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Library of Congress Digital Collections Today in History May 29
Today in History - May 29
Today's Stories:
Patrick Henry, Orator of Liberty
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Patrick Henry was born on May 29, 1736, in Studley, Virginia. He was a brilliant orator and an influential leader in the Revolutionary opposition to British government. As a young lawyer in 1763, Henry astonished his courtroom audience with an eloquent defense based on the doctrine of natural rights—the political theory that man is born with certain inalienable rights.
Patrick Henry, half-length portrait. (Photograph of a painting by George B. Matthews in the United States Capitol). c1904. Detroit Publishing Company. Prints & Photographs Division
On his twenty-ninth birthday, as a new member of Virginia's House of Burgesses, Henry presented a series of resolutions: the Virginia Resolves on the Stamp ActExternal, which opposed Britain's Stamp Act. The Resolves were adopted on May 30, 1765. He concluded his introduction of the Resolves with the fiery words "Caesar had his Brutus, Charles the First his Cromwell, and George the Third—" when, it is reported, voices cried out, "Treason! treason!" "—and George the Third may profit by their example! If this be treason make the most of it."
Henry went on to serve as a member of the first Virginia Committee of Correspondence, which facilitated inter-colonial cooperation, and as a delegate to the First Continental Congresses in 1774 and the Second Continental Congress in 1775. At the second Virginia Convention, on March 23, 1775, in St. John's Church, Richmond, he delivered his most famous speech. As war with Great Britain appeared inevitable, Henry proclaimed:
Gentlemen may cry, Peace, Peace —
but there is no peace. The war is actually begun!
The next gale that sweeps from the north will bring to our ears the clash of resounding arms! Our brethren are
already in the field! Why stand we here idle? What is it that gentlemen wish? What would they have? Is life so dear,
or peace so sweet, as to be purchased at the price of chains and slavery? Forbid it, Almighty God! I know not what course others may take but as for me,
give me liberty or give me death!1
"Give me liberty, or give me death!" New York: Currier & Ives, c. 1876, Popular Graphic Arts. Prints & Photographs Division
Henry was the first elected governor of Virginia, serving five one-year terms in this office from 1776 to 1779 and again from 1784 to 1786, alternating with terms as a member of the state legislature. There he led the opposition to the bill that became the Virginia Statute for Religious FreedomExternal because of his belief that state taxes should be directed to the support of all Christian denominations. The Statute, written by Thomas Jefferson and passed by the Virginia General Assembly on January 16, 1786, is the forerunner of the U.S. Constitution's First Amendment protections for religious freedom. Throughout his public career, Henry retained his leadership role, having a profound influence on Virginia's role in the new nation.
In 1788 Henry opposed Virginia's ratification of the new U.S. Constitution because of his concern that the new central government would have too much power. After the Constitution was adopted, he continued to work for the addition of the first ten amendments guaranteeing the freedoms that came to be known as the Bill of Rights. His last speech before he died in 1799 was a plea for American unity in response to early arguments favoring primacy of states' rights.
No text of the "Liberty or Death" speech in Henry's hand has survived, nor has any contemporary version of it, so the precise text is not known. However, U.S. Attorney General William Wirt recreated the speech from the recollections of those who had heard it. In 1817 Wirt published the speech, along with descriptions of Henry's speech-giving mannerisms in a biography of Patrick Henry: Sketches of the Life and Character of Patrick Henry. Another reliable full textExternal of the speech is available on the Yale Law School's Avalon ProjectExternal Website.(Return to text)
Search on Patrick Henry to find correspondence, memoranda, and other items of interest relating to this American patriot in the following document collections:
George Washington Papers
Thomas Jefferson Papers, 1606 to 1827
Andrew Jackson Papers
James Madison Papers, 1723 to 1859
A Century of Lawmaking for a New Nation: U.S. Congressional Documents and Debates, 1774-1875
Documents from the Continental Congress and Constitutional Convention, 1774 to 1789
A timeline of events related to the formation of the United States and the essay To Form A More Perfect Union, provide an overview of the events leading up to ratification. The timeline and essay also provide an introduction to the Documents from the Continental Congress and Constitutional Convention, 1774 to 1789 collection. Search the collection on Virginia AND Constitution, to find more documents pertaining to ratification by Virginia.
Learn more about the Constitution and the Bill of Rights in the Primary Documents in American History.
On May 29, 1848, Wisconsin became the thirtieth state admitted to the Union. The "Badger State" was the last state formed in its entirety from the Northwest Territory. Textured with beautiful landscapes and abundant natural resources, Wisconsin has a rich legacy of concern regarding their conservation. Tourist sites include the Wisconsin Dells and Devil's Lake.
Crystal Lake, Wis. Albert A. Kreuter, c1913. Panoramic Photographs. Prints & Photographs Division
Wisconsin is a beautiful land… by reason of its wooded hills and the multitude of its beautiful little lakes. I had imagined it to be less well settled; for although one finds the borders of civilization so near at hand that in hunting one often encounters Indians, yet the southern half of the state is developing into a great, blooming, densely populated agricultural district.
Carl Schurz to Margarethe Meyer Schurz, Letter of October 9, 1854. In Intimate Letters of Carl Schurz, 1841-1869. Madison: State Historical Society of Wisconsin, 1928. p139. Pioneering the Upper Midwest: Books from Michigan, Minnesota, and Wisconsin, ca. 1820 to 1910. General Collections
The Winnebago, Menominee, Potowatomi, Dakota (Sioux), and Ojibwa (Cherokee) were among the Native American tribes to reside in the area. Among the first Europeans in this region were Jean Nicolet, who started a profitable fur trade between France and the native population, and Jacques Marquette and Louis Joliet, Catholic priests who first explored the upper Mississippi territory.
The first permanent European settlement in this area was established in 1717, but only after the War of 1812 did the number of settlers increase notably. In 1832, the Sauk and Fox, under Chief Black Hawk, sought to regain their lands in the Illinois and Wisconsin territory but, after their defeat, settlers rapidly moved in. Miners poured into the southwestern sector of Wisconsin early. Lumberjacks came to the northern and central portions of the state. Farmers found abundant fresh water sources and rich land. Factory workers populated the southeastern industrial belt along Lake Michigan.
Panoramic View of Milwaukee, Wis… Milwaukee, Wis.: The Gugler Lithographic Co., c1898. Panoramic Maps. Geography & Map Division
Last evening I went with my parents to a summer refreshment place near the city, which was opened last Sunday with a great bowling contest. In such places things are conducted with much cheerfulness and wholly in the German style. The arrangement of the garden and all the grounds, and the predominance of the German language, would almost make you feel that you were in the fatherland if you did not hear the most varied German dialects and here and there a couple of Americans talking. At another place near the town, in the woods, there is target shooting on Sunday, and when the setting sun ends the work of the marksman a piano in the hall invites the young people to dance.
Carl Schurz to Margarethe Meyer Schurz, Letter of August 12, 1855. In Intimate Letters of Carl Schurz, 1841-1869. Madison: State Historical Society of Wisconsin, 1928. p147. Pioneering the Upper Midwest: Books from Michigan, Minnesota, and Wisconsin, ca. 1820 to 1910, ca. 1820 to 1910. General Collections
Political refugees from Germany found a haven in Wisconsin during the mid-nineteenth century, especially around Milwaukee. German immigrants contributed their social idealism to community life and German influence was also seen in the development of music, theater, and leisure activities. The Progressive Movement of the early 1900s, which introduced innovative ideas in education and government, found a particular resonance in the state, resulting in legislation that made Wisconsin a leader in the social reform of industry and government.
Weimar Manner Gesang Vereine, Milwaukee. Geo. R. Lawrence Co., c1907. Panoramic Photographs Prints & Photographs Division
A singing society [Gesangverein] has been organized which has already given a very successful concert. A lot of balls were given during the winter, and an amateur theatre is organizing. Of course all this is only a beginning, but it is something. It is a sign that spiritual needs are strongly making themselves felt….
Carl Schurz to Margarethe Meyer Schurz, Letter of March 4, 1855. In Intimate Letters of Carl Schurz, 1841-1869. Madison: State Historical Society of Wisconsin, 1928. p143. Pioneering the Upper Midwest: Books from Michigan, Minnesota, and Wisconsin, ca. 1820 to 1910, ca. 1820 to 1910. General Collections
Search the following collections using the keyword Wisconsin or the names of Wisconsin localities for more images of the state:
Panoramic Photographs
Detroit Publishing Company
Farm Security Administration/Office of War Information Black-and-White Negatives
View the Today in History feature on Carl Schurz, a German-American conservationist and politician. Read more of Carl Schurz's correspondence in Pioneering the Upper Midwest: Books from Michigan, Minnesota, and Wisconsin, ca. 1820 to 1910. Discover other first-person accounts and historical documents from the state of Wisconsin in the same collection. Also featured is a collection of essays titled The History of the Upper Midwest: An Overview.
Manuscripts related to Wisconsin in the collection American Life Histories: Manuscripts from the Federal Writers' Project, 1936 to 1940, provide other stories of those who have lived in this state.
View a manuscript map of Indian lands of eastern Wisconsin annotated by Henry Rowe Schoolcraft, ca. 1831. This item is found in the Manuscript Division's collection of Henry Rowe Schoolcraft Papers.
Map Collections include early maps of a number of Wisconsin cities. In the Cities and Towns section, search on Wisconsin. See, for example, Appleton in 1867, River Falls in 1880, or Menomonee Falls in 1886. Zoom in to see houses, parks, factories, railroad trains, and more in fine detail.


20th Century Fox's X-Men franchise may be in the process of being "reconfigured", but the studio is wasting no time moving on to the next chapter. A new report has revealed that the next X-Men film will begin filming next May in Montreal, and director Josh Boone (The Fault in Our Stars) dropped a pretty clear hint that that movie is going to be New Mutants.
A report in Le Journal de Montreal revealed that the production office for the next X-Men office is already set at MELS Studios with set construction beginning in January. Michel Trudel, the president of MELS confirmed, "They will start shooting in May and they will occupy Studios 2 and 3 of MELS for several months." While the report didn't explicitly state which X-Men film will film next year, Boone retweeted Den of Geek's coverage of the story with the note "Hmmmm, what movie could it be?" So yeah, it's probably New Mutants.
And that makes sense. Fox finds themselves at a bit of a crossroads with their long-running mutant verse. It's a cash cow, earning them more than $4 billion, worldwide, but this year's release, Bryan Singer's X-Men: Apocalypse, was met with critically and commercially disappointing results, earning only $544 million worldwide to Days of Future Pasts' $748. On top of that, X-Men stars Jennifer Lawrence, James McAvoy, Michael Fassbender and Nicholas Hoult have reached the end of their three-picture contracts, and if the studio wants them to re-up, it's going to be costly, and the long-planned Gambit movie has yet to come together again after losing two directors.
Meanwhile, Boone has been hard at work on New Mutants alongside his The Fault in Our Stars screenwriting duo Scott Neustadter and Michael H. Weber. The film adaptation will reportedly have a YA tone and feature the mutants Wolfsbane, Magik, Sunspot, Danielle Moonstar, Mirage, and Cannonball. They'll also be joined by Professor X and, if early reports are to be believed, Alexandra Shipp's young Storm, who was introduced in X-Men: Apocalypse.
New Mutants doesn't have a confirmed release date, but after a recent release date shakeup, the next "Untitled Marvel/Fox Film" is scheduled for March 2, 2018.


