In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be known simultaneously.

which has the same form as Hamilton's principle but in which x < sub > 3 </ sub > takes the role of time in classical mechanics.

A common choice of estimate is the one provided by the principle of maximum likelihood, and using this yields the predictive density over a future sample x < sub > n + 1 </ sub >, conditioned on the observed samples x = ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >) given by

The one truly new principle was one he called the Basic Law V: the " value-range " of the function f ( x ) is the same as the " value-range " of the function g ( x ) if and only if ∀ x = g ( x ).

The transfer principle states that true first order statements about R are also valid in * R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals ; since R is a real closed field, so is * R. Since for all integers n, one also has for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś ' theorem of 1955.

This word has a definite meaning, if the sentence " x is the principle of y " is supposed to be equivalent to the sentence " y exists by virtue of x " or " y arises out of x ".

They assert that no empirical relation between x and y can completely explain the meaning of " x is the principle of y ", because there is something that cannot be grasped by means of the experience, something for which no empirical criterion can be specified.

The uniform boundedness principle states that if for all x in X we have

Behavioral subtyping is trivially undecidable in general: if q is the property " method for x always terminates ", then it is impossible for a program ( e. g. a compiler ) to verify that it holds true for some subtype S of T even if q does hold for T. The principle is useful however in reasoning about the design of class hierarchies.

The discovery was made using Cavalieri's principle before the invention of calculus, but today calculus can be used to calculate the volume and surface area of the horn between x

For example, the second-order sentence says that for every set P of individuals and every individual x, either x is in P or it is not ( this is the principle of bivalence ).

If all such predicates are included, then the second principle as formulated above can be trivially and uncontroversially shown to be a logical tautology: if x is non-identical to y, then there will always be a putative " property " which distinguishes them, namely " being identical to x ".

Finally, Quine objects in principle to Carnap's proposed translation of statements like " quality q is at point-instant x ; y ; z ; t " into his sense-datum language, because he does not define the connective " is at ".

It became the sole `` subject '' of `` international law '' ( a term which, it is pertinent to remember, was coined by Bentham ), a body of legal principle which by and large was made up of what Western nations could do in the world arena.

Given the conceptual context within which ancient thought thrived, how could anyone have questioned this principle??

It will probably explain more of my attitudes toward society than any other phrase or principle could.

In fact, some -- Anzilotti is the principle example -- went so far as to say that all international law could be traced to the single legal norm, Pacta sunt Servanda.

) Here again Mr. Justice Frankfurter could not lightly accept the principle of wholesale judicial legislation.

Perhaps under the guidance of this Nazi principle one could, as Eichmann declared, feel personally friendly toward the Jews and still be their murderer.

Furthermore, even the highly trained law clerk who was a part of Jack's total make-up could not understand how the principle could ever be codified.

Corpuscularianism is similar to the theory of atomism, except that where atoms were supposed to be indivisible, corpuscles could in principle be divided.

To prevent this unphysical situation from happening, Dirac proposed that a " sea " of negative-energy electrons fills the universe, already occupying all of the lower-energy states so that, due to the Pauli exclusion principle, no other electron could fall into them.

This provision has been dormant since Queen Victoria ascended the throne, because she did not inherit Hanover under the Salic Laws of the German states, but in principle it could again become relevant in the future.

Russell and Whitehead thought they could derive all mathematical truth using axioms and inference rules of formal logic, in principle opening up the process to automatisation.

The " heuristic " approach of the Logic Theory Machine tried to emulate human mathematicians, and could not guarantee that a proof could be found for every valid theorem even in principle.

While administrative decision-making bodies are often controlled by larger governmental units, their decisions could be reviewed by a court of general jurisdiction under some principle of judicial review based upon due process ( United States ) or fundamental justice ( Canada ).

The Germans referred to a Schwerpunkt ( focal point and also known as Schwerpunktprinzip or concentration principle ) in the planning of operations ; it was a center of gravity or point of maximum effort, where a decisive action could be achieved.

In 1978 An Australian Prayer Book was produced which sought to adhere to this principle, so that where the Liturgical Committee could not agree on a formulation, the words or expressions of the BCP were to be used.

Archimedes ' principle provided the next link: coins could now be easily tested for their fine weight of metal, and thus the value of a coin could be determined, even if it had been shaved, debased or otherwise tampered with ( see Numismatics ).

One of the most common objections to rule-consequentialism is that it is incoherent, because it is based on the consequentialist principle that what we should be concerned with is maximizing the good, but then it tells us not to act to maximize the good, but to follow rules ( even in cases where we know that breaking the rule could produce better results ).

