A modern approach to quantum mechanics pdf download

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Different from the possibly misleading notion of a direct interaction, suggesting an interpretation in terms of scheme A of Section 2 , he describes this feature in a more subtle manner. The requirement that the mental and material outcomes of an actual occasion must match, i. Stapp The notion of interaction is thus replaced by the notion of a constraint set by mind-matter correlations see also Stapp At a level at which conscious mental states and material brain states are distinguished, each conscious experience, according to Stapp , p.

An intentional decision for an action, preceding the action itself, is then the key for anything like free will in this picture. Stapp argues that the mental effort, i. Concerning the neurophysiological implementation of this idea, intentional mental states are assumed to correspond to reductions of superposition states of neuronal assemblies. For further progress, it will be mandatory to develop a coherent formal framework for this approach and elaborate on concrete details.

For instance, it is not yet worked out precisely how quantum superpositions and their collapses are supposed to occur in neural correlates of conscious events. Some indications are outlined by Schwartz et al. With these desiderata for future work, the overall conception is conservative insofar as the physical formalism remains unchanged.

From the point of view of standard present-day quantum physics, however, it is certainly unorthodox to include the mental state of observers in the theory. Although it is true that quantum measurement is not yet finally understood in terms of physical theory, introducing mental states as the essential missing link is highly speculative from a contemporary perspective.

This link is a radical conceptual move. This hypothesis leads into mental influences on quantum physical processes which are widely unknown territory at present. In the s, Ricciardi and Umezawa suggested to utilize the formalism of quantum field theory to describe brain states, with particular emphasis on memory.

The basic idea is to conceive of memory states in terms of states of many-particle systems, as inequivalent representations of vacuum states of quantum fields. Major recent progress has been achieved by including effects of dissipation, chaos, fractals and quantum noise Vitiello ; Pessa and Vitiello ; Vitiello For readable nontechnical accounts of the approach in its present form, embedded in quantum field theory as of today, see Vitiello , Quantum field theory see the entry on quantum field theory deals with systems with infinitely many degrees of freedom.

For such systems, the algebra of observables that results from imposing canonical commutation relations admits of multiple Hilbert-space representations that are not unitarily equivalent to each other. This differs from the case of standard quantum mechanics, which deals with systems with finitely many degrees of freedom. For such systems, the corresponding algebra of observables admits of unitarily equivalent Hilbert-space representations. The inequivalent representations of quantum field theory can be generated by spontaneous symmetry breaking see the entry on symmetry and symmetry breaking , occurring when the ground state or the vacuum state of a system is not invariant under the full group of transformations providing the conservation laws for the system.

If symmetry breaks down, collective modes are generated so-called Nambu-Goldstone boson modes , which propagate over the system and introduce long-range correlations in it. These correlations are responsible for the emergence of ordered patterns. Unlike in standard thermal systems, a large number of bosons can be condensed in an ordered state in a highly stable fashion.

Roughly speaking, this provides a quantum field theoretical derivation of ordered states in many-body systems described in terms of statistical physics.

In the proposal by Umezawa these dynamically ordered states represent coherent activity in neuronal assemblies. The activation of a neuronal assembly is necessary to make the encoded content consciously accessible. This activation is considered to be initiated by external stimuli. Unless the assembly is activated, its content remains unconscious, unaccessed memory.

According to Umezawa, coherent neuronal assemblies correlated to such memory states are regarded as vacuum states; their activation leads to excited states and enables a conscious recollection of the content encoded in the vacuum ground state. The stability of such states and the role of external stimuli have been investigated in detail by Stuart et al. A decisive further step in developing the approach has been achieved by taking dissipation into account.

Dissipation is possible when the interaction of a system with its environment is considered. Vitiello describes how the system-environment interaction causes a doubling of the collective modes of the system in its environment. This yields infinitely many differently coded vacuum states, offering the possibility of many memory contents without overprinting.

Moreover, dissipation leads to finite lifetimes of the vacuum states, thus representing temporally limited rather than unlimited memory Alfinito and Vitiello ; Alfinito et al. Finally, dissipation generates a genuine arrow of time for the system, and its interaction with the environment induces entanglement.

Pessa and Vitiello have addressed additional effects of chaos and quantum noise. In the language of Section 3. Another merit of the quantum field theory approach is that it avoids the restrictions of standard quantum mechanics in a formally sound way. Conceptually speaking, many of the pioneering presentations of the proposal nevertheless confused mental and material states and their properties.

For a corresponding description of brain states, Freeman and Vitiello , , studied neurobiologically relevant observables such as electric and magnetic field amplitudes and neurotransmitter concentration.

They found evidence for non-equilibrium analogs of phase transitions Vitiello and power-law distributions of spectral energy densities of electrocorticograms Freeman and Vitiello , Freeman and Quian Quiroga However, Vitiello also points out that the emergence of self-similar, fractal power-law distributions in general is intimately related to dissipative quantum coherent states see also recent developments of the Penrose-Hameroff scenario, Section 3.

