Talk:TFNR - 3.2.2 Space and Spatiality
Def Property Extent Fundamental quantity in physics Perspectives Onto Pheno Dyna Nature, essence and the mode of existence of space Fundamental spatial relations Absolute and Relative space Gravity and space Space and time Shape the universe Representation of space Space is a property of the Elementary Field, emerging from the interaction between the components of the Source, the Force and the Field Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. Space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and mass), space can be explored via measurement and experiment. Fundamental spatial relations: - connection: primitive - distance: connection relations using a third object - orientation: distance comparison relation
Debates concerning the nature, essence and the mode of existence of space date back to antiquity; Both the absolute and relative vision of space are correct… Abs space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. example of water in a spinning bucket to demonstrate his argument. Water in a bucket is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water.[10] Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was considered decisive in showing that space must exist independently of matter. Rel space as a collection of relations between objects, given by their distance and direction from one another. According to theory of general relativity, space around gravitational fields deviates from Euclidean space.[4] Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space. There is no actual time. There's only space-time. Space and time are interwoven inseparably. And they are related in a way that space-time around a gravity field gets contracted. Space is more than relations between information, structures, forms, material objects. For a relationist there can be no real difference between inertial motion, in which the object travels with constant velocity, and non-inertial motion, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates forces, it must be absolute. Space as objective features of the world, or a framework for organizing experience. (NO) The form of space Curvature and flatness non-Euclidean geometry is usually used to describe spacetime. Type of geometry Number of parallels Sum of angles in a triangle Ratio of circumference to diameter of circle Measure of curvature Hyperbolic Infinite < 180° > π < 0 Euclidean 1 180° π 0 Elliptical 0 > 180° < π > 0 the futility of any attempt to discover which geometry applies to space by experiment??? special theory of relativity led to the concept that space and time can be viewed as a single construct known as spacetime. In this theory, the speed of light in a vacuum is the same for all observers—which has the result that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to tick more slowly than one that is stationary with respect to them; and objects are measured to be shortened in the direction that they are moving with respect to the observer. general theory of relativity, a theory of how gravity interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Furthermore, in Einstein's general theory of relativity, it is postulated that space-time is geometrically distorted- curved -near to gravitationally significant masses. Gravity and time are intimately connected. There are two important effects to consider; gravitational redshift and gravitational time dilation: - Gravitational redshift concerns the loss of energy experienced by light as it climbs out of the gravitational well of a massive body, so that it appears shifted towards the red end of the electromagnetic spectrum (i.e. lower frequency, longer wavelength, and therefore less energy): http://en.wikipedia.org/wiki/Gra... - Gravitational time dilation concerns the effect of gravity on the rate at which clocks run at a given location in the gravitational field; the stronger the gravitational field (i.e. the closer the clock is to the source of the field), the slower time runs, relative to a fixed reference clock: http://en.wikipedia.org/wiki/Gra... In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of manifolds, which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example, vector spaces such as function spaces may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and topological spaces replace the concept of distance with a more abstract idea of nearness. Many of the laws of physics (>> properties of Physical Reality, combined and complex expressions of the Fundamental Principles, such as the various inverse square laws, depend on dimension three.[20]
