Is a photon of dimension zero?

[Nemoto]

I have read that the elementary particles of the Standard Model have dimensions 0.

Is this the case or not? I have read on this site relevant answers to similar questions, but have not found them to be very clear.

If it is the case, surely much of quantum weirdness is thereby explained: after all, why should an object having no spatial or time dimensions behave (within out perceived four-dimensional space) like something that has such dimensions?

 

[PeterDonis]

The short answer is "mu"; that is, the question you are asking is not well-defined, so it doesn't have a definite yes or no answer.

The quantum field theory that describes the Standard Model particles is often referred to as a quantum field theory of "point particles", but this is a very oversimplified way of looking at it. A better way of looking at it, which is basically the mainstream modern perspective on quantum field theory, is that the Standard Model is an "effective field theory", which is only valid below some cutoff energy scale. Since in quantum field theory, energy has units of inverse length, this corresponds to the theory only being valid above some cutoff length scale. On smaller length scales, the theory is no longer valid and has to be replaced by something else. Since we don't know exactly what the something else is, we don't know whether that new theory will still tell us that photons, electrons, etc. are point particles, or not. (If the new theory turns out to be string theory, then they won't; they'll be modes of vibration of strings.)

 

[rootone]

I haven't heard of the supposition that all elementary particles are dimensionless, and it doesn't make intuitive sense to me, (not that it has to),
Consider for example a proton, it can be described as being constructed from quarks.
The quarks can't all exist at the same point in space, therefore they must be at different points in space, this implying that the proton does have extent in space and therefore has dimensionality.

 

[PeterDonis]

Consider for example a proton

A proton isn't an elementary particle; as you note, it's made up of quarks. "Elementary particles" in the sense of the Standard Model are particles that aren't made up of anything else. Quarks are elementary particles according to the SM; so are electrons and neutrinos, and the gauge bosons that mediate the fundamental interactions (photon, W and Z, and gluons).

 

[rootone]

Thanks, that makes sense, I don't know why I was considering a proton as fundamental now.
Given that a proton isn't fundamental though, do we have any notion of it's size?, or volume?

 

[PeterDonis]

Given that a proton isn't fundamental though, do we have any notion of it's size?

It's generally taken to be around $10^{-15}$ meters, which is the approximate range within which the strong force between the quarks confines them.

 

[Finny]

It's also useful to keep in mind that in theoretical physics, elementary 'particles' as we model them are based on rather complicated mathematical models. They seem to be a bit more mysterious than we envision them in everyday language. We contruct models, calculate some mathematical outcomes, and see if we can validate the predictions by observation/detection.

In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. I think that part is generally accepted.

Here are two posts discussing particles that I like:

"... there is not a definite line differentiating virtual particles from real particles; The equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. [So we can't observe/detect the virtual particle but we can the latter.]

Here is a post from another discussion:

"(The following argument is based roughly on section 11.4 of Schutz's book, "... A classical configuration of a field typically does not have a single frequency, but it can be Fourier decomposed into modes with fixed frequencies. In quantum field theory, modes with positive frequencies correspond to particles, and those with negative frequencies correspond to antiparticles. {and complex numbers correspond to virtual particles…..


rootone says:
"I haven't heard of the supposition that all elementary particles are dimensionless,.."

As already posted, that's a simplified explanation of the standard model. On the other hand, as far as I know, all the interactions we detect are dimensionally smaller than we can so far measure.

 

[strangerep]

I have read that the elementary particles of the Standard Model have dimensions 0.

Please give a link or reference to the source of this statement. It sounds misleading at best to me. E.g., electrons are sometimes described as "pointlike", but this really just means that they have no internal composite structure (as far as we can tell with current apparatus). Interpreting this as "dimensions 0" is a mistake. (Personally, I wish the misleading term "pointlike" were abandoned.)

 

[Nemoto]

Please give a link or reference to the source of this statement. It sounds misleading at best to me. E.g., electrons are sometimes described as "pointlike", but this really just means that they have no internal composite structure (as far as we can tell with current apparatus). Interpreting this as "dimensions 0" is a mistake. (Personally, I wish the misleading term "pointlike" were abandoned.)

