## Quantum realism and fields.

Discussions ranging from space technology, near-earth and solar system missions, to efforts to understand the large-scale structure of the cosmos.

### Re: Quantum realism and fields.

Well, if quantum field theory is merely an adjunct of Relativity theory, then, what is meant by an 'observer' in quantum field theory?

Events and observers with observations of them are what relativity theory gives us. An observer, observing an event does so only because light from the event traverses the distance (at fixed speed) and informs the observer of the event. One can draw inferences about the event knowing the distance and speed of light. But observers, without intelligence, can only respond to them as if they were random variables. Evolution by natural selection has made it possible for organisms with brains and eyes to become informed of objects at some distance from them. But, that's a narrower class of observers than has come to be regarded more recently, as I understand it, anyway.

Can observers observe light? If one thinks about this, it doesn't seem to make sense. Light itself is not an event. Similarly light cannot be an observer. Relativity theory regards light merely as a limiting factor to the speed of massive particles. It is supposed that light exists as a form of radiation and has been packetized in the form photons, but these are known only indirectly through observations of a particular kind, and understood as carriers of information, information that observers receive about what is observed. Perhaps such information is gathered only because of the accumulation of similar observations, notwithstanding, as in the EPR experiments, one is sufficient.

So, what about the reality of the passage of light from the event to the observer? This is what is being sought. Does it pass through a field of its own making? And does this field affect the passage? Is that what is being talked about in QFT? I chose the electron field in my previous post because of the work of Maxwell/Faraday. But, I was motivated to write about it in the way I did because this "field theory" being promoted seemed to me to draw attention to the primacy of the field over the particle supposedly generating it? If I understand Faradave's approach, photons themselves are ghosts, and don't play a significant role in relativity theory. The quantization of QFT is associated with the field, not the particle, reducing the particulate property to the events and observations that take place within it, not having any more effect than that. (Of course, massive (and energetic) objects are affected by being in a gravitational field, and charged objects are affected by being in a charged field, but I'm not aware of how this plays out, respecting the quantized, particulate formulation of these objects.)

Note, my apologies if I'm off-base. I'm more or less throwing out thoughts as they occur to me, trying to make sense of all these new ideas that I have the privilege of reading about, and can only thank Marshall as he has great patience in bringing them to us as well as tirelessly explaining what is being said about them. I'm in great debt to you all. BTW, Marshall. My apologies. It was Max Born, not Niels Bohr, who coined the probability wave idea. And I'd read this earlier (but misattributed it to Bohr) when I was presenting Greene's "Fabric of Space-Time" book on this forum last year. I think I was influenced by Bohr's interpretation being in opposition to Einstein's, respecting Einstein's assertion that Quantum theory must be incomplete, which I'd been reading in the '90s on the Aspect experiments.
owleye

### Re: Quantum realism and fields.

owleye » Thu May 22, 2014 11:05 am wrote:Well, if quantum field theory is merely an adjunct of Relativity theory,...

Hi Owl, I would never say that, myself.

Of course when one says "Relativity" one should be clear (implicitly, explicitly or contextually, somehow anyway!) which Relativity one means, SR or GR. I've been woefully confused by people in the past because this wasn't made clear.

I think you mean SR. Special Rel. Special Rel did in fact COME OUT OF FIELD THEORY, as I explained.
SR developed from Faraday's idea after Maxwell equationized it. When Max equationized Far's field, it amazingly turned out that twangs in that field would travel at a definite speed that was the same no matter who was looking! A really radical idea!

(That's part of the reason Prof. Einstein had pictures of Faraday and Maxwell on his study wall, I guess)

So you could say "Special Relativity is a mere adjunct of Maxwell's EM field equation." But that doesn't sound right either. However, the first important field in the modern sense was the EM field and it was relativistic already in 1850 long before there was any relativity theory. This EM field embodied the core idea of SR (Lorentz invariance) and by revealing that, gave rise to SR.

Since then it is kind of a TRADITION that modern fields obey SR and are Lorentz invariant. Being a Realist, I think this reflects something about how Nature is, and about the fields she is made of. :^D Maybe I got that notion from reading Wilczek's 12 pager.

But that doesn't make other fields mere adjuncts of their historical antecedents. (There are THREE MAIN FIELDS in QFT's Std Mdl, I'd say, if you group them by their gauge symmetries.) . They are much more than mere adjuncts of the historical fields that prefigured them, and their compatible algebraic manipulations.

I wouldn't be surprised if you were of the same mind, or had thoughts along the same line. Historical antecedents are significant but they don't tell the whole story.
Marshall

### Re: Quantum realism and fields.

The standard model fields are operator-valued functions defined on (x,t) In quantum theory an operator can be associated with the idea of OBSERVING something. Given a state vector in the Hilbert space it can correspond to measuring something. An operator can be an "observable". I don't want to suggest it is limited to that, but that is one way of imagining a field.

Faraday imagined the magnetic field as a funny kind of "force" distributed throughout the world that you could measure with various instruments like a compass needle or a current loop that you moved around various ways. So that was a "force" or a force-measuring OPERATOR, hard to separate the two ideas. And in modern times the values a field takes go on being operators. It's traditional. And maybe nature wants it that way.

Interestingly, these operators have groups of SYMMETRIES.

Imagine three matrices of complex numbers:

a 1x1 matrix ( just a single complex number)
a 2x2 matrix (a square array of 4 complex numbers)
a 3x3 matrix ( 9 complex numbers)

Suppose that in each case, if you flip the matrix over its main diagonal (the downhill one) and replace each number by its complex conjugate the matrix becomes its own inverse! In the 1x1 case that's trivial and just means that the number times it's complex conjugate equals one. IOW it's on the unit circle around the origin. As matrices these can be made to act on other stuff and define symmetries. These are ones that instead of applying to the (x,t) terrain (as Lorentz transformations do) apply to the operators that live on that terrain.

