The Pondicherry interpretation of quantum mechanics
From Wikipedia, the free encyclopedia
The Pondicherry interpretation of quantum mechanics (PIQM) was developed by Ulrich Mohrhoff, who teaches at the Sri Aurobindo International Centre of Education in Puducherry (formerly Pondicherry), India.
From the mathematical point of view, quantum mechanics is a generalized probability calculus. Quantum states — including density operators and wavefunctions — are algorithms for calculating the probabilities of the possible outcomes of measurements on the basis of actual measurement outcomes. They take as their input (i) one or more measurement outcomes, (ii) a measurement M, and (iii) the time of M. They yield as their output the probabilities of the possible outcomes of M. In other words, quantum states encapsulate correlations between measurement outcomes.
Quantum mechanics — in the inclusive sense that makes no distinction between quantum mechanics, quantum physics, and quantum theory — is also the general theoretical framework of contemporary physics. Thus there exists a wide gulf between the laboratory use of quantum mechanics and its ontology. The aim of interpretations of quantum mechanics is to bridge this gulf, or else to explain why that aim is unachievable.
The PIQM offers an objective description of the world, free from invocations of consciousness, knowledge, or purposeful experimental interventions, without construing any element of the quantum-mechanical probability calculus as representing a state of affairs of some kind. It arrives at its ontological affirmations by analyzing quantum-mechanical probability assignments in various measurement contexts.
Contents |
[edit] Interpretational principles
Given a sequence of measurements and a specific outcome of the first, quantum mechanics lays down two distinct rules for calculating the probabilities of the possible outcomes of the final measurement. The first rule applies if the intermediate measurements are made but their outcomes are not taken into account. The second rule applies if the intermediate measurements are not made. To explain the need for this distinction is one aspect (or possible formulation) of the measurement problem.
The PIQM is based on the following interpretational principles:
- Whenever the second rule applies, the distinctions we make between the possible sequences of intermediate outcomes are distinctions that "Nature does not make": they correspond to nothing in the real world.
A double-slit experiment with electrons may serve as an example. We consider a single intermediate measurement with two possible outcomes: the electron goes through the left slit or it goes through the right slit. Under the conditions stipulated by the second rule, the distinction between these alternatives lacks a counterpart in the real world; it exists solely in our minds.
- If quantum mechanics implies that something X cannot be observed (e.g., the particle trajectories of Bohmian mechanics or the evolving instantaneous quantum state of a system between consecutive measurements), the reason this is so is that X does not exist.
[edit] Ontological affirmations
[edit] Objective fuzziness
One of the key problems leading to the discovery of quantum mechanics was the stability of atoms. Thanks to quantum mechanics, we now know that this rests on the fuzziness of every composite object's internal relative positions and momenta. (Heisenberg's original term Unschärfe, the literal translation of which is "fuzziness", is generally mistranslated as "uncertainty.")
According to the PIQM, the proper way to define and quantitatively describe a fuzzy observable is to assign nontrivial probabilities — probabilities other than 0 and 1 — to the possible outcomes of a measurement of such an observable. The existence of fuzzy observables may thus be seen as one of the reasons why quantum mechanics is a generalized probability calculus, and the stability of atoms may be seen as one of the reasons (in the anthropic sense) for the existence of fuzzy observables.
[edit] To be is to be measured
Implicit in every quantum-mechanical probability assignment is the assumption that a measurement is successfully made: there is an outcome. This also holds in the special case in which the probability of a particular outcome equals 1. In other words, probability 1 is not sufficient for "is" or "has". Quantum mechanics yields probabilities with which this or that outcome is obtained in a successful measurement, not probabilities with which this or that property or value is possessed, regardless of measurements.
If probability 1 is not sufficient for the possession of a property (by a system) or a value (by an observable), then what is? According to the PIQM, no property or value is possessed unless its possession is indicated by (or inferable from) an actual event or state of affairs. To be is to be measured. (Any event or state of affairs from which the truth or falsity of a proposition of the form "system S has the property P", or "observable O has the value V", can be inferred, qualifies as a measurement.).
[edit] The shapes of things
According to the PIQM, physical space is not a self-existent (substantial) expanse, nor does it have parts, nor is it a set of points or pointlike positions. Physical space is a set of relations. It contains (in the proper, set-theoretic sense of "containment") the spatial relations that hold among material objects.
The form of a composite material object is the totality of its internal spatial relations. A structureless particle (lacking internal relations) is a formless object. (According to the standard model of particle physics, quarks, leptons, and gauge bosons lack internal structure and should therefore be thought of as formless rather than as pointlike.)
If space contains spatial relations, and if forms are sets of spatial relations, then space contains the forms of all things that have forms, but it does not contain the formless ultimate constituents of matter.
Nor is there such a thing as empty space. The reason this is so is not that space is teeming with virtual particles but that unpossessed positions do not exist. Where "there" is nothing, there is no there.
