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That's why Quantum Field Theory is more basic than quantum mechanics

If you allow a tennis ball to fall on a hard surface like a table, you can be sure it will bounce back. If you were to do the same experiment with a quantum particle, you would find that this classic path was only one of the possible results, with less than 100% probability. Surprisingly, there is a limited chance that the quantum particle will pass through the tunnel to the other side of the table and go through the barrier as if it were no obstacle at all. Wikimedia comments on user MichaelMaggs and (edited by) Richard Bartz [19659003] If we lived in a completely classic, non-quantum universe, it would be easy to feel things. When we split things into smaller and smaller pieces, we would never reach a limit. There would be no basic, indivisible building blocks in the universe. Instead, our cosmos would be made of continuous material, where if we built a word-like sharper knife, we could always cut something in smaller and smaller pieces. That dream went dinosaur's way in the early 20th century. Experiments by Planck, Einstein, Rutherford and others showed that matter and energy could not be made of a continuous substance but rather divided into discrete pieces, known as quantum today. The original idea of ​​quantum theory had too much experimental support: The universe was not basically classic. Going to smaller and smaller distance scales reveals more basic nature views, which means that we can understand and describe the smallest waves, We…

If you allow a tennis ball to fall on a hard surface like a table, you can be sure it will bounce back. If you were to do the same experiment with a quantum particle, you would find that this classic path was only one of the possible results, with less than 100% probability. Surprisingly, there is a limited chance that the quantum particle will pass through the tunnel to the other side of the table and go through the barrier as if it were no obstacle at all.

Wikimedia comments on user MichaelMaggs and (edited by) Richard Bartz [19659003]

If we lived in a completely classic, non-quantum universe, it would be easy to feel things. When we split things into smaller and smaller pieces, we would never reach a limit. There would be no basic, indivisible building blocks in the universe. Instead, our cosmos would be made of continuous material, where if we built a word-like sharper knife, we could always cut something in smaller and smaller pieces.

That dream went dinosaur’s way in the early 20th century. Experiments by Planck, Einstein, Rutherford and others showed that matter and energy could not be made of a continuous substance but rather divided into discrete pieces, known as quantum today. The original idea of ​​quantum theory had too much experimental support: The universe was not basically classic.

Going to smaller and smaller distance scales reveals more basic nature views, which means that we can understand and describe the smallest waves, We can build ourselves into an understanding of the largest ones.

Perimeter Institute

Perhaps the first three decades of the 20th century, physicists struggled to develop and understand the nature of the universe on these small, puzzling scales. New rules were needed, and to describe them, new and contra-intuitive equations and descriptions. The idea of ​​an objective reality went out of the window, replaced by terms such as: probability distributions rather than predictable results

  • wave functions rather than positions and moments,
  • Heisenberg uncertainty relationships rather than individual characteristics.

The particles describing reality can no longer be described solely as particle-like. 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 quantum level. There is a limit to how well you can measure these two quantities at the same time, as they are not only physical properties anymore but rather quantum mechanical operators with inherent undisputed aspects of their nature. Heisenberg’s uncertainty appears in places where people usually expect the least.

E. Siegel / Wikimedia Commons user Maschen

Originally, these descriptions concerned a large part of the physicists. These problems did not arise simply because of the philosophical difficulties associated with accepting a non-deterministic universe or a changed definition of reality, although there were certainly many who were disturbed by these aspects.

Instead, the difficulties were more robust. The theory of special relativity was well understood, but quantum mechanics, which was originally developed, only worked for non-relativistic systems. By converting quantities as position and momentum from physical properties to quantum mechanics & nbsp; – A specific class of mathematical function & nbsp; – These bizarre aspects of reality can be incorporated into our equations.

Traces of a particle in a box an infinite square well) in classical mechanics (A) and quantum mechanics (BF). In (A) the particle moves at a constant speed, bounces back and forth. In (B-F), wave-function solutions for time-dependent Schrodinger equation are shown for the same geometry and potential. The horizontal axis is position, the vertical axis is the real part (blue) or the imaginary part (red) of the wave function. (B, C, D) are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrodinger Equation. (E, F) are non-stationary states, solutions for the time-dependent Schrodinger equation. Note that these solutions are not invariant during relativistic conversions; They are only valid in a given frame of reference.

Steve Byrnes / Sbyrnes321 by Wikimedia Commons

But the way you allowed your system to develop depends on time, and the term time is different for different observers. It was the first existential crisis that faced quantum physics.

