A Dual Ontology of Nature, Life, and Person

Transcription

1 A Dual Ontology of Nature, Life, and Person The III Principle of Thermodynamics and the notion of quantum vacuum (QV): the thermal QFT of dissipative systems Unit 6: The III Principle of Thermodynamics and the notion of Quantum Vacuum: the thermal QFT of dissipative systems Course WI-FI-BASTIONTO-ER 2017/18 1

2 By GIANFRANCO BASTI Full Professor of Philosophy of Nature and of Sciences At the Faculty of Philosophy of the Pontifical Lateran University Address: Pontifical Lateran University Piazza S. Giovanni Laterano, Rome Phone: Cell.: Web: 2

3 Summary 3

4 Bibliography Bibliography of the Units 6 and 7

5 Bibliography Main References: G. Basti, Philosophy of Nature and of Science, vol. 1: The foundations, transl. by Philip Larrey, Rome 2012 (for student use only), ch. 2 [attached] G. Basti, QFT: An Evolutionary Interpretation Of Nature From Cosmology To Neuroscience [Lecture Notes:attached]. M. Kuhlmann, «Quantum field theory». In: The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = (accessed 29/10/2014). Other References: 1. M. BLASONE, P. JIZBA, G. VITIELLO, «Preface», in: Quantum field theory and its macroscopic manifestations. Boson condensations, ordered patterns and topological defects, Imperial College Press, London, 2011, pp. vii-xii. 2. G. VITIELLO, «Links. Relating different physical systems through the common QFT algebraic structure», Lecture Notes in Physics, 718 (2007), [attached]. 5

6 Bibliography II 3. J. RUTTEN, Universal coalgebra: a theory of systems, Theoretical computer science, 249,1(2000), pp [attached]. 4. B. JACOBS & J. RUTTEN, An introduction to (co)algebra and (co)induction in: Advanced topics in bisimulation and coinduction, D. SANGIORGI & J. RUTTEN (EDS.), Cambridge UP, Cambridge UK, 2012, pp P. W. ANDERSON, More is different, Science, New Series, 177,4047 (1972), pp [attached]. 6

7 A historical survey From QM to QFT in Fundamental Physics

8 The «new» physics of the XX century. I As to the original Newtonian paradigm in classical mechanics (CM), the revolutions in fundamental physics at the end of XIX cent. and during the XX cent. are related to the discovery of new phenomena that are irreducible to classical mechanics: 1. The birth and development of thermodynamics as a statistical theory (statistical mechanics) of molecular aggregates introducing a temporal irreversibility (arrow of time) in such physical phenomena non compatible with CM. 2. The birth and development of QM during the first 30 years of last century principles of quantization, uncertainty, exclusion, complementarity with no parallel in CM. What is important to emphasize is that Schrödinger wavefunction Y in QM is not a physical object like a radiation wave or a water wave but an abstract mathematical object, effectively a statistical object expressing, by its square module ψ 2, the probability density of finding a particle in a given position x at a given time t, if the particle position has to be measured. 8

9 The «new» physics of the XX century. II 3. The birth and development of the special theory of relativity, with its fundamental dimensional law E = mc 2 that shows the reciprocal transformability between mass and energy for bodies accelerated to velocities close to the limit-velocity of electromagnetic radiation (light). This is an idea that, combined with the principles of QM, has shown to be quite fruitful in the domain of the physics of microscopic, relativistic quantum systems, under the form of quantum electrodynamics and quantum cromodynamics ordinary QFT as second quantization as to QM. 4. The general theory of relativity, which provides a mathematical explanation of the force of gravity G that Newtonian physics did not have, even if Newton described its mathematical form, by means of the law of universal gravitation. In general relativity, this force, for the first time in the history of humanity, finds a mathematical explanation, as a curvature of the space-time due to the action of the mass of single bodies (and not between two massive bodies like in the Newtonian formulation) exerting this force explanation of the curvature of photon trajectories even though non endowed with masses. 9

10 The «new» physics of the XX century. III 5. The new science of complexity in many-body systems and condesed matter physics, related: On one side, to Poincaré discovery of the intrinsic unpredictability of «three body gravitational systems» in the classical non-quantum realm - they are non-integrable, even though differentiable systems notion of chaotic dynamic systems. On the other side, to the development of non-linear thermodynamics and of the notion of dissipative structures in the condensed matter realm of chemical and biological systems. Unifying view of all these phenomena by QFT as a «thermal field theory» applied to many body physics realm (mesoscopic and macroscopic realms) and not only to the quantum relativistic realm of the Standard Model (microscopic realm) dissipative QFT is irreducible to QM (it is not a «second quantization» as to QM). Unifying view also between the microscopic and the (meso)macroscopic realms because of the notion of «long range correlations» implying an intrinsic change of scales macroscopic phenomena have a direct quantum explanation at the microscopic level 10

