La “Loop Quantum Gravity” (LQG) opera, nel 1990, di Carlo Rovelli e Lee Smolin basata sul concetto di “spin network” (rete di spin), ideato nei primi anni ’70, da Roger Penrose, rappresenta una delle piu’ affascinanti ed eleganti teorie gravitazionali.
In fisica, una rete di spin è un tipo di diagramma che puo’ essere usato per rappresentare gli stati e le interazioni tra particelle e campi in meccanica quantistica. Dal punto di vista matematico, i diagrammi sono un modo conciso per rappresentare funzioni multilineari e funzioni tra gruppi di matrici. La notazione diagrammatica spesso semplifica il calcolo perché semplici diagrammi possono essere usati per rappresentare funzioni complicate. A Roger Penrose è attribuita l'invenzione delle “reti di spin” nel 1971, anche se simili tecniche diagrammatiche esistevano anche prima di allora. Le reti di spin sono state applicate alla teoria della gravità quantistica da Carlo Rovelli, Lee Smolin, Jorge Pullin e altri.
Una rete di spin, come descritta da Penrose nel 1971, è una sorta di schema in cui ogni segmento di linea rappresenta la linea di universo di una "unità" (una particella elementare o un sistema composto di particelle). Tre segmenti di linea convergono in ogni vertice. Un vertice può essere interpretato sia come un evento in cui una singola unità si divide in due, sia come uno in cui due unità si scontrano e si uniscono a formare una singola unità. Schemi le cui linee-segmenti sono tutti uniti nei vertici sono chiamati reti di spin chiuse. Il tempo può essere visto scorrere in una direzione, piuttosto che dal basso verso l'alto dello schema, ma per le reti di spin chiuse la direzione del tempo è irrilevante per i calcoli. Ogni segmento è marcato con un numero intero chiamato “numero di spin”. Un’unità con numero di spin n è detta “n-unità” e ha momento angolare nh/2л. Per i bosoni, come fotoni e gluoni, n è un numero pari. Per i fermioni, come gli elettroni e i quark, n è dispari.
Nella gravità quantistica a loop (LQG), una rete di spin rappresenta uno "stato quantico" del campo gravitazionale su una ipersuperficie tridimensionale.
La gravità quantistica a loop è conosciuta anche come “geometria quantistica” e “relatività generale canonica”. E 'stata proposta come teoria quantistica dello spazio-tempo che tenta di unificare le teorie apparentemente incompatibili della meccanica quantistica e relatività generale. Si tratta di una teoria quantistica della gravità in cui è quantizzato lo spazio reale in cui accadono tutti gli altri fenomeni fisici. La LQG conserva gli aspetti fondamentali della relatività generale, come l’invarianza per trasformazioni di coordinate e, al tempo stesso, utilizza la quantizzazione dello spazio e del tempo alla scala di Planck, caratteristica della meccanica quantistica. I critici della LQG fanno spesso riferimento al fatto che la teoria non predice l'esistenza di dimensioni extra dello spazio-tempo , o la supersimmetria. La risposta dei fautori LQG è che, attualmente, nonostante le ripetute ricerche sperimentali, non ci sono prove di altre dimensioni o particelle supersimmetriche, per cui le dimensioni aggiuntive dello spazio e del tempo e la supersimmetria devono essere considerate ipotesi speculative.
Estratto da “on LQG” di Carlo Rovelli.
