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Visualization of a computation of quantum field theory showing virtual particles in quantum vacuum. (More precisely, for strong interactions.) Even in empty space, this vacuum energy is non-zero. When pairs of particles and antiparticles appear and disappear, they can interact with real particles such as the electron, making corrections of vital importance to its own energy. On Quantum Field Theory offers the possibility to calculate properties like this one.
Derek Leinweber
If you want to answer the question of what is really fundamental in this universe, you have to study the material and the energy at the smallest possible scale. If you were trying to split particles into smaller and smaller components, you would notice extremely fun things once you've become smaller than distances of a few nanometers, where the classic rules of physics still apply.
At even smaller scales, reality begins to behave in a strange and counter-intuitive way. We can no longer describe the & nbsp; reality as being composed of individual particles with well-defined properties, such as position and momentum. Instead, we enter the quantum domain: & nbsp; where fundamental indeterminacy reigns and & nbsp; we need an entirely new description of how nature works. But even quantum mechanics itself has its failures. & Nbsp; They & nbsp; condemned Einstein's greatest dream – of a complete and deterministic description of reality & – from the beginning. Here's why.
If you let a tennis ball fall on a hard surface, like a table, you can be certain that it will bounce. If you were to perform the same experiment with a quantum particle, you would discover that this "classical" trajectory was only one of the possible outcomes, with a probability less than 100%. Surprisingly, there is a chance that the quantum particle loses its tunnel on the other side of the table, crossing the barrier as if it were no obstacle.
Wikimedia users like MichaelMaggs and (edited by) Richard Bartz
If we lived in an entirely classical and non-quantum world, it would be easy to make sense of things. By dividing the material into smaller and smaller pieces, we would never reach a limit. There would be no fundamental and indivisible building blocks of the universe. Instead, our cosmos would be made of continuous materials, where if we built a sharper knife, we would still be able to cut something into smaller and smaller pieces.
This dream followed the path of the dinosaurs at the beginning of the 20th century. The experiments of Planck, Einstein, Rutherford, and others have shown that matter and energy could not consist of a continuous substance, but rather divisible into discrete pieces, called quanta today. The original idea of quantum theory had too much experimental support: the Universe was not fundamentally classic after all.
Going to smaller and smaller distance scales reveals more fundamental views of nature, which means that if we can understand and describe the smaller scales, we can build our way to an understanding of the larger ones.
Perimeter Institute
For perhaps the first three decades of the 20th century, physicists have struggled to understand and understand the nature of the Universe at these puzzling little scales. New rules were needed, and to describe them, new and counter-intuitive equations and descriptions. The idea of an objective reality is out of the window, replaced by notions such as:
- probability distributions rather than predictable outcomes,
- wave functions rather than positions and moments,
- Heisenberg uncertainty relations rather than individual properties.
Particles describing reality could no longer be described just as particles. Instead, they had elements of both waves and particles and behaved according to a new set of rules.
An illustration between the inherent uncertainty between position and momentum at the quantum level. There is a limit to the extent to which you can measure these two quantities simultaneously because they are no longer simply physical properties, but rather quantum operators, with aspects inherent to their unknowable nature. The uncertainty of Heisenberg appears in places where people expect the least.
E. Siegel / Wikimedia Commons Maschen user
Initially, these descriptions disturbed many physicists. These problems are not simply due to the philosophical difficulties of accepting a non-deterministic universe or a modified definition of reality, although many of these problems have certainly disturbed it.
Instead, the difficulties were more robust. The theory of special relativity was well understood, and yet quantum mechanics, as originally developed, only worked for non-relativistic systems. By transforming quantities such as the position and momentum of physical properties into quantum mechanics operators – a specific class of mathematical functions – these strange aspects of reality could be integrated into our equations.
Trajectories of a particle in a box (also called infinite square well) in classical mechanics (A) and in quantum mechanics (B-F). In (A), the particle moves at constant speed, bouncing. In (B-F), the wave function solutions of the Schrodinger equation as a function of time are presented for the same geometry and the same potential. The horizontal axis is the position, the vertical axis is the real part (blue) or the imaginary part (red) of the wave function. (B, C, D) are stationary states (eigenstates of energy), derived from solutions to the time-independent Schrodinger equation. (E, F) are non-stationary states, solutions to the time-dependent Schrodinger equation. Note that these solutions are not invariant under relativistic transformations; they are valid only in one frame of reference.