They are symmetries, respectively of the
EM field operators
the weak force field operators
the strong force field operators

I'm glossing over details (some of which I don't properly understand) to quickly sketch the idea. You might google "standard model" and look at the Wikipedia. The Std Mdl is amazingly compact, what used to be hundreds of particles (back in the Sixties) now boil down to a neat diagram consisting of a few pigeonholes. It's an admirably economical way of condensing the whole Matter Kaboodle, based on those three symmetries.
Marshall

### Re: Quantum realism and fields.

What is the standard model field of a photon? Does it apply to itself (self-interference)?
owleye

### Re: Quantum realism and fields.

And maybe nature wants it that way.

Marshall, curious what you meant by this.

I'm cautious around the SM, given that it has always said that all bosons of the electroweak force should be massless. In a low energy universe, of course, there is spontaneous symmetry breaking and any actual measurement yields either an EMF boson, the photon, or a weak force boson (the W or Z) which is massive. To make the SM be compatible with observation, a Higgs mechanism has to be postulated so that the weak bosons are given some mass. So the SM has pluses and minuses - the pluses being to greatly reduce the population of the particle zoo, the minuses including the glaring wrong prediction of all massless electroweak bosons. Correct me if I have this wrong, but it looks like the SM necessitated the introduction of a new field to make sense of measurements of weak and strong force interactions. W and Z bosons needed mass, and the baryons had 5% more mass than expected from just binding energy. So, again, just feel cautious about embracing the SM. Now the LHC finds a spike at 125 GeV and many say, "Ok, that's a Higgs, and that takes care of these other mass problems," but I want to wait and see. How this all impacts a Realist stance is something that will take a while to unpack.

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### Re: Quantum realism and fields.

Hi Owl and Brain, I've been casting around on the internet hoping to find someone who tries to describe the Standard Model in plain, artless, language. I'm hoping for a "tell-it-like-it-is" account, without relying on artistic metaphors (which might only give me the ILLUSION of understanding), without relying too much on math language, and in simple as possible everyday English.

If either of you find any exposition you think has any merit at all (free online) please share the link. Even if it doesn't seem to be exactly what I'm asking for, if you personally like it. I'm willing to give pretty much anything a try.

Today I found this blog by a young German theorist named Axel Maas. His work is in just the right area: incrementally building out the Std Mdl. Not radically changing, just extending, with a lot of numerical checking and keeping a close watch on the ongoing experimental work. For some reason he also has a naive uncommercial drive to explain Std Mdl to the layperson.
http://axelmaas.blogspot.com/2010/09/sy ... model.html

This blog post is one of a series of several posts about the symmetries of the standard model. In the subsequent one he gives an example, the simplest example of gauge symmetry: the electromagnetism part.

Don't get your hopes up! This guy does not write the best English, his heart is in the right place, but the overall result is frustrating. I'm going to keep looking. But also I'm going to read some of Axel Maas.

His blog is innocently titled "Looking Inside the Standard Model: a tourist guide to the standard model of particle physics". It spans several years, he is still continuing it, hasn't given up, which says something about the patience and persistence of his character. The particular post I pointed to ("Symmetries of the standard model") was from September 2010. Again, not to raise hopes of satisfactory enlightenment, but at least it is an honest (and completely non-mathematical) try.

Actually Braininvat, you may have some better online sources than I've stumbled across so far! Don't hesitate to suggest any you like. There could be online video lecture university courses, or all kinds of other stuff out there.
Marshall

### Re: Quantum realism and fields.

owleye » Fri May 23, 2014 4:05 am wrote:What is the standard model field of a photon? Does it apply to itself (self-interference)?

It just happened that the next Axel Maas post, after the one I just linked to, was about the electromagnetic field in the Std Mdl, which you asked about. The post (October 2010) is called "Electromagnetism, photons, and symmetry".
http://axelmaas.blogspot.com/2010/10/el ... metry.html
The overall blog is called "A Tourist Guide…"

One basic feature to make sure we are clear about is that in the Standard Model there is no individual field of an individual photon. Or any particle, there is no individual field for a single electron or anything else.
The field is a COLLECTIVE entity which was Wilczek's first point in his 12page QFT essay and it is WHY all instances of the electron are the same.

There is a global photon field that can describe any number of excitations (I've called them twangs). If something is glowing hot and emitting photons then there is a creation process that just keeps twanging the field, loading it up with more and more excitations. And there is an annihilations process that can eliminate them when they get absorbed or converted to something else. I think it is more common to call the photon field the "electromagnetic field". Photons are the quanta of that field, and the field can handle any number. I don't yet understand how it does this, maybe I should write to Axel Maas (he seems to like explaining things in simple terms :^D)

Axel describes the electromagnetic field (this is QFT, i.e. the Std Mdl, not the classical version) as given by 6 numbers at every point in spacetime. This is strange, because that is just how it is done in the classical version! I'll have to read more in his October 2010 post.

Oh, about SELF-INTERFERENCE. I think we need to wonder what it means to claim that there is only one photon's-worth (of excitation in the given frequency/energy range) in the apparatus at any one time. Since the field is twanging with gazillions of quanta, that seems somewhat of an idealized artificial statement that can only be true in an approximate sense. But we put lots of shielding around the apparatus and turn the light source down very low and assume that to an extremely good approx there is only one photon-worth in there during a one-second interval and so when we see interference----it is the FIELD which interferes with itself, really, but---we say it was the photon self-interfering. That's my understanding of the self-interference you asked about, Owl. I'd welcome hearing how Braininvat would describe it, he might have a different take.
Marshall

### Re: Quantum realism and fields.

Marshall » May 23rd, 2014, 1:10 pm wrote:But we put lots of shielding around the apparatus and turn the light source down very low and assume that to an extremely good approx there is only one photon-worth in there during a one-second interval and so when we see interference----it is the FIELD which interferes with itself, really, but---we say it was the photon self-interfering.

