The Collapse of the Theory of Evolution in 20 Questions
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One considers a fermion field coupled to a meson field and puts forward the idea of inducing localizations for the fermions through their coupling to the mesons and a stochastic dynamical reduction mechanism acting on the meson variables. In practice, one considers Heisenberg evolution equations for the coupled fields and a Tomonaga-Schwinger CSL-type evolution equation with a skew-hermitian coupling to a c-number stochastic potential for the state vector.
This approach has been systematically investigated by Ghirardi, Grassi, and Pearle , to which we refer the reader for a detailed discussion. Here we limit ourselves to stressing that, under certain approximations, one obtains in the non-relativistic limit a CSL-type equation inducing spatial localization.
However, due to the white noise nature of the stochastic potential, novel renormalization problems arise: the increase per unit time and per unit volume of the energy of the meson field is infinite due to the fact that infinitely many mesons are created. This point has also been lucidly discussed by Bell b in the talk he delivered at Trieste on the occasion of the 25th anniversary of the International Centre for Theoretical Physics. For these reasons one cannot consider this as a satisfactory example of a relativistic reduction model. In the years following the just mentioned attempts there has been a flourishing of researches aimed at getting the desired result.
Let us briefly comment about them. As already mentioned, the source of the divergences is the assumption of point interactions between the quantum field operators in the dynamical equation for the statevector, or, equivalently, the white character of the stochastic noise. Having this aspect in mind P. Pearle , L. Diosi and A. Bassi and G. Ghirardi reconsidered the problem from the beginning by investigating nonrelativistic theories with nonwhite Gaussian noises. The problem turns out to be very difficult from the mathematical point of view, but steps forward have been made.
Further work is necessary. This line of thought is very interesting at the nonrelativistic level; however, it is not yet clear whether it will lead to a real step forward in the development of relativistic theories of spontaneous collapse. In the same spirit, Nicrosini and Rimini Nicrosini tried to smear out the point interactions without success because, in their approach, a preferred reference frame had to be chosen in order to circumvent the nonintegrability of the Tomonaga-Schwinger equation.
Also other interesting and different approaches have been suggested. Among them we mention the one by Dove and Squires Dove based on discrete rather than continuous stochastic processes and those by Dawker and Herbauts Dawker a and Dawker and Henson Dawker b formulated on a discrete space-time. However, we must recognize that no one of these attempts has led to a fully satisfactory solution of the problem of having a theory without observers, like Bohmian mechanics, which is perfectly satisfactory from the relativistic point of view, precisely due to the fact that they are not genuinely Lorentz invariant in the sense we have made precise before.
Mention should be made also of the attempt by Dewdney and Horton Dewdney to build a relativistically invariant model based on particle trajectories. Let us come back to the relativistic DRP. Some important changes have occurred quite recently. Tumulka a succeeded in proposing a relativistic version of the GRW theory for N non-interacting distinguishable particles, based on the consideration of a multi-time wavefunction whose evolution is governed by Dirac like equations and adopts as its Primitive Ontology see the next section the one which attaches a primary role to the space and time points at which spontaneous localizations occur, as originally suggested by Bell To my knowledge this represents the first proposal of a relativistic dynamical reduction mechanism which satisfies all relativistic requirements.
In particular it is divergence free and foliation independent. However it can deal only with systems containing a fixed number of noninteracting fermions. At this point explicit mention should be made of the most recent steps which concern our problem. Bedingham following strictly the original proposal by Pearle of a quantum field theory inducing reductions based on a Tomonaga-Schwinger equation, has worked out an analogous model which, however, overcomes the difficulties of the original model. In fact, Bedingham has circumvented the crucial problems deriving from point interactions by paying the price of introducing, besides the fields characterizing the Quantum Field Theories he is interested in, an auxiliary relativistic field that amounts to a smearing of the interactions whilst preserving Lorentz invariance and frame independence.
It has also to be mentioned that, taking once more advantage of the ideas of the paper by Ghirardi , various of the just quoted authors see Bedingham et al. In view of these results and taking into account the interesting investigations concerning relativistic Bohmian-like theories,the conclusions that Tumulka has drawn concerning the status of attempts to account for the macro-objectification process from a relativistic perspective are well-founded:. Very recently, a thorough and illuminating discussion of the important approach by Tumulka has been presented by Tim Maudlin in the third revised edition of his book Quantum Non-Locality and Relativity.
Since the only unified, mathematically precise and formally consistent formulations of the quantum description of natural processes are Bohmian mechanics and GRW-like theories, if one chooses the first alternative one has to accept the existence of a preferred reference frame, while in the second case one is not led to such a drastic change of position with respect to relativistic concepts but must accept that the ensuing theory disagrees with the predictions of quantum mechanics and acquires the status of a rival theory with respect to it. In spite of the fact that the situation is, to some extent, still open and requires further investigations, it has to be recognized that the efforts which have been spent on such a program have made possible a better understanding of some crucial points and have thrown light on some important conceptual issues.
First, they have led to a completely general and rigorous formulation of the concept of stochastic invariance. Second, they have prompted a critical reconsideration, based on the discussion of smeared observables with compact support, of the problem of locality at the individual level.
This analysis has brought out the necessity of reconsidering the criteria for the attribution of objective local properties to physical systems. In specific situations, one cannot attribute any local property to a microsystem: any attempt to do so gives rise to ambiguities.