We say that a theory is relativist invariant if its laws do not change for different observers: for two people move at different speeds or in different directions. The formulation of a relativist invariant version of quantum mechanics was a challenge that took the greatest thoughts in physics many years to overcome, and was finally achieved by Paul Dirac in the late 1920s.

Different reference frames, including different positions and movements, would see different physical laws (and would disagree with reality) if a theory is not relativistic invariant. The fact that we have a symmetry under “boosts” or speed transformations tells us that we have a conserved amount: linear momentum. This is much more difficult to understand when momentum is not just a quantity associated with a particle, but rather a quantum mechanical operator.

Wikimedia Commons user Krea

The result of his efforts gave what is now called Dirac equation which describes realistic particles like the electron and also stands for:

  • antimatter,
  • internal angular momentum (aka, spin), [19659013] magnetic torque, the fine structure of matter, and the appearance of charged particles in the presence of electric and magnetic fields.

This was a big step forward and the Dirac equation did an excellent job of describing many of the earliest known basic particles, including the electron, positron, muon, and even (to some extent) proton, neutron and neutrino.

A universe where electrons and protons are free and collide with photons transitions to a neutral that is transparent to photos that Univer se expands and cools. Here, the ionized plasma (L) is shown before CMB is emitted, followed by the transition to a neutral universe (R) which is transparent to photons. The scatter between electrons and electrons, as well as electrons and photons, can be well described by the Dirac equation, but photon-photon interactions that occur in reality are not.

Amanda Yoho

But it could not “I do not take everything into account. Photons, for example, could not be fully described by the Dirac equation, because they had error particle properties. Photon interactions were not, explain phenomena such as radioactive decay were completely impossible within Dirac’s framework of relativistic quantum mechanics, even with this huge progress, an important part of history was missing.

The major problem was that quantum mechanics, even relativistic quantum mechanics, was not large enough to describe everything in our universe.

If you have a point load and a metal conductor nearby, it is an exercise in classical physics alone to calculate the electric field and its strength at each point in space. we how particles respond to the electric field, but the field itself is not quantized as well. in quantum mechanics formulation.

J. Belcher at MIT

Think about what happens if you place two electrons close together. If you think classically, you think of these electrons, each of which generates an electric field, and also a magnetic field if they are moving. Then, the second electron will see the field generated by the first, experiencing a force because it interacts with the outer field. This works both ways, and thus a force is exchanged.

This would work just as well for an electric field as it would for any other type of field: as a gravity field. Electrons have mass as well as charge, so if you place them in a gravity field, they would respond based on their mass in the same way their electric charge would force them to respond to an electric field. Even in general relativity, where mass and energy curve space, the curved space is continuous, just like any other field.

If two objects of matter and antimatter at rest are destroyed, they produce photons of an extremely specific energy. If they produce these photons after falling deeper into a gravity curve, the energy should be higher. This means that there must be some form of gravity cruise / blueshift, the kind not predicted by Newton’s gravity, otherwise the energy would not be preserved. In general relativity, the field carries energy in waves: gravity radiation. But at a quantum level, we strongly suspect that just as electromagnetic waves consist of quanta (photons), gravity waves should also consist of quanta (gravitons). This is one reason why general relativity is incomplete.

Ray Shapp / Mike Luciuk; modified by E. Siegel

The problem with this type of formulation is that the fields are in the same way as position and momentum is during a classical treatment. Fields press particles that are in certain positions and change their momentum. But in a universe where positions and moments are uncertain, and need to be treated as operators rather than a physical quantity with a value, we change ourselves by letting our treatment of fields be classic.

The fabric of spacetime, illustrated with ripples and deformations due to mass. A new theory must be more than identical to general relativity; It must make new, clear predictions. Since general relativity only offers a classic, non-quantum description of space, we fully expect that its possible successor will contain space which is also quantized, although this space may be either discrete or continuous.

It was the great advance of the idea of ​​quantum field theory or its related theoretical advances: second quantization . If we treat the field itself as quantum, it will also become a quantum mechanical operator. Sudden processes that were not predicted (but observed) in the universe, such as:

  • matter creation and destruction, radioactive decay, [quantumtunnelingtocreateelectron-positronpairs
  • Today, Feynman charts are used to calculate each basic interaction spanning the strong, weak and electromagnetic forces, including at high energy and low temperature / condensed conditions. The great way in which this frame differs from quantum mechanics is not only the particles, but also the fields are quantized. The Carvalho, Vanuildo S. et al. Nucl.Phys. B875 (2013) 738-756

    Although physicists typically think of quantum field theory in particle exchange and Feynman charts, this is just a computational and visual tool that we use to try to add some intuitive feeling to this concept. . The Feynman charts are incredibly useful, but they are a perturbative (ie approximate) method of calculating, and quantum field theory often provides fascinating, unique results when you take a non-perturbative approach.

