Wednesday, December 31, 2014

Colorado's "Year of Green" (MJ): The Highs, the Lies and the Lows

Justin Auchenbach of Casper, Wyo., gives a high-five inside LoDo Wellness in Denver in anticipation of making a marijuana purchase during Colorado's first day of recreational pot sales on Wednesday.
One of the first retail MJ customers delivers high fives at a Denver Pot Outlet in January.

Now that nearly 365 days have elapsed it is possible to assess the past historical year whereby one state (Colorado) came to be the marijuana mecca of the world.  Enough data is now available to show how successful Amendment 64 has been, in legalizing the retail sale of marijuana. Despite that, too many are unaware of the level of success, as well as the level of failure - given the fact that one less-publicized aspect of 64 is  that local communities, even counties, could opt out. (This had been an important part of the amendment's wording, allowing choice in whether any given locale would take on MJ retail sales or exclude them.)

First, some of the facts compiled from the Denver Post ('Legalization Review', Dec. 28):

- Colorado's annual demand for MJ:  130. 3 metric tons

- Adults 21 and older using MJ at least once per month:   485,000

- Total medical MJ sales - January-October:  $326, 716, 273

- Proportion of MJ sales to out of state tourists in mountain communities - 90 percent

- The proportion of Colorado MJ users who consume it each day:  23 percent

- Amount brought in from taxes, licenses and fees - January-October: $60.1 million 

To read through the preceding, the unwary might conclude the state is awash in stoners, leaning against buildings and barely able to get themselves from point A to point B. They might also wrongly conclude retail pot stores are all over the state. In fact, the Post's stats show that more Colorado communities (165) have chosen to disallow retail pot sales than have accepted them (53).  Check that ratio again and it is more than three to one NO. Yet this is one of the aspects that has rarely been publicized.

According to industry spokesman Mike Elliot, of the Marijuana Industry Group:

"I think the local option is one of the best aspects of Amendment 64. If communities don't want this, it shouldn't be forced down their throats."

Well, that depends. What if, for an entire county, the Amendment passed, but its city council decided to ignore the voters' will?  The Post has noted two radically different approaches, one that respects the citizen and the other which basically spits on his vote.

For example, in Lakewood, CO in November, the City Council gave voters the chance to cast votes in a specific separate referendum that would have allowed the opening of pot retail stores. According to Mayor Bob Murphy, "the issue was important enough that city leaders felt the decision ought to go to a vote of the people, rather than be decided by the city council".

The referendum result was to scrap pot shops in Lakewood for now by a 53- 47 % majority.

Colorado Springs, conservative bastion of military interests that it is, chose to go in the opposite direction, making a city council decision that took it out of citizens' hands. They probably knew, given the fact the amendment passed by 5,000 votes in 2012, they might not win and they didn't wish to take that chance. In other words, they didn't trust we the citizens to make the right decision.

The fallout as many have noted, is that the $6-9 million a year the Springs might have gotten via taxes, fees - to fund its Pioneers Museum - will now go to neighboring Manitou Springs which has recently allowed retail pot, wisely noting COS' negative is Manitou's gain. Sadly, the City Council will have to continue to beg for $ for its daffy museum, but most of us will have no sympathy for them - given they already "made their bed".

The Lies and the Lows:

Yes, there were lies and lows that emerged over the year. First, some of the lows:

- The death of an African college student from Wyoming who - after eating an MJ cookie and not attending to the warning dose- jumped off a building

- A father of two, shooting and killing his wife after he ate several MJ candies and began hallucinating.

- Incidents of MJ edibles ingestion by children rushed to ERs

- NY Times columnist Maureen Dowd comes to Colo. and eats an MJ cookie without noting the dose, then writes a crap column about her "psychotic" experience.

Since these transpired, Colorado MJ regulators and the businesses have gone all out to more properly assay THC content in each product, including cannabis oil.  They have also packaged edibles more securely with  more prominent warning messages and the THC doses in edibles such as cookies, candies.   Of course, as many in the MJ business have pointed out, parents are also expected to do their part in minding what their kids are doing.

The lies:

- You can openly buy MJ on the street (only in the black market- not the regulated one!)

- If an adult purchases marijuana edibles only he or she can transport them across state lines. (Absolutely not!)

