The emergence of the Bernie Madoff financial flim-flam has people pointing to “Ponzi schemes” once again, especially as we now know Madoff made no genuine bond or stock purchases. However, when they try to use the term against Social Security, suggesting it is a “government Ponzi scheme’ they are comparing chalk and cheese.
The reason is that the 1935 Social Security law was out front in terms of how it would be funded: from current workers to current beneficiaries. (See also Michael A. Hiltzik’s ‘The Plot Against Social Security’). This is understood from the get go.
Now, forget the Madoff ruse and think of Wall Street in general, and specifically stock investments. It can be shown that they are the complete embodiment of a classical Ponzi scheme.
Consider: Company XYZ goes public and issues 10 million shares of stock to 2 million people, for $50 a share. The market capitalization here is therefore $500 million. The 2 million shareholders own variable amounts-shares, but all are priced at the stock issuance rate of $5.
Now, one particular person - Joe Schmoe - has bought 100 shares of XYZ, and so at the outset he owns $5,000 worth. Each month he buys a further 5 shares a month via “dollar cost averaging” and so invests $250 a month, or $3,000 a year..
After ten years, he’s plowed $30,000 in, and owns 596 more shares, with the share price of XYZ going up to $250 the last month of the 10th year.
After this final month, his total paper worth is 696 x $250 = $174,000.
This again is his paper worth, while he has actually put in $35,000.
So also, each XYZ investor has reaped 4.97 x more than the actual money invested. The total paper wealth has thus increased to:
4.97 x $500 million = $2, 485, 000, 000
The question becomes: What happens if ALL 2 million investors sense a crash coming and want to cash out their shares on the same day? How much would each receive on average?
This average cashout can easily be computed and works out to just $1,243 each.
This simple computation discloses that stocks and their managers prevail only by betting stock holders will not all redeem shares on the exact same day. For them to do so would be disastrous, because the company’s actual market capitalization would not support such a payout. There is simply not enough money to give all share holders what their paper profits indicate. If this isn’t a “Ponzi scheme’ I don’t know what is!
What this spread means, in concrete terms, is that when stock prices rapidly inflate most of what appears on paper is phantom money, not real money. By the same token, most of what disappears in a market crash is phantom money.
Joe Schmoe similarly, may be elated at beholding a $174,000 balance after his 10th year of holding XYZ stock, but he needs to understand that the bulk of this:
$174,000 - $35,000 = $139, 000
is phantom money.
By the same token, if the following month the share prices collapses back to $5, Joe has not lost $139, 250 but only the money he actually put in up to THAT point, or $35,250.
In a recent PARADE column (Feb. 22), Marilyn vos Savant - the magazine’s resident genius - dealt with a question related to this, which asked about investors recently losing a large amount of money and where did it go?
Her correct answer was “much of the lost money never existed”.
As we see from the illustration I gave, this is exactly true. The bulk of Joe’s money was certainly not his to lose. It merely existed temporarily in virtual or paper space. It had been subjected to what we call "asset inflation" via uptick in share price, not having more actual money.
Now, if he had the prescience and boldness to act in time, it is true he would have collected it (minus capital gains taxes). But the chances of this were actually very slim: about ½ of 1 percent of investors do a maximally profitable cashout, without any benefit of advance knowledge.
The bottom line here is that if all shareholders demanded their paper worth at the highest share price, they’d likely not get it, since it would bankrupt most companies. The real Ponzi scheme here is Wall Street’s stock scheme.
Despite this, one still sees egregious advice being given to little guys, such as ‘Keeping Your Financial Plans Afloat’ in the current U.S. News and World Report (march, p. 65) wherein it is noted that financial advisers still recommend that retirees “maintain a significant proportion exposure to stocks” But what would one assume a FA to say? Not to do so? He would soon be out of work!
The article is honest enough to go on to say:
“But investors who followed this advice are now suffering the steepest losses”
Indeed, and this will continue to happen for YEARS – perhaps even decades, as long as they remain in the market. The reason (as I noted in a previous article from last year) is that $55 trillion in credit default swaps locked in banks has still to unwind. Those who are realists believe this unwinding will continue asset deflation for a long time. Those Pollyannas who anticipate a quick “capitulation” and back toward the 10,000 DOW days of yore are in for a brutal shock as their nest eggs shrink to nothing.
The further advice (or warning) in the U.S. News piece to the effect that “Still, avoiding the stock market completely means you nest egg may not stay ahead of inflation” is not a reason to place 50% or more in stocks, or even 20%. What one must do, rather, as Vicki Robins and Joe Dominguez noted (in ‘Your Money or Your Life’) is to re-evaluate one’s spending and drop those items which are the most inflation prone in so far as possible. But risking major loss to a market Ponzi scheme is no better than playing the craps tables in Vegas.
