List of Fields in Quantum Mechanics: Real vs. Mathematical

[ParticleMan]

In beginning to learn about Quantum Mechanics, I am getting confused by what seems like a lot of overloaded terminology. One example is with fields (and perhaps for another thread..."spaces").

I generally understand the idea of a field in the sense of temperature variations in a room or of electrons being "disturbances" in a Quantum Electro-Dynamic Field, but I do not understand what these "all-pervasive" fields "are" or why/how they can all co-exist... I also understand that there are/were Classical Fields most of which I believe have been superseded by fields in Quantum Mechanics. I would assume there is now only a Quantum Field, Higgs Field, and Gravity Field, but I cannot seem to find a good list.

Would someone be so kind as to list all currently known/defined fields? Please, also make a distinction between any fields which are "real & physical" versus those that are purely mathematical such that they only "exist" to solve mathematical problems.

Hope that all makes sense. Sometimes its difficult when beginning to know the right questions to ask.

 

[A. Neumaier]

Would someone be so kind as to list all currently known/defined fields? Please, also make a distinction between any fields which are "real & physical"

Any property that can be present to a variable degree at any point in some region of space or space-time defines a corresponding field. Thus in principle there are as many real & physical fields as there are real & physical space-dependent properties, and it is impossible to get a complete list.

In physics, one generally concentrates on those properties that are most useful for describing the situation under study. For example, hydromechanics studies velocity fields (3 components at each point), mass density fields, temperature fields and pressure fields of a fluid, QED studies the electromagnetic field (6 components at each point) and the electron field (4 components at every point). QCD studies quark fields, etc..

 

[Vanadium 50]

It sounds an awful lot like you are trying to start in the middle: studying quantum fields without quantum mechanics and classical fields, and possibly without mechanics, electromagnetism and waves. This is unlikely to work out for you.

 

[PeroK]

In beginning to learn about Quantum Mechanics, I am getting confused by what seems like a lot of overloaded terminology. One example is with fields (and perhaps for another thread..."spaces").

You should say where you are learning QM and the context in which your confusion arises. I wonder, for example, whether you are referring to vector spaces here, which have a scalar field (the complex numbers) associated with them.

 

[ParticleMan]

My questions about fields are very general and not specific to a particular text. As an autodidact, I plan to fill in learned deficiencies as I go. The time limit for the end of my studies is the end of my life or senility, whichever comes first, so I’m not afraid of being told to go back and learn something specific.

Any property that can be present to a variable degree at any point in some region of space or space-time defines a corresponding field. Thus in principle there are as many real & physical fields as there are real & physical space-dependent properties, and it is impossible to get a complete list.

This makes sense on one level, but I would have thought that the standard model constrains the number of fields. Perhaps I am incorrectly thinking of fields as “a plucked string” which produces things we call fundamental particles. This, of course, leads to the question, “What is the plucked string?”

I don’t mean to wax philosophical, I just thought there might be a limited number of fields which I could see at a glance now rather than having new ones pop up at me throughout my learning. I like to see the overarching big picture of things before plunging into the heavy details.

 

[martinbn]

My questions about fields are very general and not specific to a particular text.

But you could give examples to make it clearer the level of answers you expect. So far it seems that your questions arise because you have read popular texts, on the other hand the thread is marked as "I" level.

 

[ParticleMan]

But you could give examples to make it clearer the level of answers you expect. So far it seems that your questions arise because you have read popular texts, on the other hand the thread is marked as "I" level.

I gave the example of Quantum Field, Higgs Field, and Gravitational Field. I also tried to clarify what I am looking for or invite correction of my view about fields. I did not think the questions were too vague.

The question is certainly general, and although it may come from a beginner/layperson view, I do not want high school answers but prefer in-depth explanations I can chew on. I thus marked it intermediate. I am currently reading Dirac’ Principles of Quantum Mechanics, but I tend to read multiple books at a time (also in progress are Feynman’s QED, Susskind’s Quantum Mechanics The Theoretical Minimum, and Klauber’s Student Friendly Quantum Field Theory).