Nel 1915 Einstein si rese conto che la gravità doveva anche essere descritta da una teoria di campo in modo da essere coerente con la relatività speciale. Finché restiamo nell'ambito del regime classico, piuttosto che in quello quantistico, il campo gravitazionale definisce un continuum 4D. Possiamo, cioe’, pensare ancora al campo come a una sorta di spazio-tempo che si piega, oscilla e obbedisce alle equazioni di campo. Tuttavia se portiamo la meccanica quantistica in scena questo continuum si rompe. I campi quantistici hanno una struttura granulare - il campo elettromagnetico, per esempio, è composto da fotoni - e subiscono le fluttuazioni probabilistiche. E’ difficile pensare lo spazio come un oggetto granulare e fluttuante. Possiamo, naturalmente, ancora chiamarlo "spazio", o "spazio quantico". Ma è davvero un campo quantistico, in un mondo dove ci sono solo campi su campi, e nessun residuo di spazio sullo sfondo. John Wheeler della Princeton University ha suggerito che lo spazio-tempo deve avere una “schiuma” come struttura a scale molto piccole e, insieme a Bryce DeWitt ora alla Texas University, ha introdotto l'idea di una "funzione d'onda su geometrie". Questa è una funzione che esprime la probabilità di avere una geometria dello spazio-tempo piuttosto che un altro, nello stesso modo in cui la funzione d'onda di Schrödinger esprime la probabilità che una particella quantistica sia qui o là. Questa funzione d'onda su geometrie obbedisce a un'equazione molto complessa che si chiama equazione di Wheeler-DeWitt, che è una sorta di equazione di Schrödinger per il campo gravitazionale stesso. Queste idee erano brillanti e di grande ispirazione, ma è stato più di due decenni dopo che sono diventate concrete. La svolta si è avuta improvvisamente intorno alla fine degli anni’80, quando una teoria matematica ben definita che descrive lo spazio-tempo quantistico ha cominciato a formarsi. La chiave che rese possibile il funzionamento della teoria fu una vecchia idea di fisica delle particelle: le variabili naturali per descrivere una teoria di Yang-Mills sono proprio le "linee di forza" del campo di Faraday. Una linea di Faraday può essere vista come uno stato di eccitazione del quanto di campo elementare e, in assenza di cariche, queste linee devono chiudersi su se stesse a formare un loop. La Loop Quantum Gravity è la descrizione matematica del campo gravitazionale quantistico mediante di tali loops. Cioè i cicli sono eccitazioni quantistiche delle linee di forza di Faraday del campo gravitazionale. In approssimazioni a bassa energia della teoria, questi loop appaiono come gravitoni - le particelle fondamentali che portano la forza gravitazionale. Nella LQG i loop stessi non sono nello spazio, perché non c'è spazio. I loop sono lo spazio, perché sono le eccitazioni quantistiche del campo gravitazionale, che è lo spazio fisico. Pertanto non ha senso pensare a un loop disposto in una piccola quantità di spazio. Ha senso solo la posizione relativa di un loop rispetto agli altri e la posizione di un loop rispetto allo spazio circostante è determinata solo dagli altri loops con i quali si interseca. Uno stato dello spazio è quindi descritto da una rete di loops che si intersecano. Non esiste una posizione della rete, ma solo la posizione sulla stessa rete, non ci sono loops di spazio, ma solo loop su loop. I loops interagiscono con le particelle nello stesso modo in cui, ad esempio, un fotone interagisce con un elettrone, tranne per il fatto che i loops non sono nello spazio come i fotoni e gli elettroni. I grani elementari di spazio sono rappresentati, su una "rete di spin", dai nodi. Le linee che uniscono i nodi, o i grani adiacenti dello spazio, sono chiamati link. Gli spin sui link (numeri interi o semi-intero) sono i numeri quantici che determinano l'area delle superfici elementari di separazione dei grani adiacenti dello spazio. I numeri quantici dei nodi determinano il volume dei grani. Gli spin e il modo in cui si riuniscono presso i nodi possono assumere qualsiasi numero intero o semi-intero e sono regolati dalla stessa algebra del momento angolare in meccanica quantistica. L'idea che non ci possono essere regioni dello spazio arbitrariamente piccole può essere compresa con semplici considerazioni di meccanica quantistica e relatività generale classica. Il principio di indeterminazione impone che per osservare una piccola regione dello spazio-tempo abbiamo bisogno di concentrare una grande quantità di energia e momento. Tuttavia la relatività generale implica che se si concentra troppa energia e quantità di moto in una piccola regione, quella regione collassa in un buco nero e sparisce. Mettendo dei numeri scopriamo che la dimensione minima di tale regione è dell'ordine della lunghezza di Planck - circa 1,6 × 10-35m. La LQG aveva cominciato a rendere concreta questa intuizione e stava emergendo un’immagine dello spazio quantico fatta di reti di loops. Ma allora non sapevamo davvero cosa significava. Ma lo spazio non è solo un insieme di elementi di volume. C'è anche la considerazione chiave che alcuni elementi sono vicino agli altri. Un "link" della rete - la porzione di rete tra due nodi - indica con precisione i quanti di spazio che sono adiacenti l'uno all'altro. Due elementi adiacenti dello spazio sono separati da una superficie, e l'area di questa superficie risulta essere pure quantizzata. Infatti, ben presto divenne chiaro che i nodi portano numeri quantici di elementi di volume e i collegamenti portano numeri quantici degli elementi dell'area. Ogni nodo di una rete di spin determina una cella, o un chicco elementare di spazio. I nodi sono rappresentati da piccole sfere nere e i collegament come linee nere, mentre le celle sono separate da superfici elementari. Ogni superficie corrisponde a un link, e la struttura costruisce uno spazio 3D. Quando le superfici sono tirate via possiamo vedere la sequenza di collegamenti formare un anello. Questi sono gli "anelli" della gravità quantistica a loop. Per il momento non c'è stata alcuna prova sperimentale diretta della teoria. Una costruzione teorica deve rimanere umile fino a quando le sue predizioni non sono stati testate direttamente e senza ambiguità. Questo vale per le stringhe così come per i loops. La natura non sempre condivide i nostri gusti su una teoria bellissima. La teoria di Maxwell è diventata credibile quando le onde radio sono state osservate.