The other interesting article in the U.S. News special finance issue was by Katy Marquardt, ‘Time to Buy Stocks or a House’ wherein she notes how people are still being advised to pass over home mortgage payouts for stock investment. According to one finance hotshot, Richard Moody – chief economist at Mission Residential:
“you always hear that owning a home is the best way to build wealth but in terms of returns it’s not that great an investment”
However, as we already saw, returns are mostly imaginary (on paper) anyway. Only a tiny percentage of stock investors actually manage to reap the high returns. Most ‘buy and HOLD’ and get incinerated later by crashes, corrections and bear markets in the process. Whereupon they must proceed to “square one”, work longer, and start all over. When will they ever learn? Maybe never.
And besides, in the stock Ponzi scheme there isn’t enough money to pay out all investors in the event they all wanted to cash out at once. So it is mostly flim-flam sold to those susceptible to the ploys, pleas and PR of finance hacks.
Fortunately, Marquardt gives the exactly appropriate response to Moody’s drumbeating:
“Stocks seem like a simpler choice, but buying a house guarantees a huge return for me – even if it’s not financial”.
But who cares, given the financial returns of stocks are mostly smoke and mirrors for the few. (Or people, like Warren Buffet, who can afford to be wrong on when they guess the market’s capitulation to occur. Bottom line, what Buffet does or not with his billions is totally irrelevant to what investors with tiny sums of precious nest eggs and savings do.)
One final parting shot to take is at Pat Toomey, CEO of club for Growth in the same issue (p. 18, ‘Use the Free Market’) . This fool once again embraces and recommends private accounts to save Social Security and “entitlements” (a right wing buzz word if ever there was one) once and for all. But it is false, a false solution. The current market crash, with no end in sight and the DOW melting lower each day, shows personal accounts are not viable. A better solution is for the FICA income limit to be raised past $250,000 as Obama proposed during his campaign.
Toomey is even more whacked in the head when, instead of Medicare for oldsters, he alternatively proposes “accumulated savings used to purchase a health care policy at retirement”
Yes, Mr. Toomey, and please tell me WHO is going to provide such a policy to any but the most healthy and wealthy seniors? As it is, most 62- 64 year old people can’t beg, borrow or steal a policy even if they have the money. The insurance companies aren’t inclined to insure anyone over 55. If you think an over-65 person will have an easier time, you are dreaming, live on another planet, or …..detached from all modes of existing health care reality in this country.
Monday, February 23, 2009
Wednesday, February 11, 2009
Radical Life Extension....or expensive urine?
Dr. Nancy Sniderman's reference (in a recent NBC Today interview) to vitamin therapy merely generating "expensive urine" reminded me of when I first started taking them more than 33 years ago. It was about three months before my wedding (in August, 1975) that I first met Cecil Warner, a 79-year old friend of my wife's family. He had just returned from playing 9 holes of Golf and then an hour of handball.
As he recounted the day's efforts while on my fiancee's veranda, I asked him how he did it. Where did he get the energy? What was his secret for being so fit (and not looking a day past 59). He said with a broad smile:
"My secret is vitamins. And don't let one damned soul tell you that they don't work!"
Almost from that instant, I became an unapologetic vitamin taker, incorporating them into my regimen along with a daily aspirin (this was long before people were advised to take a daily aspirin). After our wedding, my wife joined me and we have contiued thus for nearly 34 years.
Some years later, 1980 to be exact, I happened to see Durk Pearson - author of many vitamin tracts, books, on a Larry King show while in Port Charlotte, Florida. Pearson extolled the benefits, especially of lecithin and vitamin C. Not so much as cancer cures but rather as preparing the nutrient and health basis to avoid the conditions that may lead to cancer. Durk's theory was that interferon and its use by the body was augmented by a specific vitamin combination that included high doses of vitamin C.
Over the years, we have used Pearson's vitamin and mineral usage prescription, and indeed - saw it heartily endorsed by our (then) primary care physician in 1998. This physician, originally a vitamin skeptic, told me after one annual exam:
"I have finally come around to your way of thinking after doing lots of nutritional studies and seeing just how low in nutrients most modern foods, vegetables are."
Indeed!
So why then the mainstream health media's distrust of vitamins or vitamin therapy and the consistent negative thrust? Most recently, with release after press release inundating the news, slamming vitamins as "a waste of money" and asserting categorically they don't work.
