Photon Size: Uncertainty Principle & QM Explained

[Thinker007]

I was listening to a physics professor lecturing on QM and he raised the question "How big is a photon?" and indicated it had arisen during his PhD defense.

He than began to discuss the accurately known frequency and wavelength of a laser emitted photon (and thus accurately known momentum) in the context of the uncertainty principle. The product of the uncertainty in position and accurately measured momentum is greater than or equal to (up to a small numerical factor) Planck's constant. He then concluded that in the direction of travel, the position was unknown to within a surprisingly large distance - a meter or so. Or more accurately, that is how I interpreted it. He didn't say position is unknown, he was still talking about "size".

Without really saying it, the implication was that the answer to the question was that a photon was a meter or so long in the direction of travel (and the emitting aperture wide in the transverse direction).

Does that description of "size" make sense to those here? I would probably have said that the photon is a point particle unless we're doing string theory, and the location was just poorly known along the travel direction. If the photon was truly "big" I'd think it would take 3 nanoseconds to finish arriving at a detector assuming a foot or so per nanosecond speed of light, and that should easily be measurable. Do photons take a finite amount of time to "arrive" at a detector?

Thanks.

 

[dextercioby]

The current theory works very well with a pointlike particle approximation of a quanta of the electromagnetic field. I don't know of a successful model (i.e. predictive and confirmed by experiments) of a finite size photon particle.

 

[K^2]

Uncertainty and size aren't the same thing. Like dextercioby said, photons, like all elementary particles, are point-like.

Uncertainty in position of a photon produced by a finely tuned laser can, indeed, be quite macroscopic. That shouldn't be surprising. Even in classical treatment, in order to have a precise frequency, the oscillation must have significant duration. Therefore, a precisely localized photon cannot possibly have a precise frequency.

But it doesn't mean the photon is one meter long now. It means that the photon is still a point particle that's distributed over span of space of one meter.

 

[Redbelly98]

The size of a photon depends on its environment. If you have a cube with mirrored surfaces on the inside, then the photons that describe the electromagnetic field inside that cube are the size of the cube -- whether it is 1 micrometer or 1 kilometer.

 

[K^2]

The size of a photon depends on its environment. If you have a cube with mirrored surfaces on the inside, then the photons that describe the electromagnetic field inside that cube are the size of the cube -- whether it is 1 micrometer or 1 kilometer.

You are still talking about the probability distribution, not the location of a particle. If you insist on talking about EM field in terms of particles, photon is point-like.

 

[atyy]

I think your professor is just expressing a sentiment like "the particle is part of a beam, and that beam is extracted at some time. So the particle is localized to some extent. ... To a particle the beam is the whole universe, and it is big!" http://books.google.com/books?id=CNCHDIobj0IC&dq=veltman+mysteries+facts&source=gbs_navlinks_s (p117).

It's similar to Redbelly98's reply.

You are still talking about the probability distribution, not the location of a particle. If you insist on talking about EM field in terms of particles, photon is point-like.

Can a photon be localized? Some people think not eg. http://arxiv.org/abs/0903.3712.

 

[K^2]

Can a photon be localized?

Photon in a cavity might as well be considered localized. Yes, realistically, the barrier is finite, so there will be an exponentially decaying tail. But you can make skin depth thin enough and walls thick enough to make the description of localized photon be as valid as it needs to be.

But none of this still has anything to do with size of a photon.

 

[Thinker007]

Because this was a simplified minimal mathematics lecture series for the general public I would have assumed that his "size" comment was just a fuzzy way of introducing related concepts, except that he presented it as a specific trick question he was asked during his PhD defense.

Perhaps what he was getting at is that when detected, the photon has size that interacts with the detector with pointlike properties, but while propagating before detection it has size that is described with wavelike properties distributed over the meter distance. IOW, I suppose he was trying to emphasize wave particle duality and that both are legitimate descriptions of the real world, with an equal claim to the concept of "size."

I know I tend to think of the particle as the "real" thing and the wave function as describing a probability for where that real thing is "really" located, but I know that's sort of a non-QM bias I have from growing up in a macro sized world.

Thanks for the comments.

 

[PhilDSP]

It's been known since the mid 20th century that the wave trails of photons are typically some millions of cycles long (several meters). But that says nothing about a photon's possible extent in other spatial directions.