La MT (“Marius Theory”) è stata ideata da Marius quando ancora non conosceva la LQG. L’impressionante analogia dei concetti ha portato Marius a confrontarsi con tale teoria. L’esito è stato che le conclusioni apparentemente “surreali” della MT (sostanziale identità tra spazio, energia, massa e materia : logica “S.E.M.M". ; inesistenza del tempo, gravità compressiva, etere stazionario e altro…) tutto sommato tanto fantasiose non fossero.
Dove la MT marca una sostanziale differenza rispetto alla LQG è nella quantizzazione di un normale spazio euclideo 3d, anziche’ della ipersuperficie 3d della LQG che, secondo Marius, avrebbe bisogno di liberarsi della dimensione temporale, atteso che, la "freccia temporale" risulta ininfluente per la chiusura dei loops. Certo questo non consentirebbe di mettere d’accordo RG e MQ ma, sempre secondo Marius, lo spin network, come la quantizzazione dello spazio 3d, rappresentano solo l’approssimazione di quella che è la realtà fisica sottostante, una matrice a – temporale costituita da onde elettromagnetiche stazionarie.
Nella formulazione “compatta” della MT : DU = nhv, il termine di quantizzazione n rappresenta il numero di volte in cui il cammino di una massa concentrata in un punto tra due orbite di un campo gravitazionale puo’ essere diviso in “spazi di Planck” : 10^-35 m. Cio' che sviluppa energia è l'elettromagnetismo rappresentato dal secondo membro dell’uguaglianza nhv, con v frequenza della radiazione. L’applicazione di questa formula “grossolana” ha consentito a Marius di calcolare, su un percorso piu’ o meno verosimile, le frequenze necessarie a spostare alcuni pianeti del sistema solare dall’orbita mareale del sole fino alle orbite attuali e, con suo grande stupore, a scoprire che tali frequenze erano dell’ordine di grandezza di normali raggi gamma ad alta energia. Il termine di quantizzazione n, che rappresenta il parametro fondamentale della formula, contiene tutte le variabili in gioco, ossia l’energia necessaria a compattare la massa inizialmente fluida e incandescente del pianeta in forma sferica a partire dall’orbita di Roche del Sole, il guadagno di momento angolare nelle fasi di allontanamento e lo stazionamento a una certa distanza dal sole e con una certa velocità angolare. Tutto questo grazie, ritiene Marius, all’aver considerato la massa del pianeta puntiforme e, quindi, in grado di mobilitare tutti i quanti di spazio realmente attraversati dalla massa “distribuita” lungo il percorso, indipendentemente dal tempo impiegato.
Stefano Gusman
sabato 21 gennaio 2012
"MT" vs "LQG". Beyond the last gravity frontier
The "Loop Quantum Gravity" (LQG), designed by Carlo Rovelli and Lee Smolin in 1990, based on the concept of "spin networks", designed in the early '70s by Roger Penrose, is one of the most fascinating and elegant theories of gravity.
