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Limi$ e paradossi della meccanica quan$s$ca Roma, 6 maggio 2015 Gino Tarozzi Dipar,mento di Scienze di Base e Fondamen, Università di Urbino Carlo Bo La MQ come teoria fondamentale La meccanica quan$s$ca ha portato avan$ il processo di unificazione sul piano formale e ontologico delle leggi fondamentali della fisica, iniziato da Galileo e Newton nel caso della materia, aEraverso l’individuazioni di leggi universali comuni sia per i corpi celes$ sia per i corpi terrestri e proseguita da Maxwell nel caso della radiazione formulando un’unica teoria dei fenomeni oHci, eleErici e magne$ci. La teoria corpuscolare dei quan$ di luce di Einstein e successivamente la teoria ondulatoria della materia di de Broglie e Schroedinger portano alla caduta della bipar$zione tra le due teorie della fisica classica, meccanica ed eleEromagne$smo e dei due conceH fondamentali di materia e radiazione. Due caraEeris$che contraddiEorie Questa unificazione delle due principali teorie e dei due principali conceH della fisica classica è stata realizzata aEraverso una struEura matema$ca caraEerizzata da una parte da uno straordinario potere prediHvo e da una grande vas$tà di campi di applicazione, e dall’altra da una scarsa portata esplica$va e dalla presenza di profonde contraddizioni e problemi irrisol$, che si sono configura$ in un aEeggiamento di rinuncia epistemologica mirabilmente sinte$zzato dall’affermazione di Feynman it is all quite mysterious and we more we look at it the more mysterious it seems. Origine dei paradossi La radice logica dei paradossi quan$s$ci può essere ricondoEa a tre generi di dualità irrisolte presen$ nella teoria la prima di $po ontologico tra onde e par$celle e le altre due di $po formale: l’una tra evoluzione determinis$ca della funzione d'onda e risulta$ probabilis$ci delle nostre misurazioni l’altra tra le due diverse (e osservabilmente incompa$bili) descrizioni delle coppie di par$celle correlate, basate rispeHvamente su sta$ entangled e sta$ faEorizzabili di prima specie. Conseguenze filosofiche e metafisiche dei paradossi quan$s$ci (1) -­‐ an*realismo che emerge sia in relazione al mancato impegno ontologico della teoria rispeEo ai suoi conceH fondamentali, come quello di funzione d’onda, sia alla negazione della realtà delle proprietà prevedibili dal suo stesso formalismo, caraEeris$ca della soluzione ortodossa al paradosso di EPR, un an$realismo che si sposta inevitabilmente come cercheremo di mostrare anche a livello degli oggeH e degli aEribu$ macroscopici; Conseguenze filosofiche e metafisiche dei paradossi quan$s$ci (2, 3) -­‐ violazione delle principali formulazioni del principio casuale, dal determinismo di Laplace al principio di uniformità della natura di John Stuart Mill, dalla causalità kan$ana come conformità a regole alla causalità humeana come congiunzione costante -­‐ non separabilità quan$ca tra sistemi distan$ e soluzione olis$ca con conseguente irriducibilità del tuEo alle par$ che lo compongono; Conseguenze filosofiche e metafisiche dei paradossi quan$s$ci (4, 5, 6) -­‐  limi* alla comprensibilità della natura esemplifica$ dalla tesi popperiana della meccanica quan$s$ca come la fine della strada in fisica; -­‐  assunzione di una prospeHva soggeHvis$ca e idealis$ca derivante dalla intrusione della coscienza dell’osservatore nei paradossi della misurazione e le conseguen$ soluzioni mentalis$che e interazionalis$che del problema mente corpo; -­‐  proprietà fisiche del conce;o ultrametafisico di nulla, la cui mancata rivelazione può modificare lo stato quan$co. Science and metaphysics as two dis$nct and distant fields of enquire •  In the epistemology of the twen$eth century the an$-­‐philosophical outcomes of logical posi$vism led to consider science and metaphysics as two completely dis,nct and distant fields of inves$ga$on, between which it would not be possible, even in principle, to establish any form of dialogue, interac$on or fruicul exchange of ideas. The rejec$on of tradi$onal metaphysics in classical physics Already classical physics, with Galileo’s renounce to tentar l’essenza and Newton’s refusal to fingere hypotheses about occult quali$es, had discarded the tradi$on of ancient metaphysics, ending however to present itself as a new metaphysics, in which certainty was no longer to be sought and found in some form of extra sensi$ve and transcendent knowledge, but in the very mathema$cal descrip$on of the world of phenomena. Classical physics as the new metaphysics This was Galileo’s concep$on of the mathema$cal laws governing natural processes and of our ability to know some of them intensive as necessary truths, that Kant would later resumed, albeit from a subjec$vist oriented perspec$ve, with his famous doctrine of synthe$c a priori knowledge, according to which there are truths of reason that applies without excep$on to the world of experience. Similarly, the natural philosophy of Newton, while recognizing on the one hand (in spite of their extraordinary predic$ve power) the con$ngent character of its own basic laws, had reintroduced, on the other hand, something very similar