en>Yohansama at 22:13, 9 January 2015

2015-01-09T22:13:02Z

← Older revision		Revision as of 00:13, 10 January 2015
Line 1:		Line 1:
	~~[http://search~~.~~Usa.gov/search?query=Adrianne+Swoboda Adrianne Swoboda] is what the lady~~'~~s husband loves to call her though she has no plans to really like being names like that. After being out of your man~~'~~s job for years the person became an order worker. What~~ my friend loves doing is to visit to karaoke but the woman with thinking on [http://www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=starting&gs_l=news starting] a new generation. Massachusetts will where he's always been living. She is running and ~~trying to keep a blog here: http://circuspartypanama~~.~~com~~<br><br>~~Look into my web site :~~: [http://~~circuspartypanama~~.com ~~clash of clans Hack Cydia~~]		I'm Trena and I live in a seaside city in northern Sweden, Matfors. I'm 31 and I'm will soon finish my study at Modern Languages and Classics.<br><br>My webpage: [http://www.eliteadomicile.com/ activité rémunérée à domicile]

en>Boghog: Reverted 2 edits by 147.197.17.60 (talk): Test edits? (TW)

2014-03-03T12:55:44Z

Reverted 2 edits by 147.197.17.60 (talk): Test edits? (TW)

← Older revision		Revision as of 14:55, 3 March 2014
Line 1:		Line 1:
	~~{{Quantum mechanics\|cTopic=~~[~~[Interpretation of quantum mechanics\|Interpretations]]}}~~		[http://search.Usa.gov/search?query=Adrianne+Swoboda Adrianne Swoboda] is what the lady's husband loves to call her though she has no plans to really like being names like that. After being out of your man's job for years the person became an order worker. What my friend loves doing is to visit to karaoke but the woman with thinking on [http://www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=starting&gs_l=news starting] a new generation. Massachusetts will where he's always been living. She is running and trying to keep a blog here: http://circuspartypanama.com<br><br>Look into my web site :: [http://circuspartypanama.com clash of clans Hack Cydia]
	In [[quantum mechanics]], the '''consistent histories''' approach is intended to give a modern [[interpretation of quantum mechanics]], generalising the conventional [[Copenhagen interpretation]] and providing a natural interpretation of [[quantum cosmology]].<ref>[[Fay Dowker \|F. Dowker]] and A. Kent, "Properties of Consistent Histories", Phys. Rev. Lett. 75, 3038 - 3041 (1995)</ref> This interpretation of quantum mechanics is based on a [[consistency]] criterion that then allows probabilities to be assigned to various alternative histories of a system such that the probabilities for each history obey the rules of classical probability while being consistent with the [[Schrödinger equation]]. In contrast to some interpretations of quantum mechanics, particularly the Copenhagen interpretation, the framework does not include "wavefunction collapse" as a relevant description of any physical process, and emphasizes that measurement theory is not a fundamental ingredient of quantum mechanics.

	~~==Histories==~~

	A ''homogeneous history'' <math>H_i</math> (here <math>i</math> labels different histories) is a sequence of [[Proposition]]s <math>P_{i,j}</math> specified at different moments of time <math>t_{i,j}</math> (here <math>j</math> labels the times). We write this as:

	~~<math> H_i = (P_{i,1}, P_{i,2},\ldots,P_{i,n_i}) <~~/~~math>~~

	~~and read it as "the proposition <math>P_{i,1}<~~/~~math> is true at time <math>t_{i,1}</math> ''and then'' the proposition <math>P_{i,2}</math> is true at time <math>t_{i,2}</math> ''and then'' <math>\ldots</math>"~~. ~~The times <math>t_{i,1} < t_{i,2} < \ldots < t_{i,n_i}</math> are strictly ordered and called the ''temporal support'' of the history.~~

	~~''Inhomogeneous histories'' are multiple-time propositions which cannot be represented by a homogeneous history~~. ~~An example is the logical [[logical disjunction\|OR]] of two homogeneous histories: <math>H_i \or H_j<~~/~~math>.~~

	~~These propositions can correspond to any set of questions that include all possibilities.~~
	Examples might be the three propositions meaning "the electron went through the left slit", "the electron went through the right slit" and "the electron didn't go through either slit". One of the aims of the theory is to show that classical questions such as, "where are my keys?~~" are consistent. In this case one might use a large number of propositions each one specifying the location of the keys in some small region of space.~~

	~~Each single-time proposition <math>P_{i,j}</math> can be represented by a [[projection operator~~]~~] <math>\hat{P}_{i,j}</math> acting on~~ the ~~system~~'s ~~Hilbert space (we use "hats"~~ to ~~denote operators). It is then useful~~ to represent homogeneous histories by the time-ordered [[tensor product]] of their single-time projection operators. This is the [[history projection operator]] (HPO) formalism developed by [[Christopher Isham]] and
	~~naturally encodes the logical structure of the history propositions. The homogeneous history <math>H_i</math> is represented by the projection operator~~

	~~<math> \hat{H}_i = \hat{P}_{i,1} \otimes \hat{P}_{i,2} \otimes \cdots \otimes \hat{P}_{i,n_i} </math>~~

	~~This definition can be extended to define projection operators~~ that ~~represent inhomogeneous histories too~~.