 

[ParticleMan]

Further development of quantum field theory changed the focus of searching for unified field theory from classical to quantum description. Because of that, many theoretical physicists gave up looking for a classical unified field theory.[11] Quantum field theory would include unification of other two fundamental forces of nature, strong and weak nuclear force which act on subatomic level.[12][13]

https://en.m.wikipedia.org/wiki/Classical_field_theory

Considering attempts at unification, I would have thought there was a relatively small list of fields with the introduction of Quantum Mechanics, but I cannot seem to find a list of them. If they can be enumerated for Classical Field Theory, it seems like there would still be a relatively small list. Perhaps not, or perhaps no one has bothered with such a high level overview?

 

[ParticleMan]

I’m coming a bit closer to understanding A.Neumaier’s answer, I think. I finally found the video below. Please correct anything you find incorrect or misleading in it. Although the video made me chuckle, I can’t decide whether to call it funny. So, anyway, it seems like the best answer I might be able to get at my current level would be 37 fields, one for each item in the standard model. Agreed? Anyone like to muddy the water as food for thought?



Again, this also seems to beg the question, “What the heck is a field, really?”. Are they really just values that are somehow properties of space-time? Do we know? Speaking cosmologically, I assume these fields would have emerged with space-time at the big bang rather than somehow having a pre-existence?

Still really hoping for a bit more insight from others before I move on. I’m not the type to just learn and apply equations. I want to really get as good an intuitive understanding as possible.

 

[PeroK]

Still really hoping for a bit more insight from others before I move on. I’m not the type to just learn and apply equations. I want to really get as good an intuitive understanding as possible.

Do you have a specific question? That video, although crazy, just about said it all!

 

[ParticleMan]

Do you have a specific question? That video, although crazy, just about said it all!

Aside from all of my question marks above, I guess not. Where I work, we have a gentleman of high learning who loves to teach electromagnetics among other things and has the patience of a saint. Ask him a question, and you’ll get a book worth of information. Folks refer to these little sessions as “Chester Chats”. Unfortunately, I can’t take advantage of this rennaisance man as much as I would like. I guess I’m looking for but can’t necessaily expect that kind of intellectual stimulation elsewhere.

 

[A. Neumaier]

I like to see the overarching big picture of things before plunging into the heavy details.

Sometimes, the main purpose of learning is to figure out how to see properly! The big picture can hardly be understood before having first digested (at least to some extent) a number of paradigmatic special cases. You may wish to look at my theoretical physics FAQ, especially the sections in Chapter C4: How to learn theoretical physics.

t seems like the best answer I might be able to get at my current level would be 37 fields, one for each item in the standard model.

That's a good starting point., giving you a collection of (at the present level of understanding) fundamental fields. But there are also composite fields, an endless variety of them, and some of them come up when you go deeper in your studies. For example, out of the quark fields people make fields of mesons and baryons (figuring in effective field theories), and there are already a lot of different mesons and baryons.

See also the extended discussion of the question ''What is a field, really?''

 

[bhobba]

I think the following book will help and amaze you at the same time:
http://physicsfromsymmetry.com/

It explains, in a very natural way, the extension of particles to fields and the underlying core of it all, symmetry, a big part of which is a famous theorem by Emmy Noether - the greatest mathematician you probably never head of:
https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math

Why do we believe in fields like the EM field real in the same sort of way we think a particle is - deep question and requires a thread of its own to discuss. Start one if interested - you will learn a lot.

Thanks
Bill

 

[ParticleMan]

Thanks, both of you. Very good info I am starting to read through.

I can’t say the “What is a field, really?” was completely satisfactory to me. Unlike the questioner, I did ok in math, but I very much understand his frustration with having to just accept and apply without really understanding. It seems like, in the case of the fields discussed above, that no one really knows (added: i.e., what a field really is, which the answerer seemed to acknowledge on some level). Feynman’s (in)famous quote about QM comes to mind. We apply math and come up with answers which match real-world experimentation to a high degree, but we don’t really completely understand why. I read through the “myths” (a little strong, I think) about QM posted in another thread, so I need to rethink (unlearn?) some of the ideas I’ve taken away from the more popular literature I’ve read.

I might start a thread on the EM field as was suggested because I am interested, but it may be later. I’ve spent a bit too much time here the past couple of days and need to digest all the good info thrown my way.

 

[Vanadium 50]

It seems like, in the case of the fields discussed above, that no one really knows.

There is a difference between "I don't know" and "nobody knows". Like others have suggested, I think you should start with EM fields.

 

[ParticleMan]

There is a difference between "I don't know" and "nobody knows". Like others have suggested, I think you should start with EM fields.

Yes, I am currently revisiting my rusty college engineering studies from many years ago. I’m still not sure why you seem to be judging so harshly in this and other threads when I’m sincerely looking for answers, V., but when you provide information I find useful, I will listen to you just as well as to others. Do you feel I do not have the right to be a curious layperson with the time, interest, and possible capability to learn these subjects, or do you just think I’m too dumb based on a few posts on the internet? Don’t answer that. I don’t think I’d like the answer.

 

[Vanadium 50]

No, but I do think you need to get the basics down before jumping into more advanced subjects, and I think your suggestion that because you don't understand something nobody does deserves attention.

 

[ParticleMan]

No, but I do think you need to get the basics down before jumping into more advanced subjects, and I think your suggestion that because you don't understand something nobody does deserves attention.

I understand your reasonable opinion about the “basics”. I do. But, perhaps there is more common ground in our thinking than you might believe. In fact, were I talking to a college student bound for a physics career, I would certainly say the same. On some level, you might even say I am sort of doing what you suggest, just in a different manner. When I encounter something I don’t get, I go read about it or ask about it and then come back to the subject I’m interested in with a more informed perspective. When I first encountered an unexplained equation with a Bra and Ket, I thought “What the heck is this?”. So, I watched Leonard Susskind, yes, on youtube, and bought his book, Quantum Mechanics: The Theoretical Minimum. I know it’s a simple and somewhat popular treatment, but hopefully this says I’m not a crackpot assuming I know things I don’t.

With all due respect to what it takes to obtain a PhD, I disagree that a self-learner shouldn’t jump into advanced subjects they may not be fully prepared for if it’s something they’re interested in. I’ve had PhDs tell me tell me this before, but I learned and even contributed to their community. I have a lot of experience over the years learning tough subjects on my own by jumping in the deep end of the pool. Sometimes I sink. Sometimes I swim. I struggle. I embarrass myself. And I have AHA! moments. I love those. And I love learning things I’m interested in.

Oh, and I certainly did not mean for you to infer that because I do not know something, no one does. I thought I had read in the proffered link I was addressing that, yes, there are fields and they have meaning, but no one knows what they really are. That may be a poor paraphrase, sorry. I now understand there are quark fields, etc., and that they serve a purpose, but can you tell me what those fields really are? It just makes a neophyte think “Ether”. If I learn the equations others here know, will I then truly understand what those “particle fields” really are? Some would say it just doesn’t matter, but that answer rightly or wrongly bothers me.

 

[Vanadium 50]

Do you understand what an electric field is?

 

[PeterDonis]

If I learn the equations others here know, will I then truly understand what those “particle fields” really are?

It depends on what you think would count as an answer to the question of what those fields "really are". If you have a model that makes accurate predictions about all experiments we have currently done, up to and including the latest data from the LHC, is that enough to know what all the fields in that model (in this case the Standard Model of particle physics) "really are"? If not, what else would you need to know?

 

[PeterDonis]

will I then truly understand what those “particle fields” really are?

Another way of approaching this would be to ask: is there something that you think you do understand what it "really is"? If so, what is that something, and why do you think you understand what it "really is"?

 

[bhobba]

Ok what is an EM field? Well Feynman and Wheeler formulated EM without fields - by using some very weird assumptions:
https://en.wikipedia.org/wiki/Wheeler–Feynman_absorber_theory

But if you want to avoid that you need fields. Here is the exact reasoning. Let us say you have two charged particles interacting - the force between them can be calculated from Coulombs Law. Now move one particle and according to that law the other particle moves instantaneously. However relativity forbids this. So it moves a bit later. But there is a brief period of time when one is moving and the other is not. We however believe quite strongly in energy/momentum conservation (Noether's Theorem is very difficult to circumvent) so we need something to hold it during that small time period. That something is the field. From Coulombs Law alone and relativity you can derive Maxwell's equations:
http://www.cse.secs.oakland.edu/haskell/Special Relativity and Maxwells Equations.pdf

But the reason for fields is due to wanting energy/momentum conservation because of Noethers Theorem. Now another interesting thing - once you have Maxwell's Equations you can use Noether's Theorem and show the fields have energy and momentum. Mass is a form of energy - relativity tells us that - we think of mass as quite real hence we are forced to conclude, reasonably, that fields are real as well. A philosopher (and we do not discuss philosophy here) may challenge this but its reasonable and represents the kind of reasoning physicists do.