- People who purchase marijuana at a retail outlet can then smoke it  -like a cigarette- on the street. (No you may not, you are expected to take it back to your domicile to use it)

- Any kid can just grab an MJ edible off the shelf of a pot retail shop. (Fact: No kid is even allowed close to an MJ shop and no kid would be permitted entry!)

- MJ businesses can openly advertise their wares in newspapers, magazines and on billboards. (Absolutely not - any marketing has to be via word of mouth!)

- MJ edible candies look exactly like name brand candies such as Tootsie Rolls, M & Ms, Snickers bars.

- More people have been busted for driving under MJ influence than for alcohol.

Meanwhile, the Denver Post in its editorial yesterday, did correctly note that with the implementation of the new law, marijuana use by Colorado citizens has increased. But this would be expected if any new business had opened up, in any state, and it sought growth. After all, to survive a business must grow which means building a customer base. And many of these will be people who are curious about the product, and have never tried it before.

As the owner of the Pot retail chain Euflora observed on MSNBC's series 'The Pot Barons of Colorado', many of her customers are trying it for the first time, largely in the form of the edibles. As word spreads on how good the edibles are, and their mellow effects - taken in the proper dose - then many more new customers sign on. Basically, their numbers are only limited by the types, amounts of product they desire.

But as the earlier stat cited from the Post showed, that still means only 485,000 people using even once per month. That is barely 9 percent of Colorado's population, so it's not as if the whole state is under the influence of pot or even a tenth of the state's populace.  This is important so that outsiders keep it in perspective.

There is still much to be done, and the next year may well show if the pot business is here to stay or if it turns out to be merely a temporary craze. My bet is that - having seen the MSNBC series and the Post's review - it is likely to stay and become a credible model for responsible MJ businesses for other states.

There will always be naysayers, of course, and this is to be expected with the end of any era of prohibition, look at the 1930s with alcohol. But in the end, the fewer laws on the books which can put people away - take away their freedom for an individual choice - the better. And the more the states can regulate and tax the more likely they are to be able to fund such things as education and pensions - when other sources are collapsing.  It is certainly to be preferred over casinos!

Tuesday, December 30, 2014

Solutions to General Relativity -Tensor Problems

1) Write out in long form the full sum (all terms) for the interval ds2   =  g mn dx m dx n


We write the interval:   ds2   =  g mn dx m dx n
   = g 11 dx12    + g 22 dx22    + g 33 dx32    + g 44 dx42                           
+   2 g 12 dx1 dx+   2 g 13 dx1 dx3 +   2 g 14 dx1 dx4
+   2 g 24 dx2 dx+   2 g 34 dx3 dx4 +   2 g 41 dx4 dx1
+   2 g 42 dx4 dx2 +   2 g 43 dx4 dx3

2 (a)Using the appropriate relations, estimate  the density of the universe  at a time 0.01 second after the Big Bang


a) The density is expressed:

r(t) = 3/  8 p G t 2

Where G =  6.6726 × 1011 m3s2kg1

t = 0.01 s

r(t) =   3/  8 p [6.6726 × 1011 m3s2kg1](0.01s) 2

r(t) =  1.78  x  10 13  kg/ m3

b) Repeat your computation if the Hubble constant is found to be H =   100 km/ sec/Mpc.

The result is unaffected because r(t) does not depend on H, the Hubble constant.

The U.S. Hangs Onto To Its "North Korea Dunnit" Malarkey - Why Be Surprised?

Randall Park as Kim Jong-un, as his head explodes in 'The Interview, and Jeremy Renner as doomed journalist Gary webb in 'Kill t
Left:Little Kim after being head shot and just before his head is exploded by CIA assassins in 'The Interview' - which lap dog patrons have paid good money to cheer and say the 'Pledge of Allegiance' to before watching. Who are they allegiant to, murderers? Or are they just ordinary jingoistic assholes? Right:  Jeremy Renner stars as journalist Gary Webb in 'Kill the Messenger' - a worthwhile film all REAL Americans ought to see.

The U.S. appears to be sticking to the "North Korea dunnit" line despite all signs pointing to an enclave of hackers belonging to a group called 'The Guardians of Peace'.   Every indicator shows the malware and other attributes were deliberately employed as decoys to set up the North Koreans. Far fetched? Hell no, especially not when there's a sordid history of this country setting up decoys in order to take the heat off the real perps.

