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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
ebc2a9e9bd19b1995c26769cf39b5039e7574472	philosopher paavo pylkkänen, ilkka pättiniemi and hiley are	philosopher paavo pylkkänen, ilkka pättiniemi and hiley are of the view that bohm's emphasis on notions such as "structural process", "order" and "movement" as fundamental in physics point to some form of scientific structuralism, and that hiley's work on symplectic geometry, which is in line with the algebraic approac...	wikipedia
ca824eef6955aeda13fe7f87a18606010db7ca2d	ignazio licata cites bohm and hiley's approach as	ignazio licata cites bohm and hiley's approach as formulating "a quantum event as the expression of a deeper quantum process " that connects a description in terms of space-time with a description in non-local, quantum mechanical terms. hiley is cited, together with whitehead, bohr and bohm, for the "stance of elevatin...	wikipedia
2665cc56c79193e5a7707e8f47ab6a21ee827fb5	for his purely algebraic approach, hiley takes reference	for his purely algebraic approach, hiley takes reference to foundations in the work of gérard emch, the work of rudolf haag on local quantum field theory, and the work of ola bratteli and d.w. robertson. he points out that the algebraic representation allows to establish a connection to the thermo field dynamics of hir...	wikipedia
cde186f3047e8c631b57d50287e090dae3601f5a	hiley has repeatedly discussed the reasons for which	hiley has repeatedly discussed the reasons for which the bohm interpretation has met resistance, these reasons relating for instance to the role of the quantum potential term and to assumptions on particle trajectories. he has shown how the energy–momentum-relations in the bohm model can be obtained directly from the e...	wikipedia
caba844d090ac9390e19bb0fa85f4cd890751ad6	in 2018, hiley showed that the bohm trajectories	in 2018, hiley showed that the bohm trajectories are to be interpreted as the mean momentum flow of a set of individual quantum processes, not as the path of an individual particle, and related the bohm trajectories to feynman 's path integral formulation as an average of an ensemble of feynman paths.	wikipedia
adebfdca85c1b08c4e926bd20530568af13a910d	glen dennis, de gosson and hiley, expanding further	glen dennis, de gosson and hiley, expanding further on de gosson's notion of quantum blobs, emphasized the relevance of a quantum particle's internal energy – in terms of its kinetic energy as well as its quantum potential – with regard to the particle's extension in phase space.	wikipedia
b0942a2a5e0769ee52c408cc0734ce601d50d607	later in 2011, for the first time experimental	later in 2011, for the first time experimental results were published that showed paths that display the properties expected for bohm trajectories. more specifically, photon trajectories were observed by means of weak measurements in a double-slit interferometer, and these trajectories displayed the qualitative feature...	wikipedia
77ec5ac3d672a23d49adbcd0c8007420da184fe9	in 2011, de gosson and hiley showed that	in 2011, de gosson and hiley showed that when in bohm's model a continuous observation of a trajectory is performed, the observed trajectory is identical to the classical particle trajectory. this finding puts the bohm model in connection to the well-known quantum zeno effect. they confirmed this finding when they show...	wikipedia
66c99285f144e8b12f67f9dde3b3da9564bc5e5f	hiley has worked with maurice a. de gosson	hiley has worked with maurice a. de gosson on the relation between classical and quantum physics, presenting a mathematical derivation of the schrödinger equation from hamiltonian mechanics. together with mathematicians ernst binz and maurice a. de gosson, hiley showed how "a characteristic clifford algebra emerges fro...	wikipedia
3ba4492834c86eccf1b7cc3e0aa369581bdacb73	hiley refers to bohm's ink droplet analogy for	hiley refers to bohm's ink droplet analogy for a rather easily understandable analogy of the notion of implicate and explicate order. regarding the algebraic formulation of the implicate order, he has stated: "an important new general feature that emerges from these considerations is the possibility that not everything...	wikipedia
b2adbf60e1d3afe12c463f5366bd18c6d92331e6	this result is in line with hiley's striving	this result is in line with hiley's striving for a purely algebraic approach to quantum mechanics that is not a priori defined on any external vector space. in this purely algebraic approach, the information normally contained in the wave function is encoded in an element of a minimal left ideal of the algebra.	wikipedia
8f9f5d56dfea7a877b226727accac00907e3815b	using this approach to describe relativistic particle quantum	using this approach to describe relativistic particle quantum mechanics, hiley and r. e. callaghan presented a complete relativistic version of the bohm model for the dirac particle in analogy to bohm's approach to the non-relativistic schrödinger equation, thereby refuting the long-standing misconception that the bohm...	wikipedia
08d43de2537395699a3a4e0d3fe91c350c0dd32b	hiley expanded on the notion of a process	hiley expanded on the notion of a process algebra as proposed by hermann grassmann and the ideas of distinction of louis h. kauffman. he took reference to the vector operators introduced by mário schönberg in 1957 and by marco fernandes in his phd thesis of 1995, who had constructed orthogonal clifford algebras for cer...	wikipedia