Llangrove and District Gardening Society held their annual Flower Show awards at Llangrove school on Saturday 2nd September. There were many fine exhibits produced by people of all ages on display for the judges to see. These included single roses, beautiful floral arrangements, gardens on plates, home made jams, chutneys and cakes and vegetables, amongst others. There were delicious refreshments available throughout the day and a raffle was held during the afternoon.
Cup and prize winners are listed below the photographs.
Hello from NW Sichuan in China (On the Tibetan border).
My wife, her son and my son (from Dymock) are off to Lhasa on the new train tomorrow. Are you interested in the tale? 58 hours and 4000kms.
Yes, I'm still here after three years and very settled, probably forever. Teaching in two wonderful schools, own a timber-framed and panelled 'English' pub, 'The Flags', complete with darts and pool and football tables and with our own super home.
What do I miss from England? Well I can drink thirty different foreign beers so that's no problem. The weather is great, winters short and mild. The cost of living is a seventh here of UK's. I listen to Radio 2; use Columbian coffee beans; read all the papers online; can buy perfectly packaged DVDs for 35 pence and have 2000 songtracks on the computer. I miss good bread. That's it.
It's all very civilized, safe and clean here in my city, with very few foreigners.
Thanks for all your efforts to keep people like me in touch with Ross. They might tack your effigy somewhere prominent one day as a reminder of your saintliness.
From Ralph who used to live in Ross.
Thanks Ralph. Nice to hear from you on the other side of the world.
Your wife and sons' story would be very interesting to run! If possible, with a photo or two.
Not sure about the last bit - there are plenty here who would be only too willing to stick pins in it and I'd end up with my head in a sling.
I was recently given this postcard which came from Ebay and I was told that it was Walford Herefordshire but I can't seem to find any details about it. Is there any chance you could put out a request for information in your next issue of Wyenot news?
Are you able to help Simon? If so, please email and I will put you in touch.
I am a little disappointed as Christmas started late this year. I usually leave my Christmas shopping until Christmas Eve but thought I would get a little more organized this year and so, on Friday, 1st September I went about the supermarkets in town looking to buy some Christmas goodies. There were nothing festive to be found in any of them though and I gave up hope, thinking, 'What am I going to do? Time is ticking by and there are only 115 shopping days left'.
It was not until I went out the following day to pick up the more mundane necessities of life, such as toilet rolls and chocolate biscuits that my faith in commercialism was fully restored. Christmas had begun in earnest at last, with an isle being prepared for the Season of Goodwill. I only had my pocket digital camera with me at the time and the battery was virtually flat but I did manage to squeeze the shot below out of it.
I can already feel the chill of winter snow approaching, hear the distant sound of sleigh bells ringing (not forgetting Slade in the Maltings) and I look forward to seeing the first house in Ross fill the night sky with bling. I'm so excited in fact that I didn't get a wink of sleep last night.
One hundred Brownie points for the first person to send in a photographs of September mince pies on sale (preferably with the 'use-by' date visible).
Let me be the first to wish you all a Merry Christmas and a Happy New Year!
And a packet of Morrison's chocolate digestives.


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Aprons hand made with love for the home cook, potter, baker, gardener or crafter.
Reinforced riveted pockets for hands & brushes, tea towels & tools, chalk & scissors.
Tan leather straps removable for washing and adjustable to fit all.
Natural weave strong cottons – can handle any bout of creative frenzy.


Do look for one that has a proper, valid license to operate from the region you are located. With that said, you must not make any mistakes in the process and focus on the proceedings. Here, hiring a licensed company for the job is the only way forward. You shouldn't delay things any further and accelerate your search for a licensed service if possible.
It is one of the most important requirements so pay attention to it and make sure to hire the experienced service only. When you do that, you certainly end up finding, and hiring the service that has enough experience in hand. These entities, having dealt with so many different types of customers over the years, know what it takes to satisfy them. They'll do so and you will see that happening with own eyes. It will happen and you will see it yourself as soon as you hire Canada immigration consultants in Sharjah.


Paper Clip / Bookmark Gray Monster. Made of a Natural Fiber Paper. You can use them as a paperclip or a bookmark. If you put them in the water for 5 min, they will bend to any shape you like. Becomes a great toy!


BARD IN THE BACKCOUNTRY provides a rare glimpse into the relevance that classic Shakespearean theater still holds in the lives of everyday people across the most rural regions of Montana. It's a behind-the-scenes look at a summer of Montana Shakespeare in the Parks – from first read through to final performance.
Cindy Stillwell is a film artist whose films have screened at venues worldwide, including the Museum of Modern Art in New York, Sundance Film Festival, and the International Film Festival of Rotterdam. Stillwell received her MFA from New York University's Tisch School of the Arts. She currently lives in Bozeman, Montana, where she is a professor of film production in the School of Film and Photography at Montana State University.


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Larry Greenemeier
VA Had Many Security Warnings Before Its 26.5 Million-Person Breach
The organization didn't take the risk seriously enough and broke with security best practices.
Much of last week's howling outrage over the theft of a laptop containing personal data on millions of veterans and spouses focused on the Veterans Affairs Department's poor IT security record. The political grandstanding and indignation last week were on the mark, but we should be long past the need to chastise organizations for poor security practices. It's time for execution and enforcement.
A VA analyst took home electronic data from the office to do after-hours work on his personal computer. The data included names, Social Security numbers, and dates of birth on 26.5 million people. The laptop and an external hard drive the analyst was using, along with the data, were stolen in a May 3 burglary.
The VA ran afoul of standard security practices on many levels. The analyst was authorized to access the sensitive information, which was required for a policy-related project, but not to remove it from the office. Yet that policy was little known or largely ignored. The unidentified analyst had been taking data home as part of his work routine since 2003, unbeknownst to his supervisors, the VA inspector general's investigation found.
VA Secretary James Nicholson has plenty of company in the "mad as hell" club
Photo by AP Photo/Charles Dharapak
What's more, the VA has a policy of encrypting sensitive data to mitigate damage in the event of a breach, but the missing data wasn't encrypted. And top brass wasn't informed until two weeks after the theft, VA Secretary James Nicholson said last week.
This confluence of sloppy security practices opened the floodgates last week on the VA and Nicholson, who at one point had to excuse himself from the shellacking he was taking at a House hearing to endure another one in the Senate. Nicholson vacillated between taking responsibility for the data breach and expressing anger. "As a veteran myself, I have to tell you I'm outraged. Frankly, I'm mad as hell," Nicholson told the House Committee on Veterans' Affairs. He won't be the only one when taxpayers find out that the gaffe will cost them at least $100 million to notify affected veterans and provide them with credit-checking services.
With the VA having done wrong by 26.5 million veterans and their relatives, members of Congress were in speech-making mode last week. Sen. Larry Craig, R-Idaho, wondered whether the VA really needs to retain all the data it has. "But I also know that when Americans contact their government or veterans file a claim, they expect in this day and age that [the government] will have their information," said Craig, chairman of the Senate's Committee on Veterans' Affairs.
"I hope what took place at the VA a few weeks ago is only an isolated incident of bad judgment by a dedicated employee seeking to do a little work at home on his own time," Craig said. "But we must not ignore the fact that at this time getting that information to his or her home was very easy. That cannot be tolerated."
That's really what this breach is all about: Companies and organizations can't rely too much on the good judgment of employees or their ability to follow policies. They need security systems that back them up when judgment and policies fail. As data is increasingly mobile--laptops, memory sticks, personal devices like iPods--the risk of loss is too great to ignore.
VA Ignored Risks
The VA failure is the largest since last summer's hack of credit card processor CardSystems, according to the Privacy Rights Clearinghouse, though that was a clear case of targeted data theft. Investigators so far don't suspect the VA loss was anything but a home burglary. Yet what's stunning about the VA case is the amount of data that one person could access and remove without requiring encryption or interacting with a supervisor. A March blunder by Fidelity Investments, in which an employee's laptop containing the names, addresses, Social Security numbers, birth dates, and other employment-related information of 196,000 participants in Hewlett-Packard retirement plans was stolen, pales in comparison with the VA mess.
The VA hadn't taken the risks related to mobile data and data security seriously enough, according to the VA's inspector general and the Government Accountability Office, which for years has criticized the agency's IT security policies and practices. "Our Federal Information Security Management Act reviews have identified significant information security vulnerabilities since fiscal 2001 that place VA at risk of denial-of-service attacks, disruption of mission-critical systems, and unauthorized access to sensitive data," George Opfer, inspector general for the Veterans Affairs Department, testified last week.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: No index.php file in yii2 basic and yii migration error I'm a beginner and really struggling to get an existing yii2 project running on localhost.  As far as I can see, there's no index.php file, but all my online searches say that only happens with the advanced framework (I don't see any backend or frontend folders that come with the advanced framework in my project though?).
I've followed all the instructions in the project's readme file and it installed the vendor folder, but is giving me an exception when I type in the yii migrate command. It installed 13 of the 47 migrations without problem but then gets stuck on this:
*** applying m170317_154007_current_date
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in C:\xampp\htdocs\Duals\vendor\yiisoft\yii2\di\Container.php:428
$reflection = new ReflectionClass($class);

Stack Trace:
#0 C:\xampp\htdocs\Duals\vendor\yiisoft\yii2\di\Container.php(428): ReflectionClass->__construct('m170317_154007_...')
#1 C:\xampp\htdocs\Duals\vendor\yiisoft\yii2\di\Container.php(364): yii\di\Container->getDependencies('m170317_154007_...')

So basically a two part question

*

*This is all existing code from a working site, how do I fix this?

*Will this create the index.php file at the end, and if not, am I just missing something simple as a beginner or is the installation just really complicated sometimes?

redpajama_set_name: RedPajamaStackExchange


Can a book change its story each time it's read? Read on for a free download!
In my story, "The Secret Treasons of the World," Braelin has sambocade as part of her birthday feast, so I thought I would include the recipe here in Middle English and with a modern redaction.