You need look no further than how Lee Harvey Oswald was set up just over 51 years ago in the Kennedy assassination. The CIA, desperate not to leave its fingerprints on the assassination, made sure to paint Oswald as a lunatic commie loner - complete with purchased useless weapon - in order to target the Soviet Union and Cuba. The original plan was to make it look like a commie plot to justify attacking Russia and Cuba.  But even then there were savvy journalists, like Newsweek's Kenneth Crawford, that didn't buy it. It was too easy, too pat and besides, as Crawford observed in his column a week after the assassination: "How explain the irony of a lone pro-Castro gunman being fingered in a city - Dallas- that is a Right Wing citadel?"

How indeed! But when agendas are afoot - especially launched by an agency of one's own government, anything is possible.

Yesterday, according to Politico the FBI was briefed on the alternate but much more credible theory that unknown hackers set the North Koreans up.  Especially noteworthy, that at least one Sony insider - a former employee- played a major role in engineering the hack.

Rather than the U.S. government, then, most savvy in the know people are turning to experts like Norse, a Silicon Valley cyber security firm. Also, the FBI wanted to know from Norse who it thought was behind the attack on Sony Pictures.

Kurt Stammberger a senior Vice President at Norse, had already informed CBS News in an interview a week earlier that "all signs indicated the attack was an inside job". As the Norse VP put it:

"There are certainly North Korean fingerprints on this, but when we run all of those leads to ground they turn out to be decoys or red herrings."

He added that Norse's own investigation points to a woman who calls herself "Lena". According to Stammberger, this Lena worked at Sony Los Angeles for ten years until leaving the company in May. As he explains:

"This woman was in precisely the right position and had the deep technical background to locate the specific servers that were compromised."

Despite all this, the State Dept. said Monday it "had no plans to change its position", adding "we are confident that North Korea is responsible for this destructive attack and we stand by that conclusion"

And why wouldn't they - given that State is still loaded with Neocons, and they were instrumental (especially State harpy Victoria Nuland) in ratcheting up the Ukraine crisis back in the spring - by spurring on the unrest in Kiev?  These Neocons in State already have an agenda to stir up the trouble pot so why not here too?

Backing up my contention is the take of cyber-security expert Hector Monsegur who noted on CBS:

"There wasn't enough time to do an investigation, looking at all the attack vectors, looking at all the logs."

In other words, the government's conclusion on who orchestrated the attack came far too soon, exactly parallel to the gov't modus operandi in the Warren Commission Report - finding Lee Oswald guilty  even before the Commission formally commenced (Google "Katzenbach memo") despite the fact all signs pointed to Lee being an obvious decoy, a patsy.

According to Monsegur:

"North Korea would not be able to handle such a massive amount of information, going into it from an external source - without raising any red flags. "

Skeptics like me point to not only the short length of time the FBI took to draw its conclusion (again, similar to what they did under J. Edgar Hoover in the Kennedy assassination case) but also the malware used in the attack which use by N. Korea is not exclusive. It's used around the world, including the U.S. in its Stuxnet worm.

So who are you going to believe, the government - with an obvious agenda- or objective security experts like Kurt Stammberger and Victor Monsegur? Given the government's hideous record in concealing the truth - including in past bogus whitewash investigations, I choose to believe the experts - who are in the business of detecting the cyber-leaks and tracing them to the actual perps as opposed to decoys.

See also:


"The U.S. government, including the security apparatus and the State Department, have a long history of bald-faced lies, and the corporate media has a long history of taking its talking points from the State Department. I don’t even want to waste time reprising the litany of lies that accompanied the preparations for the criminal assault on Iraq. Anyone paying attention knows what happened."


Monday, December 29, 2014

A Look At General Relativity (Part 4): Expanding Universe and the Big Bang

6. Expanding Universe – The Big Bang

It is generally little known or appreciated that when Einstein’s field equations are generalized to take into account the effects on the radius of the universe, the expansion of the universe naturally results.

Einstein's gravitational equations (with cosmological term, L, for the sake of generality) are

 R mn    – ½  R g mn = T mn  +  L  g mn   

After inserting the stress energy tensor equations into the Einstein field equations one gets:

(dR/dt ) (/R)2  = (8 p)/ 3 (G r) – k / R2


(d2R/ dt2 )/ R  =  - 4 p G mn    (p + r/3)  + L/ 3

After setting the cosmological constant  L = o and eliminating r, one obtains as soln. for R (radius of universe as power law function).