I suspect the real answer goes back to an article I read some years ago, I think in 'Mother Jones' (a progressive magazine) where one economist was quoted as saying the country needs to back off its never-ending campaigns against smokers....and just let them do their thing. His point was that smoking led to much earlier deaths on average, and often before one qualified for any entitlements such as Social Security. Since the entitlements like Social Security and Medicare were "going broke" one needed to indirectly encourage a higher death rate, not a longer lifespan.
I firmly believe that this is at least partly behind the campaign to curb vitamin use. The cognoscenti of the medical matrix are rightly concerned that: a) too many millions are taking vitamins and will likely outlive their money, forcing state support, and b) their purchase of vitamins makes it less likely they will need pharmaceuticals - thereby depleting the coffers of one of the primary political campaign contributors.
Contrary to the critics, as I noted, it isn't that anyone claims vitamins "cure cancer or heart disease" or even mitigates them - but rather that they provide the nutritional basis to avoid all such conditions. As Pearson put it in his interview with King, it is known that interferon can be wielded powerfully to fight most cancers, and it is also the product of taking megadoses of vitamin C (far beyond the MDA level).
All one has to do is examine the foods available to most Americans and then realize they'd likely have to spend 4-5 times more per week than they already do in order to obtain the vitamins and nutrients needed to make vitamin therapy redundant. For many Americans today, this simply is not on, since they can barely afford what they get at the grocers (and many now have to reckon in food stamps too!)
Vitamins provide a relatively economical solution, especially in particular cases such as for vitamin D (now key in preventing colon cancer) and vitamin C. Bottom line, rather than consuming three broccoli crowns, four cabbages, five romaine lettuce heads, and ten oranges per day - one can obtain all the needed nutrients in 1 or 2 vitamin pills.
As for B-complex, I saw the value of those during the early 1970s when I used to visit a friend in the Barbados Psychiatric Hospital. I saw a stress-ridden, overly worried neurotic able to return to her life and put the valium and largatyl aside, thanks to high combined doses of B vitamins (B-6, B-1, B-12, B-3). Needless to say, since we value our mental equilibrium, both my wife and myself have incorporated 50 mg B-complex multivitamins into our regimen. We ignore any and all media reports to the effect that the B-complex combo doesn't work. To us, that is what we expect them to say.
Another aspect of vitamin therapy is one that Pearson emphasized in that 1980 interview on CNN: that is, merely attaining the minimum daily requirements (MDA) is not adequate. Especially in a stress-ridden environment and under those conditions (such as now with this economic meltdown) people need many times more the "minimum" in order to preserve health. Look at it as a far less expensive alternative to therps!
Will the mainstream gurus and sources (like those funded from Big Pharma research) disagree? Of course. This is what we fully expect, after all, since vitamin consumption by large segments of the populace challenges their vested-monied interests.
But just remember what was said earlier concerning the downsides of stopping people from smoking! As for not oultiving your money, the best advice I can give here is: don't invest your hard-earned money in the stock market, unless you can easily afford to lose it.
As he recounted the day's efforts while on my fiancee's veranda, I asked him how he did it. Where did he get the energy? What was his secret for being so fit (and not looking a day past 59). He said with a broad smile:
"My secret is vitamins. And don't let one damned soul tell you that they don't work!"
Almost from that instant, I became an unapologetic vitamin taker, incorporating them into my regimen along with a daily aspirin (this was long before people were advised to take a daily aspirin). After our wedding, my wife joined me and we have contiued thus for nearly 34 years.
Some years later, 1980 to be exact, I happened to see Durk Pearson - author of many vitamin tracts, books, on a Larry King show while in Port Charlotte, Florida. Pearson extolled the benefits, especially of lecithin and vitamin C. Not so much as cancer cures but rather as preparing the nutrient and health basis to avoid the conditions that may lead to cancer. Durk's theory was that interferon and its use by the body was augmented by a specific vitamin combination that included high doses of vitamin C.
Over the years, we have used Pearson's vitamin and mineral usage prescription, and indeed - saw it heartily endorsed by our (then) primary care physician in 1998. This physician, originally a vitamin skeptic, told me after one annual exam:
"I have finally come around to your way of thinking after doing lots of nutritional studies and seeing just how low in nutrients most modern foods, vegetables are."
Indeed!
So why then the mainstream health media's distrust of vitamins or vitamin therapy and the consistent negative thrust? Most recently, with release after press release inundating the news, slamming vitamins as "a waste of money" and asserting categorically they don't work.