to those occult quali$es that seemed to have been permanently banned from his methodological precepts: the concepts of absolute space and absolute $me. The elimina$on of metaphysics from physics Newton’s concepts of absolute space and $me required indeed the assump$on of existence of a privileged frame of reference, in contradic$on with Galileo’s principle of rela$vity. Einstein's extension of this principle to the laws of classical electromagne$sm led to the formula$on of rela$vis$c theories, with the abandonment of the concept of absolute simultaneity, and therefore of absolute space and $me and the apparent elimina$on of any residual metaphysics from the new physics. Einstein’s revolu$on derived from the impossibility of solving the problem of synchroniza$on of clocks in two different, and in rela$ve mo$on, reference frames with the consequent inability to define absolute simultaneity. Therefore the laEer concept becomes a meaningless no$on. The opera$onis$c criterion •  Such iden$fica$on of the meaning of a concept with the procedures for its measurement, which was then be systema$zed by Bridgman through the opera$onal defini$on of concepts in a new concep$on of science, was a benchmark for neo-­‐posi$vist philosophy, which aimed to bring on the same an$-­‐metaphysical issue in philosophy. •  To achieve this goal, it was necessary to find a linguis$c correlated of opera$onism, i.e. a criterion through which to eliminate meaningless proposi$ons, in a similar way to that opera$onism had banished not measurable concepts from physics and later also from other sciences (think for instance to behaviorism in psychology, who had argued for the abandonment of non-­‐overt phenomena as consciousness, feeling and emo$on) The principle of verifica$on •  Neo-­‐posi$vists iden$fied the linguis$c correlate of opera$onism in the criterion of verifica$on, or verifiability, according to which the meaning of a sentence is given by the method for its verifica$on. Therefore, if there is not such a possibility and, moreover, we are not dealing with an analy$c and tautological sentence, we have met a meaningless pseudo-­‐proposi$on. •  Neo-­‐posi$vism therefore was in large measure a return to Hume and, in par$cular, with its rejec$on of Kan$an doctrine of synthe$c a priori, to the famous Humean dis$nc$on between analy$cal ("rela$ons of ideas") and synthe$c ("maEers of fact"). The elimina$on of metaphysical principles from philosophy In spite of this logical posi$vism introduced two important new elements: first, a re-­‐evalua$on of cogni$ve value of the rela$onship between ideas, i.e. of the proposi$ons of logic and pure mathema$cs, with the recogni$on of their essen$al role in the formaliza$on of most advanced scien$fic theories and secondly a completely new posi$on against those proposi$ons (such as metaphysical) that were neither analy$c nor synthe$c, which Hume had merely considered false and that neo-­‐posi$vists consider completely free of meaning, with the excep$on of the doctrine of synthe$c a priori The elimina$on of metaphysical principles from philosophy in the words of a happy and effec$ve expression of one of the most influen$al members of the Vienna Circle: “The synthe,c a priori does not exist”, if the whole empiricism should have to be put in a nutshell, this would be a good way for doing it. The influence of neoposi$vist an$metaphysical istances on quantum mechanics •  The an$-­‐metaphysical program carried out by rela$vis$c physics therefore cons$tuted an essen$al prerequisite for the formula$on of the famous principle of verifiability as a criterion of meaning of a sentence, which extended to a linguis$c level the opera$onis$c requirement of measurability, as a criterion of significance for a physical concept. •  On the other hand neo-­‐posi$vis$c ideas, followed by Heisenberg, Bohr, Born, Pauli, Jordan, Dirac and von Neumann, found their most eloquent expression in the orthodox interpreta$on of quantum mechanics, leading to the myth of the observable, the forbidding to build a intelligible representa$on of the physical world and the idea of a "withdrawal into mathema$cal formalism”. The EPR argument and the physical reality principle The an$-­‐metaphysical perspec$ve endorsed by the orthodox interpreta$on of quantum mechanics, however, was applied so radically and unyielding to become quickly a boomerang, when, since the formula$on of the paradox of Einstein, Podolsky and Rosen, a clear form of logical incompa$bility (which some thirty years later, John Bell showed it could be turned in an experimental discrepancy) emerged between the quantum descrip$on given by some par$cular state vectors (ini$ally defined as second kind, or EPR, or non-­‐factorizable state vectors, now known as entangled states) and a very reasonable criterion of reality, which iden$fied scien$fic objec$vity, in terms of predictability with certainty, with a sufficient condi$on for physical reality. The EPR reality principle sa$sfies Ayer’s indirect verifiability This showed undeniably that such a realis$c principle was able to meet those requirements of verifiability, that neo-­‐posi$vists