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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?

- Thread starter albroun
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- #1

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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?

- #2

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

- #3

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And the dimensions?

- #4

mathman

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

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- #6

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- #7

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Yes.

- #8

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- #9

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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.

- #10

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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" [Broken] for a good overview.

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

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" [Broken] for a good overview.

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- #11

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This is the opinion of a layman

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