B Shape of elementary particles in QFT, etc?

[icantevenn]

Hello,
I hope this is not a stupid question as I am not a physicist. But I was curious about how contenders for the so-called Theory of Everything view the shape of the elementary particles. I know that the basic idea of string theory is related to the shape of elementary particles as one dimensional, as opposed to zero-dimensions of classical mechanics, to include Quantum Theory. I am curious what is the shape of elementary particles in other theories that seek to unify QT and GR, such as Quantum Field Theory?
Thanks.

 

[ShayanJ]

Quantum Field Theory (QFT) doesn't unify QT and GR, it applies the framework of QT to classical special relativistic field theories.
In QFT, particles are assumed to be point-like.

 

[bhobba]

Quantum Field Theory (QFT) doesn't unify QT and GR, it applies the framework of QT to classical special relativistic field theories. In QFT, particles are assumed to be point-like.

That's true, but just to flesh it out a bit more.

For GR see:
https://arxiv.org/abs/1209.3511

And what a particle is in QFT is a bit more nuanced - its analious to what's happening in the quantum treatment of the harmonic oscillator:
http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

Thanks
Bill

 

[icantevenn]

Quantum Field Theory (QFT) doesn't unify QT and GR, it applies the framework of QT to classical special relativistic field theories.
In QFT, particles are assumed to be point-like.

I guess I used the wrong word. What I meant, I realize, is Quantum Gravity and not QFT.

 

[bluecap]

That's true, but just to flesh it out a bit more.

For GR see:
https://arxiv.org/abs/1209.3511

And what a particle is in QFT is a bit more nuanced - its analious to what's happening in the quantum treatment of the harmonic oscillator:
http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

Thanks
Bill

Just read the above paper, interesting. Is it possible the electron fields are subject to interpretations too like the wave function in QM where the electron fields can also be real like Bohmian?

 

[Demystifier]

Is it possible the electron fields are subject to interpretations too like the wave function in QM where the electron fields can also be real like Bohmian?

It's possible:
http://arxiv.org/abs/quant-ph/0302152

 

[bluecap]

It's possible:
http://arxiv.org/abs/quant-ph/0302152

If fields are considered as beables (i.e. elements of reality) then an appropriate detector can be constructed that should be able to detect such fields? But the fields are everywhere, it should be able to detect them like the microwave background radiation?

 

[Demystifier]

If fields are considered as beables (i.e. elements of reality) then an appropriate detector can be constructed that should be able to detect such fields? But the fields are everywhere, it should be able to detect them like the microwave background radiation?

Even in classical field theory you detect not fields as such but field variations.

 

[bluecap]

Even in classical field theory you detect not fields as such but field variations.

Can the theoretical bohmian quantum fields also have field variations?
The microwave background radiation was discovered accidentally.
What kinds of setups can theoretically detect these bohmian quantum fields variations?

 

[Demystifier]

Can the theoretical bohmian quantum fields also have field variations?
The microwave background radiation was discovered accidentally.
What kinds of setups can theoretically detect these bohmian quantum fields variations?

How do you detect light from the bulb?

 

[bluecap]

How do you detect light from the bulb?

The electromagnetic field is real in QED.. but in electron or quark matter fields.. they are not beables in orthodox QFT.. so are you saying the bohmian electron field can be detected by bohmian electron field detector? What kind of detector can differentiate between electromagnetic field and bohmian electron, quark fields?

 

[bhobba]

Even in classical field theory you detect not fields as such but field variations.

Just to elaborate the reason classical fields are considered 'real' is because they carry energy and momentum. Things are more 'obscure' in QFT because the fields are quantum operators which are rather mathematical to begin with. The 'realty', if such exists are like to be with the Fock space thee operators act on.

Thanks
Bill

 

[bhobba]

The electromagnetic field is real in QED

Again its reality is an interpretational issue. Classically its real - but in QFT its much more complicated.

Thanks
Bill

 

[Demystifier]

The electromagnetic field is real in QED.. but in electron or quark matter fields.. they are not beables in orthodox QFT..

Electromagnetic field is not a beable in orthodox QFT.

 

[anorlunda]

In QFT, particles are assumed to be point-like.

That is what I was taught. But another recent thread pointed me to "transversely shaped photons" and to Bessel beams as an example of how to shape them.

Not always: http://extremelight.eps.hw.ac.uk/publications/Science-Express-slow-photons-Giovannini(2015).pdf

https://en.wikipedia.org/wiki/Bessel_beam

I don't understand. Point-like photons and shaped photons sounds like a contradiction. What gives?

