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Twodogs
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Are there thoughts as to why there is a quantum field. Does it arise from something more fundamental?
Thanks for considering.
Thanks for considering.
rootone said:String theorists might argue that the strings which they make a case for are more fundamental.
https://en.wikipedia.org/wiki/Relationship_between_string_theory_and_quantum_field_theory
bhobba said:Dirac gave EM a quantum injection to create the first quantum field theory. In this way photons emerged naturally. Could it be all particles emerge the same way? So field theories of Electrons were cooked up and sure enough electrons could be explained similarly. Then it was realized - well electrons carry an electric field - it would be rather difficult to have a combined theory unless they were both field theories - so Quantum Electrodynamics (QED) was borne.
Then one Dr Julian Schwinger came along and showed that if one writes down a general theory of fields - one for spin 1/2 particles (which electrons are) and one for spin one particles (which photons are) you notice something interesting - they have global U(1) symmetry without detailing exactly what it is (it simple - but its better if you look it up), But relativity says it should really be local - not global. So we check local U(1) symmetry - drats - it fails - an extra term appears when you try it. But it jumps out at you - its very easy to cancel that term if you add a term to the combined filed theory - you do this and - lo and behold - we have the equation of QED.
Now it turns out if you try the same trick but demand SU(2) symmetry - you get the W, Higgs etc ie the electroweak theory. Then we do it for SU(3) symmetry and lo and behold you get quarks.
All this has convinced physicists that everything is fundamentally a quantum field that obeys certain local symmetry rules - in fact its the 3 simplest symmetries U(1), SU(2), and SU(3). Why? Well its very beautiful but exactly why is a deep, deep, mystery. Nobel's galore to those that can sort it out. String theory may - but so far has fallen short. Last I heard it gets so tantalizingly close you want to cry - but sorry - no cigar - yet.
You can find the technical detail for these claims here:
https://www.amazon.com/dp/3319192000/?tag=pfamazon01-20
I fact it turns the process on it head and finds those equations via symmetry then shows how QFT and particles reasonably emerge. Even standard QM emerges in the same way - its a quite different approach.
For example you look at the most general symmetries a complex field can have. If it has spatial symmetry then a certain operator (the QM momentum operator P) is conserved. But what does it mean to apply such an operator to a field? Well reasonably if u is the field and you have Pu = pu where p is a number you can say that the field has momentum p. That way you get the eigenvalue interpretation. But what if u is not an eigenvector? That's where one must evoke the Born Rule - why the Born rule - well it just seems that's how nature is - with due deference to Gleason which can justify it somewhat (the main ingredient is non contextuality and a willingness to introduce probabilities).
Thanks
Bill
Twodogs said:Are there thoughts as to why there is a quantum field. Does it arise from something more fundamental?
Thanks for considering.
Let me be a little less wishy-washy. As we currently understand it, empty space is filled with a number of all-pervasive, interpenetrating fields. To a physicist, these fields are mathematical objects: they are functions that take a particular value (or vector of values) at every point in space. But for the daydreamer (which, of course, includes those same physicists), these fields can be visualized as something like a stretchy fabric, or a fluid. To be concrete with the imagery, let’s say that a field is something like the surface of a pond. When not perturbed, that surface is placid (as long as you don’t look too closely, say, at the molecular level). But when something disturbs the pond, it creates a ripple that propagates stably across the surface.
So you, the five-year-old, start asking audacious and annoying questions. For example:
What are people made of?
People are made of muscles, bones, and organs.
Then what are the organs made of?
Organs are made of cells.
What are cells made of?
Cells are made of organelles.
What are organelles made of?
Organelles are made of proteins.
What are proteins made of?
Proteins are made of amino acids.
What are amino acids made of?
Amino acids are made of atoms.
What are atoms made of?
Atoms are made of protons, neutron, and electrons.
What are electrons made of?
Electrons are made from the electron field.
What is the electron field made of?
…
And, sadly, here the game must come to an end, eight levels down. This is the hard limit of our scientific understanding.
mike1000 said:Here are links to two internet articles written by the Physicist, Brian Skinner. In the second article he tells us where the electron field comes from. In the first article he gives a very nice definition of a field.
https://www.ribbonfarm.com/2015/06/23/where-do-electric-forces-come-from/
https://www.ribbonfarm.com/2015/08/20/qft/
Here is a quote from the first article
And here is a quote from the second article
Twodogs said:Thanks, good perspective. Comforting to find with a physicist a place where we both know nothing. Best.