believed completely inapplicable to philosophical proposi$ons. •  I agree you have shown the possibility to obtain non trivial empirical consequences from what you choose to call a realist philosophical hypothesis, but I am non persuaded that your result could be interpreted by an instrumentalist accordig to his own fashion •  Alfred Ayer, private communica*on (1981) A widely accepted point of view •  More precisely, it correspond to the rejec$on of a point of view shared both by supporters and by detractors of logical posi$vism, and that could be expressed as follows: •  If the principle of verifica,on, even in a weak form like Carnap’s confirmability or Ayer’s incomplete verifiability, is accepted as a criterion of meaning, then all the main philosophical theses appears completely devoid of cogni,ve meaning. •  The previous statement was shared for en$rely different reasons both by neo-­‐posi$vists and by their opponents. Are scien$fic proposi$ons the only ones endowed with meaning? •  The first because they are convinced of the validity and effec$veness of their principle proposed as a criterion of meaning but became suddenly a criterion of scien$ficity since "the only proposi$ons endowed with sense were those of science", a claim that Weinberg iden$fied with "the last and final thesis of logical empiricism”. •  The second refusing the iden$fica$on with meaning with confirmability, believed that this principle should be decisively abandoned also because of its an$-­‐philosophical outcomes. The proposal of a different perspec$ve •  Research on the EPR paradox and Bell's theorem showed instead the possibility of suppor$ng a point of view that rejects the very validity of the previous statement, showing how the acceptance of confirmability as a criterion of meaning but not of science, which is subject to the stronger requirements of Popper’s falsifiability, allows to reformulate some of the main metaphysical theses in terms of philosophical principles endowed with meaning in a factual sense. Why the EPR criterion is not falsifiable •  An example could clarify the point. The EPR criterion of reality is confirmable in the sense that a physical theory could confirm it. For instance in classical mechanics each predictable property is considered real in that conceptual framework. On the other side, it is well known that quantum mechanics and especially the viola$on of Bell’s inequality are against this criterion. •  Could we say that EPR principle of reality is falsified? No, because the rela$on between scien$fic and philosophical thesis is not merely logical. Scien$fic proposi$on can be falsified, whereas philosophical principles can only be disconfirmed •  In this sense metaphysical sentences could be confirmed by our best scien$fic theories, but they could not falsified. Note that “falsifica$on” is opposed to “verifica$on” not to “confirma$on”. Therefore we could say that quantum mechanics “disconfirms” Einstein’s reality principle. In this perspec$ve different forms of realism could con$nue to be empirically relevant even aser disconfirma$on of EPR criterion. To sum up, scien$fic sentences must be falsifiable and confirmable, whereas philosophical sentences must be confirmable and disconfirmable. Carnap’s macrorealism •  It is easy to see, and this is always found in connec$on with the debate on the founda$ons of quantum mechanics, that there were other formula$ons of realism endowed with meaning. •  The first was proposed one year aser EPR by Carnap, who analyzed a realis$c hypothesis proposed by Lewis in terms of the proposi$on: •  If all minds disappear from the universe, stars s,ll go on on their courses •  Moreover he highlighted how this was a statement sa$sfying the most stringent requirements of factual significance since it is controllable, albeit incompletely. Probabilis$c generaliza$ons of the EPR reality principle The other nonmetaphysical principle of reality include probabilis$c generaliza$ons of the criterion of EPR, in which the original concept of predictability with certainty, which requires a strong idealiza$on compared to actual physical situa$ons, has been replaced by a predictability with a high degree of induc$ve probability in a first step and, subsequently, from the assump$on that the same a priori probabili$es have to be regarded as real proper$es Reality as a property not of the object but of its predictable aEributes •  The common feature of these different realis$c principles (EPR, EPR probabilis$c, Carnap) is the concept of shising the no$on of reality from the object to its predictable proper$es, thus acknowledging the logical empiricist refuta$on – an$cipated by Kant's cri$que of existence as a predicate – of the iden$fica$on of reality with a (further) property of a physical object, error that persisted for a long $me in the debate on the EPR paradox and corresponds to an improper use of the criterion of physical reality. The shising of the no$on of empirical reality Such a shising of reality from the object to its predictable proper$es allows to preserve the no$on of independence from the observer (and from his mind and consciousness), which