In physics a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups. The diagrammatic notation often simplifies calculation because simple diagrams may be used to represent complicated functions. Roger Penrose is credited with the invention of spin networks in 1971, although similar diagrammatic techniques existed before that time.
Spin networks have been applied to the theory of quantum gravity by Carlo Rovelli, Lee Smolin, Jorge Pullin and others.
A spin network, as described by Penrose in 1971, is a kind of diagram in which each line segment represents the world line of a "unit" (either an elementary particle or a compound system of particles). Three line segments join at each vertex. A vertex may be interpreted as an event in which either a single unit splits into two or two units collide and join into a single unit. Diagrams whose line segments are all joined at vertices are called closed spin networks. Time may be viewed as going in one direction, such as from the bottom to the top of the diagram, but for closed spin networks the direction of time is irrelevant to calculations.
Each line segment is labeled with an integer called a spin number. A unit with spin number n is called an n-unit and has angular momentum nh/2л. For bosons, such as photons and gluons, n is an even number. For fermions, such as electrons and quarks, n is odd.
In loop quantum gravity (LQG), a spin network represents a "quantum state" of the gravitational field on a 3-dimensional hypersurface.
The loop quantum gravity is also known by terms of gravity loop quantum geometry and quantum canonical general relativity. It has been proposed as a quantum theory of spacetime which attempts to unify seemingly incompatible theories of quantum mechanics and general relativity. This theory is part of a family of theories called canonical quantum gravity. It is a quantum theory of gravity in which the real space in which happen all the other physical phenomena is quantized.
The LQG retains the basic aspects of general relativity, such as invariance to coordinate transformations, and at the same time, using the quantization of space and time at the Planck scale, feature of quantum mechanics. In this sense it combines general relativity and quantum mechanics. Critics of the LQG often refer to the fact that the theory doesen't predict the existence of extra dimensions of space-time, or supersymmetry. The response of the LQG proponents is that at present, despite repeated experimental researches, there is no experimental evidence or other dimensions or supersymmetric particles, so the additional dimensions of space and time, both supersymmetry must be considered speculative hypotheses found to run faster than they do on Earth.
Abstract from “on LQG” by Carlo Rovelli.
In 1915 Einstein realized that gravity also had to be described by a field theory in order to be consistent with special relativity. As long as we stay within the classical regime, rather than the quantum one, the gravitational field defines a 4D continuum. We can therefore still think of the field as a sort of spacetime, albeit one that bends, oscillates and obeys field equations. However, once we bring quantum mechanics into the picture this continuum breaks down. Quantum fields have a granular structure – the electromagnetic field, for example, consists of photons – and they undergo probabilistic fluctuations. It is difficult to think of space as a granular and fluctuating object. We can, of course, still call it “space”, or “quantum space”. But it is really a quantum field in a world where there are only fields over fields, and no remnant of background space. John Wheeler of Princeton University suggested that spacetime must have a foam like structure at very small scales and, along with Bryce DeWitt now at Texas University, he introduced the idea of a “wavefunction over geometries”. This is a function that expresses the probability of having one spacetime geometry rather than another, in the same way that the Schrödinger wave function expresses the probability that a quantum particle is either here or there. This wave function over geometries obeys a very complicated equation that is now called the Wheeler–DeWitt equation, which is a sort of Schrödinger equation for the gravitational field itself. These ideas were brilliant and inspiring, but it was more than two decades before they become concrete. The turn around came suddenly at the end of the 1980s, when a well defined mathematical theory that described quantum spacetime began to form. The key input that made the theory work was an old idea from particle physics: the natural variables for describing a Yang–Mills field theory are precisely Faraday’s “lines of force”. A Faraday line can be viewed as an elementary quantum excitation of the field, and in the absence of charges, these lines must close on themselves to form loops. Loop quantum gravity is the mathematical description of the quantum gravitational field in terms of these loops. That is the loops are quantum excitations of the Faraday lines of force of the gravitational field. In low energy approximations of the theory, these loops appear as gravitons – the fundamental particles that carry the gravitational force. In LQG the loops themselves are not in space because there is no space. The loops are space because they are the quantum excitations of the gravitational field, which is the physical space. It therefore makes no sense to think of a loop being displaced by a