The other big implication of imposing quantum rules on the ball-and-spring motion is that it changes pretty dramatically the meaning of empty space. Normally, empty space, or vacuum, is defined as the state where no particles are around. For a classical field, that would be the state where all the ball-and-springs are stationary and the field is flat. Something like this:
But in a quantum field, the ball-and-springs can never be stationary: they are always moving, even when no one has added enough energy to the field to create a particle. This means that what we call vacuum is really a noisy and densely energetic surface:
bhobba said:Dirac gave EM a quantum injection to create the first quantum field theory. In this way photons emerged naturally. Could it be all particles emerge the same way? So field theories of Electrons were cooked up and sure enough electrons could be explained similarly. Then it was realized - well electrons carry an electric field - it would be rather difficult to have a combined theory unless they were both field theories - so Quantum Electrodynamics (QED) was borne.
Then one Dr Julian Schwinger came along and showed that if one writes down a general theory of fields - one for spin 1/2 particles (which electrons are) and one for spin one particles (which photons are) you notice something interesting - they have global U(1) symmetry without detailing exactly what it is (it simple - but its better if you look it up), But relativity says it should really be local - not global. So we check local U(1) symmetry - drats - it fails - an extra term appears when you try it. But it jumps out at you - its very easy to cancel that term if you add a term to the combined filed theory - you do this and - lo and behold - we have the equation of QED.
Now it turns out if you try the same trick but demand SU(2) symmetry - you get the W, Higgs etc ie the electroweak theory. Then we do it for SU(3) symmetry and lo and behold you get quarks.
All this has convinced physicists that everything is fundamentally a quantum field that obeys certain local symmetry rules - in fact its the 3 simplest symmetries U(1), SU(2), and SU(3). Why? Well its very beautiful but exactly why is a deep, deep, mystery. Nobel's galore to those that can sort it out. String theory may - but so far has fallen short. Last I heard it gets so tantalizingly close you want to cry - but sorry - no cigar - yet.
You can find the technical detail for these claims here:
https://www.amazon.com/dp/3319192000/?tag=pfamazon01-20
I fact it turns the process on it head and finds those equations via symmetry then shows how QFT and particles reasonably emerge. Even standard QM emerges in the same way - its a quite different approach.
For example you look at the most general symmetries a complex field can have. If it has spatial symmetry then a certain operator (the QM momentum operator P) is conserved. But what does it mean to apply such an operator to a field? Well reasonably if u is the field and you have Pu = pu where p is a number you can say that the field has momentum p. That way you get the eigenvalue interpretation. But what if u is not an eigenvector? That's where one must evoke the Born Rule - why the Born rule - well it just seems that's how nature is - with due deference to Gleason which can justify it somewhat (the main ingredient is non contextuality and a willingness to introduce probabilities).
Thanks
Bill
cube137 said:When state vector reduced to a random value (or what they call collapse of the wave function or born rule activated).. what happens in the field version.. is the field behavior smooth or undergoes sudden break.. like sea wave or tsunami moving in one place then suddenly appearing elsewhere (random behavior from the deterministic schoedinger equeation prior to reduction)?
The existence of a quantum field is necessary to explain the behavior of particles at a subatomic level. According to quantum mechanics, particles such as electrons and photons are not solid objects but rather exist as probability waves until they are observed. The quantum field is the medium through which these particles interact and exchange energy, allowing for their unpredictable behavior.
The purpose of a quantum field is to provide a mathematical framework for understanding and describing the behavior of particles at a subatomic level. It allows scientists to make predictions and calculations about the behavior of particles, such as their location and momentum, with a high degree of accuracy.
The concept of a quantum field was proposed by physicist Max Planck in 1900 to explain the quantization of energy in blackbody radiation. It was further developed and refined by Albert Einstein, Niels Bohr, and others in the early 20th century through their work on quantum mechanics. The existence of the quantum field was confirmed through experiments, such as the double-slit experiment, which demonstrated the wave-particle duality of particles at a subatomic level.
No, the quantum field and the Higgs field are two different concepts. The quantum field is a fundamental field that exists throughout space and time, while the Higgs field is a type of quantum field that is responsible for giving particles mass. The Higgs field is a specific manifestation of the quantum field.
The quantum field is the medium through which particles interact and exchange information, including the phenomenon of quantum entanglement. When two particles become entangled, they share a quantum state and can influence each other's behavior instantaneously, regardless of distance. This is possible because the particles are connected through the quantum field, allowing for the transfer of information faster than the speed of light.