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Paavo Pylkkänen University of Helsinki, Finland and University of Skövde, Sweden E-‐mail: [email protected] Web: http://tuhat.halvi.helsinki.fi/portal/en/person/pylkkane
¡ “In physics, the theory that energy does not have a continuous range of values, but is, instead, absorbed or radiated discontinuously, in multiples of definite, indivisible units called quanta.
¡ Just as earlier theory showed how light, generally seen as a wave motion, could also in some ways be seen as composed of discrete particles (photons), quantum theory shows how atomic particles such as electrons may also be seen as having wavelike properties.
¡ Quantum theory is the basis of particle physics, modern theoretical chemistry, and the solid-‐state physics that describes the behaviour of the silicon chips used in computers.”
Hutchinson Pocket Dictionary of Physics
¡ Biology (photosynthesis, avian magnetoreception) § Ball, P. (2011) The dawn of quantum biology, Nature 474,
272-‐274. ¡ Information technology (quantum computation and
cryptography) § Bouwmeester, D., Ekert, A. and Zeilinger, A.K. Eds., The Physics
of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation. Heidelberg and Berlin: Spinger, 2000.
¡ Cognitive modelling (decision making, memory, concepts and perception). § Pothos, M & Busemeyer J. R. (2013) Can quantum probability
provide a new direction for cognitive modeling?, Behavioral and Brain Sciences 36, 255-‐327.
¡ Ironically in relation to this success, quantum theory comes with many puzzles and paradoxes, e.g. claims that § electrons are in two places at once § cats are alive and dead at the same time § the world at the macroscopic level is constantly branching into copies (“many worlds”)
§ to solve these problems the consciousness of the observer has to play an active role.
¡ A more sober version of quantum theory which solves the above problems was discovered by de Broglie in 1927
¡ rediscovered and developed by Bohm in 1952 (see also Bohm and Hiley 1987, 1993).
¡ In this theory the electron is seen as a particle AND a quantum wave field.
¡ Bohm and Hiley: this wave field is not an ordinary physical field, but rather a field of information, which literally informs the energy of the particle.
¡ Further: such notion of “active information” applies beyond quantum physics, e.g. in § biology (e.g. in the way the DNA molecule in-‐forms the construction of proteins),
§ information technology § psychological and social phenomena.
¡ Traditionally quantum theory was not given an ontological interpretation § The wave function was seen as part of an algorithm for calculating probabilities of finding e.g. an electron at a given location.
§ QT was thought to concern our knowledge of the system, rather than the system itself ▪ For a penetrating discussion of the traditional view, see Plotnitsky, A. (2010)
Epistemology and Probability. Bohr, Heisenberg, Schrödinger and the Nature of Quantum-‐Theoretical Thinking. (Springer)
¡ However: in recent years much attention have been given to various ontological interpretations of QM, due to de Broglie (1927), Bohm (1952), Everett (1957), Ghirardi-‐Rimini-‐Weber (GRW, 1986) etc. § Saunders, S. et al. ed. (2010) Many Worlds? Everett, Quantum Theory, &
Reality. Oxford University Press. § Albert, D. and Ney, A. ed. (2013) The Wave Function: Essays on the
Metaphysics of Quantum Mechanics. Oxford University Press.
¡ My own long-‐term research interest: philosophical relevance of the ontological interpretation of Bohm & Hiley (1987, 1993) § Bohm, David and Hiley, Basil J. 1987. An Ontological Basis for
Quantum Theory: I. Non-‐relativistic Particle Systems. Physics Reports 144 (6): 323-‐348.
§ Bohm, D. and Hiley, B. J. (1993) The Undivided Universe: An Ontological Interpretation of Quantum Theory. London: Routledge
¡ Pylkkänen, P., Hiley, B.J. & Pättiniemi, I. (forthcoming) “Bohm approach and individuality”, in Guay, A. & Pradeu, T. eds. Individuals Across Sciences – a Revisionary Metaphysics?, Oxford University Press.