In physics, our three-dimensional space is viewed as embedded in four-dimensional spacetime, called Minkowski space (see special relativity). The idea behind space-time is that time is hyperbolic-orthogonal to each of the three spatial dimensions. Before Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries showed that due to relativity of motion our space and time can be mathematically combined into one object–spacetime. It turns out that distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along space-time intervals are—which justifies the name. In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space-time. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in special relativity (where time is sometimes considered an imaginary coordinate) and in general relativity (where different signs are assigned to time and space components of spacetime metric). One consequence of this postulate, which follows from the equations of general relativity, is the prediction of moving ripples of space-time, called gravitational waves. While indirect evidence for these waves has been found (in the motions of the Hulse–Taylor binary system, for example) experiments attempting to directly measure these waves are ongoing. what shape the universe is, and where space came from? It appears that space was created in the Big Bang, 13.8 billion years ago[22] and has been expanding ever since. The overall shape of space is not known, but space is known to be expanding very rapidly due to the Cosmic Inflation. Spatial measurement The measurement of physical space has long been important. Although earlier societies had developed measuring systems, the International System of Units, (SI), is now the most common system of units used in the measuring of space, and is almost universally used. Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the second is based on the special theory of relativity in which the speed of light plays the role of a fundamental constant of nature. Geographical space See also: Spatial analysis Geography is the branch of science concerned with identifying and describing the Earth, utilizing spatial awareness to try to understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device. Geostatistics apply statistical concepts to collected spatial data to create an estimate for unobserved phenomena. Geographical space is often considered as land, and can have a relation to ownership usage (in which space is seen as property or territory). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership, while still other cultures such as Australian Aboriginals, rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming. Ownership of space is not restricted to land. Ownership of airspace and of waters is decided internationally. Other forms of ownership have been recently asserted to other spaces—for example to the radio bands of the electromagnetic spectrum or to cyberspace. Public space is a term used to define areas of land as collectively owned by the community, and managed in their name by delegated bodies; such spaces are open to all, while private property is the land culturally owned by an individual or company, for their own use and pleasure. Abstract space is a term used in geography to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit extraneous variables such as terrain. In psychology Psychologists first began to study the way space is perceived in the middle of the 19th century. Those now concerned with such studies regard it as a distinct branch of psychology. Psychologists analyzing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived, see, for example, visual space. Other, more specialized topics studied include amodal perception and object permanence. The perception of surroundings is important due to its necessary relevance to survival, especially with regards to hunting and self preservation as well as simply one's idea of personal space. Several space-related phobias have been identified, including agoraphobia (the fear of open spaces), astrophobia (the fear of celestial space) and claustrophobia (the fear of enclosed spaces). The understanding of three-dimensional space in humans is thought to be learned during infancy using unconscious inference, and is closely related to hand-eye coordination. The visual ability to perceive the world in three dimensions is called depth perception. Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame. Before Newton A version of the concept of absolute space can be seen in Aristotelian physics.[1] Westman writes that "whiff" of absolute space can be observed in Copernicus De revolutionibus orbium coelestium, where he exploits the concept of immobile sphere of stars.[2] Newton
Originally introduced by Sir Isaac Newton in Philosophiæ Naturalis Principia Mathematica, the concepts of absolute time and space provided a theoretical foundation that facilitated Newtonian mechanics.[3] According to Newton, absolute time and space respectively are independent aspects of objective reality:[4]
Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time ...
According to Newton, absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe. Unlike relative time, Newton believed absolute time was imperceptible and could only be understood mathematically. According to Newton, humans are only capable of perceiving relative time, which is a measurement of perceivable objects in motion (like the Moon or Sun). From these movements, we infer the passage of time.
Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space ... Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another ... — Isaac Newton
These notions imply that absolute space and time do not depend upon physical events, but are a backdrop or stage setting within which physical phenomena occur. Thus, every object has an absolute state of motion relative to absolute space, so that an object must be either in a state of absolute rest, or moving at some absolute speed.[5] To support his views, Newton provided some empirical examples: according to Newton, a solitary rotating sphere can be inferred to rotate about its axis relative to absolute space by observing the bulging of its equator, and a solitary pair of spheres tied by a rope can be inferred to be in absolute rotation about their center of gravity (barycenter) by observing the tension in the rope. Absolute time and space continue to be used in classical mechanics, but modern formulations by authors such as Walter Noll and Clifford Truesdell go beyond the linear algebra of elastic moduli to use topology and functional analysis for non-linear field theories.[6] Differing views Two spheres orbiting around an axis. The spheres are distant enough for their effects on each other to be ignored, and they are held together by a rope. The rope is under tension if the bodies are rotating relative to absolute space according to Newton, or because they rotate relative to the universe itself according to Mach, or because they rotate relative to local geodesics according to general relativity. Historically, there have been differing views on the concept of absolute space and time. Gottfried Leibniz was of the opinion that space made no sense except as the relative location of bodies, and time made no sense except as the relative movement of bodies.[7] George Berkeley suggested that, lacking any point of reference, a sphere in an otherwise empty universe could not be conceived to rotate, and a pair of spheres could be conceived to rotate relative to one another, but not to rotate about their center of gravity,[8] an example later raised by Albert Einstein in his development of general relativity. A more recent form of these objections was made by Ernst Mach. Mach's principle proposes that mechanics is entirely about relative motion of bodies and, in particular, mass is an expression of such relative motion. So, for example, a single particle in a universe with no other bodies would have zero mass. According to Mach, Newton's examples simply illustrate relative rotation of spheres and the bulk of the universe.[9]
When, accordingly, we say that a body preserves unchanged its direction and velocity in space, our assertion is nothing more or less than an abbreviated reference to the entire universe. —Ernst Mach; as quoted by Ciufolini and Wheeler: Gravitation and Inertia, p. 387
These views opposing absolute space and time may be seen from a modern stance as an attempt to introduce operational definitions for space and time, a perspective made explicit in the special theory of relativity. Even within the context of Newtonian mechanics, the modern view is that absolute space is unnecessary. Instead, the notion of inertial frame of reference has taken precedence, that is, a preferred set of frames of reference that move uniformly with respect to one another. The laws of physics transform from one inertial frame to another according to Galilean relativity, leading to the following objections to absolute space, as outlined by Milutin Blagojević:[10]
The existence of absolute space contradicts the internal logic of classical mechanics since, according to Galilean principle of relativity, none of the inertial frames can be singled out.
Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames.
Absolute space acts on physical objects by inducing their resistance to acceleration but it cannot be acted upon.
Newton himself recognized the role of inertial frames.[11]
The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line.
As a practical matter, inertial frames often are taken as frames moving uniformly with respect to the fixed stars.[12] See Inertial frame of reference for more discussion on this. Special relativity The concepts of space and time were separate in physical theory prior to the advent of special relativity theory, which connected the two and showed both to be dependent upon the reference frame's motion. In Einstein's theories, the ideas of absolute time and space were superseded by the notion of spacetime in special relativity, and curved spacetime in general relativity.
Absolute simultaneity refers to the concurrence of events in time at different locations in space in a manner agreed upon in all frames of reference. The theory of relativity does not have a concept of absolute time because there is a relativity of simultaneity. An event that is simultaneous with another event in one frame of reference may be in the past or future of that event in a different frame of reference,[7]:59 which negates absolute simultaneity. Einstein Main article: Einstein's views on the aether Quoted below from his later papers, Einstein identified the term aether with "properties of space", a terminology that is not widely used. Einstein stated that in general relativity the "aether" is not absolute anymore, as the geodesic and therefore the structure of spacetime depends on the presence of matter.[13]
