Should QM or QED be used?

*Alfrez*

Supposed external energy is added to the system such that the electron is rise to the next orbital releasing photon. Can QM still be used to model it or does one need Quantum Field Theory? How about additional external energy that increase say the molecular rotational or translational speed, is QM still used here or QFT? If QM is no longer used, does it mean that whenever new external energy is added to the system. QM is no longer valid or do you just add the new energy to the kinetic energy component of the Schroedinger equations??

fzero

QFT is necessary to compute the corrections arising from special relativistic effects. These will be large when the transition energies approach the mass of the electron. At lower energies there are still small corrections that can be important for precision measurements. If we consider energy scales in the H-atom, the ground state energy is ~10 eV, while the electron mass is 1/2 x 10⁶ eV. The ratio is 2 x 10^-5, so QFT corrections will appear if we compare theory with experiment to that accuracy.

*Alfrez*

Quote by fzero

QFT is necessary to compute the corrections arising from special relativistic effects. These will be large when the transition energies approach the mass of the electron. At lower energies there are still small corrections that can be important for precision measurements. If we consider energy scales in the H-atom, the ground state energy is ~10 eV, while the electron mass is 1/2 x 10⁶ eV. The ratio is 2 x 10^-5, so QFT corrections will appear if we compare theory with experiment to that accuracy.

In biological chemical reactions. The energy appears to go beyond the mass of electron, right? If so, then QFT must be used. How come we have quantum chemistry but not quantum field chemistry if that's the case?

fzero

Quote by Alfrez

In biological chemical reactions. The energy appears to go beyond the mass of electron, right? If so, then QFT must be used. How come we have quantum chemistry but not quantum field chemistry if that's the case?

It's not the total energy of a reaction between some bulk quantities of reagents that's important when considering atomic effects, it's the energies associated with the bond energies. Those are much smaller than the ground state energy of hydrogen and so relativistic effects can be ignored when dealing with chemical reactions. Especially when you consider that it's nearly impossible to accurately measure the quantity of reagents with the accuracy explained above.

To further explain, let's say that you put some compound in a beaker and heat it with a bunsen burner. Overall you are putting a great deal of energy into the system when you compared with typical atomic scales. However, this energy is distributed over a number of molecules that is many orders of magnitude. Some molecules will absorb more than their fair share and you will break all bonds and ionize atoms, etc., but the huge bulk of molecules will absorb a much more modest amount of energy and experience less drastic chemical transformations.

*Alfrez*

Quote by fzero

It's not the total energy of a reaction between some bulk quantities of reagents that's important when considering atomic effects, it's the energies associated with the bond energies. Those are much smaller than the ground state energy of hydrogen and so relativistic effects can be ignored when dealing with chemical reactions. Especially when you consider that it's nearly impossible to accurately measure the quantity of reagents with the accuracy explained above.

To further explain, let's say that you put some compound in a beaker and heat it with a bunsen burner. Overall you are putting a great deal of energy into the system when you compared with typical atomic scales. However, this energy is distributed over a number of molecules that is many orders of magnitude. Some molecules will absorb more than their fair share and you will break all bonds and ionize atoms, etc., but the huge bulk of molecules will absorb a much more modest amount of energy and experience less drastic chemical transformations.

I see. So QED is used when high energy photons interact with the orbitals. QCD is used when quarks dynamics are investigated. QED, QCD, Supersymmetry, String Theory need QFT for the reasons relativistic effects are important.

But one of the new concepts introduced by QFT is that particles are field momenta. Field is now the primary ingredient and particles just momentum of the field. Using this interpretation. The Hydrogen and electron could be consider field momenta of the hydrogen and electron field. If so. Then QFT must be used to replace QM. In this situation. We could use QFT even if there is no relativistic effects, but just to obey the new finding that field is primary, particles just momentum of the field. What do you say about this? Maybe QM is still used to make the calculations easier even though QFT is the right interpretation that must be used where the electron and hydrogen are just quanta of the electron an hydrogen field?

Chopin

Quote by Alfrez

Maybe QM is still used to make the calculations easier even though QFT is the right interpretation that must be used where the electron and hydrogen are just quanta of the electron an hydrogen field?

