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The invariant set postulate concerns the possible relationship between fractal geometry and quantum mechanics and in particular the hypothesis that the former can assist in resolving some of the challenges posed by the latter. It is underpinned by nonlinear dynamical systems theory and black hole thermodynamics. [1]
The proposer of the postulate is climate scientist and physicist Tim Palmer. Palmer completed a PhD at the University of Oxford under Dennis Sciama, the same supervisor that Stephen Hawking had and then worked with Hawking himself at the University of Cambridge on supergravity theory. He later switched to meteorology and has established a reputation pioneering ensemble forecasting. [2] He now works at the European Centre for Medium-Range Weather Forecasts in Reading, England. [3]
Palmer argues that the postulate may help to resolve some of the paradoxes of quantum mechanics that have been discussed since the Bohr–Einstein debates of the 1920s and 30s and which remain unresolved. The idea backs Einstein's view that quantum theory is incomplete, but also agrees with Bohr's contention that quantum systems are not independent of the observer.
The key idea involved is that there exists a state space for the Universe, and that the state of the entire Universe can be expressed as a point in this state space. This state space can then be divided into "real" and "unreal" sets (parts), where, for example, the states where the Nazis lost WW2 are in the "real" set, and the states where the Nazis won WW2 are in the "unreal" set of points. The partition of state space into these two sets is unchanging, making the sets invariant.
If the Universe is a complex system affected by chaos then its invariant set (a fixed state of rest) is likely to be a fractal. According to Palmer this could resolve problems posed by the Kochen–Specker theorem, which appears to indicate that physics may have to abandon the idea of any kind of objective reality, and the apparent paradox of action at a distance. In a paper submitted to the Proceedings of the Royal Society he indicates how the idea can account for quantum uncertainty and problems of "contextuality". [3] For example, exploring the quantum problem of wave-particle duality, one of the central mysteries of quantum theory, the author claims that "in terms of the Invariant Set Postulate, the paradox is easily resolved, in principle at least". [1] The paper and related talks given at the Perimeter Institute and University of Oxford also explores the role of gravity in quantum physics. [1] [4] [5]
New Scientist quotes Bob Coeke of Oxford University as stating "What makes this really interesting is that it gets away from the usual debates over multiple universes and hidden variables and so on. It suggests there might be an underlying physical geometry that physics has just missed, which is radical and very positive". He added that "Palmer manages to explain some quantum phenomena, but he hasn't yet derived the whole rigid structure of the theory. This is really necessary." [3]
Robert Spekkens has said: "I think his approach is really interesting and novel. Other physicists have shown how you can find a way out of the Kochen–Specker theorem, but this work actually provides a mechanism to explain the theorem." [3]
The two opinions above are dated 2009. The third opinion, below, is dated 2018.
According to Todd Brun, it is a tall order, to make a serious rival to quantum mechanics, a really predictive theory, out of Palmer's ideas. This goal has not been achieved yet. [6]
The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics principally attributed to Niels Bohr and Werner Heisenberg. It is one of the oldest of numerous proposed interpretations of quantum mechanics, as features of it date to the development of quantum mechanics during 1925–1927, and it remains one of the most commonly taught.
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe. In contrast to some other interpretations, such as the Copenhagen interpretation, the evolution of reality as a whole in MWI is rigidly deterministic. Many-worlds is also called the relative state formulation or the Everett interpretation, after physicist Hugh Everett, who first proposed it in 1957. Bryce DeWitt popularized the formulation and named it many-worlds in the 1970s.
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Leonard Susskind said, “The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional (2D) surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence.
The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces, and operators on these spaces. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space.
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
In quantum mechanics, Schrödinger's cat is a thought experiment that illustrates a paradox of quantum superposition. In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead as a result of its fate being linked to a random subatomic event that may or may not occur.
A theory of everything, final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe. Finding a theory of everything is one of the major unsolved problems in physics. String theory and M-theory have been proposed as theories of everything.