The overall conclusion is that the application of quantum field theory describes why and how classical behavior emerges at the level of brain activity considered. The relevant brain states themselves are viewed as classical states. Similar to a classical thermodynamical description arising from quantum statistical mechanics, the idea is to identify different regimes of stable behavior phases, attractors and transitions between them.

This way, quantum field theory provides formal elements from which a standard classical description of brain activity can be inferred, and this is its main role in large parts of the model.

Only in their last joint paper, Freeman and Vitiello envision a way in which the mental can be explicitly included. For a recent review including technical background see Sabbadini and Vitiello Probably the most concrete suggestion of how quantum mechanics in its present-day appearance can play a role in brain processes is due to Beck and Eccles , later refined by Beck It refers to particular mechanisms of information transfer at the synaptic cleft.

However, ways in which these quantum processes might be relevant for mental activity, and in which their interactions with mental states are conceived, remain unclarified to the present day. As presented in Section 3. This process is called exocytosis, and it is triggered by an arriving nerve impulse with some small probability.

In order to describe the trigger mechanism in a statistical way, thermodynamics or quantum mechanics can be invoked. A look at the corresponding energy regimes shows Beck and Eccles that quantum processes are distinguishable from thermal processes for energies higher than 10 -2 eV at room temperature.

Assuming a typical length scale for biological microsites of the order of several nanometers, an effective mass below 10 electron masses is sufficient to ensure that quantum processes prevail over thermal processes.

The upper limit of the time scale of such processes in the quantum regime is of the order of 10 sec. This is significantly shorter than the time scale of cellular processes, which is 10 -9 sec and longer. The sensible difference between the two time scales makes it possible to treat the corresponding processes as decoupled from one another. The detailed trigger mechanism proposed by Beck and Eccles is based on the quantum concept of quasi-particles, reflecting the particle aspect of a collective mode.

Skipping the details of the picture, the proposed trigger mechanism refers to tunneling processes of two-state quasi-particles, resulting in state collapses. It yields a probability of exocytosis in the range between 0 and 0.

Using a theoretical framework developed earlier Marcus ; Jortner , the quantum trigger can be concretely understood in terms of electron transfer between biomolecules. However, the question remains how the trigger may be relevant for conscious mental states. There are two aspects to this question. The idea, as indicated in Section 1 , is that the fundamentally indeterministic nature of individual quantum state collapses offers room for the influence of mental powers on brain states.

Further justification of this assumption is not given. The second aspect refers to the problem that processes at single synapses cannot be simply correlated to mental activity, whose neural correlates are coherent assemblies of neurons. Most plausibly, prima facie uncorrelated random processes at individual synapses would result in a stochastic network of neurons Hepp Although Beck has indicated possibilities such as quantum stochastic resonance for achieving ordered patterns at the level of assemblies from fundamentally random synaptic processes, this remains an unsolved problem.

Nevertheless, their biophysical approach may open the door to controlled speculation about mind-matter relations. A more recent proposal targeting exocytosis processes at the synaptic cleft is due Fisher , The nuclear spins of phosphate ions serve as entangled qubits within the molecules, which protect their coherent states against fast decoherence resulting in extreme decoherence times in the range of hours or even days.

If the Posner molecules are transported into presynaptic glutamatergic neurons, they will stimulate further glutamate release and amplify postsynaptic activity. This is a sophisticated mechanism that calls for empirical tests. One of them would be to modify the phosphorus spin dynamics within the Posner molecules. For instance, replacing Ca by different Li isotopes with different nuclear spins gives rise to different decoherence times, affecting postsynaptic activity.

Corresponding evidence has been shown in animals Sechzer et al. In fact, lithium is known to be efficacious in tempering manic phases in patients with bipolar disorder. In the scenario developed by Penrose and neurophysiologically augmented by Hameroff, quantum theory is claimed to be effective for consciousness, but the way this happens is quite sophisticated.

It is argued that elementary acts of consciousness are non-algorithmic, i. Unlike the approaches discussed so far, which are essentially based on different features of status quo quantum theory, the physical part of the scenario, proposed by Penrose, refers to future developments of quantum theory for a proper understanding of the physical process underlying quantum state reduction.

The grander picture is that a full-blown theory of quantum gravity is required to ultimately understand quantum measurement see the entry on quantum gravity. This is a far-reaching assumption. His conceptual starting point, at length developed in two books Penrose , , is that elementary conscious acts cannot be described algorithmically, hence cannot be computed. As such a physical process remains empirically unconfirmed so far, Penrose proposes that effects not currently covered by quantum theory could play a role in state reduction.

Ideal candidates for him are gravitational effects since gravitation is the only fundamental interaction which is not integrated into quantum theory so far. Rather than modifying elements of the theory of gravitation i. In this way, he arrives at the proposal of gravitation-induced objective state reduction. Why is such a version of state reduction non-computable? Initially one might think of objective state reduction in terms of a stochastic process, as most current proposals for such mechanisms indeed do see the entry on collapse theories.