I suspect the real answer goes back to an article I read some years ago, I think in 'Mother Jones' (a progressive magazine) where one economist was quoted as saying the country needs to back off its never-ending campaigns against smokers....and just let them do their thing. His point was that smoking led to much earlier deaths on average, and often before one qualified for any entitlements such as Social Security. Since the entitlements like Social Security and Medicare were "going broke" one needed to indirectly encourage a higher death rate, not a longer lifespan.
I firmly believe that this is at least partly behind the campaign to curb vitamin use. The cognoscenti of the medical matrix are rightly concerned that: a) too many millions are taking vitamins and will likely outlive their money, forcing state support, and b) their purchase of vitamins makes it less likely they will need pharmaceuticals - thereby depleting the coffers of one of the primary political campaign contributors.
Contrary to the critics, as I noted, it isn't that anyone claims vitamins "cure cancer or heart disease" or even mitigates them - but rather that they provide the nutritional basis to avoid all such conditions. As Pearson put it in his interview with King, it is known that interferon can be wielded powerfully to fight most cancers, and it is also the product of taking megadoses of vitamin C (far beyond the MDA level).
All one has to do is examine the foods available to most Americans and then realize they'd likely have to spend 4-5 times more per week than they already do in order to obtain the vitamins and nutrients needed to make vitamin therapy redundant. For many Americans today, this simply is not on, since they can barely afford what they get at the grocers (and many now have to reckon in food stamps too!)
Vitamins provide a relatively economical solution, especially in particular cases such as for vitamin D (now key in preventing colon cancer) and vitamin C. Bottom line, rather than consuming three broccoli crowns, four cabbages, five romaine lettuce heads, and ten oranges per day - one can obtain all the needed nutrients in 1 or 2 vitamin pills.
As for B-complex, I saw the value of those during the early 1970s when I used to visit a friend in the Barbados Psychiatric Hospital. I saw a stress-ridden, overly worried neurotic able to return to her life and put the valium and largatyl aside, thanks to high combined doses of B vitamins (B-6, B-1, B-12, B-3). Needless to say, since we value our mental equilibrium, both my wife and myself have incorporated 50 mg B-complex multivitamins into our regimen. We ignore any and all media reports to the effect that the B-complex combo doesn't work. To us, that is what we expect them to say.
Another aspect of vitamin therapy is one that Pearson emphasized in that 1980 interview on CNN: that is, merely attaining the minimum daily requirements (MDA) is not adequate. Especially in a stress-ridden environment and under those conditions (such as now with this economic meltdown) people need many times more the "minimum" in order to preserve health. Look at it as a far less expensive alternative to therps!
Will the mainstream gurus and sources (like those funded from Big Pharma research) disagree? Of course. This is what we fully expect, after all, since vitamin consumption by large segments of the populace challenges their vested-monied interests.
But just remember what was said earlier concerning the downsides of stopping people from smoking! As for not oultiving your money, the best advice I can give here is: don't invest your hard-earned money in the stock market, unless you can easily afford to lose it.
Monday, January 12, 2009
The Bible: Inerrant Word of God?
IF the Bible is truly the “inerrant word of God” then it can have no errors, correct? It must be free of factual or religious errors. If there exists one such error – just one – all bets are off and the book becomes manifestly fallible.
Let us look at Genesis – Chapter One:
We read (Gen.:1: 1-5)
“In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, Let there be light and there was light. And God saw the light, that it was good: and God divided the light from the darkness. And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day”
Now, it is clear that the “light” referred to in the last three sentences is none other than the SUN. However, it is clear from reading each line through that the Earth was supposedly made BEFORE the Sun. (E.g. Earth without form, darkness upon face of the deep).
However, this is physically impossible. We know from modern astrophysics that the solar proto-nebula had to collapse first to yield the SUN. (No planets, since they had yet to spin off the collapsing nebular cloud – it hadn’t cooled enough to allow it). As the proto-solar nebula collapsed it also began spinning and gained angular momentum. This angular momentum was then transferred to regions of the nebula that cooled and separated from the whole, and these regions became separate clouds of dust and gas that aggregated into the planets.
Under a combination of electrostatic attraction (between larger charged particles) and gravity (attracting the whole mass from the center of the cloud) each planet was formed as what we call a “planetesimal”.