To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view. For the mechanical behaviour of a corporeal system hovering freely in empty space depends not only on relative positions (distances) and relative velocities, but also on its state of rotation, which physically may be taken as a characteristic not appertaining to the system in itself. In order to be able to look upon the rotation of the system, at least formally, as something real, Newton objectivises space. Since he classes his absolute space together with real things, for him rotation relative to an absolute space is also something real. Newton might no less well have called his absolute space “Ether”; what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real. — Albert Einstein, Ether and the Theory of Relativity (1920)[14] Because it was no longer possible to speak, in any absolute sense, of simultaneous states at different locations in the aether, the aether became, as it were, four-dimensional, since there was no objective way of ordering its states by time alone. According to special relativity too, the aether was absolute, since its influence on inertia and the propagation of light was thought of as being itself independent of physical influence....The theory of relativity resolved this problem by establishing the behaviour of the electrically neutral point-mass by the law of the geodetic line, according to which inertial and gravitational effects are no longer considered as separate. In doing so, it attached characteristics to the aether which vary from point to point, determining the metric and the dynamic behaviour of material points, and determined, in their turn, by physical factors, namely the distribution of mass/energy. Thus the aether of general relativity differs from those of classical mechanics and special relativity in that it is not ‘absolute’ but determined, in its locally variable characteristics, by ponderable matter. — Albert Einstein, Über den Äther (1924)[15]
General relativity Special relativity eliminates absolute time (although Gödel and others suspect absolute time may be valid for some forms of general relativity)[16] and general relativity further reduces the physical scope of absolute space and time through the concept of geodesics.[7]:207–223 There appears to be absolute space in relation to the distant stars because the local geodesics eventually channel information from the these stars, but it is not necessary to invoke absolute space with respect to any system's physics.[17]. Aether theories in physics propose the existence of a medium, the aether (also spelled ether, from the Greek word (αἰθήρ), meaning "upper air" or "pure, fresh air"[1]), a space-filling substance or field, thought to be necessary as a transmission medium for the propagation of electromagnetic or gravitational forces. The assorted aether theories embody the various conceptions of this "medium" and "substance". This early modern aether has little in common with the aether of classical elements from which the name was borrowed. Since the development of special relativity, theories using a substantial aether fell out of use in modern physics, and were replaced by more abstract models.[2] Historical models Luminiferous aether Isaac Newton suggests the existence of an aether in The Third Book of Opticks (1718): "Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?"[3] In the 19th century, luminiferous aether (or ether), meaning light-bearing aether, was a theorized medium for the propagation of light (electromagnetic radiation). However, a series of increasingly complex experiments had been carried out in the late 1800s like the Michelson-Morley experiment in an attempt to detect the motion of Earth through the aether, and had failed to do so. A range of proposed aether-dragging theories could explain the null result but these were more complex, and tended to use arbitrary-looking coefficients and physical assumptions. Joseph Larmor discussed the aether in terms of a moving magnetic field caused by the acceleration of electrons. James Clerk Maxwell said of the aether, "In several parts of this treatise an attempt has been made to explain electromagnetic phenomena by means of mechanical action transmitted from one body to another by means of a medium occupying the space between them. The undulatory theory of light also assumes the existence of a medium. We have now to show that the properties of the electromagnetic medium are identical with those of the luminiferous medium."[4] Hendrik Lorentz and George Francis FitzGerald offered within the framework of Lorentz ether theory a more elegant solution to how the motion of an absolute aether could be undetectable (length contraction), but if their equations were correct, Albert Einstein's 1905 special theory of relativity could generate the same mathematics without referring to an aether at all. This led most physicists to conclude that this early modern notion of a luminiferous aether was not a useful concept. Einstein however stated that this consideration was too radical and too anticipate and that his relativity still needed the presence of a medium with certain properties. Mechanical gravitational aether Main article: Mechanical explanations of gravitation
From the 16th until the late 19th century, gravitational phenomena had also been modelled utilizing an aether. The most well-known formulation is Le Sage's theory of gravitation, although other models were proposed by Isaac Newton, Bernhard Riemann, and Lord Kelvin. None of those concepts is considered to be viable by the scientific community today. Non-standard interpretations in modern physics General relativity Main article: Einstein's views on the aether Einstein sometimes used the word aether for the gravitational field within general relativity, but this terminology never gained widespread support.[5]