The interference demonstrates that the photon is a field quantum, plus that field quanta have a wave nature. So, no more double slit mystery. Ok, that's solved, as well as gravity. What's next?

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### Re: Quantum realism and fields.

Braininvat » Fri May 23, 2014 6:51 am wrote:
And maybe nature wants it that way.

Marshall, curious what you meant by this.

I'm cautious around the SM,...

Just an unserious personification…expressing my general confidence that physics is on track towards an increasingly true mathematical description of how the world really is. As I've said so often, my big worry is how can we semi-evolved (often beautiful) monkeys adapt our language and grow our intuition so as to *make sense* the ever-truer math we're arriving at. Just an attitude, when I say "maybe nature wants…" I trust that overall the math part is on track, even when I can't make sense of all of it.

My personal attitude is that of course the SM is wrong, incomplete because it is built on SR (flat, non expanding Minkowski space). It has to be completely rebuilt so as to live on a dynamic geometry. Only then could we hope to understand what physics goes on down in the pit of a black hole or went on at the (bounce?) start of expansion. And maybe in other extreme situations.

So more power to your cautiousness. You identify some specific flaws that appear even in the low-energy flat geometry case! Some of those are doubtless being worked on. They are still changing the SM.
My guess is that they will figure out what dark matter is over the next 5 or 10 years and that will involve building out the SM. And I suppose it isn't really settled yet about how the Higgs field fits in.
But even when all the minor problems are fixed, doesn't it still have to be completely rebuilt on a dynamic geometry basis? I'm completely non-expert, shouldn't try to say anything, but that's my personal response to your "I'm cautious about the SM…"

Getting back to the main problem, let me illustrate the GAP between the math and the non-math commonsense making sense. I just linked to a couple of ordinary language posts by Axel Maas. Here, for comparison is a paragraph from Wikipedia "Standard Model" It's actually good! It's informative! It's helping me get clearer, just as Axel's blog is, in a different way. But it sure is different!

http://en.wikipedia.org/wiki/Standard_Model_(mathematical_formulation)

==quote Wiki==
The standard model is a quantum field theory, meaning its fundamental objects are quantum fields which are defined at all points in spacetime. These fields are

the fermion field, $\psi$, which accounts for "matter particles";
the electroweak boson fields W1, W2, W3, and B;
the gluon field, Ga; and
the Higgs field, $\phi$.

That these are quantum rather than classical fields has the mathematical consequence that they are operator-valued. In particular, values of the fields generally do not commute. As operators, they act upon the quantum state (ket vector).

The dynamics of the quantum state and the fundamental fields are determined by the Lagrangian density $\mathcal{L}$ (usually for short just called the Lagrangian). This plays a role similar to that of the Schrödinger equation in non-relativistic quantum mechanics, but a Lagrangian is not an equation — rather, it is a polynomial function of the fields and their derivatives. While it would be possible to derive a system of differential equations governing the fields from the Langrangian, it is more common to use other techniques to compute with quantum field theories.

The standard model is furthermore a gauge theory, which means there are degrees of freedom in the mathematical formalism which do not correspond to changes in the physical state. The gauge group of the standard model is $\mathrm{U}(1) \times \mathrm{SU}(2) \times \mathrm{SU}(3)$, where U(1) acts on B and $\phi$, SU(2) acts on W and $\phi$, and SU(3) acts on G. The fermion field $\psi$ also transforms under these symmetries, although all of them leave some parts of it unchanged.

==end Wiki==

The quantum state (ket vector) is fixed for all time and represents the uncertain info about the system, so it enables all the operators (which inhabit every spacetime point) to give numbers.

If you change the "ket" state of the system, you will change what numbers all the operators of every type will say. So the quantum state is not associated with any one "particle" or type of particle. It is basically a number-giving functional defined on all the operators. There is an equivalent alternative formulation von Neumann came up with where there is a C* algebra of operators with the state simply a functional defined on the operator algebra. You don't even need a hilbert space. I think it's cleaner. But the Hilbert space "ket" way is entrenched custom. Doesn't matter, just a side comment.
Marshall

### Re: Quantum realism and fields.

Hi Marshall,

Over on the thread split-off from this one, I posted some Wiki Links I thought did a fair explanation of the Subjects you are covering here.. they are:

http://en.wikipedia.org/wiki/Lattice_%28order%29
http://en.wikipedia.org/wiki/Boolean_algebra_%28structure%29
http://en.wikipedia.org/wiki/Quantum_logic
http://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics

I'm mostly interested in the Boolean Math/Lattice approaches to defining the Fields in question.

Best regards,
Dave :^)

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### Re: Quantum realism and fields.

Marshall....

I'm reading your latest from Axel Metz for the third time and still can't get my arms around it. Indeed, I'm not quite sure how you managed to conclude what you did from it.

Here's what he says about fields: "Fields in physics are something which associate with each point in space and with each instance in time a quantity."

I can appreciate this only if I understand it in the context of specific source for that field around which the quantities mentioned vary depending on their distance from it. In EM and gravitational fields, I can think of their extent as infinite, though I suppose there are restraints on its growth from the moment the source for it originates. In the case of nuclear sub-atomic sources, the quantities drop off significantly with distance, if I understand it right. Basically, these extended fields become force fields, allowing "disturbances in the Force", as Stars Wars made famous, when charged or magnetic objects find their way into them. Similarly, if the sources accelerate suddenly -- say by an explosion or collision -- the field itself adapts to that acceleration by sending off energy bursts in the form of energetic photons in the case of EM fields or gravitons in the case of gravitational fields, which have the effect of communicating information about the changes it needs to all parts of it in light time.

Given EM fields, with its source, then, is this the only way that photons comes to exist? Perhaps it is. If so, I'm learning something. Of course, this is not how I read your (Marshall's) summary of Metz.

