignatieff said Sunday.
Michael Ignatieff, the front runner in the current race for the leadership of the Liberal Party of Canada, showed his true colors recently when he called the Israeli bombing of Lebanese village of Qana last July 30 that caused 28 civilian deaths “a war crime.” Ignatieff was a professor of human rights and the laws of war at Harvard from 2000 to 2005.
"Govt must respect the rights of Egyptian people & turn on social networking and internet," White House spokesman Robert Gibbs warned in a tweet.
Egypt kills internet and Obama complains while push through his own kill switch legislation:
As Egypt's government attempts to crackdown on street protests by shutting down internet and mobile phone services, the US is preparing to reintroduce a bill that could be used to shut down the internet. The legislation, which would grant US President Barack Obama powers to seize control of and even shut down the internet, would soon be reintroduced to a senate committee, Wired.com reported. It was initially introduced last year but expired with a new Congress.
Senator Susan Collins, a co-sponsor of the bill, said that unlike in Egypt, where the government was using its powers to quell dissent by shutting down the internet, it would not. “My legislation would provide a mechanism for the government to work with the private sector in the event of a true cyber emergency,” Collins said in an emailed statement to Wired. “It would give our nation the best tools available to swiftly respond to a significant threat.”
Egypt proves it; Islam is the most retrograde force ever to have been visited upon the Earth. It is the atomic bomb of cultural phenomenon. It destroys everything it touches. An Islamic nation is only good to the extent that the other cultures within it can maintain their own sense of purpose in the withering nuclear aftermath of Allah's manifestation. As Pope Benedict quoted at Regensburg, "Show me just what Muhammad brought that was new and there you will find things only evil and inhuman." Egypt will not recover until it can be cleansed of the radioactive fallout of Allah and his Sharia. --- Pastorius
This is an important point in this article :'By contrast, the Obama administration has no idea what is happening or what it is doing, and Hillary Clinton is actually overrated as a secretary of state.
This means that American influence -- potentially decisive until quite recently -- can now be fully discounted.' ----- (I've always felt that Hilary took the job as it has real power, whereas the VP position is only fit for a figurehead. She figured it would be a launch pad for 2012. I don't think that's going to work out.)
Of course depends on how the military decides to act. They are trained largely by America and may not turn on the citizenry. (The police and secret service is very different and could open fire on a demonstration.)At the same time they may decide Mubarak's time is up. Then what? Either way Obama is going to lose the influence America has held for 30 years and will have to pick a new path. What is to become of future US aid to the tune of $2B/yr?
Can the US provide aid when the new political influence is possibly ElBaradi in a pact with the MB?
As 'they' say; stay tuned for further developments.
The key fact, in Egypt (paralleled in Yemen and elsewhere), is that the Muslim Brotherhood has not declared itself. The Islamists could put vastly more people on the street. They could subvert the loyalties of policemen and soldiers, who already resent the moneyed middle class. They could generate just enough heat to make large districts of Cairo and Alexandria, now simmering, boil over.
The Mideast presents a chaotic quagmire of unforgiving choices for Obama. The turmoil in Egypt, Yemen, Lebanon, and Tunisia is piled atop wars in Iraq and Afghanistan and the civil war with Islamists in Pakistan. Add to these woes the concerns over Islamist Iran’s emerging atomic threat, the re-emergent neo-Ottoman Turkey, the mischievous Syria, the ever-present Israeli-Palestinian standoff, and the global Islamic terror campaign.
This collection of Mideast challenges threatens our national security interests and totally befuddles President Obama. That shouldn’t surprise anyone after Obama began his administration by naively promising to talk Tehran out of its nukes and to resolve the age-old Israeli-Palestinian conflict.
The beam energy won't be raised from 3.5 TeV to 4 TeV as previously speculated. Also, the LHC won't be stopped at the end of 2011. Instead, it will continue to run in 2012, too.
On December 21st, 2012, CERN will invite a Mayan engineer, Dr Nostradamus, to play with the device for the last time and to turn everything off. This final procedure will stop all the suffering in this world, too. That's why I don't have to tell you that the plan from 2014 would be to continue at 2x 7 TeV. ;-)
The justification of the previously unplanned run in 2012 - namely that "they won't get enough data for a discovery in 2011" - either means that they're saying arbitrary things - because no one knows how many femtobarns one will actually need to discover what Nature is still hiding - or it means that they actually have a rather quantitative clue already what to expect and what its mass is - but we haven't been told yet.
I find the latter option somewhat unlikely because if 45/pb were already enough to see convincing hints what to expect, less than 1/fb (the minimum plan for 2011) would almost surely be enough to discover it at 5 sigma.
2. My 8yo filled out a data sheet about height, weight, coloring, and egg production for the King penguin. He used our penguin measurement wall to record how tall the King is as compared to the Rockhopper, his brother, and himself.
3. We read about penguin predators.
4. My son wrote on a chart, comparing/contrasting the penguins we've studied so far. He'll continue to add to it as we go.
5. He cut out "fact cards," each with one fact describing either the King or the Rockhopper penguin. We made mini pockets (seal an envelope, cut in half, and use the two halves for pockets) to make little fact sorting pockets. He labeled one "Rockhopper," one "King," and sorted the fact cards into each. Although the fact cards come with the curriculum, I'm tempted to have him make his own when we do the next set of two contrasting penguins.
PLAY!!! Then, the boys spent a huge portion of the day OUTSIDE. For once, it was not too rainy. Not too cold. And I'd just read "The Children Must Play". Here's a pertinent quote:
"While observing recess outside the Kallahti Comprehensive School on the eastern edge of Helsinki on a chilly day in April 2009, I asked Principal Timo Heikkinen if students go out when it’s very cold. Heikkinen said they do. I then asked Heikkinen if they go out when it’s very, very cold. Heikkinen smiled and said, “If minus 15 [Celsius] and windy, maybe not, but otherwise, yes. The children can’t learn if they don’t play. The children must play.”
So, let 'em PLAY!!!! It's a required part of every child's education!
Despite treatment with renin—angiotensin—aldosterone system (RAAS) inhibitors, patients with diabetes have increased risk of progressive renal failure that correlates with albuminuria.
281 patients with type 2 diabetes and albuminuria who were receiving angiotensin-converting enzyme inhibitors or angiotensin receptor blockers were enrolled in this study.
Patients were assigned to receive 24 weeks' treatment with:
Paricalcitol (trade name Zemplar, Abbott Laboratories) is an analog of calcitriol, the active form of vitamin D.
The primary endpoint was the percentage change in mean urinary albumin-to-creatinine ratio (UACR).
The change in urinary albumin-to-creatinine ratio (UACR) was: −14% in the 1 μg paricalcitol group, and −20% in the 2 μg paricalcitol group.
The addition of 2 μg/day paricalcitol to RAAS inhibition safely lowers albuminuria in patients with diabetic nephropathy, and could be a novel approach to lower renal risk in diabetes.
