Is the QFT field real or just a mathematical tool?

[ftr]

Sorry, I know this has been talked about many times before but I like to put the question in a direct way so I may understand.

Since there are more than 10^80 particles and radiation, how can a single point in space carry the values for all these fields at the SAME time all the time if they are real/intrinsic(i.e. not effective like classical variables like pressure, temperature).

 

[Demystifier]

If you think that each of the $10^{80}$ particles has its own field, then you are wrong. Independent of the number of particles in the Universe, there is only about 20 different kinds of fields.

That being said, it is not known whether these 20-or-so fields are effective or fundamental ("real").

 

[A. Neumaier]

Independent of the number of particles in the Universe, there is only about 20 different kinds of fields.

On the fundamental level, there are according to present knowledge only 6 fields - the lepton field, the quark field, the gluon field, the electroweak field, the Higgs field, and the gravitational field, each with a fairly large (but compared to the baryon number of the universe exceedingly small) number of components.

On the level of everyday experience there are many more fields - for example, each fluid has its own field.

 

[Demystifier]

On the fundamental level, there are according to present knowledge only 5 fields - the lepton field, the quark field, the gluon field, the electroweak field, and the gravitational field, each with a fairly large (but compared to the baryon number of the universe exceedingly small) number of components.

There are several different ways of counting. I like to count components with different mass as different fields.

But if you want to split hairs, if electroweak SU(2)xU(1) field is counted as one field, then gluo-electroweak SU(3)xSU(2)xU(1) field can also be counted as one field.

And by the way, you forgot Higgs.

 

[A. Neumaier]

There are several different ways of counting. I like to count components with different mass as different fields.

But this is unnatural since there is mass mixing. There is no reason to prefer the mass basis over any other basis.

But if you want to split hairs, if electroweak SU(2)xU(1) field is counted as one field, then gluo-electroweak SU(3)xSU(2)xU(1) field can also be counted as one field.

No, it is you who are splitting - not hairs but fields!
But one cannot naturally split the electroweak field into an SU(2) field and an U(1) field as these have no independent meaning - the electromagnetic U(1) is the diagonal of the SU(2)xU(1)!
On the other hand, if one wants to unsplit hairs as you suggest, one should put all fields into one big field with many components.

you forgot Higgs.

Yes, corrected. I think of it as the scalar part of the gravitational field, but this is not the accepted usage.

 

[ftr]

Thanks both.

So does the lepton field exist inside the proton? what are they doing there, when their values possible change to indicate an electron has materialized and how does the proton then behave, it certainly has a strong charge?

Moreover, isn't the wavefunction should cover all of spacetime even at extremely low probability?

 

[Nugatory]

So does the lepton field exist inside the proton?

A field is defined to be something that has a value (not necessarily a number - there are vector and tensor fields) at every point in spacetime, so the lepton field has a value everywhere, including "inside a proton".

The quotes around the words "inside a proton" are there because none of these particles that we're talking about are little tiny balls with an inside and an outside.

 

[A. Neumaier]

So does the lepton field exist inside the proton? what are they doing there, when their values possible change to indicate an electron has materialized and how does the proton then behave, it certainly has a strong charge?

Moreover, isn't the wavefunction should cover all of spacetime even at extremely low probability?

Yes, strictly speaking, all fields are everywhere in space and time, but one can neglect them where the field strength is too tiny.

For a proton inside a hydrogen atom in the ground state the lepton field even has its maximal density at the center of the proton!

On the level of quantum chemistry (systems of nuclei and electrons), electrons are conserved, hence they cannot materialize but have to flow. Macroscopically, this is seen as the flow of electricity in the electromagnetic field. Microscopically, the lepton (electron) field accounts for such things as delocalization, smearing out the electrons. The pointlike picture is adequate only in electron beams.

 

[ftr]

For a proton inside a hydrogen atom in the ground state the lepton field even has its maximal density at the center of the proton!

can you give a reference please, thanks.

 

[ftr]

A field is defined to be something that has a value (not necessarily a number - there are vector and tensor fields) at every point in spacetime, so the lepton field has a value everywhere, including "inside a proton".

So my question again, how is it that a single point(unless it is a world by itself) carries all these fields of scalar, vector , tensor ... this is like superposition running really wild. On top of that the good old mysterious CC, and at a point where a quark or an electron exists all these fields are jamming.

 

[Nugatory]

So my question again, how is it that a single point(unless it is a world by itself) carries all these fields of scalar, vector , tensor ...

The same way it "carries" the classical electrical, magnetic, and gravitational fields - those are vector fields, and there's no problem saying that all three can have values at the same point.

 

[Vanadium 50]

can you give a reference please, thanks.

Any QM book that covers the hydrogen atom: Liboff, Schiff, Eiseberg and Resnick...Any QM book that covers the hydrogen atom: Liboff, Schiff, Eiseberg and Resnick...

 

[ftr]

The same way it "carries" the classical electrical, magnetic, and gravitational fields - those are vector fields, and there's no problem saying that all three can have values at the same point.

My understanding is that these are classical and not fundamental like QM picture(suppose to be).