In many cases, such as the cabinet-directed prohibition on foreign ownership for broadcasters and the legislated principle of the predominance of Canadian content, these acts and orders often leave the CRTC less room to change policy than critics sometimes suggest, and the result is that the commission is often the lightning rod for policy criticism that could arguably be better directed at the government itself.

Ten years later, limited liability, the key provision of modern corporate law, passed into English law: in response to increasing pressure from newly emerging capital interests, Parliament passed the Limited Liability Act 1855, which established the principle that any corporation could enjoy limited legal liability on both contract and tort claims simply by registering as a " limited " company with the appropriate government agency.

According to the logical positivists, unless a statement could be verified by experience, or else was true or false by definition ( i. e. either tautological or contradictory ), then it was meaningless ( this is a summary statement of their verification principle ).

We could extend this principle to an even more important sphere.

He believed that in principle this could be done, by showing that:

I fled, however, not from what might have been the natural fear of being unable to disguise from you that the things about my bridegroom -- in the sense you meant the word `` things '' -- which you had been galvanizing yourself to tell me as a painful part of your maternal duty were things which I had already insisted upon finding out for myself ( despite, I may now say, the unspeakable awkwardness of making the discovery on principle, yes, on principle, and in cold blood ) because I was resolved, as a modern woman, not to be a mollycoddle waiting for Life but to seize Life by the throat.

It was indeed a remarkable feat that a man who had had no experience of bridge building should have applied the principle of the arch, which appears in his famous bridges at Portsmouth, Haverhill, and Philadelphia.

By applying this general principle, a great number of complex compounds of osmium, ruthenium, iridium, and rhenium, with triphenylphosphine, triphenylarsine, and triphenylstibine have been obtained in this laboratory during the past few years.

The central city areas, in other words, exhibit the two characteristics which violate the life principle of congregations of the major denominations: they have too few middle-class people ; ;

In any case, anyone who fails to make significant distinction between primary and secondary applications of economic pressure would in principle already have justified that use of economic boycott as a means which broke out a few years ago or was skillfully organized by White Citizens' Councils in the entire state of Mississippi against every local Philco dealer in that state, in protest against a Philco-sponsored program over a national TV network on which was presented a drama showing, it seemed, a `` high yellow gal '' smooching with a white man.

Such a decision should have placed a powerful weapon in the hands of the entire housing industry, but there is little evidence that realtors, or at least their associations, have repudiated the principle in such clauses.

Three elements have been important in holding the Communion together: First, the shared ecclesial structure of the component churches, manifested in an episcopal polity maintained through the apostolic succession of bishops and synodical government ; second, the principle of belief expressed in worship, investing importance in approved prayer books and their rubrics ; and third, the historical documents and standard divines that have influenced the ethos of the Communion.

Also, as we now know, bosons also have antiparticles, but since bosons do not obey the Pauli exclusion principle ( only fermions do ), hole theory does not work for them.

Samuel Clemens ( Mark Twain ) is also known to have spread the story while lecturing, personalizing it by adding " I have a higher and greater standard of principle.

All versions of the principle have been accused of discouraging the search for a deeper physical understanding of the universe.

These groupings have since been revised to improve consistency with the Darwinian principle of common descent.

Attempts have been made to connect both " Omanus " and " Haman " with the Zoroastrian term Vohu Mana ; however this denotes the principle of " Good Thoughts " and is not the name of a deity.

Scots common law differs in that the use of precedents is subject to the courts ' seeking to discover the principle that justifies a law rather than searching for an example as a precedent, and principles of natural justice and fairness have always played a role in Scots Law.

Steven Weinberg and a number of string theorists ( see string landscape ) have used this as evidence for the anthropic principle, which suggests that the cosmological constant is so small because life ( and thus physicists, to make observations ) cannot exist in a universe with a large cosmological constant, but many people find this an unsatisfying explanation.

According to some versions of functionalism, even non-human systems, such as other animal species, alien life forms, or advanced computers can, in principle, have mental states.

It is particularly acute for people who believe in the possibility of philosophical zombies, that is, people who think it is possible in principle to have an entity that is physically indistinguishable from a human being and behaves like a human being in every way but nevertheless lacks consciousness.

: The claim that EPR effects violate the principle that information cannot travel faster than the speed of light have been countered by noting that they cannot be used for signaling because neither observer can control, or predetermine, what he observes, and therefore cannot manipulate what the other observer measures.

The Vedic literature, Srimad-Bhagavatam, reject from its very beginning kaitava-dharma or false philosophy, thus it frankly speaks about the principle of material life, and it does have a meaningful relation to celibacy.

These variations have been classified on the basis of the quasi-equivalence principle proposed by Caspar and Klug.

David Hume and later Paul Edwards have invoked a similar principle in their criticisms of the cosmological argument.