As more angular momentum was transferred – the planetesimals each acquired their own spin (in a period of revolution) and specific shapes. The giant planets (e.g. Jupiter, Saturn, Neptune, Uranus) garnered more spin momentum than the more dense, terrestrial planets. Thus Jupiter’s planetesimal ended up as an oblate spheroid with diameter of about 88,000 mile and rotating rapidly with a day of ~ 10 hours. Earth meanwhile ended up as a relatively spherical orb with diameter of ~ 8,000 miles and day approaching approach 24 hrs. Mars ended up in a similar shape to that of Earth and a diameter of 4200 miles and day ~ 24 hours.
Thus, the Earth spun off about 1.1 billion years after the solar nebula fully collapsed, and it could not have come BEFORE the Sun. Indeed, the absence of the central mass of the Sun, or ~ 10^33 kilograms, would have meant the Earth- if made with no Sun present- would instantly have been hurled into a direction toward the constellation Hercules at 12 miles per second with no central mass to keep it in check. We can compute this exactly using the basic principles of celestial mechanics.
It is clear from this that Gen.1:1-5 has stated a patent impossibility which violates all known laws of physics and dynamics and is therefore WRONG!
It is clear from this that the Bible must be in error, certainly in this one passage – and if here then likely in many other places too. If this is so then it must have been written by flawed humans using limited conceptions of space, time and astrophysics which accounts are not even correct in their general form.
Conclusion: it cannot be a “divinely inspired” book. Rather it is a HUMAN-inspired work with all the errors we expect to see from a work of humans.
Let us look at Genesis – Chapter One:
We read (Gen.:1: 1-5)
“In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, Let there be light and there was light. And God saw the light, that it was good: and God divided the light from the darkness. And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day”
Now, it is clear that the “light” referred to in the last three sentences is none other than the SUN. However, it is clear from reading each line through that the Earth was supposedly made BEFORE the Sun. (E.g. Earth without form, darkness upon face of the deep).
However, this is physically impossible. We know from modern astrophysics that the solar proto-nebula had to collapse first to yield the SUN. (No planets, since they had yet to spin off the collapsing nebular cloud – it hadn’t cooled enough to allow it). As the proto-solar nebula collapsed it also began spinning and gained angular momentum. This angular momentum was then transferred to regions of the nebula that cooled and separated from the whole, and these regions became separate clouds of dust and gas that aggregated into the planets.
Under a combination of electrostatic attraction (between larger charged particles) and gravity (attracting the whole mass from the center of the cloud) each planet was formed as what we call a “planetesimal”.
As more angular momentum was transferred – the planetesimals each acquired their own spin (in a period of revolution) and specific shapes. The giant planets (e.g. Jupiter, Saturn, Neptune, Uranus) garnered more spin momentum than the more dense, terrestrial planets. Thus Jupiter’s planetesimal ended up as an oblate spheroid with diameter of about 88,000 mile and rotating rapidly with a day of ~ 10 hours. Earth meanwhile ended up as a relatively spherical orb with diameter of ~ 8,000 miles and day approaching approach 24 hrs. Mars ended up in a similar shape to that of Earth and a diameter of 4200 miles and day ~ 24 hours.
Thus, the Earth spun off about 1.1 billion years after the solar nebula fully collapsed, and it could not have come BEFORE the Sun. Indeed, the absence of the central mass of the Sun, or ~ 10^33 kilograms, would have meant the Earth- if made with no Sun present- would instantly have been hurled into a direction toward the constellation Hercules at 12 miles per second with no central mass to keep it in check. We can compute this exactly using the basic principles of celestial mechanics.
It is clear from this that Gen.1:1-5 has stated a patent impossibility which violates all known laws of physics and dynamics and is therefore WRONG!
It is clear from this that the Bible must be in error, certainly in this one passage – and if here then likely in many other places too. If this is so then it must have been written by flawed humans using limited conceptions of space, time and astrophysics which accounts are not even correct in their general form.
Conclusion: it cannot be a “divinely inspired” book. Rather it is a HUMAN-inspired work with all the errors we expect to see from a work of humans.
Tuesday, December 30, 2008
The Amazing Aurora
In Alaska in March, 2005, I took the above photo of an auroral display just outside Chena Hot Springs, Alaska. I was glad my wife was with me to behold the sight (her first time) since it later evolved to an exciting electronic scene with bursts of red and green interacting and changing positions.
How are these magnificent displays caused?
One can visualize the Earth as a giant spherical magnet, with magnetic
field lines extending from its north to south magnetic poles. These
magnetic field lines, have the property that any charged particles (+
protons, - electron or ions) that approach, will spiral along them.
