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Nick V
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In QFM, what does it mean to say that an electron is just an excitation of the electron field? Does this apply to all particles? Does it mean to say that an electron is the quanta of the electron field?
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I don't really know what your saying. When Quantum field theory says that an electron is a excitation in the electron field, what does that mean? Does that mean that it is a quanta of the field or a particle of the field... what does excitation of the field mean?naima said:I think that there is a vacuum for the electrons, another for photons and so on. There is creation operator ##a^\dagger## for each field. The vacuum has a null occupation number. You can call quantum the result of a creation operator on a vacuum (as the result has a number of 1)
bhobba said:You need to become familiar with the quantisation of the Harmonic oscillator:
http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
It turns out when you quatitsise a field its mathematically similar with the creation and annihilation operators defined for the harmonic oscillator behaving the same as creating and destroying particles in a quantum field.
To fully understand it though you need to study the theory:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20
That text explains very carefully exactly what's going on.
Thanks
Bill
Edward Wij said:but why do we still discuss about whether electrons are particle or wave in the atoms.. why not just mention them as field excitations?
Edward Wij said:But then, is it possible this model of electron as field excitations can be replaced with other models.. meaning qft is just a temporary or effective field theory?
bhobba said:Advanced texts do not discuss if electrons are particles or waves - that's the domain of popularisations and beginning texts. It well known to be neither and that was decided ages ago when Dirac came up with his transformation theory at the end of 1926.
Due to mathematical difficulty you do not use QFT to solve the usual problems of QM. QM is in fact a limit of QFT so while its correct to say electrons are excitations of an electron field a hammer is not usually chosen to crack a nut and for ordinary QM its a bit more vague - but mathematically easier.
Indeed the Effective Field Theory approach to renormaliation thinks of QFT as basically just effective.
I think you might find the following book interesting:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20
Thanks
Bill
bhobba said:Well I think we need to be clear what explain means. With the assumption the field changes on observation then the double slit is explained. Did you expect the explanation not to assume some things? Any explanation does that.
It doesn't explain the measurement 'problem' (postulate is probably a better description than problem - but its pretty standard so I will stick with it) which any observation in QM has - but in general QM merely accepts it as a primitive of the theory.
In modern times decoherence is used to elucidate better the measurement postulate which has a number of parts. It explains a number of those parts such as a preferred basis - it doesn't explain the so called problem of outcomes which colloquially is why do we get any outcomes at all, or more technically how an improper mixed state becomes a proper one. Exactly what that issue is, is explained here (sorry that its rather technical but we are getting into deep waters here):
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf
If I remember correctly that book you got also mentions decoherence - but doesn't give any details. This may help at your level:
http://www.ipod.org.uk/reality/reality_decoherence.asp
Thanks
Bill
Edward Wij said:Bill. Have you actually read the book you recommended days ago (the "Fields color theory escaped Einstein"? I finished reading it and it's a very unusual book with a different interpretation of QFT and even special relativity. For example. There is a passage inside that says:
bhobba said:I have read it.
There are a few areas of disagreement, but it's overall OK.
Please understand this is written at the populist level. For example why C can't be exceeded is the reason he states - but what he didn't point out is the laws of physics must be the same in all inertial frames, nor does he give an exact definition of inertial frames, which are in fact the most important things - the speed of light thing simply fixes a constant that follows from those. It must be said neither do other books at the lay level either - the full truth requires a reasonable grasp of calculus and linear algebra:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf
So you are left with analogies and picturesque language.
Its different - and it's intended to be because its presenting a very advanced topic, QFT, to a lay audience.
Thanks
Bill
Edward Wij said:QFT is about operators acting on the state vectors and these are not supposed to be physical
Edward Wij said:but why did the author kept emphasizing the field is physical and in fact literally pass thru both slits and then the fields vanish when one part gets "detected" by the detector atom? Who are other physicists who hold this view?
bhobba said:Why do you think that? IMHO its about putting time and position on equal footing as required by relativity and making position a parameter rather than an observable. This leads to quantum fields which means operators are assigned to points in space - the state space becomes a lot trickier being a Fock space. There are deeper analysis possible as detailed in Wienberg's texts but challenging would be a very mild way of describing it.
Because it is physical in exactly the same way as any other observable in QM is physical eg in ordinary QM momentum and position are physical.
He isn't talking about ordinary QM here - he is talking about its most fundamental and advanced incarnation - QFT.
Thanks
Bill
Edward Wij said:How could these operator fields be physical like in qm position or momentum?