text:
Bellwether Education Partners
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Christine Wade
Background: Christine Wade is an associate partner with Bellwether Education Partners in the Strategic Advising practice area. Christine began her consulting career in 2014 at Bain & Company, where she worked across a broad range of industries and strategic topics and supported strategic planning and organizational effectiveness projects. In 2018, Christine joined KIPP DC for five months as a Strategic Projects Extern, where she developed research and recommendations for growth and other focus areas, including the meal program. Additionally, she supported several teams with data analysis and reporting. Christine holds a bachelor's degree in Commerce and Economics from the University of Virginia McIntire School of Commerce.
Experience at Bellwether: Christine has focused on guiding a range of organizations through strategic planning processes, including a handful of efforts to support early childhood education and students with disabilities.
Why I do this work: I have always been passionate about education. I was so excited for kindergarten that when I climbed onto the bus for my first day, I didn't even look back to wave at my parents. (They weren't so excited about that part.) The more I've learned about the enormity and breadth of challenges and the inequities across the system, the more I've wanted to be a part of working to improve opportunities and outcomes for all children.
christine.wade@bellwethereducation.org
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\'BEL-'weth- r\ noun; A leader of a movement or activity; also, a leading indicator of future trends.
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Whether you're an athlete or someone struggling to hit a fitness goal, meagrely the bathroom scale or a height-weight chart won't do. You need to know what your body is made of and how it responds to nutrition and training. In fact your metabolic rate and body fat percentage surface much higher on the getting fit priority list. You can weigh 120 pounds (at 25% Body Fat) and still look bigger that an individual weighing 140 pounds (at 15% Body fat). The concept of "muscle weighs more than fat" is pretty much garbage. MUSCLE OCCUPIES LESS VOLUME THAN FAT. Remember the whole what weighs more a pound of iron or pound of cotton. One pound is one pound, irrespective.
So what the hell is body fat and what's all the hype about?
In the simplest form, it's the amount of fat stored in your body, compared to it's other components, namely your organs, muscles, bones, blood etc. Having said that men and women tend to display different amounts of body fat. An elite male athlete may have a percentage as low as 3-4%. While an elite female athlete would carry 8-9% of Body Fat.
You're probably thinking about 0% Body fat now. Well body fat is essential to survival and each and every person, ranging from the most ripped athlete to the average individual requires a certain amount of "Essential fat". That's the minimal amount required to survive. Fat serves as fuel when the carbohydrate stores are plundered. It even protects the internal organs. In absolute dearth, you put yourself at the risk of organ failure and other health risks.
So with that attitude isn't the 3-4% also extremely detrimental?
What you need to understand is that most professional athletes maintain these low levels while competing or during season. Through the rest of the year, they maintain healthier levels of body fat to stay healthy and keep their internals in peak shape. Their livelihood depends on it and they themselves have a range of health care professionals around looking out for them at each and every step. Their bodies are conditioned and accustomed to working the way they do, without harming performance. However, if a non-professional aims to hit these minimalistic numbers, it's most likely that his performance and strength might suffer. Like I've said time and again women face special concerns when it comes to training. If they don't want to impact their menstrual cycles and fertility negatively, they mustn't aim for a number lower than 15%.
There are a number of available tools in the market to help you determine your body fat percentage. There's Cadaver Analysis, Underwater Weighing, Bioelectrical Impedance, Skinfold Calipers, etc. However, most of them aren't always accurate. The Manual Skin fold calipers often have the smallest margin of errors and are one of the better methods of gauging body fat. Around 50% of the body fat is under the skin. The thicker the skin fold; the more the fat the individual is lugging around. These callipers measure this thickness at specific body spots and substitute the values in a predetermined mathematical equation; to give you your reading of body fat.
You've been told more than once, "Your body is 80% diet and 20% training." While there is some truth to the fact, that healthy eating can drastically sculpt your body, you can't neglect the importance of training. The lower you want your numbers, the more you're going to have to give it your 100%. And yes, that includes both, your daily nutrition and training plan.
Sooo if that's all you need to know about body fat, what is BMI?
You see a healthcare professional. He measures your weight, looks at your height and quickly charts out a ratio based on which he categorizes you as underweight, normal, overweight or obese. That's your BMI (Body Mass Index). Shockingly enough, it isn't always the best representation of your efforts or outcome. It will give you the same reading; whether you're 150 pounds of muscle or 150 pounds of chips. Take a minute and think for yourselves. This methodology would put a 180 lb., 6 foot athlete athlete (10% body fat) into the same category as a 180 lb., 6 foot male (30% body fat). Just picture the two and you'll be able to tell for yourself. BMI has its standing when you're extremely overweight. It will signal your need to shed fat. However, once you get serious, train and eat well, it's importance begins to diminish.


Locking File Box Small Security Fireproof Waterproof Home Office Documents Cash. 38 cu ft Legal Size Waterproof 1-Hour Fire Chest, 1104. UL class 350: 1-hour fire, 1700 degrees/927 degrees C. Honeywell Fire water chest, waterproof: 48 hours, 39/1m depth. Fits letter, A4, and legal size documents flat. Protects paper documents and digital media. 38 cu ft of storage space. Allows you to keep all your valuable, important documents safe and secure.
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We usually respond within 24 hours on weekdays. The item "Locking File Box Small Security Fireproof Waterproof Home Office Documents Cash" is in sale since Sunday, August 5, 2018. This item is in the category "Home & Garden\Home Improvement\Home Security\Safes". The seller is "bestdealsrus1" and is located in NY. This item can be shipped to United States, Canada, United Kingdom, Denmark, Romania, Slovakia, Bulgaria, Czech republic, Finland, Hungary, Latvia, Lithuania, Malta, Estonia, Australia, Greece, Portugal, Cyprus, Slovenia, Japan, China, Sweden, South Korea, Indonesia, Taiwan, South africa, Thailand, Belgium, France, Hong Kong, Ireland, Netherlands, Poland, Spain, Italy, Germany, Austria, Israel, Mexico, New Zealand, Philippines, Singapore, Switzerland, Norway, Saudi arabia, Ukraine, United arab emirates, Qatar, Kuwait, Bahrain, Croatia, Malaysia, Brazil, Chile, Colombia, Costa rica, Dominican republic, Panama, Trinidad and tobago, Guatemala, El salvador, Honduras, Jamaica.


Is Hana a female or a male name and where does Hana originate from?
What is the full meaning of Hana ?
Is the gender of the name Hana male or female and what people use it most often?
Like to add another meaning or definition of Hana?
What is the meaning/definition of the letters in the name Hana?
Tags: Horoscope & Zodiac Meaning of Hana. Meaning of Hana. Did you find the numerology meaning of the name Hana? Please, add a meaning of Hana if you did not find one from a search of Hana.


text:
<?php

/** */
namespace CoreTest\Mail\MailService;

use PHPUnit\Framework\TestCase;

use Core\Mail\MailService;
use Core\Mail\Message;
use Laminas\Mail\AddressList;
use Laminas\ServiceManager\ServiceManager;

/**
 * Tests sending mails via MailService
 *
 * @covers \Core\Mail\MailService
 * @author Mathias Gelhausen <gelhausen@cross-solution.de>
 * @group Core
 * @group Core.Mail
 * @group Core.Mail.MailService
 */
class SendMailTest extends TestCase
{
    /**
     * Class under Test
     *
     * @var MailService
     */
    private $target;

    public $expectedMail;

    protected function setUp(): void
    {
        $test = $this;
        $sendCallback = function ($value) use ($test) {
            return $value === $test->expectedMail;
        };
        $transport = $this->getMockForAbstractClass('\Laminas\Mail\Transport\TransportInterface');
        $transport->expects($this->once())->method('send')->with($this->callback($sendCallback));

        $target = new MailService(new ServiceManager());
        $target->setTransport($transport);

        $this->target = $target;
    }

    /**
     * @testdox Gets mail service when passed a string to send()
     */
    public function testRetrieveMailBeforeSending()
    {
        $mail = new \Core\Mail\Message();

        $this->target->setService('retrieveme', $mail);
        $this->expectedMail = $mail;

        $this->target->send('retrieveme');
    }

    public function provideFromAddresses()
    {
        return array(
            array(null),
            array('ownfrowm@address'),
        );
    }

    /**
     * @dataProvider provideFromAddresses
     *
     * @param string $from
     */
    public function testSetsDefaultFromAddressOrUsesFromAddressSetInMail($from)
    {
        $mail = new Message();

        $defaultFrom = 'default@from';
        if (null !== $from) {
            $mail->setFrom($from);
            $expectedFrom = $from;
        } else {
            $expectedFrom = $defaultFrom;
        }

        $this->expectedMail = $mail;

        $this->target->setFrom('default@from');
        $this->target->send($mail);

        $mailFrom = $mail->getFrom();
        $this->assertInstanceOf('\Laminas\Mail\AddressList', $mailFrom);
        $mailFrom = $mailFrom->get($expectedFrom);
        $this->assertInstanceOf('\Laminas\Mail\Address', $mailFrom);
        $mailFrom = $mailFrom->getEmail();
        $this->assertEquals($expectedFrom, $mailFrom);
    }

    /**
     * @testdox recipients gets overidden if override recipients are set
     */
    public function testOverrideRecipient()
    {
        $overrideEmail = 'overidden@email';
        $ccEmail="cc@email";
        $bccEmail="bcc@email";
        $toEmail="to@email";

        $recipients = new AddressList();
        $recipients->add($overrideEmail);

        $this->target->setOverrideRecipient($recipients);

        $mail = new Message();
        $mail->addTo($toEmail);
        $mail->addCc($ccEmail);
        $mail->addBcc($bccEmail);

        $this->expectedMail = $mail;

        $this->target->send($mail);

        $headers = $mail->getHeaders();
        $expectedTo = 'To: ' . $overrideEmail;
        $this->assertFalse($headers->has('cc'));
        $this->assertFalse($headers->has('bcc'));
        $this->assertTrue($headers->has('X-Original-Recipients'));

        $this->assertEquals($expectedTo, $headers->get('to')->toString());
        $this->assertEquals('X-Original-Recipients: To: ' . $toEmail . '; Cc: ' . $ccEmail . '; Bcc: ' . $bccEmail, $headers->get('X-Original-Recipients')->toString());
    }

    public function testSetsXMailerHeader()
    {
        $mail = new Message();

        $this->expectedMail = $mail;
        $mailer = 'test/mailer';

        $this->target->setMailer($mailer);
        $this->target->send($mail);

        $headers = $mail->getHeaders();

        $this->assertTrue($headers->has('X-Mailer'));
        $this->assertEquals("X-Mailer: $mailer", $headers->get('X-Mailer')->toString());
    }
}


text:
NEWS shut down Back to previous
Naxos of America: 6 Questions with Hanzhi Wang2018-10-23
In August 2018, Naxos released its first-ever solo accordion album, Hanzhi Wang's "In the Path of H.C. Andersen." The release features works by Danish composers that explore both the darkness and luminosity of Hans Christian Andersen's famous stories. We had the opportunity to speak with Hanzhi about her recent album, misconceptions about accordion music, and more.
Read the text
New York Music Daily: Classical Accordionist Hanzhi Wang Brings Darkly Dynamic New Nordic Compositions to Carnegie Hall2018-10-20
Hanzhi Wang isn't the first accordionist to specialize in new classical music, but she is the first-ever squeezebox player to earn inclusion on the Young Concert Artists roster. Even though more composers these days are writing for the accordion, that's still a pretty big deal. Wang has a magically dynamic album of concise new works by Nordic composers, On the Path to H.C. Andersen, streaming at Spotify. She's making her Carnegie Hall debut on Oct 22 at 8:30 PM in Zankel Hall, playing works by B...
CDN: Classical accordion? YCA artist Hanzhi Wang dazzles at the KenCen2018-10-19
Ms. Wang's appearance at the Terrace in this opening recital of YCA's 2018-2019 Washington season was co-presented with Washington Performing Arts (WPA). In this, her DC debut, Ms. Wang dazzled all in attendance with her skills, her musicianship. She also offered the audience a surprisingly daring and eclectic repertoire in this (mostly) solo program.
Hanzhi Wang Debut at Kennedy Center2018-10-18
On October 11, 2018,Hanzhi Wang held her Washington Debut Concert in 'Terrace Theater' at the renowned Kennedy Center in USA. The program contained works by Bach, Gubaidulina, Mozart, Lohse and Moszkovsky, as well as Piazzolla's Tango Sensations with the wonderful Omer String Quartet. The concert received standing ovations from a full hall, and the reviews praised the performance.
Tallahassee Democrat – Best Bets: Hanzhi Wang visits Opening Nights after the hurricane2018-10-17
Yes, it's an accordion. No, it's not a novelty. Keep in mind that fresh-faced artist Hanzhi Wang is the first accordionist to win a place on the roster of Young Concert Artists in 58 years. Hear if she is the real thing or not when Wang visits Opening Nights for a concert at 7:30 p.m. Wednesday at St. John's Episcopal Church , 211 N. Monroe St. Tickets are $30 for general public and $15 for students. Call 850-644-6500 or visit openingnights.fsu.edu.
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How many beats per minute should the track with @mikepush be?
Editor-in-Chief. I am a student Ithaca College in central New York and hail from Northampton, Massachusetts. If you have some feedback, want to talk music or just want to say hi you can get in touch with me at [email protected] Also, you can follow me on twitter at @Jacob_YourEDM.


text:
\section{Introduction}

Quantum mechanics and general relativity are regarded as the two pillars of modern theoretical physics,
but despite many attempts in finding a satisfactory theory of quantum gravity, this goal has proved elusive.
Understanding how the two theories can fit together harmoniously is a serious intellectual challenge.
Approaches such as string theory \cite{Polchinski,Green}, loop quantum gravity \cite{Ashtekar,Rovelli},
twistor theory \cite{Penrose}, causal set theory \cite{Sorkin}, and others
each assume distinct mathematical and philosophical foundations, and necessarily possess a high degree of
mathematical sophistication.
Whether any one of these approaches can ultimately lead to the definitive theory of quantum gravity is purely
speculative at present because there is no observational evidence to support or disregard them.
While there is yet no experimental or observational justification to tamper with either quantum mechanics
or general relativity, there are suggestions that a modification of one or both theories may be required to incorporate
Planck-scale physics.
Whether such modifications are justifiable or not is also debatable.
Because both quantum mechanics and general relativity are very successful in their respective domains, it is a
challenge to propose a modification without compelling evidence to support the change.

