Abstract symmetry: Low and Icke

Francis E. Low, writing in his 1967 book Symmetries and Elementary Particles, says:

A symmetry principle can usually be formulated as a statement about the impossibility of knowing something. Thus translation invariance states that all points in space-time are equivalent—there is no way of knowing where you are. Any inhomogeneity observed so far has always been accounted for by identifying a field which produces it. Thus translational invariance applies to an isolated system.

Vincent Icke, a Dutchman, says in his 1995 book The Force of Symmetry:

If you wanted to organize a universe, you could compile a whole book full of rules, a long list of entries that say ‘Thou shalt not this,’ ‘Thou shalt not that.’ But if your universe consisted of a possibly infinite multitude of inhabitants, which could do an infinite multitude of things at an infinite number of points in time and space, then such a rule book would surely be multiply infinite. . . .

Alternatively, you could lump together a large (possibly infinite) number of rules in a single all-encompassing one. Thus, you might write in the Constitution of your universe, ‘Do unto others as thou wouldst others do unto thee’, or even more briefly, ‘Love thy neighbour as thyself’. Such an overall rule, that summarizes a multitude of individual possibilities, is called a symmetry. The symmetry just mentioned is between you and your neighbor. You are surely familiar with social symmetries: you and your neighbour have the same rights, even though you are certainly not the same, and may differ as to age, race, sex, creed, ethnic origin, and what not. It turns out that the symmetries that govern the quantum world are of a very special type, called a symmetry group by mathematicians.  . . .

Symmetry and redundancy in physics

A February 1992 journal entry of mine, the first entry in that particular journal:

 

Last 2013 journal entries: Order, disorder, symmetry

Dec. 19th, damn near 20th (11:55 p.m.).  Bed.

Long range order.  What is it?  Kitaigorodsky says on p. 47 of Order and Disorder in the World of Atoms, "This term can rightfully be applied to the arrangement of atoms in a crystal.” He also says, as the reason for this crystalline property, “along the directions of axes of the cell, similar atoms will be found at strictly equal distances hundreds and thousands of times.”  I put that comma in there myself.  But I do like K’s writing and would like to own a better—not falling apart—copy of the book.

I want to look at this idea in relation to the idea of symmetry.  Long range order implies a lack of symmetry.  This idea has been bugging me since I don’t know when.  Nineteen-ninety-four or a little earlier.  Long range disorder implies, as I understand it, perfect symmetry.  In other words, rotational and translational invariance.  Or, in other other words, isotropy and homogeneity.  I don’t like this idea of symmetry.  I like to think of symmetry as having to do with orderly structure, not just nothingness!  Well, one more thought: look into order, noncommutativity, and addition (summing).

6:15 p.m.  December 22.  Also, to continue the discussion above, I need to order another copy of Kitaigorodsky’s book.  Mine has fallen to pieces (it’s an old paperback, old meaning printed in 1980, although I have had it probably only since the mid-nineties.)

Thought number two:  I’ve really gotten habitual with writing the time of my journal entries.  I’m not sure I even like that.

Number three:  Oppenheimer had such great promise as a theoretical physicist, but he failed.  Why?  As Crease & Mann see it, he had no personal feeling in him for where he wanted physics to go.  He was not “his own man” is one way they describe Oppenheimer’s failure to do great things in physics.  He was clever, subtle, but in the end a physics failure.  (I’m using some applicable words from the classroom dream scene in A Serious Man.)

I view quantum field theory in exactly that way.  Gauge invariance, virtual particles, and . . . well, I’m not sure what all I’m thinking of that I don’t like, oh, yeh, the application of perturbation theory and of renormalization—these are all like Oppenheimer himself.  Cleverness to the n^th power, precocious, lacking in a clear philosophical view of what physics should be.  Now, like Oppenheimer in the 1930s, QFT and the Standard Model are having their field day.  In spite of the Higgs discovery—an amazing effort and accomplishment—I believe this field day of the Standard Model will also pass.  I think it will be replaced by something much simpler and better that puts it to shame by explaining all the current experimental high-energy data and also the electron, proton and neutron charges and masses.

1:55 a.m.  (I will keep writing down the time. Seems significant that I'm awake at 2 a.m., doesn't it?)  The day after Christmas.  "The Effervescence of the Vacuum" seems like it should be a term to describe some of the observed effects now attributed to virtual particles.

8:10 p.m.  Sunday Dec. 29.  The “law of conservation of electric charge, which is exact” (p. 194 Crease & Mann) is something I would like to now discuss.  The charge could change subtly in some situations, but may be unmeasurable in these situations.  This is in fact like symmetry:  the changes are unobservable.  E. g., changes in electromagnetic potentials are such that electromagnetic fields are not changed.

Can we also have, then, changes in electric charge of electron and proton such that the electromagnetic field is not observably different?  Huh.  Far-fetched, Frank.

