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GALILEI Il Trittico - 2010-ristampa 2012 GALILEO GALILEI GENIUS IN ALL FIELDS OF HUMAN KNOWLEDGE LA GENIALITÀ DI GALILEO GALILEI IN TUTTI I CAMPI DELL’UMANO SAPERE III.5.5 THE HISTORY OF PHYSICS TEACHES US THAT THE MOST FORMIDABLE DISCOVERIES HAPPENED IN TOTALLY UNEXPECTED WAYS The History of Physics teaches us that the most formidable discoveries all came totally unexpected. Cosmic rays that end up on Earth after travelling through the Universe for billions and billions of miles are an example of truly unexpected discoveries (on page 2 is an example of cosmic rays reaching the City of Bologna). The so-called “strange particles”, the first example (shown in the photo on page 2) of Subnuclear Universe, were so named because no one could understand why they existed. The same applies to the so-called Fermi Forces. Enrico Fermi discovered them after inventing the technique of “slow neutrons” through which he managed to transform that extremely rare phenomenon called “radiation” into a property common to all the elements of the chemical table. But without the invention of the so-called new “slow neutrons” technology, Enrico Fermi would not have been able to discover the Forces that bear his name and that explain the existence of a starry sky and why the Sun can shine for billions of years without ever turning off or blowing up. Nobody had been able to foresee the Subnuclear Universe – with its laws and its regularities – which we now work with at CERN. It took 50 years of experiments to discover. That is why we are working to build technologies that can discover something that none of us could imagine. 1 The photo shows the results of a cosmic ray shower in the atmosphere over the city of Bologna (Italy), as envisaged by a computer simulation in which the shower is generated at the summit of the atmosphere (at an altitude of 15 km) by a very high energy primary proton (one hundred million billion eV (electronVolt)). This unit of energy corresponds to the one at play in a candle flame. A million muons (the red dots) reach the ground on an area of over 10 million square metres. The discovery of the first “strange particles” in the Blackett Laboratory (George Rochester and Clifford Butler, photos dated 15 October 1946 and 23 May 1947). 2 The peaks of Science Science will never stop discovering fundamental “truths” that go beyond human imagination. It is like climbing a mountain. Before reaching peak n. 1, the mountain climber thinks it is the highest one. When it reaches the summit he sees another one and his horizon broadens immensely. Science has reached peaks that were “perhaps” considered to be final five times already. And something that no one had foreseen has always come up. We are now at the top of the “superworld”. I wonder what will come out of that. III.9 MODERN SCIENCE’S DEBT TOWARDS GALILEO GALILEI Modern Science is in total debt towards Galilei. This view must be further clarified also because Galilei’s name is often associated, as if it was of secondary importance, to Copernicus, Kepler, Newton and Einstein. Science owes little to Copernicus. It was Aristarchus who established with precise astronomical measurements that the Sun was much larger than the Earth. On these bases the great Greek astronomer said it was absurd to believe that the Earth was stationary while the Sun revolved around it. Heliocentrism was born with Aristarchus. If Galilei had not been born one hundred years after Copernicus, his heliocentrism would have suffered the same fate as Aristarchus. Heraclitus (fourth century BC) also fell into the oblivion of History with his idea that it is not the heavens that turn clockwise around the Earth but the Earth that spins counter clockwise like a top. So why does an apple fall to the base of the tree? It should fall very far to the west of the base, as seen in the Figure on page 114. Galilei discovered why this is not the case. When the apple is on the branch it has a “momentum” which it does not lose when falling from the 3 tree. It was Galilei who was able to respond to the “obvious” objections on the Earth’s spinning motion; these objections had resisted for two thousand years. And what does Science owe Kepler? A lot. But Galilei is its father. Kepler devoted himself to the study of the Sun’s satellites. Which means second-level Galilean Science. Kepler tried to understand why there should be six “planets”. III.9.2 IF GALILEI HAD NOT DISCOVERED AND MEASURED GRAVITATIONAL ACCELERATION, NEWTON WOULD NOT HAVE BEEN ABLE TO DISCOVER HIS LAW Had he known that the “planets” were nine, Kepler would have given up in his intent, because he had used all of the perfect figures that you can build in the three-dimensional Space of Euclidean geometry. Kepler’s enormous work in Geometry and Mathematics was thus useless. What remain are his “three laws”, which it would be more correct to call “regularities” (see page 200). The fundamental law that leads to these regularities was found by Newton. However, if Galilei had not discovered the law of falling bodies, managing to measure “g” (acceleration due to Gravity) and the properties of the pendulum, Newton would not have been able to discover his law. Finally, what remains is comparing Einstein and Galilei. Without two hundred years of Galilean experiments on electricity, magnetism and optics, it would not have been possible for Lorentz to discover that Time and Space are an inseparable and complex combination: it is impossible to separate the two components of the complex space-time reality. This combination cannot be “real”. If we give Time the imaginary property, then Space will be real. If we give Space the imaginary property instead, Time will be real. But Space and Time can never both be real. Without Lorentz’s discovery, Einstein would not have been able to discover that mass is the curvature of 4 Space-Time. This is Einstein’s real achievement. Galilei had discovered relativity. And Newton had had the idea of “falling” light. Kepler’s three Regularities 1st Regularity. The orbit of each satellite of the Sun is an ellipse (almost in the same plane) with the Sun at one of the foci of the ellipse. The geometric shape of an orbit is not a perfect circle but an ellipse, which is a squashed circle. circle ellipse 2nd Regularity. The satellites move faster as they get closer to the Sun. Areal velocity: equal areas are covered in equal time. This is why a satellite moves faster when it gets closer to the Sun. velocity = L/t Since the distance L, diminishes, velocity L/t has to increase for L2/t to be constant. areal velocity = L2/t Satellites Sun lower velocity higher velocity 3rd Regularity. The further away from the Sun, the slower the satellites move. The square of the orbital period, T2, is proportional to the cube of the semi-major axis, R3, of its orbit (taken as circular as indeed it almost is): T2 R3. 