This review is for both books at once as they have only minor differences.
Summary: These are workbooks designed to encourage spiritual growth, inner strength and self awareness. The exercises are a bit different in each book as outlined below.
Girl's Guide: Your chakras, keep a healthy aura, learn the pendulum, aromatherapy crafts, crystals, explore inner self, create your own future.
Boy's Guide: Make a drum, find your totem, discover spirit guide, Native-American lore, chakras, crystals, Pendulum, strong aura, self-esteem.
All though I do think it's a good idea to have separate guides for boys and girls I think it would have made more sense to make them different in the text and specific activities perhaps, not necessarily different activities. I would make the drum and find the totem with my girls and I would teach aromatherapy to my boy.
In general the idea of the books is awesome, however I do think the books have some problems.
Girl's Guide:
Mainly it wasn't edited enough, or at all. There were grammatical errors, missing words and repeated words. There's a section on ESP that says to pick 5 designs and then right after says you have 3 designs. The instructions are bit messed up although I'm sure most people can figure it out themselves.
The word bestie is used which I didn't know meant best friend. I work with Girl Guides and have heard all kinds of slang and short forms, never heard Bestie. I don't think it's a good idea to use slang in a book anyway because as the book gets older, the term would be not in use anymore.
In Both:
We are given a section to write down tarot readings but it's not like tarot cards come with the book or we are taught much about them. I'm not sure the purpose of that section. The boy's guide is only a little better in that it suggests a book to explain tarot and doesn't sound as if you must have cards already.
The dream section says to look up your dreams in a dream dictionary to keep track of what your subconscious may be telling you. The boy's guide is even more adamant that you MUST look up your dreams in a book to know what they mean. Dreambooks aren't definite meanings though, they are just ideas and they even say in small print in them that it's mostly just for fun.
Despite all this the book has it's merits and I can use what I want out of it which would be most of it. Also the chakracize (chakra exercises) is the best part of the book with photos to go along with it. I just think they need to be reprinted with proper editing and more thought.
Self-described physicist Joe Romm has discovered that climate change has overthrown Ben Ali in Tunisia and has brought demonstrations to Egypt, too.
The insanity of Romm and his likes becomes particularly flagrant if you realize that the food prices recently grew also (if not mostly) because of the world governments' misguided support for biofuels which was justified almost entirely by the global warming fear-mongering.
The Bangles - Walk Like An Egyptian: it was the main song used in our Rock'n'Roll training sessions I attended around 1988 (yes, during communism!): of course, my skills were incredibly hopeless. But I had never realized that the 1986 song was so relatively fresh at that time.
In the past days, the Western media have presented the demonstrators as saints but they didn't offer us any particular reason to think that their goals are noble and they should be supported in their battle against Hosni Mobarak.
Over the weekend and in the recent hours, my neutral attitude has largely transformed into a positive attitude to Mubarak. I don't claim that his regime is a textbook of democracy but do you know what? The idea that such nations may do well in a full-fledged democracy is just a politically correct myth.
Egypt - and also Tunisia, in fact - have been doing well as tourist destinations. The economy worked sensibly well and one could feel safe on the street. We've had all these stories in which Tunisian men were impressed by our knives but they couldn't have bought them because they would be severely punished if they possessed one.
This is an extreme attitude but I must say, it has worked.
For democracy to work well, one requires the typical citizens to display a certain level of education, intelligence, impartiality, calm rational reasoning, as well as asceticism. And my feeling is that the degree of democracy in Egypt was close to the right degree that similar nations may constructively swallow.
Hosni Mubarak of Egypt just won a lukewarm endorsement from TRF
The average national IQ of Egypt is 83, one standard deviation below the Western average. My guess is that Mubarak is above 100 and the bulk of the nation simply has to be directed by someone around this level for it to remain civilized.
I am also very uncertain, to put it euphemistically, about the specific goals of the opposition. A loud group is the Muslim Brotherhood - which is banned in Mubarak's Egypt. This movement wants to restore the caliphate - a pan-Islamic constitutional monarchy governed by a caliph. And you know what? I just don't want it. This needs to be said - regardless of the fact that the Muslim Brotherhood has officially renounced 9/11 and other bad things.
Hosni Mubarak is a top member of the National Democratic Party of Egypt. And although contemporary Egypt is not quite a paradise, you must admit that the name of this party sounds better than the Muslim Brotherhood. The National Democratic Party builds on the pharaohs' tradition of the Egyptian governance. And yes, this is the Egypt I have been taught to understand and this is the tradition I want them to continue.
A perverse superficial fad connected with the names of Allah, Mohammed, and others should have faded away already 1,400 years ago and I am afraid that the only thing that a replacement of Mubarak may create is another Islamic regime. This would be bad news for Egypt's ally Israel, this would be bad for the Middle East, and it would be bad for other civilized nations in the world, too.
Some of the demonstrators may be hungry today but hunger is not a noble value by itself. If Mubarak didn't manage to defend himself, the country would ultimately have to decide about the recipe to defeat hunger and I am afraid that by the popular vote, Allah would win as the popular solution.
There is one more potential loser whose fate in the case of Mubarak's loss worries me tremendously. Many people imagine that Egypt is an entirely Muslim country. But this is breathtakingly ignorant and arroant opinion. In fact, a sizable fraction - 10-20 percent - of Egypt's population are Christians known as Copts. They include Meriam George, the 2005 Pantene Miss Egypt on the picture, who was brought up in an orthodox Coptic family. I have problems to believe that groups such as the Muslim Brotherhood would respect basic human rights of the Copts.
Courtesy Ryan Crompton, the figure above shows the most recent insured loss estimates from the recent Queensland flooding based on an update from the Insurance Council of Australia (here in PDF). The estimated costs of the flood have increased from A$1.2 billion to A$1.51 billion (and shown as the bright blue bar on the far right of the figure above -- and is not normalized (the normalized values would be lower) -- the other data shows the normalized losses from Crompton and McAneney 2008 updated through 2010, more details here).
Writing in the Sydney Morning Herald, Ross Gittins offers a valuable perspective on the economic magnitude of the losses from the Queensland floods. I'll skip over the issues of domestic politics that he discusses to focus on the comments that he makes about the magnitude of the losses. He provides a useful bit of advice, which is exactly the advice that I give to my students (emphasis added):
The wise and much-loved econocrat Austin Holmes used to say that one of the most important skills an economist needed was ''a sense of the relative magnitudes'' - the ability to see whether something was big enough to be worth worrying about.
That sense has been absent from the comments of those business and academic economists on duty over the silly season, happily supplying the media's demand for comments confirming the immensity of the floods' economic and budgetary implications.
Gittins then gets into the numbers:
If this is the most expensive natural disaster in Australian history, all it proves is the cost of earlier disasters was negligible. If you can ''rebuild Queensland'' for just $5.6 billion, it must be a pretty tin-pot place.