The Earth itself, is "bathed" in the solar wind, a stream of high speed
charged particles that flows into space, originating from the Sun's
corona. (A hot, gaseous envelope that spews these particles out continuously – moreso when there is a violent explosion known as a Solar Flare)
Around the Earth the speed of these particles can reach 400- 500
km/second. (Because of its high temperature, over a million degrees, the
corona gas is *ionized* so must consist of charged particles, mainly (+)
protons, and (-) electrons).
During high solar activity (e.g. near sunspot maximums) a higher flux of
these charged particles inundates the solar wind, and the region around
the Earth.
The Earth's magnetic field traps these charged particles, and the highest
density is around the polar regions - which we refer to as the "auroral
ovals". In these regions, very high electric currents are set up, as the
charged particles start moving in unison about the magnetic field lines.
These currents can easily reach a few MILLION amperes.
As this discharge occurs, one or more outer electrons is stripped from the
atoms, for example from oxygen in the atmosphere - then RECOMBINES again -
to form new )e.g. oxygen) atoms.
With this RECOMBINATION - there is EMISSION of light, for a certain part
of the visible spectrum.
For example, in the case of recombination of oxygen atoms - their emitted
light is in the GREEN region of the spectrum. The aurora or northern
lights we see displays a kind of green curtain-like shimmering. The remarkable
red aurora is produced by emission at the 630 nm (nanometer) line of oxygen and at relatively high altitudes (e.g. 200-600 km) compared to green - which tends to form below 100 km and the oxygen line at 557 nm is excited.
Auroras can display as both diffuse and discrete. In the first case the shape is ill-defined and the aurora is believed to be formed from trapped particles originally in the magnetosphere which then propagate into the lower ionosphere via wave-particle interactions.
Thus, multiple colored auroras can be explained by emissions from
different atoms in the upper atmosphere, mainly in the region of the
magnetic poles. This is also why, of course, they are more often seen in
the vicinity of the N, S magnetic poles. (Though there have been reports
of N. lights being seen as far south as northern Florida, especially
during periods of esxceptional sunspot activity or LARGE SOLAR FLARES,
massive explosions on the Sun).
A great analogy has been given – by Syun Akasofu- comparing the aurora to images on a TV screen. In this case the (polar) upper atmosphere corresponds to the screen and the aurora to the image that would be projected on it, say for a TV. The electron beam in the TV (remember we are talking about the old-style cathode ray jobs!) corresponds the electron beam in the magnetosphere. In the conventional TV motions of the image are generated by the changing impact points of the electron beam on the screen. Similarly, with the aurora, its motions – such as moving sheets or curtains- are produced by moving impact points of the magnetospheric electron beams.
In gauging the power and intensity of auroras at different times, it is useful to remember that ultimately the aurora derives its power and potential from the Sun and specifically the charged particles of the solar wind. This is why the most spectacular displays are usually near sunspot maximum. Around those times the currents I noted earlier are “amped” up – no pun intended- to 10^6 A or more. To give an example, during a quiet Sun interval like we are in now the residual power for the magnetospheric generator is on the order of maybe a tenth of a megawatt. If we see a new cycle coming on and solar wind activated – we may get that power up to a million megawatts for a few hours.
If intense enough, such solar storms can herald the onset of enormous induction currents such as caused parts of the Ottawa grid to melt down in 1989.
But, as solar cycle 23 slowly ramps up, the aurora - of whatever color or shape- will be eagerly anticipated.
Monday, December 22, 2008
Star of Bethlehem? Or a MacGuffin?
At many lectures I've given one of the most asked questions has been: "Was there really a star of Behtlehem?"
This is a difficult question. In the preliminary pass for any sort of validating records, it entails assuming any or all of the ancient scriptures were true historical artifacts, not mere mythological escapism masquerading as such. For example, Matthew 2:1-1 notes such a "star" - but not one of the other quadriforms peeps a syllable about it. Why not? Why - if it was such a signal event (no pun intended) and an actual occurrence- did none of the other New Testament authors note it? This is disturbing and makes one recall the words of Catholic historian, the Rev. Thomas Bokenkotter, in his monograph ‘A Concise History of the Catholic Church’,(page 17):
“The Gospels were not meant to be a historical or biographical account of Jesus. They were written to convert unbelievers to faith in Jesus as the Messiah, or God.”
This is a shattering admission indeed, and from a historian of Christendom’s largest Church. It is a de facto admission that no historical support exists for any of the accounts in the New Testament, including Matthew's star. But for the sake of this article, let us assume there is something there, some faint signal amidst the noise.
We consider ordinary bright stars first. For an observer in Middle Eastern latitudes 2,000 years ago, there would have been at least ten visible at this time of year. Each one in a different direction, location of the Celestial sphere. Thus, no one star would be visible long, and certainly not at a fixed location or altitude such that it might provide a "search beacon".