Steve Byrnes / Sbyrnes321 from Wikimedia Commons
But & nbsp; the way you have allowed your system to evolve depends on time, and the notion of time is different for different observers. It was the first existential crisis to face quantum physics.
We say that a theory is relativist invariant if its laws do not change for different observers: for two people moving at different speeds or in different directions. Formulating a relatively invariant version of quantum mechanics was a challenge that the greatest minds of physics took many years to overcome, and was finally directed by Paul Dirac in the late 1920s.
Different frames of reference, including different positions and movements, would see different laws of physics (and would disagree on reality) if a theory is not invariant in a relativistic way. The fact that we have a symmetry in the "boost" or velocity transformations tells us that we have a conserved quantity: the linear moment. This is much more difficult to understand when momentum is not simply a quantity associated with a particle, but rather a quantum operator.
Wikimedia Commons Krea User
The result of his efforts resulted in the Dirac equation, which describes realistic particles like the electron, and also explains:
- antimatter,
- intrinsic angular momentum (a.k.a., spin),
- magnetic moments,
- the fine structure properties of the material,
- and the behavior of charged particles in the presence of electric and magnetic fields.
This was a big step forward, and the Dirac equation described very well many of the oldest fundamental particles, including the electron, the positron, the muon and even (to some extent) the proton, the neutron and the neutrino.
A universe where electrons and protons are free and collide with photons turns into a neutral that is transparent to photons as the Universe expands and cools. Here we see the ionized plasma (L) before the emission of CMB, followed by the transition to a neutral (R) transparent to photons. The dispersion between electrons and electrons, as well as electrons and photons, can be well described by the Dirac equation, but the photon-photon interactions, which actually occur, are not.
Amanda Yoho
But that could not explain everything. Photons, for example, could not be completely described by the Dirac equation because they had the poor properties of particles. Electron-electron interactions were well described, but photon-photon interactions did not occur. Explaining phenomena such as radioactive decay was quite impossible within Dirac's framework of relativistic quantum mechanics. Even with this huge breakthrough, a major element of the story was missing.
The big problem was that quantum mechanics, even relativistic quantum mechanics, was not quantum enough to describe everything in our universe.
If you have a point charge and a metal conductor nearby, it's an exercise in classical physics that calculates the electric field and its strength at each point in space. In quantum mechanics, we discuss how particles respond to this electric field, but the field itself is not quantified. This seems to be the biggest flaw in the formulation of quantum mechanics.
J. Belcher at MIT
Think about what happens if you approach two electrons. If you think of a classic way, you will consider these electrons as each generating an electric field, as well as a magnetic field if they are moving. Then, the other electron, seeing the field (s) generated by the first, will feel a force when it will interact with the external field. It works both ways, and in this way a force is exchanged.
This would work for an electric field as well as any other type of field: like a gravitational field. Electrons have a mass and a charge. Therefore, if you place them in a gravitational field, they will react according to their mass in the same way that their electric charge would force them to react to an electric field. Even in general relativity, where mass and energy curve space, this space is continuous, like any other domain.
If two objects of matter and antimatter at rest cancel, they produce photons of extremely specific energy. If they produce these photons after falling deeper into a region of gravitational curvature, the energy should be higher. This means that there must be some sort of redshift / gravitational blueshift, the type that did not predict Newton's gravity, otherwise the energy would not be conserved. In general relativity, the field transports energy by waves: the gravitational radiation. But at a quantum level, we strongly suspect that just as electromagnetic waves are made up of quanta (photons), gravitational waves should also be composed of quanta (gravitons). This is one of the reasons why general relativity is incomplete.
Ray Shapp / Mike Luciuk; edited by E. Siegel
The problem with this type of formulation & nbsp; is that the fields are on the same footing as the position and the momentum is subject to a conventional treatment. The fields push the particles located at certain positions and change their moments. But in a universe where positions and moments are uncertain and must be treated as operators rather than as a physical quantity with a value, we change ourselves by allowing our field processing to remain classical.