If $5.6 billion seems a lot, consider some ''relative magnitudes'': the economy's annual production of goods and services (gross domestic product) totals $1400 billion, and the budget's annual revenue collections total $314 billion.
Note that, though no one's thought it worthy of mention, the $5.6 billion in spending will be spread over at least three financial years, making it that much easier to fund.
We know that more than a third of the $5.6 billion will be paid out in the present financial year with, presumably, most of the rest paid in 2011-12. So just how the flood reconstruction spending could threaten the budget's promised return to surplus in 2012-13 is something no one has explained.
And if $5.6 billion isn't all that significant in the scheme of things, how much less significant is the $1.8 billion to be raised from the tax levy? The fuss economists have been making about it tells us more about their hang-ups over taxation than their powers of economic analysis.
It turns out that domestic politics are difficult to avoid! But what about the possible GDP impacts? Gittins explains:
Turning from the budget to the economy, Treasury's estimate is that the floods will reduce gross domestic product by about 0.5 percentage points, with the effect concentrated in the March quarter.
Thereafter, however, the rebuilding effort - private as well as public - will add to GDP and probably largely offset the initial dip. So the floods will do more to change the profile of growth over the next year or two than to reduce the level it reaches.
Most of the temporary loss of production will be incurred by the Bowen Basin coal miners. But, though it won't show up directly in GDP, their revenue losses will be offset to some extent by the higher prices they'll be getting as a consequence of the global market's reaction to the disruption to supply.
And despite all the fuss the media have been making over higher fruit and vegetable prices, Treasury's best guess is that this will cause a spike of just 0.25 percentage points in the consumer price index for the March quarter, with prices falling back in subsequent quarters.
So the floods do precious little to change the previous reality that, with unemployment down to 5 per cent and a mining investment boom on the way, the economy is close to its capacity constraint and will soon need to be restrained by higher interest rates.
Foreign Affairs in Ottawa has arranged charter flights to fly Canadians out of Egypt starting on Monday. Those who take advantage of these flights will be flown into Europe and will be responsible for their own flight back to Canada. They'll also have to foot the bill for the flight out of Egypt.
Gamal Nasser, a spokesman for the Brotherhood, told DPA that his group was in talks with Mohammed ElBaradei - the former UN nuclear watchdog chief - to form a national unity government without the National Democratic Party of Mubarak. The group is also demanding an end to the draconian Emergency Laws, which grant police wide-ranging powers The laws have been used often to arrest and harass the Islamist group. Nasser said his group would not accept any new government with Mubarak. On Saturday the Brotherhood called on President Mubarak to relinquish power in a peaceful manner following the resignation of the Egyptian cabinet. Speaking to CNN later Sunday, ElBaradei said he had a popular and political mandate to negotiate the creation of a national unity government. "I have been authorized -- mandated -- by the people who organized these demonstrations and many other parties to agree on a national unity government," he told CNN.
The Mail has today run an extraordinary story in which Labour ‘Lord’ Ahmed (another fake peer in the mould of bogus ‘Baroness’ Warsi) has spoken up in defence of predatory Pakistani paedophiles. Instead of blaming these despicable men for their repellent crimes, he instead has the gall to blame white English society, our women in particular, for the perpetration of these misdeeds. The pro-paedophile peer was speaking in response to the recent reporting of the phenomenon of on-street underage grooming of young English girls which has been conducted almost exclusively by Muslims, predominantly Pakistanis.
The Climate Fix: What Scientists and Politicians Won’t Tell You About Global Warming
University of British Columbia Tuesday February 1st 2011 12 - 1pm AERL room 120
The world’s response to climate change is deeply flawed. The conventional wisdom on how to deal with climate change has failed and it’s time to change course. To date, climate policies have been guided by targets and timetables for emissions reduction derived from various academic exercises. Such methods are both oblivious to and in violation of on-the-ground political and technological realities that serve as practical “boundary conditions” for effective policy making. Until climate policies are designed with respect for these boundary conditions, failure is certain. Using nothing more than arithmetic and logical explanation, this talk provides a comprehensive exploration of the problem and a proposal for a more effective way forward.
ROGER PIELKE, Jr., has been on the faculty of the University of Colorado since 2001 and is a Professor in the Environmental Studies Program and a Fellow of the Cooperative Institute for Research in Environmental Sciences (CIRES). At CIRES, Roger served as the Director of the Center for Science and Technology Policy Research from 2001-2007. Roger’s research focuses on the intersection of science and technology and decision making. In 2006 Roger received the Eduard Brückner Prize in Munich, Germany for outstanding achievement in interdisciplinary climate research. Before joining the University of Colorado, from 1993-2001 Roger was a Scientist at the National Center for Atmospheric Research. Roger is a Senior Fellow of the Breakthrough Institute. He is also author, co-author or co-editor of seven books, including The Honest Broker: Making Sense of Science in Policy and Politics published by Cambridge University Press in 2007. His most recent book is The Climate Fix: What Scientists and Politicians Won’t Tell you About Global Warming (September, 2010, Basic Books).
And then Thursday evening in Portland:
Fixing Climate Through Energy Innovation Illahee Lecture Series Thursday February 3rd 7 PM at the First Congregational Church, 1126 SW Park Avenue in Portland Tickets here
February 3, 2011 Political scientist Roger Pielke maintains that we'll make better progress on climate if we focus on energy innovation. Pielke is Professor of Environmental Studies at University of Colorado, and has held leadership positions at NCAR, CIRES, and the Breakthrough Institute. He is also author, co-author or co-editor of seven books, including The Honest Broker: Making Sense of Science in Policy and Politics, and The Climate Fix: What Scientists and Politicians Won't Tell you About Global Warming. More about Roger Pielke here and here.
Cross posted at SDA: There is a massive power vacuum in Egypt and no possibility for a pro-democracy group to make any moves simply because none was ever permitted to exist. The Muslim Brotherhood no doubt has supporters in the conscripted army and the police. Their allies in Hamas are now moving over the border has the police have 'mysteriously' disappeared.
How much of the military decides to act in concert with the MB will show how messy this will get. There is no chance for democracy in Egypt and the country is now forever changed. The talking heads on CBC and other media blabbing on about how this uprising is good for the people is ludicrous - these TV bobble-heads have no concept of what lays ahead for the regular folk. The choices are chaos and oppression and strict sharia law under the MB.
This will be very bloody very soon. JMHO
Hot Fur has some comment and pics Egypt is not Free . Clearly democracy is nowhere in sight.
Mikael has pointed out a video of a fresh 100-minute talk (100 minutes is equal to one decimal Nima hour) that Nima Arkani-Hamed gave at the Perimeter Institute three days ago. Before I began to watch, I wasn't sure whether I would finish.
