In mathematics, model theory is the study of (classes of) mathematical structures (e.g. groups, fields, graphs, universes of set theory) using tools from mathematical logic.

Objects of study in model theory are models for formal languages which are structures that give meaning to the sentences of these formal languages. If a model for a language moreover satisfies a particular sentence or theory (set of sentences satisfying special conditions), it is called a model ''of'' the sentence or theory.

Model theory has close ties to algebra and universal algebra.

This article focuses on finitary first order model theory of infinite structures. Finite model theory, which concentrates on finite structures, diverges significantly from the study of infinite structures in both the problems studied and the techniques used. Model theory in higher-order logics or infinitary logics is hampered by the fact that completeness does not in general hold for these logics. However, a great deal of study has also been done in such languages.

Introduction

Model theory recognises and is intimately concerned with a duality: It examines semantical elements by means of syntactical elements of a corresponding language. To quote the first page of Chang and Keisler (1990):

:universal algebra + structure (mathematical logic) = model theory.

Model theory developed rapidly in during the 90's, and a more modern definition is provided by Wilfrid Hodges (1997):

:model theory = algebraic geometry - fields.

In a similar way to proof theory, model theory is situated in an area of interdisciplinarity between mathematics, philosophy, and computer science. The most important professional organization in the field of model theory is the Association for Symbolic Logic.

An incomplete and somewhat arbitrary subdivision of model theory is into classical model theory, model theory applied to groups and fields, and geometric model theory. A missing subdivision is computable model theory, but this can arguably be viewed as an independent subfield of logic. Examples of early theorems from classical model theory include Gödel's completeness theorem, the upward and downward Löwenheim–Skolem theorems, Vaught's two-cardinal theorem, Scott's isomorphism theorem, the omitting types theorem, and the Ryll-Nardzewski theorem. Examples of early results from model theory applied to fields are Tarski's elimination of quantifiers for real closed fields, Ax's theorem on pseudo-finite fields, and Robinson's development of nonstandard analysis. An important step in the evolution of classical model theory occurred with the birth of stability theory (through Morley's theorem on uncountably categorical theories and Shelah's classification program), which developed a calculus of independence and rank based on syntactical conditions satisfied by theories. During the last several decades applied model theory has repeatedly merged with the more pure stability theory. The result of this synthesis is called geometric model theory in this article (which is taken to include o-minimality, for example, as well as classical geometric stability theory). An example of a theorem from geometric model theory is Hrushovski's proof of the Mordell–Lang conjecture for function fields. The ambition of geometric model theory is to provide a ''geography of mathematics'' by embarking on a detailed study of definable sets in various mathematical structures, aided by the substantial tools developed in the study of pure model theory.

Example

To illustrate the basic relationship involving syntax and semantics in the context of a non-trivial model, one can start, on the syntactic side, with suitable axioms for the natural numbers such as Peano axioms, and the associated theory. Going on to the semantic side, one has the usual counting numbers as a model. In the 1930s, Skolem developed alternative models satisfying the axioms. This illustrates what is meant by interpreting a language or theory in a particular model. A more traditional example is interpreting the axioms of a particular algebraic system such as a group, in the context of a model provided by a specific group.

Universal algebra

Fundamental concepts in universal algebra are signatures σ and σ-algebras. Since these concepts are formally defined in the article on structures, the present article can content itself with an informal introduction which consists in examples of how these terms are used.

:The standard signature of rings is σ_ring = {×,+,−,0,1}, where × and + are binary, − is unary, and 0 and 1 are nullary. :The standard signature of semirings is σ_smr = {×,+,0,1}, where the arities are as above. :The standard signature of (multiplicative) groups is σ_grp = {×,⁻¹,1}, where × is binary, ⁻¹ is unary and 1 is nullary. :The standard signature of monoids is σ_mnd = {×,1}. :A ring is a σ_ring-structure which satisfies the identities and :A group is a σ_grp-structure which satisfies the identities and :A monoid is a σ_mnd-structure which satisfies the identities and :A semigroup is a {×}-structure which satisfies the identity :A magma is just a {×}-structure.

This is a very efficient way to define most classes of algebraic structures, because there is also the concept of σ-homomorphism, which correctly specializes to the usual notions of homomorphism for groups, semigroups, magmas and rings. For this to work, the signature must be chosen well.

Terms such as the σ_ring-term ''t''(''u'',''v'',''w'') given by are used to define identities but also to construct free algebras. An equational class is a class of structures which, like the examples above and many others, is defined as the class of all σ-structures which satisfy a certain set of identities. Birkhoff's theorem states:

:A class of σ-structures is an equational class if and only if it is not empty and closed under subalgebras, homomorphic images, and direct products.

An important non-trivial tool in universal algebra are ultraproducts $\backslash Pi\_\{i\backslash in\; I\}A\_i/U$, where ''I'' is an infinite set indexing a system of σ-structures ''A_i'', and ''U'' is an ultrafilter on ''I''.

While model theory is generally considered a part of mathematical logic, universal algebra, which grew out of Alfred North Whitehead's (1898) work on abstract algebra, is part of algebra. This is reflected by their respective MSC classifications. Nevertheless model theory can be seen as an extension of universal algebra.

Finite model theory

Finite model theory is the area of model theory which has the closest ties to universal algebra. Like some parts of universal algebra, and in contrast with the other areas of model theory, it is mainly concerned with finite algebras, or more generally, with finite σ-structures for signatures σ which may contain relation symbols as in the following example:

:The standard signature for graphs is σ_grph={''E''}, where ''E'' is a binary relation symbol. :A graph is a σ_grph-structure satisfying the sentences $\backslash forall\; u\; \backslash forall\; v(uEv\; \backslash rightarrow\; vEu)$ and $\backslash forall\; u\backslash neg(uEu)$.

A σ-homomorphism is a map that commutes with the operations and preserves the relations in σ. This definition gives rise to the usual notion of graph homomorphism, which has the interesting property that a bijective homomorphism need not be invertible. Structures are also a part of universal algebra; after all, some algebraic structures such as ordered groups have a binary relation <. What distinguishes finite model theory from universal algebra is its use of more general logical sentences (as in the example above) in place of identities. (In a model-theoretic context an identity ''t''=''t''' is written as a sentence $\backslash forall\; u\_1u\_2\backslash dots\; u\_n(t=t\text{'})$.)

The logics employed in finite model theory are often substantially more expressive than first-order logic, the standard logic for model theory of infinite structures.

First-order logic

Whereas universal algebra provides the semantics for a signature, logic provides the syntax. With terms, identities and quasi-identities, even universal algebra has some limited syntactic tools; first-order logic is the result of making quantification explicit and adding negation into the picture.

A first-order formula is built out of atomic formulas such as ''R''(''f''(''x'',''y''),''z'') or ''y'' = ''x'' + 1 by means of the Boolean connectives $\backslash neg,\backslash land,\backslash lor,\backslash rightarrow$ and prefixing of quantifiers $\backslash forall\; v$ or $\backslash exists\; v$. A sentence is a formula in which each occurrence of a variable is in the scope of a corresponding quantifier. Examples for formulas are φ (or φ(x) to mark the fact that at most x is an unbound variable in φ) and ψ defined as follows:

:$\{\backslash phi\; \backslash ;=\backslash ;\; \backslash forall\; u\backslash forall\; v(\backslash exists\; w\; (x\backslash times\; w=u\backslash times\; v)\backslash rightarrow(\backslash exists\; w(x\backslash times\; w=u)\backslash lor\backslash exists\; w(x\backslash times\; w=v)))\backslash land\; x\backslash ne\; 0\backslash land\; x\backslash ne1,\}$ :$\backslash psi\; \backslash ;=\backslash ;\; \backslash forall\; u\backslash forall\; v((u\backslash times\; v=x)\backslash rightarrow\; (u=x)\backslash lor(v=x))\backslash land\; x\backslash ne\; 0\backslash land\; x\backslash ne1.$

(Note that the equality symbol has a double meaning here.) It is intuitively clear how to translate such formulas into mathematical meaning. In the σ_smr-structure $\backslash mathcal\; N$ of the natural numbers, for example, an element ''n'' satisfies the formula φ if and only if ''n'' is a prime number. The formula ψ similarly defines irreducibility. Tarski gave a rigorous definition, sometimes called "Tarski's definition of truth", for the satisfaction relation $\backslash models$, so that one easily proves:

:$\backslash mathcal\; N\backslash models\backslash phi(n)\; \backslash iff\; n$ is a prime number. :$\backslash mathcal\; N\backslash models\backslash psi(n)\; \backslash iff\; n$ is irreducible.

A set ''T'' of sentences is called a (first-order) theory. A theory is satisfiable if it has a model $\backslash mathcal\; M\backslash models\; T$, i.e. a structure (of the appropriate signature) which satisfies all the sentences in the set ''T''. Consistency of a theory is usually defined in a syntactical way, but in first-order logic by the completeness theorem there is no need to distinguish between satisfiability and consistency. Therefore model theorists often use "consistent" as a synonym for "satisfiable".

A theory is called categorical if it determines a structure up to isomorphism, but it turns out that this definition is not useful, due to serious restrictions in the expressivity of first-order logic. The Löwenheim–Skolem theorem implies that for every theory ''T'' which has an infinite model and for every infinite cardinal number κ, there is a model $\backslash mathcal\; M\backslash models\; T$ such that the number of elements of $\backslash mathcal\; M$ is exactly κ. Therefore only finite structures can be described by a categorical theory.

Lack of expressivity (when compared to higher logics such as second-order logic) has its advantages, though. For model theorists the Löwenheim–Skolem theorem is an important practical tool rather than the source of Skolem's paradox. First-order logic is in some sense (for which see Lindström's theorem) the most expressive logic for which both the Löwenheim–Skolem theorem and the compactness theorem hold:

:Compactness theorem :Every unsatisfiable first-order theory has a finite unsatisfiable subset.

This important theorem, due to Gödel, is of central importance in infinite model theory, where the words "by compactness" are commonplace. One way to prove it is by means of ultraproducts. An alternative proof uses the completeness theorem, which is otherwise reduced to a marginal role in most of modern model theory.

Axiomatizability, elimination of quantifiers, and model-completeness

The first step, often trivial, for applying the methods of model theory to a class of mathematical objects such as groups, or trees in the sense of graph theory, is to choose a signature σ and represent the objects as σ-structures. The next step is to show that the class is an elementary class, i.e. axiomatizable in first-order logic (i.e. there is a theory ''T'' such that a σ-structure is in the class if and only if it satisfies ''T''). E.g. this step fails for the trees, since connectedness cannot be expressed in first-order logic. Axiomatizability ensures that model theory can speak about the right objects. Quantifier elimination can be seen as a condition which ensures that model theory does not say too much about the objects.

A theory ''T'' has quantifier elimination if every first-order formula φ(x₁,...,x_''n'') over its signature is equivalent modulo ''T'' to a first-order formula ψ(x₁,...,x_''n'') without quantifiers, i.e. $\backslash forall\; x\_1\backslash dots\backslash forall\; x\_n(\backslash phi(x\_1,\backslash dots,x\_n)\backslash leftrightarrow\; \backslash psi(x\_1,\backslash dots,x\_n))$ holds in all models of ''T''. For example the theory of algebraically closed fields in the signature σ_ring=(×,+,−,0,1) has quantifier elimination because every formula is equivalent to a Boolean combination of equations between polynomials.

A substructure of a σ-structure is a subset of its domain, closed under all functions in its signature σ, which is regarded as a σ-structure by restricting all functions and relations in σ to the subset. An embedding of a σ-structure $\backslash mathcal\; A$ into another σ-structure $\backslash mathcal\; B$ is a map f: A → B between the domains which can be written as an isomorphism of $\backslash mathcal\; A$ with a substructure of $\backslash mathcal\; B$. Every embedding is an injective homomorphism, but the converse holds only if the signature contains no relation symbols.