An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories. The "local" in this case refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields can only occur at speeds no greater than the speed of light. "Hidden variables" are hypothetical properties possessed by quantum particles, properties that are undetectable but still affect the outcome of experiments. In the words of physicist John Stewart Bell, for whom this family of results is named, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."
In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Philosophy of physics can be broadly divided into three areas:
In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of unobservable hypothetical entities. The existence of fundamental indeterminacy for some measurements is assumed as part of the mathematical formulation of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle. Most hidden-variable theories are attempts at a deterministic description of quantum mechanics, to avoid quantum indeterminacy, but at the expense of requiring the existence of nonlocal interactions.
In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories (CFT) which are quantum field theories, including theories similar to the Yang–Mills theories that describe elementary particles.
The black hole information paradox is a puzzle that appears when the predictions of quantum mechanics and general relativity are combined. The theory of general relativity predicts the existence of black holes that are regions of spacetime from which nothing — not even light — can escape. In the 1970s, Stephen Hawking applied the rules of quantum mechanics to such systems and found that an isolated black hole would emit a form of radiation called Hawking radiation. Hawking also argued that the detailed form of the radiation would be independent of the initial state of the black hole and would depend only on its mass, electric charge and angular momentum. The information paradox appears when one considers a process in which a black hole is formed through a physical process and then evaporates away entirely through Hawking radiation. Hawking's calculation suggests that the final state of radiation would retain information only about the total mass, electric charge and angular momentum of the initial state. Since many different states can have the same mass, charge and angular momentum this suggests that many initial physical states could evolve into the same final state. Therefore, information about the details of the initial state would be permanently lost. However, this violates a core precept of both classical and quantum physics—that, in principle, the state of a system at one point in time should determine its value at any other time. Specifically, in quantum mechanics the state of the system is encoded by its wave function. The evolution of the wave function is determined by a unitary operator, and unitarity implies that the wave function at any instant of time can be used to determine the wave function either in the past or the future.
A physical paradox is an apparent contradiction in physical descriptions of the universe. While many physical paradoxes have accepted resolutions, others defy resolution and may indicate flaws in theory. In physics as in all of science, contradictions and paradoxes are generally assumed to be artifacts of error and incompleteness because reality is assumed to be completely consistent, although this is itself a philosophical assumption. When, as in fields such as quantum physics and relativity theory, existing assumptions about reality have been shown to break down, this has usually been dealt with by changing our understanding of reality to a new one which remains self-consistent in the presence of the new evidence.
The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006. In 2009, the authors published a stronger version of the theorem in the Notices of the American Mathematical Society. Later, in 2017, Kochen elaborated some details.
In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–Kochen–Specker theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved by Kochen and Specker also gave an explicit example for this constraint in terms of a finite number of state vectors.
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from the usual mathematical representation of measurements in quantum physics together with the assumption of non-contextuality. Andrew M. Gleason first proved the theorem in 1957, answering a question posed by George W. Mackey, an accomplishment that was historically significant for the role it played in showing that wide classes of hidden-variable theories are inconsistent with quantum physics. Multiple variations have been proven in the years since. Gleason's theorem is of particular importance for the field of quantum logic and its attempt to find a minimal set of mathematical axioms for quantum theory.
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena.
This is a glossary for the terminology applied in the foundations of quantum mechanics and quantum metaphysics, collectively called quantum philosophy, a subfield of philosophy of physics.
In theoretical physics, the problem of time is a conceptual conflict between general relativity and quantum mechanics in that quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of time as malleable and relative. This problem raises the question of what time really is in a physical sense and whether it is truly a real, distinct phenomenon. It also involves the related question of why time seems to flow in a single direction, despite the fact that no known physical laws at the microscopic level seem to require a single direction. For macroscopic systems the directionality of time is directly linked to first principles such as the second law of thermodynamics.