small amount in space. There is only sense in the relative location of a loop with respect to other loops, and the location of a loop with respect to the surrounding space is only determined by the other loops it intersects. A state of space is therefore described by a net of intersecting loops. There is no location of the net, but only location on the net itself; there are no loops on space, only loops on loops. Loops interact with particles in the same way as a photon interacts with an electron, except that the two are not in space like photons and electrons are. Elementary grains of space are represented by the nodes on a “spin network”. The lines joining the nodes, or adjacent grains of space, are called links. Spins on the links (integer or half- integer numbers) are the quantum numbers that determine the area of the elementary surfaces separating adjacent grains of space. The quantum numbers of the nodes determine the volume of the grains. The spins and the way they come together at the nodes can take on any integer or half-integer value, and are governed by the same algebra as angular momentum in quantum mechanics. The idea that there cannot be arbitrary small spatial regions can be understood from simple considerations of quantum mechanics and classical general relativity. The uncertainty principle states that in order to observe a small region of spacetime we need to concentrate a large amount of energy and momentum. However, general relativity implies that if we concentrate too much energy and momentum in a small region, that region will collapse into a black hole and disappears. Putting in the numbers, we find that the minimum size of such a region is of the order of the Planck length – about 1.6× 10–35m. Loop gravity had begun to make this intuition concrete, and a picture of quantum space in terms of nets of loops was emerging. But at the time we did not really under stand what that meant. But space is more than just a collection of volume elements. There is also the key fact that some elements are near to others. A “link” of the net – the portion of loop between two nodes – indicates precisely the quanta of space that are adjacent to one another. Two adjacent elements of space are separated by a surface, and the area of this surface turns out to be quantized as well. In fact, it soon became clear that nodes carry quantum numbers of volume elements and links carry quantum numbers of area elements. Each node in a spin network determines a cell, or an elementary grain of space. Nodes are represented by small black spheres and the links as black lines, while cells are separated by elementary surfaces. Each surface corresponds to one link, and the structure builds up a 3D space. When the surfaces are pulled away we can see that the sequence of links form a loop. These are the “loops” of loop quantum gravity. Finally, for the moment there has not been any direct experimental test of the theory. A theoretical construction must remain humble until its predictions have been directly and unambiguously tested. This is true for strings as well as for loops. Nature does not always share our tastes about a beautiful theory. Maxwell’s theory became credible when radio waves were observed.
The MT ("Marius Theory") was created by Marius when he still did not know the LQG. The striking similarity of the concepts brought Marius to deal with this theory. The outcome was that the seemingly "surreal" conclusions of MT (substantial identity between space, energy, mass and matter: "S.E.M.M. logic”, absence of time, pushing gravity, standing aether and more ...) all things were not so fanciful.
Where MT makes substantial difference respect to LQG is in the quantization of a normal 3d Euclidean space, rather than the 3d hypersurface of LQG which, according to Marius, would need set free from temporal dimension standing that "time arrow" is irrelevant for the closure of loops. Of course this does not allows to conciliate GR and QM but, according to Marius, the spin networks, such as the quantization of 3d space, represent only the nearest approximation of the underlying physical reality, that is an a-temporal matrix made up by standing electromagnetic waves.
In the "compact" form of MT : DU = nhv, the quantization term “n” represents the number of times that the path between two orbits in a gravitational field of a point mass can be divided into Planck’s sizes" : 10 ^ -35 m. The thing that generates energy is electromagnetism represented by the second term of equality: nhv, with v frequency of the radiation. The application of this formula allowed Marius to calculate, on a path more or less likely, the frequencies necessary to move some solar system planets from the tidal Sun’s orbit since to the actual one and, with his large surprise, to discover that these frequencies have the sizes of normal high-energy gamma rays. The quantization term n, which is the fundamental parameter of the formula, contains all the variables involved : the energy required to compact the, at the beginning, fluid and incandescent mass of the planet in a spherical form starting out from Roche’s orbit of the Sun, the gain of angular momentum during removal since to parking at a certain distance from the sun with a certain angular speed. All this thanks, Marius believes, to having seen the planet mass point and, therefore, able to make work all the quantum space really crossed by the “distributed” mass along the path, regardless by the time it takes.