The only other stellar candidate one might invoke is a nova or exploding star. Certainly the indredible brightness common to such entities would attract attention, but could any have occurred then and provided the basis for the Matthew citation? Interestingly, this very attirbute of attention -getter eliminates the nova theory from contention. Such a cataclysmic event could not have escaped notice yet there is no mention in any astronomical records of the time - including the Chinese who were already consummate star gazers.
an alternative explanation is that the object was a bright comet. An exceptionally brilliant comet was recorded in 45 B.C. but this is too far in advance of the probable Nativity date. Could such a comet have appeared suddenly and unpredictably around the time. Possibly, but it's doubtful such an event would have been associated with anything beneficent. Two thousand years ago comets were uniformly regarded by all cultures as omens of impending disaster, so we can rule them out.
The only other reasonable explanation is that the Magi witnessed an uncommon astronomical alignment of bright planets. One such candidate is the triple conjuncti9on of the planets Jupiter and Saturn in 7 B.C. A "triple conjunction" here means that Jupiter and Saturn appeared in close proximity no less than three times in succession.
One can spculate here that the Magi in preparing for their jounrey witnessed the first conjunction ca. May 29. A second event was observed on September 29 could have established that Jerusalem was in the general direction they needed to go. Finally, a third conjunction on Dec. 4 would presumably provided the final directional "fix", leading to Bethlehem some eight kilometers away.
The accuracy of the above speculations (and I reinforce that's all these are!) is subject to the dubious assumption that our present calendar is actually a bit off and Christ was actually born in 7 B.C. rather than the 1 B.C. usually quoted.
Given this, one is forced to concede that at the present time there is no comprehensive astronomical explanation which consistently explains all the details. The triple conjunction sounds like the best, assuming we are really in the year 2001 and not the end of 2008.
Perhaps the event must remain forever intangible and beyond the realm of any scientific investigation. Or, perhaps there never was such an object in the first place - and Matthew simply resorted to some elaborate poetic license.
This is a difficult question. In the preliminary pass for any sort of validating records, it entails assuming any or all of the ancient scriptures were true historical artifacts, not mere mythological escapism masquerading as such. For example, Matthew 2:1-1 notes such a "star" - but not one of the other quadriforms peeps a syllable about it. Why not? Why - if it was such a signal event (no pun intended) and an actual occurrence- did none of the other New Testament authors note it? This is disturbing and makes one recall the words of Catholic historian, the Rev. Thomas Bokenkotter, in his monograph ‘A Concise History of the Catholic Church’,(page 17):
“The Gospels were not meant to be a historical or biographical account of Jesus. They were written to convert unbelievers to faith in Jesus as the Messiah, or God.”
This is a shattering admission indeed, and from a historian of Christendom’s largest Church. It is a de facto admission that no historical support exists for any of the accounts in the New Testament, including Matthew's star. But for the sake of this article, let us assume there is something there, some faint signal amidst the noise.
We consider ordinary bright stars first. For an observer in Middle Eastern latitudes 2,000 years ago, there would have been at least ten visible at this time of year. Each one in a different direction, location of the Celestial sphere. Thus, no one star would be visible long, and certainly not at a fixed location or altitude such that it might provide a "search beacon".
The only other stellar candidate one might invoke is a nova or exploding star. Certainly the indredible brightness common to such entities would attract attention, but could any have occurred then and provided the basis for the Matthew citation? Interestingly, this very attirbute of attention -getter eliminates the nova theory from contention. Such a cataclysmic event could not have escaped notice yet there is no mention in any astronomical records of the time - including the Chinese who were already consummate star gazers.
an alternative explanation is that the object was a bright comet. An exceptionally brilliant comet was recorded in 45 B.C. but this is too far in advance of the probable Nativity date. Could such a comet have appeared suddenly and unpredictably around the time. Possibly, but it's doubtful such an event would have been associated with anything beneficent. Two thousand years ago comets were uniformly regarded by all cultures as omens of impending disaster, so we can rule them out.
The only other reasonable explanation is that the Magi witnessed an uncommon astronomical alignment of bright planets. One such candidate is the triple conjuncti9on of the planets Jupiter and Saturn in 7 B.C. A "triple conjunction" here means that Jupiter and Saturn appeared in close proximity no less than three times in succession.
One can spculate here that the Magi in preparing for their jounrey witnessed the first conjunction ca. May 29. A second event was observed on September 29 could have established that Jerusalem was in the general direction they needed to go. Finally, a third conjunction on Dec. 4 would presumably provided the final directional "fix", leading to Bethlehem some eight kilometers away.