If a theory does not have quantifier elimination, one can add additional symbols to its signature so that it does. Early model theory spent much effort on proving axiomatizability and quantifier elimination results for specific theories, especially in algebra. But often instead of quantifier elimination a weaker property suffices:

A theory ''T'' is called model-complete if every substructure of a model of ''T'' which is itself a model of ''T'' is an elementary substructure. There is a useful criterion for testing whether a substructure is an elementary substructure, called the Tarski–Vaught test. It follows from this criterion that a theory ''T'' is model-complete if and only if every first-order formula φ(x₁,...,x_''n'') over its signature is equivalent modulo ''T'' to an existential first-order formula, i.e. a formula of the following form: :$\backslash exists\; v\_1\backslash dots\backslash exists\; v\_m\backslash psi(x\_1,\backslash dots,x\_n,v\_1,\backslash dots,v\_m)$, where ψ is quantifier free. A theory that is not model-complete may or may not have a model completion, which is a related model-complete theory that is not, in general, an extension of the original theory. A more general notion is that of model companions.

Categoricity

As observed in the section on first-order logic, first-order theories cannot be categorical, i.e. they cannot describe a unique model up to isomorphism, unless that model is finite. But two famous model-theoretic theorems deal with the weaker notion of κ-categoricity for a cardinal κ. A theory ''T'' is called κ-categorical if any two models of ''T'' that are of cardinality κ are isomorphic. It turns out that the question of κ-categoricity depends critically on whether κ is bigger than the cardinality of the language (i.e. $\backslash aleph\_0$ + |σ|, where |σ| is the cardinality of the signature). For finite or countable signatures this means that there is a fundamental difference between $\backslash aleph\_0$-cardinality and κ-cardinality for uncountable κ.

A few characterizations of $\backslash aleph\_0$-categoricity include: :For a complete first-order theory ''T'' in a finite or countable signature the following conditions are equivalent: :#''T'' is $\backslash aleph\_0$-categorical. :#For every natural number ''n'', the Stone space ''S_n''(''T'') is finite. :#For every natural number ''n'', the number of formulas φ(''x''₁, ..., ''x''_n) in ''n'' free variables, up to equivalence modulo ''T'', is finite.

This result, due independently to Engeler, Ryll-Nardzewski and Svenonius, is sometimes referred to as the Ryll-Nardzewski theorem.

Further, $\backslash aleph\_0$-categorical theories and their countable models have strong ties with oligomorphic groups. They are often constructed as Fraïssé limits.

Michael Morley's highly non-trivial result that (for countable languages) there is only ''one'' notion of uncountable categoricity was the starting point for modern model theory, and in particular classification theory and stability theory: :Morley's categoricity theorem :If a first-order theory ''T'' in a finite or countable signature is κ-categorical for some uncountable cardinal κ, then ''T'' is κ-categorical for all uncountable cardinals κ.

Uncountably categorical (i.e. κ-categorical for all uncountable cardinals κ) theories are from many points of view the most well-behaved theories. A theory that is both $\backslash aleph\_0$-categorical and uncountably categorical is called totally categorical.

Model theory and set theory

Set theory (which is expressed in a countable language) has a countable model; this is known as Skolem's paradox, since there are sentences in set theory which postulate the existence of uncountable sets and yet these sentences are true in our countable model. Particularly the proof of the independence of the continuum hypothesis requires considering sets in models which appear to be uncountable when viewed from ''within'' the model, but are countable to someone ''outside'' the model.

The model-theoretic viewpoint has been useful in set theory; for example in Kurt Gödel's work on the constructible universe, which, along with the method of forcing developed by Paul Cohen can be shown to prove the (again philosophically interesting) independence of the axiom of choice and the continuum hypothesis from the other axioms of set theory.

Other basic notions of model theory

Reducts and expansions

A field or a vector space can be regarded as a (commutative) group by simply ignoring some of its structure. The corresponding notion in model theory is that of a reduct of a structure to a subset of the original signature. The opposite relation is called an ''expansion'' - e.g. the (additive) group of the rational numbers, regarded as a structure in the signature {+,0} can be expanded to a field with the signature {×,+,1,0} or to an ordered group with the signature {+,0,<}.

Similarly, if σ' is a signature that extends another signature σ, then a complete σ'-theory can be restricted to σ by intersecting the set of its sentences with the set of σ-formulas. Conversely, a complete σ-theory can be regarded as a σ'-theory, and one can extend it (in more than one way) to a complete σ'-theory. The terms reduct and expansion are sometimes applied to this relation as well.

Interpretability

Given a mathematical structure, there are very often associated structures which can be constructed as a quotient of part of the original structure via an equivalence relation. An important example is a quotient group of a group.

One might say that to understand the full structure one must understand these quotients. When the equivalence relation is definable, we can give the previous sentence a precise meaning. We say that these structures are interpretable.

A key fact is that one can translate sentences from the language of the interpreted structures to the language of the original structure. Thus one can show that if a structure ''M'' interprets another whose theory is undecidable, then ''M'' itself is undecidable.

Using the compactness and completeness theorems

Gödel's completeness theorem (not to be confused with his incompleteness theorems) says that a theory has a model if and only if it is consistent, i.e. no contradiction is proved by the theory. This is the heart of model theory as it lets us answer questions about theories by looking at models and vice-versa. One should not confuse the completeness theorem with the notion of a complete theory. A complete theory is a theory that contains every sentence or its negation. Importantly, one can find a complete consistent theory extending any consistent theory. However, as shown by Gödel's incompleteness theorems only in relatively simple cases will it be possible to have a complete consistent theory that is also recursive, i.e. that can be described by a recursively enumerable set of axioms. In particular, the theory of natural numbers has no recursive complete and consistent theory. Non-recursive theories are of little practical use, since it is undecidable if a proposed axiom is indeed an axiom, making proof-checking a supertask.

The compactness theorem states that a set of sentences S is satisfiable if every finite subset of S is satisfiable. In the context of proof theory the analogous statement is trivial, since every proof can have only a finite number of antecedents used in the proof. In the context of model theory, however, this proof is somewhat more difficult. There are two well known proofs, one by Gödel (which goes via proofs) and one by Malcev (which is more direct and allows us to restrict the cardinality of the resulting model).

Model theory is usually concerned with first-order logic, and many important results (such as the completeness and compactness theorems) fail in second-order logic or other alternatives. In first-order logic all infinite cardinals look the same to a language which is countable. This is expressed in the Löwenheim–Skolem theorems, which state that any countable theory with an infinite model $\backslash mathfrak\{A\}$ has models of all infinite cardinalities (at least that of the language) which agree with $\backslash mathfrak\{A\}$ on all sentences, i.e. they are 'elementarily equivalent'.

Types

Fix an $L$-structure $M$, and a natural number $n$. The set of definable subsets of $M^n$ over some parameters $A$ is a Boolean algebra. By Stone's representation theorem for Boolean algebras there is a natural dual notion to this. One can consider this to be the topological space consisting of maximal consistent sets of formulae over $A$. We call this the space of (complete) $n$-types over $A$, and write $S\_n(A)$.

Now consider an element $m\; \backslash in\; M^n$. Then the set of all formulae $\backslash phi$ with parameters in $A$ in free variables $x\_1,\backslash ldots,x\_n$ so that $M\; \backslash models\; \backslash phi(m)$ is consistent and maximal such. It is called the ''type'' of $m$ over $A$.

One can show that for any $n$-type $p$, there exists some elementary extension $N$ of $M$ and some $a\; \backslash in\; N^n$ so that $p$ is the type of $a$ over $A$.

Many important properties in model theory can be expressed with types. Further many proofs go via constructing models with elements that contain elements with certain types and then using these elements.

Illustrative Example: Suppose $M$ is an algebraically closed field. The theory has quantifier elimination . This allows us to show that a type is determined exactly by the polynomial equations it contains. Thus the space of $n$-types over a subfield $A$ is bijective with the set of prime ideals of the polynomial ring $A[x\_1,\backslash ldots,x\_n]$. This is the same set as the spectrum of $A[x\_1,\backslash ldots,x\_n]$. Note however that the topology considered on the type space is the constructible topology: a set of types is basic open iff it is of the form $\backslash \{p:\; f(x)=0\; \backslash in\; p\backslash \}$ or of the form $\backslash \{p:\; f(x)\; \backslash neq\; 0\; \backslash in\; p\backslash \}$. This is finer than the Zariski topology.

Early history

Model theory as a subject has existed since approximately the middle of the 20th century. However some earlier research, especially in mathematical logic, is often regarded as being of a model-theoretical nature in retrospect. The first significant result in what is now model theory was a special case of the downward Löwenheim–Skolem theorem, published by Leopold Löwenheim in 1915. The compactness theorem was implicit in work by Thoralf Skolem, but it was first published in 1930, as a lemma in Kurt Gödel's proof of his completeness theorem. The Löwenheim–Skolems theorem and the compactness theorem received their respective general forms in 1936 and 1941 from Anatoly Maltsev.

See also

Axiomatizable class

Compactness theorem

Descriptive complexity

Elementary equivalence

First-order theories

Forcing

Hyperreal number

Institutional model theory

Kripke semantics

Löwenheim–Skolem theorem

Proof theory

Saturated model

Notes

References

Canonical textbooks

Other textbooks

Free online texts

Hodges, Wilfrid, ''First-order Model theory''. The Stanford Encyclopedia Of Philosophy, E. Zalta (ed.).

Simmons, Harold (2004), ''An introduction to Good old fashioned model theory''. Notes of an introductory course for postgraduates (with exercises).

J. Barwise and S. Feferman (editors), Model-Theoretic Logics, Perspectives in Mathematical Logic, Volume 8, New York: Springer-Verlag, 1985.

*Model Category:Metalogic

ar:نظرية النموذج bn:মডেল তত্ত্ব bg:Теория на моделите ca:Teoria de models hu:Modellelmélet cs:Teorie modelů de:Modelltheorie el:Θεωρία μοντέλων eo:Modela teorio es:Teoría de modelos fa:نظریه مدل fr:Théorie des modèles ko:모형 이론 ia:Theoria de modellos it:Teoria dei modelli nl:Modeltheorie pms:Teorìa dij modej pl:Teoria modeli pt:Teoria dos modelos ru:Теория моделей fi:Malliteoria sv:Modellteori tr:Modeller kuramı zh:模型论

Thomas Metzinger (born 12 March 1958) is a German philosopher. he holds the position of director of the theoretical philosophy group at the department of philosophy at the Johannes Gutenberg University of Mainz and is an Adjunct Fellow at the Frankfurt Institute for Advanced Studies and on the advisory board of the Giordano Bruno Foundation. From 2008 to 2009 he served as a Fellow at the Wissenschaftskolleg zu Berlin.

He has been active since the early 1990s in the promotion of consciousness studies as an academic endeavour. As a co-founder, he has been particularly active in the organization of the Association for the Scientific Study of Consciousness (ASSC), and sat on the board of directors of that organisation from 1995 to 2008. He served as president of the ASSC in 2009/10. Metzinger is director of the MIND group and has been president of the German cognitive science society from 2005 to 2007. In English he has published two edited works, ''Conscious Experience'' (1995), and ''Neural correlates of consciousness: empirical and conceptual issues'' (2000). The latter book arose out of the second ASSC meeting, for which he acted as local organizer.

In 2003 Metzinger published the monograph ''Being No One''. In this book he argues that no such things as selves exist in the world: nobody ever had or was a self. All that exists are phenomenal selves, as they appear in conscious experience. He argues that the phenomenal self, however, is not a thing but an ongoing process; it is the content of a "transparent self-model." In 2009 Metzinger published a follow-up book to ''Being No One'' for a general audience: ''The Ego Tunnel'' (Basic Books, New York, ISBN 0-465-04567-7).

