The Stimulus Is A Failure

[Jon Miller]

I rewrote that sentence.

Model uncertainty is systematic uncertainty. However, if you are wanting to compare results of various models, or the models mean that you are measuring different quantities even then you won't include the model uncertainty in the uncertainty you quote and in the latter case can't even give an estimation for it.

JM

[Jon Miller]

examples of systematic errors as usually understood in this community are theory uncertainty (from calculation limits) and experimental systematics (for example, a miscalibrated calorimeter or tracking system)

It's the same in nuclear physics. A lot of the time, we are measuring exactly the same quantities.

As I said, I understand, and addressed, exactly the issue you brought up (in my first post, even). Nuclear physics has these same issues, as we use the same techniques and are sometimes testing the same models.

JM

[KrazyHorse]

Jon, in all reasonable models the weak mixing angle is a well-defined quantity. The fact that a measurement of sin(theta_w) using q_weak is subject to new physics doesn't mean that the new physics are a source of systematic error. The whole reason people want to measure q_weak is as a TEST of the standard model.

[Jon Miller]

There can sometimes be systematic errors that you don't understand. Then you publish your data with the correct significant figures for the uncertainty that you present, but you mention (if you can) what other possible systematic uncertainty exists and try to estimate it's size.

We have this all the time in experimental science.

JM

Bolded for emphasis.

JM

[Jon Miller]

Jon, in all reasonable models the weak mixing angle is a well-defined quantity. The fact that a measurement of sin(theta_w) using q_weak is subject to new physics doesn't mean that the new physics are a source of systematic error. The whole reason people want to measure q_weak is as a TEST of the standard model.

When did I say anything differently?

JM

[KrazyHorse]

KH, is it possible to actually explain why we need the Higgs boson at roughly my level of understanding? All the news ever prints is "it explains why particles have mass", if they even say that much. I have no idea why we would need to explain that, if the explanation is even partially true.

It may be possible. I will do my best. Jon, close your eyes. I may get a bit fast and loose.

The standard model (and in fact pretty much all models of high energy physics) are so-called gauge theories. To explain what this means, I will use electrodynamics as an example. In quantum electrodynamics the electron is a complex-valued fermionic field (I'll get back to this later). Now, if we apply a global phase rotation to the electron field (rotate the electron field in the complex plane by the same amount everywhere) then our physical quantities remain the same. The absolute phase of the electron field is unobservable. So our theory is invariant under the group of global rotations (U(1)). You can imagine this as taking a bunch of electrons and switching them all for positrons. What changes? Nothing, of course. However, what happens if you rotate locally in U(1) i.e. you switch only some electrons for positrons? All hell breaks loose, of course. Specifically, because of the derivative operator in the action



a local rotation is distinguishable. However, if you add in a term to the derivative operator then you can arrange to leave the action invariant under any local U(1) rotation. Adding in this term makes the derivative the "gauge covariant derivative" and is equivalent to adding in a new massless vector field (called the gauge field) with a coupling to the electron. The gauge field of electrodynamics is the photon.

Electroweak theory has gauge group SU(2) X U(1). It is the product group of rotations on the surface of a 3-sphere and rotations in the complex plane. This gauge group has 4 gauge fields associated with it. Now, one of the gauge fields is massless (the photon). But 3 of the gauge fields have masses (W and Z bosons). The problem is that we can't add a mass term without breaking gauge invariance.

There is also a problem with writing down a mass term for fermions. Different polarization (spins) of fermions live in different representations of the gauge group. Specifically, right-handed fermions live in a "1" of SU(2) while left-handed fermions live in a "2". The upshot is that right-handed fermions don't talk to the weak force AT ALL. Now, the only Lorentz-invariant way to write a fermion mass term is to couple a right-handed fermion and a left handed fermion together. But since they live in different representations, this is impossible....naively.

The higgs field solves both these problems. It is a "2" of SU(2), so it combines with left-handed fermions to make a "1" and this combination can couple with right-handed fermions to give a mass. Also, its vacuum state "spontaneously" breaks gauge invariance, and can give mass to gauge bosons. The reason spontaneous breaking is better than explicitly breaking with a mass term is that we get to leave the theory as a whole gauge invariant; the only reason we don't "see" gauge invariance is that we are surrounded by this condensate of the Higgs field. You can think about it in terms of Lorentz invariance; the laws of nature are lorentz invariant, but we live IN an atmosphere, and this gives us a preferred reference frame.

Now, a "2" of SU(2) has 4 degrees of freedom. 3 of these go into giving the W and Z mass. The left over degree of freedom is the higgs boson.

[Kuciwalker]

Sweet, I actually understood most of that. Thanks.

[Jon Miller]

I already know all of that
When did I imply otherwise?

JM

[Jon Miller]

I got confused about who you were replying to

I am on my cell phone which sicks

[One_more_turn]

Most of this stimulus money will be spent next year, just in time for the mid-term election.

Obama appears to me as the most politically shrewed President since Lyndon Johnson.

Although I agree with his policy goals, I'm not sure how our nation can get down from this mountain of debt in one piece.

[Drake Tungsten]

Obama appears to me as the most politically shrewed President since Lyndon Johnson.

That's good news for the country.

[Drake Tungsten]

[Sava]

The guy is a smoker. How can he not have a lighter?

What do you think... zippo? something expensive? a gift from someone... maybe something of sentimental value

or Bics that Secret Service tests for him

[Theben]

The subtle note is that if lit, the rocket looks as though it'll flame the kids behind it... i.e., the Stimulus will leave our children burned.

[SlowwHand]

Absolutely correct.