5 III.9.3 “FALLING” LIGHT Let us open a parenthesis on “falling” light. For Newton, light had a corpuscular not a wavy nature. It had to be made of luminiferous particles possessing mass. It was therefore obvious that these particles should be subjected to the same Gravitational Pull that makes stones fall. When the light of a Star does not encounter the Sun in its path (Figure 1, on page 7) it comes straight to Earth. If it finds the Sun, what happens is shown in Figure 2 (page 7). The light from the Star is deviated from its path because of Gravitational Attraction due to the Sun’s mass: it is as if the light fell. This deviation is greater the closer the light passes to the Sun’s surface. In fact, Gravitational Attraction decreases with the square of the distance. Under normal conditions sunlight prevents us from seeing these stellar rays. It would be necessary to turn off the sun or raise a screen to avoid being dazzled by its light. This is what the Moon causes when it happens to come between us and the Sun: a Solar eclipse (Figure 2 on page 7). Every year, on 29 May, the Sun finds itself facing a group of very bright Stars: the constellation of the Hyades. This is of little value. Sunlight stops us from seeing those Stars. But in 1919 a Solar eclipse happened exactly on 29 May. In March 1917 Royal Astronomer Frank Watson Dyson (1868-1939) realised that this would be an opportunity to measure the effect of the light that is deflected by the solar mass. Arthur Stanley Eddington (1882-1944) – Professor at Cambridge – organized an expedition to an island off the coast of Africa, north of Congo. They intended to record starlight on sheets of photographic emulsions. The desired effect on the plate corresponded to a deviation smaller than a pencil tip. During transport from West Africa, the heat had made the emulsion so gelatinous that it was impossible to obtain the necessary accuracy. The expedition failed for a number of reasons. Eddington organized a second expedition, in another continent: South America, in 6 “Falling” light northern Brazil. When the plates came from Brazil, a special micrometer was made to obtain the necessary precision to determine whether the light of the Stars had been deflected by the Sun. Eddington discovered that light “fell” due to the Gravitational Attraction exerted by the huge solar mass. 7 APPENDIX THE DEVELOPMENT OF THE CONCEPT OF “CHARGE” OVER THE LAST 3/4 OF A CENTURY Over the last century, the concept of “charge” has undergone enormous development. Up to the beginning of the XX century it was thought that the “electric charge” was the generator of a fundamental force, while ensuring matter stability (Einstein). With the discovery of the anti-electron (Dirac and Anderson), it has been necessary to introduce the “baryonic charge” (Stueckelberg). With the advent of Grand Unification Theories, the baryonic charge has lost its privileged position, giving rise to 12 “flavour charges” to ensure matter stability and 4 “colour charges” to generate the 4 fundamental forces of nature (gravitational, weak, electromagnetic, and strong). The 4 “colour charges” have different origin. The (colour) gravitational charge has its origin in the four-dimensional space-time (3 spatial dimensions and 1 time dimension) with a “complex” structure. The four dimensions are indeed composed of an inseparable mixture of a real and an imaginary part. The (colour) electric charge has its origin in a fictitious one-dimensional complex space (having nothing to do with space-time) The (colour) weak charge has its origin in a fictitious two-dimensional complex space (having nothing to do with space-time) The (colour) strong charge has its origin in a fictitious three-dimensional complex space (having nothing to do with space-time) In these fictitious spaces, the fundamental forces have to obey to the laws dictated by the symmetry groups U(1), SU(2) e SU(3) for the electromagnetic, weak and strong forces, respectively. The connection between the fictitious spaces and the Lorentz space-time is one of the topical questions of frontier physics, that has in the concept of “superspace”, with 11 “bosonic” and 32 “fermionic” dimensions, the hope for a solution. Two facts are well-established: i) four space-time bosonic dimensions are not enough to explain the experimental results obtained over the last 3/4 of a century; ii) the eleven bosonic dimensions are: one for time; one for Newton’s constant, that is obtained collapsing one dimension; and nine spatial dimensions, three of them corresponding to the ordinary space we are made of and where we live. The six bosonic space dimensions that are left are exactly as many as the six “fictitious” dimensions cited before. Many theoretical models have been proposed to derive from the compactification of the 6 bosonic dimensions the U(1), SU(2) e SU(3) symmetries laws. A question which is still open is how, from the superspace with 43 dimensions, both the four colour charges generating the four fundamental forces (two of which, the electromagnetic and the weak force, mix at the Fermi energy scale of ~300 GeV), and the twelve flavour charges that guarantee the stability of matter can be derived. 8 MAXWELL da: ISSP 2012 COMPLEXITY and the QGCW Project 6 THE BASIC POINTS ON THE CORRELATION BETWEEN COMPLEXITY AND PREDICTIONS We have seen in chapter 1 that in the various attempts to identify the meaning of Complexity the problem of Predictions has been assumed to be granted by the mathematics needed to describe a problem in the complex system. It is therefore necessary to clearly establish the relation which exist between Complexity and Predictions. In the previous chapters 3 and 4 we have discussed the experimental basis for the existence of Complexity, i.e., AFB and UEEC events. We will now discuss the experimental evidence for the existence of predictions and the sequence which correlates UEEC and predictions. Predictions. The experimental evidences for the existence of Predictions are the very many results of scientific reproducible experiments. Quantum Electro-Dynamics, QED, is the best example. The anomalous magnetic moments, in symbols (g–2), of the electron (e) and of the muon (): (g–2)e, are theoretically computed at an extraordinary level of precision (few parts in ten billion parts for the electron) and are experimentally verified to be correct. Could the (g–2)e, be theoretically predicted before the discovery of the Maxwell equations and the existence of Quantum Electro-Dynamics (QED)? The answer is obviously no. The sequence which correlates UEEC events and Predictions is very clear. Predictions at the fundamental level of scientific knowledge depend on UEEC events. For example: it is the discovery of the laws governing electric, magnetic and optical phenomena (all totally unpredicted) which produced the mathematical structure called QED. The mathematical structure was not discovered before the innumerable series of UEEC events was found in electricity, magnetism and optics. This series of UEEC events allowed Maxwell to express 200 years of experimental discoveries in a set of 4 equations. 