We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an aether. According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.[6]
Quantum vacuum Quantum mechanics can be used to describe spacetime as being non-empty at extremely small scales, fluctuating and generating particle pairs that appear and disappear incredibly quickly. It has been suggested by some such as Paul Dirac[7] that this quantum vacuum may be the equivalent in modern physics of a particulate aether. However, Dirac's aether hypothesis was motivated by his dissatisfaction with quantum electrodynamics, and it never gained support by the mainstream scientific community.[8] Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University, had this to say about ether in contemporary theoretical physics:
It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed [..] The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo.[9]
Pilot waves Main articles: Pilot wave and De Broglie–Bohm theory Louis de Broglie stated, "Any particle, ever isolated, has to be imagined as in continuous “energetic contact” with a hidden medium."[10][11] Conjectures and proposals According to the philosophical point of view of Einstein, Dirac, Bell, Polyakov, ’t Hooft, Laughlin, de Broglie, Maxwell, Newton and other theorists, there might be a medium with physical properties filling 'empty' space, an aether, enabling the observed physical processes. Albert Einstein in 1894 or 1895: ”The velocity of a wave is proportional to the square root of the elastic forces which cause [its] propagation, and inversely proportional to the mass of the aether moved by these forces."[12] Albert Einstein in 1920: ”We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an Aether. According to the general theory of relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.”[13] Paul Dirac wrote in 1951:[7] "Physical knowledge has advanced much since 1905, notably by the arrival of quantum mechanics, and the situation [about the scientific plausibility of Aether] has again changed. If one examines the question in the light of present-day knowledge, one finds that the Aether is no longer ruled out by relativity, and good reasons can now be advanced for postulating an Aether ... We have now the velocity at all points of space-time, playing a fundamental part in electrodynamics. It is natural to regard it as the velocity of some real physical thing. Thus with the new theory of electrodynamics [vacuum filled with virtual particles] we are rather forced to have an Aether". John Bell in 1986, interviewed by Paul Davies in "The Ghost in the Atom" has suggested that an Aether theory might help resolve the EPR paradox by allowing a reference frame in which signals go faster than light. He suggests Lorentz contraction is perfectly coherent, not inconsistent with relativity, and could produce an aether theory perfectly consistent with the Michelson-Morley experiment. Bell suggests the aether was wrongly rejected on purely philosophical grounds: "what is unobservable does not exist" [p. 49]. Einstein found the non-aether theory simpler and more elegant, but Bell suggests that doesn't rule it out. Besides the arguments based on his interpretation of quantum mechanics, Bell also suggests resurrecting the aether because it is a useful pedagogical device. That is, many problems are solved more easily by imagining the existence of an aether.[citation needed] According to Albert Einstein, “God does not play dice with the Universe”. And those agreeing with him are looking for a classical, deterministic aether theory that would imply quantum-mechanical predictions as a statistical approximation, a hidden variable theory. In particular, Gerard 't Hooft[14] conjectured that: “We should not forget that quantum mechanics does not really describe what kind of dynamical phenomena are actually going on, but rather gives us probabilistic results. To me, it seems extremely plausible that any reasonable theory for the dynamics at the Planck scale would lead to processes that are so complicated to describe, that one should expect apparently stochastic fluctuations in any approximation theory describing the effects of all of this at much larger scales. It seems quite reasonable first to try a classical, deterministic theory for the Planck domain. One might speculate then that what we call quantum mechanics today, may be nothing else than an ingenious technique to handle this dynamics statistically.” In their paper Blasone, Jizba and Kleinert:[15] “have attempted to substantiate the recent proposal of G. ’t Hooft in which quantum theory is viewed as not a complete field theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The underlying dynamics are taken to be classical mechanics with singular Lagrangians supplied with an appropriate information loss condition. With plausible assumptions about the actual nature of the constraint dynamics, quantum theory is shown to emerge when the classical Dirac-Bergmann algorithm for constrained dynamics is applied to the classical path integral...”. Louis de Broglie, "If a hidden sub-quantum medium is assumed, knowledge of its nature would seem desirable. It certainly is of quite complex character. It could not serve as a universal reference medium, as this would be contrary to relativity theory.