Here's what he says next:

"In case of electromagnetism this is a quantity describing the electric and magnetic properties at this point. Each of these two properties turn out to have a strength and a direction. Thus the electric and magnetic fields associate with each point in space and time an electric and a magnetic magnitude and a direction."

So what we have here is a vector quantity at each point of the field (well, two of them, which turn out to be related to each other in the right hand screw formulation that I seem to remember lo those many years ago). In the next paragraph he says this in the following way:

"When in the 19th century people tried to understand how electromagnetism works they also figured this out. However, they made also another intriguing discovery. When writing down the laws which govern electromagnetism, it turns out that electric and magnetic fields are intimately linked, and that they are just two sides of the same coin."

And this is where he introduces the photon:

"In the early 20th century it then became clear that both phenomena can be associated with a single particle, the photon. But then it was found that to characterize a photon only two numbers at each point in space and time are necessary."

If I understand his meaning, it implies that at every point (in the field), the vector quantity is identified with a photon. If so, this is rather an odd statement to make and has me puzzled. Perhaps what it means is not that it represents a packet of energy radiating away at the speed of light, but rather that it has the potential of becoming a packet that radiates away at the speed of light. And one might conclude that it would be actualized if there was a disturbance in the field at that point.

This is how I'm reading Metz. It seems so different from how I'm reading your (Marshall's) summary. Am I wrong?
owleye

### Re: Quantum realism and fields.

owleye » Fri May 23, 2014 2:44 pm wrote:...
Here's what he says about fields: "Fields in physics are something which associate with each point in space and with each instance in time a quantity."

I can appreciate this only if I understand it in the context of specific source for that field around which the quantities mentioned vary depending on their distance from it...

Hi Owl, I don't think Axel Maas mentions any specific source. It doesn't seem to be an essential part of his picture of a field. That makes sense to me because you might be out in intergalactic space and the EM field would be made up of radiation from many many sources most of which you might not be able to identify or tell the distance to. Some of those countless sources might no longer exist. The real thing would be the FIELD as you experience it. Or anyway that's how I look at it, and Axel didn't introduce the specific source idea, anywhere in his blog that I saw.

In case you want to acquire the option of thinking EM field independently of a specified source, I've tried to think of a kind of thought experiment or imagination exercise that would help someone do that. This is just in case you WANT to get the option of a different way of thinking. I'm not saying you should, it's only if you choose.

Out in a generic cubic kilometer of space, if you could take a "photon detector" and count EM quanta events, you would find that almost all are CMB, with a peak wavelength of 1 mm.
That is the OVERWHELMING MAJORITY SPECIES OF THE ELECTROMAGNETIC FIELD. Dwarfing starlight, or the warm glow of dust clouds, or anything else.
So since it's such an important part of the EM field, let's just focus on that radiation, coming from everywhere, peak wavelength very close to 1 mm. I think 1.06 mm more exactly.

Suppose you are out there studying the EM field, pointing your antenna this way, and that way, and the other way, recording the radiation. Where is the source? What is your distance to the source?

In what sense does the source even exist at present? And if it does exist in some sense, where is it?

It used to exist around 13.7 billion years ago. It was very hot gas comparatively near to where OUR matter was, roughly the same in all directions. Now that matter is some 45 billion LY from us in all directions. So which one is the correct distance to the source? The distance to that matter NOW or the much smaller distance to that matter THEN, when it was hot and emitted the radiation?

This doesn't seem practical. It's more complicated than it's worth, to worry about the source. So I would suggest we imagine the EM field in the "here and now" without trying to pinpoint a source and relate it to that one specific source. The THEORY, namely QFT, would not be general enough if it had to be tied to some single designated source...

But I have to admit that if we are picturing EM field on a *space time* diagram then there certainly would be a place on the diagram (way in the past) where you could put a hot cloud of hydrogen! So it seems POSSIBLE at least in principle to always include sources in how you imagine the fields.

I guess I'll leave it unresolved, in my mind, and try to be able to think of fields EITHER WAY.
Marshall

### Re: Quantum realism and fields.

The idea of a field's "source" is an interesting one. Much of the excitation of in certain fields could be so OLD that it has "forgotten" what its source was---where and how and from what it originated.

Does the neutron in a nucleus remember in what star it was cooked? Does it matter?

Many electrons are made by BETA DECAY of neutrons. The neutron is the "source". It spits out a proton and an electron and a neutrino.

So if I take a bite of breakfast cereal, the "sources" of a few of the electrons in it---those long-lasting excitations of the electron field---could have been various neutrons in various different stars, that were made by various fusion reactions, mostly starting from hydrogen, which then underwent beta decay and produced them.

In every case I can think of at the moment, it is the FIELD that exists. It is what matters. And the field has various (sometimes temporary, often very long lasting) excitations in it.

There is no one "source" of, say, the electron field. It has many many excitations, each of which can have its own variegated history. But does the "source" of a particular electron really matter? In most cases I think not.

One physicist Rovelli quoted (I don't recall who) has described matter as a "monotonous" process. The individual excitations tend to be long-lasting. But nevertheless the basic PATTERN is for excitations of a field to occur, and after some lifespan to change into excitations of some other type of field (e.g. by a decay) or to be annihilated in some manner.
Matter is comparatively monotonous, but nevertheless mutable. Excitations of the EM field can often be much shorter lived, but even some of them (like the ancient light of the CMB) can survive for ages.

It seems to me that in most cases I can think of the "source" of a particular excitation is irrelevant.

And as for "the source of the field itself", I do not believe anything is known. According to Std Mdl, reality consists of a a handful of basic fields. One may be able to trace the provenance of a particular excitation, a particular photon or electron. But the single overall electron field (which hosts all the electrons in the universe) is, I think, simply a given. The same with the electromagnetic field, which is host to swarms of photon excitations each with some source history, but is itself simply a given. This is the ontology we are GIVEN.