I am confused because of statements like this one, from Wikipedia, under the heading "Point Particle":
"For example, for the electron, experimental evidence shows that the size of an electron is less than 10−18 m.[6] This is consistent with the expected value of exactly zero. (This should not be confused with the classical electron radius, which, despite the name, is unrelated to the actual size of an electron.)"

Or this, from physics.stackexchange: http://physics.stackexchange.com/qu...ze-measurement-because-of-its-particle-nature
"The elementary particles of the standard model have dimensions 0. This certainty comes because the theoretical standard model fits very well practically all available particle data, and the zero dimension of its constituent particles is one of the basic blocs in the computations."

 

[Nemoto]

The short answer is "mu"; that is, the question you are asking is not well-defined, so it doesn't have a definite yes or no answer.

... On smaller length scales, the theory is no longer valid and has to be replaced by something else. Since we don't know exactly what the something else is, we don't know whether that new theory will still tell us that photons, electrons, etc. are point particles, or not. (If the new theory turns out to be string theory, then they won't; they'll be modes of vibration of strings.)

Thank you, this answer is very helpful, in that it explains why I am having difficulty understanding this.

 

[Nemoto]

"... there is not a definite line differentiating virtual particles from real particles; The equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. [So we can't observe/detect the virtual particle but we can the latter.]

I am not sure why, but this gives me a horrible feeling like butterflies in my stomach. It feels as though the whole underpinning of reality is so unstable that it could just disappear on a whim. Yet the tree outside my window continues to dance in the wind, all its constituent particles cheerfully moving about in synchrony, as its leaves merrily produce sugars from the morning sunlight, and its roots interact with the myriads of bacteria and fungi below.

 

[PeterDonis]

"... there is not a definite line differentiating virtual particles from real particles; The equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. [So we can't observe/detect the virtual particle but we can the latter.]

Do you have a reference for this quote? It seems questionable to me; there is no such thing as "amplitude for non-existence" of a particle.

 

[Finny]

"Do you have a reference for this quote? It seems questionable to me; there is no such thing as "amplitude for non-existence" of a particle."

I was able to trace back where I got it...
[I assume they mean 'negative amplitude'...as when a negative amplitude anti particle interacts with positive amplitude particle. Is that an imprecise way to say it?

This discussion,
https://www.physicsforums.com/showthread.php?t=386051
What is a Particle?

Post #28...
The source seems to be, the third paragraph here

http://en.wikipedia.org/wiki/Virtual_particle

My intent was to illustrate that a while a 'particle' has a common laymen connotation, perhaps quite immutatble and stable, in physics it might even be considered in a sense [Nemoto] as an "...underpinning of reality is so unstable that it could just disappear on a whim. .." as posted in the current thread above.

Like Nemoto, I had a difficult time appreciating the true nature of 'particle' ...
for example, first it seemed ,say an electron, 'orbits' a nucleus, is a point particle, then no, its really a 'cloud' , later an 'orbital' , then its better described as a wave, then as a local excitation of a wave, and finally , here in Physicsfoums, that such wave representations of particles have positive, negative and complex amplitudes, mathematically.

One of the greatest quotes for me came from ,maybe, Marcus,

"Particles appear in rare situations, namely when they are registered."

Aha, a particle can be described as a wave [function] until it is detected as a local quanta...For me that's a much clearer view than think about 'point particles'...

Nemoto:
"I am not sure why, but this gives me a horrible feeling like butterflies in my stomach. It feels as though the whole underpinning of reality is so unstable that it could just disappear on a whim. Yet the tree outside my window continues to dance in the wind..."

yes, that is a reconciliation I have yet to fully make myself

 

[PeterDonis]

I assume they mean 'negative amplitude'...as when a negative amplitude anti particle interacts with positive amplitude particle.

Amplitudes are complex numbers. There is nothing about amplitudes that corresponds to an "amplitude for nonexistence".

Post #28...