A photon may even be considered enigmatic if we ask the question: "What is a photon? Is it a particle that binds energy into a highly compressed region or is it a wave that potentially spreads into infinity as it's edges dissipate in time and space?"

 

[mfb]

It's been known since the mid 20th century that the wave trails of photons are typically some millions of cycles long (several meters).

Which parameter do you mean here?
Coherence length of most light sources is shorter than that (just a few wavelengths). You need a laser to get coherence lengths of meters with visible light.

 

[PhilDSP]

Which parameter do you mean here?

I think we'd need to look at the experiments that produced those results. Sorry, I don't have a reference handy at the moment.

 

[jliu135]

How about re-framing the question as follows:

If a photon travels down a direction in vacuum, how small a hole will need to be to stop it entirely.

The question might need to be asked first for visible light and then for other wavelengths should there be interesting differences (like the barrier might need to of different material).

The answer might need to be in probabilistic form, like if the photon is 450nm wavelength and if the hole is 500nm in diameter, the photon might go through 70% time.

 

[bahamagreen]

It means that the photon is still a point particle that's distributed over span of space of one meter.

I think you should explain this.

 

[mfb]

The answer might need to be in probabilistic form, like if the photon is 450nm wavelength and if the hole is 500nm in diameter, the photon might go through 70% time.

This depends on the way the light approaches the hole. A well-focused laser beam? A flashlight?
There will always be some light getting through, but for lengths smaller than the wavelength a better focus does not help any more, and the maximal (!) fraction going through begins to drop.

 

[jliu135]

laser or flashlight? It shouldn't matter. The question is for one photon. The source should not matter except for a laser, all the photons would be same wavelength and the flashlight would be many.

 

[f95toli]

laser or flashlight? It shouldn't matter. The question is for one photon. The source should not matter except for a laser, all the photons would be same wavelength and the flashlight would be many.

No, photons certainly have different propties depending on the source. You can't strictly speaking have a single photon from a flashlight, since those photons are thermal; you can only talk about a definitite number of photons (e.g. 1) for sources that emitt photons in a number state. This is why you can't create a real single photon source by simply attenuating a normal source of light (not even a laser, sine a laser emitts coherent photons).

Moreover, and perhaps more relevant to the OP, single photons can even have different "shapes"; at least if you believe that what is being measured is actually a "real" property of a photon

see e.g.

http://arxiv.org/abs/1203.5614

The correlation plots in e.g. fig 2 represent the "shape" of a single "two-peak" photon, at least if you believe the authors (I saw a talk about this at a confence a couple of months ago)

 

[jliu135]

No, photons certainly have different propties depending on the source. You can't strictly speaking have a single photon from a flashlight, ...

http://arxiv.org/abs/1203.5614
...

Ah, a bit of clarification needed here. I meant when you get down to one photon, the source should not matter except that the source would determine the wavelength or a range of wavelengths.

From the article, I find this "Here, we demonstrate that single photons deterministically emitted from a single atom into an optical cavity...". So it seems now feasible to emit single photons at will.

 

[f95toli]

Ah, a bit of clarification needed here. I meant when you get down to one photon, the source should not matter except that the source would determine the wavelength or a range of wavelengths.

But it DOES matter. There are lots of different single photon sources available, so we now know how to generate snlge photons at many different wavelenghs.
However, all of these sources are fundamentally "quantum mechanical" in that they are able to generate a single excitation, they are very different from a flashlight.
If you start with a thermal source you can of course attenuate it so that it looks like it on average emitts say a single photon per second when you measure the energy it outputs; but it won't be a true single photon source since a thermal field (as it is known) does not contain a fixed number of photons. The emitted radiation simply does not HAVE a property "X number of photons". A source that can generate single photons emitts radiation that is in what is known as a number (or Fock) state, and then this property exists (but the price you pay is that now the phase is undetermined).

 

[Naty1]

From the OP:

Perhaps what he was getting at is that when detected, the photon has size that interacts with the detector with pointlike properties, but while propagating before detection it has size that is described with wavelike properties distributed over the meter distance. IOW, I suppose he was trying to emphasize wave particle duality and that both are legitimate descriptions of the real world, with an equal claim to the concept of "size."

That's a good description, I think...