    But the motivation for quantifying the field is more fundamental than the argument between those who favor disturbing or non-interfering methods. You need a quantum field theory to successfully describe the interactions between & nbsp; not just particles and particles or particles and fields, but also between fields and fields as well. With quantum field theory and further advances in their applications, everything from photon photo spreading to the strong nuclear power was now explained.

    A diagram of the neutrinolic double case, which is possible if the neutrino shown here is a separate antiparticle. This is an interaction that is allowed with a finite probability in quantum field theory in a universe with the right quantum properties, but not in quantum mechanics, with non-quantified interaction fields. The delay time through this path is much longer than the age of the universe.

    At the same time, it immediately became clear why Einstein’s way of uniting would never work. Motivated by Theodr Kaluza’s work, Einstein became fond of the idea of ​​unifying general relativity and electromagnetism in a single frame. But general relativity has a fundamental limitation: it is a classical theory that is the core, with its perception of continuous, non-quantized space and time.

    If you refuse to quantify your fields, you make yourself lack the important, inherent universe characteristics. This was Einstein’s fatal error in his unity attempt, and the reason why his attitude toward a more fundamental theory has been completely (and rightly) abandoned.

    Quantum gravity attempts to combine Einstein’s general theory of relativity with quantum mechanics. Quantum adjustments to classical gravity are visualized as loop diagrams, such as the one shown here in white. Whether space (or time) itself is discrete or continuous not yet determined, as well as the question of gravity is quantified at all or particles, which we know of today, are fundamental or not. But if we hope for a basic theory of everything, it must contain quantified fields.

    SLAC National Accelerator Lab

    The universe has proven time and again to be quantum in nature. These quantum properties occur in applications ranging from transistors to LED screens to the Hawking radiation that cause black holes to decompose. The reason why quantum mechanics is fundamentally flawed on its own is not because of the strange nuclear that the new rules adopted, but because it did not go far enough. Particles have quantum properties, but they also interact through fields that are quantum themselves and all exist in a relativist invariant way.

    Perhaps we will really achieve a theory of everything, where every particle and interaction is & nbsp; relativistic and quantized. But this quantum leap must be part of every aspect of it, even those parts that we have not yet successfully quantified. In Haldane’s immortal words, “my own suspicion that the universe is not only more alien than we suppose but alien to we can assume.”

    “>

    Visualizing a quantum field orthography that shows virtual particles in the quantum vacuum. ( Especially for the strong interactions.) Even in empty space, this vacuum energy is non-zero, as particle-antiparticle pairs pop in and out of existence, they can interact with real particles like the electron, which provides corrections to their self-esteem that is crucial. Theory allows you to calculate properties like this

    Derek Leinweber

    If you wanted to answer the question of what is really fundamental in this universe, you need to examine matter and energy on the smallest scale, if you tried to divide particles into smaller ones and smaller elements, you would start to notice some extremely funny things when you walked less than a distance of a few nanometers, where physical physics The rules still apply.

    On even smaller scales, reality begins to work in strange, contra-intuitive ways. We can no longer describe reality as made up of individual particles with well-defined properties such as position and momentum. Instead, we go into the quantum kingdom: where basic indeterminism regulates, and we need a whole new description of how nature works. But even the quantum mechanics have their failures here. They condemned Einstein’s greatest dream – from a complete, deterministic description of reality – from the beginning. Here’s why.

    If you allow a tennis ball to fall on a hard surface like a table, you can be sure it will bounce back. If you were to do the same experiment with a quantum particle, you would find that this classic path was only one of the possible results, with less than 100% probability. Surprisingly, there is a limited chance that the quantum particle will pass through the tunnel to the other side of the table and go through the barrier as if it were no obstacle at all.

    Wikimedia commenting on users MichaelMaggs and (edited by) Richard Bartz [19659069] If we lived in a completely classic, non-quantum universe, it would be easy to feel things. When we split things into smaller and smaller pieces, we would never reach a limit. There would be no basic, indivisible building blocks in the universe. Instead, our cosmos would be made of continuous material, where if we built a word-like sharper knife, we could always cut something in smaller and smaller pieces.