Metzinger's work addresses some of the fundamental issues in neurobiology, consciousness, and the relationship between mind and body. His views about the self are the subject of considerable controversy and ongoing debate.

Metzinger's interests include:

Philosophy of mind (esp. philosophical aspects of empirical theories in the neuro- and cognitive sciences, artificial intelligence, and related areas of research).

Ethics (esp. conceptual connections between applied ethics, the philosophy of mind and anthropology)

Metzinger supervises The Neuroethics Web Portal.

Literature

;Monographs

(1985) ''Neuere Beiträge zur Diskussion des Leib-Seele-Problems.'' Peter Lang, Frankfurt am Main, ISBN 3820489274

(1993) ''Subjekt und Selbstmodell.'' Die Perspektivität phänomenalen Bewußtseins vor dem Hintergrund einer naturalistischen Theorie mentaler Repräsentation. mentis, Paderborn, ISBN 3897850818

(2003) ''Being No One.'' The Self-Model Theory of Subjectivity. MIT Press, Cambridge, MA., ISBN 0262134179 (Hardcover)/ISBN 0262633086 (Paperback)

(2009) ''The Ego Tunnel - The Science of the Mind and the Myth of the Self'' Basic Books, New York, ISBN 0465045677

(2009) ''Der Ego-Tunnel - Eine neue Philosophie des Selbst: Von der Hirnforschung zur Bewusstseinsethik '' Berlin Verlag, Berlin, ISBN 3827006309

(2010) ''Der Ego Tunnel. Eine neue Philosophie des Selbst: Von der Hirnforschung zur Bewusstseinsethik.'' Berlin: Berlin Verlag. eBook ISBN: 9783827070371

(2011) ''Being No One. The Self-Model Theory of Subjectivity''. Cambridge MA: MIT Press. Kindle edition; ASIN: B004ELBJ56

;Editorship

(1995) ''Bewußtsein – Beiträge aus der Gegenwartsphilosophie.'', Paderborn, mentis, Paderborn, ISBN 3897850125

(1995) ''Conscious Experience''. Imprint Academic, Thorverton und mentis, Paderborn, ISBN 090784510X (Hardcover)

(2000) ''Neural Correlates of Consciousness'' – Empirical and Conceptual Questions. MIT Press, Cambridge, MA., ISBN 0262133709 (Hardcover)

(2006) ''Grundkurs Philosophie des Geistes'' – Band 1: ''Phänomenales Bewusstsein'' mentis, Paderborn, ISBN 3897855518

(2007) ''Grundkurs Philosophie des Geistes'' – Band 2: ''Das Leib-Seele-Problem'' mentis, Paderborn, ISBN 3897855526

(2010) ''Grundkurs Philosophie des Geistes'' – Band 3: ''Intentionalität und mentale Repräsentation mentis'' Paderborn, ISBN 9783897855533. All three volumes can be purchased for 78 Euros, ISBN 978-3-89785-554-0.

; Selected articles and book chapters

(2003; with Vittorio Gallese) ''The emergence of a shared action ontology: building blocks for a theory'' In G. Knoblich, B. Elsner, G. von Aschersleben, und T. Metzinger (eds), Self and Action. Special issue of Consciousness & Cognition (12:4), 549-571.

(2003) ''Phenomenal transparency and cognitive self-reference'' Phenomenology and the Cognitive Sciences, 2, 353-393. doi:10.1023/B:PHEN.0000007366.42918.eb.

(2003) ''Phänomenale Transparenz und kognitive Selbstbezugnahme'' In U. Haas-Spohn (Hrsg.), Intentionalität zwischen Subjektivität und Weltbezug. Paderborn: mentis. Seite 411-459.

(2003) ''Why are identity-disorders interesting for philosophers?'' In Thomas Schramme und Johannes Thome (Hrsg.), Philosophy and Psychiatry. Berlin: de Gruyter. S. 311-25.

(2004) ''Précis of "Being No One"'' In PSYCHE - An Interdisciplinary Journal of Research on Consciousness, 11 (5), 1-35.

(2005) ''Out-of-body experiences as the origin of the concept of a "soul"'' Mind and Matter, 3(1), 57-84.

(2005) ''Die Selbstmodell-Theorie der Subjektivität: Eine Kurzdarstellung in sechs Schritten'' In C. S. Herrmann, M. Pauen, J. W. Rieger und S. Schicktanz (Hrsg.), Bewusstsein: Philosophie, Neurowissenschaften, Ethik. Stuttgart: UTB/Fink . S. 242-269.

(2006) ''Being No One – Eine sehr kurze deutsche Zusammenfassung'' In Grundkurs Philosophie des Geistes – Band 1: Phänomenales Bewusstsein. S. 424-475.

(2006) ''Conscious volition and mental representation: Towards a more fine-grained analysis'' In N. Sebanz und W. Prinz (Hrsg.), Disorders of Volition. Cambridge, MA: MIT Press. S. 19-48.

(2007; with B. Lenggenhager, T. Tadi und O. Blanke) ''Video Ergo Sum: Manipulating bodily self-consciousness'' Science, 317, 1096-1099.

(2008) ''Empirical perspectives from the self-model theory of subjectivity: A brief summary with examples'' In Rahul Banerjee and Bikas K. Chakrabarti (eds.), Progress in Brain Research, 168: 215-246. Amsterdam: Elsevier.

(2009; mit O. Blanke) ''Full-body illusions and minimal phenomenal selfhood'' Trends in Cognitive Sciences 13(1): 7-13.

(2010) ''The No-Self-Alternative'' Chapter 11 in S. Gallagher (ed.), ''Oxford Handbook of the Self''. Oxford, UK: Oxford University Press. Seite 277-294.

(2011a; with Elisabeth Hildt). ''Cognitive Enhancement'' . In J. Illes and B.J. Sahakian (eds.), ''Oxford Handbook of Neuroethics''. Oxford, UK: Oxford University Press. P. 245-264.

;DVD-Set

(2009) ''Philosophie des Bewusstseins (5 DVDs)- 15 Vorlesungen an der Johannes Gutenberg-Universität Mainz vom Wintersemester 2007/2008'' Auditorium-Netzwerk.

External links

Scholarpedia article on Self Models

Video of 2004 Foerster lecture at UC Berkeley

List of publications

Homepage

Association for the Scientific Study of Consciousness

Neuroethics Webportal

Sutherland's criticism of Metzinger

MIND Group

Public Lecture on ''Spirituality and Intellectual Honesty'' (You Tube with a link to English translation)

''To Be or Not To Be: The Self as Illusion'' ("Perspectives on the Self: Conversations on Identity & Consciousness ") at the New York Academy of Sciences)

Guest on All in the Mind with Natasha Mitchell

Brain Science Podcast with Dr. Ginger Campbell

Category:1958 births Category:Living people Category:University of Mainz faculty Category:20th-century philosophers Category:Consciousness researchers and theorists Category:Philosophers of mind

de:Thomas Metzinger fr:Thomas Metzinger pl:Thomas Metzinger ru:Метцингер, Томас fi:Thomas Metzinger zh:湯瑪斯·梅辛革

name	Antony Garrett Lisi
birth date	January 24, 1968
nationality	American
field	Theoretical physics
alma mater	UCLAUCSD
work institutions	none: independent
known for	"An Exceptionally Simple Theory of Everything"Surfing }}

Antony Garrett Lisi (born January 24, 1968), who uses the name Garrett by preference, is an American theoretical physicist and adventure sports enthusiast. Lisi works as an independent researcher without an academic position. He is a strong proponent of balance in life, in his case between scientific research and enjoyment of the outdoors.

Lisi is known for "An Exceptionally Simple Theory of Everything," a paper proposing a unified field theory based on the E₈ Lie group, combining particle physics with Einstein's theory of gravitation.

Biography

Early life

Born in Los Angeles and raised in San Diego, California, Lisi graduated the Cate School (south of Santa Barbara, California) in 1986. He learned to surf in San Diego, where he traveled between surf breaks in an old VW Bus. Lisi went on to receive two B.S. degrees with highest honors in physics and mathematics from the University of California, Los Angeles in 1991. Lisi received a Ph.D. in physics from the University of California, San Diego in 1999.

After the Ph.D.

After getting his Ph.D., Lisi left academia and moved to Maui — expressing his dissatisfaction with the state of theoretical physics: }} On Maui, Lisi volunteered as a staff member at a local Sudbury school, and split his time between working on his own physics research and surfing.

While living in a customized van with his girlfriend, Crystal Baranyk, Lisi taught physics classes at University of Hawaii – Maui College. After two years on Maui, Lisi says he was offered a tenure track teaching position at the local college, but turned it down (even though he was nearly broke) because it wouldn't have given him enough time for his physics research. At the same time, he submitted a grant application to the newly formed Foundational Questions Institute (FQXi). Lisi says the decision to turn down the job offer and hope for FQXi funding was "a hell of a gamble."

Academic reentry

On July 31, 2006, Lisi was awarded an FQXi grant to develop his research in quantum mechanics and unification. The grant allowed Lisi to devote his full attention to physics and create his personal research wiki, Deferential Geometry. On June 9, 2007, Lisi realized that the algebraic structure he had constructed to unify the standard model of particle physics with general relativity perfectly matched the algebraic structure of the E₈ Lie group.

On July 21, 2007, Lisi traveled to the inaugural FQXi conference in Reykjavik, Iceland. He was invited to give several academic talks. On invitation from Lee Smolin, Lisi visited the Perimeter Institute for Theoretical Physics in October, and posted his paper, "An Exceptionally Simple Theory of Everything," to the arXiv on November 6, 2007. Discussions of Lisi's theory developed rapidly over most major physics blogs, and the story of Lisi's theory and personal history was reported by many online and traditional media sources around the world.

Lisi presented at the TED Conference on February 28, 2008, and has since presented several academic talks and colloquia.

On July 8, 2009, at a FQXi conference in the Azores, Lisi made a public bet with Frank Wilczek that superparticles would not be detected by July 8, 2015.

In July, 2010, mathematicians and physicists met with Lisi at the Banff International Research Station in Alberta, Canada, for a week to discuss his theory.

Physics research

Work on quantum mechanics

On May 8, 2006, in an arXiv preprint, "Quantum mechanics from a universal action reservoir," Lisi described how the path integral formulation of quantum mechanics can be derived from information theory and the existence of a universal action reservoir.

Deferential Geometry

Lisi is an early practitioner of open notebook science. Lisi created his "personal wiki notebook in theoretical physics" — the Deferential Geometry website — by using TiddlyWiki and jsMath. Lisi uses this wiki to organize his research notes in theoretical physics, referring to this as "open source physics."

An Exceptionally Simple Theory of Everything

Lisi's main work in theoretical physics is his Exceptionally Simple Theory of Everything, which proposes a unified field theory combining a grand unification theory of particle physics with Albert Einstein's general relativistic description of gravitation, using the largest simple exceptional Lie algebra, E₈. In a paper posted to the physics arXiv on November 6, 2007, and in a popular article published in Scientific American in December, 2010, Lisi describes how gravity, the standard model bosons and fermions can be unified as parts of an E₈ superconnection. This unified field theory attempts to describe all fundamental interactions observed in nature, and stands as a possible theory of everything, unifying Albert Einstein's general relativity with the standard model of particle physics. The theory, called E8 Theory, also predicts the existence of many new particles.

Lisi designed a web application, the Elementary Particle Explorer, for visualizing the charge structure of the elementary particles in the standard model, in grand unified theories, and in E8 Theory.