¡ Pylkkänen, P. (forthcoming) “Weak vs. strong quantum cognition”, to be published in Liljenström, H. ed. Proceedings of ICCN the 4th International Conference on Cognitive Neurodynamics. Springer
¡ Pylkkänen, P. (forthcoming) “Fundamental physics and the mind – is there a connection”, in T. Filk ed. Quantum Interaction. 8th International Conference, Springer.
¡ What happens if you pass e.g. electrons through the 2-‐slits?
¡ The electron was initially assumed to be a particle (it has mass and charge) § so we expect that it should behave like a little bullet!
¡ Notice that we get an interference pattern even if the electrons enter the slit system one by one
¡ An individual system exhibits both § particle properties ▪ it arrives at the detector at a single spot
¡ and § wave properties ▪ the place where the spot appears is constrained by the mathematics of wave behaviour ▪ how else would such individual particles build up a wave interference pattern?
¡ Note in particular: opening of 2nd slit may prevent an electron reaching a point where it could arrive if only one slit were open.
¡ Natural to ask: how does the electron move through the slit system? How could a particle obey the mathematics of waves?
¡ The easiest way to answer these questions would be to make further experiments § “Let’s look what happens”
¡ Unfortunately we cannot observe the motion of an individual electron in detail! § This relates to the Heisenberg indeterminacy principle
§ “If we observe precisely where it is, we have no idea of where it is going” (and vice versa)
¡ Note especially: to predict the movement of an electron we should measure both position x (“where it is”) and momentum p (“where it is going”) at a single moment. § we cannot do this as long as we stay within current quantum theory!
§ without the initial conditions we cannot predict what the individual system does! ▪ -‐> indeterminism, probability…
Source: WikiPremed, a trademark of Wisebridge Learning Systems LLC.
¡ The mystery is this: the electrons leave as particles, and they arrive as particles, one by one, to the screen. § as a large number of them passes through the system, a pattern builds up.
§ what is this pattern? § it is an interference pattern! § interference is a signature of a wave.
¡ But how can the particles, sent into the system one by one, collectively build up an interference pattern?
¡ Surely each individual “particle” must also have some wave property § how otherwise could such a “particle” obey the interference pattern (e.g. avoid certain classically allowed areas)?
¡ Bohr ¡ Von Neumann (collapse interpretations) ¡ “many worlds” ¡ deBroglie-‐Bohm ¡ etc.
From N. Bohr 1949/1983: Discussions with Einstein on Epistemological Problems in Atomic Physics, p. 27.
Yves Couder et al.
¡ The Bohm theory postulates that an electron is a particle always accompanied with a new type of quantum field, which guides it
¡ In the two-‐slit experiment the particle goes through one of the slits, and then appears at a point in a photographic place § this explains why we see the appearance of a spot § note especially that there is no need to assume a collapse of the wave function
¡ The accompanying field goes through both slits, interferes afterwards, and guides the movement of the particle so that the particles collectively, spot by spot, build up an interference pattern.
¡ The field gives rise to a new type of potential energy which Bohm called the “quantum potential”
¡ The usual interpretation of QT: the wave function Ψ does NOT describe an individual quantum system directly § rather: Ψ describes our knowledge of the quantum system to be observed (typically in terms of probabilities)
¡ BH: Ψ describes an objectively real field, guiding a particle such as an electron
How to calculate quantum ‘trajectories’.
Insert the wave function into the Schrödinger equation.�(x, t) = R(x, t)e�iS(x,t)
Real part gives: �S
�t+
(rS)2
2m+ Q + V = 0 Quantum Hamilton-Jacobi.
EB = ��S
�tPB = rS Quantum Potential = Q = � ~2
2m
r2R
R
Schrödinger trajectories
[Philippidis, Dewdney and Hiley, Nuovo Cimento 52B, 15-28 (1979)]
Quantum Potential
[Bohm & Hiley, The Undivided Universe, 1993]
Tuesday, 12 June 2012 [This slide is made by B.J. Hiley]
¡ Note: R appears both in denominator and
numerator so that it can be multiplied by an arbitrary constant without changing Q. § size doesn’t matter here, as a small wave can have
exactly the same effect as a large one! § this means that Q (and thus the effect on the
particle) can be strong even if the amplitude of the quantum field is very weak.
