text:
Life imprisonment in the United States
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In the United States, life imprisonment is amongst the most severe punishments provided by law, depending on the state, and second only to the death penalty. According to a 2013 study, 1 of every 20,000 inhabitants of the U.S. were imprisoned for life as of 2012[update].[1] Many U.S. states can release a convict on parole after a decade or more has passed, but in California, people sentenced to life imprisonment can normally apply for parole after seven years.[2] The laws in the United States categorize life sentences as "determinate life sentences" or "indeterminate life sentences," the latter indicating the possibility of an abridged sentence, usually through the process of parole. For example, sentences of "15 years to life," "25 years to life," or "life with mercy" are called "indeterminate life sentences", while a sentence of "life without the possibility of parole" or "life without mercy" is called a "determinate life sentence". The potential for parole is not assured but discretionary, making it an indeterminate sentence.[3] Even if a sentence explicitly denies the possibility of parole, government officials may have the power to grant an amnesty to reprieve, or to commute a sentence to time served.
1.1 Schick's case and life imprisonment without parole
1.2 Minors
3 Statistics
4 Parole and nonviolent offenses
4.1 Three-strikes law
5 Debates
6 Notable examples
In the 1861, reformation became favored over penitence in American penology, with the role of prisons seen as reforming prisoners, who were imprisoned until reform was achieved. The concepts of parole and indeterminate sentencing were regarded as forward-looking in the 1870s. The initial concept of parole came from the idea that prisoners began their path to rehabilitation during their sentence, and their successful rehabilitation could be recognizable by a parole board.[4] The importance was placed on eradicating crime and having prisoners deemed ready to enter society as soon as possible. However, the ideals were not as successful as had been hoped. Crime was not eradicated, reformatories had the same problems as prisons on politicization and underfunding, and indeterminate sentencing became undermined by prisoners, who quickly found that it was possible to "beat the system" by pretense to get a better chance of winning parole. Many were soon back in custody. Similarly, prison authorities could twist it to their advantage by using those granted parole or probation to spy on and actively help to imprison other people, or sometimes by selectively denying parole.[5] However, the biggest cause of the reformatories' failure to live up to expectations was that despite the enthusiasm of reformers and Zebulon Brockway's call for an end to vengeance in criminal justice, those within the prison environment, both inmates and guards alike, continued to conceive of prison as a place of retribution.[6]
Schick's case and life imprisonment without paroleEdit
In 1954 (November 28), Master Sergeant Maurice L. Schick was convicted by military court-martial of the murder of nine-year-old Susan Rothschild at Camp Zama in Japan (Tokyo).[7] The soldier admitted the killing stating he had a sudden "uncontrollable urge to kill something quickly and quietly" and had chosen his victim "just because she was there."[8]
Schick was sentenced to death. Six years later, the case was forwarded to President Dwight Eisenhower for final review. He exercised his right of executive clemency to commute Schick's death sentence to confinement with hard labor for the term of his natural life, with the express condition that he "shall never have any rights, privileges, claims or benefits arising under the parole and suspension or remission of sentence laws of the United States."
In 1971, Schick began a legal challenge against his whole life sentence. The appeal eventually reached the U.S. Supreme Court in 1974. It examined the constitutional basis of the punishment: life imprisonment without parole.[9] Had Schick been given an ordinary life sentence, he would have been eligible for parole in 1969.[citation needed]
Although Schick's sentence was given only cursory mention, the court concluded a whole life sentence was constitutional.[10] Schick, together with only five other federal prisoners who were still ineligible for parole at the time, was made eligible for parole by a separate pardon from President Gerald Ford in 1976 or 1977, and he may have died a free man in Palm Beach, Florida, in 2004.[11][12]
Despite the Schick opinion's lack of thorough analysis on life imprisonment without a chance of parole, an imposing amount of precedent has developed based upon it.[13] After Furman v. Georgia,[14] the constitutionality of the death penalty in question as life imprisonment without parole received increased attention from lawmakers and judges, as an alternative to the death penalty.[clarification needed]
Such penalties predate Schick.[15] One early American case was Ex parte Wells (1856);[16] Wells was convicted of murder in 1851 and sentenced to be hanged. On the day of his execution, President Millard Fillmore gave him a conditional pardon commuting his sentence to "imprisonment for life in the penitentiary at Washington." Wells appealed the conditions of his pardon, but the sentence was upheld with no discussion by the majority of the purpose of the substituted punishment.
MinorsEdit
Main article: Life imprisonment
A few countries worldwide have allowed for minors to be given lifetime sentences that have no provision for eventual release. Countries that allow life imprisonment without a possibility of parole for juveniles include Antigua and Barbuda, Cuba, Dominica, Israel, Nigeria, Saint Vincent and the Grenadines, the Solomon Islands, Sri Lanka, Tanzania and the United States. Of these, only the U.S. currently has minors serving such sentences. The University of San Francisco School of Law's Center for Law & Global Justice conducted international research on the use of the sentence of life without parole for juveniles, and has found no cases outside the U.S. in which the sentence is actually imposed on juveniles.[17] As of 2009, Human Rights Watch has calculated that there are 2,589[18] youth offenders serving life without parole in the U.S.[19]
In the U.S, juvenile offenders started to get life without parole sentences more frequently in the 1990s due to John J. DiIulio Jr's. Teenage Superpredator Theory.[20][21][22][23]
In 2010, in the U.S. Supreme Court ruled that sentencing minors to automatic sentences of life without a chance of parole for crimes other than those involving a homicide (generally, first-degree murder, and usually with aggravating factors or accompanying felonies) violated the Eighth Amendment's ban on "cruel and unusual punishments", in the case of Graham v. Florida.[24] In finding that the U.S. Constitution prohibits as cruel and unusual punishment a life without parole sentence for a juvenile in a non-homicide case, the U.S. Supreme Court stated that "the overwhelming weight of international opinion against" juvenile life without a chance of parole "provide[s] respected and significant confirmation for our own conclusions".[25] In 2012, in the Case of Miller v. Alabama, the Court considered whether to ban the automatic use of it completely as a sentence for minors. The Court had already judged the death penalty unconstitutional for minors in 2005. In June 2012, the Court ruled that it could never be automatically used as a sentence for a minor (under 18), although the Court left room for it as a sentence that can eventually be given (for now) in certain first-degree murder cases once the judge has taken mitigating circumstances and other factors into account. The U.S. practice of sentencing juveniles to life imprisonment without a possibility of parole violates international standards of justice, as well as treaties to which the U.S. is a party. Each state must ensure that its criminal punishments comply with the United States' international treaty obligations:
The International Covenant on Civil and Political Rights; the oversight Committee instructed the U.S. to: "ensure that no such child offender is sentenced to life without parole [and] adopt all appropriate measures to review the situation of persons already serving such sentences".
The United Nations Convention Against Torture; the oversight Committee warned the U.S. that juvenile life sentences without a possibility of parole could constitute "cruel, inhuman or degrading treatment or punishment" for youth.
The oversight body of the Committee on the Elimination of Racial Discrimination found that juvenile life without a chance of parole is applied disproportionately to black minors, and the U.S. has done nothing to reduce what has become pervasive discrimination. The Committee recommended that the U.S. discontinue the use of this sentence against persons under the age of eighteen at the time the offense was committed, and review the situation of persons already serving such sentences and in 2016, in the case of Montgomery v. Louisiana, the Supreme Court ruled that Miller v. Alabama was to be applied retroactively to offenders convicted before 2012.
The United Nations General Assembly has called upon governments to: "abolish by law, as soon as possible...life imprisonment without possibility of release for those below the age of 18 years at the time of the commission of the offense".
International standards of justice hold that a juvenile life imprisonment without a possibility of parole is not warranted under any circumstances because juvenile offenders lack the experience, education, intelligence and mental development of adults and must be given a reasonable opportunity to obtain release based on demonstrated maturity and rehabilitation.[26]
By April 2021, 25 states and the District of Columbia have completely banned life without parole sentences for all juvenile offenders while five states have not banned the sentence but do not have any juvenile offenders serving life without parole.[27][28][29][30]
UseEdit
Although sentences vary for each state, life imprisonment is generally mandatory for first-degree murder, particularly if it is done during the commission of another felony (the felony murder rule), or there are other aggravating circumstances present (such as rapes before such murders or for murder of any law enforcement official or other public servant) in all 50 states and the District of Columbia, including states without the death penalty, and as one or the only alternative sentence in states that have the death penalty and in federal and military courts. Life imprisonment is also a mandatory punishment in Idaho for aircraft hijacking, in New York State for terrorism, in Florida for capital sexual battery (sexual abuse of a child under 12 that causes injury to the child) and in Georgia for a second conviction for armed robbery, kidnapping, or rape and other serious violent felonies under Georgia's seven-deadly-sins law. Life imprisonment is a possibility for aggravated mayhem and torture in California. Life imprisonment is mandatory for kidnapping in Nebraska.[31] Other specifics about life sentences in the United States continue to vary widely by individual states.
In addition, the sentence of life imprisonment may also be given for "drug kingpins" and "habitual criminals." It has been applied in every state except Alaska, as well as in the federal courts.[32][33] In Alaska, the maximum term of imprisonment is for 99 years, but that is almost always considered to be a practical life sentence as a sentence of 99 years' imprisonment, especially without parole, generally lasts beyond a normal lifespan.[34]
StatisticsEdit
Over 200,000 people, or about 1 in 7 prisoners in the United States, were serving life or virtual life sentences in 2019. Over 50,000 are serving life without a chance of parole.[35] In 1993, the Times survey found, about 20 percent of all lifers had no chance of parole. By 2004, that had risen to 28 percent.[36]
As a result, the U.S. is now housing by far the world's largest and most permanent population of prisoners who are guaranteed to die behind bars. At the Louisiana State Penitentiary, for instance, more than 3,000 of the 5,100 prisoners are serving life with a chance of parole, and most of the remaining 2,100 are serving sentences so long that they cannot be completed in a typical lifetime. About 150 inmates have died there in the time period between the years of 2000 and 2005.[36] The United States holds 40% of the world's prisoners with life sentences, more than in any other country.[37]
Parole and nonviolent offensesEdit
Under the federal criminal code, however, with respect to offenses committed after December 1, 1987, parole has been abolished for all sentences handed down by the federal system, including life sentences. A life sentence from a federal court will therefore result in imprisonment for the life of the defendant unless a pardon or reprieve is granted by the President or if, upon appeal, the conviction is quashed.
In the states of Illinois, Iowa, Louisiana, Maine, Pennsylvania, and South Dakota, all life sentences are issued without the possibility of parole.
Over 3,200 people nationwide are serving life terms without a chance of parole for nonviolent offenses. Of those prisoners, 80 percent are behind bars for drug-related convictions: 65 percent are African-American, 18 percent are Latino, and 16 percent are white.[38] The ACLU has called the statistics proof of "extreme racial disparities." Some of the crimes that led to life sentences include stealing gas from a truck and shoplifting but only for those with a pattern of habitual criminal offenses. A large number of those imprisoned for life had no prior criminal history but were given the sentence because of the aggravated nature of their crimes.[39]
Three-strikes lawEdit