This would certainly be indeterministic, but probabilistic and stochastic processes can be standardly implemented on a computer, hence they are definitely computable. Penrose , Secs 7. In order for them to become viable candidates for explaining the non-computability of gravitation-induced state reduction, a long way still has to be gone. With his background as an anaesthesiologist, Hameroff suggested to consider microtubules as an option for where reductions of quantum states can take place in an effective way, see e.

The respective quantum states are assumed to be coherent superpositions of tubulin states, ultimately extending over many neurons. Their simultaneous gravitation-induced collapse is interpreted as an individual elementary act of consciousness.

The proposed mechanism by which such superpositions are established includes a number of involved details that remain to be confirmed or disproven. The idea of focusing on microtubuli is partly motivated by the argument that special locations are required to ensure that quantum states can live long enough to become reduced by gravitational influence rather than by interactions with the warm and wet environment within the brain.

Speculative remarks about how the non-computable aspects of the expected new physics mentioned above could be significant in this scenario [ 13 ] are given in Penrose , Sec.

Influential criticism of the possibility that quantum states can in fact survive long enough in the thermal environment of the brain has been raised by Tegmark He estimates the decoherence time of tubulin superpositions due to interactions in the brain to be less than 10 sec.

Compared to typical time scales of microtubular processes of the order of milliseconds and more, he concludes that the lifetime of tubulin superpositions is much too short to be significant for neurophysiological processes in the microtubuli. In a response to this criticism, Hagan et al.

More recently, a novel idea has entered this debate. Theoretical studies of interacting spins have shown that entangled states can be maintained in noisy open quantum systems at high temperature and far from thermal equilibrium.

This indicates that, under particular circumstances, entanglement may persist even in hot and noisy environments such as the brain. However, decoherence is just one piece in the debate about the overall picture suggested by Penrose and Hameroff. In a different vein, Craddock et al.

As the correlation between anesthetics and consciousness seems obvious at the phenomenological level, it is interesting to know the intricate mechanisms by which anesthetic drugs act on the cytoskeleton of neuronal cells, [ 14 ] and what role quantum mechanics plays in these mechanisms. Craddock et al. Recent empirical results about quantum interactions of anesthetics are due to Li et al. From a philosophical perspective, the scenario of Penrose and Hameroff has occasionally received outspoken rejection, see e.

Indeed, their approach collects several top level mysteries, among them the relation between mind and matter itself, the ultimate unification of all physical interactions, the origin of mathematical truth, and the understanding of brain dynamics across hierarchical levels. Combining such deep and fascinating issues certainly needs further work to be substantiated, and should neither be too quickly celebrated nor offhandedly dismissed.

After more than two decades since its inception one thing can be safely asserted: the approach has fruitfully inspired important innovative research on quantum effects on consciousness, both theoretical and empirical. Today there is accumulating evidence in the study of consciousness that quantum concepts like complementarity, entanglement, dispersive states, and non-Boolean logic play significant roles in mental processes.

Corresponding quantum-inspired approaches address purely mental psychological phenomena using formal features also employed in quantum physics, but without involving the full-fledged framework of quantum mechanics or quantum field theory.

Perhaps a more appropriate characterization would be non-commutative structures in cognition. On the surface, this seems to imply that the brain activity correlated with those mental processes is in fact governed by quantum physics.

The quantum brain approaches discussed in Section 3 represent attempts that have been proposed along these lines. But is it necessarily true that quantum features in psychology imply quantum physics in the brain? A formal move to incorporate quantum behavior in mental systems, without referring to quantum brain activity, is based on a state space description of mental systems.

If mental states are defined on the basis of cells of a neural state space partition, then this partition needs to be well tailored to lead to robustly defined states. Ad hoc chosen partitions will generally create incompatible descriptions Atmanspacher and beim Graben and states may become entangled beim Graben et al.

This implies that quantum brain dynamics is not the only possible explanation of quantum features in mental systems. Assuming that mental states arise from partitions of neural states in such a way that statistical neural states are co-extensive with individual mental states, the nature of mental processes depends strongly on the kind of partition chosen.

If the partition is not properly constructed, it is likely that mental states and observables show features that resemble quantum behavior although the correlated brain activity may be entirely classical: quantum mind without quantum brain. Intuitively, it is not difficult to understand why non-commuting operations or non-Boolean logic should be relevant, even inevitable, for mental systems that have nothing to do with quantum physics.

Simply speaking, the non-commutativity of operations means nothing else than that the sequence, in which operations are applied, matters for the final result. And non-Boolean logic refers to propositions that may have unsharp truth values beyond yes or no, shades of plausibility or credibility as it were. Issue Vol. Authorization Required. Log In.

Figure 1 Illustration of the confined-SIR model. Figure 3 Fraction of susceptible, infected, and recovered agents as a function of time, depicted with continuous black, red, and blue lines, respectively, shown as a time-dependent histogram through the color gradation more intense corresponding to larger probabilities , along with their average values shown in continuous lines and the theoretical predictions of the SIR model in dashed lines.

Figure 9 Effect of different vaccination schedules on a fixed network: a random vaccination, b highest degree, c highest local betweenness centrality LBC , and d highest betweenness centrality BC.

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