I suggest you first start with Noether's Theorem:
https://www.amazon.com/dp/1421422670/?tag=pfamazon01-20

Then not to move onto EM, but rather what I consider THE book on mechanics - Landau Mechanics:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

That will provide you with the background necessary to understand with greater ease more advanced stuff like the book I mentioned before (you could study it without the other stuff, but its easier if you do it first - just my opinion):
http://physicsfromsymmetry.com/

Once you have done that we can look deeper into what's going on with fields, even Quantum Fields.

Thanks
Bill

 

[ParticleMan]

Another way of approaching this would be to ask: is there something that you think you do understand what it "really is"? If so, what is that something, and why do you think you understand what it "really is"?

I liked the idea of the pilot wave theory to bring things back into the classical realm, but that seems dead now and was probably considered so before recent news.

Well, I’m definitely going to annoy someone with the following poor analogy and terminology, but I’ll take a stab at it with my currently limited knowledge.

A temperature field has a medium, for instance air.

Take a quark field. I can’t call quarks waves and/or particles if I read the “QM myths” paper correctly, but whatever they are, it seems like they need some medium...space-time? What do these fundamental particles arise from, or vibrate in, or whatever it is they do? Do the equations answer this question? Or would they simply tell me there is no need for a medium and I am stuck in classical thinking? Can you see where I am coming from? If not, I won’t belabor it anymore until I’ve read more. I need to take a break and go back to my reading anyway. This has all taken much more of my time than I expected for what I incorrectly thought would be simple answers...though partly because I should leave well-enough alone.

 

[ParticleMan]

Just wanted to say thanks, Bill and A. Neumaier. I am reading your posts and links lest you think my lack of response means your responses to me are being ignored. You may hold the same beliefs about how to go about learning that have been expressed, but I appreciate your tone and all the information.

 

[PeterDonis]

A temperature field has a medium, for instance air.

Ok, and how do you know what the air "really is"? If you dig down, you find that the air is made of molecules, which are made of atoms, which are made of electrons and quarks, which are made of--what? Fields? I would say they are fields, but either way, this thing you appear to think helps you to know what temperature "really is"--a medium--is actually made of the things that you don't know what they "really are". So what has all of this gained you? Nothing, as far as I can see.

I can’t call quarks waves and/or particles if I read the “QM myths” paper correctly, but whatever they are, it seems like they need some medium...space-time?

If you want to call spacetime a "medium", yes, but it might not have all the properties you expect a medium to have.

But more importantly, I think you are using a mistaken analogy here. The "medium" of a temperature field is made of fields, as I said above. So I don't see how "having a medium" helps you to understand what fields "really are".

 

[ParticleMan]

Ok, and how do you know what the air "really is"? If you dig down, you find that the air is made of molecules, which are made of atoms, which are made of electrons and quarks, which are made of--what? Fields? I would say they are fields, but either way, this thing you appear to think helps you to know what temperature "really is"--a medium--is actually made of the things that you don't know what they "really are". So what has all of this gained you? Nothing, as far as I can see.

Granted. It certainly makes it seem like a reductio ad absurdum with no answer. So, the point is that a field is just a field and that’s that?

I guess I’m being told that the question just doesn’t make sense in QM?

If you want to call spacetime a "medium", yes, but it might not have all the properties you expect a medium to have.

Unless the question doesn’t make sense, then this sounds like a possible thought to keep in the back of my head.

I just have difficulty thinking about something that seems to have no “frame” to hang on or emerge from. Well, anyway, I won’t continue to beat a dead horse. Thanks for continuing to humor me.

 

[PeterDonis]

the point is that field is just a field and that’s that?

The point is that you need to think very carefully about what would count as an acceptable answer to your question of what a field "really is".

I guess I’m being told that the question just doesn’t make sense in QM?

It's much more basic than QM. You need to get clear about what you really want to know when you ask what something "really is". I don't think you're clear about that, and you can't expect a clear answer if you aren't asking a clear question.

 

[ParticleMan]

A last anecdote for those who teach, if I may be indulged. Ironically, it was a college Physics professor who initiated me into self-study. He would read from his own textbook and then tell folks to read the book rather than actually try to teach. I was so bored to tears in his class, that I completely stopped going to his class and just read his book instead. I passed the class with flying colors. Just my two cents.