Any sort of observation involving gravity and matter at the microscopic level is notoriously difficult to
perceive, let alone perform, which makes the advancement of quantum gravity research extremely challenging outside of
purely theoretical considerations.
From investigating quantum field theory in a classical space-time background, the topic of black hole entropy and the
prediction of Hawking radiation \cite{Hawking} from black holes is widely cited as an indicator of an effect that a successful quantum
gravity theory must reproduce.
Similarly, the analogous prediction of thermal radiation observed by an accelerated observer in flat space-time,
now known as the Unruh effect \cite{Unruh}, suggests a type of confirmation that supports this viewpoint, via the principle
of equivalence.
However, a closer inspection of certain outstanding issues \cite{Helfer} involving Hawking radiation may indicate that
inherent assumptions about the nature of space-time at the quantum level need to be very clearly identified
and addressed.
If it turns out that a subtle change is required on the assumptions for how particles behave in curved backgrounds,
it may force one to question the reliability of quantum field theory in curved space-time and the consequences that
follow, such as Hawking radiation.

One avenue where the interface between quantum mechanics and general relativity may be explored involves the intrinsic
nature of particles in a curved space-time background.
From standard quantum field theory in flat space-time, the classification of subatomic particles according to their
mass and spin angular momentum via the Poincar\'{e} symmetry group \cite{Ryder} is a well known and accepted procedure.
Yet it must be emphasized that the Poincar\'{e} group is applicable only for particles in strictly inertial motion.
In reality, the notion of a truly inertial reference frame is merely an idealization,
since general relativity demonstrates that any mass-energy source generates space-time curvature,
which produces a gravitational field.
At best, the closest approximation to an inertial frame in a gravitational field is the so-called
{\it freely falling frame}, in which a particle propagates along a geodesic and feels no external forces while
on this worldline.
Even here, however, it is impossible to completely neutralize the gravitational field effects for any particle
that is not strictly pointlike, since an extended object can sense tidal forces acting upon it due to space-time
curvature, as determined by neighbouring geodesics along the object's centre-of-mass worldline.
As well, it is certainly possible to describe noninertial motion in Minkowski space-time, where
the deviations from force-free motion are treated classically as effects due to ``fictitious'' forces.
These facts indicate that the Poincar\'{e} group is insufficient for the description of intrinsic properties of
subatomic particles while in noninertial motion.

Although it is currently difficult to envision a suitable generalization of the Poincar\'{e} group to operate on a
general curved space-time background, there exists one type of generalization called the {\it de~Sitter group}
\cite{Gursey} for the special case of conformally flat space-times in four dimensions.
Because the de~Sitter space-time can be embedded in a flat five-dimensional space-time described by an
overall radius of curvature $R$, the momentum operators are elements of a ten-parameter set of rotation generators.
The Casimir invariants of the de~Sitter group are then generalizations of the squared mass and spin
involving $R$, which then reduce to their corresponding expressions for the Poincar\'{e} group as
$R \rightarrow \infty$.
However, it also appears that the de~Sitter group suffers from the same limitations as the Poincar\'{e} group,
in that its properties rely heavily on inertial motion of the particle to obtain the associated Casimir invariants.
This is because, in all known formulations of such space-time symmetry groups, cartesian co-ordinates are automatically
assumed for the co-ordinates and derivative operators to compose the group generators.
Because physical properties should be independent of the choice of co-ordinate system, it seems reasonable to
re-examine the Poincar\'{e} and de~Sitter groups assuming general curvilinear co-ordinates.

The purpose of this paper is to investigate the properties of one aspect of the Poincar\'{e} group in
curvilinear co-ordinates, namely the Pauli-Lubanski four-vector which describes spin-1/2 particle spin in covariant form.
If a particle's trajectory appears as a curved path in three-dimensional space, it can be mapped by a
non-cartesian co-ordinate system which best reflects the symmetry of the particle's motion.
By now describing the Pauli-Lubanski vector with respect to curvilinear co-ordinates, it may be
possible to see whether a breakdown occurs in describing the particle's associated Casimir invariant,
as determined by some inertial laboratory frame defined at the origin.
It must be clearly understood that this paper is not an attempt to establish new theory, but rather to
examine the phenomenological consequences of exploring the limitations of the Poincar\'{e} group when applied to
noninertial motion.
If there is a significant {\em observational} deviation that appears from exploring this perspective,
then it seems reasonable to propose a modification to accommodate the difference and explore the consequences
that follow.

The paper begins in Sec.~II with a brief description on the hypothesis of locality employed for the description of
particle motion in a noninertial reference frame.
This is followed by Sec.~III, which describes the Pauli-Lubanski vector for a spin-1/2 particle
generalized in terms of curvilinear co-ordinates, with interesting consequences when the intended Casimir invariants are evaluated.
An application of the main results is presented in Sec.~IV, which consider the effects of noninertial motion on muon decay
in a circular storage ring.
It is then shown in Sec.~V that a new form of covariant spin operator can be constructed from the Pauli-Lubanski vector
which satisfies the Casimir invariant conditions for both inertial and noninertial motion, with interesting properties to follow.
This leads to a conclusion in Sec.~VI, which explores possible future developments of this investigation.

\section{The Hypothesis of Locality for Noninertial Motion}
\begin{figure*}
\psfrag{x}[cl][][2.5][0]{\tiny ${\rm x}$}
\psfrag{y}[cr][][2.5][0]{\tiny ${\rm y}$}
\psfrag{th}[cc][][2.5][0]{\tiny $\ensuremath{\phi}$}
\psfrag{x1}[bl][][2.5][0]{\tiny $\hat{x}$
\psfrag{y1}[tb][][2.5][0]{\tiny $\hat{y}$
\psfrag{r1}[bl][][2.5][0]{\tiny $\hat{r}$
\psfrag{th1}[bl][][2.5][0]{\tiny $\hat{\ensuremath{\phi}}$
\begin{minipage}[t]{0.3 \textwidth}
\centering
\subfigure[\hspace{0.2cm} cartesian]{
\label{fig:cartesian}
\rotatebox{0}{\includegraphics[width = 5cm, height = 5cm, scale = 1]{1a}}}
\end{minipage}%
\hspace{2.0cm}
\begin{minipage}[t]{0.3 \textwidth}
\centering
\subfigure[\hspace{0.2cm} polar]{
\label{fig:polar}
\rotatebox{0}{\includegraphics[width = 5cm, height = 5cm, scale = 1]{1b}}}
\end{minipage}
\caption{\label{fig:co-ordinate} Comoving co-ordinate frames for a quantum particle moving along a curved trajectory.
For muon decay, it is possible to identify the beam's instantaneous location with either local cartesian co-ordinates $(\hat{x}, \hat{y}, \hat{z})$
or cylindrical polar co-ordinates $(\hat{r}, \hat{\ensuremath{\varphi}}, \hat{z})$ with respect to the laboratory frame $\rm (x, y, z)$,
as shown in Figures~\ref{fig:cartesian} and \ref{fig:polar}.
However, the fundamental issue is whether one local frame is more appropriate than the other for accurately mapping the
muon beam's trajectory, with implications for describing potential non-inertial effects.}
\end{figure*}
A central assumption used in describing noninertial motion is the
{\it hypothesis of locality} \cite{Mashhoon}, in which an accelerated observer can be equated with an
instantaneously comoving inertial observer at a given moment of proper time.
This is described mathematically by defining a family of velocity vectors tangent to each point on the observer's
worldline, which smoothly correspond one-to-one with their respective comoving inertial frames.
Embedded with this assumption is an intrinsic length and time scale associated with the accelerated observer.
The hypothesis of locality is certainly reasonable for an accelerated classical particle,
since its instantaneous position and velocity occupy the same state as that of comoving inertial particle.
As well, in the limit as the particle becomes pointlike, this hypothesis is also well-defined.
However, the situation becomes more complicated when applied to a quantum mechanical system because
the quantum particle has wavelike properties and requires a {\it region} of space-time to define its location properly.
It is possible to surmise that the hypothesis of locality may become violated when considering accelerated quantum systems possessing
long wavelengths.
Conversely, it is possible to retain this hypothesis if the time scale associated with the measurement of
a quantum particle is much shorter than the accelerated observer's intrinsic time scale.

\section{General Formalism}
Assuming $c = 1$ units throughout, a flat metric in terms of curvilinear co-ordinates and $-2$ signature is described by
$\vec{g} = \eta_{\hat{\mu}\hat{\nu}} \, \vec{e}^{\hat{\mu}} \otimes \vec{e}^{\hat{\nu}} \,$,
given a set of orthonormal tetrads
$\ensuremath{\left}\{\vec{e}_{\hat{\mu}} \ensuremath{\right}\}$ and basis one-forms $\ensuremath{\left}\{\vec{e}^{\hat{\mu}} \ensuremath{\right}\}$
labelled by caratted indices to define a local Minkowski frame satisfying
$\ensuremath{\left}\langle \vec{e}^{\hat{\mu}} , \vec{e}_{\hat{\nu}} \ensuremath{\right}\rangle =
\delta^{\hat{\mu}}{}_{\hat{\nu}} \,$.
A general metric tensor in curved space-time and its Minkowski counterpart are related
by vierbein sets $\ensuremath{\left}\{ e^{\hat{\alpha}}{}_\mu \ensuremath{\right}\} \,$,
$\ensuremath{\left}\{ e^\mu{}_{\hat{\alpha}} \ensuremath{\right}\}$ satisfying
$\vec{e}^{\hat{\alpha}} = e^{\hat{\alpha}}{}_\beta \, \vec{e}^\beta$ and
$\vec{e}_{\hat{\alpha}} = e^\beta{}_{\hat{\alpha}} \, \vec{e}_\beta \,$, such that
$e^{\hat{\alpha}}{}_\mu \, e^\mu{}_{\hat{\beta}} =
\delta^{\hat{\alpha}}{}_{\hat{\beta}} \, $,
$
e^{\mu}{}_{\hat{\alpha}} \, e^{\hat{\alpha}}{}_{\nu} =
\delta^\mu{}_\nu \, $,
and
$g_{\mu \nu} = \eta_{\hat{\alpha}\hat{\beta}} \,
e^{\hat{\alpha}}{}_\mu \, e^{\hat{\beta}}{}_\nu$.
The caratted indices are raised and lowered by the Minkowski metric $\eta_{\hat{\ensuremath{\alpha}}\hat{\ensuremath{\beta}}}$, while
the uncaratted indices are manipulated with the general metric $g_{\mu \nu}$.