This is the QFT Standard Model picture of reality as a small number of quantum fields, which Wilczek was describing as "the stuff of existence" in that classic 12page paper! This is physics as we know it today--and of course the picture is approximate and evolving. Each of the multitude of particular excitations of a field can have its various source and provenance, but the FIELD has no source, it simply IS.

Do you see my viewpoint, Owl? I'm kind of responding to what you said about needing to think of a field as having a source. I think I understand where your picture comes from---Newtonian inverse square law, central body attraction force. Or Coulomb electrostatic field around a charged body also inverse square. I want to make clear a different perspective that I think is more in line with contemporary Std Mdl picture of reality. Let's see if we can get the alternative pictures in sharp focus. I'm finding your questions very helpful. thanks!
Marshall

### Re: Quantum realism and fields.

I'm trying to get a better understanding of the significance of those symmetry groups. To recapitulate, the groups we talked about earlier were 1x1, 2x2, and 3x3 matrices of cx numbers, obeying some limitations. And the quoted Wikipedia had this summary of the five Std Mdl fields:
$\phi$ is the Higgs field
B is the electromagnetic field ( excitations of which are called photons)
W is the WEAK field which hosts a threesome of weak force carriers
G is the STRONG field and hosts an eightsome of gluons
$\psi$ is the fermion field.

The 3x3 matrix group acts on gluon field
the 2x2 matrix group acts on the weak field and the Higgs field
and the 1x1 group acts on electromagnetism field and the Higgs field

For reference, here's the passage from the Wiki article on Std Mdl quoted earlier. It treats the B and W fields as a single "electroweak" unit, so it only has 4 Std Mdl fields. I just broke that down when I listed them.
==quote Wiki==
The standard model is a quantum field theory, meaning its fundamental objects are quantum fields which are defined at all points in spacetime. These fields are

the fermion field, $\psi$, which accounts for "matter particles";
the electroweak boson fields W1, W2, W3, and B;
the gluon field, Ga; and
the Higgs field, $\phi$.

That these are quantum rather than classical fields has the mathematical consequence that they are operator-valued. In particular, values of the fields generally do not commute. As operators, they act upon the quantum state (ket vector).

... The gauge group of the standard model is $\mathrm{U}(1) \times \mathrm{SU}(2) \times \mathrm{SU}(3)$, where
U(1) acts on B and $\phi$,
SU(2) acts on W and $\phi$, and
SU(3) acts on G.
The fermion field $\psi$ also transforms under these symmetries,...
==end Wiki==

That 1x1 group, officially called "U(1)", is really simple it is just the unit circle on the cx plane. The complex numbers z = x+iy with x2+y2=1. What it boils down to is rotations by any phase angle from zero to 360 degrees. This symmetry business may be more detail than is right for this thread and risks bogging us down. Maybe we can just set these symmetry groups aside, note their existence and take a look at something else.
Marshall

### Re: Real Maps

Marshall wrote:The field is a COLLECTIVE entity which was Wilczek's first point in his 12page QFT essay and it is WHY all instances of the electron are the same.

You (and obviously, many talented physicists) seem preoccupied by the fact that particles of a kind are identical. That is, if any two electrons in the universe were to instantly switch with each other, there would be no physical way to determine that it occurred. This indeed appears to have important consequences in quantum statistics but I think it falls short of justifying new fields for every particle. There are problems with such fields and I don't think those fields even explain the phenomenon of identical particles.

You use the word "twang" in association with a creation event, say of an electron in the "electron field". OK, but we must now have identical twangs in order to cause identical perturbations in that field. It seems that all we've done is shift the burden of explaining identical-ness to a different source.

While I greatly appreciated your recounting of the origin of field theory with Faraday and Maxwell, I would remind that particle fields are clearly not Faraday fields. Faraday fields have specific sources. As you know, to him, particles are the origins and terminations of fields as depicted with his field lines.

Marshall wrote:...the electromagnetic field, which is host to swarms of photon excitations...

Granted, if you had probes an a multitude of locations throughout the universe and if you could collect readings from them of electric potential at each location, you'd have a collection of numbers which some might call an electric EM "field". I would call that a MAP! Specifically, the EM "field" you refer to appears to be a map of electric potential in the space of a particular reference frame at a given time.

Suppose I similarly collected density readings all around the earth at an altitude of 1000 feet above sea level. I'd have a density map indicating air in most places and rock in others. I might surmise certain things about rocky perturbations of the atmosphere but I wouldn't have a mountain! For that, a better perspective is needed. Instead, my map is just a mosaic of cross-sections of many different mountains.

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### Re: Quantum realism and fields.

Marshall...

There are two reasons I had for regarding fields as having a source. The first is that they resolve an issue I had related to the relativity of events in such a way that if we knew their sources (and perturbations) we could compare the ages of the events, signifying a compatibility with Relativity theory. Were it the case that fields had no source at all, I think there would be issues surrounding their absolute character, just as Newton had with space itself. The second reason is that, as I began to think about it, it gave me a better understanding of the origin and demise of photons. Not only are photons (in their potentiality) associated with Faraday fields, but also include suns, galaxies, and, as you say, the CMB. More specifically, though, they derive from the fields within what constitute atoms and molecules. All of these to me fit one model for EM fields. Moreover, to me, they make for a better understanding of what you were speaking about when you spoke of a Relational QM (though you translated it as an Interactive QM, which I think is helpful), insofar as they were moving toward a realism of observations. And, by introducing fields, we can conceivably connect the observations with the probabilities of a given observation. So, it is with all this that I'm not inclined to drop out the significance of what it took to create the field in the first place. (Note that I do acknowledge that one gains something by ignoring a source, cosmologically, but, if one is interested in realism, as opposed to an instrumentalist outlook, then, I think one has to keep it in mind. In retrospect, then, I suppose the above two reasons can be lumped together by this point.)
owleye

### Re: Quantum realism and fields.

Faradave, I'm just spitballing here, but I wonder if the problem of identical particles is a kind of semantic illusion derived from remnants of classical thinking in which, say, electrons are thought of as distinct objects. There are some ways of looking at electrons, as in experiments in superconductivity, in which it seems clearer that we aren't really talking about distinct individual electrons - in a superconductor, properly chilled, "they are all as one."

