Particles in the Standard Model - Mass & Size

[albroun]

A quick question from a non-physicist and non-mathematician.

Do the equations of the Standard Model (without the Higgs Mechanism and any other speculative theories) presuppose that all the particles have zero mass and zero dimensions i.e. are they purely "mathematical" points?

 

[cosmik debris]

Yes, the masses are put in by hand from lab measurements.

 

[albroun]

And the dimensions?

 

[mathman]

And the dimensions?

This gets a little fuzzy because of quantum theory, i.e. wave-particle nature.

 

[albroun]

In terms of the Standard Model, however, do the basic set of equations treat the particles as dimensionless?

 

[albroun]

In other words, once the masses and dimensions (understood in the fuzzy way of statistical probabilities and indeterminacy etc) are added to the equations, do the equations run into problems which then require speculative modifications (such as the Higgs Mechanism) to make them work? Or am I on the wrong track here?

 

[cosmik debris]

In terms of the Standard Model, however, do the basic set of equations treat the particles as dimensionless?

Yes.

 

[albroun]

Is this the main reason that the Standard Model is regarded as inadequate (despite its predictive accuracy) - that the particles have to be treated as dimemsionless, massless points? Is that why the Higgs Mechanism is postulated to bring mass into the equations? Is there a similar kind of theory as to how particles gain size?

 

[cosmik debris]

That the whole process of re-normalisation is required is due to particles (quantum field excitations) being point sized. As one approaches a particle (mathematically) the forces go to infinity or zero depending on the force. At high energies you can force particles closer and closer together, if they had a size there would be a natural limit to this.

Why the masses of particles are what they are is a mystery. The Higgs mechanism breaks symmetry and gives mass to some of the vector bosons that carry the weak force, this limits the range of the force. As far as I understand the mechanism does not give mass to all particles.

As for the size I don't think there is any kind of mechanism for this. The dimensionlessness is a mathematical necessity. String theory does get around this problem a little by postulating a length to a string. This does solve one of the infinity problems associated with point particles.

 

[henry_m]

To dispel a misconception: the standard model contains the Higgs mechanism as an essential part. The Higgs mechanism is not regarded as a speculative theory and the evidence for it is very strong. There is a missing piece of evidence, in that we haven't seen the Higgs particle yet, but if it wasn't found I think it's fair to say that it would be a big surprise.

As to the size of particles: this isn't a particularly well-defined of meaningful question. Particles certainly aren't like little billiard balls whizzing around.
The fundamental objects in particle physics are fields, of which the electromagnetic field is probably the best-known example. Classically, energy and momentum should propagate through the field like ocean waves on water. But the laws of quantum physics mean that energy and momentum are carried by the field only in discrete lumps. When these lumps of energy and momentum are transferred all in one go, it's a bit like the impact of a billiard ball, and so these lumps are called particles.

So in answer to a few of the specific questions raised:
1. Do the basic set of equations treat the particles as dimensionless?
The formulation of the standard model and other quantum field theories don't start with particles at all, only fields. Particles come later as a consequence. So the equations don't have any supposition about particles at all, dimensionless or otherwise.
2. Where do the values of the masses come from?
They're put in by hand; they are free parameters of the theory which can basically be adjusted to fit experiment.
3.Why is the standard model considered inadequate?
There are quite a few reasons why we are looking to go beyond the standard model; see http://en.wikipedia.org/wiki/Beyond_the_Standard_Model" for a good overview.

 

[mquirce]

The elctric charge is a definite thing in space that not change in time. In the same "point" is another kind of charge "gravity. That is, i think, in that point must be something that posses both properties : electric force and gravity force. This concentration of force and energy in max. amount near the "point" is colled mater. Mater is alpha and omega of everything because it posses both main forces of natyre. The fields are property of matter, that is of particles that are supporter of mater.
This is the opinion of a layman