    That dream went dinosaur’s way in the early 20th century. Experiments by Planck, Einstein, Rutherford and others showed that matter and energy could not be made of a continuous substance but rather divided into discrete pieces, known as quantum today. The original idea of ​​quantum theory had too much experimental support: The universe was not basically classic.

    Going to smaller and smaller distance scales reveals more basic nature views, which means that we can understand and describe the smallest waves, We can build ourselves into an understanding of the largest ones.

    Perimeter Institute

    Perhaps the first three decades of the 20th century, physicists struggled to develop and understand the nature of the universe on these small, puzzling scales. New rules were needed, and to describe them, new and contra-intuitive equations and descriptions. The idea of ​​an objective reality went out of the window, replaced by terms such as: probability distributions rather than predictable results

  • wave functions rather than positions and moments,
  • Heisenberg uncertainty relationships rather than individual characteristics.

The particles describing reality can no longer be described solely as particle-like. 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 quantum level. There is a limit to how well you can measure these two quantities at the same time, as they are not only physical properties anymore but rather quantum mechanical operators with inherent undisputed aspects of their nature. Heisenberg’s uncertainty appears in places where people usually expect the least.

E. Siegel / Wikimedia Commons user Maschen

Originally, these descriptions concerned a large part of the physicists. These problems did not arise simply because of the philosophical difficulties associated with accepting a non-deterministic universe or a changed definition of reality, although there were certainly many who were disturbed by these aspects.

Instead, the difficulties were more robust. The theory of special relativity was well understood, but quantum mechanics, which was originally developed, only worked for non-relativistic systems. By converting quantities as position and momentum from physical properties to quantum mechanics – a specific class of mathematical function – these bizarre aspects of reality can be incorporated into our equations.

Traces of a particle in a box (also called an infinite square well) in classical mechanics (A) and quantum mechanics (BF). In (A) the particle moves at a constant speed, bounces back and forth. In (B-F), wave-function solutions for time-dependent Schrodinger equation are shown for the same geometry and potential. The horizontal axis is position, the vertical axis is the real part (blue) or the imaginary part (red) of the wave function. (B, C, D) are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrodinger Equation. (E, F) are non-stationary states, solutions for the time-dependent Schrodinger equation. Note that these solutions are not invariant during relativistic conversions; They are only valid in a given frame of reference.

Steve Byrnes / Sbyrnes321 by Wikimedia Commons

But the way you got your system to develop was due to the time, and the term time is different for different observers. It was the first existential crisis that faced quantum physics.

We say that a theory is relativist invariant if its laws do not change for different observers: for two people move at different speeds or in different directions. The formulation of a relativist invariant version of quantum mechanics was a challenge that took the greatest thoughts in physics for many years to overcome, and finally achieved by Paul Dirac in the late 1920s.

Different reference frames, including different positions and movements, would see different physical laws (and would not agree on reality) if a theory is not relativistic invariant. The fact that we have a symmetry under “boosts” or speed transformations tells us that we have a conserved amount: linear momentum. This is much more difficult to understand when momentum is not just a quantity associated with a particle, but rather a quantum mechanical operator.

Wikimedia Commons user Krea

The result of his efforts gave what is now called Dirac equation which describes realistic particles like the electron and also stands for:

  • antimatter,
  • internal angular momentum (aka, spin), [19659013] magnetic torque, the fine structure of matter, and the appearance of charged particles in the presence of electric and magnetic fields.

This was a big step forward and the Dirac equation did an excellent job of describing many of the earliest known basic particles, including the electron, positron, muon, and even (to some extent) proton, neutron and neutrino.

A universe where electrons and protons are free and collide with photons transitions to a neutral that is transparent to photos that Univer se expands and cools. Here, the ionized plasma (L) is shown before CMB is emitted, followed by the transition to a neutral universe (R) which is transparent to photons. The scatter between electrons and electrons, as well as electrons and photons, can be well described by the Dirac equation, but photon-photon interactions that occur in reality are not.

Amanda Yoho

But it could not “I do not take everything into account. Photons, for example, could not be fully described by the Dirac equation, because they had error particle properties. Photon interactions were not, explain phenomena such as radioactive decay were completely impossible within Dirac’s framework of relativistic quantum mechanics, even with this huge progress, an important part of history was missing.

The major problem was that quantum mechanics, even relativistic quantum mechanics, was not large enough to describe everything in our universe.

If you have a point load and a metal conductor nearby, it is an exercise in classical physics alone to calculate the electric field and its strength at each point in space. we how particles respond to the electric field, but the field itself is not quantized as well. in quantum mechanics formulation.

