# Amount of quantum fields

1. Aug 8, 2015

### guywithdoubts

Most threads discussing this subject have only confused me further, gone offtopic and later been locked. I have a basic yes/no question, which is the following: is there one single electromagnetic field in the universe that is excited locally (creating fields, in apparent plural, although empirically there is only one) such as in the Higgs field?

If so, as a follow up, is this supposed to have a physical nature (that this one field is real) or is it understood as a mathematical device?

2. Aug 8, 2015

### Orodruin

Staff Emeritus
All fields are assumed to exist everywhere. Quantum excitations in these fields are what we call particles.

This is a purely philosophical question with little physical content.

3. Aug 8, 2015

No.

4. Aug 8, 2015

### Staff: Mentor

There is an electromagnetic (photon) field, a Higgs field, an electron field, a muon field, an up-quark field, a W-field, etc. These are separate fields. They are not excitations of the electromagnetic field.

5. Aug 8, 2015

### Feeble Wonk

I think the OP is asking whether the EM field is extended throughout the universe, like the Higgs field.

Sorry GuyWithDoubts, but while it is absolutely reasonable for you to be curious about the "physical nature" of the field (any field), the field's ontological existence is not relevant to theory, and is therefore considered a "philosophical" matter on this forum. Trying to pursue that line of inquiry will result in the thread getting "locked", as you had previously noticed.

Disappointing, yes, but that's the way it is.

6. Aug 8, 2015

### guywithdoubts

Thanks everyone for your replies. I apologize for the philosophical bit, it was not where I was heading with that question, but thinking about it now, it might inevitably end in philosophy so I will refrain from it.

Exactly. So is it? Avodyne gives a plain no, whereas Orodruin says all fields are assumed to exist everywhere, using a plural that confuses me. All fields as in "all types of fields/any field by definition", or all different, individual fields? For instance, if I apply a current to a coil, is this magnetic field separate (however interacting) from a magnetic field produced by another coil, or is it the same, one universal EM field?

Perhaps I should address the question in the Cosmology section?

7. Aug 8, 2015

### Orodruin

Staff Emeritus
You are reading his answer wrong. Your question is multifaceted and the "no" refers to there being only one field of which the Higgs field and other field are excitations. There is not.

It is unclear how you distinguish between those situations.

There is only one magnetic field. It may have different values at different points in space and time, but it is the same magnetic field. You will sometimes hear things like "the electric field produced by a point charge". This simply refers to the non-zero values of the electric field that are resulting from the point charge. The only reason you can refer to it as coming from the point charge is that Maxwell's equations are linear.

8. Aug 8, 2015

### guywithdoubts

Thanks, this clears my doubt.

9. Aug 8, 2015

### Feeble Wonk

But is that not the unrealized goal of physics... to unify all the various particles/fields into the fundamental Grand Unified Theory?

10. Aug 9, 2015

### Orodruin

Staff Emeritus
This does not mean there is only one field. It is about describing nature with a single gauge theory with a high degree of symmetry.

11. Aug 10, 2015

### vanhees71

Perhaps one should start discussing this question first for classical fields. Then we get rid of the uncertainties due to different interpretations associated by different physicists with the mathematical objects used in QFT.

The only fundamental field observable in a classical sense is the electromagnetic field. Clearly, there is one and only one electromagnetic field. At any place of space-time it has a specific value, which can be meausured by measuring the force on a test charge, and each observer is giving his result in terms of his coordinate system and time. It's expressed either covariantly by the 6 components $F_{\mu \nu}$ of an antisymmetric 2nd-rank Mikowski tensor or in terms of the corresponding two 3D-Euclidean vector components $(\vec{E},\vec{B})$.

Nowadays we know more such fundamental fields, describing all the known interactions among the known and observed fundamental particles (which are the spin 1/2 leptons and quarks as well as the spin-0 Higgs boson). The quanta of the interaction fields (all spin-1 gauge fields) are known as photons (electromagnetic field), gluons (strong interaction among color charges), and W- and Z bosons (weak interactions). The Higgs boson is the excitation of the Higgs field, which is somewhat special, because it has a non-zero vacuum expectation value, i.e., there is a classical constant scalar Higgs field at each point in spacetime, and all the particles (and the W und Z gauge bosons) get their fundamental masses due to the coupling of their corresponding fields to the Higgs field. There's thus for each of these quanta one appropriate quantum field (Dirac fields for quarks and leptons, vector gauge fields for the force fields, and a scalar field, the Higgs field).

It should be mentioned however that the largest part of the mass (~95%) of the matter around us (which consists almost exclusively protons, neutrons (bound states of three light quarks), and electrons) is in the protons and neutrons and is dynamically created by the strong interaction.

12. Aug 10, 2015

### guywithdoubts

Thank you for expanding on the subject. I guess my problem is with semantics—I understand there is only one Higgs field, but then you say that "there is a classical constant scalar Higgs field at each point in spacetime". That makes it sound like there are more fields of the same kind, which laymen like me find extremely confusing.