R=  (9/ 2GM)1/3   t 2/3

    One can deduce from this that at the Planck energy of 1019 GeV, the symmetries of gauge theory were still united in a single force. This is at a time of 10-44 seconds of cosmic age.

     This also represents the closest approach of physics to the cosmic singularity (t = 0) but still defines the ‘Big Bang’ since the explosion is already underway and forces are still unified.

    Note also that as t increases, R increases, thereby disclosing the expansion of the universe. Originally, Einstein had set out a value for the cosmological constant, which some sources had cited as:

L  »  - 10 . 3  x 10 -34 sec -2

Which disclosed a retarding  force that for any given instant t, allowed the universe to remain static, i.e. rate of instantaneous expansion canceled by retardation.   Einstein later admitted this as “the biggest blunder” of his life and thereafter agreed that the best approach was to let  L = 0 so that the result conforms with the observations.

 It is interesting that we can use basic physics concepts to do with the conservation of energy, along with  cosmic expansion as embodied in the Hubble law, i,.e.  v = H R

Showing that the velocity v of recession for an object increases with distance R, to find the  density near the time of the Big Bang.

     The age of the universe (in seconds) related to the Hubble constant by:

 t = 1/ H

Currently, we estimate H   » 70 km/ sec/Mpc, where Mpc denotes ‘megaparsec’ – where 3.26 light years is equal one parsec)

      Since the recession is isotropic (in all directions) we can assume an expanding sphere, for which the total energy must be:

E(total) =   K    +   V

Where K and V respectively denote the kinetic and potential energies (In the latter case, we visualize the work done in displacing a reference mass, say m, away  from a central attracting object – doing work against the gravitational force,:

F = . GM m/ R2  so that: V  =  ò ¥ o  (GM m/ R2  ) dR 


K = mv2 / 2      and V  =   - GM m/ R

where R is the radius and G is the Newtonian gravitational constant, G = 6.67 x 10 –11  N- m 2/ kg 2

Let M =   r (4 p R 3/ 3)

Where the bracketed quantity denotes the sphere volume and r is the density. Using the above expression for M (total mass) and elementary algebra , we can rewrite the equation for the total energy of the expanding universe as:

E(total) =  K  +   V  = 

  m (HR)2 / 2  -   G m r (4 p R 2/ 3)

where the recessional velocity v = HR has been substituted in the first term. We can factor common quantities (to both terms) out and obtain:

K  +  V  =  m R2  [ H2/ 2   -  G r (4 p / 3)]

Note that the condition for minimal “escape velocity” for a distant object will be attained when E(total) = 0, or the bracketed term is zero., which implies:

H2/ 2   =   G r (4 p / 3)

This is exactly the equation that can be used to determine the critical density r c , of the cosmos – beyond which we may expect it to expand forever.  Thus:

  r c    =   3 H2 /  8 p G

This works out – using the current estimated  value of H – to about 9.3  x  10 –27 kg/ m3

We can even go beyond this, generalizing the same physics, to obtain an estimate of the cosmic density in the very earliest instants after the Big Bang. We can do so by recognizing that all the above key quantities (H, R, r) are in reality functions of the time t elapsed after the Big Bang. Thus, we can replace R with R(t),  H with H(t) and r with r(t). H(t) is not a big worry since we already saw that t = 1/H , so we can re-arrange the earlier equation for critical density replacing H = H(t) with 1/ t, and obtain a simple expression to solve for r(t).

r(t) = 3/  8 p G t 2

Where various values for t can be substituted into the equation to obtain r(t).- the cosmic density at that instant. For example, say we want to know the density at a time of 0.03 seconds after the Big Bang. Then, substitute t = 0.03 sec, and the value of G (assuming it has not changed with time, and is truly constant!)

r(t). =  1.98  x  10 12  kg/ m3

This is a truly astounding density that fully comports with our expectation that the Big Bang was initiated in an extremely high density state. By way of comparison, plutonium has a density of 19, 200 kg/ m3 . Thus, the cosmic density at t = 0.03 sec after the primordial fireball was just over 100 million times more dense than plutonium!