The source seems to be, the third paragraph here

I'm not seeing anything in either of these places that talks about an "amplitude for nonexistence". Nor am I seeing any text like what you put in quotation marks.

 

[strangerep]

[...] from physics.stackexchange: http://physics.stackexchange.com/qu...ze-measurement-because-of-its-particle-nature
"The elementary particles of the standard model have dimensions 0. This certainty comes because the theoretical standard model fits very well practically all available particle data, and the zero dimension of its constituent particles is one of the basic blocs in the computations."

The rest of that stackexchange answer goes on to talk briefly about form factors and structure functions (without which, the paragraph you quoted would be nonsense). But these are rather more advanced topics. I don't know how much QM/QFT and scattering theory you've studied, so it's hard to compose a helpful answer. Maybe do some reading on "form factors" in the context of scattering theory?

 

[Finny]

Hi Peter...
I just copied the following from Wikipedia, English version:

But I just realized the quote is from the third paragraph under the SECOND SECTION, "PROPERTIES"...[1] in the listed index on that page.

"Written in the usual mathematical notations, in the equations of physics, there is no mark of the distinction between virtual and actual particles. The amplitude that a virtual particle exists interferes with the amplitude for its non-existence, whereas for an actual particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more..."
Source:
http://en.wikipedia.org/wiki/Virtual_particlePlease note I am not arguing it is accurate...only that I did not dream it up out of the blue.

If there is a clearer way to state the concept, help me out. Thanks.

 

[ZapperZ]

I have read that the elementary particles of the Standard Model have dimensions 0.

Please note that from now on, you should make it a habit of citing your sources. This is a practice that we wish to instill on all posts in this forum where members want us to explain what they read, heard, learned, etc from another source.

Zz.

 

[Nemoto]

Please note that from now on, you should make it a habit of citing your sources. This is a practice that we wish to instill on all posts in this forum where members want us to explain what they read, heard, learned, etc from another source.

Zz.

Thank you for your admonition: I am sorry for this failing, and will try harder.

Richard Baxter, in his 1667 tract The Reasons of the Christian Religion, says:

"And Schibler with others, maketh the difference of extension to be this, that Angels can contract their whole substance into one part of space, and therefore have not partes extra partes. Whereupon it is that the Schoolmen have questioned how many Angels may fit upon the point of a Needle?".

Sometimes, to a lay person such as myself, who has studied so little QM/QFT and scattering theory as to have no idea what they are, some of the arguments relating to virtual particles, or energy with units of inverse length, seem similar in their flights of conjecture to Baxter's complaint from earlier times.

On the other hand, I can easily grasp, almost by instinct, that anything of zero dimensions would have zero regard for time and distance in its behaviour, and that the universe from its POV would have zero dimensions. No doubt this view is so naive as to be silly, especially to anyone who has spent years immersed in the complexities of mathematics, but to me it explains quantum entanglement at a distance, quantum tunnelling, and even how it may appear as a wave or a particle, or be in more than one place at a time.

I am hoping that someone can teach me why I am wrong, but I am only an old granny, so is it possible to explain it in terms I can understand?

 

[ZapperZ]

This is not a valid reference to be used in a Science forum such as this. You need to read again the PF Rules that you had agreed to.

Zz.

 

[Nugatory]

Sometimes, to a lay person such as myself, who has studied so little QM/QFT and scattering theory as to have no idea what they are, some of the arguments relating to virtual particles, or energy with units of inverse length, seem similar in their flights of conjecture to Baxter's complaint from earlier times.

Mathematics is the language of physics, and the mathematics of QFT is clear, unambiguous, and rigorous. When we attempt to express the same ideas in English, which is ill-suited for this purpose, the precision and intellectual rigor is lost in the translation. That's not a problem with QFT, it's a problem with the translation.
(Compare with studying the literature of another culture - if you're going to do this at more than a superficial level, you will learn the language and read the originals instead of relying on translations into your native language).

 

[Nugatory]

The short answer is "mu"; that is, the question you are asking is not well-defined, so it doesn't have a definite yes or no answer.

That's the first reply in this thread, and repeating it seems like a good note on which to close the thread.