¡ What matters then? ¡ Note that Q depends on the second spatial derivative of R
¡ This reflects the way in which R changes, or the form of the wave.
¡ Thus, Q depends only upon the form of the quantum wave!
¡ Bohm & Hiley: the quantum field is not pushing and pulling the particle mechanically
¡ Rather, it is putting form into the activity of the particle, literally IN-‐FORMING the energy of the particle
-‐> A new notion of active information!
¡ A form having very little energy enters into a directs a much greater energy. § the activity of the greater energy is given a form similar to that of the smaller energy
¡ The original energy-‐form will “inform” (i.e. put form into) the activity of the larger energy
¡ An analogy: a ship on automatic pilot being guided by radio waves § Here, too, the effect of the radio waves is independent of their intensity and depends only on their form
¡ The essential point: the ship is moving with its own energy, and the information in the radio waves is taken up to direct the much greater energy of the ship § Bohm & Hiley propose that an electron too moves under its own energy, and that
§ the information in the form of the quantum wave directs the energy of the electron
¡ DNA molecule guiding biological processes ¡ reading a map
SHANNON INFORMATION
¡ A quantitative measure of information that represents the way in which the state of a system is uncertain to us § e.g. we can only specify
probabilities of various states
ACTIVE INFORMATION
¡ Not essentially related to our knowledge or lack of it § e.g. information that is
relevant to determining the movement of the electron itself
§ information for the electron § information as an “objective
commodity”
¡ The two-‐body system: Q depends on the position of both particles in a way that does not necessarily fall off with the distance § -‐> the possibility of a non-‐local interaction between the two particles
¡ The N-‐body system: the behaviour of each particle may depend non-‐locally on all the others § no matter how far away they may be
¡ Non-‐locality is an important new feature of the quantum theory § however: there is an even more radical feature!
¡ The quantum potential depends on the “quantum state” of the whole system in a way that cannot be defined simply as a pre-‐assigned interaction between all the particles
¡ Its wave function is a product of § f(x) (where x is the centre-‐of-‐mass coordinate)
and
§ g(r) (where r is the relative coordinate) Ψ = f(x ) g(r).
¡ The quantum potential will contain a term representing the interaction of electron and proton
[μ is the reduced mass of the electron]
¡ In the s-‐state, Q is a function only of r itself § however: with a linear combination of s-‐ and p-‐wave functions it is easily shown to depend on the relative angles, θ and Φ, as well.
¡ Evidently, it is impossible to find a single pre-‐assigned function of r, which would simultaneously represent the interaction of electron and proton in both s-‐ and p-‐states. § the problem is still more sharply expressed if we bring in all the other states (d, f, etc.).
¡ The relationship between parts of a system described above implies a new quality of wholeness of the entire system
¡ This goes beyond anything that can be specified solely in terms of the actual spatial relationships of all the particles. § this is the feature which makes the quantum theory go beyond mechanism of any kind!
¡ The essence of mechanism: the basic reality consists of the parts of a system which are in a pre-‐assigned interaction. § the concept of the whole has only a secondary significance
§ it is only a way of looking at certain overall aspects of what is in reality the behaviour of the parts.
¡ Even if the interaction is non-‐local, the system is still mechanical as long as the interaction potential is a fixed and pre-‐assigned function of the particle variables.
¡ In the Bohm theory this interaction depends upon the wave function of the entire system § this is contingent on the state of the whole § it also evolves with time according to Schrödinger’s equation
¡ So: in the Bohm theory a key role is played by something § dynamical that § refers directly to the whole system and that is § not reducible to a property of the parts and their relationships
¡ Bohm: this is the most fundamentally new ontological feature implied by the quantum theory!
¡ The above holistic feature should, in principle, apply to the entire universe § however, when the wave function of a system factorises into two parts, the corresponding subsystems will behave independently
¡ Note that there are by now also different versions of the Bohm theory.