When a quantum field vibrates a certain way, we call it an electron when the vibration interacts with a detector. The detector is a LARGE object, composed of a huge number of particle/field excitations, and as such has become a classical object. It is a classical object which is showing us quantized events. Hmm, I know what I'm getting at here, but not sure I'm conveying it too well.

If a surfer knows 12 different kinds of waves and he's out on the beach this morning and points at a wave and says (I'm making up surfer jargon here, being a landlocked fellow most of my life), "OK, that's a low-ball tube twirler....those are good to ride when you are just waking up." It's not like that wave has a single distinct identity - it's really just part of the ocean that "twangs" a certain specific way that is easily recognized by surfers. All the low-ball tube twirlers are a manifestation of a single sort of oceanic energy. It does certain things, say it repels surfers who have a negative attitude (ha!). It's all about the interaction between ocean and surfer, and one which is consistent (here, my analogy may be starting to tatter, I realize...).

The problem with the analogy, of course, is that we don't see the electron coming, we don't have a positional fix on it as it approaches our surfer detector. It would be like surfing blind and only knowing what kind of wave you have when it actually interacts with your board.

TheVat

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Location: Black Hills

### Re: Quantum realism and fields.

Braininvat, Owleye and Faradave, thanks for the feedback!
What I'm looking for at the moment is intuition about what QFT-Standard Model says and ways of talking about it or making sense of it.
At this point in the thread I am not interested in how true or not true it is, or whether you or I like it or not, for this or that reason. After we make some modicum of sense of it we can decide individually if we like it.

So I am not trying to "sell" you the theory. I'm trying to understand it better myself and if possible I'd like us to share a clearer idea of it.

If you read the Wilczek account or the Wikipedia "QFT" article, for example, you can check my paraphrase and say did I get the paraphrase right or not, or offer your own paraphrase, which might be more helpful than mine. Here's the Wilczek link again.

http://arxiv.org/abs/hep-th/9803075

Some statements (T or F?) in the context of Std Mdl QFT

1. A quantum field isn't brought into existence by anything, it is a given. The theory doesn't have any idea of what could have created it. In the theory context, the field always was. It has no source. (This is a SEMANTIC point--a subtle change in the meaning of the word "field"--don't let it throw you :^D)

2. A quantum field "knows" what its quanta are. It can only be excited in certain definite ways. E.g. There is a limited variety of ways the EM field can be excited--e.g. its photons have a fixed relation between frequency and energy--e.g. they all interact with the other fields the same way. Something similar holds for the FERMION field--say for simplicity we just consider its electron sector, it can only be host to electrons (recognizably similar to each other, all the SAME in certain basic ways, obeying the same rules).

3. Because at least for now I'm splitting the electroweak field into B (electromagnetism part) and W (weak part), I'm listing FIVE fields that make up the QFT picture of reality. The wiki enumeration just has four.

Fermion field
Higgs field
G (gluons) = field of strong force carriers
W = field of weak force carriers
B (photons) = electromagnetism field

There are other points to be added later, but I'll post this much for now.
Marshall

### Re: Quantum realism and fields.

Reading Biv's post a second time, the thought occurred to me that (given that words can have various meanings depending on context) one meaning of the word "quantum" might be "limited variety"

As in, a quantum field is a field that can only be excited in a limited variety of ways.

So contemporary physics is pointing us towards a certain ontology where the world is made of five everlasting fields, each of which can only be excited in a specific limited variety of ways.

The general name for these excitations is "quanta", each type is characterized by some definite rules. The excitations, or quanta, of the field symbolized by B (in the wiki article) are called called "photons" and it has been discovered that they conform to some definite rules.

The Std Mdl THEORY is more than just describing these five (limited variety of excitation) fields. It also has a LAGRANGIAN. This is an algebraic engine in which all five fields appear, and their parts are coupled in various ways, and using the engine you can CRANK OUT HOW ALL FIVE WILL EVOLVE together, starting from whatever chosen conditions

In other words the theory does not merely name the five fields, it describes their collective dynamics by a Lagrangian.

Wilczek mentioned a handful of main principles of QFT, and so far we only talked about one of them (identical particles, part of the limited variety of excitations idea). I should get on to some of the other ones he listed.
Marshall

### Re: Quantum realism and fields.

==Wilczek "QFT"==
...It is clear, from all these examples, that quantum field theory occupies a central position in our description of Nature. It provides both our best working description of fundamental physical laws, and a fruitful tool for investigating the behavior of complex systems. But the enumeration of examples, however triumphal, serves more to pose than to answer more basic questions: What are the essential features of quantum field theory? What does quantum field theory add to our understanding of the world, that was not already present in quantum mechanics and classical field theory separately?
The first question has no sharp answer. Theoretical physicists are very flexible in adapting their tools, and no axiomization can keep up with them. However I think it is fair to say that the characteristic, core ideas of quantum field theory are twofold. First, that the basic dynamical degrees of freedom are operator functions of space and time – quantum fields, obeying appropriate commutation relations. Second, that the interactions of these fields are local. Thus the equations of motion and commutation relations governing the evolution of a given quantum field at a given point in space-time should depend only on the behavior of fields and their derivatives at that point. One might find it convenient to use other variables, whose equations are not local, but in the spirit of quantum field theory there must always be some underlying fundamental, local variables. These ideas, combined with postulates of symmetry…
==endquote==

We can think of an operator as a (typically large) square matrix (typically of cx numbers) that acts on a vector space with inner product called a Hilbert space. These operators (think: matrices) can be multiplied together and form an "algebra" (a system of things you can add and multiply almost like numbers but potentially embodying more info than simple numbers). John von Neumann came up with a simplified more abstract form of quantum theory where you start with the algebra and forget about the original Hilbert space.
The algebra of operators (some of which might correspond to measurements or observations) are what's essential. So to instantiate a quantum field you distribute this new kind of "number" (that looks like a large square matrix) all over the (x,t) terrain. It's an operator-valued function (or "distribution" if you make a technical distinction between function and distribution, which I won't here).
Because you can add and subtract this kind of "number" you can actually take derivatives (like "slopes") of this this function, in any spacetime direction. So you can do something we could call "operator-valued calculus" and set up "operator-valued waves" and all that stuff you do with old-style numbers differential equations.