Given the covariant Dirac equation
\begin{eqnarray}
\ensuremath{\left}[i \ensuremath{\gamma}^\mu(x) \ensuremath{\left}[\partial_\mu + i \, \Gamma_\mu(x) \ensuremath{\right}] - m/\ensuremath{\hbar}\ensuremath{\right}]\psi(x) & = & 0 \,
\label{Dirac-eq}
\end{eqnarray}
with the spin connection $\Gamma_\mu(x)$, the associated momentum operator is
$\ensuremath{\vec{P}}^\mu = i \hbar \, g^{\mu \nu}\ensuremath{\left}[\partial_\nu + i \, \Gamma_\nu(x)\ensuremath{\right}] =
e^\mu{}_{\hat{\mu}} \, \ensuremath{\vec{P}}^{\hat{\mu}}$, where $\ensuremath{\vec{P}}^{\hat{\mu}} = \ensuremath{\vec{p}}^{\hat{\mu}} + \ensuremath{\vec{\Omega}}^{\hat{\mu}}$
is described in terms of the operator
$\ensuremath{\vec{p}}^{\hat{\mu}} = \ensuremath{i \hbar} \, \ensuremath{\vec{\nabla}}^{\hat{\mu}}$ in curvilinear co-ordinates \cite{Hassani} and
the spin connection contribution $\ensuremath{\vec{\Omega}}^{\hat{\mu}} \,$.
The $\ensuremath{\vec{p}}$-momentum components are explicitly described by
\begin{eqnarray}
\ensuremath{\vec{p}}^{\hat{0}} & = & \ensuremath{i \hbar} \, \pt{t} \, ,
\qquad
\ensuremath{\vec{p}}^{\hat{\jmath}}
\ = \ - {\ensuremath{i \hbar} \over \lambda^j(u)} \, \pt{u^{\hat{\jmath}}} \, ,
\label{momentum-curve}
\end{eqnarray}
where $\lambda^j(u)$ are the scale functions corresponding to the co-ordinate system that best reflects
the symmetries of the particle's motion in space.
Consider now the Pauli-Lubanski four-vector $\ensuremath{\vec{W}}^\mu = e^\mu{}_{\hat{\mu}} \, \ensuremath{\vec{W}}^{\hat{\mu}}$
in curved space-time as a vierbein projection onto a local tangent space, such that \cite{Itzykson}
\begin{eqnarray}
\ensuremath{\vec{W}}^{\hat{\mu}} & = & -{1 \over 4} \, \varepsilon^{\hat{\mu}}{}_{\hat{\ensuremath{\alpha}}\hat{\ensuremath{\beta}}\hat{\ensuremath{\gamma}}} \,
\ensuremath{\sigma}^{\hat{\ensuremath{\alpha}}\hat{\ensuremath{\beta}}} \, \ensuremath{\vec{P}}^{\hat{\ensuremath{\gamma}}} \, ,
\label{Wvec-defn}
\end{eqnarray}
where $\ensuremath{\vec{W}}^{\hat{\mu}}$ is the Pauli-Lubanski vector in Minkowski space-time,
$\varepsilon^{\hat{\mu}\hat{\ensuremath{\alpha}}\hat{\ensuremath{\beta}}\hat{\ensuremath{\gamma}}}$ is the Levi-Civita alternating symbol with
$\varepsilon^{0123}~\equiv~1$, and
$\ensuremath{\sigma}^{\hat{\ensuremath{\alpha}}\hat{\ensuremath{\beta}}} = \ensuremath{\left}(i/2\ensuremath{\right})[\ensuremath{\gamma}^{\hat{\ensuremath{\alpha}}}, \ensuremath{\gamma}^{\hat{\ensuremath{\beta}}}]$
are the spin matrices.
By introducing a decomposed representation of $\ensuremath{\sigma}^{\hat{\ensuremath{\alpha}}\hat{\ensuremath{\beta}}}$ in the form
\begin{eqnarray}
\ensuremath{\sigma}^{\hat{\ensuremath{\alpha}}\hat{\ensuremath{\beta}}} & = &
i \ensuremath{\left}(\delta^{\hat{\ensuremath{\alpha}}}{}_0 \, \delta^{\hat{\ensuremath{\beta}}}{}_{\hat{\jmath}} -
\delta^{\hat{\ensuremath{\beta}}}{}_0 \, \delta^{\hat{\ensuremath{\alpha}}}{}_{\hat{\jmath}} \ensuremath{\right}) \ensuremath{\vec{\al}}^{\hat{\jmath}}
- \varepsilon^{0\hat{\ensuremath{\alpha}}\hat{\ensuremath{\beta}}}{}_{\hat{m}} \, \ensuremath{\vec{\sg}}^{\hat{m}} \, ,
\label{sg-defn}
\end{eqnarray}
where $\ensuremath{\vec{\al}}^{\hat{\jmath}} = \ensuremath{\beta} \, \gamma^{\hat{\jmath}}$,
$\ensuremath{\vec{\sg}}^{\hat{\jmath}} = {1 \over 2} \, \epsilon^j{}_{kl} \, \ensuremath{\sigma}^{\hat{k}\hat{l}}$, and
$\epsilon^{ijk}$ is the three-dimensional Levi-Civita alternating symbol with $\epsilon^{123}~\equiv~1$,
it follows naturally that
\begin{eqnarray}
\ensuremath{\vec{W}}^{\hat{\mu}} & = & {1 \over 2} \ensuremath{\left}[-\eta^{\hat{\mu} \hat{0}} \, \ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{m}} \ensuremath{\right}.
\nonumber \\
& &{} + \ensuremath{\left}. \eta^{\hat{\mu} \hat{m}} \ensuremath{\left}[\ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{0}}
+ i \, \epsilon_{mjk} \, \ensuremath{\vec{\al}}^{\hat{\jmath}} \, \ensuremath{\vec{P}}^{\hat{k}} \ensuremath{\right}] \ensuremath{\right}] \, .
\label{Wvec}
\end{eqnarray}

Because it is generally true that $\ensuremath{\left}(i/\ensuremath{\hbar}\ensuremath{\right})\ensuremath{\left}[\ensuremath{\vec{p}}^{\hat{\imath}}, \ensuremath{\vec{p}}^{\hat{\jmath}}\ensuremath{\right}] \equiv
N^{\hat{\imath}\hat{\jmath}}~\neq~0 \,$ in curvilinear co-ordinates, there exists a Hermitian three-vector
$\ensuremath{\vec{R}}$ called the {\em noninertial dipole operator} \cite{Singh1,Singh2}, whose more general form in
terms of $\ensuremath{\vec{\Omega}}$ is now
\begin{eqnarray}
\ensuremath{\vec{R}}^{\hat{k}} & = & {i \over 2\hbar} \, \epsilon^{ijk} \, [\ensuremath{\vec{P}}_{\hat{\imath}}, \ensuremath{\vec{P}}_{\hat{\jmath}}]
\nonumber \\
& = & \epsilon^{kmn} \ensuremath{\left}[\ensuremath{\left}(\ensuremath{\vec{\nabla}}_{\hat{m}} \, \ln \lambda^n\ensuremath{\right}) \ensuremath{\vec{p}}_{\hat{n}} - \ensuremath{\vec{\nabla}}_{\hat{m}} \ensuremath{\vec{\Omega}}_{\hat{n}}\ensuremath{\right}]\, .
\label{Rvec}
\end{eqnarray}
For example, if the locally flat tangent space-time is described by spherical co-ordinates, then for
\begin{eqnarray}
\ensuremath{\vec{P}}^{\hat{r}} \ = \ - \ensuremath{i \hbar} \ensuremath{\left}(\pt{r} + {1 \over r}\ensuremath{\right}) \, , \quad
\ensuremath{\vec{P}}^{\hat{\th}} & = & - {\ensuremath{i \hbar} \over r} \ensuremath{\left}(\pt{\th} + {1 \over 2} \, \cot \th\ensuremath{\right}) \, ,
\nonumber \\
\ensuremath{\vec{P}}^{\hat{\ensuremath{\phi}}} & = & - {\ensuremath{i \hbar} \over r \, \sin \th} \, \pt{\ensuremath{\phi}} \, ,
\label{momentum1}
\end{eqnarray}
it follows that
\begin{subequations}
\begin{eqnarray}
\ensuremath{\vec{R}}^{\hat{r}} & = & {i \over \ensuremath{\hbar}}\ensuremath{\left}[\ensuremath{\vec{P}}^{\hat{\th}}, \ensuremath{\vec{P}}^{\hat{\ensuremath{\phi}}}\ensuremath{\right}] \ = \
- {\cot \th \over r} \, \ensuremath{\vec{p}}^{\hat{\ensuremath{\phi}}} \, ,
\label{Rvec1}
\\
\ensuremath{\vec{R}}^{\hat{\th}} & = & {i \over \ensuremath{\hbar}}\ensuremath{\left}[\ensuremath{\vec{P}}^{\hat{\ensuremath{\phi}}}, \ensuremath{\vec{P}}^{\hat{r}}\ensuremath{\right}] \ = \
{1 \over r} \, \ensuremath{\vec{p}}^{\hat{\ensuremath{\phi}}} \, ,
\label{Rvec2}
\\
\ensuremath{\vec{R}}^{\hat{\ensuremath{\phi}}} & = & {i \over \ensuremath{\hbar}}\ensuremath{\left}[\ensuremath{\vec{P}}^{\hat{r}}, \ensuremath{\vec{P}}^{\hat{\th}}\ensuremath{\right}] \ = \
- {1 \over r} \, \ensuremath{\vec{P}}^{\hat{\th}} \, ,
\label{Rvec3}
\end{eqnarray}
\end{subequations}
where $r$ is interpreted as the local radius of curvature associated with the trajectory
of the particle.
As $r~\rightarrow~\infty$, it is self-evident that $\ensuremath{\vec{R}} \rightarrow \vec{0}$
for fixed momentum.
If the $\ensuremath{\vec{P}}^{\hat{\jmath}}$ are defined by cartesian co-ordinates to represent rectilinear motion, then $\ensuremath{\vec{R}}$
vanishes identically, justifying its label to describe noninertial effects due to rotation.

For a spin-1/2 particle in a rotating frame, it can be shown that while
$\ensuremath{\vec{P}}^\mu \, \ensuremath{\vec{P}}_\mu = m^2$ remains a Lorentz scalar, the corresponding scalar operator
associated with particle spin is now {\it frame-dependent}, in the form
\begin{eqnarray}
\ensuremath{\vec{W}}^\mu \, \ensuremath{\vec{W}}_\mu & = & \ensuremath{\vec{W}}_\mu \, \ensuremath{\vec{W}}^\mu
\nonumber \\
& = &
-{1 \over 2} \ensuremath{\left}({1 \over 2} + 1\ensuremath{\right})m^2  + {\ensuremath{\hbar} \over 2} \dotprod{\ensuremath{\sigma}}{R} \, .
\label{W^2}
\end{eqnarray}
In addition, the orthogonality condition between $\ensuremath{\vec{W}}$ and $\ensuremath{\vec{P}}$ is no longer
satisfied for noninertial motion due to rotation, since
\begin{eqnarray}
\ensuremath{\vec{W}}^\mu \, \ensuremath{\vec{P}}_\mu & = & -\ensuremath{\vec{P}}^\mu \, \ensuremath{\vec{W}}_\mu \ = \ -{\ensuremath{\hbar} \over 2} \dotprod{\ensuremath{\alpha}}{R} \, .
\label{W.p}
\end{eqnarray}
It may seem contradictory to now regard the Casimir invariant $\ensuremath{\vec{W}}^\mu \, \ensuremath{\vec{W}}_\mu$ as a frame-dependent quantity
when it is constructed as a Lorentz scalar.
However, when this operator is applied to an {\it eigenstate}, the associated eigenvalue is $-{1 \over 2} \ensuremath{\left}({1 \over 2} + 1\ensuremath{\right})m^2$,
and any contribution due to $\ensuremath{\vec{R}}$ does not appear.
As well, $\ensuremath{\vec{W}}^\mu \, \ensuremath{\vec{P}}_\mu = 0$ when applied to an eigenstate.
For both (\ref{W^2}) and (\ref{W.p}), the apparent violation of Lorentz symmetry and the
orthogonality condition is due to a spin interaction with $\ensuremath{\vec{R}}$, which suggests that noninertial motion induces a
spin precession about the particle's worldline.