¡ Much attention has in recent years been given to a minimalist version known as “Bohmian mechanics” (see Goldstein 2013; Dürr et al. 2013).
¡ Bohm himself developed since the mid-‐1970s, with Basil Hiley, a philosophically more radical version they called the “ontological interpretation”, culminating in their 1993 book The Undivided Universe (this has been presented above)
¡ While there has been a tendency in the Bohmian mechanics camp (see also Bacciacaluppi and Valentini 2009) to downplay the significance of Bohm and Hiley’s approach, a more balanced examination suggests that both approaches have their value § see Holland, P. (2011) A quantum of history. Contemp. Phys. 52, 355.
¡ Durr, Goldstein, Zanghi: ”Bohm’s rewriting of Schrödinger’s equation via variables that seem interpretable in classical terms does not come without a cost.”
¡ Paavo P: but how do you interpret in classical terms Q = -‐h2/2m (Grad)2R/R Isn’t Q highly non-‐classical?
¡ DGZ: ”The most obvious cost is increased complexity: Schrödinger’s equation is rather simple, not to mention linear, whereas the modified Hamilton-‐Jacobi equation is somewhat complicated, and highly nonlinear – and still requires the continuity equation for its closure”
¡ PP: who knows which gives a better description what is actually ”out there”?
¡ DGZ: ”The quantum potential itself is neither simple nor natural”
¡ PP: nature at the quantum level may not be simple and (what our intuitions call) ”natural”
¡ DGZ: ”It might also be objected that notions such as … the quantum potential are necessary if BM is to provide us with any sort of intuitive explanation of quantum phenomena, i.e. explanation in familiar terms, presumably such as those involving only the concepts of classical mechanics.”
¡ PP: Bohm’s later interpretation of the quantum potential as active information can hardly be seen as relying on ”classical mechanics”.
¡ DGZ: ”…in the present century fundamental physics has moved sharply away from the search for … intuitive explanations in favor of explanations having an air of mathematical simplicity and naturalness, if not inevitability, and this has led to an astonishing amount of progress”
¡ PP: again, who knows what sort of explanations best describe what is actually ”out there”. Nature might not (always) care about mathematical simplicity and naturalness.
Floridi, Luciano, "Semantic Conceptions of Information”, The Stanford Encyclopedia of Philosophy
¡ The series of concentric rings visible in the wood of a cut tree trunk may be used to estimate its age.
¡ Also: consider a situation where you turned the ignition key and the red light of the low battery indicator flashed. § this signal, too, can be interpreted as an instance of environmental information
¡ Two systems a and b are coupled so that: § a's being (of type, or in state) F is correlated to § b being (of type, or in state) G, thus § carrying for the information agent the information that b is G.
¡ a = wave function, F = (let’s say) 2 slit interference
¡ b = slit wall, G = (let’s say) 2 slits open ¡ Information agent = the particle
¡ Floridi: environmental information may involve no semantics at all.
¡ May consist of correlated data understood as mere differences or constraining affordances. § plants (e.g., a sunflower), animals (e.g., an amoeba) and mechanisms (e.g., a photocell) are capable of making practical use of environmental information even in the absence of any (semantic processing of) meaningful data.
§ the same applies to the Bohmian particle!?
¡ Two main varieties: factual and instructional. ¡ In the car battery example, one may translate the red light flashing into semantic content in two senses: § 1) as a piece of factual information, representing the fact that the battery is flat
§ 2) as a piece of instructional information, conveying the need for a specific action, e.g., the re-‐charging or replacing of the flat battery.
¡ In the 2-‐slit experiment, one may take (say) two-‐slit interference in the wave function in two senses: § 1) as a piece of factual information, representing the fact that both slits are open
§ 2) as a piece of instructional (active) information, bringing about a specific action, a certain motion.
¡ Wittgenstein: the notion of “semantic information” is intended in a declarative or factual mode.
¡ Factual information may be true or untrue (false, in case one adopts a binary logic).