[edit] Detectors, the rôle of the measurement apparatus
Because space is not an intrinsically partitioned expanse, spatial distinctions are relative and contingent: relative because the distinction between (what we think of as) two disjoint regions may be real for one object and nonexistent for another; and contingent because the reality of a given distinction for a given object O (for example the distinction between "inside region R" and "outside region R") depends on whether the corresponding proposition ("O is in R") has either of the truth values "true" or "false", which in turn depends on whether either truth value is indicated ("measured").
It follows that a particle detector is needed not only to indicate the presence of a particle in its sensitive region but also to realize a region of space, thereby making it possible to attribute to a particle the property of being in this region.
This conclusion bears generalization. The measurement apparatus, which is presupposed by every quantum-mechanical probability assignment, is needed not only for the purpose of indicating the possession, by a material object, of a particular property (or the possession, by an observable, of a particular value) but also for the purpose of realizing a set of properties or values, which thereby become available for attribution.
[edit] Top-down, but not all the way
No object ever has a sharp (mathematically exact) position relative to another object. (In a non-relativistic world this is so because the exact localization of a particle implies an infinite momentum dispersion and hence an infinite mean energy. In a relativistic world the attempt to produce a strictly localized particle results instead in the production of particle-antiparticle pairs.) An important consequence of this is that the spatial differentiation of the physical world is incomplete; it does not go "all the way down." If in our minds we partition the world into smaller and smaller regions, there comes a point beyond which there isn't any material object for which these regions, or the corresponding distinctions, exist. (The same holds for the temporal and hence for the spatiotemporal differentiation of the world.)
Attempts to model the world "from the bottom up", on the foundation of an intrinsically and completely differentiated spacetime manifold, are therefore at odds with the ontological implications of the quantum-mechanical probability calculus, in particular the world's incomplete spatiotemporal differentiation. For this reason the PIQM repudiates ontologies that (i) treat quantum fields — the probability algorithms of relativistic quantum mechanics — as ultimate constituents of reality or (ii) feature evolving quantum states — with our without wavefunction collapse. (Such ontologies require, or entail the existence of, a completely differentiated spacetime manifold.)
[edit] A single ultimate constituent
Because the number of particles in an isolated, non-relativistic quantum system is conserved, such a system can be thought of a being made up of particles. Because there is no conservation law for the number of particles in a relativistic quantum system, this number is a quantum observable. As such it has a (definite) value only if, and only when, it is actually measured. (In particle collision experiments, the number of incoming particles and the number of outgoing particles are measured and therefore in possession of values, whereas the unmeasured number of particles existing at an intermediate time lacks a value.) The number of particles in a relativistic quantum system should therefore not be thought of as counting the system's material constituents.
This conclusion is frequently but wrongly (as pointed out) taken to imply an ontology in which quantum fields are the ultimate existents. According to the PIQM, the correct conclusion, which may also be drawn from the phenomenon of quantum entanglement, is that a quantum system's aspects of multiplicity are subordinate to an inalienable ontological unity.
What can we say of a particle without internal structure, considered by itself, out of relation to anything else? According to the PIQM, the answer is: nothing. As said, we cannot attribute to it a form. Since motion is relative, we cannot attribute to it any of the properties that derive their meanings from the quantum-mechanical description of motion (that is, from external symmetry operations such as translations in time or space or rotations). Nor can we attribute to it any kind of charge, since charges derive their meanings from the quantum-mechanical description of interactions (that is, from internal symmetry operations).
According to the identity of indiscernibles, A and B are one and the same thing just in case there is no conceivable way of telling the difference between A and B. Hence, considered out of relation to each other, all elementary particles are one and the same thing. Quantum statistics (Bose-Einstein or Fermi-Dirac) confirms this metaphysical conclusion, inasmuch as it prohibits the association of distinct identities with particles lacking properties by which they can be distinguished.
[edit] The macroworld
The possibility of obtaining evidence of the departure of an object O from its classically predictable position calls for detectors whose position probability distributions are narrower than O's — detectors that can probe the (intrinsically undifferentiated) region over which O's fuzzy position extends. Such detectors evidently do not exist for those objects that have the sharpest positions in existence. For them the probability of obtaining evidence of departures from the classically predictable motion is very low. Hence among them there are many of which the following is true: every one of their indicated positions is consistent with (i) every prediction that can be made on the basis of their previously indicated positions and (ii) a classical law of motion. These are the objects that deserve to be called "macroscopic". (This definition does not require that the probability of finding a macroscopic object where classically it could not be, is strictly zero. What it requires is that there be no position-indicating event that is inconsistent with predictions that could in principle be made on the basis of a classical law of motion and earlier position-indicating events.) To permit a macroscopic object to indicate a measurement outcome, one exception has to be made: its position may change unpredictably if and when it serves to indicate an outcome.
The positions of macroscopic objects (macroscopic positions, for short) indicate each other's values so abundantly, so persistently, and so sharply that they are fuzzy only in relation to an imaginary background that is more differentiated than the actual world. The region over which a macroscopic position is "smeared out" is never probed. Relating as it does to a purely imaginary background, its fuzziness is itself purely imaginary. The contentious question of whether macroscopic objects (properly defined) obey the classical or the quantum laws, is therefore ill-posed. Macroscopic objects obey both the classical and the quantum laws, inasmuch as the quantum laws degenerate into the classical laws whenever the fuzziness of observables can be ignored. Where the positions of macroscopic objects are concerned, this is always.