Lisi's theory has been applauded but also criticized in the scientific community. He has addressed the criticism, while acknowledging that the theory is incomplete. In a Scientific American post, Garrett himself states:

Adventure sports

Garrett Lisi is an adventure sports enthusiast — surfing, snowboarding, and kitesurfing at the expert level as well as participating in many other adventure sports. In an interview for Wired News, Lisi says:

Lisi brings some of his physics to his sports activities. During graduate school and years in Maui, most of Lisi's surfboards were adorned with the wave equation as decorative art. And when riding an extra-long carving board, for alpine snowboarding, in Colorado and Tahoe, Lisi always wears a long white lab coat. He has also become a sponsored team rider for an Oregon surfboard manufacturer, 42 Surfboards.

Although concentrating on surfing, kitesurfing and snowboarding, Lisi participates in a wide variety of adventure sports. On his online journal, Lisi describes his experiences surfing, snowboarding, windsurfing, sailing, kitesurfing, mountain biking, skateboarding, motorcycling, cliff diving, rock climbing, hang gliding, paragliding, backpacking, water skiing, wakeboarding, flying, sky diving, and scuba diving. Lisi is working on a film about young scientists who combine cutting-edge research with adventure sports.

Science hostel

Lisi proposes the creation of a more casual kind of science institutea science hostel which he says "would essentially be large houses in beautiful locations where theorists could live and work." Citing his experience living in Maui and the mountains of Tahoe and Colorado, Lisi says that for theoretical research it is good to have opportunities for hiking and things to do outside in attractive environments. Describing the idea more formally, Lisi says:}}

Personal articles and interviews

Garrett Lisi's story attracted a great deal of media attention. Numerous news sites from all over the world reported on his new theory, also noting his unorthodox personal background. Lisi has been the subject of many biographical articles and interviews:

August 6, 2007 – On her blog, "Backreaction," in "Garrett Lisi's Inspiration," Sabine Hossenfelder interviews Lisi about his views and theory. October 26, 2007 – In an article commissioned by FQXi, "Surfing the Folds of Spacetime," Scott Dodd reports on Lisi's history and theory. November 14, 2007 – In The Daily Telegraph, Roger Highfield reports "Surfer dude stuns physicists with theory of everything." November 15, 2007 – In New Scientist, Zeeya Merali reports "Is mathematical pattern the theory of everything?" November 15, 2007 – For Fox News, Jim Patton reports "'Physics is Beautiful' And a few other thoughts from Garrett Lisi." November 16, 2007 – CBC News reports "Surfer makes waves with scientific 'theory of everything'." November 16, 2007 – The Daily Galaxy reports "How a Surfer Dude Stunned the World of Science With the 'Theory of Everything'." November 18, 2007 – User Friendly features Garrett in its Sunday morning comic, as a "Wave Mechanic." November 18, 2007 – In The Sunday Times, Steve Farrar reports on "Einstein on a snowboard." November 19, 2007 – In Surfer Magazine, Scott Bass interviews Lisi in "ONE BIG THEORY: A Q & A w/ Surfing Scientist Garrett Lisi." November 20, 2007 – On an FQXi forum, "An Exceptionally Simple Personal FAQ," Lisi provides his detailed responses to questions from the media. November 21, 2007 – In The Daily Telegraph, Roger Highfield reports "Surfer Dude's Theory of Everything – The Movie." November 22, 2007 – The Economist reports "Geometry is all." December 1, 2007 – In Surfer Magazine, Scott Bass lists Lisi as #3 in "Most interesting surfers of 2007: The Top Ten." December 3, 2007 – In The San Diego Union Tribune, Brad Melekian reports "Physicist balances waves with world of science." January 4, 2008 – The Edge Foundation includes Garrett's response to the question, "What Have You Changed Your Mind About?" February 26, 2008 – Discover Magazine reports "Could the Next Einstein Be a Surfer Dude?" February 27, 2008 – In Wired Magazine, Kim Zetter reports "Surfer-Physicist's Unified Theory Leads to Fame, Backlash." March 1, 2008 – In Scientific American, Graham P. Collins reports "Wipeout?" In this article, Collins briefly describes Lisi's theory and the related discussion, referring to previous criticisms from Marcus Du Sautoy and Jacques Distler. March 1, 2008 – The Science Channel interviews Garrett in "Ten Quick Questions With... Garrett Lisi." April 1, 2008 – In Symmetry Magazine, Amber Dance reports on "Outsider Science." May 1, 2008 – In Outside Magazine, Evan Ratliff writes "Has A Surfer/Snowboarder Who Lives In A Van Rewritten Physics? Maybe" June 1, 2008 – In Men's Journal, James Owen Weatherall writes "No Strings Attached." July 21, 2008 – In The New Yorker, Benjamin Wallace-Wells writes "Surfing the Universe." September 20, 2008 – For The Center for Science Writings, John Horgan writes "Surfing Einstein's Really Revolutionary Idea," discussing Lisi's idea for a Science Hostel. September 25, 2008 – On O'Reilly Community, Timothy M. O'Brien writes "A. Garrett Lisi on Using Wikis to Support Open Source Science," discussing and presenting a video of Lisi describing his Deferential Geometry wiki. November 17, 2008 – In SEED Magazine, Greg Boustead writes "Garrett Lisi's Exceptional Approach to Everything." January 4, 2009 – The Edge Foundation includes Garrett's response to the question, "What will change everything?" April 10, 2009 – On surfing.about.com, in "Garrett Lisi: Dropping in and Dropping Science," Jay DiMartino interviews Lisi. April 25, 2009 – In the Financial Times, John O'Connor writes "First Person: A. Garrett Lisi." November 10, 2009 – In The Daily Telegraph, Roger Highfield writes "Surfer dude's theory of everything: the magic of Garrett Lisi." January 30, 2010 – In the Toronto Star, Mitch Porter writes "Surfer inspires comparisons to Albert Einstein." June 9, 2010 – Lisi was profiled in Morgan Freeman's science show, Through the Wormhole. December 1, 2010 – In Scientific American, Garrett Lisi and James Owen Weatherall write "A Geometric Theory of Everything." February 2, 2011 – In Maui Time Weekly, Jacob Shafer writes on "Physicist Garrett Lisi And His Theory of Everything." May 4, 2011 - In Scientific American, Garrett Lisi Responds to Criticism of his Proposed Unified Theory of Physics

References

External links

Antony Garrett Lisi's home page

@garrettlisi on Twitter

TED Talks: Garrett Lisi on "The Beauty of Particle Physics" at TED in 2008

Deferential Geometry – Lisi's personal research wiki

Elementary Particle Explorer – a Flash application designed by Lisi

Lisi's publications in high energy physics

Scientific American: A Geometric Theory of Everything – an article co-authored by Lisi in 2010.

Category:1968 births Category:American physicists Category:Living people Category:Particle physicists Category:Theoretical physicists Category:University of California, Los Angeles alumni Category:University of California, San Diego alumni Category:American surfers Category:People from Los Angeles, California

es:Antony Garrett Lisi fr:Antony Garrett Lisi it:Antony Garrett Lisi nl:Antony Garrett Lisi ru:Лиси, Энтони Гаррет sv:Antony Garrett Lisi tr:Antony Garrett Lisi

Name	Albert Einstein
Birth date	March 14, 1879
Birth place	Ulm, Kingdom of Württemberg, German Empire
Death date	April 18, 1955
Death place	Princeton, New Jersey, United States
Spouse	Mileva Marić (1903–1919)
Residence	Germany, Italy, Switzerland, United States
Citizenship
Ethnicity	Jewish
Fields	Physics
Workplaces
Alma mater
Doctoral advisor	Alfred Kleiner
Academic advisors	Heinrich Friedrich Weber
Notable students
Known for
Awards
Signature	Albert Einstein signature 1934.svg }}

Albert Einstein (; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history. He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect". The latter was pivotal in establishing quantum theory within physics.

Near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led to the development of his special theory of relativity. He realized, however, that the principle of relativity could also be extended to gravitational fields, and with his subsequent theory of gravitation in 1916, he published a paper on the general theory of relativity. He continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He also investigated the thermal properties of light which laid the foundation of the photon theory of light. In 1917, Einstein applied the general theory of relativity to model the structure of the universe as a whole.

He was visiting the United States when Adolf Hitler came to power in 1933, and did not go back to Germany, where he had been a professor at the Berlin Academy of Sciences. He settled in the U.S., becoming a citizen in 1940. On the eve of World War II, he helped alert President Franklin D. Roosevelt that Germany might be developing an atomic weapon, and recommended that the U.S. begin similar research; this eventually led to what would become the Manhattan Project. Einstein was in support of defending the Allied forces, but largely denounced using the new discovery of nuclear fission as a weapon. Later, together with Bertrand Russell, Einstein signed the Russell–Einstein Manifesto, which highlighted the danger of nuclear weapons. Einstein was affiliated with the Institute for Advanced Study in Princeton, New Jersey, until his death in 1955.

Einstein published more than 300 scientific papers along with over 150 non-scientific works. His great intelligence and originality have made the word "Einstein" synonymous with genius.

Biography

Early life and education

Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire on 14 March 1879. His father was Hermann Einstein, a salesman and engineer. His mother was Pauline Einstein (née Koch). In 1880, the family moved to Munich, where his father and his uncle founded ''Elektrotechnische Fabrik J. Einstein & Cie'', a company that manufactured electrical equipment based on direct current.

The Einsteins were non-observant Jews. Albert attended a Catholic elementary school from the age of five for three years. Later, at the age of eight, Einstein was transferred to the Luitpold Gymnasium where he received advanced primary and secondary school education until he left Germany seven years later. Although it has been thought that Einstein had early speech difficulties, this is disputed by the Albert Einstein Archives, and he excelled at the first school that he attended.

His father once showed him a pocket compass; Einstein realized that there must be something causing the needle to move, despite the apparent "empty space". As he grew, Einstein built models and mechanical devices for fun and began to show a talent for mathematics. When Einstein was ten years old Max Talmud (later changed to Max Talmey), a poor Jewish medical student from Poland, was introduced to the Einstein family by his brother, and during weekly visits over the next five years he gave the boy popular books on science, mathematical texts and philosophical writings. These included Immanuel Kant's ''Critique of Pure Reason'' and ''Euclid's Elements'' (which Einstein called the "holy little geometry book").

In 1894, his father's company failed: direct current (DC) lost the War of Currents to alternating current (AC). In search of business, the Einstein family moved to Italy, first to Milan and then, a few months later, to Pavia. When the family moved to Pavia, Einstein stayed in Munich to finish his studies at the Luitpold Gymnasium. His father intended for him to pursue electrical engineering, but Einstein clashed with authorities and resented the school's regimen and teaching method. He later wrote that the spirit of learning and creative thought were lost in strict rote learning. At the end of December 1894 he travelled to Italy to join his family in Pavia, convincing the school to let him go by using a doctor's note. It was during his time in Italy in 1895 without formal schooling that he wrote a short essay with the title "On the Investigation of the State of the Ether in a Magnetic Field."

In late summer 1895, at the age of sixteen, Einstein sat the entrance examinations for the Swiss Federal Polytechnic in Zurich (later the Eidgenössische Polytechnische Schule, ETH). He failed to reach the required standard in several subjects, but obtained exceptional grades in physics and mathematics. On the advice of the Principal of the Polytechnic, he attended the Aargau Cantonal School in Aarau, Switzerland, in 1895-96 to complete his secondary schooling. While lodging with the family of Professor Jost Winteler, he fell in love with Winteler's daughter, Marie. (His sister Maja later married the Wintelers' son, Paul.) In January 1896, with his father's approval, he renounced his citizenship in the German Kingdom of Württemberg to avoid military service. In September 1896 he passed the Swiss Matura with mostly good grades (gaining maximum grade 6 in physics and mathematical subjects, on a scale 1-6), and though still only seventeen he enrolled in the four year mathematics and physics teaching diploma program at the Zurich Polytechnic. Marie Winteler moved to Olsberg, Switzerland for a teaching post.