Here are a few from others:

Carlo Rovelli:

“…we observe that if the mathematical definition of a particle appears somewhat problematic, its operational definition is clear: particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier…”

A particle is in some sense the smallest volume/unit in which the field or action of interest can operate….Most discussions regarding particles are contaminated with classical ideas of particles and how to rescue these ideas on the quantum level. Unfortunately this is hopeless.

... A particle detector measures a local observable field quantity (for instance the energy of the field, or of a field component, in some region). This observable quantity is represented by an operator that in general has discrete spectrum.

presented in Weinberg's "The quantum theory of fields" vol.1...

For realistic systems with varying numbers of particles we build the Fock space as a direct sum of products of irreducible representations spaces. Then the sole purpose of quantum fields (=certain linear combinations of particle creation and annihilation operators) is to provide "building blocks" for interacting generators of the Poincare group in the Fock space. In this logic quantum fields are no more than mathematical tools.

... strictly speaking there are two distinct notions of particles in QFT. Local particle states correspond to the real objects observed by finite size detectors. ... On the other hand, global particle states...can be defined only under certain conditions... uniquely-defined particle states do not exist in general, in QFT on a curved spacetime.

and from a prior discussion in these forums:

Marcus quoting a prior post:

Marcus :

As a general rule the world is not made of particles, it is more correct and less confusing to say that it is made of fields. Unless I'm mistaken all or most of us at the Forum realize this?

Marcus' comment:

I don't count myself in this group. As Naty1's quote said "particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier." This means that particles (not some mysterious fields) are the objects studied by real experimental physics. If "curved spacetime" does not agree with the particle concept, so bad for the "curved spacetime".

And you will note, of course, these are not all in agreement...

 

[cnickford]

My understanding is that when we make a measurement we are really poking at the wavefunction, which holds all the measurable information about a particle within it. When the measurement is made it causes any probabilities to collapse and take on a definite value.

 

[godw2718]

Let us assume that a photon propagate in z direction.
For the z direction size, we can make it as small as possible (at least theoretically) by superpositioning a various wavelength photon states, which becomes a delta function in position space while it's just a plane wave in momentum space. Moreover, we can also make it small in x and y direction by superpositioning standing waves, thereby make it small.
If you express a photon as a wave packet, we can see that the wavefunction does not spread as time goes on.(for a mass zero particle while for electrons which as a finite mass it spreads out)
I think, if the principle of superposition in quantum mechanics is valid in all circumstances, we can make it localized in position space.

 

[Cthugha]

Let us assume that a photon propagate in z direction.
For the z direction size, we can make it as small as possible (at least theoretically) by superpositioning a various wavelength photon states, which becomes a delta function in position space while it's just a plane wave in momentum space.

This already implies that this "duration" of the wavepacket defines some photon size. This is incorrect - besides that you do not take into account emission time uncertainties, there is no reasonable and accepted definition of photon size.

Moreover, we can also make it small in x and y direction by superpositioning standing waves, thereby make it small.
If you express a photon as a wave packet, we can see that the wavefunction does not spread as time goes on.(for a mass zero particle while for electrons which as a finite mass it spreads out)
I think, if the principle of superposition in quantum mechanics is valid in all circumstances, we can make it localized in position space.

Can you? Really? So what defines your "photon size" then. You can get some superposition to get some kind of spatial localization of the real space photon wavefunction. If you then go ahead and calculate the energy density distribution of that photon, you will find that it is not locally connected to your real space wavefunction. It spreads and falls off as r^-7. Even worse you will find a non-zero detection probability away from the position where you "localized" your wavefunction. This probability also falls off as r^-7. So, which of these quantities defines size now?

For details, read the famous quantum optics bible "optical coherence and quantum optics" by Mandel and Wolf. In my edition chapter 12.11 discusses the problems of a meaningful localization of photons.

 

[Naty1]

So while we are at it describing the 'size of a fundamental particle' and seeing there is no 'real' answer, at least no simple one, here is perhaps the craziest explanation of all. From Leonard Susskind whose work in black hole complementarity has won him widespread recognition, from THE BLACK HOLE WAR, Chapter 20:

[Susskind is relating here views of quantum field theory and string theory and while he uses 'atom' in the following description, he is could just as well have used 'particle' or 'photon'

Black Hole complementary was proposing something...radical. Depending on the state of motion an atom might remain a tiny microscopic object or it might spread out over an entire horizon of an enormous black hole...William Unruh showed that near a black hole horizon thermal and quantum jitters get mixed up in a odd way...