11 The Standard Model (SM) in Quantum Physics: the background The QFT is strictly related to the SM in fundamental physics that concerns the elementary constitution of matter at the microscopic, atomic and sub-atomic, level, where the special relativity fundamental law E = mc 2, concerning the reciprocal transformability between mass and energy, holds and where, therefore, the particles involved change their nature during the process. In this way, it became untenable the old atomistic, mechanistic ontology in fundamental physics, so to determine the passage in quantum physics to QFT, where to each particle is associated a force field. The problem becomes thus to define rigorously the nature of such an association from which different interpretations of QFT derive, as we see. Anyway, according to Bohr s picture, at the beginning of XX cent. after E. Rutheford s ( ) discovery of the atom structure (i.e., they are not atoms or elementary particles). Atoms are mainly constituted by baryons ( heavy particles ), i.e., the protons and the neutrons, located in the nuclei of atoms, in which the largest part of the atomic mass is therefore concentrated, and by leptons ( light particles ), i.e., the electrons (discovered by Thompson in 1897), being the electro-magnetic force the glue connecting baryons and leptons in the atom system, because of the opposite electromagnetic charge of protons (+) and electrons (-), making each atom an electromagnetic neutral composed particle. In such a way, there can exist also isotopes of each atom, by adding neutrons to the nucleus, so to leave unchanged the atomic number (number of protons of each atom and of its isotope(s)). 11

12 The Standard Model (SM) in Quantum Physics: the quark model and the strong force During the first 50 s years of the XX cent. several other particles were discovered in high energy particle accelerators and in the study of cosmic rays, mainly several types of other baryons (lambda, omega, ) and mesons (pions, kaons, ) and of other leptons, i.e., neutrinos of different types. In 1964 M. Gell-Man (1929-), Nobel Prize in 1969, proposed a unified theory of nuclear interactions and hence of nuclear particles (nucleons), based on the existence of six quarks, with the relative antiquarks. They are the elementary components of all nucleons, baryons (protons, neutrons, lambda,, with the relative antiparticles and opposed interaction charges, and each composed of three quarks) and mesons (composed by a quark and an antiquark) distinct by different flavors divided into three generations (families) of growing mass (up & down, charme & strange, top & bottom). Quarks are charged with a fractional opposed electromagnetic charge (+/- 1/3), and a new force, the nuclear strong force characterized by three different, opposed color/anticolor (+/-) charges (red, blue green). The combination of the color charges are conceived so to grant the color neutrality of the composed particle, just as the opposite electromagnetic charges of protons and electrons make the composed atom electrically neutral. The carrier particles of the strong interactions are gluons that are massless like photons, the carrier particles of the electromagnetic interactions, but differently from them are endowed with two color charges (+/-), so to have eight different types of gluons (not nine, as expected, because one of the 3 2 possible combinations is forbidden). The residual of the strong force justifies the stability of protons in the nuclei, despite they are endowed with the same positive and hence repulsive electromagnetic charge, just as the residual of electromagnetic force justifies the stability of atom compositions in the molecules. All the elementary and composed particles endowed with the strong interaction strength (force) are named adrons. 12

13 The Standard Model (SM) in Quantum Physics: the electro-weak interaction Among others, two are the original characters of sub-nuclear particles as to the ordinary matter: 1. The mass of adrons has a significant relativistic component related to the E=mc 2 relation, so to be measured in energetic terms of electron-volts (ev/c 2 ). E.g., the (rest) mass of the three quarks (uud) composing a proton contributes only for about 1/100 ( 10 MeV/c 2 ) of the overall proton mass ( 1GeV/c 2 ). A property difficult to interpret in the classical atomistic ontology (the quarks would move inside a proton with a velocity c), while it is perfectly understandable in terms of QFT duality principle (see below), where the composing parts of a particle exist in it, not as sub-particles, but as their relative, massive force fields. A force field might acquire a mass (inertia) by interacting with the Higgs field. 2. The quarks can change their nature (flavors), particularly the heavier quarks of the 2 nd and 3 rd (c,s,t,b) generations spontaneously decay into the lightest quarks of the 1 st generation (u,d) stability of protons (neutrons) composed by them stability of atomic nuclei of the ordinary matter. I.e., the other hadrons exist only at higher energy where no stable atomic structure is possible. To mediate hadron flavor changes, necessity of supposing a fourth interaction fundamental strength (force): the nuclear weak force with which hadrons and neutrinos are endowed. The vector particles (=quanta of the relative force field) of such an interaction are the massive bosons W +, W - (electrically charged) and Z 0 (electrically neutral). 13