9 The mathematical formalism comes after a totally unexpected discovery: an UEEC event which no one was able to predict. In the whole of our knowledge rigorous predictions exist only in Science. These predictions are based on the mathematical description of a single UEEC event or a series of UEEC events. This description can either be the result of new mathematics (example the Dirac -function) or the use of existing mathematical formalism (example: the Einstein use of the Ricci tensor calculus). The UEEC event at the origin of the Dirac equation is the fact that the electron was not a ‘scalar’ particle but a spin ½ object. The UEEC events at the origin of Einstein mathematical formulation of the gravitational forces are the discoveries of Galilei (F = mg), of æ m ×m ö Newton çF = G 1 2 2 ÷, R 12 ø è and of Lorentz that Space and Time could not be both real and that all electromagnetic phenomena obeyed a new invariance law, now called Lorentzinvariance. These are just two examples of the fact that the greatest steps in the progress of Science come from totally unpredicted discoveries. It is the mathematical formulation of these discoveries with allow Predictions to be made. Once made, these Predictions need experimental checks. Even when we have a mathematical formalism coming from a series of UEEC events, if this formalism opens a new frontier, as it is the case for the Superworld, the experimental proof is needed to verify the validity of the new theoretical frontier. Today we have a reasonable mathematical formalism to describe the Superworld, but in order to know if the Superworld exists we need the experimentally reproducible proof for its existence. And it could be that, while searching for the Superworld a totally unexpected discovery (UEEC) comes in. This is the reason why we need to perform experiments, as Galileo Galilei realized 400 years ago. 10 MAXWELL – LORENTZ – PLANCK da “Subnuclear Physics the first 50 years: highlights from Erice to ELN pagina 1 INTRODUCTION ……..The development of electricity and magnetism in the XIX century, the Maxwell synthesis, which allowed mankind to realize that the enormous variety of optical phenomena was a further manifestation of electromagnetism, started with the (Cu-Zn) junction. All this looks obvious nowadays, but think of the enthusiasm which brought Lord Kelvin to say, in his opening lecture at a physics conference a hundred years ago, that with the Maxwell equations the basic conceptual understanding of physics was over: few details are left to be measured. Six months later J.J. Thomson discovered the negative electron. During the succeeding three decades, three important developments took place: i) the discovery by Planck of his quantum of action; ii) the Einstein reinterpretation of the Lorentz-invariance of the Maxwell equations in terms of the relative property of space and time, not being as conceived by Newton (absolute and independent) but relative and so strongly linked that all physics had to be described in four dimensions; iii) the discovery that the electron has half-integer spin and its gyromagnetic ratio is not one (as for the orbital angular momenta) but two. These developments culminated with one of the greatest achievements of mankind: the discovery by Paul Adrien Maurice Dirac of his equation. This opened a new horizon in physics: the virtual phenomena with all their rigorously predicted and measurable effects. 11 BECQUERELL 50mo ANTIMONDO (febbraio 2015) Negli anni trenta del XX secolo, Enrico Fermi, usando la tecnica dei neutroni lenti riuscì a rendere radioattivi tutti gli elementi della Tavola di Mendeleev. La rarissima proprietà scoperta da Becquerel nel 1896 e detta “radioattività” non era poi così rara; bastava inviare sul nucleo atomico un neutrone di bassa energia per farlo diventare “radioattivo”. E qui ci stanno due novità. La prima è quella della “rottura” di un nucleo. La seconda è quella della esistenza di una nuova Forza Fondamentale della Natura. Per secoli e secoli la rottura di una pietra dipendeva dal colpo del martello. Più violento è il colpo, più facile è rompere la pietra. Passando dalle pietre ai nuclei dagli atomi i nostri padri pensavano che i neutroni veloci avrebbero rotto più facilmente i nuclei. Un nucleo di un atomo, esempio l’Ossigeno, è fatto con sei protoni e sei neutroni, tenuti insieme dalla “colla nucleare”. Un neutrone più è veloce meglio entra dentro al nucleo, così si pensava, prima che Enrico Fermi scoprisse: “invece no”. Infatti quando il neutrone lentamente viene “assorbito” dal nucleo. Più lentamente si muove e più alta è la probabilità di essere assorbito dal nucleo. Nucleo che poi però si disintegra. La radioattività è dovuta al fatto che l’equilibrio tra il numero di protoni e neutroni viene rotto quando si aggiunge un neutrone al nucleo. Le forze nucleari, che garantiscono l’esistenza dei nuclei atomici, hanno una formidabile proprietà. Se il nucleo è troppo grande (esempio l’Uranio-235 fatto con 235 palline nucleari) tende a rompersi (fissione nucleare), producendo energia. Se il nucleo è troppo leggero (esempio il Deutone fatto con appena due palline nucleari) tende a fondersi con un altro nucleo leggero (fatto con due palline). Nasce così la fusione nucleare che produce il nucleo con quattro palline (due protoni e due neutroni) facendo il nucleo di Elio e producendo molta energia. Nel Sole avviene questa fusione e il fuoco nucleare di tutte le Stelle simili al Sole è un fuoco di fusione. Il fuoco di fusione è più potente del fuoco di fissione. 12 PLANCK PAS 2014 Appendix 4 From the Planck Universe to Einstein, Schwarzschild and the Universe now Table 1 Conclusion: we can understand why: N(p n e) ≃ 1080 and V(U) ≃ 98% ; and predict the existence of two types of Black–Holes: Primordial Black–Holes where matter has only the gravitational charge and Standard Black–Holes where matter is made with p, n, e. 13 17 aprile 2014 Max Karl Ernst Ludwig Planck (1858-1947), who discovered in 1900 the “quantum of action”. PLANCK Il padre della Fisica Quantistica, Max Planck, fu uomo di grande integrità civile e morale. La sua vita fu colpita da tante tragiche realtà. Dei suoi cinque figli il primo (Karl) perse la vita nel corso della Prima Guerra Mondiale, le sue due figlie morirono partorendo nel giro di appena due anni: Grete nel 1917 ed Emma nel 1919. I nazisti gli condannarono a morte il figlio Erwin con l’accusa di aver preso parte all’attentato contro Hitler. Il motivo vero è dovuto al fatto che Planck rifiutò di dirigere il progetto nazista per la costruzione della bomba a