A nice thing is that operators can have uncertainty. What numbers they give can depend on something called the "state" of the system. A given operator can embody the potential for a lot of different hard-number outcomes. Its "spectrum". the transition from classical to quantum physics has a lot to do with switching over from ordinary numbers to an algebra of operators.

And if you know how to add and multiply two square matrices together it is not such an outlandish step to take, they are very like ordinary numbers (except the multiplication does not commute, and except that the hard numbers a given operator gives is contingent on what you choose for the state of the system)
Marshall

### Re: Quantum realism and fields.

FWIW I'll extract Wilczek's list of general QFT principles simply by highlighting excerpts quoted from the essay:
==quote starting bottom page 2, continuing at top of page 3==
The three outstanding facts we have discussed so far:
the existence of indistinguishable particles,
the phenomenon of quantum statistics, and
the existence of antiparticles,

are all essentially consequences of free quantum field theory. When one incorporates interactions into quantum field theory, two additional general features of the world immediately become brightly illuminated.

The first of these is
the ubiquity of particle creation and destruction processes.
Local interactions involve products of field operators at a point. When the fields are expanded into creation and annihilation operators multiplying modes, we see that these interactions correspond to processes wherein particles can be created, annihilated, or changed into different kinds of particles. This possibility arises, of course, in the primeval quantum field theory, quantum electrodynamics, where the primary interaction arises from a product of the electron field, its Hermitean conjugate, and the photon field. Processes of radiation and absorption of photons by electrons (or positrons), as well as electron- positron pair creation, are encoded in this product. Just because the emission and absorption of light is such a common experience, and electrodynamics such a special and familiar classical field theory, this correspondence between formalism and reality did not initially make a big impression. The first conscious exploitation of the potential for quantum field theory to describe processes of transformation was Fermi’s theory of beta decay. He turned the procedure around, inferring from the observed processes of particle transformation the nature of the underlying local interaction of fields. Fermi’s theory involved creation and annihilation not of photons, but of atomic nuclei and electrons (as well as neutrinos) – the ingredients of ‘matter’. It began the process whereby classic atomism, involving stable individual objects, was replaced by a more sophisticated and accurate picture. In this picture it is only the fields, and not the individual objects they create and destroy, that are permanent.

The second is
the association of forces and interactions with particle exchange.
When Maxwell completed the equations of electrodynamics, he found that they supported source-free electromagnetic waves. The classical electric and magnetic fields thus took on a life of their own. Electric and magnetic forces between charged particles are explained as due to one particle acting as a source for electric and magnetic fields, which then influence others. With the correspondence of fields and particles, as it arises in quantum field theory, Maxwell’s discovery corresponds to the existence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual photons. The association of forces (or, more generally, interactions) with exchange of particles is a general feature of quantum field theory. It was used by Yukawa to infer the existence and mass of pions from the range of nuclear forces, and more recently in electroweak theory to infer the existence, mass, and properties of W and Z bosons prior to their observation, and in QCD to infer the existence and properties of gluon jets prior to their observation.
The two additional outstanding facts we just discussed:
the possibility of particle creation and destruction, and
the association of particles with forces,
are essentially consequences of classical field theory supplemented by the connection between particles and fields we learn from free field theory. Indeed, classical waves with nonlinear interactions will change form, scatter,..
==endquote==
I keep referring to these so I'll tack the links on here to keep them handy
http://en.wikipedia.org/wiki/Standard_M ... ormulation)
http://en.wikipedia.org/wiki/Quantum_field_theory
http://arxiv.org/abs/hep-th/9803075
Marshall

### Re: Quantum realism and fields.

On the indistinguishable particles of a certain kind, I assume only that they have the same properties, not that the properties have the same value. Clearly one can distinguish one photon from another by its frequency. One might say the same thing of its direction, though this is a bit obscure to me. My quick reading of the Wilszek paper, most of which was over my head, seemed to be discussing them in their potentiality, having, classically, infinite degrees of freedom, thus all directions and frequencies are possible, though I believe he went to some length in showing by way of quantum theory how the degrees would be reduced to a few, particularly as it related to spin-states. In any case, because one would expect that photon potentials line up in accordance with a gradient, if sources were considered, Quantum Field theory, as Wilszek explains it, needs to begin from a different theoretical framework in order to wind up with the three observables he is keen to explain, and that you cite.
owleye

### Re: Quantum realism and fields.

This may be of limited (or no!) interest but a new Realist interpretation of quantum mechanics came out today, using "modal logic", posing a clear alternative to other ways of addressing the various paradoxes, such as Rovelli's Relational QM. I have no idea whether or not it will catch on. Probably it won't. Both the authors have no established reputation and very few previous publications. One is at Harvard and the other at Dartmouth.
They are probably both young. However I want to keep tabs on this to see if it picks up any adherents. They claim their interpretation is uncompromisingly Realist, more so than, e.g., RQM-- the state is not observer-dependent, but instead is global. See footnote on page 5. and reference [249]
http://arxiv.org/abs/1405.6755
The Minimal Modal Interpretation of Quantum Theory
Jacob A. Barandes, David Kagan
(Submitted on 26 May 2014)
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, and address a number of familiar no-go theorems. In particular, we argue that our interpretation is compatible with Lorentz invariance, and we highlight a subtle loophole in the original Bell theorem for EPR-Bohm two-particle systems. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure---which we call subsystem space---that we believe merits further study. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text.
84 pages, 8 figures
This is too much for a casually interested person such as I am to read, but the link can be used to find out if any other researchers eventually cite the paper. The authors also posted a short 8 page synopsis:
http://arxiv.org/abs/1405.6754
A Synopsis of the Minimal Modal Interpretation of Quantum Theory
Jacob A. Barandes, David Kagan
(Submitted on 26 May 2014)
We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory...
8 pages, 1 figure
Marshall