The tissue of space-time, illustrated, with undulations and deformations due to mass. A new theory must be more than identical to general relativity; he has to make new, different predictions. Since general relativity offers only a classical, non-quantum description of space, we expect that its successor will also contain a quantized space, although this space may be either discrete or continuous.
This was the big advance of the idea of quantum field theory, or its related theoretical advance: second quantification. If we treat the field itself as being quantum, it also becomes a quantum mechanics operator. Suddenly, unpredicted (but observed) processes in the universe, such as:
- creation and annihilation of matter,
- radioactive decays,
- quantum tunneling to create electron-positron pairs,
- and quantum corrections at the electronic magnetic moment,
everything made sense.
Today, Feynman diagrams are used to calculate each fundamental interaction covering strong, weak and electromagnetic forces, including in high energy and low temperature / condensation conditions. The main difference between this framework and quantum mechanics lies in the fact that not only particles but also fields are quantified.
of Carvalho, Vanuildo S. et al. Nucl.Phys. B875 (2013) 738-756
Although physicists generally think of quantum field theory in terms of particle exchange and Feynman diagrams, it is only a computational and visual tool that we use to attempt to give an intuitive meaning to this notion. Feynman's diagrams are incredibly useful, but they constitute a perturbative (ie approximate) computational approach, and quantum field theory often gives fascinating and unique results when using a non-perturbative approach.
But the motivation to quantify the field is more fundamental than the argumentation between those who favor disruptive or nondisruptive approaches. You need a quantum field theory to successfully describe the interactions between particles and particles or particles and fields, but also between fields and fields. With quantum field theory and progress in their applications, everything from photon-photon scattering to the powerful nuclear force was now explicable.
Diagram of beta-free double decay, which is possible if the neutrino shown here is its own antiparticle. This is an allowed interaction with finite probability in quantum field theory in a universe with the appropriate quantum properties, but not in quantum mechanics with unquantized interaction fields. The decay time by this route is much longer than the age of the universe.
At the same time, it became immediately obvious why Einstein 's approach to unification would never work. Motivated by the work of Theodr Kaluza, Einstein fell in love with the idea of unifying general relativity and electromagnetism in a unique setting. But general relativity has a fundamental limit: it is a classical theory, with its notion of continuous and unquantified space and time.
If you refuse to quantify your fields, you are condemning yourself to miss important intrinsic properties of the universe. This was Einstein's fatal flaw in his unification attempts and the reason why his approach to a more fundamental theory was totally (and rightly so) abandoned.
Quantum gravity attempts to combine Einstein's general theory of relativity with quantum mechanics. Quantum corrections to classical gravity are visualized in the form of loop diagrams, like the one shown here in white. Whether space (or time) itself is discrete or continuous is not yet determined, nor is the question of whether gravity is quantified, or whether particles, as we know them today, are fundamental or not. But if we want a fundamental theory of everything, it must include quantified fields.
SLAC National Accelerator Lab
The universe has been shown time and time again of quantum nature. These quantum properties appear in applications ranging from transistors to light-emitting diode displays, through the Hawking radiation that causes the decomposition of black holes. The reason why quantum mechanics is fundamentally flawed in itself is not due to the strangeness that the new rules introduced, but because it did not go far enough. Particles have quantum properties, but they also interact through fields that are quantum themselves, and all of this exists in a relativist invariant way.
Perhaps we will really arrive at a theory of everything, where each particle and each interaction is relativistic and quantified. But this quantum strangeness must be part of it, even parts that we have not yet quantified successfully. In the immortal words of Haldane, "My own suspicion is that the Universe is not only strange as we suppose, but as strange as we can suppose."
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Visualization of a computation of quantum field theory showing virtual particles in quantum vacuum. (More precisely, for strong interactions.) Even in empty space, this vacuum energy is non-zero. When pairs of particles and antiparticles appear and disappear, they can interact with real particles such as the electron, making corrections of vital importance to its own energy. On Quantum Field Theory offers the possibility to calculate properties like this one.
Derek Leinweber
If you want to answer the question of what is really fundamental in this universe, you have to study the material and the energy at the smallest possible scale. If you were trying to split particles into smaller and smaller components, you would notice extremely fun things once you've become smaller than distances of a few nanometers, where the classic rules of physics still apply.