 

[Demystifier]

That is what I was taught. But another recent thread pointed me to "transversely shaped photons" and to Bessel beams as an example of how to shape them.

I don't understand. Point-like photons and shaped photons sounds like a contradiction. What gives?

Photons are pointlike, while the shape is the shape of the wave function. One should distinguish the photon from its wave function.

 

[bluecap]

Just to elaborate the reason classical fields are considered 'real' is because they carry energy and momentum. Things are more 'obscure' in QFT because the fields are quantum operators which are rather mathematical to begin with. The 'realty', if such exists are like to be with the Fock space thee operators act on.

Thanks
Bill

So since the quantum fields in Bohmian QFT is a beable.. and this is supposed to be really there.. so what kind of instruments can theoretically image Bohmian electron fields for example? For bohmians particles. We can see them with our own eyes.

 

[Vanadium 50]

This thread is kind of drifting.

I think the OP needs to clearly specify what he means by "shape". What measurements would one make to determine "shape". Only then can we discuss what theoretical predictions are with any confidence. For example, for a charged particle, one might ask if the electric field lines are identical to what is produced from a small charged sphere or whether and how they deviate.

 

[bhobba]

So since the quantum fields in Bohmian QFT is a beable.. and this is supposed to be really there.. so what kind of instruments can theoretically image Bohmian electron fields for example? For bohmians particles. We can see them with our own eyes.

You are missing a key point.

BM has been deliberately cooked up to be indistinguishable from standard QM so there is no way to do what you suggest.

There was a bit of interest in doing that a while ago eg:
http://arxiv.org/abs/quant-ph/0206196

However it soon became apparent it was incorrect. When you think about it it must be the case as it reduces to standard QM there is unlikely any way to tell the the difference.

Thanks
Bill

 

[A. Neumaier]

Even in classical field theory you detect not fields as such but field variations.

A compass routinely detects the direction of the magnetic field itself not only deviations.

Point-like photons and shaped photons sounds like a contradiction.

A point particle is a particle responding to an external electromagnetic field like a classical point charge. Point-like means it is almost that - the e/m form factor deviates from it only through corrections by other fields. Thus being pointlike or not is a property of the particle species just like mass, charge, or spin.

The shape of a particle is, in contrast, a property of the state of the particle just like mean position (if it exists), mean momentum etc. Hence it depends on the particular electron, photon etc. you are considering. It is given in the Heisenberg picture by $\psi^*E(x)\psi$ where $E(x)$ is the relativistic energy density operator. The geometric shape is obtained as the set of $x$ where this is significant - similarly to how one speaks of the shape of a cloud or the corona of the sun.

 

[A. Neumaier]

What I meant, I realize, is Quantum Gravity and not QFT.

In quantum gravity the only particle is the graviton, and it is pointlike, with properties similar to the photon.

As with the photon, there are no longitudinal modes but only two helicity modes, and therefore no position operator exists and it is impossible to define a consistent probability of being in any given bounded region of time.

In a unified quantum field theory of gravity and standard model one expects the properties of the combined particle content. But in a unifying string theory, the most elementary systems would be no longer particles but extended strings.

 

[ShayanJ]

In quantum gravity the only particle is the graviton

Could you please clarify?

 

[Demystifier]

Could you please clarify?

He meant pure gravity, without matter.

 

[Demystifier]

so what kind of instruments can theoretically image Bohmian electron fields for example? For bohmians particles. We can see them with our own eyes.

When you see a macroscopic object, e.g. a chair, do you see the particles or the field?

 

[Demystifier]

A compass routinely detects the direction of the magnetic field itself not only deviations.

Interesting argument, but let me try to a give a counterargument. Suppose that, for convenience, I fix some gauge condition so that I can ignore the fact that electrodynamics is a gauge theory. Then I can say that the fundamental dynamical fields are not $E$ and $B$, but the potential $A^{\mu}$. Then the force on the compass is not given by $A^{\mu}$ itself, but by derivatives of $A^{\mu}$. The derivatives of the field describe how the field changes.

By the way, even without gauge fixing one can argue that $A^{\mu}$ is more fundamental than $E$ and $B$ due to the Aharonov-Bohm effect.

 

[vanhees71]

Well, I think there's a lot of confusion in this thread. In my opinion it doesn't make any sense to talk about "shape" of an elementary particle in the context of QT. As this is about relativistic QT the best and even oversuccessful model is the Standard Model of elementary particles based on local relativistic QFT. "Elementary particle" is here defined in a quite abstract way by the single-particle Fock states of a local irreducible unitary representation of (a covering) of the proper orthochronous Poincare group.