[This refers to the fact than a hovering observer and a free falling observer will 'read' very different radiations emanating from a black hole horizon. So the observed 'size' of a particle as well as the very existence of a particle is impacted by the presence of a cosmological horizon.]

Elementary particles are usually imagined to be very small objects. Quantum Field Theory begins by postulating particles that are so small they can be regarded as mere points in space. But that picture soon breaks down...

He compares such 'particles' to a rotating airplane propeller...where maybe all we can see is the hub, and maybe the inner portion of the blades...but progressively faster high speed photos would reveal additional extended structure...we can see further out on the rotating blades...see further quantum jitters!

...If experiments cannot tell us whether particles have outlying high-frequency, vibrating structures, then we have to appeal to out best theories...[so when you speed up the shutter] what you see is is that every piece of the string is fluctuating and vibrating so the new pictures looks more tangled and spread out...String theory and QFT share the property that things appear to change as the shutter speed increases. But in QFT, the objects do not grow...String theory is different and works more like [an airplane propeller]...as things slow down, more and more 'stringy' propellers come into view. They occupy an increasing amount of space so that the entire complex structure grows...To most [Quantum Field Theorists] the notion of growing particles with unbounded, jittering structures was extremely foreign...Ironically the only other person who had hinted at such a possibility...was Gerard't Hooft...his work also expressed a sense that things grow as they are examined with increasing time resolution.

 

[Khashishi]

Size isn't something with a precise physical meaning in this context. The size of a photon depends on how you measure it.

 

[0xDEADBEEF]

There are basically two (compatible) definitions of a photon. The usual one is that it is an eigenmode of the electromagnetic spectrum. In the strict sense an eigenmode does not change in time. Therefore in a cavity the eigenmode fills the whole cavity, and in free space a photon is an infinite plain wave (with no amplitude... but well...) Inside these eigenmodes energy is stored, and that is the real idea of a photon. The intensity of the eigenmode drops by a quantized amount a multiple of \hbar \omega when the light field interacts with something else.

When particle physics are discussed they are usually discussed in Fourier space. One infinite plain wave of say protons interacts with another infinite plain wave of protons and they exchange an infinite plain wave of photons or other stuff. The reason why one sees the particle traces in collider experiments is that protons in colliders are a short bit of such a plain wave: a wave packet. But the main physics is captured by the plain wave description.

The interaction of a photon with the other elementary particles in the beams is point like, because its interaction does not depend on the momentum of the particles that it interacts width, leading to flat line in Fourier space and thus a delta peak in real space, for particles like neutrons which have an extend the interaction changes with the momentum of the interacting partners.

So in a way photons are point like (in their interaction) but in another way they can be really large, in a mathematical description as large as the universe.

Sorry if this reply is very technical, but we have gone a long way since the corpuscle theory of Newton, and this is all very much wave particle duality stuff.

 

[sophiecentaur]

I think it's worth pointing out that 'the photon' cannot be pictured as some sort of 'burst of oscillations' passing through the aether or as a little bullet. These seem to be the most popular visualisations.
Old habits die hard and, before finally biting the bullet and realising that it's much harder than that, people tend to hang on to the idea that QM is, in fact, just like the old mechanical system but with a few inconsequential tweaks. No. It's 180 degrees different and you just have to get over it. "Physical Interpretation"? Not possible.

 

[Ger]

Size defined as the apparture of your measuring device? Being build of the same stuff your detector is made off, it becomes complex to measure size of your own building block. It then is going to depend on how well (a part of) the wave will interact with your detector, transfering just enough energy to make a difference.

 

[sophiecentaur]

Sounds ever so much like a diffraction argument is creeping in, in disguise.

 

[remocat2222]

Perhaps what he was getting at is that when detected, the photon has size that interacts with the detector with pointlike properties, but while propagating before detection it has size that is described with wavelike properties distributed over the meter distance. IOW, I suppose he was trying to emphasize wave particle duality and that both are legitimate descriptions of the real world, with an equal claim to the concept of "size."