At even smaller scales, reality begins to behave in a strange and counter-intuitive way. We can no longer describe reality as consisting of individual particles with well-defined properties such as position and momentum. Instead, we enter the realm of quantum: where fundamental indeterminism reigns and we need an entirely new description of how nature works. But even quantum mechanics itself has its failures. They condemned Einstein's biggest dream – a complete and deterministic description of reality – from the beginning. Here's why.
If you let a tennis ball fall on a hard surface, like a table, you can be certain that it will bounce. If you were to perform the same experiment with a quantum particle, you would discover that this "classical" trajectory was only one of the possible outcomes, with a probability less than 100%. Surprisingly, there is a chance that the quantum particle loses its tunnel on the other side of the table, crossing the barrier as if it were no obstacle.
Wikimedia users like MichaelMaggs and (edited by) Richard Bartz
If we lived in an entirely classical and non-quantum world, it would be easy to make sense of things. By dividing the material into smaller and smaller pieces, we would never reach a limit. There would be no fundamental and indivisible building blocks of the universe. Instead, our cosmos would be made of continuous materials, where if we built a sharper knife, we would still be able to cut something into smaller and smaller pieces.
This dream followed the path of the dinosaurs at the beginning of the 20th century. The experiments of Planck, Einstein, Rutherford, and others have shown that matter and energy could not consist of a continuous substance, but rather divisible into discrete pieces, called quanta today. The original idea of quantum theory had too much experimental support: the Universe was not fundamentally classic after all.
Going to smaller and smaller distance scales reveals more fundamental views of nature, which means that if we can understand and describe the smaller scales, we can build our way to an understanding of the larger ones.
Perimeter Institute
For perhaps the first three decades of the 20th century, physicists have struggled to understand and understand the nature of the Universe at these puzzling little scales. New rules were needed, and to describe them, new and counter-intuitive equations and descriptions. The idea of an objective reality is out of the window, replaced by notions such as:
- probability distributions rather than predictable outcomes,
- wave functions rather than positions and moments,
- Heisenberg uncertainty relations rather than individual properties.
Particles describing reality could no longer be described just as particles. Instead, they had elements of both waves and particles and behaved according to a new set of rules.
An illustration between the inherent uncertainty between position and momentum at the quantum level. There is a limit to the extent to which you can measure these two quantities simultaneously because they are no longer simply physical properties, but rather quantum operators, with aspects inherent to their unknowable nature. The uncertainty of Heisenberg appears in places where people expect the least.
E. Siegel / Wikimedia Commons Maschen user
Initially, these descriptions disturbed many physicists. These problems are not simply due to the philosophical difficulties of accepting a non-deterministic universe or a modified definition of reality, although many of these problems have certainly disturbed it.
Instead, the difficulties were more robust. The theory of special relativity was well understood, and yet quantum mechanics, as originally developed, only worked for non-relativistic systems. By transforming quantities such as the position and momentum of physical properties into quantum mechanics operators – a specific class of mathematical functions – these strange aspects of reality could be integrated into our equations.
Trajectories of a particle in a box (also called infinite square well) in classical mechanics (A) and in quantum mechanics (B-F). In (A), the particle moves at constant speed, bouncing. In (B-F), the wave function solutions of the Schrodinger equation as a function of time are presented for the same geometry and the same potential. The horizontal axis is the position, the vertical axis is the real part (blue) or the imaginary part (red) of the wave function. (B, C, D) are stationary states (eigenstates of energy), derived from solutions to the time-independent Schrodinger equation. (E, F) are non-stationary states, solutions to the time-dependent Schrodinger equation. Note that these solutions are not invariant under relativistic transformations; they are valid only in one frame of reference.
Steve Byrnes / Sbyrnes321 from Wikimedia Commons
But the way you have allowed your system to evolve depends on time, and the notion of time is different for different observers. It was the first existential crisis to face quantum physics.
We say that a theory is relativist invariant if its laws do not change for different observers: for two people moving at different speeds or in different directions. To formulate a relatively invariant version of quantum mechanics has been a challenge that the greatest physicists have taken many years to overcome and which was finally raised by Paul Dirac in the late 1920s.
Different frames of reference, including different positions and movements, would see different laws of physics (and would disagree on reality) if a theory is not invariant in a relativistic way. The fact that we have a symmetry in the "boost" or velocity transformations tells us that we have a conserved quantity: the linear moment. This is much more difficult to understand when momentum is not simply a quantity associated with a particle, but rather a quantum operator.