Einstein's future wife, Mileva Marić, also enrolled at the Polytechnic that same year, the only woman among the six students in the mathematics and physics section of the teaching diploma course. Over the next few years, Einstein and Marić's friendship developed into romance, and they read books together on extra-curricular physics in which Einstein was taking an increasing interest. In 1900 Einstein was awarded the Zurich Polytechnic teaching diploma, but Marić failed the examination with a poor grade in the mathematics component, theory of functions. There have been claims that Marić collaborated with Einstein on his celebrated 1905 papers, but historians of physics who have studied the issue find no evidence that she made any substantive contributions.

Marriages and children

In early 1902, Einstein and Mileva Marić (Милева Марић) had a daughter they named Lieserl in their correspondence, who was born in Novi Sad where Marić's parents lived. Her full name is not known, and her fate is uncertain after 1903.

Einstein and Marić married in January 1903. In May 1904, the couple's first son, Hans Albert Einstein, was born in Bern, Switzerland. Their second son, Eduard, was born in Zurich in July 1910. In 1914, Einstein moved to Berlin, while his wife remained in Zurich with their sons. Marić and Einstein divorced on 14 February 1919, having lived apart for five years.

Einstein married Elsa Löwenthal (née Einstein) on 2 June 1919, after having had a relationship with her since 1912. She was his first cousin maternally and his second cousin paternally. In 1933, they emigrated permanently to the United States. In 1935, Elsa Einstein was diagnosed with heart and kidney problems and died in December 1936.

Patent office

After graduating, Einstein spent almost two frustrating years searching for a teaching post, but a former classmate's father helped him secure a job in Bern, at the Federal Office for Intellectual Property, the patent office, as an assistant examiner. He evaluated patent applications for electromagnetic devices. In 1903, Einstein's position at the Swiss Patent Office became permanent, although he was passed over for promotion until he "fully mastered machine technology".

Much of his work at the patent office related to questions about transmission of electric signals and electrical-mechanical synchronization of time, two technical problems that show up conspicuously in the thought experiments that eventually led Einstein to his radical conclusions about the nature of light and the fundamental connection between space and time.

With a few friends he met in Bern, Einstein started a small discussion group, self-mockingly named "The Olympia Academy", which met regularly to discuss science and philosophy. Their readings included the works of Henri Poincaré, Ernst Mach, and David Hume, which influenced his scientific and philosophical outlook.

Academic career

In 1901, Einstein had a paper on the capillary forces of a straw published in the prestigious ''Annalen der Physik''. On 30 April 1905, he completed his thesis, with Alfred Kleiner, Professor of Experimental Physics, serving as pro-forma advisor. Einstein was awarded a PhD by the University of Zurich. His dissertation was entitled "A New Determination of Molecular Dimensions". That same year, which has been called Einstein's ''annus mirabilis'' or "miracle year", he published four groundbreaking papers, on the photoelectric effect, Brownian motion, special relativity, and the equivalence of matter and energy, which were to bring him to the notice of the academic world.

By 1908, he was recognized as a leading scientist, and he was appointed lecturer at the University of Bern. The following year, he quit the patent office and the lectureship to take the position of physics docent at the University of Zurich. He became a full professor at Karl-Ferdinand University in Prague in 1911. In 1914, he returned to Germany after being appointed director of the Kaiser Wilhelm Institute for Physics (1914–1932) and a professor at the Humboldt University of Berlin, with a special clause in his contract that freed him from most teaching obligations. He became a member of the Prussian Academy of Sciences. In 1916, Einstein was appointed president of the German Physical Society (1916–1918).

In 1911, he had calculated that, based on his new theory of general relativity, light from another star would be bent by the Sun's gravity. That prediction was claimed confirmed by observations made by a British expedition led by Sir Arthur Eddington during the solar eclipse of 29 May 1919. International media reports of this made Einstein world famous. On 7 November 1919, the leading British newspaper ''The Times'' printed a banner headline that read: "Revolution in Science – New Theory of the Universe – Newtonian Ideas Overthrown". (Much later, questions were raised whether the measurements had been accurate enough to support Einstein's theory.)

In 1921, Einstein was awarded the Nobel Prize in Physics. Because relativity was still considered somewhat controversial, it was officially bestowed for his explanation of the photoelectric effect. He also received the Copley Medal from the Royal Society in 1925.

Travels abroad

Einstein visited New York City for the first time on 2 April 1921, where he received an official welcome by the Mayor, followed by three weeks of lectures and receptions. He went on to deliver several lectures at Columbia University and Princeton University, and in Washington he accompanied representatives of the National Academy of Science on a visit to the White House. On his return to Europe he was the guest of the British statesman and philosopher Viscount Haldane in London, where he met several renowned scientific, intellectual and political figures, and delivered a lecture at Kings College.

In 1922, he traveled throughout Asia and later to Palestine, as part of a six-month excursion and speaking tour. His travels included Singapore, Ceylon, and Japan, where he gave a series of lectures to thousands of Japanese. His first lecture in Tokyo lasted four hours, after which he met the emperor and empress at the Imperial Palace where thousands came to watch. Einstein later gave his impressions of the Japanese in a letter to his sons: "Of all the people I have met, I like the Japanese most, as they are modest, intelligent, considerate, and have a feel for art."

On his return voyage, he also visited Palestine for 12 days in what would become his only visit to that region. "He was greeted with great British pomp, as if he were a head of state rather than a theoretical physicist", writes Isaacson. This included a cannon salute upon his arrival at the residence of the British high commissioner, Sir Herbert Samuel. During one reception given to him, the building was "stormed by throngs who wanted to hear him". In Einstein's talk to the audience, he expressed his happiness over the event:

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Emigration from Germany

In 1933, Einstein decided to emigrate to the United States due to the rise to power of the Nazis under Germany's new chancellor, Adolf Hitler. While visiting American universities in April, 1933, he learned that the new German government had passed a law barring Jews from holding any official positions, including teaching at universities. A month later, the Nazi book burnings occurred, with Einstein's works being among those burnt, and Nazi propaganda minister Joseph Goebbels proclaimed, "Jewish intellectualism is dead." Einstein also learned that his name was on a list of assassination targets, with a "$5,000 bounty on his head." One German magazine included him in a list of enemies of the German regime with the phrase, "not yet hanged".

Einstein was undertaking his third two-month visiting professorship at the California Institute of Technology when Hitler came to power in Germany. On his return to Europe in March 1933 he resided in Belgium for some months, before temporarily moving to England.

He took up a position at the Institute for Advanced Study at Princeton, New Jersey, an affiliation that lasted until his death in 1955. He was one of the four first selected (two of the others being John von Neumann and Kurt Gödel). At the institute, he soon developed a close friendship with Gödel. The two would take long walks together discussing their work. His last assistant was Bruria Kaufman, who later became a renowned physicist. During this period, Einstein tried to develop a unified field theory and to refute the accepted interpretation of quantum physics, both unsuccessfully.

Other scientists also fled to America. Among them were Nobel laureates and professors of theoretical physics. With so many other Jewish scientists now forced by circumstances to live in America, often working side by side, Einstein wrote to a friend, "For me the most beautiful thing is to be in contact with a few fine Jews—a few millennia of a civilized past do mean something after all." In another letter he writes, "In my whole life I have never felt so Jewish as now."

World War II and the Manhattan Project

In 1939, a group of Hungarian scientists that included emigre physicist Leó Szilárd attempted to alert Washington of ongoing Nazi atomic bomb research. The group's warnings were discounted. Einstein and Szilárd, along with other refugees such as Edward Teller and Eugene Wigner, "regarded it as their responsibility to alert Americans to the possibility that German scientists might win the race to build an atomic bomb, and to warn that Hitler would be more than willing to resort to such a weapon." In the summer of 1939, a few months before the beginning of World War II in Europe, Einstein was persuaded to lend his prestige by writing a letter with Szilárd to President Franklin D. Roosevelt to alert him of the possibility. The letter also recommended that the U.S. government pay attention to and become directly involved in uranium research and associated chain reaction research.

The letter is believed to be "arguably the key stimulus for the U.S. adoption of serious investigations into nuclear weapons on the eve of the U.S. entry into World War II". President Roosevelt could not take the risk of allowing Hitler to possess atomic bombs first. As a result of Einstein's letter and his meetings with Roosevelt, the U.S. entered the "race" to develop the bomb, drawing on its "immense material, financial, and scientific resources" to initiate the Manhattan Project. It became the only country to develop an atomic bomb during World War II.

For Einstein, "war was a disease . . . [and] he called for resistance to war." But in 1933, after Hitler assumed full power in Germany, "he renounced pacifism altogether . . . In fact, he urged the Western powers to prepare themselves against another German onslaught." In 1954, a year before his death, Einstein said to his old friend, Linus Pauling, "I made one great mistake in my life — when I signed the letter to President Roosevelt recommending that atom bombs be made; but there was some justification — the danger that the Germans would make them..."

U.S. citizenship

Einstein became an American citizen in 1940. Not long after settling into his career at Princeton, he expressed his appreciation of the "meritocracy" in American culture when compared to Europe. According to Isaacson, he recognized the "right of individuals to say and think what they pleased", without social barriers, and as result, the individual was "encouraged" to be more creative, a trait he valued from his own early education. Einstein writes:

What makes the new arrival devoted to this country is the democratic trait among the people. No one humbles himself before another person or class. . . American youth has the good fortune not to have its outlook troubled by outworn traditions.

As a member of the National Association for the Advancement of Colored People NAACP at Princeton who campaigned for the civil rights of African Americans, Einstein corresponded with civil rights activist W. E. B. Du Bois, and in 1946 Einstein called racism America's "worst disease". He later stated, "Race prejudice has unfortunately become an American tradition which is uncritically handed down from one generation to the next. The only remedies are enlightenment and education".

After the death of Israel's first president, Chaim Weizmann, in November 1952, Prime Minister David Ben-Gurion offered Einstein the position of President of Israel, a mostly ceremonial post. The offer was presented by Israel's ambassador in Washington, Abba Eban, who explained that the offer "embodies the deepest respect which the Jewish people can repose in any of its sons". However, Einstein declined, and wrote in his response that he was "deeply moved", and "at once saddened and ashamed" that he could not accept it:

All my life I have dealt with objective matters, hence I lack both the natural aptitude and the experience to deal properly with people and to exercise official function. I am the more distressed over these circumstances because my relationship with the Jewish people became my strongest human tie once I achieved complete clarity about our precarious position among the nations of the world.''

Death

On 17 April 1955, Albert Einstein experienced internal bleeding caused by the rupture of an abdominal aortic aneurysm, which had previously been reinforced surgically by Dr. Rudolph Nissen in 1948. He took the draft of a speech he was preparing for a television appearance commemorating the State of Israel's seventh anniversary with him to the hospital, but he did not live long enough to complete it. Einstein refused surgery, saying: "I want to go when I want. It is tasteless to prolong life artificially. I have done my share, it is time to go. I will do it elegantly." He died in Princeton Hospital early the next morning at the age of 76, having continued to work until near the end.

During the autopsy, the pathologist of Princeton Hospital, Thomas Stoltz Harvey, removed Einstein's brain for preservation without the permission of his family, in the hope that the neuroscience of the future would be able to discover what made Einstein so intelligent. Einstein's remains were cremated and his ashes were scattered at an undisclosed location.

In his lecture at Einstein's memorial, nuclear physicist Robert Oppenheimer summarized his impression of him as a person: "He was almost wholly without sophistication and wholly without worldliness . . . There was always with him a wonderful purity at once childlike and profoundly stubborn."

Scientific career

Throughout his life, Einstein published hundreds of books and articles.