### Re: Quantum realism and fields.

I suspect the Barades-Kagan paper will be the topic of much discussion. It doesn't pretend to do everything with its minimalist determination. The main point I saw with it is that it removes a characterization of reality as an exact science -- intending, I think, that reality ought not to be confused with the the study of the set of real numbers. By differentiating reality from actuality, the former being at bottom what's really possible, while the latter is what is observed, an ontic/epistemic demarcation, this minimalist approach gives realism of the sort being discussed by Wilzek, something to work with.
owleye

### Re: Quantum realism and fields.

I'm in favor of healing the "Heisenberg Cut" and hope to make some sense of the paper. First try, in a mildly distracting environment, had me floundering in some of the jargon, but I will try to get through it this week. If this is a way out of having the classical eye there to collapse the wavefunction, then it is surely progress towards a more viable realism. Farewell, Copenhagen. I hope Owl is right, that the B-K paper will spur some creative responses.

TheVat

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Joined: 21 Jan 2014
Location: Black Hills

### Re: Quantum realism and fields.

Hi Owleye and Brain,
Since there's some provisional interest in the B-K paper, I checked out the authors. They are young unknowns.
I'd guess Jacob Barandes was born around 1983, so recently turned 30. His CV says he's been teaching graduate level courses at Harvard (as a Lecturer in Physics, not tenure-track faculty yet).
http://users.physics.harvard.edu/~barandes/?CV
His CV is long so you may not want to read down to the end, where it says:

...
I.B.M. Award for Outstanding Achievement in Mathematics
January 1998

United States Chess Champion, Pre-Kindergarten through Second Grade
1987-1990
:^D

It looks like David Kagan was born around 1981, got his bachelors in 2002. He's a Lecturer at Dartmouth.
http://www.faculty.umassd.edu/david.kag ... e.cfm?pg=4
http://www.faculty.umassd.edu/david.kagan/ (snapshot)
Marshall

### Re: Quantum realism and fields.

Marshall » Wed May 28, 2014 10:35 am wrote:Hi Owleye and Brain,
Since there's some provisional interest in the B-K paper, I checked out the authors. They are young unknowns.
I'd guess Jacob Barandes was born around 1983, so recently turned 30. His CV says he's been teaching graduate level courses at Harvard (as a Lecturer in Physics, not tenure-track faculty yet).
http://users.physics.harvard.edu/~barandes/?CV
His CV is long so you may not want to read down to the end, where it says:

...
I.B.M. Award for Outstanding Achievement in Mathematics
January 1998

United States Chess Champion, Pre-Kindergarten through Second Grade
1987-1990
:^D

It looks like David Kagan was born around 1981, got his bachelors in 2002. He's a Lecturer at Dartmouth.
http://www.faculty.umassd.edu/david.kag ... e.cfm?pg=4
http://www.faculty.umassd.edu/david.kagan/ (snapshot)

Well, I suppose that's important to know. However, in reading the paper, the full text now available, coupled with its bibliography, which includes Rovelli's RQM stuff, they don't seem as if they were newcomers to the issues of quantum theory. Indeed, I believe the authors acknowledged their advisors, among whom if I recall was Steven Weinberg. The paper itself is a modest one, but as I see it, clears the air for further on-going work being done by others. Predicting the future is not one of my strong suits :), but I'd say there is something groundbreaking in what it says about the nature of reality and the limits of science and I believe it will cause a sea change among physicists who wish to make sense of quantum theory.
owleye

### Re: Quantum realism and fields.

owleye » Thu May 29, 2014 4:39 am wrote:... However, in reading the paper, the full text now available, coupled with its bibliography, which includes Rovelli's RQM stuff, they don't seem as if they were newcomers to the issues of quantum theory. Indeed, I believe the authors acknowledged their advisors, among whom if I recall was Steven Weinberg. The paper itself is a modest one, but as I see it, clears the air for further on-going work being done by others. Predicting the future is not one of my strong suits :), but I'd say there is something groundbreaking in what it says about the nature of reality and the limits of science and I believe it will cause a sea change among physicists who wish to make sense of quantum theory.

Scott Aaronson too! (we've had a thread about some of his ideas) They acknowledged valuable interactions with both Weinberg and Aaronson, for example, on page 7 of the short 8-page paper.
Both were also acknowledged on page 64 of the longer paper http://arxiv.org/abs/1405.6755 which incidentally cites four things of Scott Aaronson (!) including the paper of his (The Ghost in the Quantum Turing Machine) that we had a thread about.

There's certainly reason to be hopeful, and it's good both to hope, and also to guard against disappointment.
Personally I find it oddly encouraging that Jacob Barandes was the U.S. Chess Champion (in his age group) for three or four consecutive years, and moreover that there is no indication that his interest in competitive chess continued into adulthood--he's after bigger game now.

To have for reference, in case there happens to be some discussion of B-K: http://www.scottaaronson.com/blog/
Marshall

### Re: Quantum realism and fields.

Hi Everyone,

I have recently made an update to my Preonic Field Thread that I believe is relevant to this thread, if you want to check it out.
http://sciencechatforum.com/viewtopic.php?f=39&t=25882&p=261549#p261549

Regards,
Dave :^)

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