Wikimedia Commons Krea User
The result of his efforts resulted in the Dirac equation, which describes realistic particles like the electron, and also explains:
- antimatter,
- intrinsic angular momentum (a.k.a., spin),
- magnetic moments,
- the fine structure properties of the material,
- and the behavior of charged particles in the presence of electric and magnetic fields.
This was a big step forward, and the Dirac equation described very well many of the oldest fundamental particles, including the electron, the positron, the muon and even (to some extent) the proton, the neutron and the neutrino.
A universe where electrons and protons are free and collide with photons turns into a neutral that is transparent to photons as the Universe expands and cools. Here we see the ionized plasma (L) before the emission of CMB, followed by the transition to a neutral (R) transparent to photons. The dispersion between electrons and electrons, as well as electrons and photons, can be well described by the Dirac equation, but the photon-photon interactions, which actually occur, are not.
Amanda Yoho
But that could not explain everything. Photons, for example, could not be completely described by the Dirac equation because they had the poor properties of particles. Electron-electron interactions were well described, but photon-photon interactions did not occur. Explaining phenomena such as radioactive decay was quite impossible within Dirac's framework of relativistic quantum mechanics. Even with this huge breakthrough, a major element of the story was missing.
The big problem was that quantum mechanics, even relativistic quantum mechanics, was not quantum enough to describe everything in our universe.
If you have a point charge and a metal conductor nearby, it's an exercise in classical physics that calculates the electric field and its strength at each point in space. In quantum mechanics, we discuss how particles respond to this electric field, but the field itself is not quantified. This seems to be the biggest flaw in the formulation of quantum mechanics.
J. Belcher at MIT
Think about what happens if you approach two electrons. If you think of a classic way, you will consider these electrons as each generating an electric field, as well as a magnetic field if they are moving. Then, the other electron, seeing the field (s) generated by the first, will feel a force when it will interact with the external field. It works both ways, and in this way a force is exchanged.
This would work for an electric field as well as any other type of field: like a gravitational field. Electrons have a mass and a charge. Therefore, if you place them in a gravitational field, they will react according to their mass in the same way that their electric charge would force them to react to an electric field. Even in general relativity, where mass and energy curve space, this space is continuous, like any other domain.
Si deux objets de la matière et de l'antimatière au repos s'annulent, ils produisent des photons d'une énergie extrêmement spécifique. S'ils produisent ces photons après être tombés plus profondément dans une région de courbure gravitationnelle, l'énergie devrait être plus élevée. Cela signifie qu'il doit exister une sorte de décalage vers le rouge / blueshift gravitationnel, le type que ne prédisait pas la gravité de Newton, sans quoi l'énergie ne serait pas conservée. Dans la relativité générale, le champ transporte de l'énergie par ondes: le rayonnement gravitationnel. Mais, à un niveau quantique, nous soupçonnons fortement que, tout comme les ondes électromagnétiques sont constituées de quanta (photons), les ondes gravitationnelles devraient également être composées de quanta (gravitons). C'est l'une des raisons pour lesquelles la relativité générale est incomplète.
Ray Shapp / Mike Luciuk; modifié par E. Siegel
Le problème avec ce type de formulation est que les champs sont sur le même pied que la position et que l’élan est sous traitement classique. Les champs poussent les particules situées à certaines positions et changent leurs moments. Mais dans un univers où les positions et les moments sont incertains et doivent être traités comme des opérateurs plutôt que comme une quantité physique avec une valeur, nous nous modifions nous-mêmes en permettant à notre traitement des champs de rester classique.
Le tissu de l’espace-temps, illustré, avec des ondulations et des déformations dues à la masse. Une nouvelle théorie doit être plus qu’identique à la relativité générale; il doit faire de nouvelles prédictions distinctes. Comme la relativité générale n’offre qu’une description classique et non quantique de l’espace, nous nous attendons à ce que son successeur contienne également un espace quantifié, bien que cet espace puisse être soit discret, soit continu.