I know I tend to think of the particle as the "real" thing and the wave function as describing a probability for where that real thing is "really" located, but I know that's sort of a non-QM bias I have from growing up in a macro sized world.

 

[sophiecentaur]

. . . . . Which leads to the conclusion that 'size' is just not a relevant property for a photon. That is, if it can be regarded as both a point and of infinite extent - haha.
The general picture that people seem to carry in their heads (and is how it's often drawn) is a a squiggle or short burst of oscillations, a few wavelengths long. I guess that fails in most respects.

 

[Dale]

What is the size operator? If there is no such operator then the question is poorly defined. If there is such an operator then it is just a matter of plugging it into a single-photon Fock state to see what the result is.

 

[sophiecentaur]

What is the size operator? If there is no such operator then the question is poorly defined. If there is such an operator then it is just a matter of plugging it into a single-photon Fock state to see what the result is.

We're into (piece of) string, perhaps?

 

[JK423]

It has been shown that a photon can be arbitrarily "localized" in spacetime, i.e. there is not fundamental limit from the theory that forbids the complete localization of a one-photon state.

http://prl.aps.org/abstract/PRL/v79/i9/p1585_1

Edit: Localization is meant in the sense of arbitrarily small extent of its mode function as it travels with 'c', not that you localize it in a position eigenstate.

 

[Naty1]

Some comments on comments:

My understanding is that when we make a measurement we are really poking at the wavefunction, which holds all the measurable information about a particle within it. When the measurement is made it causes any probabilities to collapse and take on a definite value.

That is one view of QM...one which appeals because of its analogy to classical descriptions but fails in a number of situations. One failure is that to explain entanglement it must collapse faster than light speed...

yes:

photons certainly have different propties depending on the source.

I think it's worth pointing out that 'the photon' cannot be pictured as some sort of 'burst of oscillations' ... as a little bullet.

Size isn't something with a precise physical meaning in this context. The size of a photon depends on how you measure it.

[This is analogous to what Susskind says with his 'propeller' description.

the photon has size that interacts with the detector with pointlike properties, but while propagating before detection it has size that is described with wavelike properties distributed over the meter distance.

[yes to the first part, no to the second]

'size' is just not a relevant property for a photon.

[see the following for some further clarification of this valid point.]

///////////////////////

Other descriptions:

Albert Messiah, Quantum Mechanics, pg 66:
The wave packet...

has a center that travels analogous to a classical point particle.

From another discussion,
from Vanhees:

This position of a registration of a photon is a well defined physical quantity that can be measured, the position of a photon in the strict sense of an observable cannot even be defined in principle! For details, see

http://arnold-neumaier.at/ph.../position.html

unsure of this source...

If a photon were truly free, not interacting with any other particles, its PLANE wave would extend across the universe to the cosmological horizon.

{} my clarification:
From Wikipedia:

To account for the particle interpretation that phenomenon [double slit experiment] is called probability distribution but behaves according to Maxwell's equations. However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does {MAY} not spread out as it propagates, nor does it divide when it encounters a beam splitter.
The photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory

http://en.wikipedia.org/wiki/Quantum_field_theory#Unification_of_fields_and_particles

The "second quantization" procedure that we have outlined in the previous section takes a set of single-particle quantum states as a starting point. Sometimes, it is impossible to define such single-particle states, and one must proceed directly to quantum field theory. For example, a quantum theory of the electromagnetic field must be a quantum field theory, because it is impossible (for various reasons) to define a wavefunction for a single photon.

[Zapper had posted an identical statement to the boldface portion and I found the above confirmation.]

Also, recall that VIRTUAL photons, complex numbered particles rather than the usual real numbers, are responsible for all electromagnetic interactions as described using quantum field theory. It's QFT that is used in the Standard Model of particle physics. So not only are photon characteristics 'fuzzy' in classical terms, so too they seem to be in mathematical terms.

 

[Naty1]

Anybody have any comments on the paper JK423 posted...The description seems to conflict with what has been discussed in these forums...and it is not all that new...1997...

It has been shown that a photon can be arbitrarily "localized" in spacetime, i.e. there is not fundamental limit from the theory that forbids the complete localization of a one-photon state.

http://prl.aps.org/abstract/PRL/v79/i9/p1585_1

Edit: Localization is meant in the sense of arbitrarily small extent of its mode function as it travels with 'c', not that you localize it in a position eigenstate.

