The origins of the equivalence principle begin with Galileo demonstrating in the late 16th century that all objects are accelerated towards the center of the Earth at the same rate. This was codified by Newton with his gravitational theory in which it was postulated that inertial and gravitational masses are one and the same. The equivalence principle proper was introduced by Albert Einstein in 1907. At that time, he made the observation that the acceleration of bodies towards the center of the Earth with acceleration 1g (g< ...

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Equivalence principle, Equivalence principle - History, Equivalence principle - Modern usage, Equivalence principle - The weak equivalence principle, Equivalence principle - The Einstein equivalence principle, Equivalence principle - The strong equivalence principle, Equivalence principle - Experiments

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Main discussion: Neuro-linguistic programming#Criticism Criticisms of NLP's actual principles (as opposed to NLP itself) generally fall into two camps: The subject is open ended, that is, it does not specify how the information it obtains should be used, or what can be done with it. So NLP becomes very prone to quackery, incorporation of pseudoscience, and manipulative uses. Blame for this is especially directed towards the principle "Use whatever works", which opens the floodgates for idiosyncratic dubious o ...

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Principles of NLP, Principles of NLP - Stated purpose of NLP, Principles of NLP - NLP as described by its major developers and promoters, Principles of NLP - Philosophical stance of NLP, Principles of NLP - Self-declared scope of NLP, Principles of NLP - Specific principles within NLP, Principles of NLP - The map is not the territory, Principles of NLP - Life and 'Mind' are Systemic Processes, Principles of NLP - Behind every behavior is a positive intention, Principles of NLP - Rapport, Principles of NLP - There is no failure only feedback, Principles of NLP - Choice is better than no choice and flexibility is the way one gets choice, Principles of NLP - The meaning of your communication is the response you get, Principles of NLP - People already have all the resources they need to succeed, Principles of NLP - Multiple descriptions are better than one, Principles of NLP - Other beliefs, Principles of NLP - NLP's approach to clinical conditions, Principles of NLP - Criticisms of the principles of NLP

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The concept of standard deviation pervades science in the measurement of everything. No treatment of any scientific subject, experiment, or measurement is said to be accurate without disclosing the standard deviation of the measurement. Uncertainty is the principle of standard deviation applied to the universe. Consider an experiment in which a particle is prepared in a definite state and two successive measurements are performed on the particle. The first one measures the particle's position and the second immediately after measures ...

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Uncertainty principle, Uncertainty principle - Overview, Uncertainty principle - Formulation and characteristics, Uncertainty principle - Expression of finite available amount of Fisher information, Uncertainty principle - Common observables which obey the uncertainty principle, Uncertainty principle - The theorem, Uncertainty principle - Generalizations, Uncertainty principle - History and interpretations, Uncertainty principle - The uncertainty principle in popular culture, Uncertainty principle - Humor

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Suppose X is the number of successes in twelve independent Bernoulli trials with probability θ of success on each trial, and Y is the number of independent Bernoulli trials needed to get three successes, again with probability θ of success on each trial. Then the observation that X = 3 induces the likelihood function and the observation that Y = 12 induces the likelihood function These are equivalent because each is a scalar multiple of the other. The likelihood principle therefore says the inferences drawn about t ...

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Likelihood principle, Likelihood principle - Example, Likelihood principle - The law of likelihood, Likelihood principle - Historical remarks, Likelihood principle - Arguments for and against the likelihood principle, Likelihood principle - Experimental design arguments on the likelihood principle, Likelihood principle - The voltmeter story, Likelihood principle - Bayesian arguments on the likelihood principle, Likelihood principle - Optional stopping in clinical trials

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There were five chief targets of the critical/analytical arguments of the volume: innatism (typified by Immanuel Kant); associationism (by Jeremy Bentham); materialism (by Herbert Spencer); spiritualism (by scholastic theology); and metaphysical idealism (by Georg Wilhelm Friedrich Hegel). The perception of time was a very hotly contested field in the psychology of James' day, and gave him an opportunity to explain the difficulty with innatism, which posits time as an infinite necessary continuum. This is a view that leads to unnecess ...

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Principles of Psychology, Principles of Psychology - The Analytical Arguments of The Principles, Principles of Psychology - James' Qualified Defense of Introspection, Principles of Psychology - Nineteenth Century Experimental Results, Principles of Psychology - The Consequences of Comparisons

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The uncertainty principle becomes a theorem in the theory of operators. Theorem. For arbitrary symmetric operators A: H → H and B: H → H, and any element x of H such that A B x and B A x are both defined (so that in particular, A x and B x are also defined), then This is an immediate consequence of the Cauchy-Bunyakovski-Schwarz inequality. Consequently, the following general form of the uncertainty principle, first pointed out in 1930 by Howard Percy Robertson and (independentl ...