 

[ftr]

Any QM book that covers the hydrogen atom: Liboff, Schiff, Eiseberg and Resnick...Any QM book that covers the hydrogen atom: Liboff, Schiff, Eiseberg and Resnick...

I am not sure what you are referring to. Hydrogen model is handled by plain QM, there is no talk of "fields".

 

[Nugatory]

I am not sure what you are referring to. Hydrogen model is handled by plain QM, there is no talk of "fields".

What you're calling "plain QM" is quantum field theory with the simplifying assumptions that the energy is low enough that the particle numbers are fixed and that the speeds involved are small compared with the speed of light. And I am at a loss to understand how you can say "there is no talk of fields" there when the entire problem and its solution are expressed in terms of functions of position.

 

[ftr]

What you're calling "plain QM" is quantum field theory with the simplifying assumptions that the energy is low enough that the particle numbers are fixed and that the speeds involved are small compared with the speed of light. And I am at a loss to understand how you can say "there is no talk of fields" there when the entire problem and its solution are expressed in terms of functions of position.

What I meant is that standard QM books do not use QFT to solve the hydrogen atom problem.

 

[vanhees71]

For a modern solution of the hydrogen problem in QED, see

S. Weinberg, Quantum Theory of Fields, Vol. 1

 

[ftr]

For a modern solution of the hydrogen problem in QED, see

S. Weinberg, Quantum Theory of Fields, Vol. 1

Ok thanks I will , I have all three volumes but I only see Dirac equation being solved with radiative corrections.

 

[A. Neumaier]

can you give a reference please, thanks.

In the present situation of a single electron, the field strength is proportional to the spatially probability density, which is calculated in many textbooks. For the ground state it is spherically symmetric and decays exactly exponentially with the distance from the center, hence is maximal there.

 

[A. Neumaier]

how is it that a single point(unless it is a world by itself) carries all these fields of scalar, vector , tensor

The field is everywhere, not just at a single point. To translate from the QM particle picture to the (more accurate and more basic) QFT picture you need to rewrite things in terms of second quantization language (which is quantum field theory) and evaluate the expectation of the charge density operator at an arbitrary point $x$ in the ground state of a single hydrogen atom. This is a very useful exercise.

 

[ftr]

In the present situation of a single electron, the field strength is proportional to the spatially probability density, which is calculated in many textbooks. For the ground state it is spherically symmetric and decays exactly exponentially with the distance from the center, hence is maximal there.

Isn't it maximal at Bohr distance? We are talking about hydrogen atom, right?

 

[A. Neumaier]

Is isn't it maximal at Bohr distance? We are talking about hydrogen atom, right?

Do the calculations and check!

 

[ftr]

@
meopemuk

I have been looking at your work, and surprisingly I saw you are looking at my thread. can you comment please.

 

[Demystifier]

Yes, corrected. I think of it as the scalar part of the gravitational field, but this is not the accepted usage.

Why do you think of Higgs as the scalar part of the gravitational field? (I can see a motivation for this in string theory, but I suspect your reasons are entirely different.)

 

[Demystifier]

There is no reason to prefer the mass basis over any other basis.

As far as I know, nobody ever detected a particle in a state which is not a mass eigenstate. That's a pretty good reason for me. (Of course, a solar neutrino is in a superposition of different masses before detection, but this changes when you detect it.)

 

[A. Neumaier]

Why do you think of Higgs as the scalar part of the gravitational field? (I can see a motivation for this in string theory, but I suspect your reasons are entirely different.)

Because it is a Lorentz scalar generating mass in QFT, hence must be directly related to gravitation, which couples to mass. Also many classical gravitational theories have an additional scalar field to account for inflation. In my mind these could be the same. But I am not an expert in gravitation, so this may all be wrong!

 

[Demystifier]

Because it is a Lorentz scalar generating mass in QFT, hence must be directly related to gravitation, which couples to mass.

But gravity is not the only thing that couples to mass. For instance, when experimentalists measure particle masses in CERN, it does not depend on gravity. Essentially, that's because they measure inertial (not gravitational) mass.

 

[A. Neumaier]

But gravity is not the only thing that couples to mass. For instance, when experimentalists measure particle masses in CERN, it does not depend on mass. Essentially, that's because they measure inertial (not gravitational) mass.

Of course, momentum is proportional to mass. But you had asked for my thoughts...

 

[Demystifier]

Of course, momentum is proportional to mass. But you had asked for my thoughts...

Well, I have some thoughts too. Gravity is not really coupled to mass, but to energy-momentum. And all fields have energy-momentum, even massless ones. Still, you don't think that all fields are part of the gravitational field, do you?

 

[vanhees71]

Because it is a Lorentz scalar generating mass in QFT, hence must be directly related to gravitation, which couples to mass. Also many classical gravitational theories have an additional scalar field to account for inflation. In my mind these could be the same. But I am not an expert in gravitation, so this may all be wrong!

According to GR every energy-momentum-stress tensor couples universally to the gravitatational field (aka pseudometric of the spacetime manifold). Mass terms, including those generated from the Yukawa couplings to the VEV of the Higgs field, provide only partial contributions to the energy-momentum tensor of the matter field.