Further information: three-strikes law
Under some controversial sentencing guidelines known as "three-strikes laws," existing both at state and federal level, a person who is convicted of an offense and who has one or two other previous serious convictions is to serve a mandatory or discretionary life sentence in prison, with or without parole depending on the jurisdiction. Notably, a broad range of crimes ranging from petty theft to murder could served as the trigger for a mandatory or discretionary life sentence in California from 1994 to 2012. Notably, the U.S. Supreme Court has on several occasions upheld lengthy sentences for petty theft including life with the possibility of parole and 50 years to life and stated that neither sentence conflicted with the ban on "cruel and unusual punishment" in the Eighth Amendment to the U.S. Constitution.[40] These court decisions have been the subject of considerable controversy.
DebatesEdit
Increased use of the life imprisonment sentence, especially life without parole, came in response to debates on capital punishment. In fact, many politicians, especially in the Democratic Party, expressed their emphasis on replacing the death penalty with life without parole.[41] Additionally, seeking the death penalty is more costly to the state and taxpayer than seeking life without parole.[42]
A common argument against life without parole is that it is equally as immoral as the death penalty, as it still sentences one to die in prison. Certain organizations and campaigns have been founded with a goal to work against life imprisonment and improve the rate of release. For example, the #DropLWOP campaign is dedicated to dropping the life without parole sentence and providing an automatic commutation and chance to see a parole board for all prisoners serving life sentences.[43]
Notable examplesEdit
This list is incomplete; you can help by adding missing items. (May 2020)
Robert Bales - Soldier convicted of murdering 16 civilians in Afghanistan.
Robert Berdella - A serial killer who kidnapped, raped, tortured, and murdered at least six men.
John Gotti – Boss of the New York City Gambino crime family.
Aaron Hernandez – Former NFL Player for the New England Patriots who was found guilty of first-degree murder. Died by suicide on April 19, 2017.
James Holmes – Perpetrator of the 2012 Aurora, Colorado shooting.
Lawrence Horn – Former record producer who contracted the killing of his ex-wife, his disabled son, and the son's nurse in an attempt to gain control of his son's $1.7 million trust fund.
Ted Kaczynski – The Unabomber, whose homemade bombs killed 3 people and injured 23 others.
Samuel Little - A serial killer who murdered 50 women across several states.
Terry Nichols – Main accomplice to Timothy McVeigh in the Oklahoma City bombing in 1995.
Gary Ridgway – A serial killer who murdered 49 women in and around Seattle.
Lawrence Rivera – Captured after a 9-year international manhunt and convicted for the murder of Kristina Garcia
Eric Rudolph – 1996 Olympic bomber, who killed 4 and injured 111 others.
Faisal Shahzad – The Times Square Bomber, who attempted to detonate a car bomb in Times Square.
Umar Farouk Abdulmutallab – The "Underwear Bomber", explosives hidden in his underwear while on a flight.
Ross Ulbricht – Creator and operator of Silk Road, an online black market; convicted of money laundering, computer hacking, and conspiracy to traffic narcotics.
Ramzi Yousef – Member of Al-Qaeda, who blew up the World Trade Center in 1993.
Warren Jeffs – Leader of the FLDS and convicted pedophile, who married child brides, raped two girls, and called himself Immanuel while he practiced polygamy.
Joaquín "El Chapo" Guzmán – Disposed leader of the Sinaloa Cartel, who broke out of two Mexican jails and went on the run for over a decade until he was caught in 2016 during Operation Black Swan.
Robert Hanssen - Former FBI agent, who sold state secrets to the KGB, and The Kremlin.
Mark David Chapman - A killer who murdered John Lennon.
Richard Reid – The Shoe Bomber, threatened to blow up an airliner by placing C4 explosives in his shoes.
Nikolas Cruz, the 19-year-old convicted murderer who received 34 life terms for a school shooting case that killed 17 people and injured another 17.
Wadih el-Hage – Member of Al-Qaeda who blew up the US Embassies in Africa and for being Bin Laden's secretary.
Alex Baranyi and David Anderson - Murdered four people in one day.[44][45][46]
Scott Dyleski - Murderer of Daniel Horowitz wife Pamela Vitale.[47]
Rod Ferrell - Cult leader and convicted of murder of two people he committed at age 16.[48]
Bryan and David Freeman - Murdered their parents and younger brother.[49][50][51][52][53][54]
Terrance Graham - Convicted of a parole violation he committed at age 17.[55]
Brett Jones - Convicted of the murder of his grandfather committed at age 15.
Alec Devon Kreider - Murdered his high school friend and his friend's parents.[56]
Warren Harris - A serial killer who murdered four men in New Orleans' French Quarter from February to April 1977.[58]
Joe Ligon - Convicted of participating in a stabbing spree at age 15 that resulted in one person being killed.
Nicholas Lindsey - Murderer of a police officer.[59]
Lee Boyd Malvo - A serial killer convicted in connection with the Beltway sniper attacks in the Washington Metropolitan Area over a three-week period in October 2002.[60]
Evan Miller - Convicted of a murder committed at age 14 which resulted in end to automatic life without parole sentences for juveniles.
Henry Montgomery - Convicted of a murder committed at age 17 which eventually resulted in the end to automatic life without parole sentences for juveniles retroactively.
Josh Phillips - Convicted of the murder of 8-year-old Maddie Clifton which he committed at age 14.[61]
Courtney Schulhoff - Murdered her father at age 16.[62]
Christopher Simmons - Convicted of a murder committed at age 17 which resulted in end to Capital punishment for juveniles.
Lionel Tate - Convicted of the murder of 6-year-old Tiffany Eunick which he committed at age 12, making him the youngest person in U.S. history to be sentenced to life without parole.[63]
Whole life tariff, a determinate life sentence sometimes handed down under English criminal law
Black site
^ "Life Goes On: The Historic Rise in Life Sentences in America". 2013-10-16. Archived from the original on 2013-10-18. Retrieved 2013-10-16.
^ "Lifer Parole Process". Office of Victim and Survivor Rights and Services (OVSRS). Retrieved 2020-05-08.
^ In re Jeanice D., 28 Cal. 3d 210 (1980) ("25 years to life" is an indeterminate life sentence, implying that a minor convicted of first-degree murder was eligible for commitment to the California Youth Authority, rather than determinate life sentence, which would require incarceration in a regular prison).
^ Reitz, Kevin R.; Rhine, Edward E. (2020-01-13). "Parole Release and Supervision: Critical Drivers of American Prison Policy". Annual Review of Criminology. 3 (1): 281–298. doi:10.1146/annurev-criminol-011419-041416. ISSN 2572-4568.
^ Angle, Roland E. (2014). "Build a Mass Movement: Abolish the Probation & Parole Systems to Attack the Foundation of the U.S. Police State". Race, Gender & Class. 21 (1/2): 236–245. ISSN 1082-8354. JSTOR 43496972.
^ A. E. Weiss, Prisons, A System in Trouble (1988), pp. 29–30.
^ SOLDIER ADMITS SLAYING; Sergeant in Tokyo Confesses to Killing 9-Year-Old Girl, New York Times. November 28, 1953
^ Army Seargreant Confesses. November 28, 1953. San Francisco Examiner
^ Schick v. Reed, 419 U.S. 256 (1974).
^ J. H. Wright, Jr., "Life Without Parole: An Alternative to Death or Not Much of a Life At All?" 43 Vanderbilt Law Review 529, 535 (1990).
^ Craig S. Lerner. "Life without parole as a conflicted punishment" (PDF).
^ "Ford Opens Door for Parole Of Six Once Sentenced to Die for Killings in Military". Los Angeles Times. January 22, 1977.
^ Wright, supra, at p. 536.
^ 408 U.S. 238 (1972).
^ see Green v. Teets, 244 F2d 401 (9th Cir. 1957); United States v. Ragen, 146 F2d 349 (7th Cir.), cert denied, 325 U.S. 865 (1945); and State v. Dehler, 257 Minn. 549, 102 N.W.2d 696 (1960).
^ 18 How. 307 (1856).
^ See C. de la Vega & M. Leighton, Sentencing our Children to Die in Prison: Global Law and Practice, 42 U.S.F. Law Review 983, 989 (2008). The research was conducted in 2007, updated in 2008 to clarify that Tanzania, South Africa and Israel do not allow juvenile life without parole, and cited by the U.S. Supreme Court in 2010 in Graham v. Florida. The University of San Francisco Center for Law & Global Justice continues to monitor international juvenile sentencing laws and practices.
^ State Distribution of Youth Offenders Serving Juvenile Life Without a chance of Parole (JLWOP) Human Rights Watch, October 2, 2009.
^ "The Rest of Their Lives: Life without Parole for Child Offenders in the United States", Human Rights Watch, May 1, 2008
^ Boghani, Priyanka. "They Were Sentenced as "Superpredators." Who Were They Really?". PBS Frontline. Retrieved 22 March 2020.
^ Templeton, Robin (1 January 1998). "Superscapegoating". FAIR. Retrieved 22 March 2020.
^ Taylor-Thompson, Kim (November 20, 2020). "Op-Ed: Why America is still living with the damage done by the 'superpredator' lie". The Los Angeles Times. The Associated Press.
^ Bogert, Carroll (November 20, 2020). "Analysis: How the media created a 'superpredator' myth that harmed a generation of Black youth". NBC News. U.S. News.
^ Graham v. Florida, 130 S. Ct. 2011 (2010).
^ Graham v. Florida, supra, 130 S. Ct. at 2034 (concluding that juvenile life without parole is unconstitutional for non-homicide crimes).
^ International law and practice clearly reflect the sentiments of the Graham court regarding juveniles. Graham v. Florida, supra, 130 S. Ct. at 2030.
^ "Life without parole for juvenile offenders". theappeal.org. 2020-07-22. Retrieved 2020-08-07.
^ "States That Banned Life Without Parole for juvenile Offenders". The Campaign for the fair sentencing of youth. 25 August 2015.
^ [cleveland.com/court-justice/2020/03/ohio-lawmakers-seek-to-stop-sentences-of-life-without-parole-for-youth-offenders.html "Ohio lawmakers seek to stop sentences of life without parole for youth offenders"]. {{cite web}}: Check |url= value (help)
^ "Maryland Bans Life Without Parole for Children". Equal Justice Initiative. March 12, 2021.
^ "Nebraska Legislature".
^ Life Without Parole Death Penalty Information Center
^ "Opinion | the Misuse of Life Without Parole". The New York Times. 13 September 2011.
^ "THE FACTS OF LIFE SENTENCES" (PDF). The Sentencing Project. 2018.
^ a b Liptak, Adam (2 October 2005). "To More Inmates, Life Term Means Dying Behind Bars". New York Times.
^ Clark, Roger S. (2019-10-12). "Life Imprisonment: A Global Human Rights Analysis by Dirk van Zyl Smit & Catherine Appleton (review)". Human Rights Quarterly. 41 (4): 1022–1035. doi:10.1353/hrq.2019.0059. ISSN 1085-794X. S2CID 208689254.
^ "A Living Death: Life without Parole for Nonviolent Offenses". American Civil Liberties Union. June 6, 2018.
^ "Jailed for Life for Stealing a $159 Jacket? 3,200 Serving Life Without Parole for Nonviolent Crimes". Democracy Now!. November 15, 2013. Retrieved November 20, 2019.
^ See Rummel v. Estelle, 445 U.S. 263 (1980) (upholding life sentence for fraudulent use of a credit card to obtain $80 worth of goods or services, passing a forged check in the amount of $28.36, and obtaining $120.75 by false pretenses) and Lockyer v. Andrade, 538 U.S. 63 (2003) (upholding sentence of 50 years to life for stealing videotapes on two occasions after three prior offenses)
^ "A voter's guide to Capital Punishment / Death Penalty: Compare where all the 2020 candidates stand". politico.com. Retrieved 2020-04-27.
^ "Costs". Death Penalty Information Center. Retrieved 2020-04-27.
^ "drop lwop". drop lwop. Retrieved 2020-04-26.
^ Maria Eftimiades, Susan Christian Goulding, Anthony Duignan-Cabrera, Don Campbell, Jane Sim Podesta (June 23, 1997). "Why Are Kids Killing?". People. Retrieved 25 January 2016. {{cite web}}: CS1 maint: multiple names: authors list (link)
- "Local News – Slaying Suspect's State Called 'Clearly Impaired'". The Seattle Times. July 9, 1998. Retrieved 25 January 2016.
^ Ian Ith (December 18, 1999). "Anderson Is Guilty Of Murder In 2Nd Trial – 4 Bellevue Slayings 'Difficult To Believe'". The Seattle Times. Retrieved January 25, 2016.
^ Boynton, Gary (October 14, 2009). "Gothic Murders". Crime Magazine. Retrieved November 22, 2016.
^ Gartrell, Nate (30 August 2018). "Notorious East Bay murderer becomes eligible for parole". East Bay Times. Retrieved 14 July 2019.
^ "'Vampire cult' killer's trial featured on Court TV".
^ "Bryan Freeman, one of the 'Berserker' brothers, gets new sentencing date". The Morning Call. June 1, 2016.
^ "Trial Drove Families Apart Verdict Doesn't End Families' Grief, Questions". The Morning Call. April 27, 1996.
^ "Conversation with convicted killer Bryan Freeman". One News Page. February 24, 2015.
^ "Neo-Nazi Brother to Get New Sentence in Parents' 1995 Killings". NBC Philadelphia. March 15, 2016.
^ "Blood Brothers: The despicable bond between Bryan and David Freeman". The Lineup.
^ IMDb (May 12, 2014). "Killer Kids: Allentown Massacre & the Copycat". LMN.
^ "Sentenced to Life Without Parole as a Juvenile: Terrence Graham | Age 30". 5 October 2017.
^ "Alec Kreider commits suicide in prison, was serving 3 life terms for brutal Manheim Township killings".
^ https://www.newspapers.com/clip/104334472/warren-harris/
^ "Convicted cop killer Nicholas Lindsey re-sentenced to life with review in 25 years". 27 January 2017.
^ "Documentary Series Revisits 2002 DC Sniper Case".
^ "Judge decides life sentence is warranted for Joshua Phillips in Maddie Clifton's shocking death".
^ "Altamonte Springs teenage murderer resentenced to 40 years".
^ "Lionel Tate Gets 30 Years in Jail". CBS News.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Life_imprisonment_in_the_United_States&oldid=1133530945"