14 The Standard Model (SM) in quantum physics: the electro-weak unification and the Higgs boson In1961 Sh. Glashow firstly proposed an electro-weak interactions unification theory, completed in 1967 through the insertion in Glashow s theory of the Higgs mechanism by S. Weinberg and A. Salam for justifying the attribution of mass to the W ±, Z 0 bosons and, through them, to all the massive fundamental particles of the ordinary matter. For this reason all of them share the Nobel Prize in In 1983 the existence of the W ±, Z 0 bosons and hence of the electroweak theory was experimentally confirmed at the LEP Collider of CERN in Geneva by C. Rubbia and S. Van der Meer who shared the Nobel Prize in Finally in 2012/13 the existence of a particle with some characters of the Higgs boson firstly theorized in 1964 by Robert Brout, François Englert, Peter Higgs, Gerald Guralnik, C. R. Hagen, and Tom Kibble in 1964 was experimentally confirmed by the ATLAS and CMS experiments at the LHC Collider of CERN. Further experiments at higher energies are anyway necessary to confirm the discovery. Englert & Higgs shared the Nobel Prize in

15 The Standard Model (SM) in quantum physics: fermions and bosons To complete the overall picture of fundamental particles of SM, an essential distinction concerning the spin statistics must be introduced between: 1. Twelve Fermions constituting the building bricks of the ordinary matter, characterized by fractional spins (i.e., particles following the Fermi-Dirac statistics), because at the fundamental state (minimum of energy), they distribute themselves at different energy levels (like electrons in atoms), since they all follow the Pauli principle (i.e., at each quantum state only one fermion is allowed). In the SM picture, there exist 12 fermions: the six quarks (up & down, charme & strange, top & bottom), and the corresponding six leptons (electron & electron-neutrino, muon & muon-neutrino, tau & tau-neutrino), both distributed into corresponding pairs according to three generations of growing energy. 2. Thirteen Gauge Bosons and the Higgs Boson. The Gauge bosons are the carrier particles of the four fundamental forces, the hypothetical graviton included (the photon, γ, the W ± and the Z, eight gluons, and the hypothetical g, the graviton). There are characterized by integer spins so that at the fundamental state they can occupy in an indefinite number the same quantum state. The Higgs boson is scalar (no charge), with null spin, and extremely massive ( 125 GeV) so that it decays immediately and can be revealed only at highest energies ( 1TeV). 15

16 The Standard Model (SM) in quantum physics: the overall picture GENERATIONS OF FERMIONS 16

17 The Standard Model (SM) in quantum physics: the four fundamental interactions 17

18 The Standard Model (SM) in quantum physics: baryons, mesons and atom structure 18

19 The Standard Model (SM) in quantum physics: fermions and bosons 19

20 Beyond the SM There are a lot of problems in fundamental physics that cannot be solved with the SM, such as the neutrino oscillations, the matterantimatter asymmetry, the dark energy (responsible of the universe expansion acceleration), and the dark matter (responsible of the gravitational attraction binding together galaxies, clusters of galaxies, etc.). Effectively, the ordinary matter we observe, and that SM could explain is less than 5% of the matter constituting the universe! 20

21 Behind the SM Effectively, the SM picture, separating fermions and bosons like particles and force field quanta, depends on the systematic use of a glorious mathematical method in classical and quantum mechanics: the perturbative method. Of this method Feynman diagrams of QED that are at the basis of the SM, represent one of the best example in the history of modern physics. It is not casual that the physics beyond SM is displaying a growing disaffection with the perturbative method, unable, in principle, to cope with the richness of the dynamic phenomena of the physical reality. 21