e2a8fbe89c4e0a0273214fcdc6948690c92368fa	here emerges, in hiley's words, "a radically new	here emerges, in hiley's words, "a radically new way of looking at the way quantum processes enfold in time", built on the work of bohm and hiley in the 1980s: in this school of thought, processes of movement can be seen as automorphisms within and between inequivalent representations of the algebra. in the first case,...	wikipedia
c6efeac37d0dea68540bd9037558fb2821753355	with these results, hiley gave evidence to the	with these results, hiley gave evidence to the notion that the ontology of implicate and explicate orders could be understood as a process described in terms of an underlying non-commutative algebra, from which spacetime could be abstracted as one possible representation. the non-commutative algebraic structure is iden...	wikipedia
e9a1c934cc7e36306ed940d46acd9166709d5ce5	in 2005, building on his work with brown,	in 2005, building on his work with brown, hiley showed that the construction of subspaces allows the bohm interpretation to be understood in terms of the choice of the x -representation as shadow phase space as one particular choice among an infinite number of possible shadow phase spaces. hiley noted a conceptual para...	wikipedia
2b517b86545b96478e2d0aade2a03cfe61948471	hiley demonstrated the equivalence between moyal's characteristic function	hiley demonstrated the equivalence between moyal's characteristic function for the wigner quasi-probability distribution f(x,p,t) and von neumann's idempotent within the proof of the stone–von neumann theorem, concluding: "in consequence, f(x,p,t) is not a probability density function but a specific representation of t...	wikipedia
6c23c27e068cf8e735296f3ccebe1980148ec8f0	in 2001, picking up on the "characteristic matrix"	in 2001, picking up on the "characteristic matrix" developed with bohm in 1981 and the notion of a "moment" introduced with fernandes in 1997, hiley proposed to use a moment as "an extended structure in both space and time" as a basis for a quantum dynamics, to take the place of the notion of a point particle.	wikipedia
9c89bd52956d9f1b978728fe128c24cbfc52adad	the algebraic structure of the quantum formalism can	the algebraic structure of the quantum formalism can be interpreted as bohm's implicate order, and shadow manifolds are its necessary consequence: "the order of process by its very essence cannot be displayed in one unique manifest (explicate) order. we can only display some aspects of the process at the expense of oth...	wikipedia
bfdf233de389d9d0bc28554b42f388bdbdb2ddc9	hiley has emphasized that quantum processes cannot be	hiley has emphasized that quantum processes cannot be displayed in phase space for reason of lacking commutativity. as israel gelfand had shown, commutative algebras allow a unique manifold to be constructed as a sub-space which is dual to the algebra; non-commutative algebras in contrast cannot be associated with a un...	wikipedia
92032a955aa53a18c34a074da1212079e1662470	the set of two operator equations, first derived	the set of two operator equations, first derived and published by brown and hiley in 2000, was re-derived and expanded upon in hiley's later publications. hiley also pointed out that the two operator equations are analogous to the two equations that involve the sine and cosine bracket, and that the quantum phase equati...	wikipedia
8ca01931552601ec90a821272dabf6275b093626	in 2001, hiley proposed to extend the heisenberg	in 2001, hiley proposed to extend the heisenberg lie algebra, which is defined by the pair (q ^, p ^ {\displaystyle {\hat {q}},{\hat {p}}}) satisfying the commutator bracket = iħ and which is nilpotent, by additionally introducing an idempotent into the algebra to yield a symplectic clifford algebra. this algebra makes...	wikipedia
8458b03221621e34dc115858c7cb1c0379b18052	in 2000, brown and hiley showed that the	in 2000, brown and hiley showed that the schrödinger equation can be written in a purely algebraic form that is independent of any representation in a hilbert space. this algebraic description is formulated in terms of two operator equations. the first of these (formulated in terms of the commutator) represents an alte...	wikipedia
dc114b5c2cf34311c9d68a9d0f3d4600fd7aec60	i ℏ ∂ ρ ^ ∂ t +	i ℏ ∂ ρ ^ ∂ t + − = 0 {\displaystyle i\hbar {\frac {\partial {\hat {\rho }}}{\partial t}}+_{-}=0} ρ ^ ∂ s ^ ∂ t + 1 2 + = 0 {\displaystyle {\hat {\rho }}{\frac {\partial {\hat {s}}}{\partial t}}+{\frac {1}{2}}_{+}=0}	wikipedia
0ccbfd7658d04918af59e4365de1e5e294f0484a	around the same time, in 1997, hiley's co-worker	around the same time, in 1997, hiley's co-worker melvin brown showed that the bohm interpretation of quantum physics need not rely on a formulation in terms of ordinary space (x {\displaystyle x} -space), but can be formulated, alternatively, in terms of momentum space (p {\displaystyle p} -space).	wikipedia
785a37cd71f5b7cf004c19737278813af046d4b6	in the late 1990s, hiley expanded further on	in the late 1990s, hiley expanded further on the notion he had developed with bohm on the description of quantum phenomena in terms of processes. hiley and his co-worker marco fernandes interpret time as an aspect of process that should be represented by a mathematically appropriate description in terms of an algebra o...	wikipedia
045c3c50847b63f21bc3294406ef52d74b2b15ec	hiley has pursued work on algebraic structures in	hiley has pursued work on algebraic structures in quantum theory throughout his scientific career. after bohm's death in 1992, he published several papers on how different formulations of quantum physics, including bohm's, can be brought in context. hiley also pursued further work on the thought experiments set out by ...	wikipedia