Edward Wij said:Also what is the theoretical reason why we can't apply QFT to a piece of wood
bhobba said:A field is just as real as momentum etc - you can measure it - eg you can measure EM fields.
Why don't you think we cant? It's just mathematically much more difficult than QM which is so difficult we can't even apply that to atoms more complex than hydrogen and have to use computer approximations. For wood - that's way beyond our present ability in any kind of exact sense - but qualitatively we know what's going on as biology texts explain - from dim memories of biology at school.
QFT can be applied to free fields.
Thanks
Bill
Edward Wij said:But how do you detect electron fields? We detect electron particle instead of the electron field.
Edward Wij said:But QFT deals with annihilation and creation operators.. if you apply this to wood.. won't this just destroy it since you are annihilating the wood atoms making it vanish?
bhobba said:You reasoning for such a statement escapes me. What QFT shows is that a quantum field is mathematically equivalent to creation and annihilation operators but the QM of everyday objects is the dilute limit of that where you deal with one or no particles. If you want to delve into that see the following reference:
https://www.amazon.com/dp/9812381767/?tag=pfamazon01-20
Be aware however you are delving into mathematically advanced waters.
The book I recommended takes you about as far into QFT without delving into such detail.
Thanks
Bill
bhobba said:Advanced texts do not discuss if electrons are particles or waves - that's the domain of popularisations and beginning texts. It well known to be neither and that was decided ages ago when Dirac came up with his transformation theory at the end of 1926.
Due to mathematical difficulty you do not use QFT to solve the usual problems of QM. QM is in fact a limit of QFT so while its correct to say electrons are excitations of an electron field a hammer is not usually chosen to crack a nut and for ordinary QM its a bit more vague - but mathematically easier.
Indeed the Effective Field Theory approach to renormaliation thinks of QFT as basically just effective.
I think you might find the following book interesting:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20
Thanks
Bill
peteb said:Can you recommend any other books that are as suited for the non-physicist as is the book "Fields of Color" you mention here? I have read and thoroughly enjoyed this book.
Thanks, already have that one. I was hoping for something a bit more current and comprehensive. But I will go back and read that one again!bhobba said:Feynman - QED - The Strange Theory Of Light And Matter:
https://www.amazon.com/dp/0691024170/?tag=pfamazon01-20
Thanks
Bill
Edward Wij said:But it says qft didn't solve the mystery of the double slit too. Quoting in the book:
"Field collapse: Field collapse is not an easy concept to accept- perhaps more difficult than the concept of a field. Here I have been working hard, trying to convince you that fields are a real property of space - indeed, the only reality - and now I am asking you to believe that this field quantum, spread out as it may be, suddenly disappears into a tiny absorbing atom. Yet it is the process that can be visualized without inconsistency. In fact, if a photon is an entity that lives and dies as a unit, field collapse must occur. A quantum cannot split and put half its energy in one place and half in another, or live here and die there. That would violate the basic quantum principle. While QFT does not provide an explanation for when or why collapse occurs, some day we may have a theory that does. In any case, field collapse is necessary and has been demonstrated experimentally."
Then you might enjoy large parts of my online book Classical and Quantum Mechanics via Lie algebras. The first half of the book features almost nowhere partial differential equations.peteb said:I am not adverse to math in such a book (I am a retired electrical engineer and have had many couses on the level used for QFT books) but I have never found such math-focused books to be really clear about the links to physical realities of the equations presented.
peteb said:Thanks, already have that one. I was hoping for something a bit more current and comprehensive. But I will go back and read that one again!
Quantum field theory (QFT) is a theoretical framework in physics that combines the principles of quantum mechanics and special relativity to explain the behavior of particles at the subatomic level. It describes particles as excitations of underlying fields, and interactions between particles are mediated by the exchange of virtual particles.
Quantum field theory is used in many areas of physics, including particle physics, condensed matter physics, and cosmology. It has also found applications in other fields such as chemistry and biology.
In classical field theory, particles are described as continuous objects moving through space and time. In quantum field theory, particles are described as discrete excitations of fields, and their behavior is governed by probabilities rather than definite trajectories.
Feynman diagrams are graphical representations used in quantum field theory to calculate the probabilities of particle interactions. Each diagram represents a possible interaction between particles, and their calculation involves summing over all possible diagrams to determine the overall probability of an event.
One of the biggest challenges in quantum field theory is reconciling it with general relativity and developing a theory of quantum gravity. Other challenges include understanding the nature of dark matter and dark energy, and resolving the hierarchy problem in particle physics.