1905 - Annus Mirabilis papers

The ''Annus Mirabilis'' papers are four articles pertaining to the photoelectric effect (which gave rise to quantum theory), Brownian motion, the special theory of relativity, and E = mc² that Albert Einstein published in the ''Annalen der Physik'' scientific journal in 1905. These four works contributed substantially to the foundation of modern physics and changed views on space, time, and matter. The four papers are:

{| class=wikitable |- ! Title (translated) !! Area of focus !! Received !! Published !! Significance |- | ''On a Heuristic Viewpoint Concerning the Production and Transformation of Light'' || Photoelectric effect || 18 March || 9 June || Resolved an unsolved puzzle by suggesting energy existed in discrete quanta rather than continuous levels. The theory of quanta was either pivotal to, or gave rise to, quantum theory. |- | ''On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat'' || Brownian motion || 11 May || 18 July || Empirical evidence for the atom, substantial support to the novel area of statistical physics. |- | ''On the Electrodynamics of Moving Bodies'' || Special relativity || 30 June || 26 Sept || Reconciled Maxwell's equations for electricity and magnetism with the laws of mechanics by introducing major changes to mechanics close to the speed of light. Hypothesized the speed of light as being independent of the frame of reference and an "upper limit" on velocity and information transmission in non-esoteric situations, discredited the concept of an "luminiferous ether", and the significance of frames of reference in physics. |- | ''Does the Inertia of a Body Depend Upon Its Energy Content?'' || Matter–energy equivalence || 27 Sept || 21 Nov || Equivalence of matter and energy, (and by implication, the ability of gravity—and matter generally—to "bend" light), the existence of "rest energy", and the basis of nuclear energy (the conversion of matter to energy by humans and in the cosmos). |}

Thermodynamic fluctuations and statistical physics

Albert Einstein's first paper submitted in 1900 to ''Annalen der Physik'' was on capillary attraction. It was published in 1901 titled ''Folgerungen aus den Capillaritätserscheinungen'', which was translated as "Conclusions from the capillarity phenomena". Two papers he published in 1902–1903 (thermodynamics) attempted to interpret atomic phenomena from a statistical point of view. These papers were the foundation for the 1905 paper on Brownian motion. These published calculations (1905) showed that Brownian movement can be construed as firm evidence that molecules exist. His research in 1903 and 1904 was mainly concerned with the effect of finite atomic size on diffusion phenomena.

General principles postulated by Einstein

He articulated the principle of relativity. This was understood by Hermann Minkowski to be a generalization of rotational invariance from space to space-time. Other principles postulated by Einstein and later vindicated are the principle of equivalence and the principle of adiabatic invariance of the quantum number.

Theory of relativity and E = mc²

Einstein's "Zur Elektrodynamik bewegter Körper" ("On the Electrodynamics of Moving Bodies") was received on 30 June 1905 and published 26 September of that same year. It reconciles Maxwell's equations for electricity and magnetism with the laws of mechanics, by introducing major changes to mechanics close to the speed of light. This later became known as Einstein's special theory of relativity.

Consequences of this include the time-space frame of a moving body appearing to slow down and contract (in the direction of motion) when measured in the frame of the observer. This paper also argued that the idea of a luminiferous aether – one of the leading theoretical entities in physics at the time – was superfluous.

In his paper on ''mass–energy equivalence'' Einstein produced ''E'' = ''mc''² from his special relativity equations. Einstein's 1905 work on relativity remained controversial for many years, but was accepted by leading physicists, starting with Max Planck.

Photons and energy quanta

In a 1905 paper, Einstein postulated that light itself consists of localized particles (''quanta''). Einstein's light quanta were nearly universally rejected by all physicists, including Max Planck and Niels Bohr. This idea only became universally accepted in 1919, with Robert Millikan's detailed experiments on the photoelectric effect, and with the measurement of Compton scattering.

Einstein concluded that each wave of frequency ''f'' is associated with a collection of photons with energy ''hf'' each, where ''h'' is Planck's constant. He does not say much more, because he is not sure how the particles are related to the wave. But he does suggest that this idea would explain certain experimental results, notably the photoelectric effect.

Quantized atomic vibrations

In 1907 Einstein proposed a model of matter where each atom in a lattice structure is an independent harmonic oscillator. In the Einstein model, each atom oscillates independently – a series of equally spaced quantized states for each oscillator. Einstein was aware that getting the frequency of the actual oscillations would be different, but he nevertheless proposed this theory because it was a particularly clear demonstration that quantum mechanics could solve the specific heat problem in classical mechanics. Peter Debye refined this model.

Adiabatic principle and action-angle variables

Throughout the 1910s, quantum mechanics expanded in scope to cover many different systems. After Ernest Rutherford discovered the nucleus and proposed that electrons orbit like planets, Niels Bohr was able to show that the same quantum mechanical postulates introduced by Planck and developed by Einstein would explain the discrete motion of electrons in atoms, and the periodic table of the elements.

Einstein contributed to these developments by linking them with the 1898 arguments Wilhelm Wien had made. Wien had shown that the hypothesis of adiabatic invariance of a thermal equilibrium state allows all the blackbody curves at different temperature to be derived from one another by a simple shifting process. Einstein noted in 1911 that the same adiabatic principle shows that the quantity which is quantized in any mechanical motion must be an adiabatic invariant. Arnold Sommerfeld identified this adiabatic invariant as the action variable of classical mechanics. The law that the action variable is quantized was a basic principle of the quantum theory as it was known between 1900 and 1925.

Wave–particle duality

Although the patent office promoted Einstein to Technical Examiner Second Class in 1906, he had not given up on academia. In 1908, he became a ''privatdozent'' at the University of Bern. In "über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" ("The Development of Our Views on the Composition and Essence of Radiation"), on the quantization of light, and in an earlier 1909 paper, Einstein showed that Max Planck's energy quanta must have well-defined momenta and act in some respects as independent, point-like particles. This paper introduced the ''photon'' concept (although the name ''photon'' was introduced later by Gilbert N. Lewis in 1926) and inspired the notion of wave–particle duality in quantum mechanics.

Theory of critical opalescence

Einstein returned to the problem of thermodynamic fluctuations, giving a treatment of the density variations in a fluid at its critical point. Ordinarily the density fluctuations are controlled by the second derivative of the free energy with respect to the density. At the critical point, this derivative is zero, leading to large fluctuations. The effect of density fluctuations is that light of all wavelengths is scattered, making the fluid look milky white. Einstein relates this to Raleigh scattering, which is what happens when the fluctuation size is much smaller than the wavelength, and which explains why the sky is blue. Einstein quantitatively derived critical opalescence from a treatment of density fluctuations, and demonstrated how both the effect and Rayleigh scattering originate from the atomistic constitution of matter.

Zero-point energy

Einstein's physical intuition led him to note that Planck's oscillator energies had an incorrect zero point. He modified Planck's hypothesis by stating that the lowest energy state of an oscillator is equal to ''hf'', to half the energy spacing between levels. This argument, which was made in 1913 in collaboration with Otto Stern, was based on the thermodynamics of a diatomic molecule which can split apart into two free atoms.

General relativity and the Equivalence Principle

General relativity (GR) is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses. General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where gravitational attraction is so strong that not even light can escape.

As Albert Einstein later said, the reason for the development of general relativity was that the preference of inertial motions within special relativity was unsatisfactory, while a theory which from the outset prefers no state of motion (even accelerated ones) should appear more satisfactory. So in 1908 he published an article on acceleration under special relativity. In that article, he argued that free fall is really inertial motion, and that for a freefalling observer the rules of special relativity must apply. This argument is called the Equivalence principle. In the same article, Einstein also predicted the phenomenon of gravitational time dilation. In 1911, Einstein published another article expanding on the 1907 article, in which additional effects such as the deflection of light by massive bodies were predicted.

Hole argument and Entwurf theory

While developing general relativity, Einstein became confused about the gauge invariance in the theory. He formulated an argument that led him to conclude that a general relativistic field theory is impossible. He gave up looking for fully generally covariant tensor equations, and searched for equations that would be invariant under general linear transformations only.

In June, 1913 the Entwurf ("draft") theory was the result of these investigations. As its name suggests, it was a sketch of a theory, with the equations of motion supplemented by additional gauge fixing conditions. Simultaneously less elegant and more difficult than general relativity, after more than two years of intensive work Einstein abandoned the theory in November, 1915 after realizing that the hole argument was mistaken.

Cosmology

In 1917, Einstein applied the General theory of relativity to model the structure of the universe as a whole. He wanted the universe to be eternal and unchanging, but this type of universe is not consistent with relativity. To fix this, Einstein modified the general theory by introducing a new notion, the cosmological constant. With a positive cosmological constant, the universe could be an eternal static sphere.

Einstein believed a spherical static universe is philosophically preferred, because it would obey Mach's principle. He had shown that general relativity incorporates Mach's principle to a certain extent in frame dragging by gravitomagnetic fields, but he knew that Mach's idea would not work if space goes on forever. In a closed universe, he believed that Mach's principle would hold. Mach's principle has generated much controversy over the years.

Modern quantum theory

In 1917, at the height of his work on relativity, Einstein published an article in ''Physikalische Zeitschrift'' that proposed the possibility of stimulated emission, the physical process that makes possible the maser and the laser. This article showed that the statistics of absorption and emission of light would only be consistent with Planck's distribution law if the emission of light into a mode with n photons would be enhanced statistically compared to the emission of light into an empty mode. This paper was enormously influential in the later development of quantum mechanics, because it was the first paper to show that the statistics of atomic transitions had simple laws. Einstein discovered Louis de Broglie's work, and supported his ideas, which were received skeptically at first. In another major paper from this era, Einstein gave a wave equation for de Broglie waves, which Einstein suggested was the Hamilton–Jacobi equation of mechanics. This paper would inspire Schrödinger's work of 1926.

Bose–Einstein statistics

In 1924, Einstein received a description of a statistical model from Indian physicist Satyendra Nath Bose, based on a counting method that assumed that light could be understood as a gas of indistinguishable particles. Einstein noted that Bose's statistics applied to some atoms as well as to the proposed light particles, and submitted his translation of Bose's paper to the ''Zeitschrift für Physik''. Einstein also published his own articles describing the model and its implications, among them the Bose–Einstein condensate phenomenon that some particulates should appear at very low temperatures. It was not until 1995 that the first such condensate was produced experimentally by Eric Allin Cornell and Carl Wieman using ultra-cooling equipment built at the NIST–JILA laboratory at the University of Colorado at Boulder. Bose–Einstein statistics are now used to describe the behaviors of any assembly of bosons. Einstein's sketches for this project may be seen in the Einstein Archive in the library of the Leiden University.

Energy momentum pseudotensor

General relativity includes a dynamical spacetime, so it is difficult to see how to identify the conserved energy and momentum. Noether's theorem allows these quantities to be determined from a Lagrangian with translation invariance, but general covariance makes translation invariance into something of a gauge symmetry. The energy and momentum derived within general relativity by Noether's presecriptions do not make a real tensor for this reason.

Einstein argued that this is true for fundamental reasons, because the gravitational field could be made to vanish by a choice of coordinates. He maintained that the non-covariant energy momentum pseudotensor was in fact the best description of the energy momentum distribution in a gravitational field. This approach has been echoed by Lev Landau and Evgeny Lifshitz, and others, and has become standard.

The use of non-covariant objects like pseudotensors was heavily criticized in 1917 by Erwin Schrödinger and others.

Unified field theory

Following his research on general relativity, Einstein entered into a series of attempts to generalize his geometric theory of gravitation to include electromagnetism as another aspect of a single entity. In 1950, he described his "unified field theory" in a ''Scientific American'' article entitled "On the Generalized Theory of Gravitation". Although he continued to be lauded for his work, Einstein became increasingly isolated in his research, and his efforts were ultimately unsuccessful. In his pursuit of a unification of the fundamental forces, Einstein ignored some mainstream developments in physics, most notably the strong and weak nuclear forces, which were not well understood until many years after his death. Mainstream physics, in turn, largely ignored Einstein's approaches to unification. Einstein's dream of unifying other laws of physics with gravity motivates modern quests for a theory of everything and in particular string theory, where geometrical fields emerge in a unified quantum-mechanical setting.