However, in the case of macroscopic systems, the impossibility of attributing to them local properties or, equivalently, the ambiguity associated to such properties lasts only for time intervals of the order of those necessary for the dynamical reduction to take place. Moreover, no objective property corresponding to a local observable, even for microsystems, can emerge as a consequence of a measurement-like event occurring in a space-like separated region: such properties emerge only in the future light cone of the considered macroscopic event.
Finally, recent investigations Ghirardi and Grassi ; Ghirardi have shown that the very formal structure of the theory is such that it does not allow, even conceptually, to establish cause-effect relations between space-like events. The conclusion of this section, is that the question of whether a relativistic dynamical reduction program can find a satisfactory formulation seems to admit a positive answer.
The Collapse Of The Theory Of Evolution In 20 Questions
A last comment. Recently, a paper by Conway and Kochen Conway , b , which has raised a lot of interest, has been published. A few words about it are in order, to clarify possible misunderstandings. The first and most important aim of the paper is the derivation of what the authors have called The Free Will Theorem , putting forward the provocative idea that if human beings are free to make their choices about the measurements they will perform on one of a pair of far-away entangled particles, then one must admit that also the elementary particles involved in the experiment have free will.
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One might make several comments on this statement. For what concerns us here the relevant fact is that the authors claim that their theorem implies, as a byproduct, the impossibility of elaborating a relativistically invariant dynamical reduction model. A lively debate has arisen. At the end, Goldstein et al Goldstein have made clear why the argument of Conway and Kochen is not pertinent.
We may conclude that nothing in principle forbids a perfectly satisfactory relativistic generalization of the GRW theory, and, actually, as repeatedly stressed, there are many elements which indicate that this is actually feasible. Some authors Albert and Vaidman ; Albert , have raised an interesting objection concerning the emergence of definite perceptions within Collapse Theories. The objection is based on the fact that one can easily imagine situations leading to definite perceptions, that nevertheless do not involve the displacement of a large number of particles up to the stage of the perception itself.
These cases would then constitute actual measurement situations which cannot be described by the GRW theory, contrary to what happens for the idealized according to the authors situations considered in many presentations of it, i.
This can easily be devised by considering, e. The conclusion follows: in the case under consideration no dynamical reduction can take place and as a consequence no measurement is over, no outcome is definite, up to the moment in which a conscious observer perceives the spot.
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Aicardi et al. The crucial points of the argument are the following: it is agreed that in the case considered the superposition persists for long times actually the superposition must persist, since, the system under consideration being microscopic, one could perform interference experiments which everybody would expect to confirm quantum mechanics. However, to deal in the appropriate and correct way with such a criticism, one has to consider all the systems which enter into play electron, screen, photons and brain and the universal dynamics governing all relevant physical processes.
A simple estimate of the number of ions which are involved in the transmission of the nervous signal up to the higher virtual cortex makes perfectly plausible that, in the process, a sufficient number of particles are displaced by a sufficient spatial amount to satisfy the conditions under which, according to the GRW theory, the suppression of the superposition of the two nervous signals will take place within the time scale of perception. To avoid misunderstandings, this analysis by no means amounts to attributing a special role to the conscious observer or to perception.
As such it is the only place where the reduction can and actually must take place according to the theory. It is extremely important to stress that if in place of the eye of a human being one puts in front of the photon beams a spark chamber or a device leading to the displacement of a macroscopic pointer, or producing ink spots on a computer output, reduction will equally take place. In the given example, the human nervous system is simply a physical system, a specific assembly of particles, which performs the same function as one of these devices, if no other such device interacts with the photons before the human observer does.
It follows that it is incorrect and seriously misleading to claim that the GRW theory requires a conscious observer in order that measurements have a definite outcome. A further remark may be appropriate. The above analysis could be taken by the reader as indicating a very naive and oversimplified attitude towards the deep problem of the mind-brain correspondence.
There is no claim and no presumption that GRW allows a physicalist explanation of conscious perception. It is only pointed out that, for what we know about the purely physical aspects of the process, one can state that before the nervous pulses reach the higher visual cortex, the conditions guaranteeing the suppression of one of the two signals are verified. In brief, a consistent use of the dynamical reduction mechanism in the above situation accounts for the definiteness of the conscious perception, even in the extremely peculiar situation devised by Albert and Vaidman.
As stressed in the opening sentences of this contribution, the most serious problem of standard quantum mechanics lies in its being extremely successful in telling us about what we observe , but being basically silent on what is. This specific feature is closely related to the probabilistic interpretation of the statevector, combined with the completeness assumption of the theory. Notice that what is under discussion is the probabilistic interpretation, not the probabilistic character, of the theory.
Objections to evolution - Wikipedia
Also collapse theories have a fundamentally stochastic character, but, due to their most specific feature, i. One could even say if one wants to avoid that they too, as the standard theory, speak only of what we find that they require a different interpretation, one that accounts for our perceptions at the appropriate, i. We must admit that this opinion is not universally shared. However, this cannot be the whole story: stricter and more precise requirements than the purely formal ones must be imposed for a theory to be taken seriously as a fundamental description of natural processes an opinion shared by J.
This request of going beyond the purely formal aspects of a theoretical scheme has been denoted as the necessity of specifying the Primitive Ontology PO of the theory in an extremely interesting recent paper Allori et al.