Pretty much. If you really want the correct equations for everything, then you have to use QFT because it's more fundamental, but a lot of times you don't need the power of that. It's just like other problems in physics--if you don't need speeds approaching the speed of light, you can ignore relativity. If you don't need to look at very small sizes you don't need quantum mechanics at all--classical mechanics will work just fine. All of these things are an exercise in finding the simplest formalism that still embodies the principles you're talking about.

If I understand your original question right, I think the answer in this specific scenario is that you can use QM if you just want to talk about the state of the atom before and after the energy transfer. QM will allow you to talk about the different energy eigenstates of the atom, angular momentum, and all that kind of stuff. It doesn't have as much to say about the actual interaction process that leads to this energy shift, though. You can calculate a photon-electron interaction in a kind of ham-handed way by modelling the photon as an external electromagnetic field and using time-dependent perturbation theory, but to really do things accurately you need to introduce QFT at that point.

*Alfrez*

Quote by Chopin

Pretty much. If you really want the correct equations for everything, then you have to use QFT because it's more fundamental, but a lot of times you don't need the power of that. It's just like other problems in physics--if you don't need speeds approaching the speed of light, you can ignore relativity. If you don't need to look at very small sizes you don't need quantum mechanics at all--classical mechanics will work just fine. All of these things are an exercise in finding the simplest formalism that still embodies the principles you're talking about.

If I understand your original question right, I think the answer in this specific scenario is that you can use QM if you just want to talk about the state of the atom before and after the energy transfer. QM will allow you to talk about the different energy eigenstates of the atom, angular momentum, and all that kind of stuff. It doesn't have as much to say about the actual interaction process that leads to this energy shift, though. You can calculate a photon-electron interaction in a kind of ham-handed way by modelling the photon as an external electromagnetic field and using time-dependent perturbation theory, but to really do things accurately you need to introduce QFT at that point.

Ok. Say. Quantum Mechanics has so many Interpretations like Many Worlds, Bohmian, etc. How come we seldom hear about Interpretations in Quantum Field Theory? Is there something in the quantum vacuum ontology that cancel out all the Interpretations? Or is it also valid? For example, in Many Worlds, the particles actually exist in many worlds. In particle creation and annihilations in a field.. can we say each particle dynamics like particle creation/annihilations is due to million of worlds interacting with one another just like the interference of the double slit being an interference caused by different worlds in coincident positions? If not, then why is QFT immuned to Interpetations? Anyone?

Chopin

QFT has all of the same interpretations as QM. Both of them just give you the probabilities of different events happening, but the interpretation of those probabilities (wavefunction collapse in the Copenhagen Interpretation, state decoherence in MWI, etc.) are the same in both of them. QFT is just a more powerful formalism that allows you to calculate those probabilities for more circumstances.

*Alfrez*

Quote by Chopin

QFT has all of the same interpretations as QM. Both of them just give you the probabilities of different events happening, but the interpretation of those probabilities (wavefunction collapse in the Copenhagen Interpretation, state decoherence in MWI, etc.) are the same in both of them. QFT is just a more powerful formalism that allows you to calculate those probabilities for more circumstances.

I think it's more than that. In QM, it's wave and particle. In QFT, it's wave, particle and field.
In the double slit experiment, one thinks about wave or particle in QM. But in QFT, one can think it is the field that travels and the particle being just a momentum of the field got detected in the detector. So they seem to have different interpretations. Also in QFT, position is not an observable. It's like the field self-observe its position, hence eliminating the need for observer?? I read the following the wikipedia about QFT:

"In quantum field theory, unlike in quantum mechanics, position is not an observable, and thus, one does not need the concept of a position-space probability density."

http://en.wikipedia.org/wiki/Quantum_field_theory

Chopin

Yes but the field is just a new way of talking about the position-space density, which makes it easier to include the effects of relativity. You can still ask questions like "what is the probability that the particle is here?", just like you can in QM. You can still talk about a wave packet moving around in space just like before, you just use slightly different language to do it. The real power of QFT is that the number of particles isn't fixed, so it's possible to talk about things like an electron and a positron annihilating to form photons, etc. QM can't do that.

