What is the definition of Particle ?

[what_are_electrons]

What is the definition of "Particle"?

I have a good idea what a wave is, but am not sure of what a particle is.

What is the definition of Particle in the singular sense?
Please do not describe particles in a group sense.

Please try to use one of the following lead-ins
1. A Particle is ...
2. A Particle is NOT ...
3. A Particle has...
4. A Particle does NOT have...

 

[dshaw]

Here is a very nice resource, with good real-world representations. http://www.sas.org/E-Bulletin/2001-10-12/mot/column.html

Indeed, what we normally think of as particles (electrons and the like) are not really particles at all, they are bundles of waves that are neither particles nor waves in their entirety, but something that look alarmingly like either one depending upon what we are looking for...

...What we are doing is generalizing the motion ... so that we can make it simpler. The technical term for such a generalization is abstraction. We abstract (take from) the specific example those parts that are common to all similar problems. Since we are looking at motion,we look to see what the [particle] has in common with [other particles]

...The highest level of abstraction for an object of any kind is to treat it as a particle.

 

[what_are_electrons]

Here is a very nice resource, with good real-world representations. http://www.sas.org/E-Bulletin/2001-10-12/mot/column.html

After reviewing that article, the thought occurred:
Should we then think of a free electron traveling through a vacuum chamber to be a wave or a wave-packet and abandon all thoughts of what a particle is?

What about the proton with its 1836X higher mass? Or the positron, or the neutron...?

Should we imagine that physical or mechanical mass, free of charge or field, does NOT exist in our universe?

 

[what_are_electrons]

Do particles have physical mechanical mass or is it electromagnetic mass?

 

[Gonzolo]

If a particle does not have physical mechanical mass, what does?

 

[what_are_electrons]

If a particle does not have physical mechanical mass, what does?

Quite possibly Nothing.
Do we or does QM/QED/QFT need physical mechanical mass?

 

[humanino]

The mass of ordinary matter around us is almost only hadronic mass, because the electrons have such a tiny contribution. So I am not dealing with electron mass here. I wanted to point that hadronic mass is almost entirely due to the glue fluctuations. This in turn is a dynamical mass, it is really in the form of trapped energy.

We would need Pete's help here. Mass is really the same as energy.

 

[Calculex]

The mass of ordinary matter around us is almost only hadronic mass, because the electrons have such a tiny contribution. So I am not dealing with electron mass here. I wanted to point that hadronic mass is almost entirely due to the glue fluctuations. This in turn is a dynamical mass, it is really in the form of trapped energy.

We would need Pete's help here. Mass is really the same as energy.

Yes. The mass of a nucleon is about 60 times greater than the mass of the individual quarks that comprise it. There are no other real particles in there. So the additional mass has to be due to the energy of the strong nuclear force (gluon 'field'). That part I can understand.

But what about the quarks themselves and the leptons. These are 'fundamental' particles. What gives them mass?

Calculex

 

[humanino]

The mass of a nucleon is about 60 times greater than the mass of the individual quarks that comprise it.

Depending on the value you take for the quark masses... A very difficult question really.

But what about the quarks themselves and the leptons. These are 'fundamental' particles. What gives them mass?

In the standard Electroweak model, the Higgs field is responsible for the mass of the force carriers, which are vector bosons. This is a very neat mechanism. It is used very often in condensed matter, but its relevance for the generation of mass at a fundamental level is yet to be proven.

A very short and poor explanation : consider the shape of a mexican hat. A particle can roll freely in the gutter, it costs no energy to trigger the movement : that is, this shape exhibits a symmetry corresponding to a massless particle movement. Yet the true physical degrees of freedom must be constructed from the vacuum state. The vacuum state picks up one particular point in the gutter, and spontaneously breaks the symmetry of the mexican hat. From this particular point consider the direction along the gutter : the massless mode is a a scalar and called the Goldstone boson. The great discovery of Peter Higgs was, starting from a gauge theory with massless vertor bosons and adding the symmetry breaking scheme as well as a coupling between the Goldstone scalar and the massless gauge bosons, to find that one can formulate a new theory equivalent to that of a massive vector gauge field. The massless gauge boson had only two degrees of freedom (out of the three of the vector) just as the photon can only be left and right polarized. Through the Higgs mechanism, the gauge boson 'eats' the scalar degree of freedom, and becomes massive.

This is the Standard Eletroweak model. It is very likely to be true, because it works very well and is so elegant. But as long as we do not have detected this Higgs particle, we cannot tell for sure.

As Marlon will want to add one can generalize this, and actually create the mass of fundamental matter particles. I am not familiar with this though. I will let him to describe the dual abelian Higgs model.


From Wikipedia

In 1993, the UK Science Minister, William Waldegrave, challenged physicists to produce an answer that would fit on one page to the question 'What is the Higgs boson, and why do we want to find it?'
A quasi-political Explanation of the Higgs Boson
http://www.phy.uct.ac.za/courses/phy400w/particle/higgs.htm
From DESY
[thread=43685]Elementary Particles Presented[/thread]

 

[Calculex]

A very short and poor explanation : consider the shape
of a mexican hat.

Thanks for this post. Very helpful. I am a little 'weak' on my
understanding of the weak interaction. I am finding this thread and the
"Elemenary particles presented thread to be very well done and the links
are very useful. You and Marlon are doing a very good job here.

(PS. I hope you are enjoying Paris. I spent 4 months there many years ago. It was really cheap then).