¡ True semantic content is the most common sense in which information seems to be understood § E.g. Quine equates “likeness of meaning” “sameness of proposition” and “sameness of objective information” by treating propositions as information in the factual sense
¡ Note also: information as true semantic content is a necessary condition for knowledge.
¡ Example: an instruction booklet provides instructional information § either imperatively — in the form of a recipe: first do this, then do that
§ or conditionally, in the form of some inferential procedure: if such and such is the case do this, otherwise do that.
¡ Instructional information is not about a situation, a fact, or a state of affairs w and does not model, or describe or represent w. § Rather, it is meant to (help to) bring about w. ▪ For example, when the mechanic tells one over the phone to connect a charged battery to the flat battery of one’s car, the information one receives is not factual, but instructional.
¡ So: quantum active information is about something (the environment, slits, etc.),
¡ It is for the particle and ¡ it helps to bring about something (a certain movement of the particle). § environmental § semantic or not? § instructional or factual or both or neither?
¡ Floridi: Dretske [1981] and Barwise and Seligman [1997] attempt to ground information, understood as factual semantic contents, on environmental information. § can Bohm’s quantum active information ground factual semantic contents?
¡ Albert, D. and Ney, A. ed. (2013) The Wave Function: Essays on the Metaphysics of Quantum Mechanics. Oxford University Press. ¡ Bohm, D. (1990) A New Theory of the Relationship of Mind and Matter. Philosophical Psychology vol. 3 no. 2, pp. 271-‐286 ¡ Bohm, David and Hiley, Basil J. (1987) An Ontological Basis for Quantum Theory: I. Non-‐relativistic Particle Systems. Phys. Rep. 144
(6): 323-‐348. ¡ Bohm, D. and Hiley, B. J. (1993) The Undivided Universe: An Ontological Interpretation of Quantum Theory. London: Routledge ¡ Dürr, D., Goldstein, S. and Zanghi, N. (2013) Quantum Physics Without Quantum Philosophy. Berlin: Springer. ¡ Floridi, Luciano, "Semantic Conceptions of Information", The Stanford Encyclopedia of Philosophy (Spring 2015 Edition), Edward N.
Zalta (ed.), forthcoming URL = http://plato.stanford.edu/archives/spr2015/entries/information-‐semantic/ ¡ Goldstein, Ss. (2013), "Bohmian Mechanics", The Stanford Encyclopedia of Philosophy (Spring 2013 Edition), Edward N. Zalta (ed.), URL
= http://plato.stanford.edu/archives/spr2013/entries/qm-‐bohm/ ¡ Hiley, B.J. and Pylkkänen, P. (2005), “Can mind affect matter via active information?”, Mind and Matter, vol. 3, no. 2, 7-‐26. Url:
http://www.mindmatter.de/resources/pdf/hileywww.pdf ¡ Pylkkänen, P. (2007) Mind, Matter and the Implicate Order. Berlin and New York: Springer Frontiers Collection. ¡ Pylkkänen, P., Hiley, B.J. and Pättiniemi, I., (forthcoming) Bohm’s approach and individuality. To appear in Guay, A. and Pradeu, T.
eds. Individuals Across Sciences: A Revisionary Metaphysics?, Oxford University Press. http://arxiv.org/abs/1405.4772 ¡ Riggs, P. (2009) Quantum Causality: Conceptual Issues in the Causal Theory of Quantum Mechanics. Heidelberg and New York: Springer. ¡ Saunders, S. et al. ed. (2010) Many Worlds? Everett, Quantum Theory, & Reality. Oxford University Press. ¡ Towler, M. (2009) Pilot-‐wave theory, Bohmian metaphysics, and the foundations of quantum mechanics, a graduate course at the
Cavendish Laboratory, University of Cambridge ¡ http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html ¡ Wallace , D. (2012) The Emergent Multiverse. Quantum Theory according to the Everett Interpretation. Oxford University Press. ¡ For criticisms of Bohm’s approach, see Goldstein (above), as well as Riggs, P. (2009) Quantum Causality: Conceptual Issues in the
Causal Theory of Quantum Mechanics. Heidelberg and New York: Springer.
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