22 The representation of the QV in the QFT formalism 22

23 The mechanistic bias of the perturbative method The possibility of identifying outgoing and/or incoming particles in a Feynman diagram representation resides in the possibility of setting our particle detector far away from the interaction region (at a space distance x = ± from the interaction region) and to let it be active well before and/or well after the interaction time (at a time t = ± with respect to the interaction time) =asymptotic condition QFT as an extension of QM = standard or ordinary interpretation of QFT supposed by the SM (QFT as a second quantization as to QM) In fact, Laplace s asymptotic condition of his perturbative method in statistical mechanics allows to extend Newtonian mechanics and Newtonian calculus to many-body physics. Ontologically mechanistic interpretation of fermions, and bosons like particles and quanta of the force fields But the above asymptotic condition, switching off the interaction forces, is assumed to be not changing the properties of the system. This is no longer true when a system is endowed with many different phases. QFT, interpreted not as an extension of QM like QED or QCD based on Feynman diagrams, but as a different ontological paradigm, where each particle (both fermions and bosons) are quanta of the relative force fields, even though characterized by different spin statistics. In this way, for instance the change of flavors of fermions, are interpreted like as many phase transitions of the relative fermionic field new interpretation of the quantum wave-particle duality, as we have seen (see Unit 2). 23

24 The canonical commutation relations (CCRs) in QM and Heisenberg matrix representation of QM In classical mechanics, the Hamiltonian theory of dynamic systems, a system is defined in terms of a set of canonical coordinates r = (q, p), where each component of the coordinate q i, p i is indexed as to a given frame of reference. The time evolution of the system is defined by Hamilton s equations: dp dq =, =+ dt q dt p Where H = H qq, pp, tt is the Hamiltonian that generally corresponds to the total energy of the system = in a closed system, the sum of the kinetic and potential energy of the system. By using the binary operation of the so-called Poisson brackets it is possible to give an algebraic, matricial representation of a Hamiltonian system, where the system dynamics is represented on the phase space in terms of canonical transformations mapping canonical coordinate systems into canonical coordinate systems. This is at the basis of Heisenberg matrix representation of QM (1925). The core-point of this representation: it is well-known that the main difference between classical mechanics and QM is that the canonical variables of a classic mechanical system, i.e., the position x and the momentum p, do not commute in QM (i.e., they are conjugate variables) because are dependent on each other, according to the uncertainty principle: x p 2 I.e., in QM the canonical variables are conjugate and not independent like in classical mechanics. This implies that in QM the commutability of the relationship can be recovered only as a function of the uncertainty quantum relation by the action of an operator, a commutator. In other terms, in QM the Canonical Commutation Relation (CCR) is the fundamental relation between canonical conjugate quantities, which are related in such a way that each of them commute with the Fourier transform of the other according, according to the following (Max Born, 1925): [ xˆ pˆ ], x Where p x is the momentum operator in the x direction in one dimension, x is the position operator, and [x,p x ] = xp x p x x is the commutator of x and p x, and i is the imaginary unit. = i

25 Inner product and the bra-ket notation in QM In QM and matrix algebra we define generally the inner product and the sesquilinear form with linearity in the second argument instead of the first the first argument becomes conjugate linear rather than the second. In QM, we therefore write the vector product xx, yy as yy xx, that is, using Dirac s bra φφ - ket ψψ notation for signifying the product of vectors/co-vectors of eigenvalues of the wave functions φφ and ψψ. Or, respectively, we write yy xx, for denoting the dot product as a case of the convention of forming the matrix product AAAA as the dot products (eigenvectors) of rows of AA, with columns of BB. In this case, the kets and the columns are identified with the vectors of V, and the bras and the rows with the linear functionals (co-vectors) in the dual vector space V*, with conjugacy associated with duality. Anyway, there is the necessity of restricting the base-field of such vector spaces to R and C in order to have an ordered sub-field for granting non-negativity and a characteristic equal to 0, as required by any ordered field. This excludes finite fields, and requires a proper automorphism so to grant completeness. All finite-dimensional inner product spaces over R and C such as those used in the computations of QM are automatically metrically complete and then are Hilbert spaces. 25

26 To sum up (see Units 2-4) In classical and statistical mechanics the phase space representing the dynamics of a mechanical system is a vector space of two different vectors of values of positions q and momenta p in time, which commute each other (they are dually isomorphic equivalent). 26