Stefano Gusman
In physics a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups. The diagrammatic notation often simplifies calculation because simple diagrams may be used to represent complicated functions. Roger Penrose is credited with the invention of spin networks in 1971, although similar diagrammatic techniques existed before that time.
Spin networks have been applied to the theory of quantum gravity by Carlo Rovelli, Lee Smolin, Jorge Pullin and others.
A spin network, as described by Penrose in 1971, is a kind of diagram in which each line segment represents the world line of a "unit" (either an elementary particle or a compound system of particles). Three line segments join at each vertex. A vertex may be interpreted as an event in which either a single unit splits into two or two units collide and join into a single unit. Diagrams whose line segments are all joined at vertices are called closed spin networks. Time may be viewed as going in one direction, such as from the bottom to the top of the diagram, but for closed spin networks the direction of time is irrelevant to calculations.
Each line segment is labeled with an integer called a spin number. A unit with spin number n is called an n-unit and has angular momentum nh/2л. For bosons, such as photons and gluons, n is an even number. For fermions, such as electrons and quarks, n is odd.
In loop quantum gravity (LQG), a spin network represents a "quantum state" of the gravitational field on a 3-dimensional hypersurface.
The loop quantum gravity is also known by terms of gravity loop quantum geometry and quantum canonical general relativity. It has been proposed as a quantum theory of spacetime which attempts to unify seemingly incompatible theories of quantum mechanics and general relativity. This theory is part of a family of theories called canonical quantum gravity. It is a quantum theory of gravity in which the real space in which happen all the other physical phenomena is quantized.
The LQG retains the basic aspects of general relativity, such as invariance to coordinate transformations, and at the same time, using the quantization of space and time at the Planck scale, feature of quantum mechanics. In this sense it combines general relativity and quantum mechanics. Critics of the LQG often refer to the fact that the theory doesen't predict the existence of extra dimensions of space-time, or supersymmetry. The response of the LQG proponents is that at present, despite repeated experimental researches, there is no experimental evidence or other dimensions or supersymmetric particles, so the additional dimensions of space and time, both supersymmetry must be considered speculative hypotheses found to run faster than they do on Earth.
Abstract from “on LQG” by Carlo Rovelli.
In 1915 Einstein realized that gravity also had to be described by a field theory in order to be consistent with special relativity. As long as we stay within the classical regime, rather than the quantum one, the gravitational field defines a 4D continuum. We can therefore still think of the field as a sort of spacetime, albeit one that bends, oscillates and obeys field equations. However, once we bring quantum mechanics into the picture this continuum breaks down. Quantum fields have a granular structure – the electromagnetic field, for example, consists of photons – and they undergo probabilistic fluctuations. It is difficult to think of space as a granular and fluctuating object. We can, of course, still call it “space”, or “quantum space”. But it is really a quantum field in a world where there are only fields over fields, and no remnant of background space. John Wheeler of Princeton University suggested that spacetime must have a foam like structure at very small scales and, along with Bryce DeWitt now at Texas University, he introduced the idea of a “wavefunction over geometries”. This is a function that expresses the probability of having one spacetime geometry rather than another, in the same way that the Schrödinger wave function expresses the probability that a quantum particle is either here or there. This wave function over geometries obeys a very complicated equation that is now called the Wheeler–DeWitt equation, which is a sort of Schrödinger equation for the gravitational field itself. These ideas were brilliant and inspiring, but it was more than two decades before they become concrete. The turn around came suddenly at the end of the 1980s, when a well defined mathematical theory that described quantum spacetime began to form. The key input that made the theory work was an old idea from particle physics: the natural variables for describing a Yang–Mills field theory are precisely Faraday’s “lines of force”. A Faraday line can be viewed as an elementary quantum excitation of the field, and in the absence of charges, these lines must close on themselves to form loops. Loop quantum gravity is the mathematical description of the quantum gravitational field in terms of these loops. That is the loops are quantum excitations of the Faraday lines of force of the gravitational field. In low energy approximations of the theory, these loops appear as gravitons – the fundamental particles that carry the gravitational force. In LQG the loops themselves are not in space because there is no space. The loops are space because they are the quantum excitations of the gravitational field, which is the physical space. It therefore makes no sense to think of a loop being displaced by a small amount in space. There