As was stressed already in one posting above, nothing makes sense in physics, if you can't define it in terms of how to observe/measure it in the lab. We observe particles with several detectors. For the very general question posed here, it's sufficient to discuss one simple possibility. So take a charged elementary particle (like an electron). It can be detected by a photo plate. If the electron hits the plate it leaves a single spot at some position, which is not determined before but we know, given the usual setup of a particle collider, where one prepares particles with rather well defined momentum (and thus also energy), a probability distribution for the position of the particle, where it hits the photo plate. Any single electron will make a spot at a position that is determined with some uncertainty, roughly given by the grain size of the photo plate. That's it. There's nothing defining a "shape" in any sense. All you can see in a microscope is the shape of the grain of your photo plate. You may use other, more modern ways to detect the particle like a CCD camera or an electromagnetic calorimeter. So here the "shape" of a "pixel" varies arbitrarily, dependent on the specific setup of the detector, but all this doesn't determine anything about the elementary particle under investigation but only about the detectors used to observe it.

So it's pretty clear that an elementary particle, as we define them today, has nothing observable that can be identified as any kind of "shape" in the usual sense of what we understand by this notion in the macroscopic world. An elementary particle is identified by its mass, spin, and various charges describing how it interacts via the fundamental interactions described by the Standard Model (strong and electroweak forces). There's not more we know about them, and that's all we can observe today.

 

[A. Neumaier]

The derivatives of the field describe how the field changes.

The electromagnetic field describes how the vector potential changes. But the field itself is measured, not the potential.

 

[A. Neumaier]

An elementary particle is identified by its mass, spin, and various charges describing how it interacts via the fundamental interactions described by the Standard Model (strong and electroweak forces). There's not more we know about them, and that's all we can observe today.

This holds for elementary particles as anonymous, indistinguishable objects, but not for particular ones. Individual particles (made distinguishable by putting them into context, e.g. the outer electron of an atom in an ion trap, or a single photon in a beam created by a photons-on-demand source, have more properties, namely those determined by their state. So they have a shape, as described in my other post. At least this is the way how people working in the field talk about it.

 

[vanhees71]

Sure, but how do you define "shape"? Note that it must be an intrinsic property, defined in the particle's frame (let's concentrate on massive particles which at least have a position in the literal sense). What you described is not the shape of a particle but the shape (or better said pattern) of probability (distributions) of observables. E.g., I'd not say an electron in the ground state of a hydrogen atom is a sphere with extension of one Bohr radius. When I measure, e.g., it's position I'll find a "pointlike" spot on the detector (thereby kicking it out of the bound state).

 

[Demystifier]

But the field itself is measured, not the potential.

You missed my point. In a fixed gauge, this is equivalent to measurement of derivative of the potential.

 

[A. Neumaier]

You missed my point. In a fixed gauge, this is equivalent to measurement of derivative of the potential.

And you missed my point. The potential is not the field in the accepted terminology. But you had stated that in classical field theory one can only measure changes of the field.

 

[A. Neumaier]

Sure, but how do you define "shape"? Note that it must be an intrinsic property, defined in the particle's frame (let's concentrate on massive particles which at least have a position in the literal sense). What you described is not the shape of a particle but the shape (or better said pattern) of probability (distributions) of observables. E.g., I'd not say an electron in the ground state of a hydrogen atom is a sphere with extension of one Bohr radius. When I measure, e.g., it's position I'll find a "pointlike" spot on the detector (thereby kicking it out of the bound state).

It is a matter of terminology, and different people use the terminology differently. You as a nuclear physicists express everything in terms of probabilities because you think in terms of properties obtained by actually doing statistics on many identically prepared particles; But quantum chemists talk about shapes of single atoms and molecules, and the borderline where one switsches from one language to the other is fluent. If you view the shape of a single atom in a high-resolution atom microscope you actually view the charge density which is the ensemble mean of the charge density operator. But one sees it as a definite shape. Now I know that people who talk about the shape of a photon just extrapolate this to the case where things are too small to be measured directly but where onecan still compute the quantities hence talk about them in a meaningful way.

 

[vanhees71]

Well, for atoms and molecules or other "composed objects" "shape" makes some sense. You can define it as some coarse-grained geometrical observable like some averaged one-particle density or a charge or energy density (as you write yourself). Of course, such "shape" definitions make a lot of sense in chemistry.

Even this can be tricky, as the example of the proton shows: Its charge radius depends on how you measure it. There seem to be different radii when using electrons vs. when using muons to determine it. It's not yet understood, how this result comes about.