Ce fut la grande avancée de l'idée de la théorie quantique des champs, ou son avancée théorique connexe: la seconde quantification. Si nous traitons le champ lui-même comme étant quantique, il devient également un opérateur de mécanique quantique. Tout à coup, des processus non prédits (mais observés) dans l'univers, tels que:
- création et annihilation de la matière,
- désintégrations radioactives,
- tunneling quantique pour créer des paires électron-positron,
- et corrections quantiques au moment magnétique électronique,
tout avait du sens.
Aujourd'hui, les diagrammes de Feynman sont utilisés pour calculer chaque interaction fondamentale couvrant les forces fortes, faibles et électromagnétiques, y compris dans des conditions de haute énergie et de basse température / condensation. La principale différence entre ce cadre et la mécanique quantique réside dans le fait que non seulement les particules, mais aussi les champs sont quantifiés.
de Carvalho, Vanuildo S. et al. Nucl.Phys. B875 (2013) 738-756
Bien que les physiciens pensent généralement à la théorie des champs quantiques en termes d'échange de particules et de diagrammes de Feynman, il ne s'agit que d'un outil de calcul et visuel que nous utilisons pour tenter de donner un sens intuitif à cette notion. Les diagrammes de Feynman sont incroyablement utiles, mais ils constituent une approche de calcul perturbative (c’est-à-dire approximative), et la théorie quantique des champs donne souvent des résultats fascinants et uniques lorsque vous utilisez une approche non perturbative.
Mais la motivation pour quantifier le champ est plus fondamentale que l'argumentation entre ceux qui favorisent les approches perturbatives ou non perturbatives. Vous avez besoin d'une théorie quantique des champs pour décrire avec succès les interactions entre les particules et les particules ou les champs et les particules, mais également entre les champs et les champs. Avec la théorie quantique des champs et les progrès réalisés dans leurs applications, tout, de la diffusion photon-photon à la force nucléaire puissante, était désormais explicable.
Diagramme de la double désintégration sans bêta, ce qui est possible si le neutrino présenté ici est sa propre antiparticule. Il s'agit d'une interaction autorisée avec une probabilité finie en théorie des champs quantiques dans un univers possédant les propriétés quantiques appropriées, mais pas en mécanique quantique avec des champs d'interaction non quantifiés. Le temps de décroissance par cette voie est beaucoup plus long que l'âge de l'univers.
Dans le même temps, il devint immédiatement évident pourquoi l'approche d'unification d'Einstein ne fonctionnerait jamais. Motivé par le travail de Theodr Kaluza, Einstein est tombé amoureux de l'idée d'unifier la relativité générale et l'électromagnétisme dans un cadre unique. Mais la relativité générale a une limite fondamentale: il s’agit d’une théorie classique, avec sa notion d’espace et de temps continus et non quantifiés.
Si vous refusez de quantifier vos champs, vous vous condamnez à passer à côté d'importantes propriétés intrinsèques de l'univers. C’était là le défaut fatal d’Einstein dans ses tentatives d’unification et la raison pour laquelle son approche d’une théorie plus fondamentale a été totalement (et à juste titre) abandonnée.
La gravité quantique tente de combiner la théorie générale de la relativité d’Einstein avec la mécanique quantique. Les corrections quantiques à la gravité classique sont visualisées sous forme de diagrammes en boucle, comme celui présenté ici en blanc. Que l'espace (ou le temps) lui-même soit discret ou continu n'est pas encore déterminé, pas plus que la question de savoir si la gravité est quantifiée, ou si les particules, telles que nous les connaissons aujourd'hui, sont fondamentales ou non. Mais si nous souhaitons une théorie fondamentale de tout, elle doit inclure des champs quantifiés.
SLAC National Accelerator Lab
L'univers s'est montré maintes et maintes fois de nature quantique. Those quantum properties show up in applications ranging from transistors to LED screens to the Hawking radiation that causes black holes to decay. The reason quantum mechanics is fundamentally flawed on its own isn't because of the weirdness that the novel rules brought in, but because it didn't go far enough. Particles do have quantum properties, but they also interact through fields that are quantum themselves, and all of it exists in a relativistically-invariant fashion.
Perhaps we will truly achieve a theory of everything, where every particle and interaction is relativistic and quantized. But this quantum weirdness must be a part of every aspect of it, even the parts we have not yet successfully quantized. In the immortal words of Haldane, "my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose."