rich

question about fields

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A very stimulating earlier post in this group from a few months ago ("Einstein vs. Newton") taught that space is not a "container" in which objects exist, but a relation between objects. Thus, if all the matter in the universe were to disappear, space would also cease to exist.

I accept this argument.

But, is this also true for fields? For instance, if only a single electron exists in the universe, and absolutely no other matter, would that electron still project an electric field? Does a field require something to act on in order to exist?

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A very stimulating earlier post in this group from a few months ago ("Einstein vs. Newton") taught that space is not a "container" in which objects exist, but a relation between objects. Thus, if all the matter in the universe were to disappear, space would also cease to exist.

If you mean "matter" as Ayn Rand used it philosophically in ITOE (p. 289), "that of which all the things we perceive are made," there is no philosophical requirement, and none currently known to science, that "matter" be all that exists.

But, is this also true for fields? For instance, if only a single electron exists in the universe, and absolutely no other matter, would that electron still project an electric field? Does a field require something to act on in order to exist?

The "field" concept in physics is a very nebulous term, very much dependent on the particular theory being used. A "field" can be meant as anything from a mathematical convenience, to an actual existent. And, within the same theory, it can be used sometimes as both. Maxwell's field is not the same field as in quantum field theory, and it is different again in some aspects of condensed matter physics. Likewise for the gravitational field of general relativity.

Now, if you want an answer to your questions based on how I think the world actually is, then I refer you to Lewis Little's Theory of Elementary Waves (TEW). The TEW dispenses with the field concept entirely, and on the fundamental level all that exists are real particles and real elementary waves. I do not know what it means to "project an electric field," but a single electron will follow a path along its elementary wave. The elementary wave exists independent of the electron, but the electron depends on the existence of the elementary wave. You can read about this theory on a non-technical level here, or on a more technical level here.

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A very stimulating earlier post in this group from a few months ago ("Einstein vs. Newton") taught that space is not a "container" in which objects exist, but a relation between objects. Thus, if all the matter in the universe were to disappear, space would also cease to exist.

I accept this argument.

But, is this also true for fields? For instance, if only a single electron exists in the universe, and absolutely no other matter, would that electron still project an electric field? Does a field require something to act on in order to exist?

First of all you have to be careful with phrases like "if all the matter ceased to exist" or "if only a single electron exists". You were only using that wording to emphasize a dependency, but in fact all matter does exist and only one electron does not, so you have to be very careful not to rationalize about a fictitious universe.

A field is a high level abstraction. As such it has ultimate referents in physical reality, but the concept of a field depends on all kinds of prior knowledge of entities, forces and mathematical relations integrated into the abstract concept of a field. An electric field, in particular, depends on both the concepts of space and forces between charges -- which means it depends on having more than one electron as well as having the matter which gives rise to the concept of space. To literally ask if there could be such a field in a universe with one electron and no other matter is meaningless rationalism.

Just as you understand the concept of space as an abstract relation that depends on matter, to understand the concepts of different kinds of fields as high level abstractions, you have to go back and look at the physics, the mathematics and the perceptual knowledge of entities -- all the way down to human-scale measurements from which inferences are made -- that are required to form such a concept of a field and why.

An electrostatic field is a mathematical formulation of a theory that accounts, at a higher level of abstraction, for real forces between real electrons, but there are no "lines of force" reified in physical reality. The concept of an electromagnetic wave in accordance with Maxwell's equations and his prediction of the existence of such a wave as later confirmed by Hertz is a much higher level abstraction. We -- and Maxwell -- could form such a concept based on observable physical phenomenon without have to answer the more advanced questions of physics about what else is going on at a microscopic level that make this possible and how that all works. Whatever new physical phenomena are discovered and inferred to further explain that, and by whatever means we ultimately possess to know it, the electromagnetic field remains a scientific abstraction. It is objective, not intrinsic.

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A field is a high level abstraction. As such it has ultimate referents in physical reality, but the concept of a field depends on all kinds of prior knowledge of entities, forces and mathematical relations integrated into the abstract concept of a field....`

An electrostatic field is a mathematical formulation of a theory that accounts, at a higher level of abstraction, for real forces between real electrons, but there are no "lines of force" reified in physical reality. The concept of an electromagnetic wave in accordance with Maxwell's equations and his prediction of the existence of such a wave as later confirmed by Hertz is a much higher level abstraction. We -- and Maxwell -- could form such a concept based on observable physical phenomenon without have to answer the more advanced questions of physics about what else is going on at a microscopic level that make this possible and how that all works. Whatever new physical phenomena are discovered and inferred to further explain that, and by whatever means we ultimately possess to know it, the electromagnetic field remains a scientific abstraction. It is objective, not intrinsic.

But Maxwell, and some of his followers, for the most part held the electromagnetic field, not simply as an abstraction, but as the action of an actual medium. It is true that Maxwell sought to remove the Newtonian action-at-a-distance, but throughout most of his life he did so by positing various physical mechanisms that produce the electromagnetic phenomena. So the question of the reality of such an elctromagnetic medium, in each and every theory that posits its real existence, becomes a question of truth or falsity. When posited as a mathematical abstraction -- more as a concept of method -- then the truth or falsity of the abstraction is dependent on the physical content of the theory. And here I speak of physics that rises to the level of theory, not simply that which offers prediction.

The question asked by Rich contains, if not explicitly then implicitly, the desire to know the ontological status of the concept of field, and what is its nature. And to that point I think that the historical facts show what I indicated earlier, that the concept as used in various theories is often quite nebulous, and sometimes contradictory.

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The question asked by Rich contains, if not explicitly then implicitly, the desire to know the ontological status of the concept of field, and what is its nature.

That is exactly what I'm asking.

As a side note, I realize that the concept of a field is a bit wishy-washy, or "nebulous" as Stephen describes. Perhaps we need some new terminology? Maybe instead of saying "field" we would do better to say "spread" or some other word describing what we envision to occur in nature.

And I will definitely check out Little's paper, thanks for the link to that.

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The question asked by Rich contains, if not explicitly then implicitly, the desire to know the ontological status of the concept of field, and what is its nature.
That is exactly what I'm asking.

And both parts are exactly what I am talking about, too. The "ontological status of the concept" means "the problem of universals", which practically begs for AR's epistemology -- with a particular emphasis in this case on the nature of a hierarchy of conceptual knowledge and its role in forming a high level abstract concept; this is essential to understand. The "nature" of the field, on the other hand, requires physics explaining the attributes of a field. Putting those two together makes it possible for you to know what the concepts refer to and how -- while leaving it open to learn more about them as new discoveries and explanations are made.

The concept of an electrostatic and other kinds of fields are, properly construed, not just concepts of mathematics; they are formulated mathematically but are concepts of physics -- they refer, no matter how abstractly formulated, to real phenomena and not just methods of calculation of a force, etc. Especially as a physicist you naturally want to discover and understand as much about the nature of fields that you can, but you can understand the concept of a field such as E in terms of your presently known facts. Anything further that turns out to reveal and explain a mechanism, whether TEW or anything else, is an expansion of knowledge of the nature of some kind of field, obtained by further abstract inferences. Such an expansion is a worthy and desirable goal (as it was for Maxwell himself), but would be added to your understanding of a concept you can understand now.

As a side note, I realize that the concept of a field is a bit wishy-washy, or "nebulous" as Stephen describes. Perhaps we need some new terminology? Maybe instead of saying "field" we would do better to say "spread" or some other word describing what we envision to occur in nature.
It is true that as normally presented, the "concept of a field is a bit wishy-washy, or 'nebulous'" -- to say the least: this is more than a "side issue". We have all been through this. The presentation of even simple fields such as the electrostatic field and the relatively simple facts on which it is based causes conceptual confusion right from the beginning, but not because of a lack of physics, rather because of a lack of understanding of the nature of abstract concepts.

The usual questions are: But what does that concept really mean? Is it a "thing" out there? If so what is it really? The typical unsatisfactory response eventually settled on is either intrinsicism or subjectivism: either reifying the field into something mystical or treating it as an arbitrary mathematical construct. The first retains the mystery, as if the concept itself cannot be understood without somehow discovering something else (which by the standards implied, would never be enough); the second essentially gives up as a matter of principle, surrendering to arbitrary "pragmatic" mental manipulations as a chronic way of thought. But if you understand how abstract concepts work objectively, you can see how you can use the concept of a field as an integration of the known facts that give rise to it -- while recognizing that there is still more to learn about its meaning as your knowledge expands and science advances.

Rich: Perhaps we need some new terminology? Maybe instead of saying "field" we would do better to say "spread" or some other word describing what we envision to occur in nature.
You need some word as a symbol for the concept so you can treat it as a mental entity in your thought, but how would switching from "field" to "spread" make any difference? It's not that you had it confused with corn fields! If "field" had some connotation that was confusing you, that isn't the primary source of the problem as you grasp for a proper meaning.

We gain knowledge of phenomena that we cannot perceive directly by inferring its attributes and forming higher level abstract concepts. You need to think in terms of the two questions: 1)what are the known facts of the physics that give rise to the concept, and 2) what is the epistemology of how the concept is formed based on the facts and in what way does such an abstract concept refer to reality? For the first you already have the facts you need in typical physics books; for the second you should make sure you understand AR's Introduction to Objectivist Epistemology, including the large addendum on the seminars she gave.

You will find this same problem over and over throughout science. A lot of brilliant and creative science has been developed over the centuries, exploding with progress ever since the Enlightment, but the more abstract it becomes, the harder it is to properly formulate and understand. The lack of a good explicit epistemology has necessarily corrupted and undermined theoretical science, but AR's theory of concepts now makes it possible to do much better. I think that there is a lot of work to be done in properly formulating and understanding even classical physics, let alone bizarre modern theories.

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The question asked by Rich contains, if not explicitly then implicitly, the desire to know the ontological status of the concept of field, and what is its nature.

That is exactly what I'm asking.

And both parts are exactly what I am talking about, too. The "ontological status of the concept" means "the problem of universals", which practically begs for AR's epistemology -- with a particular emphasis in this case on the nature of a hierarchy of conceptual knowledge and its role in forming a high level abstract concept; this is essential to understand.

I do not know why this relatively simply issue is getting complicated by so many words. I think one thing Rich wants to know is if a field, as used in physics, exists in physical reality, or is it just a mathematical concept. And, to that point, as I have mentioned, the answer depends upon the particular theory in physics. And, even worse, unfortunately in some theories it is alternately used as one and then the other.

The concept of an electrostatic and other kinds of fields are, properly construed, not just concepts of mathematics; they are formulated mathematically but are concepts of physics -- they refer, no matter how abstractly formulated, to real phenomena and not just methods of calculation of a force, etc.

But that is simply not the case. For instance, in standard quantum field theory the canonical quantization of the scalar field results in a Fock space with states that reflect the old-fashioned wave-particle duality. This is then generalized to field-particle duality, which lies at the core of particle theory. Then along comes supersymmetry, field theories uniting particles and spin into symmetry multiplets. One formalism developed in this context is the construction of general superfields, supermultiplets of fields and supersymmetric actions. This entire mathematical apparatus has no direct referent in reality, but it is useful in solving certain problems just as is the much more simple operator "i."

And in other simpler theories, from classical physics on, one can identify aspects similar to this much more complex formulation of fields. A careful reading of even Maxwell will reveal a duality in his use of the field.

Especially as a physicist you naturally want to discover and understand as much about the nature of fields that you can, but you can understand the concept of a field such as E in terms of your presently known facts. Anything further that turns out to reveal and explain a mechanism, whether TEW or anything else, is an expansion of knowledge of the nature of some kind of field, obtained by further abstract inferences. Such an expansion is a worthy and desirable goal (as it was for Maxwell himself), but would be added to your understanding of a concept you can understand now.

But therein lies the problem. In any given theory, to the degree that the field concept is not true knowledge then to that degree there is nothing there to expand. Whether it be a mathematical concept with no direct connection to reality, or a physical concept of pure fiction, is irrelevant if the theory and the concept are wrong.

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From the way Rich put his question it appears from his example that he was talking about a simple electrostatic field related to Coulomb's law in classical physics. I think that if he develops a good understanding of the epistemology of that he will have a good start in being able to separate out what is valid from the floating abstractions and constructs that came later, as well as bad epistemology in classical physics. The quantum theory you refer to is what I had in mind by "bizarre modern theories" and which I would not begin to try to discuss :angry2:. Maybe Rich could clarify what he meant.

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From the way Rich put his question it appears from his example that he was talking about a simple electrostatic field related to Coulomb's law in classical physics.

Okay. Then using this most simple case, answer the question that was posed: "if a field, as used in physics, exists in physical reality, or is it just a mathematical concept?" Succinctly, please. Assume we understand the technical details, and already have the philosophic perspective.

The quantum theory you refer to is what I had in mind by "bizarre modern theories" and which I would not begin to try to discuss.

I wouldn't be so dismissive. Though I do not agree with supersymmetric theories in general, there are interesting issues that arise.

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Okay. Then using this most simple case, answer the question that was posed: "if a field, as used in physics, exists in physical reality, or is it just a mathematical concept?" Succinctly, please. Assume we understand the technical details, and already have the philosophic perspective.
The original question was: "if only a single electron exists in the universe, and absolutely no other matter, would that electron still project an electric field? Does a field require something to act on in order to exist?" That was later replaced with the more direct and better formulated question: what is the ontological status of the concept, and what is the nature of the field. A narrower but very important question implicit in that is whether a field exists in reality vs. being only a mathematical concept, and I wrote, "they refer, no matter how abstractly formulated, to real phenomena [i.e. in physical reality] and not just methods of calculation [i.e., mathematics]". That is as succinct as I can put it, but it doesn't say "why", and this issue (let alone the broader previous question) can't be covered in one or a few sentences.

The concepts of physics, no matter how mathematically formulated to attain the required precision, refer to physical phenomena of specific kinds in specific relations. A particular kind of field, e.g., an electric or magnetic field, a gravitational field, a stress field, or a flow field, refers to something specific in physical reality even though represented in the mathematical form of a vector or tensor function (which mathematics is therefore also included in the meaning).

In contrast to any specialized physical science, concepts in mathematics, while also based ultimately on reality, are in the form of the widest possible abstractions: Mathematics begins with and is based on abstractions of units for any kind of existents, and proceeds with methods of relating them without regard for the units or what the physical measurements are.

However, while a field is a concept of physics and not a concept of mathematics, you can say the concept is mathematical (as in "mathematical physics") because it is mathematically formulated, without which the required precision would not be possible, but that is not the same thing as being only a concept of mathematics.

A lot more could be said burrowing into all kinds of issues this raises, but I think this at least directly answers the question with a basic explanation of why.

I wouldn't be so dismissive. Though I do not agree with supersymmetric theories in general, there are interesting issues that arise.
You have more direct knowledge and experience with modern physics than I do, but from what I can tell, we agree that there are interesting, important discoveries and formulations and that many mathematical constructs have impressive predictive capacity even while modern theories are often sorely lacking in explanatory value or even lacking comprehensible basic concepts of the physics (like in quantum mechanics, hence the drive to develop TEW).

Scientific progress did not stop with the decline in Enlightenment philosophy, and we see the results of it all around us, but there are also some epistemologically bizarre theoretical notions and formulations put forth in the name of science. (That does not mean that "bizarre" actual facts cannot be discovered.) I have seen enough of this first hand to know how bad it can get, but I will also not completely dismiss out of hand as totally worthless all aspects of suspect theories I have not investigated.

I want to emphasize that I have found Objectivist epistemology to be of enormous value in gaining a sensible understanding of many concepts and principles in mathematics and physics (especially classical) that would otherwise be conceptually, if not necessarily technically, puzzling. (I hope to see the influence of AR's epistemology on your own thinking in the book on physics you once said you were going to write -- are you still doing that?) When the theories are too badly corrupted, however, the epistemology isn't enough: Someone has to go back and do or re-do the science. But that requirement does not mean nothing important or of interest had been discovered or identified.

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Okay. Then using this most simple case, answer the question that was posed: "if a field, as used in physics, exists in physical reality, or is it just a mathematical concept?" Succinctly, please. Assume we understand the technical details, and already have the philosophic perspective.

The original question was: "if only a single electron exists in the universe, and absolutely no other matter, would that electron still project an electric field? Does a field require something to act on in order to exist?" That was later replaced with the more direct and better formulated question: what is the ontological status of the concept, and what is the nature of the field. A narrower but very important question implicit in that is whether a field exists in reality vs. being only a mathematical concept, and I wrote, "they refer, no matter how abstractly formulated, to real phenomena [i.e. in physical reality] and not just methods of calculation [i.e., mathematics]".

To speak of "real phenomena" without specification is not saying much about physics. The expression sounds correct philosophically, but is devoid of physical content. Specify a field theory in physics and I will demonstrate its contradictions as presented by its originator and its standard promulgators alike. Which is essentially what I said in response to Rich, and why I pointed him to the TEW if he wants to understand the "real processes" of physics rather than the contradictions of "field."

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Specify a field theory in physics and I will demonstrate its contradictions as presented by its originator and its standard promulgators alike. Which is essentially what I said in response to Rich, and why I pointed him to the TEW if he wants to understand the "real processes" of physics rather than the contradictions of "field."
How about what may be the simplest cases because they are less abstract and known more directly: velocity and stress fields in a fluid. Or did you mean something more abstract than that like E&M or gravity?

Do you mean that TEW will replace Maxwell's equations, eliminating E, B, etc., or that it provides a completely different meaning for what E, B etc. refer to while still retaining the same mathematics of a vector function defined over space and time, or something else?

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How about what may be the simplest cases because they are less abstract and known more directly: velocity and stress fields in a fluid. Or did you mean something more abstract than that like E&M or gravity?

Not simply more abstract, but any real field theory where the field is fundamental and can possibly be taken as a mathematical description or itself as a part of physical reality. It is not possible to conflate the convenience of the mathematical representation of a simple velocity field in fluid dynamics, with the continuous medium itself. Not so with actual field theories outside of continuum mechanics, like electromagnetic, gravitational, or quantum field theories.

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Well, after glancing through Little's paper (and being completely bewildered for the most part!), it seems I am in no position to debate the physical/metaphysical/ontological status of fields. I am by no means an expert on field theories; I am a 2nd year master's student in physics, and my research is in no way related to field theory. So I'll have to do a lot of independent study before I can begin to examine the nature of a field.

To clarify my original question in this topic, I'll describe a thought I had recently. From the "Newton vs. Einstein" topic in this forum, I learned that space is defined to be a relationship between objects, and has absolutely no existence in and of itself; the old Newtonian notion that space is a "container" of matter is wrong, and Einstein's notion of space being only a relationship amongst objects is correct. Okay. But....that would mean that there exists absolutely nothing beyond the edges of physical universe; in other words, the matter that resides farthest from us defines the edge of space: there is nothing "beyond" that, not even space. So...say an electron resides at that edge. Of course this electron is surrounded by its own electric field (however one defines such a field), as are all electrons. But since the electron resides at the edge of space, can its field extend out in ALL directions, including the region of "no space"? Or will it only extend inward, toward other objects, and not outward, where there are no other objects and therefore no space?

Hence my original question: does a field require space to exist?

I hope this clarifies my original question! Thanks guys!

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To clarify my original question in this topic, I'll describe a thought I had recently. From the "Newton vs. Einstein" topic in this forum, I learned that space is defined to be a relationship between objects, and has absolutely no existence in and of itself; the old Newtonian notion that space is a "container" of matter is wrong, and Einstein's notion of space being only a relationship amongst objects is correct. Okay. But....that would mean that there exists absolutely nothing beyond the edges of physical universe; in other words, the matter that resides farthest from us defines the edge of space: there is nothing "beyond" that, not even space.

More specifically, there is no "edge" to the universe. An edge defines a boundary, and the universe is boundless by nature. The universe is ... all that is, so there cannot be edge separating the universe from something else.

So...say an electron resides at that edge. Of course this electron is surrounded by its own electric field (however one defines such a field), as are all electrons. But since the electron resides at the edge of space, can its field extend out in ALL directions, including the region of "no space"? Or will it only extend inward, toward other objects, and not outward, where there are no other objects and therefore no space?

But now the question is less clear than before. There is no region of "no space." As discussed previously, the universe is a plenum -- it is full, no gaps or holes. As I mentioned in this post , even if somewhere there are no perceptual matter objects that does not mean that , literally, nothing at all is there.

Implicit in your question as now posed is, I think, the question of the shape of the universe. This has been discussed in some detail in several threads. The bottom-line is that the very concept of "shape" does not apply to the universe. You can do a search on some of these key words to find those threads.

Hence my original question: does a field require space to exist?

Define exactly what you mean by "field" and pick the physical theory in which that concept is so understood, and then I can answer your question in the context of that theory.

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Hence my original question: does a field require space to exist?
Define exactly what you mean by "field" and pick the physical theory in which that concept is so understood, and then I can answer your question in the context of that theory.

I should add that for the TEW the answer is trivial: there is no mythical "field." The elementary waves are omnipresent -- they exist everywhere and everywhen -- and particles simply follow their associated waves. In the TEW this is true, both mathematically and physically.

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Define exactly what you mean by "field" and pick the physical theory in which that concept is so understood, and then I can answer your question in the context of that theory.

By "field" I mean whatever mechanism by which an object exerts a force on another object. For simplicity, I'll choose the electric field E of electromagnetic theory. Anything you can tell me about the existence (or lack thereof) of this field, I'd appreciate. Thanks, and I apologize for not having read the previous threads in this Forum that deal with the structure of the universe, etc.

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By "field" I mean whatever mechanism by which an object exerts a force on another object. For simplicity, I'll choose the electric field E of electromagnetic theory. Anything you can tell me about the existence (or lack thereof) of this field, I'd appreciate.

Your questions, "does a field require space to exist?" and "the existence (or lack thereof) of this field," both imply that you want to know what is real in physical reality. That being the case, your characterization of the classical E field related to force presents a problem. When field and force are specified in the theory, the E field is expressed as force per unit charge at a point. Because of the discrete nature of charge, the standard theory uses a mathematical limiting process for which there is no direct correspondence to physical reality. On that account alone the real existence of the E field is to be questioned. Also, note in the theory the E field does not itself have an independent existence. A pure E field in one reference frame can be some combination of E and B fields in another frame.

As to "space," considering the electromagnetic field, (at least one part of) Maxwell certainly speaks of his electromagnetic field as a part of space:

"(4) The electromagnetic field is that part of space which contains and surrounds bodies in electric and magnetic conditions.

It may be filled with any kind of matter, or we may endeavour to render it empty of all gross matter ..." [1]

This too is reflected in more modern formulations, such as in this standard graduate text in classical electrodynamics.

"... electromagnetic fields can exist in regions of space where there are no sources. They can carry energy, momentum, and angular momentum and so have an existence totally independent of charges and currents."

So, in this theory it seems that the electromagnetic field is taken (at times) as something existing in physical reality, but its existence is itself somehow within the context of space.

[1] "A Dynamical Theory of the Electromagnetic Field," J. Clerk Maxwell, Philosophical Transactions of the Royal Society of London, Vol. 155, p. 460, 1865.

[2] Classical Electrodynamics, J. D. Jackson, Second Edition, John Wiley and Sons, Inc., p. 3, 1975.

Thanks, and I apologize for not having read the previous threads in this Forum that deal with the structure of the universe, etc.
Nothing to apologize for. No one is expected to read all of the earlier threads, though it is always nice not to have cover the same material again. If you have a specific question related to that subject, by all means bring it up.

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Sorry to jump in here - I have a few small questions/comments. In general I'm a bit confused about the distinction between real physical existents and epistemological devices being made here (I'm not denying there is a difference, I'm just having difficulty pinning this issue down).

Your questions, "does a field require space to exist?" and "the existence (or lack thereof) of this field," both imply that you want to know what is real in physical reality. That being the case, your characterization of the classical E field related to force presents a problem. When field and force are specified in the theory, the E field is expressed as force per unit charge at a point. Because of the discrete nature of charge, the standard theory uses a mathematical limiting process for which there is no direct correspondence to physical reality.