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Uncertainty principle, Uncertainty principle - Overview, Uncertainty principle - Formulation and characteristics, Uncertainty principle - Expression of finite available amount of Fisher information, Uncertainty principle - Common observables which obey the uncertainty principle, Uncertainty principle - The theorem, Uncertainty principle - Generalizations, Uncertainty principle - History and interpretations, Uncertainty principle - The uncertainty principle in popular culture, Uncertainty principle - Humor

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The uncertainty principle becomes a theorem in the theory of operators. Theorem. For arbitrary symmetric operators A: H → H and B: H → H, and any element x of H such that A B x and B A x are both defined (so that in particular, A x and B x are also defined), then This is an immediate consequence of the Cauchy-Bunyakovski-Schwarz inequality. Consequently, the following general form of the uncertainty principle, first pointed out in 1930 by Howard Percy Robertson and (independentl ...

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Uncertainty principle, Uncertainty principle - Overview, Uncertainty principle - Wave-particle duality and the relationship to the uncertainty principle, Uncertainty principle - Formulation and characteristics, Uncertainty principle - Expression of finite available amount of Fisher information, Uncertainty principle - Common observables which obey the uncertainty principle, Uncertainty principle - The theorem, Uncertainty principle - Generalizations, Uncertainty principle - History and interpretations, Uncertainty principle - The uncertainty principle in popular culture, Uncertainty principle - Humor

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The universe, when viewed on sufficiently large distance scales, has no preferred directions or preferred places. Or, in other words, on a large scale the Universe looks the same in all directions for an observer at any place. This principle is consistent with observations of the universe from the Earth. In regard to the observations, the principle states that Earth is nowhere special. If one assumes these two properties to be true about the Universe, then the only possible cosmic evolution is a global expansion or contraction. In this case, at a time, the velocity between two points must be p ...

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Cosmological Principle, Cosmological Principle - Explanation, Cosmological Principle - Support

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The concept of probability distributions pervades the science of measurement. No treatment of any scientific subject, experiment, or measurement is said to be accurate without disclosing the nature of the probability distribution (sometimes called the error) of the measurement. Uncertainty is the characterization of the relative narrowness or broadness of the distribution function applied to a physical observation. Illustrative of this is an experiment in which a particle is prepared in a definite state and two successive measurements ...

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Uncertainty principle, Uncertainty principle - Overview, Uncertainty principle - Wave-particle duality and the relationship to the uncertainty principle, Uncertainty principle - Formulation and characteristics, Uncertainty principle - Expression of finite available amount of Fisher information, Uncertainty principle - Common observables which obey the uncertainty principle, Uncertainty principle - The theorem, Uncertainty principle - Generalizations, Uncertainty principle - History and interpretations, Uncertainty principle - The uncertainty principle in popular culture, Uncertainty principle - Humor

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A number of different forms of the equivalence principle are used in research today. Equivalence principle - The weak equivalence principle. The weak equivalence principle, also known as the universality of free fall: The trajectory of a falling test body depends only on its initial position and velocity, and is independent of its composition. or All bodies at the same spacetime point in a given gravitationa ...

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Equivalence principle, Equivalence principle - History, Equivalence principle - Modern usage, Equivalence principle - The weak equivalence principle, Equivalence principle - The Einstein equivalence principle, Equivalence principle - The strong equivalence principle, Equivalence principle - Experiments

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Landauer's principle can be understood to be a simple logical consequence of the second law of thermodynamics—which states that the entropy of a closed system cannot decrease—together with the definition of thermodynamic temperature. For, if the number of possible logical states of a computation were to decrease as the computation proceeded forward (logical irreversibility), this would constitute a forbidden decrease of entropy, unless the number of possible physical states corresponding to each logical state were to simultaneous ...

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Landauer's Principle, Landauer's Principle - Rationale, Landauer's Principle - References

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The principle of compositionality has been the subject of intense debate. Indeed, there is no general agreement as to how the principle is to be interpreted, although there have been several attempts to provide formal definitions of it. Scholars are also divided as to whether the principle should be regarded as a factual claim, open to empirical testing; an analytic truth, obvious from the nature of language and meaning; or a methodological principle to guide the development of theories of syntax and semantics. The principle has been ...

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Principle of compositionality, Principle of compositionality - Critiques

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The application of the precautionary principle is hampered by the wide range of interpretations placed on it. One study identified 14 different formulations of the principle in treaties and nontreaty declarations.[5] The range of interpretation may be characterised as running from the need to show that an action is "probably" safe, to showing that it is "definitely" safe. An analogy can be drawn with standards of proof used in law: from the "balance of probabilities" standard often used in civil law, to the "beyond a reasonable doubt" standa ...

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Precautionary principle, Precautionary principle - Origins and theory, Precautionary principle - Application, Precautionary principle - International agreements and declarations, Precautionary principle - Environment/health, Precautionary principle - Change of laws controlling societal norms, Precautionary principle - Criticisms

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The uncertainty principle is stated in popular culture in many ways, for example by stating that it is impossible to know both where an electron is and where it is going at the same time. This is roughly correct, although it fails to mention an important part of the Heisenberg principle, which is the quantitative bounds on the uncertainties. One common incorrect formulation is that observation of an event changes the event. This may be true in some cases for some ...