13. Aug 11, 2015

### vanhees71

Well, it's difficult to express this clearly. There's one and only one Higgs field. First of all it has a constant value throughout the universe, the socalled "vacuum expectation value", i.e., the vacuum state (the state of lowest energy) is one, where this field has a value. Now at the LHC through very high energy collisions of protons, one excites (among many other process) this Higgs field, which means one "creates a Higgs boson". This excitation (the Higgs boson) decays to other particles (which are in the picture of quantum field theory nothing else than excitations of their specific fields), which are detected and evaluated such to make sure that the Higgs boson really exists.

The logic behind this is the following: Over 50 years ago the physicists started to struggle with a correct mathematical description of the weak interaction, known much longer to be responsible for radioactive $\beta$ decay of atomic nuclei. There was also a very early model from the 1930ies by Fermi, which was built on quantum-field theoretical concepts, but this model had some formal shortcomings (it was not renormalizable as electrodynamics), and so one was trying to build a better renormalizable model even closer to the way electromagnetism is described by quantum electrodynamics. A prime candidate were the socalled gauge theories, based on a (btw. very beautiful, beacuse it's based on symmetries) mathematical formalism, but it turned out that this is pretty difficult, because such gauge theories lead to the prediction that the forces are mediated by fields whose quanta (i.e., elementary excitations) correspond to massless vector bosons like the photon. On the other hand, the weak interaction was known to be short-ranged, while massless fields imply long-range forces like the Coulomb field in classical electromagnetism. This force only falls off with $1/r^2$, where $r$ is the distance between two point charges. Massive gauge bosons would solve this problem, but the trouble was that giving the gauge bosons a mass in the usual naive way destroys the nice properties of gauge theories and also their renormalizability. In the mid 60ies several physicists (among others Higgs and Englert, who got the Nobel prize for this work in 2013) came to the idea that one can give mass to the gauge bosons of the weak interaction by introducing another scalar field, which in it's lowest-energy ground state is not 0 but has a finite value (the mentioned "vacuum expectation value"). This gave the gauge bosons a mass without destroying the underlying mathematical symmetry principle underlying the gauge theory. But then Higgs immediately realized that the introduction of this field not only means that it can have this desired constant vacuum expectation value but must also be excitable, leading to the existence of a new particle, the socalled Higgs boson.

For quite a while this very abstract construction was not taken too seriously, and Higgs even had a hard time to get his (very short) paper published (finally it was published in PRL back to back with a similar paper by Brout and Englert). Also in the mid 60ies the quantum field theories were somewhat out of fashion, because of several problems, even the renormalizable theories have at very high energies. On the other hand, with renormalizable theories one could make precise predictions of the outcome of experiments with elementary particles, which were pretty good. Particularly in QED the precision in the agreement between experiment and theory was unprecedented. The real breakthrough of the gauge theories came in 1971 when 't Hooft in his doctoral thesis could show, working together with his adviser, Veltman, could prove the renormalizability of the non-Abelian gauge theories, which was the kind of theory used to describe the weak interaction (putting together the models by Glashow, Weinberg, Salam and many others with the Higgs mechanism to make the weak gauge bosons massive). Only a little later (in 1973) also the strong interactions were described by such a non-abelian gauge theory, Quantum Chromodynamics QCD (which is another fascinating story). Together with the Glashow-Salam-Weinberg-Higgs theory of the weak and electromagnetic interactions QCD builds the Standard Model of elementary particle physics.

14. Aug 11, 2015

### kith

https://en.wikipedia.org/wiki/Field_(physics)

15. Aug 13, 2015

### my2cts

There is a second reason. Part of the field requires the point charge to be where it is, or will not be a solution of Maxwells equations at that position.

16. Aug 13, 2015

### Orodruin

Staff Emeritus
But this is essentially the same reason, i.e., Maxwell's equations are linear and you can therefore make superpositions of the solutions for different sources. That you can infer what the source term was from how the fields look are just going in the other direction.

17. Aug 13, 2015

### Staff: Mentor

It might perhaps be clearer to say "There is a scalar Higgs field which has a value at each point in spacetime".... But that's a bit of a pleonasm, as a field is (loosely) defined to be something that has a value at each point in spacetime.

The real takeaway here is that natural language will only take you so far; precision and complete understanding requires some math.

18. Aug 13, 2015

### guywithdoubts

I did, until I came across this paragraph: "This lead physicists to consider electromagnetic fields..." which is why I asked about the Higgs field, knowing it's supposed to be a single, universal field. But like Nurgatory said,

So I guess I'll have to improve my math anyway.

19. Aug 14, 2015

### kith

Ah, ok. It is good to include such information when starting a thread so we can better understand where you are coming from.

20. Aug 15, 2015

### my2cts

The linearity property by itself is not required let alone sufficient. What is needed is a unique way to derive source form field. ;-)