fissione nucleare. Fu infatti nel 1939 a Berlino che venne scoperta (da Otto Hahn e Fritz Strassmann) la fissione nucleare in pieno periodo di dominio nazista. Alla interpretazione teorica della fissione nucleare contribuì il lavoro di Lise Meitner. Max Planck era in stretti legami d’amicizia con Otto Hahn e Lise Meitner, the authors of a fundamental discovery: the nuclear fission, where from the nuclear power stations and the so-called “atomic bomb” came. It is obvious that Planck and Heisenberg were talking about these very crucial problems. Quando Hitler si rivolse all’altro grande nome della Fisica di quegli anni, Heisenberg, fu Planck che convinse Heisenberg a non rifiutare la direzione del progetto. La verità verrà fuori quando si scriverà la Storia di quei terribili anni; la verità su come mai il progetto nazista, pur essendo partito con tre anni di vantaggio rispetto al Progetto Manhattan, si inceppò per via di un risultato sperimentale sbagliato di un fattore trenta. Quel risultato è difficile pensare che sia sfuggito al grande Heisenberg. Max Planck – the father of Quantum Physics (the continuum is an Optical illusions). Everything is made of “pieces” of something, called “quanta”. The smallest quantity of “action”, h, cannot be zero but what is now known to be one of the three Fundamental Constants of Nature. Its symbol is h and its name is Planck constant. 14 LORENTZ Nasce dalle quattro equazioni di Maxwell la cosiddetta Relatività Ristretta scoperta da Hendrik Antoon Lorentz e portata da Einstein alle sue estreme conseguenze con la scoperta di due realtà: una denominata di “tipo-tempo” e l’altra “tipo-spazio”. Queste due realtà sono state sottoposte a numerose verifiche sperimentali. Nella realtà “tipo-spazio” il “prima” e il “dopo” dipendono da chi osserva gli eventi. Napoleone viene dopo Giulio Cesare in quanto entrambi sono vissuti in una realtà “tipo-tempo”. Chi scrive ha realizzato la prima rigorosa verifica della Relatività Ristretta nei fenomeni elettromagnetici che ha come formulazione matematica la cosiddetta Elettrodinamica Quantistica (Quantum ElectroDynamics: QED). Per far questo è stata necessaria l’invenzione di una nuova tecnica (oggi in uso in tutti i laboratori specializzati) per costruire campi magnetici polinomiali di altissima precisione. Studiando le due realtà “tipo spazio” e “tipo-tempo”, chi scrive ha scoperto la struttura “tipo-tempo” delle trottoline fondamentali di cui è fatta ogni cosa (aria, acqua, piante, montagne, sole, luna, stelle etc.), inclusi noi stessi: il protone. Per fare questa scoperta è stata necessaria l’invenzione di una nuova tecnica al fine di separare – come mai prima era stato fatto – la produzione di coppie di “leptoni carichi” dalla produzione di coppie di mesoni (la “colla” nucleare) a livello di una coppia leptonica su diecimilioni di coppie mesoniche. Queste sono soltanto alcune delle invenzioni nate da QED. Molte delle invenzioni tecnologiche nate da QED sono entrate nella vita di tutti i giorni: radio, TV, cellule fotoelettriche, telecomandi per aprire e chiudere le porte, telefonini, computer, Internet, tecnologie mediche (Raggi X, TAC, PET, Risonanza Magnetica, bisturi laser etc.) ed elettrodomestici di ogni tipo, nulla potrebbe esistere se non avessimo scoperto la logica delle Forze Elettromagnetiche che ha il suo baluardo nella velocità della luce, costante e assoluta. Se fosse stato vero che i neutrini battono la luce in velocità, sarebbe stato necessario capirne le radici. Avrebbero potuto essere numerose. Come ad esempio la violazione della cosiddetta “invarianza di Lorentz”, meglio nota come validità della Relatività Ristretta di Einstein nelle Forze Elettromagnetiche, il che 15 vuol dire: validità di QED. Se di violazione si tratta, quali esperimenti avrebbero dovuto essere fatti per selezionare il modello teorico in grado di descrivere i risultati sperimentali? Il modello preferito da chi scrive è quello del Supermondo, cui accenneremo fra poco. Come la mettiamo con la tecnologia entrata nella vita di tutti i giorni? Risposta: nessuno può prevederne gli sviluppi. Una cosa è certa: questa tecnologia non sarebbe andata in crisi. Tutto ciò che ha radici in scoperte sperimentali riproducibili non corre alcun rischio. Sono le estrapolazioni teoriche fatte a partire da queste scoperte che avrebbero potuto subire drastiche modifiche. Ecco perché nessuno può prevedere i possibili sviluppi delle nostre ricerche intese a decifrare la Logica che regge il mondo. Esattamente come nel 1896 né Kelvin né alcun altro fisico avrebbe saputo immaginare l’enorme quantità di scoperte scientifiche e di invenzioni tecnologiche occorse dal 1896 al 2011. Una tra le numerose scoperte scientifiche riguarda l’esistenza dei neutrini. Il terzo neutrino è stato proposto da chi scrive negli anni settanta. Durante questi 115 anni di dominio della luce (il che vuol dire QED) è venuto fuori che lo spazio-tempo con le 4 dimensioni (3 di spazio e una di tempo) non basta per descrivere ciò che abbiamo finora capito sulla Logica che regge l’universo. Essa va dalle minuscole strutture subnucleari alle più lontane strutture cosmiche in cui c’è bisogno di invocare l’esistenza delle cosiddette “materia” ed “energia” oscure. Proprio quest’anno il Nobel è stato attribuito a tre fisici impegnati nello studio dell’energia oscura. 16 EINSTEIN ISSP 2012 ADDENDUM 3–1 THE MASSMATTER PROBLEM The fact that mass and matter had to be two different physical quantities, i.e. the mass matter problem, started with the Einstein discovery E = mc 2. The symbol ‘m’ originally was considered to represent ‘matter’ and thus the Einstein discovery become the problem of explaining the stability of matter. The meaning of ‘m’ had to be different from ‘matter’. This is how the distinction between ‘matter’ and ‘mass’ come in the forefront of fundamental physics. Einstein proposed to solve the problem mass matter with the existence of just one ‘charge’, the electromagnetic one. But, seven decades and the sequence of UEEC events reported in figure 17 were needed to understand the stability of matter. The ‘charge’ needed for the mass matter problem is not the ‘gauge’ charge, like the electromagnetic one, but a set of ‘flavour’ charges; and these are 12, as reported in figure 18 where it is also specified that there are three classes of ‘masses’. 