27 To sum up (see Units 2-4) In QM the two canonical variables are conjugate so that the wave function of each of them commute with the Fourier transform of the other, for each quantum state. However, because quantum state are not observable what are observable are only Synthetical Von Neumann s representation of Schroedinger s wave function QM and of Heisenberg s matrix mechanics QM, as far as equivalent, by the notion of Hilbert space as a complex vector space V with inner product (i.e., each vector is endowed with its Hermitian conjugate) so that the conjugacy of the variables is represented by the dual conjugacy V-V* of the relative vector spaces and the observables are operators acting on these dual vector spaces. This duality co-vectors/vectors is synthetically connoted by Dirac s bra-ket notation: φφ ψψ By the GNS-construction it is possible to evolve the dual construction of Von Neumann into a double dual algebraic construction V**, so that it is possible to represent a quantum system dynamics in the framework of statistical mechanics through one only operator (observable) algebra of this double-dual or dually isomorphic because dual in both directions, vector space. In fact, the GNS-construction applies also to classical and not only quantum statistical mechanics (Landsman 2017) intrinsically commutative character of these algebras. 27

28 From the standard or ordinary QFT to algebraic QFT to dissipative QFT. I The QFT is actually a family of theories and not only one. 1. The ordinary interpretation of QFT (OQFT) or «second quantization» is an extension of QM to many body physics developed originally by Dirac, Fock and Jordan. It is based on the indistinguishability of particles in QM, differently from CM where each particle is defined by its own position vector r i different r i s configurations different many-body states. On the contrary, in QM many particles can occupy the same quantum state (= quantum state superposition). In QM (first quantization) exchanging two particles does not change the quantum state, r i «r j, the same wave function Y is invariant for particle exchange, symmetric in the case of bosons (photons, gluons, etc.), anti-symmetric in the case of fermions (quarks, electrons, etc.): ψ, r,, r,, = + ψ, r,, r,, ψ ( ) ( ) (, r,, r,, ) = ψ (, r,, r,, ) B i j B j i F i j F j i 28

29 From the ordinary QFT to algebraic QFT to dissipative QFT. II The OQFT overcomes the difficulties intrinsic to QM for dealing with many-body systems (redundancies in defining in which state the single particle is), because the problem becomes which is the number of particles occupying the same quantum state many-body state represented in terms of occupation number of particles in the single quantum state (or Fock state), i.e., With n α [ α] 1 2 n n, n,, n, 0,1 for fermions = 0,1,2,3... for bosons α The Fock state with all occupation numbers being zero is the vacuum state 0ñ. By applying many times the creation/annihilation operators to the vacuum state, we can add/delete as many particles to the vacuum state. All the Fock states [n a ]ñ form the basis of the many-body Hilbert space or Fock space any generic quantum many-body state is expressed as a linear combination of Fock states. 29

30 From the ordinary QFT to algebraic QFT to dissipative QFT. III Problem: for maintaining the coherence of the wave function it is necessary to eliminate all interactions with environment just as in CM, and hence to conceive the many-body system as isolated the quantum vacuum (QV) ground state at 0 K (absolute zero). 1. This is against evidence that QV temperature at the ground state is >0, an evidence emerging from cosmology ( thooft-susskind holographic universe model) and strictly connected with Third Principle of Thermodynamics 2. Recent evidence of the existence of gravitational waves Necessity of developing a dissipative QFT interpreting dynamically the infinitely many degrees of freedom that in any FT necessarily appear, as a very natural description of a «hot» QV ground state with all the energy «bounded» (no free energy), just as in classical thermodynamics SSB s of QV as inducing phase coherences and not state coherences, i.e., structures defined on oscillating fields and not on static points. 30

31 From the ordinary QFT to algebraic QFT to dissipative QFT. IV 3. Several algebraic interpretations of QFT all based on the Stone-Von Neumann theorem (1931) (Kuhlmann, 2014): In the context of QM, Schrödinger, Dirac, Jordan and von Neumann realized that Heisenberg's matrix mechanics and Schrödinger's wave mechanics are just two (unitarily) equivalent representations of the same underlying abstract structure, i.e., an abstract Hilbert space with linear operators acting on it. I.e. they are two different ways for representing the same physical structure, and it is possible to switch between these different representations by means of a unitary transformation, i.e. an operation that is analogous to an innocuous rotation of the frame of reference. Representations of some given algebra or group are sets of mathematical objects, like numbers, rotations or more abstract transformations (e.g. differential operators) together with a binary operation (e.g. addition or multiplication) that combines any two elements of the algebra or group, such that the structure of the algebra or group to be represented is preserved. 31