Well, I became much more certain about the answer during the talk. ;-)
The title uses David Gross's favorite term "uprising" instead of my "minirevolution" and if you watch the talk, you may figure out whether the twistor minimirevolution has been downgraded or upgraded. ;-)
Nima explains that the goal is to think different - to eliminate the word "Feynman" from the QFT calculations as completely as possible. ;-) In particular, the new description and calculational methods proudly make locality in the ordinary spacetime obscure while they succeed in making many other, more exotic properties of the N=4 gauge theory manifest.
As has been known for some years, the twistor variables simplify the maximally-helicity-violating and other scattering amplitudes. In recent years, it became clear that they also make the dual superconformal symmetry manifest - and the dual superconformal symmetry, together with the ordinary superconformal symmetry, generate the infinite-dimensional Yangian symmetry.
The dictionary that translates some basic spacetime and momentum space concepts to the twistor space is sketched, together with some geometric interpretation in terms of polygons. The momentum conservation becomes non-manifest as well. The quantity that is conserved (the momentum) is not linear but bilinear in the twistor fields - so it may be understood as an orthogonality. Using the space of k-dimensional planes in an n-dimensional space, a Grassmannian, one may parameterize all the possible orientations of the twistors etc.
Nima conjectures that all the amazing simplifications of the integrand, integral, and results that emerge from this formalism indicate that there is a new description of the whole AdS/CFT system - something that he called T (for "twistor") on his diagram but I will call it T-theory.
Instead of the holographic AdS/CFT duality, Nima envisions an ultratwistoholographic AdS/CFT/T-theory triality. Stay tuned. ;-)
The rest of this article was posted on January 4th, 2011 at 10:14 am Prague Winter Time
Twistor minirevolution goes on
At the end of 2010, a Princeton-Perimeter-Oxford group has released two new preprints about the miraculous simplification that Roger Penrose's twistors bring to the calculation of scattering amplitudes of the maximally supersymmetric gauge theory in 3+1 dimensions:
The lists of authors of both papers include Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo (now working for peRIMeter), and Jaroslav Trnka (yes, a Czech name!). The first paper was also co-written by Andrew Hodges, a pioneer of the gay liberation movement from the 1970s who also happens to be a top Oxford mathematician. ;-)
The short paper plays with some geometry and shows that various key mathematical objects that appear in both papers (and many previous papers) have a nice geometric interpretation in terms of areas or volumes of various polygons and polytopes that you may construct in the twistor space - a complex projective space - and its Cartesian powers.
It could have been written because of some previous insights by Andrew Hodges and his extensive knowledge of the geometry relevant for the twistors. Those mathematical suggestions looked confusing and overly abstract to physicists such as Arkani-Hamed but as you can see, the situation has changed.
The long paper is a serious paper about physics and scattering amplitudes which is why no pure mathematician is among the co-authors. It sheds a completely new light on the sequence of developments that we have seen during the last decade.
History: going back to the 1960s
In 1967, Roger Penrose proposed twistors as a fundamental tool for the physics of spacetime. He argued that they should be relevant for quantum gravity. For decades, this claim remained nothing else than a wishful thinking but in the 2000s, the statement turned out to be likely to be true even though as of January 2011, the most well-established applications of twistors remain unrelated to gravity as a force.
Twistors are closely related to spinors, objects that may be understood as "square roots of vectors". I like to say that twistors may similarly be interpreted as "square roots of spacetime points".
In 2+2-dimensional spacetimes (ours is 3+1-dimensional), twistors may also be identified with purely light-like 2-dimensional planes in spacetime. Two such planes generically intersect in a light-like line - and the light-like line may actually be identified with the twistor itself. In this dictionary, spacetime points become lines in the twistor space.
If you switch from the twistor space to the spacetime, objects of higher dimensions become objects of lower dimensions, and vice versa. The envelopes - or lines/planes connecting several points/lines - get mapped to the intersection of the higher-dimensional objects, and vice versa. It's a lot of fun.
To calculate with the twistors, one has to realize their close relationship with the spinors. In the modern treatment, a light-like momentum "p" in 3+1 dimensions is written as "lambda^c.lambda*^d", a tensor product of two 2-component spinors. One does additional procedures we may very superficially sketch later. But because I probably won't, let me say that the Fourier transform over these "lambda" variables (square roots of the momenta) is important, too. And it is very useful to transform over the right-handed "lambda*" variables only - in a left-right-asymmetric way; only in this way, the true power of twistors emerges.
But between 1967 and 2003, for more than 35 years, twistors were only used to study abstract mathematics and in the context of physics, they were only good for an unusual description of free (non-interacting) massless fields - aside from a few exceptions with solutions to non-linear equations related to instantons etc. No generic interactions were allowed, however; no genuine dynamics which is the "bulk of physics" could have been studied by twistors.
Witten enters the scene
In 2003, Edward Witten published his papers on the twistor treatment of the maximally supersymmetric Yang-Mills theory in four dimensions. For the first time, geometry in the twistor space was used to calculate scattering amplitudes - quantities knowing about some real dynamics and interactions in physics.
The scattering of N gluons (or their superpartners) in the gauge theory only occurs if the points describing the gluons in the twistor space - which replaces spacetime or momentum space and should be viewed as "something in between them" - belong to the same (complex) line. Well, that's the case if the polarizations of the gluons are "maximally helicity violating" (MHV).
What is it? Well, relabel all gluons in a scattering process so that all of them are incoming. The right-handed outgoing ones become left-handed incoming ones and the left-handed outgoing ones become right-handed incoming ones. What is the MHV amplitude?
If all the incoming gluons are left-handed (i.e. if all left-handed gluons changed to fully right-handed ones) then... well, then the scattering amplitude vanishes - a fact that is pretty nontrivial by itself. This amplitude is "more than more than allowed" helicity-violating one so it has to vanish. You won't be able to prove the vanishing "immediately" using the Feynman rules; it's not just about the angular momentum because the angular momentum is not quite the same thing as helicity (notice the variable axes of the helicity!). Witten's twistor prescription for the scattering amplitude makes the vanishing manifest.
You must add some right-handed particles for the amplitude to be nonzero. If all the gluons are left-handed and one of them is right-handed, then the amplitude... vanishes again. ;-) It's the "more than allowed" helicity-violating amplitude.
Fine, I don't want to try your patience. If all of them are left-handed but two are right-handed, the amplitude is nonzero. It's the first nonzero amplitude in this sequence so we call it the MHV, the maximally helicity-violating amplitude. (It only makes sense to study it for 4+ gluons.) Similarly, with three right-handed gluons, you would get the NMHV (here, "N" stands for "next-to-"), and so on.
In late 2003, Witten proposed a description for the MHVs in terms of lines on the twistor space and the NMHVs and NNMHVs etc. in terms of higher-degree curves on the twistor space. He has also framed all his prescriptions in terms of a topological string theory defined on a twistor space that kind of worked but so far, it hasn't been shown too useful and - apparently - hasn't quite known about the newest developments. But maybe it's just because no one has been able to deal with Witten's topological twistor string theory properly.