\begin{figure}
\psfrag{dG/G}[cc][][4][0]{${|\Delta \Gamma| \over \Gamma} \, {(\times 10^{-28})}$}
\psfrag{dG/G1}[cc][][4][0]{${|\Delta \Gamma| \over \Gamma}$}
\psfrag{r (cm)}[tr][][2][0]{\Large $r$}
\psfrag{Muon Beam Momentum (MeV)}[tc][][2][0]{\Large $|\ensuremath{\vec{p}}_\mu|$}
\psfrag{0}[tc][][2][0]{$\tiny 0$}
\psfrag{1000}[tc][][2][0]{$1000$}
\psfrag{2000}[tc][][2][0]{$2000$}
\psfrag{3000}[tc][][2][0]{$3000$}
\psfrag{4000}[tc][][2][0]{$4000$}
\psfrag{5000}[tc][][2][0]{$5000$}
\psfrag{100}[tc][][2][0]{$10^2$}
\psfrag{1}[tc][][2][0]{$1$}
\psfrag{0.01}[tc][][2][0]{$10^{-2}$}
\psfrag{0.0001}[tc][][2][0]{$10^{-4}$}
\psfrag{1e-06}[tc][][2][0]{$10^{-6}$}
\psfrag{1e-08}[tc][][2][0]{$10^{-8}$}
\psfrag{1e-10}[tc][][2][0]{$10^{-10}$}
\psfrag{1e-12}[tc][][2][0]{$10^{-12}$}
\psfrag{1e-20}[tc][][2][0]{$10^{-20}$}
\psfrag{1e-30}[tc][][2][0]{$10^{-30}$}
\psfrag{5e-29}[tc][][2][0]{$0.5$}
\psfrag{1e-28}[tc][][2][0]{$1.0$}
\psfrag{1.5e-28}[tc][][2][0]{$1.5$}
\psfrag{2e-28}[tc][][2][0]{$2.0$}
\begin{minipage}[t]{0.3 \textwidth}
\centering
\subfigure[\hspace{0.2cm} Muon Beam Momentum (MeV)]{
\label{fig:NR1a}
\rotatebox{0}{\includegraphics[width = 5.8cm, height = 3.5cm, scale = 1]{2a}}}
\end{minipage}%
\vspace{0.4cm}
\begin{minipage}[t]{0.3 \textwidth}
\centering
\subfigure[\hspace{0.2cm} Radius of Curvature (cm)]{
\label{fig:NR1b}
\rotatebox{0}{\includegraphics[width = 5.7cm, height = 3.5cm, scale = 1]{2b}}}
\end{minipage}
\caption{\label{fig:NR1} Relative contribution of $\ensuremath{\vec{R}}$ on the decay rate for $\mu^-~\rightarrow~e^-~+~\bar{\nu}_e~+~\nu_\mu$,
where $r = 711.2$~cm for Fig.~\ref{fig:NR1a}, while $|\ensuremath{\vec{p}}_\mu| = 3.0$~GeV for Fig.~\ref{fig:NR1b}.
It is evident
that $|\Delta \Gamma|/\Gamma$ becomes large as $r \rightarrow 10^{-12}$ cm,
the length scale of the muon's Compton wavelength.}
\end{figure}

\section{Applications to Muon Decay}

One of the assumptions in quantum field theory often taken for granted is the notion that every elementary
interaction within a Feynman diagram occurs at a {\it mathematical point}, where it is assumed that momentum
conservation is precisely satisfied at each vertex.
While it appears that this hypothesis is valid for interactions on a flat space-time background,
this idealization has to be examined more carefully when applied to a curved background or in situations
involving noninertial motion.
While elementary particles are reasonably assumed to be pointlike objects, quantum fields exist as a continuous distribution of matter,
and since a gravitational field is described classically as tidal forces within a local neighbourhood about
some point on the manifold, there are conceptual ambiguities involved in how best to represent the interactions of
quantum matter in a gravitational field \cite{Birrell}.
Unlike any collision involving classical objects where the properties of the incident and final products of the reaction are completely
determined, the Heisenberg uncertainty principle implies that an ambiguity exists at the precise moments when a scattering
or decay event occurs.

One example of how $\ensuremath{\vec{R}}$ may appear within an experimental context is via muon decay
inside a circular storage ring.
If an event like muon decay is only well-defined up to some identifiable interaction region, then it is reasonable
to suspect that $\ensuremath{\vec{R}}$ is a legitimate operator which leads to a meaningful prediction of physical effects.
For inertial motion, it is well-known that the computed rest-frame decay rate \cite{Scadron,Kaku}
for the reaction $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$ is
\begin{eqnarray}
\Gamma_0 & \approx & {G_{\rm F}^2 \, m_\mu^5 \over 192 \, \pi^3} \ \approx \ 2.965 \times 10^{-16} \ {\rm MeV},
\label{G0}
\end{eqnarray}
where $G_{\rm F} = 1.16639 \times 10^{-11}$~MeV$^{-2}$ \cite{Kaku} is the Fermi constant for weak interactions.
If the muon beam follows a circular trajectory and the decay products travel inertially off the orbit,
then the squared modulus of the interaction matrix element takes the form
\begin{eqnarray}
|{\cal M}|^2 & = & |{\cal M}|_0^2 + |{\cal M}|_{\rm NI}^2 \ = \
{G_{\rm F}^2 \over 2} \, L_{\hat{\mu} \hat{\nu}} \, M^{\hat{\mu} \hat{\nu}},
\label{M^2}
\end{eqnarray}
where $|{\cal M}|_0^2$ is the known contribution due to inertial motion \cite{Kaku}, and $|{\cal M}|_{\rm NI}^2$
is the correction due to $\ensuremath{\vec{R}}$.
The tensors corresponding to this reaction are then
\begin{subequations}
\begin{eqnarray}
\hspace{-0.8cm}
L^{\hat{\mu} \hat{\nu}} & = & {\rm Tr} \ensuremath{\left}[\gslash{\ensuremath{\vec{p}}}_{\nu_\mu} \, \ensuremath{\gamma}^{\hat{\mu}} \ensuremath{\left}(\gslash{\ensuremath{\vec{P}}}_\mu
+ m_\mu \, \ensuremath{\gm^5} \, \gslash{\ensuremath{\vec{n}}}_\mu\ensuremath{\right})\ensuremath{\gamma}^{\hat{\nu}} \ensuremath{\left}(1 - \ensuremath{\gm^5}\ensuremath{\right})\ensuremath{\right}] , \,
\label{L_uv}
\\
\hspace{-0.8cm}
M^{\hat{\mu} \hat{\nu}} & = & {\rm Tr} \ensuremath{\left}[\ensuremath{\left}(\gslash{\ensuremath{\vec{p}}}_e + m_e \, \ensuremath{\gm^5} \, \gslash{\ensuremath{\vec{n}}}_e\ensuremath{\right})
\ensuremath{\gamma}^{\hat{\mu}} \, \gslash{\ensuremath{\vec{p}}}_{\nu_e} \, \ensuremath{\gamma}^{\hat{\nu}} \ensuremath{\left}(1 - \ensuremath{\gm^5}\ensuremath{\right})\ensuremath{\right}] ,
\label{M_uv}
\end{eqnarray}
\end{subequations}
where $\ensuremath{\vec{n}}_\mu$ is the muon's spin polarization vector.
Prior to averaging over the spin states and using (\ref{W.p}), it can be shown that \cite{Itzykson}
\begin{eqnarray}
\ensuremath{\gm^5} \, \gslash{\ensuremath{\vec{n}}}_\mu & = &
- {2 \over m_\mu^2} \ensuremath{\left}[\ensuremath{\left}(\ensuremath{\vec{n}} \cdot \ensuremath{\vec{W}}\ensuremath{\right})\gslash{\ensuremath{\vec{P}}} + \gslash{\ensuremath{\vec{n}}} \ensuremath{\left}(\ensuremath{\vec{P}} \cdot \ensuremath{\vec{W}}\ensuremath{\right})\ensuremath{\right}]_\mu \, .
\label{slash_nvec}
\end{eqnarray}
By substituting (\ref{slash_nvec}) into (\ref{L_uv}), it follows that
\begin{eqnarray}
\lefteqn{
|{\cal M}|_{\rm NI}^2 \ = \ {20 \, G_{\rm F}^2 \, \hbar^2 \, E_\mu \over m_\mu^2 \, \ensuremath{\left}| \ensuremath{\vec{P}}_\mu \ensuremath{\right}|}
\ensuremath{\left}[\ensuremath{\left}[\ensuremath{\left}(1 - {E_e \over |\ensuremath{\vec{p}}_e|}\ensuremath{\right}) \ensuremath{\left}(\ensuremath{\vec{p}}_e \cdot \ensuremath{\vec{p}}_{\nu_\mu} \ensuremath{\right}) \ensuremath{\right}. \ensuremath{\right}. }
\nonumber \\
&&{} + \ensuremath{\left}. \ensuremath{\left}. {m_e^2 \over |\ensuremath{\vec{p}}_e|} \, E_{\nu_\mu} \ensuremath{\right}]
\ensuremath{\vec{p}}_{\nu_e}^{\hat{\jmath}}
- {3 \over 5}\ensuremath{\left}(1 - {E_e \over |\ensuremath{\vec{p}}_e|}\ensuremath{\right})\ensuremath{\left}(\ensuremath{\vec{p}}_{\nu_\mu} \cdot \ensuremath{\vec{p}}_{\nu_e}\ensuremath{\right})\ensuremath{\vec{p}}_e^{\hat{\jmath}}\ensuremath{\right}]
\nonumber \\
&&{} \times \epsilon_{jkl} \ensuremath{\left}(\ensuremath{\vec{\nabla}}^{\hat{k}} \ensuremath{\vec{R}}^{\hat{l}}\ensuremath{\right}) \, ,
\label{M^2-noninertial}
\end{eqnarray}
which leads to the noninertial contribution $\Delta \Gamma$ for the total decay rate $\Gamma = \Gamma_0 + \Delta \Gamma$
in the laboratory frame.
It is interesting to note the prediction of an induced coupling of the neutrinos due to rotational motion,
an effect not present in $|{\cal M}|_0^2$.

Adopting cylindrical co-ordinates for the muon motion in the laboratory frame, where
$\ensuremath{\vec{P}}_\mu^{\hat{\jmath}} = \ensuremath{\left}(\ensuremath{\vec{P}}_\mu^{\hat{z}}, \ensuremath{\vec{P}}_\mu^{\hat{r}}, \ensuremath{\vec{P}}_\mu^{\hat{\varphi}}\ensuremath{\right})$,
the only nonzero component of the noninertial dipole operator is
$\ensuremath{\vec{R}}^{\hat{1}} = -{1 \over r} \, \ensuremath{\vec{p}}_\mu^{\hat{\varphi}}$ \cite{Singh2}.
Figure~\ref{fig:co-ordinate} provides a comparative description of the muon beam's instantaneous location in terms of
either a local cartesian frame in Figure~\ref{fig:cartesian} or the adopted cylindrical co-ordinate frame in Figure~\ref{fig:polar}.
When evaluated in (\ref{M^2-noninertial}), it follows that $\Delta \Gamma$ is negative-valued, suggesting that
the muon's lifetime becomes enhanced when moving along a circular trajectory.
The degree of enhancement is strongly dependent on the choice of $r$, as shown in Figure~\ref{fig:NR1}, where
Figs.~\ref{fig:NR1a} and \ref{fig:NR1b} predict the relative contribution of $\Delta \Gamma$ to the overall decay rate
for varying beam momenta and radius of curvature, respectively.
For a facility like the Brookhaven National Laboratory which performs the muon $g-2$ experiment \cite{Farley},
the magnitude of $\ensuremath{\vec{R}}$ is negligibly small, where for a muon beam momentum of
$|\ensuremath{\vec{p}}_\mu| = 3.094$~GeV and storage ring radius of $r = 711.2$~cm, $|\ensuremath{\vec{R}}| = 5.760 \times 10^{-55} \ll 1$.