text:
\section{Introduction}

One of the most interesting recent results in quantum gravity is the
computation of the quantum spectra of certain geometrical quantities
\cite{spectra}.  These spectra turn out to be discrete, suggesting a
discrete structure of geometry at the Planck scale which might be, in
principle, physically measurable \cite{disc}.  Recently, Immirzi has
pointed out that the overall scale of these spectra is not determined
by the theory \cite{Immirzi}.  More precisely, Immirzi has considered a
certain scale transformation introduced by Barbero \cite{Barbero}, and
noticed that if we quantize the theory starting from {\em scaled\/}
elementary variables, we end up with different spectra for the
same geometrical quantities.

Here, we analyze the issue in detail.  We find that the quantum theory
is in fact undetermined by one para\-me\-ter.  This is due to the fact
that the holonomy algebra on which this approach is based depends on
a free parameter.  This fact gives rise to a one-parameter family of
inequivalent quantum theories, which are all, up to additional physical
inputs, physically viable. In a sense, there is a one-parameter
family of ``vacua'' in quantum general relativity, parameterized by a
free (real) parameter, which we call ``Immirzi parameter'', and denote
as $\iota$ (``iota'').  Equivalently, there is a symmetry in the
classical theory which is realized as a canonical transformation but
cannot be realized as a unitary transformation in the quantum theory.

The existence of this quantization ambiguity is due to the peculiar
kind of representation on which non-perturbative quantum gravity is
based \cite{loops,AI}.  This representation is characterized by the
fact that the holonomy is a well-defined operator in the quantum
theory.  Conventional perturbative Maxwell and Yang-Mills theories are
not defined using this kind of representation and the $\iota$
parameter does not appear in that context.  But physical and
mathematical arguments indicate that this representation is relevant at the
diffeomorphism-invariant and background-independent level
\cite{AI,ascona}.  Thus, the Immirzi parameter appears in the general
covariant context.

In this letter, we describe in some detail how this ambiguity is
originated and its consequences.  In particular, we address a certain
number of questions that have been recently posed concerning the $\iota$
parameter, and we try to rectify a number of proposed incorrect
interpretations of the appearance of this free parameter.

For a similar discussion, but centered on the loop quantization of Maxwell
theory, see \cite{k}, where an interesting speculation tying the Immirzi
parameter with charge quantization is presented.

\section{The Immirzi ambiguity}

Consider a three-dimensional compact smooth manifold $\Sigma$, and two
fields defined over it: an $su(2)$ valued vector density $E$, with
components $E^a_i$, where $a,b,c,..$ denote tensor indices, and
$i,j,k,..$ are $su(2)$ indices; and an $SU(2)$ connection $A$ with
components $A_a^i$.  In terms of these fields, one can describe Euclidean
\cite{Abhay} or Lorentzian \cite{Barbero} general
relativity, as well as $SU(2)$ Yang-Mills theory.  In both cases $A_a^i$
and $E^a_i$ are canonically conjugate and subject to the Gauss constraint.
\begin{equation} \label{Gauss}
            G_i:=\partial_a E^a_i+\epsilon_{ijk }A^j_aE^{ak}.
\end{equation}
In Yang-Mills theory, $E$ is the electric field; in general relativity,
$E^a_i=\det(e_a^i)\,e^a_i$, were $e_a^i$ and $e^a_i$ are the triad field
(related to the 3-metric by $g_{ab}=e_a^ie_b^i$) and its inverse.

In general relativity it is natural to take dimensionless coordinates.
$E$ has dimension $length^2$ and $`A=A_a dx^a$ is dimensionless.  The
fundamental Poisson brackets are $\{A_a^i(x),E^b_j(y)\}=G\, \delta_a^b
\delta^i_j \delta(x,y)$, where $G$ is $16\pi\,c^{-3}$ times the Newton
constant.

We denote by $h_e(A)\in SU(2)$ the transport propagator of $A$ along a path
$e$.  If $e$ is a closed path then $\ \mbox{tr}(h_e(A))$ is the holonomy
of $A$ around $e$, or the Wilson loop functional.  Wilson loops are
natural $SU(2)$ gauge invariant quantities, and any gauge invariant
function of $A$ can be approximated by sum of products of Wilson loops.
In conventional perturbative Yang-Mills theory, there is no
well-defined operator corresponding to the Wilson loop, because field
operators need to be smeared in more than one dimension to be well
defined. In a general covariant theory, on the other hand, one expects the
Wilson loop operators to be well-defined in the quantum theory.
Thus, one can define the quantum theory as a unitary representation of the
(non-canonical) Poisson algebra generated by the classical observables
$h_e(A)$ and $E^a_i(x)$ (with a suitable smearing of the later)
\cite{loops}.

By doing so, one obtains a quantum representation that can be
described as follows \cite{ascona,AL1,ALMMT-JMP}.  The Hilbert space
of the theory is taken as ${\cal H}= L_2({\overline{\A}},d\mu_0)$, where ${\overline{\A}}$ is
(the closure in a suitable norm of) the space of the smooth connection
fields, and $d\mu_0$ is a faithful, diffeomorphism invariant
$\sigma$-additive probability measure on ${\overline{\A}}$.  One can show
\cite{ALMMT-JMP} that the measure $\mu_0$ is the unique probability
measure on ${\overline{\A}}$ which implements the classical reality conditions
($A_a^i,E^a_i$ are real) and the given Poisson algebra.  The holonomy
observable $h_e(A)$ becomes the quantum operator $\hat h_e$ defined by
\begin{equation}
       \hat h_e \Psi = h_e \Psi, \ \ \ \ \Psi\in{\cal H}.
\end{equation}

A characteristic example of a geometric operator defined in the theory
is the area of a two-dimensional surface.  Recall that
the area $A(S)$ of a 2d surface $S$ immersed in $\Sigma$ is given by
\begin{equation}
   A(S)=f(S,E)
\label{area}
\end{equation}
where
\begin{equation}
     f(S,E) = \int_S \sqrt{n_a\, n_b\, E^a_i\, E^{bi}}\ \ ;
\end{equation}
$n_a$ is the one-form normal to the surface $S$. For every given surface
$S$, the quantity $f(S,E)$ yields (via a quantization and regularization
procedure) a well-defined operator $\hat f(S)$ on $\cal H$.  Its
spectrum is discrete and positive \cite{spectra}. For more details,
see \cite{ascona}.

Now, the triad $e_a^i$ defines a three dimensional
spin connection $\Gamma_a^i$ by
\begin{equation}
  \partial_{[a} e_{b]}^i = \epsilon^{i}{}_{jk} \Gamma_{[a}^j e_{b]}^k,
\label{gamma}
\end{equation}
which transforms under $SU(2)$ as the connection $A$ does.
Pick an arbitrary positive real number $\iota$ and define the scaled
fields
\begin{eqnarray}
A_\iota{}_a^i &=& \iota A_a^i+(1-\iota)\Gamma_a^i, \label{atransf} \\
E_\iota{}^a_i &=& {1\over\iota}E^a_i.
\end{eqnarray}
It is then easy to verify the following. i) $A_\iota$ and $E_\iota$ are
canonically conjugate, namely the map $U_\iota:(A,E) \mapsto
(A_\iota,E_\iota)$ is a canonical transformation.  ii) $A_\iota$ and
$E_\iota$ transform under gauge transformations as $A$ and $E$ do.  In
particular, $A_\iota$ is a connection.  This follows from the fact
that $A_\iota$ is a convex linear combination of two $SU(2)$
connections.  Thus $U_\iota$ preserves the affine structure of the
space of connections.  iii) Clearly $U_\iota$ preserves the reality
conditions as well.  Thus $U_\iota$ leaves the kinematical structure
of general relativity invariant.