1) Write out in long form the full sum (all terms) for the interval ds2   =  g mn dx m dx n
Be sure to include all terms  for the sum that are applicable to standard form.

2 (a) Using the appropriate relations, estimate  the density of the universe  at a time 0.01 second after the Big Bang.

b) Repeat your computation if the Hubble constant is found to be H =   100 km/ sec/Mpc.

Wait! College -Bound U.S. Kids Need Mommy & Daddy to Come Along?

"Emilio" - a Loyola freshman, ca. 1966, studies physics while his clothes dry in the laundry room of Biever Hall. He'd have been humiliated if his parents got an apartment near by so they could oversee his choices, study habits etc. (From Loyola Wolf, 1966-67)

Back in the 1960s we deemed it a badge of independence and honor to go off to college, and commence establishing our own persons and lives in the academic environment. You never remotely heard of a parent or parents accompanying the freshman - say to Loyola or State U. - and taking a rented home or apt. to be near the little dweezil so he or she didn't feel too homesick - out of sorts, or having less than optimal study conditions.  Today, it appears to be a trend, with super-helicopter parents following their charges all the way to the hallowed halls to hold their widdo hands and ensure every textbook is pre-bookmarked for later study. .

According to an AP report in yesterday's D. Post (p. 4E):

"Coldwell Banker, the real estate firm, first noticed parents making such moves in 2008 while compiling its annual College Home Price Comparison Index that ranked average home prices in more than 300 college towns."

Quoting David Siroty (a company spokesman) it was noted that agents had seen new home buys and rentals pop up around the country - always near campuses. Getting inside the numbers, they found that parents were the purchasers or renters, and typically set up home so little Debby or Bobby could come home to a nice din-din and home cookin' rather than have to eat that nasty cafeteria food.

Regina Santore, a Coldwell agent in Knoxville, TN, cited a case where she relocated one couple from a town 380 miles away on the western end of the state "so their freshman could live with them".  What ever happened to establishing one's independence which used to be something to be proud of when you were 18 - and leaving HS? Did one not "put away the things of a child" when s/he left the toys of high school behind? Apparently not any more.

According to Ms. Santore:

"They felt very strongly they did not want their daughter living on campus. They felt she would have a better study environment if she were with them."

Well, of course she'd have a better study environment! They don't usually call dormitories "zoos" for no reason! But the whole point missing this pair is that college isn't ALL about studying, it's also about learning how to negotiate interpersonal connections, interests and making life long friends.  In this case, one grasps that one might sacrifice a half a point GPA or whatever in the interest of more profound human goals. But given today's success freaks - students and parents - it's no surprise that has gone by the backboards. Better to grab that 4.0 and be a total douche than come away with friends - easier to just connect with virtual friends on FB. Sad.  But it elicits the question: What's behind the mollycoddling?

Hara Estroff Marano, editor-at-large of Psychology Today and the author, most recently, of A Nation of Wimps: The High Cost of Invasive Parenting, seems to have the answer nailed:

"But in a real sense, students don't really leave their parents behind. Their parents go to college right along with them — in their front pockets. That is, the parents are a speed dial away by cellphone. And the evidence is clear that students call parents and parents call students at an alarmingly frequent rate. This, of course, significantly reduces independence.

A student gets a C on her first paper? Instead of absorbing the negative information and figuring out how to resolve the problem or how to do better, the call gets made to home, where Mom or Dad solves the problem, often by calling the school administration. This kind of behavior is, sadly, commonplace today and is a mark of the lack of coping skills among students because all the lumps and bumps have been taken out of life for them until now."

Which is pretty much my take. Protect the precious little dears so they undergo a minimum of pain or travail. Keep them in an artificial cocoon to keep them dependent babies as long as possible. Don't allow them to have to negotiate their way in an unfamiliar college environment  - god forbid!

This take is also supported by Linda Bips, college psychologist:

"Many of today’s students lack resilience and at the first sign of difficulty are unable to summon strategies to cope. The hardship can be a failing grade on a test, a cut from the team, or a romantic breakup. At the first sign of trouble many become unable to function and persevere. Often they even anticipate difficulties and their anxiety alone paralyzes them."