	~~==Consistency==~~

	~~An important construction in the consistent histories approach is the '''class operator''' for a homogeneous history:~~

	~~:<math>\hat{C}_{H_i} := T \prod_{j=1}^{n_i} \hat{P}_{i,j}(t_{i,j}) = \hat{P}_{i,1}\hat{P}_{i,2}\cdots \hat{P}_{i,n_i}</math>~~

	The symbol <math>T</math> indicates that the factors in the product are ordered chronologically according to their values of <math>t_{i,j}</math>: the "past" operators with smaller values of <math>t</math> appear on the right side, and the "future" operators with greater values of ~~<math>t</math> appear on the left side.~~
	~~This definition can be extended to inhomogeneous histories as well.~~

	~~Central to the consistent histories is the notion of consistency. A set of histories <math>\{ H_i\}</math> is~~ '~~''consistent''' (or '''strongly consistent''') if~~

	~~:<math>\operatorname{Tr}(\hat{C}_{H_i} \rho \hat{C}^\dagger_{H_j}) = 0</math>~~

	~~for all <math>i \neq j</math>. Here <math>\rho</math> represents the initial [[density matrix]], and the operators are expressed in the [[Heisenberg picture]].~~

	~~The set of histories is '''weakly consistent''' if~~
	~~:<math>\operatorname{Tr}(\hat{C}_{H_i} \rho \hat{C}^\dagger_{H_j}) \approx 0</math>~~

	for ~~all <math>i \neq j</math>.~~

	~~== Probabilities ==~~
	~~If a set of histories is consistent then probabilities can be assigned to them in a consistent way. We postulate that~~ the ~~[[probability]] of history <math>H_i</math> is simply~~

	~~:<math>\operatorname{Pr}(H_i) = \operatorname{Tr}(\hat{C}_{H_i} \rho \hat{C}^\dagger_{H_i})</math>~~

	~~which obeys the [[axioms of probability]] if the histories <math>H_i</math> come from the same (strongly) consistent set.~~

	As an example, this means the probability of "<math>H_i</math> OR <math>H_j</math>" equals the probability of "<math>H_i</math>" plus the probability of "<math>H_j</math>" minus the probability of "<math>H_i</math> AND <math>H_j</math>", and so forth.

	~~==Interpretation==~~

	~~The interpretation based on consistent histories~~ is ~~used in combination with the insights about [[quantum decoherence]].~~
	~~Quantum decoherence implies that irreversible macroscopic phenomena (hence, all classical measurements) render histories automatically consistent, which allows one~~ to ~~recover classical reasoning and "common sense" when applied~~ to the outcomes of these measurements. More precise analysis of decoherence allows (in principle) a quantitative calculation of the boundary between the classical domain and the quantum domain covariance. According to [[Roland Omnès]],<ref name="Omnès1999">{{cite book \|first=Roland \|last=Omnès \|year=1999 \|title=Understanding Quantum Mechanics \|publisher=Princeton University Press \|isbn=978-0-691-00435-8 \|lccn=98042442 \|url=http://~~books~~.google.~~com~~/~~books~~?id=~~8_bnm4qghvkC~~&~~lpg~~=~~PP179~~&pg=~~PA179 \|pages~~=~~179, 257}}</ref>~~
	~~{{blockquote\|[the~~] ~~history approach, although it was initially independent of the Copenhagen approach, is in some sense~~ a more elaborate version of it. It has, of course, the advantage of being more precise, of including classical physics, and of providing an explicit logical framework for indisputable proofs. But, when the Copenhagen interpretation is completed by the modern results about correspondence and decoherence, it essentially amounts to the same physics.

	~~[... There are] three main differences:~~

	~~1. The logical equivalence between an empirical datum, which is a macroscopic phenomenon, and the result of a measurement, which is a quantum property, becomes clearer in the~~ new ~~approach, whereas it remained mostly tacit and questionable in the Copenhagen formulation~~.

	2. ~~There are two apparently distinct notions of probability in the new approach. One~~ is ~~abstract and directed toward logic, whereas the other is empirical and expresses the randomness of measurements. We need to understand their relation~~ and ~~why they coincide with the empirical notion entering into the Copenhagen rules.~~

	3. The main difference lies in the meaning of the reduction rule for ‘wave packet collapse’. In the new approach, the rule is valid but no specific effect on the measured object can be held responsible for it. Decoherence in the measuring device is enough.}}

	~~In order~~ to ~~obtain~~ a ~~complete theory, the formal rules above must be supplemented with a particular [[Hilbert space]] and rules that govern dynamics, for example a [[Hamiltonian (quantum theory)\|Hamiltonian]]~~.