The canonical transformation $U(\iota)$ was studied by Barbero
\cite{Barbero}.  The case $\iota=\sqrt{-1}$ corresponds to
Ashtekar's canonical transformation \cite{AbhayBeta}.  Thus, the fact
that $U(\iota)$ is a canonical transformation is a simple extension
of the important discovery due to Ashtekar \cite{Abhay} which gave
rise to the connection formulation of general relativity.  To see the
relation with these works, notice that by introducing the extrinsic
curvature $K_a^i=A_a^i-\Gamma_a^i$, we can write (\ref{atransf}) as
\begin{eqnarray}
A_a^i &=& \Gamma_a^i + K_a^i, \\
A_\iota{}_a^i &=& \Gamma_a^i + \iota K_a^i.
\end{eqnarray}
The generating function of the (infinitesimal) canonical transformation
is $C=\int K_a^iE_i^a$. Finally, notice that the area of a surface $S$ is
given in terms of the scaled variables by
\begin{equation}
   A(S) = \iota \ f(S,E_\iota).
\label{scaledarea}
\end{equation}

Now, we can view $(A_\iota,E_\iota)$ just as different coordinates on
the phase space of general relativity.  Suppose we decide to quantize the
theory following the same path as before, but starting from the scaled
variables  $(A_\iota,E_\iota)$.  In general, starting a quantization
from scaled variables has no effect on the physical predictions of the
quantum theory.  For instance, we may quantize a harmonic oscillator
starting from scaled canonical coordinates $({1\over\iota}q,\iota p)$
without affecting, say, the spectrum of the hamiltonian -- in the next
section we shall verify that this is indeed the case.  Similarly, it
is natural to expect here that physical predictions are not going to
be affected if we quantize the variables $(A_\iota,E_\iota)$ instead
of the variables $(A,E)$.  More precisely, we expect that the
canonical scale transformation $U(\iota)$ will be implemented
unitarily in the quantum theory, so that the quantization based on
$(A_\iota,E_\iota)$ will yield a different, but unitary equivalent
quantum representation.  However, this expectation turns out to be
false.

Indeed, let us define the theory requiring that the pa\-rallel transport
$h_e^\iota=h_e(A_\iota)$ be a well defined operator in the quantum
theory.  Call ${\cal H}_\iota$ the Hilbert space on which we define
the new representation.  Since the Poisson algebra formed by the
quantities $h_e^\iota$ is the same as the one formed by the quantities
$h_e$, we may use the same Hilbert space as before: ${\cal H}_\iota =
L_2({\overline{\A}},d\mu_0)$.  (We denote the two Hilbert spaces $\cal H$ and
${\cal H}_\iota$ differently because the interpretation of the same
function $\Psi\in L_2({\overline{\A}},d\mu_0)$ is different in $\cal H$ and in ${\cal
H}_\iota$).

If the two quantization paths define the same theory, there should
exist a unitary transformation $U(\iota)$ from $\cal H$ to ${\cal H}_\iota$
which sends physically corresponding states and physically corresponding
operators into each other.  Namely, we expect that the canonical
transformation $U(\iota)$ can be realized as a unitary transformation of
$L_2[\bar{\cal A},d\mu]$ into itself.

If this transformation exists\footnote{The generator of the classical
canonical transformation can be promoted to a self-adjoint operator.
It coincides with the generator of the Wick rotation transform
considered in \cite{Wick}. The corresponding operator $\hat{C}$
is defined on $\cal H$ in \cite{QSD}}, an immediate consequence is
that the spectra of observables which are unitary images of each other
are identical.  In particular, the spectrum of the area operator
defined in one theory should agree with the spectrum of the area
operator defined in the other theory.

Consider now the operator $f(S,E_\iota)$ defined in the scaled theory.
Since it is has the same form as the operator $f(S,E)$ in the unscaled
theory, it will certainly have the same spectrum.  But then equations
(\ref{area}) and (\ref{scaledarea}) show that the spectrum of the area
in the scaled theory is obtained from the one in the original theory by
multiplying it by $\iota$.  Since the spectrum of the area is
discrete, it cannot be invariant under a scaling by an arbitrary real
parameter.  Therefore the two quantizations yield unitarily
inequivalent theories.

The two theories give different physics. For instance, the predicted
spectrum of the area differ.  The other geometrical quantities having
discrete spectrum, such as volume and length, have different spectra
in the scaled theory as well.  Since $\iota$ enters linearly in $E$,
which has dimension $L^2$, the discrete spectrum of a geometrical
quantity homogeneous in $E$ with dimension $L^n$ scales as
$\iota^{n/2}$.

Thus, there is a free parameter $\iota$ in the quantization of the
theory.  It could be measured, in principle, simply by measuring, for
instance, the size of the ``quanta'' of area.  So far, there does not
seem to be any compelling reason for choosing a particular value for
$\iota$.  Better knowledge of the theory may indicate such a reason.

It has been suggested (for instance, see \cite{k}) that one could fix
$\iota$ using black hole entropy.  It was shown in \cite{blackhole}
that one can derive the Bekenstein-Hawking entropy formula Entropy
$ = const \times A$ from loop quantum gravity -- with a constant $const$
that turns out to be finite, but with an incorrect value.
This constant is affected by a rescaling of $\iota$, and therefore one
might choose a value for $\iota$ yielding the correct value
$const={1\over 4}\hbar G$.  This would fix a value of $\iota$
approximately given by
\begin{equation}
    \iota \sim {1\over 4 \pi}.
\end{equation}

\section{Incorrect interpretations}

Several interpretations of the appearance of the free parameter
$\iota$ in quantum gravity have been recently proposed.  Some
of these are incorrect.  Here we discuss some of these
interpretations.

\subsection{$\iota$ is a free constant that multiplies the connection in
the definition of the holonomy}\label{ssholo}

Let $e:[0,2\pi]\mapsto\Sigma$ be a closed path. The holonomy $h_e$ is
formally written as
\begin{equation}
	h_e = {\cal P} e^{\oint_e A},
\label{exp}
\end{equation}
and it is more precisely defined as $h_e = h_e(2\pi)$ where the
$SU(2)$-valued function $h_{e}(s)$ is the solution of the differential
equation
\begin{equation}
{d\over ds}h_e(s) - \dot e^a(s) A_a(e(s))\ h_e(s)=0,\ \ \ \ h_e(0)=1.
\end{equation}
Here $\dot e^a(s)$ is the tangent to $e$ at $s$ and $1$ the identity
in $SU(2)$.  It has been repeatedly suggested that in defining the
holonomy one if free to add a dimensionless parameter $\iota$ in the
exponent of (\ref{exp}) -- keeping any other thing fixed in the
theory.

However, this is not true.  The transformation properties of $A$ under
an $SU(2)$ gauge transformation are uniquely fixed by the classical
action, because from the action one derives the gauge constraint
(\ref{Gauss}).  If (\ref{exp}) is gauge covariant, then \begin{equation} \tilde h_e
= {\cal P} e^{\iota\oint_e A},
\label{exp2}
\end{equation}
or, more precisely, the solution of
\begin{equation}
{d\over ds}\tilde h_e(s) - \iota \dot e^a(s) A_a(e(s))\ \tilde h_e(s)=0,
 \ \ \tilde h_e(0)=1,
\end{equation}
is {\em not\/} gauge covariant, as a direct computation shows. In other
words, if we multiply a connection by a real number, we do not obtain a
quantity that transforms as a connection: connections form an affine
space, not a linear space.

\subsection{$\iota$ is the constant that multiplies the classical action}
\label{ssactio}

The quantity $\tilde h_e$ defined in (\ref{exp2}) is gauge covariant
under the gauge transformation generated by a scaled Gauss constraint
\begin{equation}
\label{Gauss2}
        G_i:=\partial_a E^a_i + \iota \epsilon_{ijk }A^j_aE^{ak}.
\end{equation}
This constraint, in turn, can be obtained by scaling the action of the
theory.  Accordingly, it has been suggested that the $\iota$
ambiguity is a consequence of the freedom in choosing the constant in
front of the action of general relativity. Equivalently: scaling
$A$, but not $E$, without absorbing this into a redefinition of the
coupling constant.

Again, this interpretation is wrong. Physically, the constant in front of
the general relativity action determines the strength of the macroscopic
Newtonian interaction.  The freedom in the choice of the Immirzi parameter
in the quantum theory consists in the fact that the overall scale of the
spectra is {\em not\/} determined by low energy physics.  In other
words, we can measure the Newton constant by means of {\em
classical\/} gravitational experiments, and measure the Planck
constant by means of {\em non-gravitational\/} quantum experiments.
From these two quantities we obtain a length, the Planck length
$l_{P}=\sqrt{\hbar G}$.  The point of the Immirzi ambiguity is
that the ratio of, say, a given eigenvalue of the area to $l_P$ is not
determined by the quantization procedure.

\subsection{Any Yang-Mills theory has a free $\iota$ parameter when
quantized in the loop representation}\label{ssany}

As the previous comments indicate, the Immirzi parameter is not
related to a multiplicative scaling of the connection.  Rather, it is
generated by the affine transformation (\ref{atransf}).  In order to
be able to write such an affine transformation, we need to have a
second, independent connection in the formalism.  In general
relativity, where the hamiltonian gauge group is $SU(2)$, the
``electric field'' $E^{a}_i$ has the correct index structure for a
connection $\Gamma_a^i$ to be defined via (\ref{gamma}).
(Furthermore, $\Gamma_a^i$ has a natural geometrical interpretation.)
There is no direct analog of this construction, as far as we can see,
for an arbitrary Yang Mills theory.\footnote{$SU(2)$ Yang-Mills theory
has essentially the same phase space as general relativity.  However,
notice that in order to define $\Gamma_a^i$ we need to invert the 3x3
matrix $E^{a}_{i}$; in general relativity this matrix is invertible,
because of the non-degeneracy condition on the metric, but in $SU(2)$
Yang-Mills it is not so in general.}

An exception of the above is the case of an abelian theory, namely for
Maxwell theory.  In the case of Maxwell, the quantity (\ref{exp2}) is
gauge invariant for any $\iota$.  Thus, we have a free parameter in
the loop representations of electromagnetism and general relativity
only.  In the ($U(1)$) Maxwell theory, the free parameter appears
because a scaled abelian connection is still a connection.  In the
($SU(2)$) general relativity it appears because a second connection
for defining an affine transformation is determined by the
triad.  There is no obvious generalization of this effect to other
gauge theories.