Which element or substructure of the theoretical structure of quantum mechanics corresponds to What Exists? According to the PIQM, not a multitude of spacetime points, nor a multitude of particles, nor quantum fields, nor wavefunctions, nor the quantum state of the universe, but the macroworld, defined as the totality of relative positions existing between macroscopic objects. Whereas one cannot attribute an existence independent of measurements to an individual position (even the Moon's position has a value only because of the myriads of macroscopic positions from which its whereabouts can be inferred), the macroworld as a whole depends on nothing external to itself.
[edit] Challenges
[edit] Completeness and consistency
How can a fundamental physical theory that is concerned with nothing but statistical correlations between property-indicating events be complete? To show that quantum mechanics is indeed a complete theory, one has to show that it in fact encompasses the property-indicating events. The PIQM does this by showing that the theoretical structure of the theory encompasses the macroworld, and that the macroworld in turn encompasses property-indicating events as unpredictable changes in the values of macroscopic positions. What is incomplete is not quantum mechanics but the spatiotemporal differentiation of the physical world.
Again, no value is possessed unless its possession is indicated — by another value. The PIQM steers clear of the threatening infinite regress by showing that, for all quantitative purposes (rather than merely FAPP), the values of macroscopic positions are self-existent.
[edit] Supervenience, manifestation
Erwin Schrödinger: quantum entanglement is the characteristic trait of quantum mechanics. John Archibald Wheeler: the central mystery of physics is the miraculous identity of particles of the same type. Richard Feynman: the double-slit experiment with electrons has in it the heart of quantum mechanics. Henry Stapp: Bell's proof that the principle of locality is incompatible with quantum mechanics is the most profound discovery in science. According to the PIQM, all of these extraordinary features of quantum mechanics are subsumed and eclipsed by the supervenience of the microscopic on the macroscopic.
The properties of the microword exist only because, and only to the extent that, they are indicated by events in the macroworld. This flies in the face of the twenty-five centuries old atomistic paradigm. It is no longer appropriate to ask: what are the ultimate building blocks, and how do they interact and combine? If we accept Mohrhoff's suggested identification of the Indian metaphysical concept of Brahman with the single ultimate constituent of the universe, the right question to ask instead is: how does Brahman manifest itself? The answer, in outline: by entering into spatial relations with itself, Brahman gives rise to both matter and space, inasmuch as space is the totality of existing spatial relations, whereas matter is the corresponding (apparent) multitude of relata — "apparent" because the relations are self-relations.
If we experience something the like of which we never experienced before, we are obliged to describe it in terms of familiar experiences. By the same token, what lies "behind" the manifested world can only be described in terms of the finished product — the manifested world. According to the PIQM, quantum mechanics affords us a glimpse "behind" the manifested world at formless particles and non-visualizable atoms, which, instead of being the world's constituent parts or structures, are instrumental in its manifestation. But it allows us to describe what we "see" only in terms of inferences from macroevents and their quantum-mechanical correlations. Hence the supervenience of the microscopic on the macroscopic.
[edit] References and external links
- U. Mohrhoff (2000), "What quantum mechanics is trying to tell us", American Journal of Physics 68, 728–45; a.k.a. "The Pondicherry interpretation of quantum mechanics".
- R. E. Kastner (2001), "Comment on 'What quantum mechanics is trying to tell us' by Ulrich Mohrhoff", American Journal of Physics, 69(8): 860-863.
- U. Mohrhoff (2001), "Objective probabilities, quantum counterfactuals, and the ABL rule: A response to R. E. Kastner", American Journal of Physics 69, 864–73.
- U. Mohrhoff (2002), "Making sense of a world of clicks", Foundations of Physics 32, 1295–1311.
- L. Marchildon (2004), "Remarks on Mohrhoff's Interpretation of Quantum Mechanics", Foundations of Physics 34, 59–73.
- U. Mohrhoff (2004), "Do quantum states evolve? Apropos of Marchildon's remarks", Foundations of Physics 34, 75–97.
- U. Mohrhoff (2004), "This elusive objective existence", International Journal of Quantum Information 2, 201–20.
- U. Mohrhoff (2005), "The Pondicherry interpretation of quantum mechanics: An overview", PRAMANA—Journal of Physics 64, 171–85.
- U. Mohrhoff (2006), "Is the end in sight for theoretical pseudophysics?", in New Topics in Quantum Physics Research, edited by V. Krasnoholovets and F. Columbus (Nova Science Publishers).
- U. Mohrhoff (2006), "Quantum mechanics explained". This article gives reasons why quantum mechanics should not be interpreted as anything but a generalized probability calculus.
- A. Shafiee, M. Jafar-Aghdami, and M. Golshani (2006), "A critique of Mohrhoff's interpretation of quantum mechanics," Studies in History and Philosophy of Modern Physics, 37(2): 316-329.