J. Belcher at MIT

Think about what happens if you place two electrons close together. If you think classically, you think of these electrons, each of which generates an electric field, and also a magnetic field if they are moving. Then, the second electron will see the field generated by the first, experiencing a force because it interacts with the outer field. This works both ways, and thus a force is exchanged.

This would work just as well for an electric field as it would for any other type of field: as a gravity field. Electrons have mass as well as charge, so if you place them in a gravity field, they would respond based on their mass in the same way their electric charge would force them to respond to an electric field. Even in general relativity, where mass and energy curve space, the curved space is continuous, just like any other field.

If two objects of matter and antimatter at rest are destroyed, they produce photons of an extremely specific energy. If they produce these photons after falling deeper into a gravity curve, the energy should be higher. This means that there must be some form of gravity cruise / blueshift, the kind not predicted by Newton’s gravity, otherwise the energy would not be preserved. In general relativity, the field carries energy in waves: gravity radiation. But at a quantum level, we strongly suspect that just as electromagnetic waves consist of quanta (photons), gravity waves should also consist of quanta (gravitons). This is one reason why general relativity is incomplete.

Ray Shapp / Mike Luciuk; modified by E. Siegel

The problem with this type of formulation is that the fields are in the same way as position and momentum is during a classical treatment. Fields press particles that are in certain positions and change their momentum. But in a universe where positions and moments are uncertain, and need to be treated as operators rather than a physical quantity with a value, we change ourselves by letting our treatment of fields be classic.

The fabric of spacetime, illustrated with ripples and deformations due to mass. A new theory must be more than identical to general relativity; It must make new, clear predictions. Since general relativity only offers a classic, non-quantum description of space, we fully expect that its possible successor will contain space which is also quantized, although this space may be either discrete or continuous.

It was the great advance of the idea of ​​quantum field theory or its related theoretical advances: second quantization. If we treat the field itself as quantum, it will also become a quantum mechanical operator. Sudden processes that were not predicted (but observed) in the universe, such as:

  • matter creation and destruction, radioactive decay, [quantumtunnelingtocreateelectron-positronpairs

  • Today, Feynman charts are used to calculate each basic interaction spanning the strong, weak and electromagnetic forces, including in high energy and low temperature / condensed conditions. The great way in which this frame differs from quantum mechanics is not only the particles, but also the fields are quantized. The Carvalho, Vanuildo S. et al. Nucl.Phys. B875 (2013) 738-756

    Although physicists typically think of quantum field theory in particle exchange and Feynman charts, this is just a computational and visual tool that we use to try to add some intuitive feeling to this concept. . The Feynman charts are incredibly useful, but they are a perturbative (ie approximate) method of calculating, and quantum field theory often provides fascinating, unique results when you take a non-perturbative approach.

    But the motivation for quantifying the field is more fundamental than the argument between those who favor disturbing or non-interfering methods. You need a quantum field theory to successfully describe the interaction between not only particles and particles or particles and fields, but also between fields and fields. Med kvantfältteori och ytterligare framsteg i deras tillämpningar var allt från fotonfotonspridning till den starka kärnkraften nu förklarlig.

    Ett diagram över neutrinolärt dubbelbetefall, vilket är möjligt om neutrinoen som visas här är en egen antipartikel. Detta är en interaktion som är tillåten med en ändlig sannolikhet i kvantfältteori i ett univers med rätt kvantegenskaper, men inte i kvantmekanik, med icke kvantifierade interaktionsfält. The decay time through this pathway is much longer than the age of the Universe.

    At the same time, it became immediately clear why Einstein's approach to unification would never work. Motivated by Theodr Kaluza's work, Einstein became enamored with the idea of unifying General Relativity and electromagnetism into a single framework. But General Relativity has a fundamental limitation: it's a classical theory at its core, with its notion of continuous, non-quantized space and time.

    If you refuse to quantize your fields, you doom yourself to missing out on important, intrinsic properties of the Universe. This was Einstein's fatal flaw in his unification attempts, and the reason why his approach towards a more fundamental theory has been entirely (and justifiably) abandoned.

    Quantum gravity tries to combine Einstein’s General theory of Relativity with quantum mechanics. Quantum corrections to classical gravity are visualized as loop diagrams, as the one shown here in white. Whether space (or time) itself is discrete or continuous is not yet decided, as is the question of whether gravity is quantized at all, or particles, as we know them today, are fundamental or not. But if we hope for a fundamental theory of everything, it must include quantized fields.

    SLAC National Accelerator Lab

    The Universe has shown itself time and time again to be quantum in nature. 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.”

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