is only sense in the relative location of a loop with respect to other loops, and the location of a loop with respect to the surrounding space is only determined by the other loops it intersects. A state of space is therefore described by a net of intersecting loops. There is no location of the net, but only location on the net itself; there are no loops on space, only loops on loops. Loops interact with particles in the same way as a photon interacts with an electron, except that the two are not in space like photons and electrons are. Elementary grains of space are represented by the nodes on a “spin network”. The lines joining the nodes, or adjacent grains of space, are called links. Spins on the links (integer or half- integer numbers) are the quantum numbers that determine the area of the elementary surfaces separating adjacent grains of space. The quantum numbers of the nodes determine the volume of the grains. The spins and the way they come together at the nodes can take on any integer or half-integer value, and are governed by the same algebra as angular momentum in quantum mechanics. The idea that there cannot be arbitrary small spatial regions can be understood from simple considerations of quantum mechanics and classical general relativity. The uncertainty principle states that in order to observe a small region of spacetime we need to concentrate a large amount of energy and momentum. However, general relativity implies that if we concentrate too much energy and momentum in a small region, that region will collapse into a black hole and disappears. Putting in the numbers, we find that the minimum size of such a region is of the order of the Planck length – about 1.6× 10–35m. Loop gravity had begun to make this intuition concrete, and a picture of quantum space in terms of nets of loops was emerging. But at the time we did not really under stand what that meant. But space is more than just a collection of volume elements. There is also the key fact that some elements are near to others. A “link” of the net – the portion of loop between two nodes – indicates precisely the quanta of space that are adjacent to one another. Two adjacent elements of space are separated by a surface, and the area of this surface turns out to be quantized as well. In fact, it soon became clear that nodes carry quantum numbers of volume elements and links carry quantum numbers of area elements. Each node in a spin network determines a cell, or an elementary grain of space. Nodes are represented by small black spheres and the links as black lines, while cells are separated by elementary surfaces. Each surface corresponds to one link, and the structure builds up a 3D space. When the surfaces are pulled away we can see that the sequence of links form a loop. These are the “loops” of loop quantum gravity. Finally, for the moment there has not been any direct experimental test of the theory. A theoretical construction must remain humble until its predictions have been directly and unambiguously tested. This is true for strings as well as for loops. Nature does not always share our tastes about a beautiful theory. Maxwell’s theory became credible when radio waves were observed.
The MT ("Marius Theory") was created by Marius when he still did not know the LQG. The striking similarity of the concepts brought Marius to deal with this theory. The outcome was that the seemingly "surreal" conclusions of MT (substantial identity between space, energy, mass and matter: "S.E.M.M. logic”, absence of time, pushing gravity, standing aether and more ...) all things were not so fanciful.
Where MT makes substantial difference respect to LQG is in the quantization of a normal 3d Euclidean space, rather than the 3d hypersurface of LQG which, according to Marius, would need set free from temporal dimension standing that "time arrow" is irrelevant for the closure of loops. Of course this does not allows to conciliate GR and QM but, according to Marius, the spin networks, such as the quantization of 3d space, represent only the nearest approximation of the underlying physical reality, that is an a-temporal matrix made up by standing electromagnetic waves.
In the "compact" form of MT : DU = nhv, the quantization term “n” represents the number of times that the path between two orbits in a gravitational field of a point mass can be divided into Planck’s sizes" : 10 ^ -35 m. The thing that generates energy is electromagnetism represented by the second term of equality: nhv, with v frequency of the radiation. The application of this formula allowed Marius to calculate, on a path more or less likely, the frequencies necessary to move some solar system planets from the tidal Sun’s orbit since to the actual one and, with his large surprise, to discover that these frequencies have the sizes of normal high-energy gamma rays. The quantization term n, which is the fundamental parameter of the formula, contains all the variables involved : the energy required to compact the, at the beginning, fluid and incandescent mass of the planet in a spherical form starting out from Roche’s orbit of the Sun, the gain of angular momentum during removal since to parking at a certain distance from the sun with a certain angular speed. All this thanks, Marius believes, to having seen the planet mass point and, therefore, able to make work all the quantum space really crossed by the “distributed” mass along the path, regardless by the time it takes.
Stefano Gusman
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