She then goes on to point out just how many incoming college students are on "meds" and writes:

"The number of students who arrive at college already medicated for unwanted emotions has increased dramatically in the past 10 years. We, as a society, don’t want to “feel” anything unpleasant and we certainly don’t want our children to “suffer.”

Bingo! The problem,of course, is that when they hit 29 or 35 they are still dependent little spoiled brats. Worse, they will lack any personal authenticity. Templates for narcissists as one psychologist put it.

As Prof. Bips also observes:

"The resulting problem is that by not experiencing negative emotions, one does not learn the necessary skills to tolerate and negotiate adversity. As a psychologist, I am well aware of the fact that some individuals suffer from depression and anxiety and can benefit from treatment, but I question the growing number of medicated adolescents today."

So kids are overly medicated because they can't withstand too much reality and hence this also explains why they need mommy and daddy to tag along to tell them when to even take a dump. In the 60s, in our college days then, we took our lumps like the adults we one day wanted to be - whether from our profs or fellow students (including for 'Hell Week' orientation). The lumps taken helped us build character, personal authenticity (not just being part of a crowd) as well as reinforced critical thinking skills, i.e. when we engaged in sometimes animated 'bull sessions' in the dorms.

Today, the presence of parents neutralizes that critical first step to adulthood and keeps the would-be college student in a prolonged state of infancy.

Fortunately, at least some of the kids saddled with parental helicopters know which end is up and aren't overly enthused. This was uncovered by a Georgetown alum, Sheila Baker Gujral - who has interviewed prospective frosh for that D.C. school. She was surprised in the course of one interview when the girl replied that her parents didn't mind "living on the east coast or west coast" then adding "so I'm applying to those places". In other words, the girl was more or less resigned to mommy and daddy tagging along.

When Ms. Gujral asked if they were going to move wherever she went to school the girl responded "Yeah" but Gujral observed "she didn't look too happy about it."

Good! Because she shouldn't! Those parents, like the misguided others, are actually retarding their charges' ability to reach adulthood. If the parents don't know that, at least the kids should.

Sunday, December 28, 2014

Why Families Can't Get Ahead In Denver

In the new MSNBC documentary series 'The Pot Barons of Colorado'  we get an inside look at the booming retail marijuana industry in Colorado and the 12 or 14 who control most aspects of - including edibles, as well as pot for smoking and cannabis oil. These people, make no mistake, are rolling in money, but they are also sticking their necks way out for that reward - including (as a recent episode showed) always facing the sharp knives of the regulators who tend to overly side with caution, But the 'barons'  admit that's the nature of their business and they're willing to lose all to gain their rewards. (Let's also bear in mind they have no banking system to rely on to deposit cash and all their tax payments have to be made in cash and taken in person to the Colorado Dept. of Revenue).

But this isn't so much about the Pot Barons as their hundreds of workers who toil in the shadows to turn out a high quality product. These people, and thousands of others who have come to Colorado to find work (including for the oil and natural gas fracking),  often also find themselves behind the 'eight ball' on account of an insufficient housing stock. Because it is insufficient, the demand outpaces it, and prices - whether for homes or rents - have soared. This leaves many either outside the market or in an unstable predicament.

As a point of fact, according to a Denver Post (Dec. 14) report, "Colorado ranks among the top five states when it comes to creating jobs and attracting new residents. But construction, for a variety of reasons, hasn't kept pace. Home prices and rents are rising sharply while the incomes to pay them are stagnant."

Quoting the President of Oread Capital and Development, Jeff Handlin, it cited the fact the currently single family permits are running at only two -thirds their historical average, This despite a record tight inventory of homes available for sale and the higher prices accompanying that situation. Apart from that, while multi-family accommodations have surged  to levels unseen since 2002, this has not prevented some of the steepest rend increases in the nation.

The Post report cites rents being up 9.2 percent in metro Denver and Boulder, 8.8 percent in Fort Collins and 13. 5 percent in Greeley - ground zero for fracking operations. By comparison, the 18 year state average is closer to 3.7 percent.

To fix ideas even more, a study released by Zillow 2 weeks ago showed a renter now needs to earn at least $35 an hour to afford even a median priced rental in metro Denver - or almost 4 1/2 times Denver's minimum wage.  Another nasty trend, and I am sure I can call it that (though the Post doesn't) is the low vacancy rates spurring investors to buy up older (low rent) complexes, condos - rehabilitate them, then boost rents to gentrified levels.