*Alfrez*

Quote by fzero

It's not the total energy of a reaction between some bulk quantities of reagents that's important when considering atomic effects, it's the energies associated with the bond energies. Those are much smaller than the ground state energy of hydrogen and so relativistic effects can be ignored when dealing with chemical reactions. Especially when you consider that it's nearly impossible to accurately measure the quantity of reagents with the accuracy explained above.

To further explain, let's say that you put some compound in a beaker and heat it with a bunsen burner. Overall you are putting a great deal of energy into the system when you compared with typical atomic scales. However, this energy is distributed over a number of molecules that is many orders of magnitude. Some molecules will absorb more than their fair share and you will break all bonds and ionize atoms, etc., but the huge bulk of molecules will absorb a much more modest amount of energy and experience less drastic chemical transformations.

You explained energy is distributed over a number of molecules and so the atoms don't absorb more energy than the ground state energy of hydrogen. However I read the following where QFT is used in biology as in:

http://en.wikipedia.org/wiki/Quantum_brain_dynamics

"In neuroscience, quantum brain dynamics (QBD) is a hypothesis to explain the function of the brain within the framework of quantum field theory.

Large systems, such as those studied biologically, have less symmetry than the idealized systems or single crystals often studied in physics. Jeffrey Goldstone proved that where symmetry is broken, additional bosons, the Nambu-Goldstone bosons, will then be observed in the spectrum of possible states; one canonical example being the phonon in a crystal.

Umezawa (1967) proposed a general theory of quanta of long-range coherent waves within and between brain cells, and showed a possible mechanism of memory storage and retrieval in terms of Nambu-Goldstone bosons. This was later fleshed out into a theory encompassing all biological cells and systems in the quantum biodynamics of Del Giudice et al., (1986, 1988)."

Well?

fzero

These Nambu-Goldstone bosons that they're talking about are low energy (with respect to bond energies) degrees of freedom that would describe deformations of the shape of the molecule around an equilibrium configuration. Their significance to chemical reactions would be several orders of magnitude smaller than van der Waals and other forces. A reaction rate doesn't depend strongly on very small changes in the shape of a molecule.

*Alfrez*

Quote by fzero

These Nambu-Goldstone bosons that they're talking about are low energy (with respect to bond energies) degrees of freedom that would describe deformations of the shape of the molecule around an equilibrium configuration. Their significance to chemical reactions would be several orders of magnitude smaller than van der Waals and other forces. A reaction rate doesn't depend strongly on very small changes in the shape of a molecule.

Ok. But do you think these Nambu_Goldstone bosons are possible in a biological system like depicted above? If not. Why?

fzero

Quote by Alfrez

Ok. But do you think these Nambu_Goldstone bosons are possible in a biological system like depicted above? If not. Why?

They are certainly there. It's completely analogous to the presence of sound waves in a crystal solid. Whether or not they have anything to do with brain function or consciousness, I couldn't say.

alxm

Quote by fzero

QFT is necessary to compute the corrections arising from special relativistic effects. These will be large when the transition energies approach the mass of the electron.

QFT isn't necessarily used for relativistic quantum chemical applications. The more common approach is to work with the Dirac equation; e.g. Dirac-Fock methods, etc.

alxm

Quote by Alfrez

Umezawa (1967) proposed a general theory of quanta of long-range coherent waves within and between brain cells, and showed a possible mechanism of memory storage and retrieval in terms of Nambu-Goldstone bosons. This was later fleshed out into a theory encompassing all biological cells and systems in the quantum biodynamics of Del Giudice et al., (1986, 1988)."

Well?

These "quantum brain" theories are a load of nonsense. They've been debunked here (not least by myself) many times.

*Alfrez*

Quote by alxm

These "quantum brain" theories are a load of nonsense. They've been debunked here (not least by myself) many times.

Pls. show the links how they were debunked. Thanks.

Chopin	QFT has all of the same interpretations as QM. Both of them just give you the probabilities of different events happening, but the interpretation of those probabilities (wavefunction collapse in the Copenhagen Interpretation, state decoherence in MWI, etc.) are the same in both of them. QFT is just a more powerful formalism that allows you to calculate those probabilities for more circumstances.