17 WEYL - BOHR THE ANTIDEUTERON EXPERIMENT RECOLLECTIONS OF THE FINE TIMES AND CLOSING REMARKS Bologna — 18 December 1995 Symposium to celebrate the 30th anniversary of THE DISCOVERY OF NUCLEAR ANTIMATTER 2 — The collapse of the Symmetry Operators in the fifties and middle sixties. The fact that the antiparticle of the electron had to be with the same mass as the electron was the starting point to believe that all antiparticles had to have the same mass as their particle states. When H. Weyl discovered that is a solution of the Dirac Equation with positive energy and the same mass, m, which appears in the Dirac Equation for , Dirac became enthusiastic about the C operator. The intrinsic mass of a particle state was considered to be the same as its other intrinsic properties, like the absolute value of the electric charge and the spin: they had to be the same for particle and antiparticle states. This belief went on until Lee and Yang discovered that there was no experimental proof for the validity of Charge Conjugation Invariance (C) and of Parity Symmetry (P) in all processes involving the Weak Forces. Up to that moment the general belief was that the equality (2.1) was a proof of C invariance. Lee and Yang pointed out that if the muon decay processes were governed by Weak Interactions and these interactions were C non-invariant, the equality (2.1) above was a consequence of CPT invariance, not of C invariance. In other words, if Weak Interactions were C invariant, this implied C invariance was violated, had to hold because of CPT. , but if What about the intrinsic masses? As the origin of these masses was unknown, many great fellows were convinced that the intrinsic mass of a particle had to obey Charge Conjugation Invariance. Even today we do not know the origin of the intrinsic masses of the elementary constituents of the world: quarks and leptons. If we believe that the intrinsic masses obey C invariance then the problem of the equality between particle and antiparticle masses is settled. But, if the intrinsic masses originate from so far unknown forces, whose C properties are unknown, it would be sufficient to postulate these forces to be describable by a Relativistic Quantum Field Theory (RQFT) for the masses of particles and antiparticles to be identical. In fact this result follows from the CPT Theorem, which is proven to hold in the context of a RQFT. 18 Dirac was convinced that C invariance had to be valid insofar as the intrinsic properties of an elementary particle were concerned. Dirac was not convinced that the proof of the CPT Theorem was on firm grounds (see later). In particular, there was no reason to believe that the nuclear binding forces had to be CPT invariant. The collapse of C and P invariance in the middle fifties was crucial for questioning the validity of the Symmetry Operators. The discovery that CP was conserved confirmed the faith in the Time Reversal Invariance (T). Nevertheless a lot of confusion was around in those years. For example the “strangeness mixing”, invented by Gell-Mann and Pais, to ̅ 0 ) physics, brought them to predict the existence of K1 and K2 , on the describe the (𝐾 0 𝐾 basis of the validity of C invariance. The discovery by Lederman of K 2 3 was interpreted as a proof that C invariance holds in Weak Interactions. Very few people know that Lee, Oehme and Yang [1], before Parity Violation was experimentally proved by C.S. Wu, pointed out that the existence of K2 invariance, nor as a proof of CP invariance. could not be taken as a proof of C Lee, Oehme and Yang showed that “strangeness mixing” does not imply C invariance as claimed by Gell-Mann and Pais. In fact, even if CP is not valid, K2 would still be there and, in order to prove that “strangeness mixing” is or is not CP invariant, other experiments needed to be done in K decay physics, as suggested by LOY. This flavour mixing problem and its CP invariance or non- invariance, is extremely topical today with many experiments being planned in order to understand the basic distinction between “flavour mixing” and CP invariance, for all flavours. The fact that the authors of the basic distinction between “flavour mixing” and CP invariance are Lee, Oehme and Yang has been forgotten. Nevertheless those who were following this physics knew that CP could be violated despite the observation of K2 3. This is why some careful fellows were seriously thinking that the proof for the existence of Antimatter was badly needed, in order to be sure about the invariance of all Symmetry Operators. From CPT one could argue that the Antideuteron had to be there but, as we will see in the next chapter, the dominant Strong Interaction Theory of the sixties was not a RQFT but the S-Matrix Theory. The S-Matrix Theory negates completely the Relativistic Quantum Field Theory, upon which the CPT Theorem is based. So, not only some Symmetry Operators (C and P) had been found to be broken, but, at the same time, the only theory able to describe Strong Interactions was not a RQFT but the negation of it. And this is not all. In 1964 another pillar collapsed: the CP invariance. Thus endangering the Symmetry Operator T, considered as “sacred” by Dirac, Wigner and 19 Heisenberg. In order to save T, the product of all Symmetry Operators, CPT, had to be broken. Clearly, there was no consensus among theorists. The decisive step had to be taken by experimentalists. Let me allow a digression on CPT. The theorem came after the three Symmetry Operators had been discovered: 1) Charge Conjugation, C, by H. Weyl and P.A.M. Dirac; 2) Parity, P, by E.P. Wigner; 3) Time Reversal, T, by E.P. Wigner. To the best of my knowledge, the CPT Theorem was first proved by W. Pauli in his article “Exclusion Principle, Lorentz Group and Reflection of Space-Time and Charge”, in “Niels Bohr and the Development of Physics” [Pergamon Press, London, p. 30 (1955)], which in turn is an extension of the work of J. Schwinger [Phys. Rev. 82, 914 (1951); 91, 713 (1953); 91, 728 (1953); 94, 1362 (1954)] and G. Lüders, “On the Equivalence of Invariance under Time Reversal and under Particle-Anti-particle Conjugation for Relativistic Field Theories” [Dansk. Mat. Fys. Medd. 28, 5 (1954)], which referred to an unpublished remark by B. Zumino. The final contribution to the CPT Theorem was given by R. Jost, in “Eine Bemerkung zum CPT Theorem” [Helv. Phys. Acta 30, 409 (1957)], who showed that a weaker condition, called “weak local commutativity” was sufficient for the validity of the CPT Theorem. The discovery in 1964 of CP violation in K decays, while confirming the suggestion of Lee, Oehme and Yang, and recalling their correctness of the distinction between “strangeness mixing” and CP invariance, prompted doubts on all symmetries, thus far considered as granted, like CP, T and CPT. The collapse of Symmetry Operators has its origin in experimental physics, with the () puzzle. The collapse of the fundamental mathematical structure, RQFT, has its origin in theoretical physics. Both structures were needed for Matter-Antimatter symmetry to hold. Having discussed the collapse of the Symmetry Operators, we now turn to the collapse of RQFT. 20 SCHRÖDINGER LIBRO: ETTORE MAJORANA: GENIUS AND MYSTERY The young Dirac realized that no one had been able to describe the evolution of the first example of ‘elementary particle’, the electron (discovered by J.J. Thomson in 1897), in such a way as to obey