\subsection{The algebra has inequivalent representations}

A characteristic phenomenon in field theory --and in finite dimensional
quantum mechanics, when the phase space is non linear-- is that the main
observable algebra may have inequivalent representations. It has
been suggested that the Immirzi parameter distinguishes inequivalent
representations of the same algebra. However, we do not think that this is
the case.  We have defined the $\iota$-scaled theory as a
representation of a physically distinct algebra (the algebra of the
scaled variables) obtaining the quantum theory on ${\cal H}_\iota$.
If this theory could be obtained also as a representation of the
original algebra of unscaled variables, then it would carry a
representation of the scaled as well as the unscaled, $h_e$ and
$h_e^\iota$, operators.  But we do not see any reason for the
operators $h_e^\iota$ to be well-defined in the Hilbert space
of the usual loop quantum theory.

\section{Models}

We now discuss a few simple models in which the Immirzi ambiguity does
or does not appear, in order to illustrate some of the statements made
above.

\subsection{Harmonic oscillator: no $\iota$ ambiguity}

Consider the phase space $\Gamma=\Rl^2$ of an harmonic oscillator with
canonical coordinate and momentum $(x,p)$ and Hamiltonian
\begin{equation}
       H = {1\over 2}p^2+{\omega^2\over 2} x^2.
\end{equation}
The quantum theory is defined by a representation of the canonical
algebra $[q,p]=i\hbar$.  Let the Hilbert space be ${\cal H}=L_2[R,dq]$
and $(\hat q=x,\hat p=-i\hbar\partial_q)$. The spectrum of the Hamiltonian
operator is
\begin{equation}
	E_n = \left(n+{1\over 2}\right)\hbar\omega.
\end{equation}

Suppose we decide to quantize the theory starting from the scaled variables
\begin{equation}
     x_\iota = \iota x, \ \ \ \ p_\iota = {1\over\iota} p.
\end{equation}
Is the spectrum of the Hamiltonian altered?  The transformation
$(x,p)\to (x_\iota,p_\iota)$ is clearly a canonical transformation.
The algebra of the scaled variables is the same as the algebra of
the unscaled ones.  Therefore we can write ${\cal H}_\iota
=L_2[R,dq]$ and $(\hat q_\iota=x,\hat p_\iota=-i\hbar\partial_q)$.
In the scaled variables, the Hamiltonian reads
\begin{equation}
     H = \iota^2 \left[{1\over 2}p_\iota^2+{\omega^2\over 2\iota^4}
     x_\iota^2\right].
\end{equation}
Thus its spectrum is $\iota^2$ times the spectrum of an
Hamiltonian of angular frequency $\omega/\iota^2$.  That is
\begin{equation}
   E_n = \iota^2 \left(n+{1\over 2}\right)\hbar{\omega\over\iota^2},
\end{equation}
precisely as before.  Therefore, in the quantization based on the
scaled variables the wave functions $\psi(q)$ have a different
interpretation, but physical predictions, such as the spectrum
of the Hamiltonian, are not altered.  This example shows that in
general a one-parameter scaling of the quantization variables that
does not alter the observable algebra will {\em not\/} alter the
theory. This was to be expected from Von-Neumann's uniqueness theorem.

\subsection{Particle on a circle: no $\iota$ ambiguity}

As a second example, we consider another simple system in which a scaling
of the basic variables does not alter the quantum theory: the theory of a
particle on a circle. We include this case because, unlike the
harmonic oscillator case, here the observable algebra has a one-parameter
family of inequivalent irreducible representations. However, this fact
turns out to irrelevant as far as the $\iota$ ambiguity is concerned.

Consider a particle constrained to move on a circle of length $L$. Let
$q\in[0,L]$ its position and $p$ its momentum. The Hamiltonian is
$H={1\over 2} p^2$, and has eigenvalues $E_n = n^2 {\pi^2\hbar^2\over
2 L^2}$.  Now, suppose we change basic variable to $ (s_\iota,p_\iota)  =
(\iota q,{1\over \iota}p)$. Then the Hamiltonian reads $H={\iota^2\over
2}p^2_\iota$. At first sight one is tempted to say that the spectrum of
$H$ has now changed, because $p_\iota$ and $q_\iota$ have the same
algebra as $p$ and $q$ and therefore $p_\iota$ must have the same
spectrum as $q$.  But of course this is wrong, because $q$ and
$q_\iota$ are defined on a circle, and the spectrum of their conjugate
momentum depends on the size of the circle.  Clearly this exactly
compensates the $\iota^2$ in $H(p_\iota)$.

More precisely, we cannot quantize the $(q,p)$ algebra in this case
because $q$ is not a global coordinate on the phase space \cite{Isham}.
We must, for instance, replace $q$ with $g={L\over 2\pi}\exp(i 2\pi q/L)\in
U(1)$,  which  is a global coordinate. If we introduce also the angular
momentum $l={L\over 2\pi} p$, we obtain the algebra
\begin{equation}
	\{g,l\}= g.
\end{equation}
This algebra has a one-parameter family of distinct irreducible
representations, which can all be defined on $L_2[S_1,d\phi]$ by
\begin{equation}
  \hat l = -i\partial_\phi, \ \ \ \ \hat g = r e^{i\phi},
\end{equation}
where $r$ labels the representation. The representation
appropriate for a given $L$ is the one obtained by choosing $r=L/2\pi$,
because this realizes the non linear condition on the basic variables
$|g|=L/2\pi$.  In terms of these variables, the
Hamiltonian is
\begin{equation}
      H = {1\over 2} {4\pi^2\over L^2} l^2.
\end{equation}
The spectrum of $\hat l$ does not depend on the representation chosen,
and we have again the correct spectrum for the Hamiltonian.

Notice that we could have written the Hamiltonian (perhaps ``more
correctly'') as
\begin{equation}
      H = {1\over 2} {1\over |g|^2} l^2.
\end{equation}
Then, the corresponding operator is different in each representation, but
since the representation is tied to $L$, the spectrum is again correct.
In any case, no free parameter $\iota$ appears.

\subsection{A simple model with the free $\iota$ parameter}

Consider a phase space $\Rl^6$ with coordinates $(K_i,E^i)$ and
Hamiltonian $H = E_i E_i/2$, and let a theory be defined by
the constraint $G_i=\epsilon_{ijk} K^j E^k$.  The theory has one
physical degree of freedom.

Consider the canonical transformation
\begin{equation}
    (K,E) \to (A:=K+\Gamma,E)
\end{equation}
where
\begin{equation}
    \Gamma_i:={\partial\sqrt{E^iE^i}\over\partial E_i}.
\end{equation}
Here we are mimicking the canonical transformation to the ``connection"
variable $A$, where $\Gamma$ is the ``spin-connection" of $E$.  In the
new variables, the constraint becomes
\begin{equation}
     G_i=\epsilon_{ijk}A^j E^k,
\end{equation}
which can be viewed as the Gauss law in $d=0$ space dimensions.

Now consider a representation of the canonical commutation relations
$[\hat{A}_j,\hat{E}^k]=i\delta_j^k$ on the Hilbert space ${\cal
H}:=L_2(G,d\mu_H(g))$ where $g=\exp(A_i\tau_i)$
is the ``holonomy" of $A$ and $\tau_i$ are the generators of $su(2)$.

Consider the map $(K,E)\to (K',E') = (\iota K,E/\iota)$.  Under this
canonical transformation the Hamiltonian scales by $H=E^i
E^i/2=\iota^2 E'_i E'_i/2$.  The spectrum of the Hamiltonian (Casimir
of $SU(2)$) is discrete; it is given by $\lambda_n =
1/2(n/2)[(n/2)+1]$, where $n$ is a positive integer.  But in the
scaled variables the spectrum of the Hamiltonian changes to $\lambda_n
= \iota^{2}/2 (n/2)[(n/2)+1]$.  Thus, we have a one parameter
quantization ambiguity in the theory.

Of course, the choice we have made of the observable algebra for the
quantization is a bit strange: it is only justified by the analogy
with gravity.  A more conventional quantization would not lead to any such
quantization ambiguity.  This shows how the $\iota$ parameter is
intimately linked with the affine structure of the configuration space
and with the choice of the holonomies as basic operators in quantum
gravity.

\section{Conclusions}

In the loop representation approach to quantum gauge theories,
one does not gauge fix the theory prior to quantization, but rather
maintains the geometrical structure of the gauge theory explicit in the
quantum theory.  In particular, one works on the group rather than on the
algebra. The quantization is based on the physical assumption that
the Wilson loops, or the ``Faraday lines'' of the theory are the
physical elementary quantum excitations, and thus correspond to finite norm
states. Equivalently, the holonomy operator is well-defined.  If there
is more than one connection ($A$ and $\Gamma$) that can be defined on
the phase space, and which transform in the same way, then one can
construct a $\iota$ scaled connection ($A_\iota$) by interpolating
between distinct connections.  Then, the assumption that the
elementary physical excitations of the theory are the Wilson loops of
$A_\iota$ turns out to be physically distinct for different values
of $\iota$.

This is manifested in the dependence of some physical spectra upon
$\iota$.  More precisely, what happens in gravity is that the metric
information is in the conjugate variable $E$.  Being conjugate to the
connection, $E$ is given in the quantum theory by derivative operators
acting on functions over the group.  Geometrical quantities which
are functions of $E$ turn out to be elliptic operators over the group
manifold.  Hence their discrete spectrum.  But these elliptic
operators have non-vanishing scaling dimension with respect to the
affine scaling of the connection.  Therefore, the $\iota$
quantization ambiguity shows up in the spectrum of the elliptic
geometric operators.

The resulting quantization ambiguity, which we have denoted here as
Immirzi ambiguity, affects the operators with a discrete spectrum that
scale with $\iota$.  A free parameter $\iota$ appears in the loop
quantization of general relativity, where it affects the scale of the
discreteness of space, and in the loop quantization of Maxwell theory,
where it has been suggested that it might be related to charge
quantization \cite{k}.  Its origin is not tied to the infinite
dimensionality of the phase space, nor (at least to a first analysis)
to the existence of inequivalent representations of the observables
algebra.

Finally, the indeterminacy is given by a single parameter, and
therefore it does not reduce the predictive power of the theory more
than, say, $\lambda_{qcd}$ in quantum cromodynamics, or the string
constant in string theory.  Notice in this regard, that also in
perturbative string theory there are two independent length scales:
string tension and Planck constant.  Similarly, there are two length
scales in quantum gravity: the Planck constant $l_{P} = \sqrt{\hbar
G/c^{3}}$ and the quantum of area $A_{0} = 8 \sqrt{3} \pi \iota
l_P^2$.  Unless some non yet understood requirement fixes the value of
the Immirzi parameter, these two length scales are independent.