is at the basis of metaphysical realism, in which reality was considered as that which, according to the defini$on of Hume, would exist, though we and every sensible creature were absent or annihilated in the sense that preserves its existence en$rely independently of the one of intelligent beings, which perceive or discovered it. Con$nuity between metaphysical and empirical realism •  There is a perfect con$nuity between metaphysical and empirical realism in the sense that the laEer preserves the basic idea of reality as independence of the mind (or consciousness) characteris$c of the first, but considering the predictability through our best theories as a guarantee of reality, empirical realism appears to be based on science, and in our case on physics, and not vice versa. Non metaphysical causality The previous results has been extended from realism to other philosophical principles. Firstly it has been shown that there are at least four formula$ons of the principle of causality endowed with empirical meaning and contradic$ng the orthodox interpreta$on of quantum theory: (a) determinis$c causality, exemplified by Laplace’s demon (b)causality as lawfulness according to Kant’s second analogy of experience (c) Mill’s principle of the uniformity of nature (d) Hume’s weak causality as ordered connec$on, which excludes any reversal of the temporal order. G. Tarozzi, "On the Different Forms of Quantum Acausality", in The Founda$ons of Quantum Mechanics , a cura di C. Garola e A. Rossi, Kluwer, Dordrecht (1995); pp.
435-­‐447 Can the absence of the collapse eliminates also the nothing? To avoid misunderstandings, this analysis by no means amounts to aEribu$ng a special role to the conscious observer or to percep$on. The observer’s brain is the only system present in the set-­‐up in which a superposi$on of two states involving different loca$ons of a large number of par$cles occurs. As such it is the only place where the reduc$on can and actually must take place according to the theory. Can the absence of the collapse eliminates also the nothing? It is extremely important to stress that if in place of the eye of a human being one puts in front of the photon beams a spark chamber or a device leading to the displacement of a macroscopic pointer, or producing ink spots on a computer output, reduc$on will equally take place. In the given example, the human nervous system is simply a physical system, a specific assembly of par$cles, which performs the same func$on 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 QMSL requires a conscious observer to make definite the macroscopic proper$es of physical systems. Unsolved open ques$ons •  But our main problem remain without an answer: •  how would percep$on of nothing on the les make a photon appear on the right? •  The nothing is the result, or perhaps the consequence, of the measurement; but isn’t necessarily all that was there before. •  Surely coherence demands that the photon had some kind of presence on the les un$l we looked; Unsolved open ques$ons •  perhaps the state of affairs on the les before measurement is best described by the sta$s$cal operator 1 l l
l
l
l
(3) ρ = (1 1 + 0 0 )
2
in which case the null measurement in fact interacts with (3). But what is (3)? Half a p€
hoton? A poten*al photon? Perhaps a photon? Unsolved open ques$ons And what happens to 1 l l
(1 1 )
2
when we look and find nothing? Does it get sent to the other side right away? Does our percep*on of the nothing push it off to the right? €
Does it reappear on the right without crossing the gap in between? A recent extension of the paradox that is to be furtherly inves$gated These difficul$es for a macrorealis$c interpreta$on of quantum mechanics do not represent however an argoment in favor of the standard interpreta$on, like in the case of Wigner’s cri$cism of the DLP theory, because of the possibility to extend our paradox from nega$ve result measurement to nega$ve result interac$ons. C. CALOSI, G. TAROZZI, (2013) Is the Mind a Quantum Computer? Proceedings of the mee$ng of the Interna$onal Academy of Philosophy of Science on The Legacy of Alan Turing (Urbino, 25-­‐27 September 2012), pp. 36-­‐47 Fer$lity of non-­‐wholly-­‐metaphysical philosophical interpreta$ons of a scien$fic theory Such new evidence of incompa$bility between certain well-­‐defined formula$ons of a philosophical concept and some of the fundamental principles and concepts of the main theory of contemporary physics are in our opinion an important confirma$on of the thesis of the fer$lity of non-­‐wholly-­‐metaphysical philosophical interpreta$ons of a scien$fic theory. Philosophical principles can be fruicully compared with the concepts and principles of physical theories But in the second place, and this is in our opinion the most interes$ng aspect, these meaningful philosophical principles can be profitably and fruicully compared with the main concepts and principles of physical theories. According to our perspec$ve it is possible in the first place to find out reformula$ons endowed with cogni$ve meaning of meaningless metaphysical principles, as we have tried to show.