the Lorentz condition, i.e. space and time united and drastically different: one real, the other imaginary. The most successful description of the evolution of the electron in space and time was the celebrated Schrödinger equation, where the charge e, the electromagnetic potential A, the mass m, the derivative with respect to the space coordinate ¶ ¶x and with respect to time, ¶ , ¶t were all present, including the concept of ‘wave function’ whose square was the ‘probability’ for the ‘electron’ to be in a given configuration state. The Lorentz invariance was not there. The Schrödinger equation describes the evolution in space and time of a numerical quantity, called ‘wave function’, whose square at any position and time gives the probability, at that time, of finding a particle at that location in space. How the ‘wave function’ changes with time and space are not treated in the same way. The rate of change with position is controlled by a second-order derivative, i.e. the rate of change with position of the rate of change of the wave function with position. But the rate of change with time, of the same function, is computed at the first order, i.e. the rate of change with time. The second order would be to compute the rate of change with time of the rate of change of the wave function with time. 21 These two ways of describing the evolution of the wave function in time (first order) and in space (second order) was in conflict with the condition of putting space and time in a perfectly symmetric way, as requested by relativistic invariance. Dirac knew that there was an equation, which described the evolution in space and time of a wave function, where the derivatives versus time and space were both of second order. In this equation, discovered by Klein and Gordon, space and time were treated in a symmetric way, as requested by relativity. But the Klein–Gordon equation gave positive and negative probabilities, negative probability being nonsense. In 1934, this difficulty was shown by Pauli and Weisskopf [Pauli and Weisskopf 1934] to be overcome, since the Klein–Gordon ‘wave function’ should not be treated as a ‘wave function’ describing a single particle, but as an operator in a field equation describing a field of relativistic massive particles having positive and negative electric charges. Pauli and Weisskopf concluded that positive and negative values should not be attributed to probabilities, but to the net charge densities at any point in space-time. Let us return to Dirac and his struggle to overcome the difficulties existing with the Schrödinger and Klein–Gordon equations. Dirac wanted an equation where time and space were treated in a symmetric way, at the first order in the derivative, and obeying the principle that the probability must be positive. Once all the conditions were fulfilled, Dirac discovered that the particle needs an intrinsic angular momentum of ½ in units of Planck’s constant. The two equations existing before Dirac [Schrödinger (can be extended to have spin, but remains non relativistic) and Klein–Gordon (relativistic but no spin)] were both having problems. And the big question was to understand why the electron was not a scalar particle. The Dirac equation corresponds to four coupled equations. Once Lorentz invariance is imposed, the result is that in order to describe the evolution in space-time of the electron, you need four coupled equations. 22 The Dirac equation (1) corresponds to the following set of equations æ i¶ 0 + m ö 0 -i(¶1 + ¶ 3 ) ¶2 ç 0 i¶ 0 + m -¶ 2 -i(¶1 - ¶ 3 )÷ ç i(¶ - ¶ ) ÷ -¶ 3 -i¶ 0 + m 0 1 3 ç ÷ i(¶1 - ¶ 3 ) 0 -i¶ 0 + m ø è ¶2 æ y e - (x)ö ç y e ¯ (x)÷ ç y - (x)÷ = 0 ; ç p ÷ è y p ¯ (x)ø the wave function that appears in equation (1), (x), is made up of four components, and the electron cannot be a scalar particle: it must be a particle with spin ½ . In the four pieces of (x), æy çye y (x) º ç e ç y e+ çy è e+ - (x)ö ÷ ÷, - (x)÷ ¯ (x)÷ ø ¯ (x) each component is a function whose values depend on space and time, as indicated by the argument (x). The four components correspond to the following four possible states: electron with spin up, e (x); electron with spin down, e (x); positron with spin up, e+ (x); positron with spin down e+ (x). The totally unexpected result was the need for the existence of the electron antiparticle, called positron, e +: a particle with the same mass, same spin, but opposite electric charge. This ‘antiparticle’ had no experimental support. But in favour of Dirac there was another property of the electron. The study of atomic spectra was giving experimental results indicating that the electron, in addition to its spin, has another unexpected property. The electron behaved as if it was a tiny magnet. The magnetic properties required the electron to be like a spinning sphere, but it had to rotate at an extraordinarily rapid rate. So rapid that at its surface the rotation corresponded to a speed higher than that of light. The model of the spinning electron had been worked out by two Dutch graduate students, Samuel Goudsmit and George Uhlenbeck, who wanted to explain the experimental data of atomic spectra. 23 Eminent physicists were sceptical about this model, and Wolfgang Pauli tried to dissuade them from publishing their paper since the model they proposed had a quantitative mismatch in the gyromagnetic ratio, the so-called g factor, i.e. the ratio of the magnetic moment divided by the angular momentum. The electron orbiting around a nucleus has an angular momentum. The same electron, since it is electrically charged, in its orbital motion produces a magnetic field. The ratio of this magnetic field to the angular momentum corresponds to the value g = 1. The problem was to understand why intrinsic rotation (spin) produces a magnetic field that is twice stronger than the one produced by the same electron when it is orbiting in an atom: this is the meaning of g = 2 and g = 1, respectively. In order to agree with the results from atomic spectra, Goudsmit and Uhlenbeck postulated g = 2. ‘One can understand the origin of the Majorana mass-spin formula by considering the Schroedinger limit in perturbation theory starting from the rest frame. For a given rest state 0 , the kinetic energy term p gives rise to a second order energy shift E = 0 pi i p 0 (E0 Ei), where the sum is over the components of the neighbouring spin states i. One expects this to yield the nonrelativistic kinetic energy p2 2E0 > 0, which requires at least one of the states i to have a lower energy than E0. One sees from this that a descending mass spectrum with an accumulation point is an inevitable feature of a relativistic Hamiltonian which is Hermitian, linear in the momenta and has only positive (nonzero) rest energies.’ From Y. Nambu ‘Majorana’s Infinite Component Wave Equation’ in Majorana Centenary Celebrations (A. Zichichi ed, World Scientific Vol. I, 2006). 