Well in classical electromagnetism charge needn't be quantized, though it is indeed quantized in QED. But regardless, I don't quite see why this means that fields cannot be regarded as a physical existent. Instead of defining a field by its action on a charge, one could take the following view. The electric/magnetic fields E and B are fundamental physical existents as are the particles. The fields are constrained by Maxwell's equations with sources, while the Lorentz force law tells charged particles how to behave in the presence of fields. (In this way the fields are not defined by their effect on charges - though that's undoubteldly how you measure them in the lab. Instead they're fundamental and the action of charges in their presence is a dynamical law.) What's wrong with this picture?

On that account alone the real existence of the E field is to be questioned.Also, note in the theory the E field does not itself have an independent existence. A pure E field in one reference frame can be some combination of E and B fields in another frame.

OK well one could take the physical existent to be the tensor F_uv instead of the field E - and I don't think the claim has substantially changed.

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Instead of defining a field by its action on a charge, one could take the following view. The electric/magnetic fields E and B are fundamental physical existents ...

By Faraday or Maxwell induction, one field produces the other, which is hardly a characteristic of "fundamental physical existents." Charge is invariant under transform, but not so for E and B. Anyway, the context here was the standard theories, not presentation of alternatives (aside from the TEW). There are other forums that are more receptive to discussion of Jefimenko, Bohm, and the endless array of ether formulations and the like. I do not want such discussions here.

OK well one could take the physical existent to be the tensor F_uv instead of the field E ...

Yes, of course. But the question was not asked about the tensor, it was asked about one of its elements, the E field.

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By Faraday or Maxwell induction, one field produces the other, which is hardly a characteristic of "fundamental physical existents." Charge is invariant under transform, but not so for E and B. Anyway, the context here was the standard theories, not presentation of alternatives (aside from the TEW). There are other forums that are more receptive to discussion of Jefimenko, Bohm, and the endless array of ether formulations and the like. I do not want such discussions here.

I have little interest in either Bohm or the ether and was certainly not attempting to promulgate the ideas behind these (and I don't know much about Jerimenko or TEW). I was merely suggesting a possible way of interpreting the standard theory so that the electric and magnetic fields are indeed physical existents. It seems to me that they are generally treated as real physical entities in standard classical electromagnetism (not least because they make a contribution to the total energy of the system, required for conservation of energy); however your first sentence confirms my suspicion that I don't really understand what properties are required of something for it to be considered a "fundamental physical existent". I'll read more then possibly get back if that's OK.

Yes, of course. But the question was not asked about the tensor, it was asked about one of its elements, the E field.

My reason for making that remark is that the content of the E,B fields is exactly equivalent to the content of the F_uv tensor - so that if your objection was indeed an obstacle to treating E,B as fundamental physical existents couldn't that be resolved by replacing E,B with the (essentially equivalent) tensor F_uv?

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I was merely suggesting a possible way of interpreting the standard theory so that the electric and magnetic fields are indeed physical existents. It seems to me that they are generally treated as real physical entities in standard classical electromagnetism (not least because they make a contribution to the total energy of the system, required for conservation of energy) ...

Yes, in the standard theory they are often treated as real (not necessarily as "physical entities"), but not consistently nor non-contradictorily so.

... however your first sentence confirms my suspicion that I don't really understand what properties are required of something for it to be considered a "fundamental physical existent".

The term "fundamental physical existents" was your own, and I take "fundamental" here to mean not explainable by, not composed of nor caused by anything more basic. That the E field can produce the B field, and that one may be transformed into the other, is evidence that they are not fundamental, whether they are "physical entities" or not.

My reason for making that remark is that the content of the E,B fields is exactly equivalent to the content of the F_uv tensor - so that if your objection was indeed an obstacle to treating E,B as fundamental physical existents couldn't that be resolved by replacing E,B with the (essentially equivalent) tensor F_uv?

One prime motivator for Einstein in his development of special relativity was the the identification that the "existence of an electric field was therefore a relative one, depending on the state of motion of the coordinate system being used, and a kind of objective reality could be granted only to this electric and magnetic field together, quite apart from the state of relative motion of the observer or the coordinate system." (Reference here .) The tensor F_uv is then a mathematical representation of the electromagnetic field, but E and B are not then "essentially equivalent" except as elements of the tensor, without implying that either are "fundamental physical existents." So, yes, we agree that (one aspect) of the objection [the relative existence of E and B] is removed by reference to the electromagnetic field (if taken as fundamental and real). But, again, that was not the question originally asked.