2004: Disconnected rules
Meanwhile, in 2004, Cachazo, Svrček, and Witten replaced the curved submanifolds of the twistor space - to calculate the NMHVs, NNMHVs, and friends - by the sum over several diagrams, each of which uses straight (complex) lines in the twistor space only.
This new picture made it much easier to derive and check various recursion relations for the amplitudes - what happens if you add a new particle to the process, and so on. Also, particle physicists are arguably much more trained in summing many diagrams than in working with a single curved manifold in algebraic geometry so the "CSW" transition has become very popular while the higher-degree curves in the twistor space slipped into silence.
(We have argued - with Andy Neitzke and Sergei Gukov - that the disconnected CSW recipe is equivalent to the connected Witten's curved recipe because integrals on both sides get localized on intersecting lines e.g. degenerate versions of the curved submanifolds in both cases.)
Imagine lots of work related to the CSW rules and various extensions during a few years.
New structures and symmetries in N=4 SYM
Meanwhile, another minirevolution, the BMN minirevolution, has begun to overlap with the twistor revolution sketched above. What is (or was) the BMN minirevolution? In 2002, Berenstein, Maldacena, and Nastase gave new life to another old invention by Penrose, namely his Penrose limit of geometries (also known as the pp-waves which is almost the same thing).
The Penrose limit of the AdS5 x S5 space was translated to a specific new refinement of the 't Hooft limit on the gauge theory side (where the R-charge of the "long" operators also scales properly with the square root of the number of colors) and it allowed the people to check that the gravitational, AdS side of the AdS/CFT correspondence contains not only gravity but also all excited string modes (and other objects) and their interactions as predicted by string theory.
So the AdS/CFT is not just a vague correspondence between a gravitational theory and a field theory: it has been known for a long time that the gravitational side (and therefore also the field-theoretical sides) contains all the special new stringy objects, exactly as they were predicted by string theory. Obviously, the gauge theory is consistent so the equivalent quantum gravitational theory has to be consistent as well. String theory is the only consistent theory of quantum gravity which implies that it had to be the full string theory on the AdS side if the correspondence works at all. (Of course, this fact was pretty much known as soon as Maldacena wrote his correspondence down: he realized that the conjecture was right by analyzing some technical details of black hole entropy calculations in string theory which worked better than expected.)
The BMN pp-wave minirevolution was interesting because it led the people to calculate complicated amplitudes in the N=4 gauge theory and see some patterns and hidden symmetries that are not obvious from the Lagrangian - and that don't exist in less supersymmetric gauge theories.
A big portion of these new symmetries may be summarized as the "Yangian symmetry". This symmetry appears in the planar amplitudes - according to 't Hooft's classification of the gauge-theoretical diagrams. It's some kind of a U(1)^{infinity} symmetry - an infinite number of new conserved charges you didn't expect. In the AdS/CFT dictionary, the planar diagrams get translated to tree-level diagrams in string theory for the AdS space (Riemann surfaces without any "handles") even though they typically contain many ordinary loops of the gauge-theoretical Feynman diagrams.
Now, the planar limit is pretty much equivalent to the tree-level string theory in the AdS space which contains the same information as the classical limit - classical string field theory in the AdS5 x S5 space, if you wish. The latter is classically integrable: you should be able to write all relevant correlators etc. for infinitely many fields of the string field theory (it's just mostly free theory with many fields but even the interacting terms are classically "manageable") in terms of rather elementary analytic functions. So the corresponding description of the same physics on the gauge-theoretical side should also be integrable and the Yangian symmetry produces the infinitely many new charges that make the theory integrable in the field-theoretical variables and that allow you to calculate the results without much work.
Experts in this subdiscipline began to get familiar with many unusual patterns and coincidences that hold for all planar N=4 gauge-theoretical scattering amplitudes and the explanation of these patterns and coincidences. Meanwhile, that's what the twistor people were doing, too. The two minirevolting cultures began to merge. The spin chain (the integrability business that evolved from the BMN breakthrough) folks should better learn some twistors and vice versa.
2008: dual superconformal symmetry, fermionic T-duality, etc.
Things didn't stop in recent years. On the contrary. As TRF readers learned from my reports from Strings 2008, the year brought us a rather extensive new stringy knowledge that has helped to explain the special form of many amplitudes.
Take the non-linear sigma-model - world sheet theory describing strings propagating on a curved background - for the AdS5 x S5 space. Read the paper by Alday and Maldacena, perform some T-duality on the four coordinates that belong to the boundary - where the CFT lives (and forgive me that they're not compact as T-duality usually expects) - and combine it with a totally new, 2008-fresh "fermionic T-duality" by Berkovits and Maldacena. Remarkably, you get the same model back while you may learn totally new things.
So the AdS string theory is kind of self-dual under an unexpected generalization of T-duality. The resulting "dual spacetime" is very cool because the theory is superconformally invariant in this "dual spacetime" as well. More precisely, the planar limit of the ordinary AdS5 x S5 string theory is "dual-superconformally invariant" - as originally pointed out by Drummond, Henn, Koršemský, and Sokačev - while the stringy loop corrections add some rather controllable "violations" of this symmetry.
All this stuff is very funny and powerful because the planar amplitudes themselves may be expressed as the expectation values of purely light-like Wilson loops living in the dual spacetime. Moreover, the dual spacetime on the CFT side has a very simple description, too: it is almost literally the Fourier transform of the original spacetime.
Use symbols "x_1, x_2, ... x_k" for the positions of "k" gluons living in the ordinary four-dimensional spacetime. The theory is translationally invariant so the correlator only depends on the coordinate differences "x_i-x_{i+1}" - including "x_k - x_1". A funny trivial fact about these "k" coordinate differences is that their sum identically cancels and vanishes.
The coordinate differences "x_i-x_{i+1}" play a very simple role in the dual spacetime: they're interpreted simply as the momenta "p_i". Note that two sentences ago, I just explained that the momenta add up to zero.
The twistor-space-based expressions for the scattering amplitudes have made the new symmetries - dual superconformal symmetry and/or the Yangian symmetry - more transparent. However, the twistor space is not diffeomorphic to the spacetime in any sense so generically, the twistor space descriptions are non-local (the association of the interactions with particular points in the spacetime is not self-evident from the form of the amplitudes). Because they're also based on chiral spinors, they like to totally obscure the left-right parity symmetry of the N=4 gauge theory!
2010: isolating the integrand with the beautiful properties
In the newest papers, Arkani-Hamed et al. do a great new step because they write the known twistor-based formulae for the scattering amplitudes as integrals over a universal domain - a Grassmannian (the space of M-dimensional subplanes of an N-dimensional space). By finding the residues, you may decompose the integral into several "seemingly topologically different" Feynman diagrams.