\section*{Acknowledgments}

We thank Giorgio Immirzi, Jos\`e Antonio Zapata, Alejandro Corichi, Kirill
Krasnov, Abhay Ashtekar and Don Marolf for useful discussions.  This
work was supported by DOE-Grant DE-FG02-94ER25228, by NSF Grants
PHY-5-3840400, PHY-9515506, PHY95-14240 and by the Eberly research fund
of PSU.

redpajama_set_name: RedPajamaArXiv


text:
Thread starter vic
crs1026
I'm a little perplexed as to why they would pour a headwall rather than just extend the golf-tee style guideway south over Wallace. Perhaps they need a span over the roadway that is longer than the pre-poured concrete method will permit and/or heavier than the round pillars can support..
To my mind, the Wallace crossing is the most critical bit of the streetscape along the guideway and deserved the most attention to creative design. So far I'm not impressed with the result….. feels claustrophobic, creates walls and a bit like the underside of the Gardiner. Maybe it's too soon to judge.
- Paul
Reactions: Patch, KevinT and vic
ProjectEnd
It is quite low, unfortunately. I'll get a pic when I can, but the bit they were pouring above was maybe 2m off the ground? It could be that the steel torques against the concrete in a way that the golf tees can't handle. It's steel to supported earth guideway up past the North Toronto too. The Paton Road underpass is super low as well.
innsertnamehere
is the plan to regrade Wallace a bit to improve vertical clearances? It definitely does a bit of a "hump" upwards a bit as it crosses the tracks from what I recall, I imagine it wouldn't be too challenging to get it to "hump" downwards a bit instead.
Reactions: KevinT
crs1026 said:
renderings indicate a steel span over Wallace, and my guess is it's to improve clearance heights for the road. You can see the height differential the steel span provides over the concrete girders in the rendering below:
Reactions: WindexBoi, fanoftoronto, Northern Light and 3 others
I notice that (old) rendering at least uses pillars instead of a solid wall on the north side. Sigh.
[The bizarre steel fencing in the rendering is another issue I will ignore]
Reactions: Towered
^That render does seem to suggest that the steel span gives more vertical clearance than the concrete span north of it does. Maybe that's part of the reason.
I hope that the span being poured does retain the H shape so there is an opening in its middle.
Reactions: KevinT and vic
vic said:
The pour going on right now mimics that rendering. The formwork is more extensive than the finished product.
It does.
Reactions: DirectionNorth, vic, KevinT and 2 others
Reactions: interchange42, kamira51, Undead and 7 others
Krypto98
KevinT said:
I suppose in theory they could drive it into the Mac yard and loop it there too. That would also be interesting...
Yes but macyard is rule 105 territory, plus freight and remote control locomotives would probably get priority
IRT_BMT_IND said:
The Newmarket sub used to have block signals (at least, not sure if full CTC) to at least Gravenhurst until sometime in the early 2010s. The signals can clearly be seen on old Google Street View imagery of the ONR station in Gravenhurst, and a decommissioned signal (the head is turned away from the track) can clearly be seen from the southbound lanes on Highway 11 just outside Gravenhurst. I assume the signals were decommissioned at least partly due to the elimination of the Northlander, I think there's only one scheduled through train on this line in each direction (there might still be one or two switchers on parts of it too) so I'm not even sure how common meets are anymore.
On my training runs to North bay meets it was usually timed so that the northbound met the southbound at Brechin Siding... on the Bala sub the signal masts are still there but turned and off now.. there is also a switcher at Huntsville but it's a small multitrack yard there
Krypto98 said:
I did say 'in theory'. There's no way I would expect CN to agree to rearrange everything in their yard and halt operations to let VIA pull off that loop a few times a week.
ShonTron
T3G said:
Yeah, I think as far as introductions to Toronto go, you can't beat the Don Valley. Easily the most picturesque part of the city.
I can think of far worse rail corridors to introduce tourists to Toronto (the Galt subdivision which the Milton GO line runs on, through Mississauga, is the bleakest rail line I have ever had the misfortune of clapping my eyes on).
The CN Uxbridge Sub (Stouffville Line) isn't great either, but at least you get to enter central Toronto with great views.
The Bala Sub is great, especially south of York Mills Road, and the Kingston Sub as it hugs Lake Ontario near Rouge Hill Station is pretty sweet.
The Weston Sub (Kitchener Line) has decent views in places, though the Weston, Junction, and Strachan underpasses aren't amazing.
I concur, the Milton Line is the least visually appealing, with the Humber River Bridge being the only real highlight. It doesn't even cross the Credit River at a scenic location.
Reactions: T3G
ShonTron said:
The Weston Sub (Kitchener Line) has decent views in places, though the king underpasses aren't amazing..
I always cringe when I take the UP home from Pearson……. what kind of first impression do first-time visitors get ? (It gets better closer in to the city).
But hey, the first couple miles on RER out of Charles de Gaulle aren't exactly the Champs Elysees, either.
Reactions: interchange42 and Undead
The first minute of the ride from Pearson offers a great view. I can't think of a major international airport - apart from HKIA or maybe SFO - that does have a great view by rail from the terminal, as you're in industrial areas or fields. Have you taken a train from EWR?
Once you get to the Humber River, the view to the city is pretty good again, especially through Mount Dennis.
Reactions: PL1
drum118
Its a lot better than places you find in Europe or the US.
Due Time restriction, visit my site https://www.flickr.com/photos/drum118/ to see updated photos of projects shot the last few weeks since I don't have the time to post them to various threads.
See my videos on YouTube https://www.youtube.com/user/Transitdrum118

redpajama_set_name: RedPajamaCommonCrawl


text:
is a railway station in Miyako, Fukuoka Prefecture, Japan. It is on the Tagawa Line, operated by the Heisei Chikuhō Railway. Trains arrive roughly every 30 minutes.

On 1 April 2009, an advertising agency headquartered in Tokyo, , acquired naming rights to the station. Therefore, the station is alternatively known as .

Platforms

External links
Sakiyama Station (Heisei Chikuhō Railway website)

References

Railway stations in Fukuoka Prefecture
Railway stations in Japan opened in 1956
Heisei Chikuhō Railway Tagawa Line

redpajama_set_name: RedPajamaWikipedia


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Something as simple as an improperly installed windshield can affect the structural integrity of your car. That's why at NACCO of Illinois, our trained technicians don't cut any corners and go beyond the industry standard to make sure your windshield is installed perfectly. We'll bring a factory quality windshield to you, anywhere in Orland Park, IL or the southern suburban area and have an experienced glass specialist install it.
The windshield is a significant part of the structural integrity of your vehicle, so when companies cut corners on the installation, you could face serious consequences in the event of a head-on or rollover accident. A windshield prevents the roof from crushing during a rollover accident. Also, anytime the passenger side airbag is deployed with an improperly installed windshield, it can pop out the windshield instead of protecting your passenger. That's why it's so important that a trained and experienced installer from NACCO handles your windshield replacement.
We use only premium, original quality equipment to ensure a better fit, finish and clarity. Many windshield installers simply cut out the glass then glue the windshield onto the old glue which can lead to leakage, rust, wind noise, and possible structural issues. Not at NACCO of Illinois. Our experienced installers go the extra mile that other installers don't. It begins with complete glass and glue removal. Then, we apply a primer and a rust inhibitor to make sure you won't have any rust damage years down the road. Next we install a brand new replacement seal to ensure that your windshield is mounted uniformly to your vehicle. Call the installer that takes your safety as seriously as you do.
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Even though Master Data Management has in recent years become a focus point of the IT industry in large corporate companies, a surprisingly low number of companies actually implement and follow proper Master Data Governance. Different Master Data cleansing projects are often executed and no or little Master Data Management practices are instituted to keep the data clean. Consulting in Master Data Governance is therefore about the creation of a corporate culture in which the importance and goals of Master Data Governance is well defined and understood, and therefore practiced in a goal orientated manner.