24 RUTHERFORD DA LIBRO BLACKETT (From left) Lord Patrick Maynard Stuart Blackett, Pyotr L. Kapitza, Paul Langevin, Lord Ernest Rutherford, Charles Thomson Rees Wilson outside Cavendish Laboratory (1929). This photo – dated 1929 – is a gift in 1955 of Professor Blackett to the youngest member of his group (A.Z.). On this occasion Professor Blackett said that on the same year (1929) the best synthesis on the future of Physics had been given in Florence by Orso Mario Corbino, the founder of what would have been the famous “Panisperna Group” where Enrico Fermi invented the “slow neutron technology” which allowed all elements of the Mendeleev Table to become “radioactive”. This is how Fermi discovered the “Weak Forces”. Here are the words of Professor Corbino(*): “The only possibility of great discoveries in Physics dwell in the eventuality of succeeding in modifying the inner nucleus of the atom. This will be the task truly worthy of the future in Physics”. __________________________ (*) «La sola possibilità di grandi scoperte in Fisica risiede nella eventualità che si riesca a modificare il nucleo interno dell’atomo. E questo sarà il compito veramente degno della Fisica futura». Rutherford [discovery of the atomic nucleus, i.e. of the fact that atoms are composite objects and that more than 99% of their mass is concentrated in a volume which is a million of a billion times smaller than the atomic volume]. 25 DA GALILEI DIVIN MAN Twentieth-century Galileans From the left in the photo: Lord Patrick Maynard Stuart Blackett, Pëtr Leonidovic Kapitza (18941984), Paul Langevin (1872-1946), Lord Ernest Rutherford (1871-1937), Charles Thomson Rees Wilson (1869-1959) fuori dal Laboratorio Cavendish nel 1929. Taken in 1929, Professor Blackett gave me this photo on my thirtieth birthday. Blackett established the English school of experimental physics. Together with Giuseppe Paolo Stanislao Occhialini (1907–1993), he discovered how to produce electron/anti-electron couples, and together with his pupils, George Dixon Rochester and Clifford Charles Butler, he also discovered “strange particles”. Kapitza – a close friend of Dirac and the man who discovered superfluidity – is a symbol of true science. He had the courage to oppose political violence (see page 390) by saying no to Stalin, who wanted to put him in charge of the Soviet H-bomb project, causing all kinds of problems for himself as a result(*). Paul Langevin explored “paramagnetism”. Lord Rutherford discovered the nucleus, thereby demonstrating that atoms are not “atomic”, that is, unbreakable entities, at all. My work as a scientist – I began as an assistant to Professor Blackett – started with studies involving the so-called cloud chamber, which was invented by Wilson to observe cosmic rays. (*) Interested readers might like to read my book Scienza ed Emergenze Planetarie (Rizzoli, three editions, 1993-1994; Supersaggi Rizzoli, twenty-three editions, 1996-2005). 26 JOHN VON NEUMANN DA GALILEI DIVIN MAN PAGINA 263 After Maxwell discovered his equations and Thomson discovered the electron, a wise and enlightened European government decided to set up a project to study the technological applications of those extraordinary scientific achievements. This government knew that the motor of progress is scientific discovery. John von Neumann would have invented the electronic computer not for military purposes but to resolve the complex problems arising from the study of the peaceful applications of electromagnetism in relation to living matter. Man would have succeeded in deciphering the genetic code (also known as the “DNA mapping”) at least fifty years earlier. This prediction is based on a precise figure, the time involved to develop the Manhattan Project. This project managed to transform, in barely five years, a complex scientific discovery far removed from everyday reality (nuclear fission) into a technological instrument within everyone’s reach. This terrible military project (set up to prevent Hitler ruling the world) carries with it (see opposite) a significant message about the time required to produce inventions based on new scientific discoveries. The time required for technological applications of scientific advances can be short-circuited: five years instead of the fifty, if not hundred, normally required for a scientific discovery to be transformed into everyday technology. The achievement of DNA “mapping” is the first stage of a new branch of technology, one that works on living matter. We need to be careful, however. 27 WERNER KARL HEISENBERG DA GALILEI DIVIN MAN PAGINA 287 If some phenomena cannot be observed directly, their effects must be measurable in a rigorous and reproducible manner in order for them to be considered part of science. Imagine a very simple particle, consisting of nothing but itself, for example the muon. If this particle possesses electric charge, it can interact with other particles by emitting an electromagnetic wave. Werner Karl Heisenberg (1901–1976) taught that everything that exists must have wave and particle properties at the same time. Stones and waves in the sea are macroscopic approximations of a reality whose roots lie in this “dual” nature of Creation. That is, being simultaneously wave and particle. An electromagnetic wave must therefore also have a particle property. When the electromagnetic wave is a particle, it is called a “photon”. It was Einstein who discovered the particle nature of light, for which he was awarded the Nobel Prize (and not for relativity, as is generally believed; relativity is the intellectual property of Galilei). To return to the muon. As it has electric charge, it must be capable of emitting a photon. If it is able to emit it, it must also be able to absorb it. When we imagine a particle evolving (moving) in space-time, we cannot ignore that this particle, as we seek to measure its properties, emits and continually absorbs a very great number of photons. We do not observe these emissions and subsequent absorptions directly. If we measure some fundamental property with precision, it must be sensitive to the innumerable series of “virtual phenomena” at play. This is in fact the case. 28 JOHNNY VON NEUMANN LIBRO: CREATIVITY IN SCIENCE Imagination in Science corresponds to thinking of a new principle, of a new phenomenon, of a new law and to imagining a new experiment. Is there an equilibrium, a balance between Memory, Imagination, Creativity, in the same man? Let me mention an example: Johnny Von Neumann. He once told me something like the following: “Nino, I could tell you how many coffees I drank on 25 June 1933”. He was convinced that his imagination was not as great as he would have liked because he had too much memory. “Think of Eugene Wigner. He is a man of formidable imagination. Fortunately for him, his memory is not as powerful as mine”. He told me a story which I have checked with Wigner and, believe it or not, it is true. They were great friends and often used to discuss physics and mathematical problems. During one such discussion, Wigner suddenly said: “My God, it is already midday. I was invited for lunch. Please excuse me Johnny, I must go immediately”. [Eugene Wigner was an extremely polite fellow. He always was exactly on time. Isidor I. Rabi used to say: “Kindness is the Wigner weapon”]. As he was running off, Von Neumann said: “Eugene, you are so smart; why don’t you stop the running of time?”