It's incredible that all the diagrams for a scattering process may be written as a single integral - a single diagram. Ordinary quantum field theory usually forces you to sum an exponentially (or factorially) large number of Feynman diagrams to obtain the amplitude for a complicated process. Of course, we know another framework in which many Feynman diagrams of field theory arise from a single diagram: perturbative string theory. In this sense, the twistor expression has similar "unifying properties" as perturbative string theory.
(The connected recipe for twistors, in terms of higher-degree curves in the twistor space, was pretty much giving a single integral as well. However, its correct generalizations to many loops isn't quite known these days - which may only be because the key researchers in the contemporary twistor business don't like curved algebraic geometry too much.)
The rules to produce the amplitudes as the unified twistor integrals could even be a "version of string theory" although the formalism that unifies these two formalisms is not known at this moment.
The rewriting of the amplitudes as a universal single integral has many advantages. The integrand actually makes both the old-fashioned locality as well as the new unusual Yangian symmetry manifest! Parity remains obscure - as in all twistor approaches.
It also removes one of the big obstacles that have always discouraged me from studying loop amplitudes in the twistor language at all: in gauge theory, the amplitudes are infrared-divergent so they're not really well-defined and it's not clear what you're calculating. So why should you do it too accurately?
However, many people were saying it didn't matter - as I also emphasize (e.g. in futile debates with Vladimir), the infared divergences were a "real insight of physics" resulting from your having asked a wrong question, not a sickness of a theory. And there was a set of well-defined finite observables behind these amplitudes. These people turned out to be right in this twistor case, too. Because Arkani-Hamed et al. can write the amplitudes as integrals, it actually turns out that the integrand itself is finite and all the infrared divergences arise from including extreme corners of the integration domain - much like the "tau = i.infinity" region of one-loop stringy diagrams (thin tori).
While the physical interpretation of the integrand is not quite clear at this point, it makes sense to argue that it is a physically meaningful object satisfying many physical criteria and constraints. And it is finite.
2011+: understanding the "twisting beast" in between AdS and CFT?
If the progress continues, people could eventually find a complete definition of this twistor-based description for any amplitudes and prove its equivalence with the perturbative Yang-Mills theory on one side, and perhaps the AdS string theory on the other side, as well as all of its desired symmetries (superconformal, dual superconformal, parity, Yangian). What are its degrees of freedom and their interactions? Are there some new types of string theory or spin chains or something else?
If that's true, the "twisting beast" could turn out to be an extremely useful intermediate diplomat who helps us to prove the AdS/CFT symmetry in an explicit way.
And it could tell us much more than that.
I have more conceptual things to say about these relationships (many of which could be wrong, vacuous, or well-known) and analogies but because I am afraid that they wouldn't be appreciated, let me stop at this point. This twistor business, while highly technical, is hiding some nontrivial wisdom that knows about hidden symmetries of supersymmetric theories. And it could perhaps shed some new light of the "full string theory" including AdS5 x S5 gravity (e.g. off-shell gauge theory - note that only on-shell gauge theory is studied in this whole business so far) and perhaps even more general mysteries.
While the U.S. Constellation Program (CxP) has been abandoned and NASA's manned flights to Mars became very unlikely, the first cosmic nation of Russia is returning to its previous positions:
In 2013, Russia will begin tests of Angara rockets which will be later modified to Amur and Yenisei rockets. In 2037, Russia will be formally unified with the Moon and Mars to the Unified Federation of Russia, Moon, and Mars, and it will send its first moloděts into the decoupled components of the new country.
Angara rockets may lift between 2 and 40.5 tons. You see that the size is OK for a single man so the rocket was also used as a part of Osama's friend's "instant atomic bomb" at 2:13 of a famous song by our ex-minister of defense
All the energy for the superheavy rockets will be obtained from nuclear fission. The pre-project version of the motor is already getting ready.
Amur and Yenisei will be able to lift up to 120 tons. Before the piloted flight, there will be a couple of remotely controlled automata that will do the same thing. At the end, Russia plans to build a science center on Mars.
Their thermal nuclear design is not new and has been planned in the U.S. NERVA program around 1972. Hydrogen is heated by a rapid nuclear reactor before the protonic exhausts are shot out of the rocket, achieving momentum efficiency that is thrice higher than the existing technologies. When you get rid of the rocket, you need a peaceful spaceship with its own nuclear source of energy, too.
So the current Russian research is focusing on a 1 MW (1341 horse powers) source of energy which could be used in ion-based or magnetohydrodynamical motors expected to reach Mars. Instead of Baikonur, Russia is refocusing on its existing military space center Plesseck and a future Vostochnyi center.
A two-cent stamp with Tsiolkovsky. Instead of living in a nice concrete block 100 km southwest of Prague, this great misanthrope has spent his life in a log cabin 100 miles southwest of Moscow. ;-) I don't have to explain you the importance of his equation, "delta v = v(exhausts)*ln(m(initial)/m(final))"
The Angara project has been running since 1995. The lightest version can lift 2 tons. The rockets, built on modular design, somewhat resemble the EELV devices. Those rockets have been used twice and both attempts have unfortunately been failures so far. One of them ended up with a South Korean explosion. Brazil also plans its space program based on Angara.
Via RIA and iDNES
Bonus: oldest galaxy
Reuters and many others have described the discovery of the oldest known galaxy.
Its red shift is z=10, beating the previous record of z=8.5, so this z=10 babe sent us signals 13.2 billion years ago when the Universe was only 0.5 billion years old.
I hope that your monitor is sharp enough and you don't just see a meaningless mottle on the picture. If it's sharp enough, you can see a planet with some funny creatures on it who are just asking "Why now? Why does life exist exactly 500 million years after the Big Bang when the cosmological constant hasn't quite surpassed the ordinary matter density yet?" :-)
They surely think that life would have become impossible in a few billion years because the Universe would get contaminated by disgusting toxins such as heavy elements.
Atrial Fibrillation - Cleveland Clinic video with information for patients. Dr. Walid Saliba, Cleveland Clinic staff cardiologist, discusses atrial fibrillation, the most common irregular heart rhythm that starts in the atria.
It's Saturday and time to mention another fun math app:
I first read about Cash Cow lite on Teach Science and Math. I downloaded the free version and DS8 started playing.Within a few minutes, I made my second math app purchase. Ever. We bought the full version of Cash Cow.
My son's description: "You add coins together to make bigger amounts: .05, .10, .25, 1.00. If you get to higher levels you can add glowing coins together to get more money. When you're done with a level you get to buy things for your farm."
It's a great little game for identifying coin values and putting various combinations together to produce higher valued coins. The game hasn't lost it's intrigue after accompanying us to a lot of basketball games. I, too, find it fun. We've definitely gotten our $.99 out of it.
Check out other math apps I've reviewed. The majority are free.
There exists a widespread misconception among the readers of popular physics books - and sometimes even unpopular physics books - that Bell's inequalities have only falsified "local realist" models of quantum phenomena but some "nonlocal realist" models could still be true and replace the probabilistic quantum mechanics.