Why use Treestation's woodfuels (firewood and woodchip)?
We offer locally produced firewood from sustainably sourced local timber, at affordable prices. Everything we do is driven by our ethics, from our day-to-day operations to our choice of bank and energy provider.
By buying TreeStation products, either directly or through our Greater Manchester network of retail outlets, you are supporting a local and genuinely ethical project. We trust that the following reasons, combined with the testimonials of satisfied customers, will encourage you to choose the TreeStation as your supplier.
Our carefully selected feedstock is handled by our skilled and trained staff, using only well-maintained and fit-for-purpose specialist equipment. This, combined with our strict policies, appropriate seasoning duration, and meticulous production process, ensures the consistent high quality of our products.
Our supervisory staff have been trained on the Ignite accredited course "Woodfuel production and supply". Our biomass chip is Woodsure Plus accredited, for an independent guarantee of quality, sustainability and traceability. We also have a strict policy of not allowing waste wood or non-virgin wood on our site, to avoid any contamination.
If you are a new customer, please have a look at our customers' testimonials for the assurance of a high grade product.
Whilst we primarily use arisings from treework as feedstock; we have established links with the Forestry Commission, Local Authorities and other land owners to ensure security of supply when arisings availability is not sufficient. Thanks to our unique integration of treework contracting, woodland management, arisings handling, products manufacture and supply; we are less dependent on external factors and agents to set our supply and costs. You can rely on us to heat your home during long winters and unexpected cold snaps.
Because we are a not-for-profit organisation and we use our own resources to undertake treework contracting, timber extraction and haulage, firewood production and supply, we are able to offer competitive prices.
We are strongly committed to our ethical values. They are the reason we are in business, and we stick to them in day-to-day practice. We are a not-for-profit co-operative (BenCom), and believe we can make a difference to the local community and global environment by successfully running the TreeStation.
We offer bespoke solutions to meet the needs of our customers, in terms of products specifications, delivery options and contract types/durations. We also offer rapid response and personalised advice.
Our skilled and reliable team works to high professional standards, and undertakes each stage of our process with our customers' satisfaction in mind. We are approachable and happy to discuss any concern, question or comment you may have.
As a Society for the Benefit of the Community, the Treestation is owned and controlled by its members, most of which are also customers, so it's fair to say that our focus on customer service literally goes to the very heart of the business. We have systems in place to ensure that concerns or complaints are dealt with honestly and quickly, and that positive feedback can be passed on to those who have generated it. We strive for customer service excellence at all times.
The environmental, social and economic issues associated with fossil fuel dependence include climate change, degradation of ecosystems & landscapes, poor air quality & health problems, resource conflicts, displacement of populations, rising sea levels, water shortages, insecurity of supply and inevitable rises in fuel costs. Recently, desperate efforts to extract ever more inaccessible fossil fuels(deep-water drilling, tar sands extraction, fracking, and drilling in the Arctic) have demonstrated the inherently damaging and unsustainable nature of our reliance on fossil fuels, and the need for alternative forms of energy.
Carbon-lean: because over its lifetime each tree absorbs the same amount of carbon dioxide as it releases when burned. If sustainably sourced, trees are re-planted to replace those felled; therefore ensuring the same amount of carbon keeps being sequestrated in the forest, creating a closed-loop carbon cycle. It is only the small amounts of fossil fuel used in harvesting, hauling and processing that makes it carbon 'lean' rather than carbon neutral  . See the carbon emission comparison graph here – firewood and woodchip have a similar footprint as they require the same level of processing.
Renewable: if woodlands are managed appropriately (e.g. trees planted at a similar/higher rate than they are harvested), wood is an abundant resource available locally on an indefinite basis. There is extensive capacity for woodland stocks to support a sustainable supply of woodfuel in the UK  .
Clean: Sulphur Dioxide emissions (responsible for acid rain) from woodfuel boilers are much lower than from fossil fuels; emissions of other air pollutants such as harmful small particles (PM10 and PM2.5) and Nitrogen Dioxide (NO2) are lower than coal, equivalent to oil and only slightly higher than gas fired boilers  .
Efficient: Modern biomass combustion systems are highly sophisticated, achieving up to 95% efficiency  .
Beneficial to woodlands: Research by the Forestry Commission amongst others indicates that much of the UK's woodland is under-managed or not managed at all. Contrary to popular belief, such woodlands are often less valuable in terms of tree health and overall biodiversity  . The use of woodfuel provides an economic incentive to manage existing woodlands and create new ones, improving habitats and biodiversity, reducing soil erosion andflood risk.
Simple and non resource-intensive production process: sustainably managed woodlands require virtually no pesticides or fertilisers, and the harvesting and transformation process to woodchip or firewood is relatively low-tech, has a small footprint, and doesn't require much external resources such as water, chemicals, etc. The main inputs are assets such as machinery, and the energy required to power them.
Local economy: a thriving woodfuels market stimulates the local economy with jobs as diverse as woodland management, haulage, treework and retail. It also supports the rural economy and small scale local businesses.
Global economy: unlike energy crops used for biodiesel production, wood requires virtually no toxic pesticides and fertilisers. It also doesn't compete with food crops and therefore doesn't impact the price of food on global markets.
Affordability: woodfuels are a cheap alternative to fossil fuels. The expenditure of the initial combustion system is offset by the fuel affordability and government /products/rhi/.
Security of supply: timber can be produced locally anywhere in the UK, contributing to the country's security of supply and self reliance.
Standardised products: international standards and accreditation schemes are in place to guarantee suitably high quality to provide trouble-free boiler operation.
Forestry residues and arboricultural arisings not used for energy or some other application will usually rot. This will generate CO2 in any case, and may also produce methane (CH4), a greenhouse gas 23 times more potent that CO2. Some figures suggest that over 68% of this material is simply going to waste in the UK  . The TreeStation's unique sourcing strategy converts these arisings into useful products, with an additional positive impact on climate change.
Biomass is defined as "biological material derived from living, or recently living organisms". As trees grow, carbon is absorbed from the atmosphere as carbon dioxide (CO2) by photosynthesis, using water, energy from the sun, and nutrients from the soil and incorporated into the wood material.
Biomass fuels include virgin wood (such as the TreeStation woodchip and firewood), energy crops (methanol and biodiesel), agricultural residues, food waste, industrial waste and co-products.
Woodchip can be used as a substitute for fossil fuels to provide heat, hot water and power (CHP); and woodchip boilers are available for all scales of operation, from 15kW domestic to multi-MW plants.
Woodchip is a convenient form of woodfuel, allowing efficient storage and automated handling and feeding. It also has a large surface-area-to-volume ratio, allowing efficient combustion. The production process is simple and low energy, making woodchip both cheap and carbon-lean.
Modern boilers are fully automated – controlling combustion parameters and fuel transfer – clean, and easy to operate. The installations require the fuel to be of stable and specified quality, to ensure optimum efficiency & uninterrupted operation.
Can I trust the biomass chip technology?
Wood chip is widely used across Europe, and has seen a sharp increase in the UK with the introduction of the RHI.
It is a tried and tested technology, with accreditation schemes and international standards.
The applications include homes, district heating, schools & universities, offices, hospitals, care homes, swimming pools, leisure centres and industrial processes, both for heating or Combined Heat and Power (CHP).
Woodchip has all the environmental, social and economic benefits of using woodfuels, as described above.
It is commonly agreed that despite a higher initial investment, biomass installations have a shorter payback period due to their relatively lower running costs compared to fossil fuel systems. The Renewable Heat Incentive further reduces the payback period, by providing a 12% return on the additional investment.
This is because over its lifetime each tree absorbs the same amount of carbon dioxide as it releases when burned. It is only the small amounts of fossil fuel used in harvesting, hauling and processing that makes it carbon 'lean' rather than carbon-neutral. The illustration below shows a comparison of carbon emissions for various fuels, including the embedded carbon (i.e. released during the production).
Source and assumptions in footnote .
If you are considering a biomass boiler installation, please look at our new installations and RHI & financial support sections, and get in touch to discuss storage design in order to secure Whole Life Cost savings.
 (^) Data available from the Biomass Energy Centre website: "Carbon emissions of different fuels".
We can also offer contract chipping where a client has their own supply of feedstock.
We have developed a unique sourcing strategy based on our ethical principles. This guarantees our woodchip is free from contamination and is as sustainable as it gets.
Our chip is predominantly derived from timber which is not usable for sawn timber nor firewood but is otherwise of good quality for chip production. We use a mixture of hardwood and conifer species, and avoid excessive concentrations of Poplar, Willow, Western Red Cedar or Lawson's Cypress. Some of these species produce more dust, have stringy bark, or have a higher chlorine content which in the long term can corrode the boiler.
The wood arisings are segregated according to shape and size, stacked and covered. They air-dry for several months until they reach the appropriate moisture content and are ready for chipping. We only air-dry our wood, because the energy used in kilning the timber reduces the positive environmental impact of using wood.
The TreeStation's woodchip is produced using a well-maintained purpose-built biomass chipper. Our Heizohack 14-800K was designed by the German company Heizomat, whose core business is manufacturing biomass boilers. The changeable screen allows the production of different particle size. It is powered by a 220hp forestry tractor with roof-mounted crane, which is used to feed the chipper.
Our chip is stored undercover for a short period of time only, directly in hook lift bins to avoid any contamination from being re-handled on the ground.
We use quality testing as a mean of checking individual batches' quality, recording an audit trail and for calculating the energy content and cost of each batch delivered. Our in-house testing capabilities and equipment form an integral part of our production process and its on-going fine-tuning.
We also analyse the particle distribution on a regular basis. This factor is relatively stable, due to our screen-fitted chipper. Where required, we will also hold a duplicate sample for as long as it takes for the batch to be used, to allow retrospective analysis of chip characteristics if necessary.
We take great care at every stage of our production process, to ensure the consistent high quality of our firewood and the safety of our staff.
At the TreeStation we have developed a unique sourcing strategy based on our ethical principles. This guarantees our firewood is free from contamination and as sustainable as it gets.
Our standard logs are made of a blend of high quality hardwoods, excluding Willow and Poplar. For specific requirements, such as softwood, we only use species with good burning properties, (e.g. Larch). Our kindling is made of softwood and Poplar.
The wood arisings are segregated according to shape, size and species, and are then stacked to begin air drying. The timber is cut and split into logs by trained operators with a semi-automated firewood processor. Logs are stored in covered stacked cages – a system combining fast air-drying with space-efficiency. Once they reach the appropriate moisture content (less than 25%), logs are netted by hand and stored undercover.
Kindling is produced in our specialised kindling machine from carefully selected and dried rings of timber. The kindling is netted by hand straight from the machine and stored undercover.
We only air-dry our wood, because the embedded energy used in the kilns offsets the positive environmental impact of using wood.
We use ongoing quality testing as a mean of checking our products quality and recording an audit trail. Our in-house testing capabilities and equipment form an integral part of our production process and its constant fine-tuning.
We use visual assessment during hand bagging to check size, shape, and absence of contamination, and a portable digital moisture meter to check the moisture content.
I've been ordering logs and kindling from TreeStation for a few years now. The quality and price are good, as are the eco credentials, so I keep coming back. What makes a big difference though is the helpful and friendly customer service from Hannah and her team. I'm a happy customer.


Mobile phone operator 3 has appointed former BT and Volkswagen marketer Alan Doyle as integrated communications director. He will head the team responsible for branding and through-the-line communications.
Doyle's appointment is part of a restructure of the company's marketing department being led by marketing director John Penberthy-Smith. The integrated communications director role is new and Doyle will report to Penberthy-Smith.
Doyle joins 3 from brand and marketing consultancy Egghead, where he was managing director. He is also a former general manager of luxury cars at Volkswagen Group and has been head of consumer marketing at Yellow Pages and BT.
Last month, Hutchison marketer Fergal Walker was moved to the new role of director of handsets and Stephen Ford was brought in from 3 Australia as director of customer propositions as part of the restructure. Penberthy-Smith is also looking for a director of product management and a director of base management to complete his new team.
3 handed its £39m advertising account to Euro RSCG at the start of May following a pitch against Hurrell & Dawson and Glue.
PHD co-founder Jonathan Durden is to enter the Big Brother house tonight. Durden, who left the Omnicom-owned media agency in May this year, will appear on the controversial Channel 4 reality show as a contestant.