The shape of a photon is even harder to define, and I don't think that it is very meaningful. Maybe you can define it as the (ensemble mean) of its energy-density, which at least is a well-defined although frame dependent quantity. Note that there's no preferred frame for a photon like for massive particles, where one chooses simply its rest frame. It's also highly state dependent. I guess you can "shape" photons in pretty arbitrary shapes (at least in principle) if you define it in that way. I'm however in doubt, whether this is a very helpful quantity to depict what a photon is beyond my more conservative attempt; it's just describes the detection probability anyway.

 

[Demystifier]

The potential is not the field in the accepted terminology.

Maybe in classical electrodynamics. But in QED it is certainly common to say that $A^{\mu}$ is a vector field with spin-1.

 

[A. Neumaier]

Maybe you can define it as the (ensemble mean) of its energy-density, which at least is a well-defined although frame dependent quantity.

I just asserted that this is the meaning with which the term is used by those who use it, by extrapolation form the interpretation that is valid for larger objects.

In the macroscopic and nonrelativistic limit it becomes the mass density which defines very obviously the shape, and since it can be defined for all objects no matter how large it is a meaningful physical concent, even though one can measure it only for sufficently robust objects such as single atoms on a surface or in a cavity, or mesoscopic or even macroscopic objects. (There is lots of nonmeasurable stuff that has a clear physical meaning, for example the detailed mass distribution in the interior of the sun or in the Andromeda galaxy.)

That shape is frame-dependent is already well-known form classical relativity (length contraction). It has to be so.

 

[A. Neumaier]

Maybe in classical electrodynamics. But in QED it is certainly common to say that $A^{\mu}$ is a vector field with spin-1.

But this is loose, formal but physically meaningless talk, since it is a gauge dependent quantity and gauge fixing is an arbitrary, unphysical procedure. Only gauge invariant quantities have a physical meaning.

 

[secur]

the borderline where one switsches from one language to the other is fluent.

That borderline may be fluid (or 'flexible', 'fuzzy', 'uncertain', 'indeterminate', 'ill-defined', etc), but I doubt it's fluent - in language or anything else. Unless you have a new theory of "conscious borderlines"? Given your belief that consciousness is a meaningless superstition, that would be quite a switsch!

 

[vanhees71]

Maybe in classical electrodynamics. But in QED it is certainly common to say that $A^{\mu}$ is a vector field with spin-1.

It is very important to say that it is a massless vector field, which together with locality implies that it must be a U(1) gauge field. See, e.g., Weinberg, Quantum Theory of Fields, vol. 1.

 

[vanhees71]

I just asserted that this is the meaning with which the term is used by those who use it, by extrapolation form the interpretation that is valid for larger objects.

In the macroscopic and nonrelativistic limit it becomes the mass density which defines very obviously the shape, and since it can be defined for all objects no matter how large it is a meaningful physical concent, even though one can measure it only for sufficently robust objects such as single atoms on a surface or in a cavity, or mesoscopic or even macroscopic objects. (There is lots of nonmeasurable stuff that has a clear physical meaning, for example the detailed mass distribution in the interior of the sun or in the Andromeda galaxy.)

True, but these quantities are measurable in principle. It's only not within our technical possibilities to do so.

That shape is frame-dependent is already well-known form classical relativity (length contraction). It has to be so.

This is a misconception you find astonishingly often. Of course, for a system with non-zero mass there's a preferred frame of reference, the center-momentum frame, and this frame is used to define intrinsic quantities of this system. If you want you can call the energy-density distribution in this frame the "shape" of the object, although I've never seen this anywhere in the literature. You can define this quantity in a frame-independent way as a scalar density. For a fluid it's given by $$\epsilon=u_{\mu} u_{\nu} \Theta^{\mu \nu},$$ where $u^{\mu}$ is the four-velocity field of the fluid (normalized such that $u_{\mu} u^{\mu}=1$) and $\Theta^{\mu \nu}$ is the energy-momentum tensor of the fluid.

 

[A. Neumaier]

If you want you can call the energy-density distribution in this frame the "shape" of the object,

This doesn't work for a photon, whereas the energy-density distribution in the lab frame always exists. This is the one of interest to the experimenter. http://arxiv.org/abs/1605.00023, http://arxiv.org/abs/1601.07142, http://arxiv.org/abs/1512.08213, http://link.aps.org/abs/10.1103/PhysRevAccelBeams.19.021304 are some recent references to photon shape.

 

[vanhees71]

Yes, that's because a single photon is a massless state, and there is no restframe for it. That's why, I don't like to call that quantity "shape". It's just proportional to the probability distribution for detecting a photon. From reading the abstracts of the cited papers, I think that's also the common understanding among quantum opticians.

 

[Arjun Wasan]

In string theory classic point like particles are in 0 dimensions.