 

[humanino]

Thank you Calculex. I do have difficulties with this part of the Standard Model too, I am not working with it really. I really thought somebody would give correction to my post. I will try to fill the gaps by myself.

So indeed one starts in the standard model with massless particles. Well, the Higgs part would be :
$${\cal L} _H=( {\cal D}_{\mu}H)^{\dagger}({\cal D}^{\mu}H)-V(H)$$ with $${\cal D}_{\mu}H = (\partial_\mu + \imath {\mathbf W}_\mu +\frac{\imath}{2}y_hB_\mu)H$$ and $$V=-\mu^2H^{\dagger}H-\lambda(H^{\dagger}H)^2$$

So really $$\mu$$ is the only "mass" term, but with the wrong sign (as usual, this is the mexican hat shape). $$y_h$$ is the hypercharge of the Higgs, which so far is only a spinless boson, weak doublet (and color singlet), this being later broken into a single scalar. So anyway, one still has to identify all the physical fields.

My point to complete the previous post, was that I do not really understand the generation of mass for the fermions. Is it only : one introduces a coupling to the Higgs and this in turn is analogous to a mass term because the Higgs is a scalar. Is that all ? I mean that in the case of the vector bosons mass generation, there is a mechanism to take one degree of freedom from the Goldstone (unwanted) to the longitudinal part of the (previously massless) vectors. On the contrary, one "only" has to break chiral invariance in the case of fermions. One "only" has to mix left and right. There is no need for any new degree of freedom (of course, only chirality gets broken, this is well known from the Dirac equation). This in turn is "only" adding a a term $$\sim h f\bar{f}=h(f^{\dagger}_Rf_L)$$ and identify the coefficient to this term as the mass of the fermionic field

I am not saying "this is the easy part", especially for quarks where one has to define the mass eigenstates for the up-like quarks.

Ref. : P. Ramond "Journeys Beyond the Standard Model" FIP n° 101
Well, I needed not the "beyond" part for this This is an excellent one.
amazon

 

[Mk]

According to quantum theory, isn't a particle a measured wave?

 

[zefram_c]

My point to complete the previous post, was that I do not really understand the generation of mass for the fermions. Is it only : one introduces a coupling to the Higgs and this in turn is analogous to a mass term because the Higgs is a scalar. Is that all ? This in turn is "only" adding a a term $$\sim h f\bar{f}=h(f^{\dagger}_Rf_L)$$ and identify the coefficient to this term as the mass of the fermionic field

Not quite. There are two terms that end up introduced in the Lagrangian: one is the interaction with the Higgs field (the coupling you mentioned), and the other is a constant term $$\sim (f^{\dagger}_Rf_L)$$ . This term is what mimics a Dirac mass term and is identified with the fermion mass. The constant is related to the vacuum expectation of the Higgs and the fermion-Higgs coupling. More details tonight.

 

[reilly]

The idea of a particle is an old and honorable one, and is clearly a fiction -- but a convenient one. Don't forget that the wave function of a particle, properly squared, gives the probability density, the probability of finding the particle at a POINT -- we'll forget about normalization problems. QM is based on point particle ideas, as is QFT, as is E&M and classical mechanics. A particle is something that can be found at a point, and whose mass/charge density is a delta function. Whether you are reading Zee or Goldstein or Jackson, a particle is a particle is a particle.

Of course, the idea of a point particle does not always apply -- hadrons have material extensions, electromagnetic form factors and all that. Photons cannot be localized to a point, only almost -- an exhaustive discussion of the space-time properties of photons and photon measurements can be found in Mandel and Wolff's classic book on Quantum Optics. (If you want to understand photons, the this book is a must read.)

During the early days of particle physics, particles were made visible in Wilson Cloud Chambers, and later with bubble detectors. Electrons, and protons, for example, made tracks, which were quite consistant with moving point particles.

When we get smarter about describing complex bodies in relativity, then perhaps the idea of a point particle will beome less important. But for now, point particles are about the only game in town.

Regards,
Reilly Atkinson

 

[Andrew Mason]

What is the definition of Particle in the singular sense? Please do not describe particles in a group sense.

The problem is that 'particle' and 'wave' are a macroscopic concepts. All we can really talk about at the sub-microscopic level are particle-like and wave-like properties and structure.

One could consider the collection of properties of particles as defining what a particle is. A particle having mass is fundamentally different than a massless particle so they require two different definitions.

I don't have much trouble thinking of massless particles - eg. photons - as waveforms having certain particle-like qualities. I have more difficulty thinking of matter particles as being wave-like.

As far as I can see, the only properties of a massless particle that appear particle-like are its discrete momentum $p = h/\lambda$ and discrete energy $E = hc/\lambda$. Other than that, you can think of them as waves always in motion. They do not have a structure nor can they define a frame of reference. They also do not seem to resist passing through each other.

Matter particles, on the other hand, have structure and define a frame of reference. Two matter particles cannot occupy the same position in space-time without destroying their structure. It seems to me that it is only the uncertainty surrounding their location and/or momentum that gives matter particles wave-like properties (eg diffraction). The less uncertainty there is, the more 'particle-like' and the less 'wave-like' they appear.

Andrew Mason

 

[what_are_electrons]

What if we add Pauli's Exclusion Principle to this?

If a particle is better represented as a wave phenomenon with wave properties, then questions arise:

1. Is a particle, even one thought to be made of pure energy, a standing wave or a decaying wave?

2. Should a wave with one single crest and one single trough be called a wave or a particle?

3. If particles are better thought of as waves that do not have any mechanical mass, and are made of pure energy, then does this mean energy moves in the form of waves?