 

[ZapperZ]

I always find it interesting that this question on the "size" of a photon (or the size of anything, really) has come up repeatedly. So let's try to narrow down what we DO know from straight-forward quantum mechanics and see if people do agree on those:

1. There is a position operator in QM, and that gives you the value of the position of the particle.

2. The spread in position of the particle is not the same as the size of the particle.

3. There is no "size operator" yet well-defined in QM.

Do we all not agree on those?

Zz.

 

[Bill_K]

1. There is a position operator in QM, and that gives you the value of the position of the particle.

This right here is the hot button issue. The situation is not so straightforward in relativistic QM, partly because a single particle cannot be localized in a region smaller than a Compton wavelength.

For particles with mass, the Newton-Wigner position operator is the accepted answer. However it is argued that for photons no position operator exists.

 

[ZapperZ]

This right here is the hot button issue. The situation is not so straightforward in relativistic QM, partly because a single particle cannot be localized in a region smaller than a Compton wavelength.

For particles with mass, the Newton-Wigner position operator is the accepted answer. However it is argued that for photons no position operator exists.

That's fine. My argument and intention here are that, when there IS a well-defined position operator, and that it gives a value or an average value, that is the value of a POSITION, and not the value of a "size". I'm seeing people confusing, say, the uncertainty in position as being the "size" of the object.

Zz.

 

[Dale]

3. There is no "size operator" yet well-defined in QM.

This is the key problem that makes the question itself ill-posed. The only way to answer questions about the size of something in QM is to have a size operator and calculate its expectation.

Since there is no generally accepted size operator, I think that the OP is free to define one. Until they do, however, the question is incomplete and cannot be answered.

 

[Bill_K]

Since there is no generally accepted size operator, I think that the OP is free to define one. Until they do, however, the question is incomplete and cannot be answered.

Of course there is. But to talk about the size of an object you have to talk about an object that has a size to begin with! Which leaves out all the elementary particles, including photons, since they are pointlike.

Composite objects such as protons and neutrons have a size. For a proton it's the charge radius. A neutron's size can be defined in terms of its form factors. Nonspherical nuclei have rotational degrees of freedom, and for them the size can be defined in terms of the moment of inertia.

 

[ZapperZ]

Of course there is. But to talk about the size of an object you have to talk about an object that has a size to begin with! Which leaves out all the elementary particles, including photons, since they are pointlike.

Composite objects such as protons and neutrons have a size. For a proton it's the charge radius. A neutron's size can be defined in terms of its form factors. Nonspherical nuclei have rotational degrees of freedom, and for them the size can be defined in terms of the moment of inertia.

But those are not "size operator" the way we have Hermitian operators in QM that give you an observable value. I can also point out similar things such as scattering or absorption cross-section, which one can easily imagine to correspond to some energy-dependent "size".

The determination of sizes of composite particles is not as simple as having an operator that spits out some average value.

Zz.

 

[Naty1]

I have a semantics question:

Bill_k posts...

The situation is not so straightforward in relativistic QM, partly because a single particle cannot be localized in a region smaller than a Compton wavelength.

Is 'relativistic QM' the same 'relativistic QFT' of the Standard Model??...or should I be aware of some distinctions...

////////////

Zapper:

I'm seeing people confusing, say, the uncertainty in position as being the "size" of the object.

When one does not know all the math and subtending assumptions, like me, and apparently for many who think they do understand, that is an easy step to take. I can attribute that to at least three things that immediately come to mind:

[1] When the Standard Model defines particle measurements, that is interactions, say a point of a detection screen, and leaves unspecified what the particle 'is' between interactions, that just begs for personal interpretations galore.

[2]When interacting point particles of the Standard Model have different position uncertainities between,say, free plane wave particles [cosmological horizon to horizon]
versus confinement as, say, an orbital electron, versus a different confinement characteristic in a metal lattice, all of which we have discussed elsewhere, no wonder people like me sometimes think Sounds like it takes on different SIZES instead of interaction characteristics.

[3] Classical analogies and classical thinking never fits completely. When you quantize the classical physical electromagnetic wave, a 'physical' interaction field, stuff changes in QM in subtle ways. Nobody even calls the [Schrodinger] wave equation a 'field'...how it becomes a 'probability distribution' seems a mystery...where did my 'physical field' go?? [LOL]

 

[Mandragonia]

To talk about the size of an object you have to talk about an object that has a size to begin with! Which leaves out all the elementary particles, including photons, since they are pointlike.