32 From the ordinary QFT, to algebraic QFT, to dissipative QFT. V The Stone-Von Neumann Theorem: In 1931 von Neumann gave a detailed proof (of a conjecture by Stone) that the canonical commutation relations (CCRs) for position coordinates and their conjugate momentum coordinates in the configuration space, fix the representation of these two sets of operators in up to unitary equivalence (von Neumann's uniqueness theorem) finitely many unitary equivalent representations of CCRs. This means that the specification of the purely algebraic CCRs suffices to describe a particular physical system Algebraic QFT (AQFT): what matters in QFT are not the fields or the particles, but the underlying algebraic structures (for a synthesis, see (Kuhlmann 2014, 4.2). Problem: in QFT the Stone-Von Neumann theorem does not hold! Because of the presence of infinitely many degrees of freedom infinitely many unitary inequivalent representations (UIR s) of CCRs sticking the usual Hilbert space formulation tacitly implies choosing one particular representation, one particular algebra (Kuhlmann 2014, 4.2). A physical QFT must give a dynamic (causal) justification of this choice, not for giving up the richness of the algebraic formalism, but for reinforcing it with a coalgebraic «partnership». UIR s are the core problem of any ordinary or algebraic QFT (Kuhlmann 2014), at least till we do not consider the alternative view of a dissipative QFT (Vitiello 2007). 32

33 The QV and the III Principle of Thermodynamics 33

34 QV in QFT The notion of quantum vacuum QV is fundamental in QFT. This notion is the only possible explanation at the fundamental microscopic level, of the third principle of thermodynamics ( The entropy of a system approaches a constant value as the temperature approaches zero ). Indeed, the Nobel Laureate Walter Nernst, first discovered that for a given mole of matter (namely an ensemble of an Avogadro number of atoms or molecules), for temperatures close to the absolute 0, T 0, the variation of entropy ΔS would become infinite (by dividing per 0). Namely: T T S = Q CdT ClnT = T = T T T T 0 0 Where Q is the heat transfer to the system, and C is the molar heat capacity, i.e., the total energy to be supplied to a mole for increasing its temperature by 1 C. 0 34

35 QV, and the change of paradigm as to CM Nernst demonstrated that for avoiding this catastrophe we have to suppose that C is not constant at all, but vanishes, in the limit T 0, so to make ΔS finite, as it has to be. This means however, that near the absolute 0 K, there is a mismatch between the variation of the body content of energy, and the supply of energy from the outside. We can avoid this paradox, only by supposing that such a mysterious inner supplier of energy is the vacuum. This implies that the absolute 0 K (-273 C) is unreachable. In other terms, there is an unavoidable fluctuation of the matter fields, at whichever level of matter organization. The ontological conclusion for fundamental physics is that we cannot any longer conceive physical bodies as isolated, as the inertia principle of Newtonian mechanics requires. The QV as opposed to the mechanical vacuum of classical mechanics (CM) plays thus the role of inner reservoir of energy of whichever physical system that the Third Principle of Thermodynamics necessarily requires. 35

36 The QV in QFT as to QM Moreover, as to QM: 1. The QV at the fundamental level cannot be interpreted as a Fock state with no occupation number, and hence with a temperature 0 K like in QM and in OQFT. The QV in cosmology must be conceived with a finite temperature >0 K, even though with all energy bounded (no free energy), as required in thermodyamics. 2. The fluctuating nature of QV fields implies the necessity of supposing an infinite number of degrees of freedom in the QV coherently with the Haag Theorem in the infinite volume representation of functional analysis we have an infinite number of CCRs 3. From coherent states algebraically represented as structures defined on points (equivalently, a Schroedinger wave function within a finite «energy box») of QM to potentially infinite number of field phase coherences in the infinite volume of QV, corresponding to the infinitely many UIR s of Haag s theorem in QFT. 36

37 To sum up «The vacuum becomes a bridge that connects all objects among them. No isolated body can exist, and the fundamental physical actor is no longer the atom, but the field, namely the atom space distributions variable with time. Atoms become the quanta of this matter field, in the same way as the photons are the quanta of the electromagnetic field» (Del Giudice, Pulselli, & Tiezzi, 2009, p. 1876). For this discovery, eliminating once forever the notion of the inert isolated bodies of Newtonian mechanics, Walter Nernst is a chemist who is one of the founders of the modern quantum physics. In this sense, QFT can be recognized as an intrinsically thermal quantum theory Of course, because of the intrinsic character of the thermal bath, the whole QFT system can recover the classical Hamiltonian character, because of the necessity of anyway satisfying the energy balance condition of each QFT (sub-)system with its thermal bath (ΔE = 0), mathematically formalized by the algebra doubling, between a q-deformed Hopf algebra and its co-algebra (Vitiello G., 2007). 37