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Sorry I've been away for a few days, I've been having computer problems.

I understand what you mean, Stephen, when you say that a field cannot be defined in terms of force, because "force per unit charge" carries some ambiguity due to the discrete nature of charge. So I will have to define "field" in a way that does not involve forces. And I'm having trouble doing this!

.... the standard theory uses a mathematical limiting process for which there is no direct correspondence to physical reality. On that account alone the real existence of the E field is to be questioned.

Are you referring to the Dirac delta function(al)?

As to Jackson's textbook: my university is one of the only universities in the country to NOT use Jackson. Much to my dismay, my graduate E&M class used Landau and Lifshitz' book The Classical Theory of Fields.

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Are you referring to the Dirac delta function(al)?

Not exactly, more to the E field at a point. As Jackson points out regarding observation (p. 28), "... one unit of charge may be so large that its presence alters appreciably the field configuration of the array. Consequently one must use a limiting process whereby the ratio of the force on the small test body to the charge on it is measured for smaller and smaller amounts of charge." This limiting process can be achieved mathematically, but not physically.

As to Jackson's textbook: my university is one of the only universities in the country to NOT use Jackson. Much to my dismay, my graduate E&M class used Landau and Lifshitz' book The Classical Theory of Fields.

Jackson is certainly more comprehensive, but L & L, like most all of their books, is an excellent presentation for physicists. These two texts really make for different courses, though it depends upon how your professor organizes the material. For instance, L & L presents relativity right up front, which I think is the proper way to do it. And of course the substantial inclusion of gravitation in L & L is absent in Jackson.

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Thanks for the reply.

The term "fundamental physical existents" was your own, and I take "fundamental" here to mean not explainable by, not composed of nor caused by anything more basic.

OK.

That the E field can produce the B field, and that one may be transformed into the other, is evidence that they are not fundamental, whether they are "physical entities" or not.

I admit I don't really understand the first part. It's possible for distinct, fundamental existents to have a causal effect on each other isn't it?

You mentioned TEW in another post. Based on my somewhat shaky understanding of this, I think it's correct to say that elementary waves and particles are both considered to be fundamental and real. The particles are guided by their elementary wave and the elementary waves, in turn, are locally affected by the configuration of the detectors.

Granted the elementary waves are not actually _produced_ by the particles per se - they are merely affected and would exist anyway. They are omnipresent (again assuming my understanding is correct). However in a similar way one could say that the E,B fields in standard electromagnetism are not actually produced by induction but are merely affected in that way - they would exist anyway, possibly with value 0.

The point being: is it anymore dubious to say that E,B fields are real and fundamental and can affect each other (through induction) than it is to say that particles and elementary waves are both fundamental and real and can affect one another?

One prime motivator for Einstein in his development of special relativity was the the identification that the "existence of an electric field was therefore a relative one, depending on the state of motion of the coordinate system being used, and a kind of objective reality could be granted only to this electric and magnetic field together, quite apart from the state of relative motion of the observer or the coordinate system." (Reference here .) The tensor F_uv is then a mathematical representation of the electromagnetic field, but E and B are not then "essentially equivalent" except as elements of the tensor, without implying that either are "fundamental physical existents." So, yes, we agree that (one aspect) of the objection [the relative existence of E and B] is removed by reference to the electromagnetic field (if taken as fundamental and real). But, again, that was not the question originally asked.

OK agreed - it was a modification. I think that regarding E,B as real probably does suffer from the problem you raise regarding Lorentz transformations. My current picture of classical electromagnetism is as follows: the tensor field F_uv and the charged particles are both real and fundamental, and these fundamental existents can each have a causal effect on each other (as described by Maxwell and the Lorentz force law).

(Of course there are other interesting issues/problems - like the self-energy problem for charged particles. However I didn't want to address these as it seems non-essential to the issue of whether the fields can be regarded as real, in principle at least.)

Thanks.

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