. And, immediately added: “Sorry, it is too late, you should be able to let time go backwards”. That started Wigner thinking about elementary particles and Fundamental Laws of Nature. An elementary particle has no brain, no watches: it cannot distinguish between past and future. All fundamental interactions among elementary particles must be invariant if time goes one way or in the opposite direction. Three months after the famous Von Neumann invitation to his friend Wigner to use his imagination in order to go back in time, Wigner discovered the famous theorem which establishes the existence of the Time-reversal Operator. All Laws of Physics should be, as we now say, “T-Invariant”, i.e. physics reality should remain the same if we invert the time flow. In 1964 a special effect was discovered which violates “T-Invariance”, in the decay of a particle now called 29 - of experiments in order to check if, in the electromagnetic interactions, “T-Invariance” was valid. Wigner was very happy to know that electromagnetic forces obey his (Wigner’s) Invariance Principle. Professor Wigner is one of the greatest scientists of this century. He created the “Time-reversal Operator” because he was able to show that this operation (i.e. to reverse the arrow of Time) does not produce any contradiction in the Logic of Nature. Furthermore his theorem has passed the baptism of fire of the experimental reproducible proofs. Here is an example of Creativity in Science. The great Wigner was also, with Enrico Fermi, the man who contributed most efficiently to the lighting of the nuclear fire (Chicago, 2 December 1942). But nuclear fire is not Science. Nuclear fire is Technology: the most recent example and probably the most used against Science. …. The advent of electronic computation, thanks to Johnny Von Neumann, gave a great impulse to meteorology. Von Neumann discovered the matter was not so simple since the experimental finding could not be easily fitted with “theoretical” forecast. Nowadays meteorology has a basic difficulty: the so-called “butterflyeffect” whereby the beat of a butterfly’s wings could initiate a series of atmospheric disturbances, which could ultimately cause a tornado, thousands of miles away. Meteorology needs still to discover its “atoms”. 30 Letter to the Editor CERN COURIER An article entitled, “The Ring on the Parking Lot”, (CERN Courier, Volume 43, Number 5, June 2, 2003, page 16) contains references to the discoveries of the tau lepton and the J/psi particle. Both represent clear departures from the documented facts which are part of the public record. In this paper the Author gives the message that the idea to search for the existence of new “narrow heavy mesons” and new “heavy leptons” with their own leptonic number was the privilege of SLAC. This is not true. The search for new “narrow heavy mesons” decaying into lepton pairs [(e+e) and (+)] and the search for new “heavy leptons” decaying in the standard but mixed leptons (e±) began at CERN with A. Zichichi whose PAPLEP (Proton-Antiproton Annihilation into Lepton Pairs) project was strongly supported by the DG of the time (Victor Weisskopf) and produced the invention of new technologies. For example: the “pre-shower” which allows the identification of electrons many orders of magnitude better than with existing technologies; another example: the detailed study of high energy muon penetration in different materials, to improve muon identification technologies; a third example: the invention of an electric device to reach 100ps in precision Time-of-Flight (TOF) technology. All these technological developments are reported in a volume (edited by B. Wiik, A. Wagner and H. Wenninger (World Scientific Series in 20th Century Physics, Vol. 31)) and were motivated by the basic new ideas to search for “heavy narrow mesons” and “heavy leptons” (with their own leptonic number). The PAPLEP project results showed that ( p p) annihilation was not effective because of the very strong “Time-Like-Electromagnetic-FormFactor” (EMFF) of the proton. The effective annihilation channel was identified to be the (e+e) annihilation in order to search for these new particles (heavy narrow mesons and heavy leptons). The PAPLEP group in fact moved to Frascati where a new (e+e) collider (ADONE) able to reach 3 GeV in C.M. energy was being implemented. At CERN the PAPLEP group changed the primary source from ( p p) to (p) using a new technology, the neutron missing mass spectometer (called NBC set up) to study the (e+e) and (+) decays of the known vector mesons (, , ) and to search for new ones. The NBC set up allowed the first measurements of the () and () mixing angles to be determined, before the existence of (e+e) colliders in the USA and in Europe. In discussions between Ting and Zichichi, during public Seminars at CERN, the idea came to Ting to study the production of “new heavy mesons” decaying in (e +e) pairs at BNL. This search was successful at BNL and brought to the discovery of the J-particle. The search for “new heavy mesons” at Frascati could not go above 3 GeV, otherwise the would have been discovered at Frascati by the Bologna-CERN-Frascati group at ADONE (as documented in the volume “Lepton Physics at CERN and Frascati” edited by N. Cabibbo and published by World Scientific in the same series quoted above, Vol. 8). 31 To conclude: the idea, the way and the technology to discover “new heavy mesons” and of “new heavy leptons” (with their own leptonic number) started at CERN, moved to Frascati and to BNL, and then to SLAC where the energy was the winning parameter. The energy and only the energy; not the ideas, not the technologies, not the identification of the correct initial states. The physics of “heavy new mesons” and “heavy leptons” did not originate at SLAC with the (e+e) collider. All this originated, was developed and implemented first at CERN, and then moved to Frascati and BNL. We are not speaking about irrelevant details. We are talking about the origin of the “Third Family”, in its leptonic part (heavy lepton) and hadronic part (heavy narrow mesons). The origin of the “Third Family” is not due to SLAC, as documented in a volume “The Origin of the Third Family” edited by C.S. Wu and published by World Scientific in the same series quoted above, Vol. 20. 32