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Uncertainty principle, Uncertainty principle - Overview, Uncertainty principle - Formulation and characteristics, Uncertainty principle - Expression of finite available amount of Fisher information, Uncertainty principle - Common observables which obey the uncertainty principle, Uncertainty principle - The theorem, Uncertainty principle - Generalizations, Uncertainty principle - History and interpretations, Uncertainty principle - The uncertainty principle in popular culture, Uncertainty principle - Humor

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In international law as well as U.S. law, there are various ways in which one can establish ownership of a piece of property. The most obvious and direct application of the homestead principle is a situation in which a group of explorers discover some previously unknown land and build a literal homestead there. However, in recent times, the homestead principle has also been applied to other things besides land: for example an item of property, or a non-tangible asset such as a business name. For instance, let's say someone creates a company ...

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Homestead principle, Homestead principle - Implications, Homestead principle - History in the United States

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The likelihood principle was first identified by that name in print in 1962 (Barnard et al., Birnbaum, and Savage et al.), but arguments for the same principle, unnamed, and the use of the principle in applications goes back to the works of R.A. Fisher in the 1920s. The law of likelihood was identified by that name by I. Hacking (1965). More recently the likelihood principle as a general principle of inference has been championed by A. W. F. Edwards. The likelihood principle ...

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Likelihood principle, Likelihood principle - Example, Likelihood principle - The law of likelihood, Likelihood principle - Historical remarks, Likelihood principle - Arguments for and against the likelihood principle, Likelihood principle - Experimental design arguments on the likelihood principle, Likelihood principle - The voltmeter story, Likelihood principle - Bayesian arguments on the likelihood principle, Likelihood principle - Optional stopping in clinical trials

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Proponents argue that in such situations, rational decision-making requires caution, in a generalisation of a maxim (falsely attributed to the Hippocratic oath, as pointed out by Phoenix and Treder)[11], of "first, do no harm". Critics may argue that such a principle, while correctly applied by a doctor who may have a significant effect an individual patient's life or death, should not be applied to broader pol ...

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Precautionary principle, Precautionary principle - Origins and theory, Precautionary principle - Application, Precautionary principle - International agreements and declarations, Precautionary principle - Environment/health, Precautionary principle - Change of laws controlling societal norms, Precautionary principle - Criticisms

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Variational principle - Variational principle in quantum mechanics. For a hamiltonian H that describes the studied system and any normalizable function Ψ with arguments appropriate for the unknown wave function of the system, we define the functional The variational principle states that , where E0 is the lowest energy eigenstate (ground state) of the hamiltonian if and only if See also:

Variational principle, Variational principle - Examples, Variational principle - Variational principle in quantum mechanics, Variational principle - Further readings

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A generalized version of this principle states that, if n discrete objects are to be allocated to m containers, then at least one container must hold no fewer than objects, where denotes the ceiling function. A probabilistic generalization of the pigeonhole principle states that if n pigeons are randomly put into m pigeonholes with uniform probability 1/m, then at least one pigeonhole will hold mo ...

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Pigeonhole principle, Pigeonhole principle - Examples, Pigeonhole principle - Generalizations

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The uncertainty principle is stated in popular culture in many ways, for example by stating that it is impossible to know both where an electron is and where it is going at the same time. This is roughly correct, although it fails to mention an important part of the Heisenberg principle, which is the quantitative bounds on the uncertainties. One common incorrect formulation is that observation of an event changes the event. This may be true in some cases for some ...

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Uncertainty principle, Uncertainty principle - Overview, Uncertainty principle - Wave-particle duality and the relationship to the uncertainty principle, Uncertainty principle - Formulation and characteristics, Uncertainty principle - Expression of finite available amount of Fisher information, Uncertainty principle - Common observables which obey the uncertainty principle, Uncertainty principle - The theorem, Uncertainty principle - Generalizations, Uncertainty principle - History and interpretations, Uncertainty principle - The uncertainty principle in popular culture, Uncertainty principle - Humor

Read more here: » Uncertainty principle: Encyclopedia II - Uncertainty principle - The uncertainty principle in popular culture

A fundamental consequence of the Heisenberg Uncertainty Principle is that no physical phenomena can be to arbitrary accuracy described as a "classic point particle" or as a wave but rather the microphysical situation is best described in terms of wave-particle duality. The uncertainty principle, as initially considered by Heisenberg, is concerned with cases in which neither the wave nor the point particle descriptions is fully and exclusively appropriate, such as a particle in a box with a particular energy value. Such systems are cha ...

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Uncertainty principle, Uncertainty principle - Overview, Uncertainty principle - Wave-particle duality and the relationship to the uncertainty principle, Uncertainty principle - Formulation and characteristics, Uncertainty principle - Expression of finite available amount of Fisher information, Uncertainty principle - Common observables which obey the uncertainty principle, Uncertainty principle - The theorem, Uncertainty principle - Generalizations, Uncertainty principle - History and interpretations, Uncertainty principle - The uncertainty principle in popular culture, Uncertainty principle - Humor

Read more here: » Uncertainty principle: Encyclopedia II - Uncertainty principle - Wave-particle duality and the relationship to the uncertainty principle