The nice picture is taken from an article hyping "time-like entanglement" which is nothing else than the ordinary entanglement without the apparent "spooky action at a distance"
I just encountered one or two fanatical anti-quantum bigots at the Physics Stack Exchange. (One of them is a freshly graduated student from the hockey stick's and LQG's PSU.) My God, those people are so annoyingly stupid and obnoxious. I can't stand them. And they're such cowards. They would only attack my answer even though Peter Shor writes the very same thing about QM as your humble correspondent.
There exist several "toy models" or "thought experiments" that have been designed to check the difference between the classical reasoning and the quantum reasoning. Bell's inequalities showed that the correlation measured in a system with two spinning particles has to belong to a certain interval according to all local realistic theories. Quantum mechanics predicts correlations that are often outside this interval - and these correlations may be verified experimentally. It follows that the local realistic theories are falsified.
For additional years, people thought that Bell's inequalities, relevant for pairs of spins, were the most spectacular toy model demonstrating that our world genuinely deviates from the classical intuition. However, other people continued to play with entanglement and they found some other, even more spectacular thought experiments.
All of them have been made into real experiments and quantum mechanics was shown to be correct in all cases. It also means that the classical models and the classical intuition were proved incorrect in all cases.
The GHZM state, invented by Greenberger, Horne, and Zeilinger, and streamlined by Mermin, is an arrangement of three spins for which the product of three spins (taken to be +1 or -1) has exactly the opposite value than what the classical intuition would lead you to believe.
Hardy's paradox: history
Hardy's paradox, designed by Lucien Hardy in 1992, is perhaps even more spectacular than Bell's inequalities and the GHZM state because in the experimental situation, the classical logic would allow us to deduce that some events can't occur at all. Instead, they do occur.
In the original Hardy's setup, one talks about an electron and its antiparticle, a positron. Both of them may be detected in one of two detectors. However, a particular combination of detectors could only be chosen by the pair if the two particles have previously traveled along trajectories that would guarantee that the particles annihilate. Because they annihilate, they can't get to the detectors. Except that in a significant fraction of cases, they actually do end up in this pair of detectors.
A lot of confusion has been said about this experiment. People discussed specific properties of antiparticles and annihilation. However, the surprising content of this thought experiment - and real experiment - has nothing whatsoever to do with antimatter. It is just another example of the difference between the incorrect classical logic and the correct quantum logic (including the rules of entanglement).
So it doesn't matter how we interpret the physical states and the operators; in particular, we don't need any antimatter.
Hardy's paradox: presentation
I will follow Frank Laloe's excellent explanation (page 35) and I will try to make it even more comprehensible.
Consider a system of two particles which are associated with letters "a" and "b", respectively. On each particle, we may perform two kinds of measurements, either A or A' for the article "a" and either B or B' for the particle "b". To be specific, imagine that the un-primed measurements A,B are spin measurements of two spin-1/2 particles with respect to the vertical z-axis and the primed measurements, A',B', are with respect to a different axis in the xz-plane that makes angle 2δ with respect to the vertical one.
I want to train your brain a little bit more so in this article, θ=δ everywhere; thanks, Mikael. :-)
Each of these measurements may produce the result −1 or +1. There are three qualitatively different types of measurements: either both "a" and "b" are asked about their "unprimed" up/down polarization (doubly unprimed choice), or one of them is measured by the "primed" gadget and the other by the "unprimed" gadget (mixed choice), or both of them have their "primed" quantities measured (doubly primed choice).
It's up to the two experimenters which experiments they perform with the particles.
Now, as we can show, it is possible to design the apparatus and the two particles so that the following three conditions are guaranteed. Each condition constrains the results with respect to one of the three kinds of a measurement - either the "two unprimed measurements" or "mixed" or "two primed measurements". All of the conditions say something about the "+1,+1" or "-1,-1" outcome - some of them are forbidden and some of them are required to occur.
The conditions are:
After the doubly unprimed measurements, A=+1 and B=+1 sometimes occurs
After the mixed measurements, A=+1 and B′=+1 never occurs, and A′=+1 and B=+1 never occurs, either
After the doubly primed measurements, A′=-1 and B′=-1 never occurs.
Can you prepare the particles "a" and "b" so that regardless of the two experimenters' choice of "primed" vs "unprimed" axes, all conditions above will be universally satisfied even if the experiment is repeated many times? The answer of any realistic theory, whether it's local or not, is "no". Classical logic itself is enough to show that the number of events in which all three conditions are satisfied is zero.
The first condition guarantees that it may happen that the particles are sometimes prepared to be measured as A=B=+1. However, for these cases, the second condition guarantees that B′=−1 - because B′=+1 is impossible since we already have A=+1. And similarly, classical logic implies that A′=−1 - because A′=+1 is impossible since we already have B=+1.
A diagram showing four (out of eight) possible outcomes of the two experimenters' measurement and 4 pairs of outcomes that may, must, must, or mustn't occur for the same event according to the 3 conditions.
We have just derived that in the situations in which the particles are prepared to be observed with A=B=+1, we have A′=B′=−1 which violates the third condition. So the conditions can't be simultaneously satisfied. It sounds like an impenetrable logic. Whenever you assume that right before the measurements, the pair of particles already objectively possesses some properties prepared for any experiments that the experimenters may choose to perform (and we may even allow the particles to superluminally communicate before the measurements), it follows that the three rules above are incompatible.
I want to emphasize that even if there's some nonlocal mechanism - a gadget that correlates the particles in any classical way and tells them how to behave - the classical logic will still hold and it will lead to the wrong conclusion that the conditions are incompatible. Locality isn't the problem; the classical realism is the problem.
Quantum mechanics: conditions are compatible
However, in quantum mechanics, they're totally compatible, and the compatibility has been demonstrated experimentally, too. With respect to the primed bases, the right two-particle state that satisfies all the three conditions may be written as
where the angle between the "primed" and "unprimed" axes was chosen to be 2δ (one axis is "z" and both belong to the "xz" plane) and we consider the spin equal to 1/2. The state vector above is not normalized, so you should normalize it if you need it.
Note that one of the four basis vectors, the vector with A′=B′=−1, is omitted, so we automatically satisfy the third condition. By a proper transformation to the rotated, unprimed basis for one of the two particles, either "a" or "b", we may also check that the second condition (a pair of similar conditions, in fact) is satisfied. That's why the coefficients were chosen to be cosines and sines of θ.
However, the first condition is also satisfied because the coefficient of the A=B=+1 can be seen to be nonzero - after the simple rotation of both bases. The coefficient of the A'=B'=+1 state is sinθ in the formula above and the similar coefficient stays nonzero even after the rotation. We may choose the angle so that the probability of the classically forbidden A=B=+1 is as high as 9.0169944%, a figure that may be enhanced further if additional particles are added.