Even for objects that are generally considered to be pointlike, one may postulate that they do have a very small but still finite size. Putting all theoretical and experimental evidence together, one can set an upper limit for this size. Clever experiment can be devised to reduce the upper limit further. Isn't that the way physicists approaches such subjects, for example regarding the existence of neutrino mass or the non-constancy of physical parameters such as the fine-structure constant?

 

[Bill_K]

Is 'relativistic QM' the same 'relativistic QFT' of the Standard Model??...or should I be aware of some distinctions...

Have you seen the two-volume set by Bjorken and Drell? The first book is called "Relativistic Quantum Mechanics", while the second is "Relativistic Quantum Field Theory". That's the kind of distinction I was thinking of. In the first case (aka First Quantization) you treat the Klein-Gordon and Dirac Equation as direct relativistic generalizations of the Schrodinger equation - wave equations for the probability amplitude of a single particle. Thus "position operator" unambiguously refers to position of that single particle. Relativistic QFT (aka Second Quantization) is about multiparticle states from the word go, and negative energy states are replaced by antiparticles.

Relativistic QM is an incomplete theory - one must avoid situations where pair production and negative energy states come into play, and these restrictions lead to the unusual properties of the position operator.

 

[Dale]

Of course there is. But to talk about the size of an object you have to talk about an object that has a size to begin with!

Then please write down the size operator for a particle that has a size.

 

[Bill_K]

Then please write down the size operator for a particle that has a size.

Sure, it's just r². The size of an object is its RMS radius, which is <r²>^1/2.

But not for a particle, I said "composite object". Do this for an atomic electron and you will get the size of the atom, not the size of the electron. The size of a composite object such as a proton or nucleus is determined by the uncertainty in the position of its components.

 

[ZapperZ]

Sure, it's just r². The size of an object is its RMS radius, which is <r²>^1/2.

But not for a particle, I said "composite object". Do this for an atomic electron and you will get the size of the atom, not the size of the electron. The size of a composite object such as a proton or nucleus is determined by the uncertainty in the position of its components.

But that is disingenuous, and could mislead people who don't know what you did!

That is still the position operator. It tells you the location, or average location, of an electron in a particular state. We then turn around, and use that to approximate the size of an atom. It is still not a "size operator" the way I described earlier. You do not have to have such redefinition or context to define the position, momentum, etc. operator.

Let's try to get at least some consensus here before we try to apply this to more complicated or specific situation. I listed those three statements, and at the very least, we should agree on something at the fundamental level. Or else, we'll be talking about apples and oranges, and this discussion will never go anywhere productive.

Zz.

 

[Dale]

Sure, it's just r². The size of an object is its RMS radius, which is <r²>^1/2.

I could accept that iff the object is located at the origin. However, since we cannot generally localize the object to the origin what this actually gives us is not just the size of the object but also the probability of finding it a certain distance from the origin. So this isn't a good candidate for a size operator.

But not for a particle, I said "composite object". Do this for an atomic electron and you will get the size of the atom, not the size of the electron. The size of a composite object such as a proton or nucleus is determined by the uncertainty in the position of its components.

If you had a valid size operator then you should simply be able to apply it to any particle's wavefunction to get the size of the particle. Whether it is a fundamental particle or not shouldn't matter.

If a valid size operator existed and had the property that it gave undefined results for fundamental particles, then it would be natural to say that fundamental particles don't have a size, but to say that such an operator exists but we are forbidden from applying it to a class of particles simply because you assert that they have no size doesn't make sense to me.

 

[Maui]

In some practical sense, can it be said that the 'classical' size of photons is the following - consider why ordinary light microscopes fail below 200 nm resolution - light travels as a wave and photons wavelength is too big and diffracts below this threshold and cannot penetrate further. On the other hand, photons are always detected at a point much smaller than 200 nm -- is the above an accurate description of why light can't penetrate further than 200 nm at all? If it is(it seems so according to Olympus' website discussing light diffraction) is that the 'classical' size of photons?

 

[Dale]

the 'classical' size of photons

There are no photons classically.