By this example, it seems that $\ensuremath{\vec{R}}$ is irrelevant for current particle experiments.
However, as $r \sim 10^{-8} - 10^{-12}$~cm, the length scales associated with atomic and nuclear dimensions \cite{Krane},
$|\Delta \Gamma|/\Gamma$ rapidly approaches unity.
In particular, the total decay rate becomes {\em negative} for $r \lesssim 10^{-11}$~cm, when the length scale
approaches the muon's Compton wavelength of $1.18 \times 10^{-12}$ cm \cite{Griffiths}.
It is difficult to make a sensible physical interpretation of such a decay rate at the Compton wavelength scale,
and it seems reasonable to suspect that some known physical effect, such as bremmstrahlung radiation,
will manifest itself to avoid this scenario.
At the same time, this may be a sign of new physics emerging at the interface between quantum mechanics and general relativity,
consistent with reported evidence claiming, for example, that space-time curvature can induce modifications
to classical electromagnetic fields at the Compton wavelength scale \cite{Rosquist}.

It is worthwhile to consider at this stage whether the external magnetic field required to curve the muon's trajectory
will influence the particle's decay rate.
For example, the external magnetic field in a storage ring will, in principle, modify the decay rate via the density of
final states.
This effect has been examined in detail for the case of neutron beta decay in a strong magnetic field \cite{Fassio-Canuto},
where it is shown that a field strength in excess of $10^{12}$~Gauss is required to significantly modify the neutron's
decay rate.
In particular, the electron's final state density reflects the decay rate corrections in terms of an overall scale factor,
which can be taken into account in any realistic measurement.
Applying this formalism to muon decay, it is found that the relative correction to the overall scale factor
is negligibly small for a typical magnetic field strength of $10^4$~Gauss required to bend the particle beam.

Concerning a more direct examination based on a leading order calculation \cite{van-Holten}, it has been shown
that the relative correction to the muon's lifetime is on the order of $10^{-14}$ times the
magnetic field strength measured in Tesla.
Based on this assumption, an external magnetic field of $10^{11}$ Tesla or $10^{15}$ Gauss is required to
achieve a radius of curvature approaching the muon's Compton wavelength scale of $10^{-12}$ cm.
It is interesting to note that this prior calculation leads to a correction of the muon's lifetime with the same
order of magnitude as shown in this paper, while not accounting for the possible existence of $\ensuremath{\vec{R}}$ described by (\ref{Rvec}).
Such a finding suggests that a much more detailed analysis may be required to better understand the implications
for either a breakdown of currently applied formalism or the emergence of new physical phenomena at this length scale.

\section{An Equivalent Expression for the Pauli-Lubanski Vector for Noninertial Motion}

Having shown that the squared magnitude of the Pauli-Lubanski vector in curvilinear co-ordinates is no longer a Lorentz
invariant for noninertial motion along a curved trajectory, is it possible to construct a new vector that satisfies this property?
It so happens that it is possible to obtain a spin vector that preserves Lorentz invariance for general particle motion.
Consider $\ensuremath{\vec{V}}^\mu = e^\mu{}_{\hat{\mu}} \, \ensuremath{\vec{V}}^{\hat{\mu}}$, where
\begin{eqnarray}
\ensuremath{\vec{V}}^{\hat{\mu}} & \equiv & A \, \ensuremath{\vec{W}}^{\hat{\mu}} + B \, \eta^{\hat{\mu}\hat{0}} \, \ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{m}}
\nonumber \\
& &{} + \eta^{\hat{\mu}\hat{m}} \ensuremath{\left}[C \, \ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{0}}
+ i \, D \, \epsilon_{mjk} \, \ensuremath{\vec{\al}}^{\hat{\jmath}} \, \ensuremath{\vec{P}}^{\hat{k}} \ensuremath{\right}] \, ,
\label{Vvec-defn}
\end{eqnarray}
with $A, B, C, D$ as algebraic constants to be evaluated.
If $C$ and $D$ are chosen such that
$C = -{A \over 2} \pm {i \, \sqrt{3} \over 6} \ensuremath{\left}(A - 2 \, B\ensuremath{\right})$ and
$D = -{A \over 2} \pm {i \over 2} \ensuremath{\left}(A - 2 \, B\ensuremath{\right}) \, $,
then it follows that
\begin{eqnarray}
\ensuremath{\vec{V}}^{\hat{\mu}} & = & {\kappa \over 2} \ensuremath{\left}[i \, \eta^{\hat{\mu}\hat{0}} \, \ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{m}} \ensuremath{\right}.
\nonumber \\
& &{} \pm \ensuremath{\left}. \eta^{\hat{\mu}\hat{m}} \ensuremath{\left}[{1 \over \sqrt{3}} \, \ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{0}}
+ i \, \epsilon_{mjk} \, \ensuremath{\vec{\al}}^{\hat{\jmath}} \, \ensuremath{\vec{P}}^{\hat{k}}  \ensuremath{\right}]  \ensuremath{\right}]
\nonumber \\
& = & {\kappa \over 2} \ensuremath{\left}[-2 \, i \, \ensuremath{\vec{W}}^{\hat{\mu}} \pm \eta^{\hat{\mu}\hat{m}}
\ensuremath{\left}[\ensuremath{\left}({1 \over \sqrt{3}}  \mp i\ensuremath{\right}) \ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{0}} \ensuremath{\right}. \ensuremath{\right}.
\nonumber \\
& &{} + \ensuremath{\left}. \ensuremath{\left}. \ensuremath{\left}(1 \pm i \ensuremath{\right})i \, \epsilon_{mjk} \, \ensuremath{\vec{\al}}^{\hat{\jmath}} \, \ensuremath{\vec{P}}^{\hat{k}} \ensuremath{\right}] \ensuremath{\right}] \, ,
\label{Vvec}
\end{eqnarray}
and
\begin{eqnarray}
\ensuremath{\vec{V}}^\mu \, \ensuremath{\vec{V}}_\mu & = & - {1 \over 4} \, \kappa^2 \, m^2 \,
\label{V^2}
\end{eqnarray}
for real-valued $\kappa \equiv i \ensuremath{\left}(A - 2 \, B\ensuremath{\right})$.
If $\kappa = \pm \sqrt{3}$, then
$\ensuremath{\vec{V}}^\mu \, \ensuremath{\vec{V}}_\mu = \ensuremath{\left}(-3/4\ensuremath{\right})m^2 = \ensuremath{\left}[-{1 \over 2}\ensuremath{\left}({1 \over 2} + 1\ensuremath{\right})\ensuremath{\right}]m^2$, resembling the Lorentz
invariance condition described by $\ensuremath{\vec{W}}^\mu \, \ensuremath{\vec{W}}_\mu$, but now applicable for all forms of motion.

In particular, if $A \equiv 1$ in (\ref{Vvec-defn}) for $\kappa = \pm \sqrt{3}$, then it follows that
$B = {1 \over 2} \pm {i \sqrt{3} \over 2}$, $C = 1$, and $D = {\sqrt{3} \over 2} - {1 \over 2}$.
By expressing $B$ in complex exponential form, it is shown that
\begin{eqnarray}
\ensuremath{\vec{V}}^{\hat{\mu}} & = & \ensuremath{\vec{W}}^{\hat{\mu}} + e^{\pm i \xi} \, \eta^{\hat{\mu}\hat{0}} \, \ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{m}}
\nonumber \\
& &{} + \eta^{\hat{\mu}\hat{m}} \ensuremath{\left}[\ensuremath{\vec{\sg}}_{\hat{m}} \, \ensuremath{\vec{P}}^{\hat{0}}
+ i \, \sqrt{2} \sin \ensuremath{\left}(\xi - {\pi \over 4}\ensuremath{\right}) \, \epsilon_{mjk} \, \ensuremath{\vec{\al}}^{\hat{\jmath}} \, \ensuremath{\vec{P}}^{\hat{k}} \ensuremath{\right}] \, ,
\nonumber \\
\label{Vvec-A=1}
\end{eqnarray}
where $\xi = {\pi \over 3}$.  As well, by letting $B = |B|\ensuremath{\left}(\cos \xi + i \sin \xi \ensuremath{\right})$ for arbitrary and complex-valued $\kappa$,
it follows that
\begin{eqnarray}
\xi & = & \sin^{-1} \ensuremath{\left}({{\rm Re}(\kappa) \over 2 |B|}\ensuremath{\right}) \ = \ \cos^{-1} \ensuremath{\left}({1 - {\rm Im}(\kappa) \over 2 |B|}\ensuremath{\right}).
\label{xi=}
\end{eqnarray}

A preliminary study of $\ensuremath{\vec{V}}$, defined in terms of (\ref{Vvec}), reveals some interesting properties worth considering.
The first is that, in combination with (\ref{W.p}), the projection of the new spin operator along $\ensuremath{\vec{P}}$ generates
the helicity operator up to the phase $\xi = {\pi \over 3}$, where
\begin{eqnarray}
\ensuremath{\left}(\ensuremath{\vec{V}}^\mu \mp \kappa \, \ensuremath{\vec{W}}^\mu\ensuremath{\right})\ensuremath{\vec{P}}_\mu & = &
\ensuremath{\vec{P}}^\mu\ensuremath{\left}(\ensuremath{\vec{V}}_\mu \mp \kappa \, \ensuremath{\vec{W}}_\mu\ensuremath{\right})
\nonumber \\
& = & \mp \, {\kappa \, E \over 2}\ensuremath{\left}({1 \over \sqrt{3}} \pm i\ensuremath{\right}) \dotprod{\ensuremath{\sigma}}{P}
\nonumber \\
& = & \mp \, {\kappa \, E \over \sqrt{3}} \, e^{\pm i \xi} \, \dotprod{\ensuremath{\sigma}}{P} ,
\label{(V+W).p}
\end{eqnarray}
where $E$ is the energy eigenvalue of $\ensuremath{\vec{P}}^{\hat{0}}$.
The second property is that, for a polarization vector defined as
\begin{eqnarray}
\ensuremath{\vec{n}}^{\hat{\mu}} & = & {E \over m} \ensuremath{\left}({\ensuremath{\left}| \ensuremath{\vec{P}} \ensuremath{\right}| \over E}, {1 \over \ensuremath{\left}| \ensuremath{\vec{P}} \ensuremath{\right}|} \, \ensuremath{\vec{P}}^{\hat{\jmath}}\ensuremath{\right})
\label{nvec}
\end{eqnarray}
subject to $\ensuremath{\vec{n}}^\mu \, \ensuremath{\vec{P}}_\mu = 0$, it can be shown that a new vector
\begin{eqnarray}
\ensuremath{\vec{k}}^{\hat{\mu}} & = & {2E \over m^2} \ensuremath{\left}({1 \over \ensuremath{\left}| \ensuremath{\vec{P}} \ensuremath{\right}|} \, \ensuremath{\vec{P}}^{\hat{\mu}} - {m \over E} \, \ensuremath{\vec{n}}^{\hat{\mu}} \ensuremath{\right})
\label{kvec}
\end{eqnarray}
can project out the helicity operator from both $\ensuremath{\vec{V}}$ and $\ensuremath{\vec{W}}$.
That is,
\begin{eqnarray}
\ensuremath{\vec{k}}^\mu \, \ensuremath{\vec{W}}_\mu \ = \
{i \over \kappa} \, \ensuremath{\vec{k}}^\mu \, \ensuremath{\vec{V}}_\mu & = & {\dotprod{\ensuremath{\sigma}}{P} \over \ensuremath{\left}| \ensuremath{\vec{P}} \ensuremath{\right}|} \, ,
\label{orthog1}
\\
\ensuremath{\vec{k}}^\mu \ensuremath{\left}(\ensuremath{\vec{V}}_\mu + i \, \kappa \, \ensuremath{\vec{W}}_\mu \ensuremath{\right}) & = & 0 \, ,
\label{orthog2}
\end{eqnarray}
where $\ensuremath{\vec{k}}^{\hat{\mu}} = \ensuremath{\left}(2 / \ensuremath{\left}| \ensuremath{\vec{P}} \ensuremath{\right}|\ensuremath{\right}) \, \delta^{\hat{\mu}}{}_{\hat{0}}$.
This expression shows that the helicity operator is rotated away from the particle's direction of propagation
due to noninertial motion along a curved trajectory.
Moreover, for massless particles, a null polarization vector can be defined as
$\ensuremath{\vec{n}}^{\hat{\mu}} = \ensuremath{\left}(1, {1 \over \ensuremath{\left}| \ensuremath{\vec{P}} \ensuremath{\right}|} \, \ensuremath{\vec{P}}^{\hat{\jmath}} \ensuremath{\right})$ orthogonal to $\ensuremath{\vec{P}}$, such that
$\ensuremath{\vec{k}}^\mu \, \ensuremath{\vec{W}}_\mu = \ensuremath{\vec{k}}^\mu \, \ensuremath{\vec{V}}_\mu = 0$, where
\begin{eqnarray}
\ensuremath{\vec{k}}^{\hat{\mu}} & = & \ensuremath{\vec{P}}^{\hat{\mu}} - \ensuremath{\left}| \ensuremath{\vec{P}} \ensuremath{\right}| \, \ensuremath{\vec{n}}^{\hat{\mu}}.
\label{kvec-null}
\end{eqnarray}
This indicates that $\ensuremath{\vec{V}}^\mu = \lambda \, \ensuremath{\vec{k}}^\mu$ for massless spin-1/2 particles, an expression now generalized
to account for both inertial and noninertial motion, where $\lambda = \pm 1/2$ is the associated helicity eigenvalue.

