Is there a tension between QM and QFT?

In summary: In the formalism of relativistic QT this occurs in the known difficulties to interpret Poincare covariant wave equations in a 1st-quantization way: It simply doesn't make sense for... particles.. with a finite lifetime to be in more than one place at the same time.
  • #1
ftr
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There seems to be some -at least- conceptual difference between particles in QFT which is just a point -eventually- in the field AND the particle in QM which is described by a wavefunction which is extended in space. As if QFT somehow "collapses" the wavefunction.
 
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  • #2
ftr said:
There seems to be some -at least- conceptual difference between particles in QFT which is just a point -eventually- in the field AND the particle in QM which is described by a wavefunction which is extended in space. As if QFT somehow "collapses" the wavefunction.
A particle in QM is described purely by a set of intrinsic quantum numbers, none of which have anything to do with space-time. Space-time enters the picture only when we attempt to describe the behavior of the particle in the observer's space-time frame. The difference with QFT is that the concept of a field has meaning only in a space-time context.
 
  • #3
mikeyork said:
A particle in QM is described purely by a set of intrinsic quantum numbers, none of which have anything to do with space-time. Space-time enters the picture only when we attempt to describe the behavior of the particle in the observer's space-time frame. The difference with QFT is that the concept of a field has meaning only in a space-time context.

the point I am trying to make is that the particle is a point in QFT in a particular place and that's that, and presumably they still have the same intrinsic quantum numbers.
 
  • #4
ftr said:
the point I am trying to make is that the particle is a point in QFT in a particular place and that's that
Where did you read this? This is not what field theory is about, nor quantum field theory.
 
  • #6
ftr said:
There seems to be some -at least- conceptual difference between particles in QFT which is just a point -eventually- in the field AND the particle in QM which is described by a wavefunction which is extended in space. As if QFT somehow "collapses" the wavefunction.

There are many types of particles in QFT. A particle is basically a quantized excitation of the field. There are many ways to describe field excitations, so there also correspondingly many types of particles in QFT. Some particles are localized, and others are spread out, like the eigenfunctions of the free particle of non-relativistic QM.

You can find a discussion an analogous discussion of different types of photons in https://books.google.com.sg/books?id=l-l0L8YInA0C&vq=photon&source=gbs_navlinks_s (section 4.6: Quantized radiation states and photons; Complement 4C: Photons in modes other than traveling planes waves; Section 5.4.3: "They might be referred to as quasi-particles states, because they are the quantum states whose properties most closely resemble those of an isolated particle propagating at the speed of light").

Roughly, a particle corresponds to the state created by a creation operator. However, fermion creation operators are usually not Hermitian, so single fermion operators are usually not observables.
 
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  • #7
atyy said:
spread out, like the eigenfunctions of the free particle of non-relativistic QM.

but these are generally do not discussed in the established textbooks correct. I have most of those, they typically rehash the same things.
 
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  • #9
The difference is quite simple, and there is no tension.

In QFT you can put it in a form similar to the second quantisiation interpretation of ordinary QM - it's one of a number of equivalent formulations:
http://www.colorado.edu/physics/phys5260/phys5260_sp16/lectureNotes/NineFormulations.pdf

The difference is the number of particles is not fixed like in ordinary QM - but can itself be in a superposition.

It's of practical importance because you need it to explain things like spontaneous emission which can't be explained otherwise:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

Thanks
Bill
 
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  • #10
ftr said:
the point I am trying to make is that the particle is a point in QFT in a particular place and that's that, and presumably they still have the same intrinsic quantum numbers.
To the contrary! In relativistic QT the QFT formulation is so much more approriate than the 1st-quantization approach, because you cannot localize particles in a more strict sense than already in non-relativistic QM. The reason is that to resolve a particles position you need other particles to scatter with sufficiently large momenta to have the wanted resolution in position. In relativistic QT an ever higher momentum to scatter particles to localize other particles doesn't lead to a better position resolution, because one creates new particles rather then get better position resolution.

In the formalism of relativistic QT this occurs in the known difficulties to interprete Poincare covariant wave equations in a 1st-quantization way: It simply doesn't make sense for interacting particles (interacting of, e.g., charged with an external em. field is already enough!) to work in a one-particle picture, because with some probability new particles are created or initially present particles are destroyed. So the natural way to formulate relativistic QT is in terms of a QFT, working with a Hilbert space of indefinite particle number.

Another formal hint about the problematic issue of position is that relativistic QT admits the possibility of massless particles (which is not so in non-relativistic physics, where massless particles just don't have a sensible dynamics), and massless particles with a spin ##\geq 1## don't admit the construction of a position operator in the strict sense, i.e., for a massless particle like the photon you cannot even define a position observable to begin with!

Another point is that within non-relativistic QT in the cases, where you deal with a fixed number of particles like in atomic physics, where you have a fixed number of electrons around a nucleus, the first-quantization formulation and the second-quantization formulation (the latter is just non-relativistic QFT) are equivalent. It's just writing the same theory in different mathematical terms, but the physics is completely the same.
 
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1. What is the difference between quantum mechanics (QM) and quantum field theory (QFT)?

Quantum mechanics is a mathematical framework used to describe the behavior of particles at the microscopic level, while quantum field theory is a theoretical framework used to describe the behavior of fields at the microscopic level.

2. Is there a contradiction between QM and QFT?

No, there is no contradiction between QM and QFT. Both theories are well-established and have been extensively tested and verified through experiments. However, there are still ongoing debates and research on how to reconcile the two theories and create a more comprehensive theory of physics.

3. What are some examples of phenomena that can be described by QM and QFT?

QM can be used to explain the behavior of individual particles, such as the double-slit experiment and quantum entanglement. QFT, on the other hand, can be used to describe phenomena involving interactions between particles, such as the behavior of particles in a vacuum or the behavior of particles in a strong magnetic field.

4. Why is it challenging to unify QM and QFT?

Unifying QM and QFT is challenging because they use different mathematical frameworks and have different conceptual foundations. QM is based on wave functions and probabilities, while QFT is based on fields and particles. Reconciling these two approaches requires a deep understanding of both theories and the development of new mathematical tools.

5. How are QM and QFT related to other theories of physics?

QM and QFT are fundamental theories in modern physics and are closely related to other theories such as classical mechanics, special relativity, and general relativity. In fact, QFT is often considered as a relativistic version of QM. Understanding the relationship between these theories is crucial in developing a unified theory of physics.

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