Wormholes

Einstein collaborated with others to produce a model of a wormhole. His motivation was to model elementary particles with charge as a solution of gravitational field equations, in line with the program outlined in the paper "Do Gravitational Fields play an Important Role in the Constitution of the Elementary Particles?". These solutions cut and pasted Schwarzschild black holes to make a bridge between two patches.

If one end of a wormhole was positively charged, the other end would be negatively charged. These properties led Einstein to believe that pairs of particles and antiparticles could be described in this way.

Einstein–Cartan theory

In order to incorporate spinning point particles into general relativity, the affine connection needed to be generalized to include an antisymmetric part, called the torsion. This modification was made by Einstein and Cartan in the 1920s.

Equations of motion

The theory of general relativity has a fundamental law  – the Einstein equations which describe how space curves, the geodesic equation which describes how particles move may be derived from the Einstein equations.

Since the equations of general relativity are non-linear, a lump of energy made out of pure gravitational fields, like a black hole, would move on a trajectory which is determined by the Einstein equations themselves, not by a new law. So Einstein proposed that the path of a singular solution, like a black hole, would be determined to be a geodesic from general relativity itself.

This was established by Einstein, Infeld, and Hoffmann for pointlike objects without angular momentum, and by Roy Kerr for spinning objects.

Other investigations

Einstein conducted other investigations that were unsuccessful and abandoned. These pertain to force, superconductivity, gravitational waves, and other research. Please see the main article for details.

Collaboration with other scientists

In addition to long time collaborators Leopold Infeld, Nathan Rosen, Peter Bergmann and others, Einstein also had some one-shot collaborations with various scientists.

Einstein–de Haas experiment

Einstein and De Haas demonstrated that magnetization is due to the motion of electrons, nowadays known to be the spin. In order to show this, they reversed the magnetization in an iron bar suspended on a torsion pendulum. They confirmed that this leads the bar to rotate, because the electron's angular momentum changes as the magnetization changes. This experiment needed to be sensitive, because the angular momentum associated with electrons is small, but it definitively established that electron motion of some kind is responsible for magnetization.

Schrödinger gas model

Einstein suggested to Erwin Schrödinger that he might be able to reproduce the statistics of a Bose–Einstein gas by considering a box. Then to each possible quantum motion of a particle in a box associate an independent harmonic oscillator. Quantizing these oscillators, each level will have an integer occupation number, which will be the number of particles in it.

This formulation is a form of second quantization, but it predates modern quantum mechanics. Erwin Schrödinger applied this to derive the thermodynamic properties of a semiclassical ideal gas. Schrödinger urged Einstein to add his name as co-author, although Einstein declined the invitation.

Einstein refrigerator

In 1926, Einstein and his former student Leó Szilárd co-invented (and in 1930, patented) the Einstein refrigerator. This absorption refrigerator was then revolutionary for having no moving parts and using only heat as an input. On 11 November 1930, was awarded to Albert Einstein and Leó Szilárd for the refrigerator. Their invention was not immediately put into commercial production, as the most promising of their patents were quickly bought up by the Swedish company Electrolux to protect its refrigeration technology from competition.

Bohr versus Einstein

alt=Two men sitting, looking relaxed. A dark-haired Bohr is talking while Einstein looks sceptical.|thumb|Einstein and Niels Bohr, 1925 The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr who were two of its founders. Their debates are remembered because of their importance to the philosophy of science.

Einstein–Podolsky–Rosen paradox

In 1935, Einstein returned to the question of quantum mechanics. He considered how a measurement on one of two entangled particles would affect the other. He noted, along with his collaborators, that by performing different measurements on the distant particle, either of position or momentum, different properties of the entangled partner could be discovered without disturbing it in any way.

He then used a hypothesis of local realism to conclude that the other particle had these properties already determined. The principle he proposed is that if it is possible to determine what the answer to a position or momentum measurement would be, without in any way disturbing the particle, then the particle actually has values of position or momentum.

This principle distilled the essence of Einstein's objection to quantum mechanics. As a physical principle, it was shown to be incorrect when the Aspect experiment of 1982 confirmed Bell's theorem, which had been promulgated in 1964.

Political and religious views

Albert Einstein's political views emerged publicly in the middle of the 20th century due to his fame and reputation for genius. Einstein offered to and was called on to give judgments and opinions on matters often unrelated to theoretical physics or mathematics (see main article).

Einstein's views about religious belief have been collected from interviews and original writings. These views covered Judaism, theological determinism, agnosticism, and humanism. He also wrote much about ethical culture, opting for Spinoza's god over belief in a personal god.

Non-scientific legacy

While travelling, Einstein wrote daily to his wife Elsa and adopted stepdaughters Margot and Ilse. The letters were included in the papers bequeathed to The Hebrew University. Margot Einstein permitted the personal letters to be made available to the public, but requested that it not be done until twenty years after her death (she died in 1986). Barbara Wolff, of The Hebrew University's Albert Einstein Archives, told the BBC that there are about 3,500 pages of private correspondence written between 1912 and 1955.

Einstein bequeathed the royalties from use of his image to The Hebrew University of Jerusalem. Corbis, successor to The Roger Richman Agency, licenses the use of his name and associated imagery, as agent for the university.

In popular culture

In the period before World War II, Einstein was so well known in America that he would be stopped on the street by people wanting him to explain "that theory". He finally figured out a way to handle the incessant inquiries. He told his inquirers "Pardon me, sorry! Always I am mistaken for Professor Einstein."

Einstein has been the subject of or inspiration for many novels, films, plays, and works of music. He is a favorite model for depictions of mad scientists and absent-minded professors; his expressive face and distinctive hairstyle have been widely copied and exaggerated. ''TIME'' magazine's Frederic Golden wrote that Einstein was "a cartoonist's dream come true".

Awards and honors

Einstein merited awards and honors, including the Nobel Prize in Physics. Please see the main article.

Publications

: ''The following publications by Albert Einstein are referenced in this article. A more complete list of his publications may be found at List of scientific publications by Albert Einstein.'' This annus mirabilis paper on the photoelectric effect was received by ''Annalen der Physik'' 18 March. . This PhD thesis was completed 30 April and submitted 20 July. . This annus mirabilis paper on Brownian motion was received 11 May. . This annus mirabilis paper on special relativity was received 30 June. . This annus mirabilis paper on mass-energy equivalence was received 27 September. . First of a series of papers on this topic. . On Baer's law and meanders in the courses of rivers. . The ''chasing a light beam'' thought experiment is described on pages 48–51. Collected Papers: Further information about the volumes published so far can be found on the webpages of the Einstein Papers Project and on the Princeton University Press Einstein Page

See also

''The Einstein Theory of Relativity'' (educational film about the theory of relativity)

German inventors and discoverers

Heinrich Burkhardt

Hermann Einstein

Historical Museum of Bern (Einstein museum)

History of gravitational theory

Introduction to special relativity

List of coupled cousins

Relativity priority dispute

Sticky bead argument

Summation convention

List of Jewish Nobel laureates

Notes

References

Further reading

Fölsing, Albrecht (1997): ''Albert Einstein: A Biography''. New York: Penguin Viking. (Translated and abridged from the German by Ewald Osers.)

Hoffmann, Banesh, with the collaboration of Helen Dukas (1972): ''Albert Einstein: Creator and Rebel''. London: Hart-Davis, MacGibbon Ltd.

Isaacson, Walter (2007): ''Einstein: His Life and Universe''. Simon & Schuster Paperbacks, New York. ISBN 9780743264730

Moring, Gary (2004): ''The complete idiot's guide to understanding Einstein'' ( 1st ed. 2000). Indianapolis IN: Alpha books (Macmillan USA). ISBN 0028631803

Pais, Abraham (1982): ''Subtle is the Lord: The science and the life of Albert Einstein''. Oxford University Press. The definitive biography to date.

Pais, Abraham (1994): ''Einstein Lived Here''. Oxford University Press.

Parker, Barry (2000): ''Einstein's Brainchild''. Prometheus Books. A review of Einstein's career and accomplishments, written for the lay public.

Schweber, Sylvan S. (2008): ''Einstein and Oppenheimer: The Meaning of Genius''. Harvard University Press. ISBN 978-0674028289.

Oppenheimer, J.R. (1971): "On Albert Einstein," p. 8–12 in ''Science and synthesis: an international colloquium organized by Unesco on the tenth anniversary of the death of Albert Einstein and Teilhard de Chardin'', Springer-Verlag, 1971, 208 pp. (Lecture delivered at the UNESCO House in Paris on 13 December 1965.) Also published in The New York Review of Books, 17 March 1966, On Albert Einstein by Robert Oppenheimer

External links

Works by Albert Einstein (public domain in Canada)

''Why Socialism?'' by Albert Einstein, ''Monthly Review'', May 1949

FBI file on Albert Einstein

Nobelprize.org Biography:Albert Einstein

The Einstein You Never Knew — slideshow by ''Life magazine''

Albert Einstein — videos

Science Odyssey People And Discoveries

MIT OpenCourseWare STS.042J/8.225J: Einstein, Oppenheimer, Feynman: Physics in the 20th century — free study course that explores the changing roles of physics and physicists during the 20th century

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name	Kelly Slater
birth date	February 11, 1972
birth place	Cocoa Beach, Florida, U.S.
residence	Florida, California and Hawaii
height
weight
years active	1990–present
best year	Ranked 1st on the ASP World Tour, 1992, 1994, 1995, 1996, 1997, 1998, 2005, 2006, 2008, 2010, 2011
career earnings	$3,030,755 (as of 2011)
sponsors	Quiksilver wetsuihievements 11 time ASP World Champion Victories: 55World championship tour (WCT) surfing wins: 48
stance	Regular (natural) foot (left foot forward)
shapers	Al Merrick
quiver	5'6", 5'8", 5'10", 6'1", 6'3" and 6'6" boards when on the road
occupation	Actor
favorite waves	Kirra and Pipe
favorite maneuvers	Airs and barrels
website	kellyslater.com }}

Robert Kelly Slater (born February 11, 1972, Cocoa Beach, FL, USA) is an American professional surfer known for his competitive prowess and style. He has been crowned ASP World Champion a record 11 times, including 5 consecutive titles from 1994–98. He is the youngest (at age 20) and the oldest (at age 39) to win the title. Upon winning his 5th world title in 1997, Slater passed Australian surfing legend Mark Richards to become the most successful champion in the history of the sport. In 2007 he also became the all-time leader in career event wins by winning the Boost Mobile Pro event at Lower Trestles near San Clemente, California. The previous record was held by Slater's childhood hero, 3-time world champion Tom Curren. In addition to the ASP tour, Slater has also competed in the X-Games (in 2003 and 2004). After earlier being awarded the title prematurely as a result of a miscalculation by the ASP, on November 6, 2011 Slater officially won his eleventh ASP world title at the Rip Curl Pro Search San Francisco, by winning his 4th round heat. In May 2005, in the final heat of the Billabong Tahiti Pro contest at Teahupo'o, Slater became the first surfer ever to be awarded two perfect scores for a total 20 out of 20 points under the ASP two-wave scoring system. (The corresponding honor under the previous three-wave system belongs to fellow American Shane Beschen who achieved the feat in 1996.)

Since 1990, Slater has been sponsored primarily by surfwear industry giant Quiksilver. He exclusively rides Channel Islands surfboards equipped with his own signature series of FCS fins.

Biography

Early life and family

Slater was born on February 11, 1972 in Cocoa Beach, Florida, where he continues to reside. He has a teenage daughter named Taylor. He is of Irish and Syrian ancestry. He has an older brother, Sean, and a younger brother, Stephen.