5233c814970123c8cf68ccce14a703b9546482a5	they investigated non-locality of spacetime also in terms	they investigated non-locality of spacetime also in terms of the time dimension. in 1985, bohm and hiley showed that wheeler's delayed choice experiment does not require the existence of the past to be limited to its recording in the present. hiley and r. e. callaghan later confirmed this view, which stands in stark co...	wikipedia
f380c0f62b99bca7fabe0d9eaf35a9cfd20e2f47	in the view of bohm and hiley, "things,	in the view of bohm and hiley, "things, such as particles, objects, and indeed subjects, are considered as semi-autonomous quasi-local features of this underlying activity". these features can be considered to be independent only up to a certain level of approximation in which certain criteria are fulfilled. in this pi...	wikipedia
a35f3de2ad34440f72e88e98a08f26d40704b9dd	the notion of another order underlying space was	the notion of another order underlying space was not new. along similar lines, both gerard 't hooft and john archibald wheeler, questioning whether space-time was the appropriate starting-point for describing physics, had called for a deeper structure as starting point. in particular, wheeler had proposed a notion of p...	wikipedia
f96e9fa383d12163f597e03f5cf21c68dfaeb536	in 1984, hiley and frescura discussed an algebraic	in 1984, hiley and frescura discussed an algebraic approach to bohm's notion of implicate and explicit orders: the implicate order is carried by an algebra, the explicate order is contained in the various representations of this algebra, and the geometry of space and time appear at a higher level of abstraction of the ...	wikipedia
a6f53f62f38c3ec29c21117c93690fcd69e64b94	in 1981, bohm and hiley introduced the "characteristic	in 1981, bohm and hiley introduced the "characteristic matrix", a non-hermitian extension of the density matrix. the wigner and moyal transformation of the characteristic matrix yields a complex function, for which the dynamics can be described in terms of a (generalized) liouville equation with the aid of a matrix ope...	wikipedia
82c7dbe2756801c6844252542a6dd707e518493e	as of 1980, hiley and his co-worker fabio	as of 1980, hiley and his co-worker fabio a. m. frescura expanded on the notion of an implicate order by building on the work of fritz sauter and marcel riesz who had identified spinors with minimal left ideals of an algebra. the identification of algebraic spinors with minimal left ideals, which can be seen as a gener...	wikipedia
dd033e941988f45cdb6e2820c72653e7841ac09f	much of bohm and hiley's work in the	much of bohm and hiley's work in the 1970s and 1980s has expanded on the notion of implicate, explicate and generative orders proposed by bohm. this concept is described in the books wholeness and the implicate order by bohm and science, order, and creativity by bohm and f. david peat. the theoretical framework underly...	wikipedia
7370177c30ab8b867faabd7fbe50553efc89680e	i emphasize that bohm–hiley ontological reformulation of rqft	i emphasize that bohm–hiley ontological reformulation of rqft always treats bose fields as continuous distributions in spacetime – basically because these quantum fields have perfectly well-defined classical analogs. the textbook spin-0, spin-1 and spin-2 bosons, such as the higgs, photons, gluons, electroweak bosons a...	wikipedia
9bd4c5f7491893dce6f0b95fff5734c6e32f59fd	the bohm–hiley approach to relativistic quantum field theory	the bohm–hiley approach to relativistic quantum field theory (rqft) as presented in bohm and hiley's book undivided universe and in the work of their co-worker kaloyerou was reviewed and re-interpreted by abel miranda, who stated:	wikipedia
220de50b978423f20aa82c7005700d15e730aa72	with pan n. kaloyerou, hiley extended the quantum	with pan n. kaloyerou, hiley extended the quantum potential approach to quantum field theory in minkowski spacetime. bohm and hiley proposed a new interpretation of the lorentz transformation and considered the relativistic invariance of a quantum theory based on the notion of be ables, a term coined by john bell to di...	wikipedia
56df33ef05f4bf5813ea1987ca274c036f3f9086	in processes of non-signalling transmission of qubits in	in processes of non-signalling transmission of qubits in a system consisting of multiple particles (a process that is generally called " quantum teleportation " by physicists), active information is transferred from one particle to another, and in the bohm model this transfer is mediated by the non-local quantum potent...	wikipedia
22fbd0435b90d82499b93588469aab993e90f278	summarizing bohm's and his own interpretation, hiley has	summarizing bohm's and his own interpretation, hiley has explained that the quantum potential "does not give rise to a mechanical force in the newtonian sense. thus while the newtonian potential drives the particle along the trajectory, the quantum potential organises the form of the trajectories in response to the exp...	wikipedia
c99ce2a06f96f5d4b8f1beba516bad4b661da7fd	they showed how in the bohm model, introducing	they showed how in the bohm model, introducing the concept of active information, the measurement problem and the collapse of the wave function, could be understood in terms of the quantum potential approach, and that this approach could be extended to relativistic quantum field theories. they described the measurement...	wikipedia