The result? Three bedroom rents for the city's newest apartments now run $1, 675  a month which would demand an annual salary of $67,500 to be considered affordable. (Remember the rubric here: your rent -housing costs should come to no more than one third of your total income.)

The perverse situation, which again is a total product of greed and the Neoliberal business model, is that "developers want to build at the highest end of affordability while the demand is all at the low end".

Again, this is what I define as manifesting insanity, because the housing construction is then detached from economic reality. The demand side is being ignored to put up a weak, vastly overpriced supply component. Any objective rational observer- say from another world - would believe those doing it had lost their marbles. They were ignoring basic laws of supply and demand and worse, were contributing to economic upheaval and stress when there is no need for it.

What would a Socialist do? Well, given the Neoliberal capitalists, builders are evidently incapable of acting in their or the communities best interests it would be to allow their selective elitist construction to go ahead but only after paying construction fees equal to at least 20 percent of the costs of their units, homes etc. It would be a corrective to their greed and also discourage building only for the rich when the demand is for the moderate income person - coming here to work in fracking operations, or in the Pot retail business, or in the booming aerospace industry.

To understand why such a corrective is rational, one need only see how many existing homeowners are pouring into food kitchens for support or to 'Almost Home'  (an advocacy group) to beg for affordable units - given many are spending up to 70 percent of their income on rent and are desperate. And as rents, home prices shoot ever higher, middle income households are being squeezed ever more - with the specter of food inadequacy now also beginning to rear its head.

The Post observes in passing that of the single family homes starts this year in metro Denver, only 17 percent were priced below $300,000, compared with 40 percent in 2012.

No matter which side of the political spectrum you fall on, this is inexcusable, and undermines any chance for real economic growth  - because this isn't happening only in Denver but other cities too, such as San Francisco.

If the Neoliberals  and their lackeys can't or won't provide sound, rational solutions to this housing problem then Socialists and others with the commonweal in mind, must do it for them.

Saturday, December 27, 2014

A Look At General Relativity and Tensors (Part 3)

4.    The Principle of Equivalence and Geodesics

Up to now, all the tensor descriptions have been for 3-space and we’ve not introduced time. But this deficiency must now be remedied as we provide for an extension and generalization of the Principle of Equivalence to incorporate the fact that the velocity of light is the same in all reference frames.
To put it into terms consistent with the examples seen in Part 1, a mass point carried by a gravitational field does not remain at rest but “falls down”.  More to the point, the path taken for this freely falling mass is a geodesic in space-time or a “world line” for the mass, i.e. described in 4 dimensions.

Thus, the formalism or representation must include changes in time and so the gravitational field is now given as a space-time tensor.  Unlike the tensors shown in the previous section, this one displays 4 x 4 components, as opposed to 3 x 3.

The reframed Principle of Equivalence therefore states that the equations of motion for this freely falling particle are expressed:

d2xk /ds2 + {mn, k} dxm /ds  dxn /ds = 0

(where m,n, k = 1,2,3,4  for the four dimensions which are then displayed as: x1, x2, x3 and x4 – the last instead of t). It is important to point out that s, the interval, is assigned the dimension of time and hence is the proper time.  This is the time measured by a clock traveling with the mass particle.  By virtue of the definition and the above equation, the observer has a full definition of a curve traced out in space-time by a moving clock – which possesses an invariant form – and thus has a coordinate system for all events in the universe.

Let a light ray now follow this path and one obtains a null geodesic, i.e.

Let the upper end of the curve be defined by event of form  t, xr  and the lower extremity by event of form,  t + dt, xr  + dxr  Then for a clock traveling with the mass the proper time between the two events is zero – given the path is a null geodesic.  Hence:

g44 (t, xr) dt2  =  1/ c2  å3 l,m = 1    g lm (t, xr) dx dxm

However, for a clock at rest at position x1, x2, x3 the proper time elapsed between the events shown in the diagram is:

dso  = [g44 (t, xr)] 1/2 dt

The distance between the two events exclusively in space coordinates is:

d ℓ =   å3 l,m = 1    g lm (t, xr) dx dxm

Then, taking the derivative:  d ℓ/ dso

d ℓ / dso    =  + c

where c is called the velocity of light at the event (t, xr). Hence, we see it emerges as a universal constant and always takes the least time between two events, hence the path taken of a null geodesic.  This is consistent with the Einsteinian postulate – also given in special relativity – that the velocity of light has the same value at all points in space –time.