If you care, the probability of A=B=1 is M(1-M)^2/(2-M) where M is sin(θ)^2.
So quantum mechanics implies that two particles may be arranged in a state such that all three conditions - for all three types of paired measurements that the two experimenters may decide to perform - will be satisfied. Some events will follow the condition 1 despite the seemingly contradictory conditions 2 and 3. This rules out all "realistic" interpretations of reality, whether they're local or not.
Where do the quantum novelties hide?
What is different about the quantum logic that doesn't allow us to derive the classical conclusion? Well, the second condition says that the state |Ψ⟩ is annihilated by two projection operators,
P(A=+1)P(B′=+1)|Ψ⟩ = 0, P(A′=+1)P(B=+1)|Ψ⟩ = 0.
It's also annihilated by the following operator, as dictated by the third condition,
P(A′=−1)P(B′=−1)|Ψ⟩ = 0.
Classically, we could derive that the state must also be annihilated by
P(A=+1)P(B=+1)|Ψ⟩ = 0 ... (no in QM!)
which is a projection operator relevant in the first condition. The classical logic was showed above. We could try to translate the classical logic into the quantum mechanical formalism by realizing that
P(Q=+1) = 1 − P(Q=−1) for Q=A,B,A',B'.
Let us do it in some detail. Using the "complementarity" of the answers +1 and −1 above, the two parts of the second condition may be rewritten as
Classically, the state vector may be "cancelled" because the projection operators have "classical values" 0 or 1. So by substituting the newest two equations, we get the following for the probability of A=B=+1:
The sloppy classical manipulations would allow us to say that the projection operator for A=B=+1 annihilates the state because we rewrote it in a form that contained P(B′=-1)P(A′=-1)|Ψ⟩ which vanished because of the third condition.
However, quantum mechanically, the state doesn't have to be annihilated by the A=B=+1 projection operator because the step highlighted by (!!!) is incorrect. We haven't proved any identity for the projection operators themselves; we have only assumed and proved the identities of the PP=P form when they act on the state vector |Ψ⟩.
You could try to invent another quantum proof by proving that the expectation value
⟨Ψ|P(A=+1)P(B=+1)|Ψ⟩ = 0 ... (???)
vanishes. That would actually be enough to prove that P(A=+1)P(B=+1)|Ψ⟩=0 because the PP product is a projection operator that squares to itself, so the square's expectation value i.e. the norm of the state P(A=+1)P(B=+1)|Ψ⟩ would have to vanish, implying that the state itself vanishes. In this strategy to calculate the matrix element in equation (???), P(B=+1)|Ψ⟩ would be replaced by the
P(B=+1)|Ψ⟩ ⇒ P(A'=-1)P(B=+1)|Ψ⟩
product above, while ⟨Ψ|P(A=+1) would be replaced by the Hermitian conjugation of the formula above, i.e. by this
⟨Ψ|P(A=+1) ⇒ ⟨Ψ|P(A=+1)P(B'=-1)
object. By now, we have rewritten our matrix element as:
Now, you're "almost" finished because the matrix element includes P(B'=-1)P(A'=-1) = P(A'=-1)P(B'=-1) which "almost" vanishes due to the third condition. Well, it doesn't: we only know that it vanishes when it acts on |Ψ⟩, but to make it act on |Ψ⟩, you have to commute the operator P(A'=-1)P(B'=-1) through P(B=+1) which blocks the approach to |Ψ⟩.
So you would also fail because you would need to permute the projection operators and the projection operators P(B'=-1) and P(B=+1) don't commute with one another, and similarly the operators that measure the A,A' spins don't commute with each other, either.
So as a more explicit quantum calculation can show very easily, and as experiments confirm, the vanishing of the A=B=+1 outcome that would contradict the condition 1 doesn't follow from the conditions 2,3 in the real (quantum) world.
The characteristic fact of quantum mechanics I mentioned a moment ago - that observables don't commute with each other, not even the projection operators describing Yes/No properties of systems - guarantees that we can't derive the third displayed equation above from the previous two lines. And the reason is not our lack of skills; the reason is that the identity that someone would like to derive is actually demonstrably invalid.
The very Yes/No properties of a particle don't commute with each other. What are the implications of this statement that is self-evident in quantum mechanics but deep and confusing away from quantum mechanics? The statement implies that we can't ever imagine that a particle is ready to react to different kinds of measurements at the same moment. In some sense, it's just another form of the uncertainty principle, optimized for the projection operators and binary properties in this case.
Different properties of a physical system can't simultaneously "exist" because of the refusal of the operators to commute with each other. And because none of the observables is privileged - experimenters may measure the spin with respect to any axis - it follows that none of the observables can "exist" prior to the measurement.
The electron "e-" and positron "e+" arrive from the bottom. The electron always moves on the right half of the picture; the positron always moves on the left half of the picture. They may only intersect - and annihilate - at the center of the picture.
The BS gadgets are 50%-50% beam splitters (with a relative "i" phase) that partly reflect and partly transmit the incoming particle, separating the wave function into pieces. The first condition, requiring that "A=B=+1" occurs sometimes, is represented by the fact that the positron and the electron are sometimes simultaneously detected in the detectors d+ and d-, respectively. So the measurements of unprimed quantities A=+1, B=+1, A=-1, B=-1 correspond to clicks in the detectors d-, d+, c-, c+.
The primed quantities A',B' are represented by whether the electron or positron took the green "v" or the blue "w" path from the bottom beam splitters. Clearly, there is no adjustable "theta" angle here: it's been set to a particular value. The equalities A'=+1, B'=+1, A'=-1, B'=-1 correspond to the electron (-) or positron (+) going through the blue or green arcs v-, v+, w-, w+. We don't measure v/w (i.e. A', B') here but we could.
Using the dictionary, the condition 2 says that v- is incompatible with d+ and v+ is incompatible with d-. It holds because the interferometer for the electron is adjusted so that the particle from e- has to end in c-, in the absence of any other particle in the w/u half-circles, and similarly for the positron e+, c+. So classically, the particles can only appear in d+, d-, instead of the ordinary c+, c-, if both of them are disturbed (phases etc.) by the other particle in the central w/u region. However, if both of them go through the central region, they have to annihilate. So classically, they can never be detected in d+, d-.
Experiments confirm the quantum predictions that in 1/16 of cases, we get a hit in d+ and d- at the same moment.
As we can see, the classical reasoning leading to the conclusion that the absence of the electrons in the red u+, u- arcs implies that the particles cannot be detected in d+, d- is incorrect. We can't imagine that the primed, "w or u arc", questions about the electron and positron can be simultaneously answered with the unprimed question "which detector, c or d". If we ultimately measure the particles via detectors, "c or d", the value of the "u or v" arc just isn't well-defined before the measure. The projection operators refuse to commute.
at amazon.com and support SMS Book Reviews
at amazon.com and support SMS Book Reviews