text:
Interesting facts about Wyoming
Wyoming is a state in the mountain region of the western United States.
It is bordered on the north by Montana, on the east by South Dakota and Nebraska, on the south by Colorado, on the southwest by Utah, and on the west by Idaho and Montana.
As of February 2019, the population of Wyoming was estimated to be about 580,000 people. It is the 50th most populous state in the United States.
Wyoming is the 10th largest state in the United States in terms of total area with 253,600 square kilometers (97,914 square miles).
Cheyenne is the capital and most populous city of Wyoming. Lying near the southeast corner of the state, Cheyenne is one of the least centrally located state capitals in the nation.
Essentially, Wyoming is one big plateau broken by many towering mountain ranges. Wyoming is a state where the Great Plains meets the Rocky Mountains.
The eastern part of Wyoming is influenced by the Great Plains, part of the interior plain that stretches from Canada through the United States to Mexico.
Sweeping across most of the state of Wyoming from the north to the south is a series of rugged Rocky Mountain ranges.
Gannett Peak is the highest mountain peak in the US state of Wyoming at 4,210 meters (13,810 feet) above sea level.
Wyoming is one of only three states (along with Colorado and Utah) to have borders along only straight latitudinal and longitudinal lines, rather than being defined by natural landmarks.
The state has 7 national parks and 12 state parks.
Yellowstone National Park is a national park located in Wyoming, Montana, and Idaho. It is the world's first and oldest national park and is one of the most awe-inspiring wilderness areas on the planet. The park was established by the U.S. Congress and signed into law by President Ulysses S. Grant on March 1, 1872. The park is known for its wildlife and its many geothermal features, especially Old Faithful geyser, one of its most popular features.
Grand Teton National Park is a national park in northwestern Wyoming. It is only 16 kilometers (10 miles) south of Yellowstone National Park. At approximately 130,000 hectares (310,000 acres), the park includes the major peaks of the 64 kilometers (40 miles) long Teton Range as well as most of the northern sections of the valley known as Jackson Hole.
Devils Tower is a laccolithic butte composed of igneous rock in the Bear Lodge Mountains (part of the Black Hills) near Hulett and Sundance in Crook County, northeastern Wyoming. It rises 386 meters (1,267 feet) above the Belle Fourche River, standing 265 meters (867 feet) from summit to base. The summit is 1,559 meters (5,112 feet) above sea level.
Built around the world's largest single mineral hot spring, Hot Springs State Park is a great place to stop for a relaxing soak. The steamy mineral water gushing from Big Spring is channeled into bathhouses and kept at a constant 40°C (104˚F). The petroglyph site at Legend Rock, some 40 kilometers (25 miles) away from Big Spring, is also part of the park
Tucked in a sprawling valley at the foot of the spectacular Teton Mountains, Jackson exudes the spirit of the Wild West. Rustic wooden buildings and boardwalks, quaint shops, galleries, and restaurants, and a town square framed by elk-horn arches add to the charm of this charismatic town. Jackson is also the gateway to beautiful Grand Teton National Park and a popular stop on the way to Yellowstone.
Several Native American groups originally inhabited the region now known as Wyoming. The Crow, Arapaho, Lakota, and Shoshone were but a few of the original inhabitants white explorers encountered when they first visited the region.
What is now southwestern Wyoming became a part of the Spanish Empire and later Mexican territory of Alta California, until it was ceded to the United States in 1848 at the end of the Mexican–American War.
The region acquired the name Wyoming when a bill was introduced to the U.S. Congress in 1865 to provide a "temporary government for the territory of Wyoming."
Wyoming became the 44th state to join the union in 1890.
Wyoming was the first US state to allow women to vote–an achievement that represented one of the early victoriesof the American women's suffrage movement.
On September 2, 1885, a group of white coal miners attacked and killed 28 of their Chinese coworkers,wounded 15 others, and torched 79 of their homes in Rock Springs. None of the perpetrators—who had been angered by the refusal of Chinese miners to join in a strike for better wages, and by the Union Pacific Coal Company's decision to allow the Chinese to work a lucrative part of the mine—were ever convicted for the brutal massacre.
In 1949, a massive blizzard blanketed Wyoming, killing 17 people, 55,000 cattle and 105,000 sheep.
Interesting facts about Angola
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Interesting facts about Venezuela
Interesting facts about Lithuania


text:
Acropolis of Athens
Acropolis in translation means "fortress, upper city" – this is how the Greeks called the fortresses built on the hills.From the hill, an excellent view of the surroundings opened up, the patrolmen noticed the enemy from afar. In the acropolis, the rulers kept valuables and built temples dedicated to the gods, where they offered prayers and made sacrifices.
History of the Acropolis
The Acropolis of Athens is a 156-meter high rocky hill with a gentle summit, on which a complex of temples, sanctuaries, sculptures and architectural structures has been erected. The Parthenon, the Erechtheion, the temples of Nika Apteros and Propylaea were erected here. The architectural ensemble includes 20 structures. The museum complex of the Acropolis of Athens is a testament to the amazing taste of Greek sculptors, painters, sculptors and architects.
The first buildings on the sacred mountain in Athens appeared long before the construction of temples. In the 15th century BC. here was the residence of the king , the construction of the acropolis did not stop even later. In 480 BC. the Persians destroyed the magnificent temple of Gekampedon, dedicated to the goddess Athena.
New construction of the Acropolis began in 447, during the heyday of the Athenian state under King Pericles. The architectural ensemble of the Acropolis was created by the greatest sculptor of Greece – Phidias, who created two statues of Athena to decorate the Acropolis: Promachos (Warrior) and Parthenos (Virgin).
In the middle of the 2nd century BC. Greece was invaded by the Roman Republic, ancient temples were turned into Christian churches. Later, the Acropolis became a Turkish fortress, and the Turks dismantled the temples to build bastions. The Venetians, holding the Turkish garrison in ambush, blew up the Parthenon, destroying the temple. With the spread of Christianity, Athens lost its influence, philosophical schools were closed, philosophers and rhetoricians were driven out.
Buildings of the Acropolis
An architectural complex of fortified ancient Greek buildings surrounded by a fence rises on a city hill in Athens. The structures of the Acropolis, built in harmony with nature, took 50 years to create. The marble walls of temples and sanctuaries represent the long-awaited victory of the Greeks in the war against the Persians. A paved road led to the top of the Acropolis, laid out along a gentle slope.
The Parthenon is the main temple of the Acropolis , dedicated to the patroness of Attica, the goddess Athena. The temple was built in the 5th century BC. e. the architect Callicrates, and the architect Phidias decorated the building with friezes. The most beautiful structure of the architectural complex is made of white marble, which in the sun takes on a golden yellow hue.
The Parthenon was erected as the new sanctuary of Athena. The building stood on a stylobate (hill), but the grandiose temple does not overwhelm the viewer when looking at it. Straight lines of a building at a distance are perceived by the human eye as slightly concave, so the architect skillfully uses the slope of the columns so that an ideally slender building rises in front of his eyes.
In the contours of the Parthenon – design findings of the architect:
The steps of the stylobate rise slightly towards the center so that the floor does not appear bent from a distance.
The corner columns are tilted towards the middle, and the middle two towards the corners to visually appear straight.
A slight thickening, carved in the middle of the columns, from afar emphasizes the slenderness and airiness of the building.
The corner columns are thicker in diameter than the others, and are not round in cross-section.
The Parthenon, with its white marble columns and walls topped with sculptural friezes and pediments, looked festive and elegant. The pediments, painted in deep red and blue friezes, surprisingly set off the sculptures of white marble. Outside, the temple was decorated with a frieze of fine work, glorifying the Athenian people on the day of the celebration of the Great Panathenae. Cheerful beautiful people: both elders, and courageous young men, and shy girls, go to worship the goddess Athena, carrying generous gifts.
The main pediment of the temple was decorated with an architectural composition about the birth of the goddess Athena from the head of Zeus. On the western pediment there is a composition about the dispute between Athena and Poseidon for power over Attica.
Inside, the temple is divided into two unequal parts. The main one was dominated by a 12-meter statue of Athena , made of gold and ivory. In the eye sockets of the goddess there are precious stones, on the chest, in the center of the shell, the deadly ivory head of the Gorgon Medusa. Athena's vestments were covered with gold plates.
Erechtheion
To the north of the Parthenon rises the Erechtheion temple, which is not inferior in beauty and grace to the Parthenon. The sanctuary, named after the most ancient king and hero of Athens, Erechtheus, according to legend, was built in the 5th century BC. at the place where the powerful gods Athena and Poseidon argued when they fought for power over Attica.
The disputants decided: one of the gods will be the ruler who will make the desired gift to the inhabitants of the cities.
Poseidon threw his club up the mountain, and sea water splashed from there. In the place where Athena threw the spear, an olive grew. The residents liked the juicy fruits, and Athena, the patroness of Attica, was awarded the victory in the dispute. The temple was dedicated to Athena, Poseidon, and the Athenian king.
Sanctuary of Artemis
The Sanctuary of Artemis is a long corridor lined with majestic columns. Artemis is the goddess who patronizes all women in Athens preparing for the birth of a child.
Temple of Nike in the Acropolis
Nika is the goddess of victory. The simple and graceful temple of Nike was built in honor of the victory in the war with the Persians in 449 BC. The temple stands on a three-step pedestal on a rock ledge above Athens, so the architect Kallikrates fortified the slope of the sanctuary dedicated to the victorious Athena with an 8-meter wall. The temple is decorated with majestic monolithic columns and a frieze depicting the victory of the Athenians over the Persians at Plataea.
From the site of the Sanctuary of Artemis, a view of the city and the Saronic Gulf, washing the coast of Attica, opens. An ancient myth tells that here King Aegeus was waiting for white sails to appear in the distance, announcing the return of Theseus' son.
The father sent his son to the island of Crete to kill the Minotaur – a monster with the body of a man and the head of a bull.
Theseus, returning with a victory, forgot about the promise made to his father, to change the black sails to white. Aegeus, seeing the black sails, decided that his son was dead, threw himself down the cliff and crashed.
Dionysus Theater
On the southeastern slope of the hill is the theater dedicated to the god Dionysus, the oldest theater in the world. Originally built of wood, 325 BC the theater was reconstructed with benches and a stage made of marble.
The stone seats were arranged in 67 rows so that the semicircular auditorium could accommodate 17,000 spectators – half of the Athenian citizens. Marble chairs in the first row are for priests and officials, as indicated by the inscriptions on the chairs. In the center, on a dais, there is a chair for the priest of the god Dionysus.
The actors, choir and spectators were located in the open air, the theatrical action took place in natural light. In the II millennium BC. a portico was added to the theater, where spectators took refuge in the sweltering heat. The tragedies of the Greek playwrights were staged on the stage: Euripides, Aeschylus, Sophocles, Aristophanes, and every Athenian could take part in the production.
Propylaea of the Acropolis
The Propylaea is the main entrance to the Acropolis, the front gate, built in the form of snow-white columns under the roof. The gate was erected in 437 by the architect Mnesikla. To the Propylaea, the ancient Greeks climbed a huge stone staircase.
The central part of the Propylaea is adjoined by side wings, built of the same marble as the Parthenon. In the north wing there is a portico with a vast rectangular hall, where an art gallery – Pinakothek – with works of the greatest Greek artists was located.
Passing through the gate, the visitor met on the way a 10-meter bronze statue of Athena on a stone pedestal. In sunny weather, the golden spear of the goddess indicated with a wonderful brilliance the way for the captains of the ships to the pier in Athens.
Behind the gates is the Sacred Road, along which the participants of the festival in honor of the divine patroness of Athens marched. The procession, which began in the city, passed through the Propylaea and headed to the Parthenon, and then to the Erechtheion.
About the Acropolis Museum
The Acropolis Museum Complex is rightfully ranked among the masterpieces of world art. The monument of ancient architecture is included in the UNESCO World Heritage List, which is visited annually by 2 million tourists from all over the world.
Recently, another gem of the museum, the Moskhofor exposition, was put on display for tourists . In the center of the composition is a young man bringing a golden calf to the goddess Athena. Around – graceful sophisticated figures of young girls.
The sculpture is made so realistically that the hairstyles and facial features of the girls, the folds on the clothes look as if they are alive. On rectangular friezes – images of the Olympian gods, scenes from ancient Greek mythology, statues of the Caryatids, ancient priestesses.
The Acropolis of Athens is especially beautiful at night, bright and contrasting illumination transforms the ensemble, around which the Greek youth spend their time with pleasure.
Public Transport in Athens
Hotels in Athens with views