In addition, (\ref{(V+W).p}) is true for both massive and {\em massless}
$\ensuremath{\left}(\ensuremath{\vec{P}}^\mu \, \ensuremath{\vec{P}}_\mu = 0\ensuremath{\right})$ spin-1/2 particles.
To show this explicitly, consider the special case of a massless particle propagating in the 3-direction
$\ensuremath{\vec{P}}^{\hat{\mu}} = \ensuremath{\left}(E, 0, 0, E\ensuremath{\right})$.
Then
\begin{subequations}
\begin{eqnarray}
\ensuremath{\vec{V}}^{\hat{0}} & = & -{i \, \kappa \, E \over 2} \, \ensuremath{\vec{\sg}}^{\hat{3}} \ = \ \mp \, i \sqrt{3} \, \ensuremath{\vec{V}}^{\hat{3}} \, ,
\label{Vvec0}
\\
\ensuremath{\vec{V}}^{\hat{1}} & = & \pm \, {\kappa \, E \over 2} \ensuremath{\left}[{1 \over \sqrt{3}} \, \ensuremath{\vec{\sg}}^{\hat{1}} + i \, \ensuremath{\vec{\al}}^{\hat{2}} \ensuremath{\right}] \, ,
\label{Vvec1}
\\
\ensuremath{\vec{V}}^{\hat{2}} & = & \pm \, {\kappa \, E \over 2} \ensuremath{\left}[{1 \over \sqrt{3}} \, \ensuremath{\vec{\sg}}^{\hat{2}} - i \, \ensuremath{\vec{\al}}^{\hat{1}} \ensuremath{\right}] \, ,
\label{Vvec2}
\\
\ensuremath{\vec{V}}^{\hat{3}} & = & \pm \, {\kappa \, E \over 2} \, {1 \over \sqrt{3}} \, \ensuremath{\vec{\sg}}^{\hat{3}}
\ = \ \pm \, {i \over \sqrt{3}} \, \ensuremath{\vec{V}}^{\hat{0}} \, ,
\label{Vvec3}
\end{eqnarray}
\end{subequations}
from which it follows naturally that
\begin{eqnarray}
\ensuremath{\vec{V}}^\mu \, \ensuremath{\vec{P}}_\mu & = & \ensuremath{\vec{V}}^{\hat{0}} \, \ensuremath{\vec{P}}_{\hat{0}} + \ensuremath{\vec{V}}^{\hat{3}} \, \ensuremath{\vec{P}}_{\hat{3}}
\nonumber \\
& = & \mp \, {\kappa \, E \over 2}\ensuremath{\left}({1 \over \sqrt{3}} \pm i\ensuremath{\right}) \ensuremath{\left}(\ensuremath{\vec{\sg}}^{\hat{3}} \, \ensuremath{\vec{P}}^{\hat{3}}\ensuremath{\right}) \, ,
\label{V.p}
\end{eqnarray}
to agree with (\ref{(V+W).p}) for inertial motion.

The third interesting feature comes from examining the commutation properties of (\ref{Vvec0})-(\ref{Vvec3}).
After setting $\kappa = \pm \sqrt{3}$ and re-defining the generators such that $\vec{\cal V} \equiv \ensuremath{\vec{V}}/E$,
it becomes evident that
\begin{subequations}
\begin{eqnarray}
{[\vec{\cal V}^{\hat{1}}, \vec{\cal V}^{\hat{2}}]} & = & - 6 \, i \, \vec{\cal V}^{\hat{3}} \, ,
\label{SU(2)-a}
\\
{[\vec{\cal V}^{\hat{2}}, \vec{\cal V}^{\hat{3}}]} & = & i \, \vec{\cal V}^{\hat{1}} \, ,
\label{SU(2)-b}
\\
{[\vec{\cal V}^{\hat{3}}, \vec{\cal V}^{\hat{1}}]} & = & i \, \vec{\cal V}^{\hat{2}} \, ,
\label{SU(2)-c}
\end{eqnarray}
\end{subequations}
which generates the Lie algebra for a broken $SU(2)$ symmetry.
This suggested property of massless spin-1/2 particles, while perhaps more physically intuitive, is quite
different from what is known from Wigner's little group procedure \cite{Ryder,Scadron}, since the latter indicates
that massless particle rotation is described by the Euclidean group $E(2)$.
The reasons for this discrepancy are unclear at present.

\section{Conclusion}

It has been shown in this paper that the Pauli-Lubanski covariant spin vector $\ensuremath{\vec{W}}^\mu$ in curvilinear co-ordinates is not a
Casimir operator, where the breakdown comes from noninertial effects due to rotation.
As well, it is shown that there exists a new covariant spin vector $\ensuremath{\vec{V}}^\mu$ whose scalar product with itself
preserves Lorentz invariance for both inertial and noninertial motion, with interesting Lie algebra properties.
While there are potential experimental consequences which follow from the stated observations for $\ensuremath{\vec{W}}^\mu$, the quantitative
relevance of the effects appears to be negligible for current experimental conditions.
There may be other ways of identifying the presence of $\ensuremath{\vec{R}}$ at least on a theoretical level,
and it seems worth exploring how to make use of this formalism for other relevant physical situations,
such as particle interactions near the event horizon of a black hole.
At present, the theoretical results presented here suggest the existence of a new avenue for better understanding
the interface between quantum mechanics and curved space-time, via the principle of equivalence, when applied to
particles in noninertial motion.

In this paper, the consequences of noninertial motion on covariant quantum spin were explored by performing explicit calculations for
spin-1/2 particles.
For future considerations, it is worth mentioning that the noninertial effects of the type discussed in the present work
are also calculable for particles of higher intrinsic spin by employing appropriate representations of the Pauli-Lubanski vector \cite{Kirchbach}.
Other possibilities may come about from future study of these ideas.

\section{Acknowledgements}

The authors wish to thank Bahram Mashhoon for his careful review of the manuscript and helpful comments to
improve its overall quality.
We also thank Bhaskar Dutta and Saurya Das for useful discussions.
Funding for this research was provided in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

redpajama_set_name: RedPajamaArXiv


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Coronary angiogram (also called cardiac catheterization or 'cath') is one of the most common invasive heart imaging procedures and is the standard method for diagnosing coronary artery disease.
During a cardiac cath, a catheter is inserted through a blood vessel in the groin or wrist and guided into the heart with the aid of a special x-ray machine. A small amount of contrast material is then injected through the catheter and into the arteries and heart.
The average catheterization procedure lasts about 30 minutes, but the preparation and recovery time add several hours. Often patients are admitted overnight for the procedure.
While coronary angiograms remain the 'gold standard' for detecting coronary artery stenosis (significant narrowing of the arteries which could require stents or bypass surgery), Coronary CTA may confidently exclude coronary stenosis in a number of patients thus avoiding the need for an invasive angiogram. Additionally, Coronary CTA can non-invasively detect cholesterol build up in the coronary artery walls that may lead to future problems without lifestyle changes or medical treatment.
Who should consider Coronary CTA?
The single most important step for patients trying to determine whether they should have a Coronary CTA is a consultation with their general practitioner or the cardiologist. Appropriate use of Coronary CTA is important as the scan carries a very small risk from X-ray exposure and contrast dye exposure.
Calcium score is a non-contrast CT that evaluates plaque which is calcified. While it gives an excellent assessment of the cholesterol burden in your arteries, it does not tell whether someone has blockages or not. It's best value is in asymptomatic patients to determine the presence and the extent of plaque buildup in their arteries allowing subsequent risk factor modifications by their practitioners.
Patients who are highly likely to have blockages are better investigated with coronary angiography since angiography is required to confirm and treat (stents or bypass surgery) any significant stenosis detected on Coronary CTA. Such patients include those with a clear history of chest pain during heavy physical activity at high risk of a cardiovascular adverse event, strongly positive stress-test results and known history of coronary artery disease or heart attack. Similarly, cardiac CT is of little value in asymptomatic patients and is generally avoided in female patients under the age of 40 years due to small long-term risks associated with radiation exposure.
What type of scanner is used?
At present we use a latest generation CT scanner (320 slice Toshiba) through MonashHeart, which produces excellent image quality at a very low dose of radiation. All necessary precautions are taken to minimize radiation dose.
Coronary CTA is a relatively simple non-invasive procedure, which takes less than 10 minutes on the scanning table. You will have a small cannula inserted in your arm to be able to give contrast material. We may need to give a medication called beta-blocker to slow down the heart rate if your heart rate is high prior to the scan. Once the heart rate is satisfactory, you will lie on the CT table and a contrast material will be injected into your vein so the imaging physician (cardiologist) can view the heart and blood vessels on the CT image. It is very important that you lie as still as possible during the entire procedure because any movement could blur the images. You may be asked to hold your breath briefly at intervals when the images are taken. After the contrast agent is injected, you may feel flushed, or you might have a metallic taste in your mouth. These are common reactions. If you experience shortness of breath or any unusual symptoms, please tell the technologist.
Generally, you can resume your usual activities and normal diet immediately after the test. If we have to give extra beta-blockers which, on rare occasions, can lower the blood pressure, we may ask someone else to drive you back.
Coronary CTA carries no cost to the patient when organized by your Melbourne Heart Care specialist.
Calcium score incurs a cost of $250, as there is no Medicare rebate currently available for this test.


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