Thus we see that in order to include non-uniform fields the Principle of Equivalence can be reformulated – to a “strong” form,  to read[1]:

In a small, freely falling laboratory, the laws of physics are the same as the laws of special relativity without any gravitational field.”

5. Einstein’s Field Equations

In the previous section we saw the coefficient  g44   appear for the expressions to do with proper time. But what is it?  This denotes the gravitational potential field given by a particular set of components, usually written as  g mn   for the tensor g.   We can now pose the interval introduced in Sec. 4. as:

ds2   =  g mn dx m dx n
Then the  g44   denotes the 16th and last element of the    g mn    matrix. In flat space-time the tensor components for g are usually given as:

(g 11      g 12      g 13           g 14 )
g 21     - g 22     g 23         g 24)
g 31       g 32      g 33        g 34 )
g 41        g 42       g 43       g 44)

For which it is convenient to specify special values of the potentials presented in “standard form” as:

g 11      g 12      g 13        g 14
             g 22     g 23        g 24
                        g 33        g 34
                                       g 44

Now, for flat space-time the values are all 0 except for those long the diagonal for which:

g 11      =  -1
g 22        = -1
g 33        = -1
g 44        =         1

Thus, we see that the value of  g44     in the previous expressions is 1.  Writing out the interval form for the above is straightforward and one only needs to include the correct subscripts for the respective dx’s,  in each component, e.g.  

g 11 dx11           and            g 12 dx1 dx 12

Now, if we take:    g mn  / x t 

We obtain the Riemann-Christofel curvature tensor:

G t mn    =  G mn 

For flat space-time the gravitational potentials satisfy:

G mn   =0

Where the values conform to those of the g’s shown above and we find:

g 11      =   -1/ g
g 22        = -x12
g 33        = - x12  sin2 x22
g 44        =       g

Where:   g  = 1  -  k / x1

And the constant k is what’s called the Gaussian curvature.  It can assume values of 0 (Euclidean 4-D flat space), -1 (Lobachevskian space) or +1 (Riemannian space).

The Einstein field equations can be summarized in the tensor form:

G mn   =  - ½ g mn  G=  - 8 p T mn   

Where the  T mn    denotes the associated  “stress-energy” tensor which incorporates internal stresses, the density of matter and its component velocities (u, v, w or in some texts: u1, u2 and u3).   From this one can see that if no matter is present, one would have:  G mn   =  0

If matter is present there must then be internal stresses and velocities so that:  G mn   =  K mn  where  (as seen from the field equations):  K mn   = - 8 p T mn   

The introduction of  K mn    to describe the matter-associated properties is generally attributed to Arthur Eddington[2].

We have then for the  T mn  : analogous to the g’s in standard form

T 11      T 12      T 13        T 14
             T 22     T 23         T 24
                         T 33         T 34
                                         T 44

p 11  + r u2, p 12 + uv,    p 13    +r uw,  - ru    

                    p 22  +
r v2,   p  23  +r vw,    - rv   

                                             p 33 +
r w2 ,      - rw 

Which again, is a vastly simplified presentation. It should also be said that radiation via  an electromagnetic energy tensor can also be included – given these will have the same rank as the T mn These components can thus be added to components of the mass energy tensor shown. In other words, the presence of radiation is taken to be equivalent to the presence of mass, given m = E/c2.

One final point: The Riemann curvature tensor is often written:

R a b m n

And so it serves as a quantitative measure of the curvature in space-time.   In flat space-time then,   R a b m n   =  0. Conversely, when R a b m n   ¹  0 matter is present and space-time is curved. Thus,  g mn    is a metric tensor from which the Riemannian curvature tensor can be calculated[3].

[1] Symon, K.R.: ‘Relativistic Dynamics’, in Mechanics, Addison-Wesley Publishing Co., 577, 1971.

[2] Eddington, A.S.:1920, Space, Time and GravitationCambridge University Press,, p. 173.

3] Another way to see the connections is that g mn    has a similar role to the vector potential A of electrodynamics.  The curvature tensor plays a similar role to the E, B fields. Thus we know Ñ X A = B, for example.