Also, here’s an old thought scribbled on a piece of paper I’m now transcribing into this notebook:  “What was the thing about time I was thinking this morning?  About t = 0 in this diagram?  [Upside down T, with t = 0 at the intersection point.]   And how it should be used in the usual Einstein rest frame Lorentz transformation?  More to it!  I’ll remember it later.  Had some other inchoate thought before that.  Also:  shoot the monkey and the question of the relativity of simultaneity.”

 

Physics Today: Higgs as portal to the dark sector?

Abstract from a recent research paper:  We investigate dark matter (DM) in the context of the minimal supersymmetric extension of the standard model (MSSM). We scan through the MSSM parameter space and search for solutions that (a) are consistent with the Higgs discovery and other collider searches; (b) satisfy the flavor constraints from B physics; (c) give a DM candidate with the correct thermal relic density; and (d) are allowed by the DM direct detection experiments. For the surviving models with our parameter scan, we find the following features: (1) The DM candidate is largely a Bino-like neutralino with non-zero but less than 20% Wino and Higgsino fractions; (2) The relic density requirement clearly pins down the solutions from the Z and Higgs resonances (Z;h;H;A funnels) and co-annihilations; (3) Future direct search experiments will likely fully cover the Z;h funnel regions, and H;A funnel regions as well except for the "blind spots"; (4) Future indirect search experiments will be more sensitive to the CP-odd Higgs exchange due to its s-wave nature; (5) The branching fraction for the SM-like Higgs decay to DM can be as high as 10%, while those from heavier Higgs decays to neutralinos and charginos can be as high as 20%. We show that collider searches provide valuable information complementary to what may be obtained from direct detections and astroparticle observations. In particular, the Z - and h-funnels with a predicted low LSP mass should be accessible at future colliders. Overall, the Higgs bosons may play an essential role as the portal to the dark sector. 

(Let's hope physics tomorrow is somehow simpler and less nutty than physics today.  That's what I'm working on anyway.)

The Corrections (to '74 UALR lab report)

What I’m doing here is correcting some of my old mistakes.  In my first-ever physics lab report (see “Car Speed Measurements UALR ’74"), I mistakenly rewrote 4/100 as .004 instead of 0.04, and I used .004 to calculate the error or uncertainty in the measured speed of a car.  Well, of six cars.  So I came out with an underestimate of the error in the measurements of speed.

 

As discussed in the lab handout, the formula for “error propagation” in this case is

 σ_v/v  =  σ_t/t  +  σ_d/d,

where v is the velocity, calculated earlier from the measured time, t, and measured distance, d.  The little sigmas represent the calculated or estimated uncertainties in the speed, distance and time.  We use t, d, and v and our estimates of σ_t and σ_d to find σ_v.  This formula simply says that the relative error in speed is the sum of the relative errors in time and distance.

The values for σ_t and σ_d are, respectively, 0.42 sec and 4 meters.  The distance d is always 100 meters, measured along the roadside before the experiment began.  One person estimates when the rear bumper of a car passes the starting point, signaling to the person with the stopwatch standing at the 100 meter point to start timing.  Then the 100 meter person stops timing when the rear bumper passes the 100 meter point.  That gives t.  Another person writes down the license number of the car.  The speed is then 100 meters divided by the measured number of seconds.

So the first thing is to check my calculated speeds. They’re all right! The speed uncertainties can now be recalculated.

Case 1.  σ_v  =  (σ_t/t  +  σ_d/d)v  =  (0.42s/5.5s  +  0.04)(18.2 m/s)   =  2.12 m/s 

Case 2.   …      (0.42/6.2  +  0.04) (16.1)  =  1.73 m/s

 

Case 3.  …    (0.42/7.2  +  0.04) (13.9)  =  1.37 m/s

Case 4.  …    (0.42/4.8  +  0.04)(20.8)  =  2.65 m/s

Case 5.  …    (0.42/6.0  +  0.04)(16.7)  =  1.84 m/s

Case 6.  …  (0.42/7.0  +  0.04)(14.3)  =  1.43 m/s

By license number, the speeds and their uncertainties are:

CCH 255                     18.2  ±  2.12 m/s                    40.8  ±  4.75 mph

CIL 164                       16.1  ±  1.73 m/s                    36.1  ±  3.88 mph

AAW 197                   13.9  ±  1.37 m/s                    31.1  ±  3.07 mph

DSY 611                     20.8  ±   2.65 m/s                   46.6  ±  5.94 mph

AAV 637                    16.7  ±  1.84 m/s                    37.4  ±  4.12 mph

MWM 646 (TX)        14.3  ±  1.43 m/s                    32.0  ±  1.43 mph

The Texan wasn’t living up to his or her reputation (in Arkansas) of being a speeder.  Could’ve been an Arkie driving a Texas car, or many other possibilities. 

Oh, you can give marriage a whirl

If you’ve got some cash in your purse

But don’t marry no one but a Texas girl

‘Cause no matter what happens, she’s seen worse

--a “courting song” introduced and sung by Pete Seeger (he was strumming a banjo also) on a folk music set of albums I have, given to my brother Steven and me by our dad in 1974.