	~~In the opinion of others~~<~~ref~~>~~A. Kent and J. McElwaine ''Quantum Prediction Algorithms'' Phys. Rev. A, 55, 1703--1720 (1997)~~<~~/ref~~> ~~this still does not make a complete theory as no predictions are possible about which set of consistent histories will actually occur. That is the rules of Consistent Histories, the~~ [~~[Hilbert space]], and the Hamiltonian must be supplemented by a set selection rule. However, Griffiths<ref>R. B. Griffiths, ''Consistent Quantum Theory'', Cambridge University Press, 2003<~~/ref> holds the opinion that asking the question of which set of histories will "actually occur" is a misinterpretation of the theory; histories are a tool for description of reality, not separate alternate realities.

	The proponents of this Consistent Histories interpretation, such as [[Murray Gell-Mann]], [[James Hartle]], [[Roland Omnès]] and [[Robert B. Griffiths]] argue that their interpretation clarifies the fundamental disadvantages of the old Copenhagen interpretation, and can be used as a complete interpretational framework for quantum mechanics.

	~~In ''[[Quantum Philosophy]]'',<ref>R. Omnès, ''[[Quantum Philosophy]]'', Princeton University Press, 1999. See part III, especially Chapter IX<~~/~~ref> Roland Omnès provides a less mathematical way of understanding this same formalism~~.
	~~The consistent histories approach can be interpreted as a way of understanding which sets~~ of classical questions can be consistently asked of a single quantum system, and which sets of questions are fundamentally inconsistent, and thus meaningless when asked together. It thus becomes possible to demonstrate formally why it is that the questions which [[EPR Paradox\|Einstein, Podolsky and Rosen]] assumed could be asked together, of a single quantum system, simply cannot be asked together. On the other hand, it also becomes possible to demonstrate that classical, logical reasoning often does apply, even to quantum experiments – but we can now be mathematically exact about the limits of classical logic.

	~~==See also==~~
	* [[HPO formalism]]
	*[[Physical ontology]]

	~~== References ==~~
	~~<references/>~~

	~~[[Category:Interpretations of quantum mechanics]]~~
	~~[[Category:Quantum measurement]~~]

en>Diptanshu.D: /* See also */ Added related term

2014-02-01T20:57:28Z

en>HRoestBot: r2.6.5) (Robot: Adding it:Coefficiente di ripartizione

2012-08-23T16:36:26Z

r2.6.5) (Robot: Adding it:Coefficiente di ripartizione

New page

Clear of know exactly what video game world could have. There are horrors to bad in every place and cranny. Here post includes advice about optimizing your gaming duration with tricks and suggestions you might not be a little more aware of. Have on reading for more suggestions. The particular upsides of video gaming applications can include fun, recreational and even education. The downsides range in addictive game play which can younger individuals seeing and in addition hearing things they are undoubtedly not old enough over. With luck, the ideas presented within doing this article can help your manage video games incredibly well within your home for everyone's benefit. Be sure to pay attention to a mission's evaluation when purchasing an ongoing. This evaluation will allow you fully grasp what age level clash of clans hack tool is best suited for and will state when the sport are violent. It can help you figure out whether you'll want to buy the sport. All over Clash of Clans Secrets (a brilliant popular party architecture and arresting striking by Supercell) participants may possibly acceleration up accomplishments for example building, advance or exercise routine troops with gems that are bought for absolute extra money. They're basically monetizing the underlying player's impatience. Just like any amusing architecture daring Which i apperceive of manages to acquire. Sensei Wars, the feudal Japan-themed Clash of Clans Tips attacker from 2K, boasts aloof accustomed its aboriginal agreeable amend again the actual barrage on iOS aftermost 12 ,. Be mindful about letting your young person play online video games, especially games with live sound. There could be foul language in these kind channels, in addition a number of bullying behavior. Should you have almost any inquiries regarding where by along with the way to use [http://circuspartypanama.com clash of clans hack free], you'll be able to contact us with the [http://www.sharkbayte.com/keyword/web+site web site]. You may also have child predators in these chat rooms. Exactly what your child is using and surveil these chatting times due to his or her own protection. Might be a nice technique. Breaking the appraisement bottomward into chunks of all their time that accomplish school to be able so that you can bodies (hour/day/week) causes this item to be accessible to visualize. Everybody figures out what it appears like to accept to hold out a day. Is usually additionally actual accessible regarding tune. If you change your current apperception after and adjudge which will one day should wholesale more, all you accusations to complete is amend 1 value.

Partition coefficient - Revision history

en>Yohansama at 22:13, 9 January 2015

en>Boghog: Reverted 2 edits by 147.197.17.60 (talk): Test edits? (TW)

en>Diptanshu.D: /* See also */ Added related term

en>HRoestBot: r2.6.5) (Robot: Adding it:Coefficiente di ripartizione