In his spare time Slater enjoys playing the guitar,composing sonnets and spending quality time with longtime girlfriend, Kalani Miller who often travels and supports him on the ASP World Tour. His favorite surf spots are Sandspit in California, Pipeline in Hawaii, Kirra in Australia, Jeffreys Bay in South Africa, Minis in Ireland, Taghazout in Morocco, Soup Bowls in Barbados, Sebastian Inlet near his home in Florida and Bilgola beach in the northern beaches of Sydney, Australia. his three favourite surfing buddys from Bilgola are Ian morrison, James Burfitt and Jose Viera. He is also an avid golfer, with a +2 handicap. Slater is interested in the sport of Brazilian Jiu Jitsu. Some of his surfing inspirations are Tom Curren, Tom Carroll, Mark Occhilupo, Martin Potter, Andy Irons, Shane Dorian, Drew Phelps, Ken Wells, Hunter Collins, and Andrew Bloom.

Other projects

Slater played the recurring character Jimmy Slade on several episodes of the popular TV show ''Baywatch'' in the early 1990s . He appeared in an episode of the reality show The Girls Next Door, and has also starred in many surf films throughout his career.

In the late '90s Slater, along with friends and fellow pro surfers Rob Machado and Peter King, formed a band called The Surfers. The trio released an album in 1998 titled ''Songs From the Pipe'', a reference to the famous surf spot Pipeline on Oahu, Hawaii. Aside from his Love of surfing, Kelly also toured Australia with his band, performing in venues such as the Opera House, and parliament house. He was also given an honourary membership to the Rickson Cricket Club in northwest Sydney.

Slater performed a song with Ben Harper during Harper's concert in Santa Barbara. on August 1, 2006. He also performed "Rockin' in The Free World" with grunge band Pearl Jam on the July 7, 2006 in San Diego. In 1999, he appeared alongside Garbage singer Shirley Manson in the promotional video for the band's single "You Look So Fine". He played a man washed up on a seashore, then rescued by Manson.

A video game named Kelly Slater's Pro Surfer, by Treyarch and published by Activision, was released in 2002. Slater also appeared as a playable character in Tony Hawk's Pro Skater 3 prior to this, complete with a surfboard.

In 2003 Slater released his autobiography, ''Pipe Dreams: A Surfer's Journey''. In 2008 he released a second book with Phil Jarratt, entitled ''Kelly Slater: For the Love.''

Slater is passionate about preserving oceans globally and protecting temperate reefs in California through his relationship with Reef.

On May 8, 2010 the United States House of Representatives honored Slater in H. Res. 792 for his "outstanding and unprecedented achievements in the world of surfing and for being an ambassador of the sport and excellent role model." This resolution, sponsored by Florida representative Bill Posey and sponsored by 10 representatives, passed without objection by a voice vote.

Stats

WCT victories: 48

World titles: 11

On 9/15/07, Kelly Slater passed Tom Curren's long standing WCT tour victory record of 33 with his win at the Boost Mobile Pro at Lowers Trestles.

2012 Stats and results

World ranking: Currently 5th Points: 5,200

Event results in 2012 Quiksilver Pro presented by Land Rover, Gold Coast (Snapper Rocks, Australia): 5th

2011 Stats and results

World ranking: 2011 Champion Points: 68,100

Event results in 2011 Quiksilver Pro, Gold Coast (Snapper Rocks, Australia): 1st Rip Curl Pro, Bells Beach, (Victoria, Australia): 5th Billabong Rio Pro (Rio de Janeiro, Brazil): 1st Nike Pro US Open (Huntington Pier): 1st Billabong Pro Teahupoo (Teahupoo, Tahiti): 1st Quiksilver Pro New York (Long Beach, New York, USA): 2nd Hurley Pro Lower Trestles (California, USA): 1st Quiksilver Pro France (Hossegor, France): 5th Rip Curl Pro Portugal (Peniche, Portugal): 2nd Rip Curl Search (Ocean Beach, San Francisco, USA): 5th Billabong Pipeline Masters (Pipeline, Oahu, Hawaii): 3rd

2010 Stats and results

World ranking: 2010 Champion Points: 69000

Event results in 2010 Quiksilver Pro, Gold Coast (Snapper Rocks, Australia): 9th Rip Curl Pro, Bells Beach (Australia): 1st Hang Loose Pro (Santa Catarina, Brasil): 2nd Billabong Pro (Jeffreys Bay, South Africa): 17th Billabong Pro Teahupoo (Teahupoo, Tahiti): 3rd Hurley Pro (Lower Trestles, San Clemente, CA): 1st Quiksilver Pro France (Hossegor, France): 2nd Rip Curl Pro Portugal (Peniche, Portugal): 1st Rip Curl Pro Search 2010 (Middles Beach, Isabela, Puerto Rico): 1st Billabong Pipeline Masters (Pipeline, Oahu, Hawaii): 3rd

2009 Stats and results

World ranking: 6th. Points: 6136

Event results in 2009 Quiksilver Pro, Gold Coast (Snapper Rocks, Australia): 17th Rip Curl Pro, Bells Beach (Australia): 17th Billabong Pro, Tahiti (Teahupoo, Tahiti): 17th Hang Loose Pro (Santa Catarina, Brasil): 1st Billabong Pro (Jeffreys Bay, South Africa): 9th Hurley Pro (Lower Trestles, San Clemente, CA): 3rd Quiksilver Pro France (Hossegor, France): 5th Billabong Pro, Mundaka (Mundaka, Spain): 3rd Rip Curl Search (Peniche, Portugal): 17th Billabong Pipeline Masters (Pipeline, Oahu, Hawaii): 2nd

2008 Stats and results

World ranking: 2008 Champion Points: 8832

Event results Quiksilver Pro, Gold Coast (Snapper Rocks, Australia): 1st Rip Curl Pro, Bells Beach (Australia): 1st Billabong Pro, Tahiti (Teahupoo, Tahiti): 17th Globe Pro, Fiji (Tavarua, Fiji): 1st Billabong Pro, J-Bay (Jeffreys Bay, South Africa): 1st Rip Curl Search (Bali, Indonesia): 17th Boost Mobile Pro (Lower Trestles, San Clemente, CA): 1st Quiksilver Pro France (Hossegor, France): 2nd Billabong Pro, Mundaka (Mundaka, Spain): 9th Hang Loose Pro (Santa Catarina, Brasil): DNS Billabong Pipeline Masters (Pipeline, Oahu, Hawaii): 1st

History of wins

2011

Quiksilver Pro (Gold Coast, Australia)

Nike US Open (Huntington Beach, CA)

Billabong Pro Teahupoo (Teahupoo, Tahiti)

Hurley Pro Trestles (California, USA)

2010

Rip Curl Pro (Bells Beach, Australia)

Hurley Pro (Lower Trestles, California, USA)

Rip Curl Pro (Peniche, Portugal)

Rip Curl Search (Middles, Isabela, Puerto Rico)

2009

Hang Loose Pro (Santa Catarina, Brasil)

2008

Quiksilver Pro (Gold Coast, Australia)

Rip Curl Pro (Bells Beach, Australia)

Glove Pro Fiji (Cloudbreak, Restaurants – Tavarua, Fiji)

Billabong Pro J-Bay (Jeffrey's Bay, South Africa)

Boost Mobile Pro (Lower Trestles, San Clemente, California)

Billabong Pipeline Masters (Pipeline, North Shore Oahu, Hawaii)

2007

Boost Mobile Pro (Lower Trestles, San Clemente, California)

2006

Quiksilver Pro (Gold Coast, Australia)

Rip Curl Pro (Bells Beach, Australia)

2005

Billabong Pro (Teahupoo, Tahiti)

The Globe WCT (Fiji)

Billabong Pro (South Africa)

Boost Mobile Pro (Lower Trestles, San Clemente, California)

2004

Snickers Australian Open (QS)

Energy Australia Open (QS)

2003

Billabong Pro (Teahupoo, Tahiti)

Billabong Pro (South Africa)

Billabong Pro (Mundaka, Spain)

Nova Schin Festival (Brazil)

2002

The Quiksilver in Memory of Eddie Aikau (Specialty-Hawaii)

2000

Gotcha Tahiti Pro presented by Globe (Tahiti)

1999

Mountain Dew Pipe Masters (Hawaii)

1997

Coke Surf Classic (Australia)

Billabong Pro (Australia)

Tokushima Pro (Japan)

Marui Pro (Japan)

Kaiser Summer Surf WCT (Brazil)

Grand Slam (Specialty-Australia)

Typhoon Lagoon Surf Challenge (Specialty-USA)

1996

Coke Surf Classic (Australia)

Rip Curl Pro Saint Leu (Reunion Island)

CSI pres. Billabong Pro (South Africa)

U.S. Open (California)

Rip Curl Pro Hossegor (France)

Quiksilver Surfmasters (France)

Chiemsee Pipe Masters (Hawaii)

Sud Ouest Trophee (Specialty-France)

Da Hui Backdoor Shootout (Specialty-Hawaii)

1995

Quiksilver Pro (Indonesia)

Chiemsee Pipe Masters (Hawaii)

Triple Crown of Surfing (Specialty-Hawaii)

1994

Rip Curl Pro (Australia)

Gotcha Lacanau Pro (France)

Chiemsee Pipe Masters (Hawaii)

The Bud Surf Tour (WQS-USA)

The Bud Surf Tour (WQS-USA)

Sud Ouest Trophee (Specialty-France)

1993

Marui Pro (Japan)

1992

Rip Curl Pro Landes (France)

Marui Pipe Masters (Hawaii)

1990

Body Glove Surfbout Trestles (California)

Filmography

Films

''"Ultimate Wave Tahiti" (2010) ''"Bustin Down the Door" (2008) ''"One Track Mind" (2008) ''"Kelly Slater Letting Go" (2008) ''"Waveriders" 2008) ''"Surf's Up" (2007) ''"Down the Barrel" (2007) ''"Surfers – The Movie" (1990) ''"Bra Boys" (2007) ''"The Ocean" (2008) ''"One Night at McCool's" (2001) ''"Letting Go" (2006) ''"Young Guns 1, 2 & 3" (2004–2008) ''"Campaign 2" (2005) ''"Doped Youth" 'Groovy Avalon' (2004) ''"Kelly Slater in Black and White" (1991) ''"Endless Summer II" (1994) ''"Wave Warriors 3" ''"A Fly in the Champagne" (2009) (featuring Kelly Slater and Andy Irons) ''"Cloud 9" (2009) ''"Riding Giants" (2004) ''"Step into Liquid" (2003) ''"Thicker than Water" (2000) ''"Fighting Fear" (2011) ''"September Sessions" (2002) ''"Kelly Slater In Kolor" (1997)

Cameo appearance

''"Surf's Up" (2007)

Television

''Baywatch'', 10 episodes

''The Girls Next Door'', "Surf's Up" 1 episode

Bibliography

''Pipe Dreams: A Surfer's Journey'' (2003) ISBN 0060096292

''Kelly Slater: For the Love'' (2008) ISBN 0811862224

References

External links

Kelly Slater the Official Website

Kelly Slater Photo Gallery at Outside Online

Kelly Slater at the Internet Movie Database

Kelly Slater Pictures & Wallpapers

Kelly Slater Interview

Interview with Kelly Slater and Eddie Vedder Regarding Surfing and Their Friendship

Kelly Slater In SPIN's November Issue

Kelly Slater Shares His Memories of Rival Andy Irons at The Inertia

Kelly Slater isn't new world champ yet; ASP says it made an error

Category:1972 births Category:American surfers Category:American people of Syrian descent Category:American people of Irish descent Category:Laureus World Sports Awards winners Category:Living people Category:People from Cocoa Beach, Florida

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