The accuracy of the above speculations (and I reinforce that's all these are!) is subject to the dubious assumption that our present calendar is actually a bit off and Christ was actually born in 7 B.C. rather than the 1 B.C. usually quoted.
Given this, one is forced to concede that at the present time there is no comprehensive astronomical explanation which consistently explains all the details. The triple conjunction sounds like the best, assuming we are really in the year 2001 and not the end of 2008.
Perhaps the event must remain forever intangible and beyond the realm of any scientific investigation. Or, perhaps there never was such an object in the first place - and Matthew simply resorted to some elaborate poetic license.
Friday, December 19, 2008
Some Fun with Transpositions
Various aspects of math can provide hours of fun, and amusement. One of these entails transpositions. Some basics on transpositions (and even and odd permutations) first:
A transposition is a permutation which interchanges two numbers and leaves the others fixed. The inverse of a transposition T is equal to the transposition T itself, so that:
T2 = I (identity permutation, e.g the permutation such that I(i) = i for all i = 1,...n)
A permutation p of the integers {1, . . . n} is denoted by
[1 .. . .. n]
[p(1).. p(n)]
So that, for example:
[1 2 3]
[2 1 3]
denotes the permutation p such that p(1) = 2, p(2) = 1, and p(3) = 3.
Now, let's look at EVEN and ODD permutations:
Let P_n denote the polynomial of n variables x1, x2……xn which is the product of all the factors x_i … xj with i < j. That is,
P_n(x1, x2... . xn) = P(x_i .. x_j)
The symmetric group S(n) acts on the polynomial P_n by permuting the variables. For p C S(n) we have:
P_n( x_p(1), x_p(2). . .x_p(n)) = (sgn p) P_n (x_1, x_2…..x_n)
where sgn p = +/-1. If the sign is positive then p is called an even permutation, if the sign is negative then p is called an odd permutation. Thus: the product of two even or two odd permutations is even. The product of an even and an odd permutation is odd.
Back to transpositions!
We just saw:
[1 2 3]
[2 1 3]
The above permutation is actually a transposition 2 <-> 1 (leaving 3 fixed).
Now, let p' be the permutation:
[1 2 3]
[3 1 2]
Then pp' is the permutation such that:
pp'(1) = p(p'(1)) = p(3) = 3
pp'(2) = p(p'(2)) = p(1) = 2
pp'(3) = p(p'(3)) = p(2) = 1
It isn’t difficult to ascertain that: sgn (ps) = (sgn p) (sgn s)
so that we may write:
pp' =
[1 2 3]
[3 2 1]
Now, find the inverse p^-1 of the above. (Note: the inverse permutation, denoted by p^-1 is defined as the map: p^-1 : Zn -> Zn),
Since p'(1) = 3, then p ^-1(3) = 1
Since p'(2) = 1 then p^ -1(1) = 2
Since p'(3) = 2 then p^ -1(2) = 3
Therefore:
p^-1 =
[1 2 3]
[ 2 3 1]
Problem: Express
p =
[1 2 3 4]
[2 3 1 4]
as the product of transpositions, and determine the sign (+1 or -1) of the resulting end permutation.
Let T1 be the transposition 2 <-> 1 leaving 3, 4 fixed, so:
T1 p =
[1 2 3 4]
[1 3 2 4]
Let T2 be the transposition 2 <-> 3 leaving 1, 4 fixed, so:
T2 T1 p =
[1 2 3 4]
[1 2 3 4]
Then:
T2 T1 p = I (identity)
TWO transpositions (T1, T2) operated on p, so that the sign of the resulting permutation (to reach identity) is +1
The permutation is even.
A transposition is a permutation which interchanges two numbers and leaves the others fixed. The inverse of a transposition T is equal to the transposition T itself, so that:
T2 = I (identity permutation, e.g the permutation such that I(i) = i for all i = 1,...n)
A permutation p of the integers {1, . . . n} is denoted by
[1 .. . .. n]
[p(1).. p(n)]
So that, for example:
[1 2 3]
[2 1 3]
denotes the permutation p such that p(1) = 2, p(2) = 1, and p(3) = 3.
Now, let's look at EVEN and ODD permutations:
Let P_n denote the polynomial of n variables x1, x2……xn which is the product of all the factors x_i … xj with i < j. That is,
P_n(x1, x2... . xn) = P(x_i .. x_j)
The symmetric group S(n) acts on the polynomial P_n by permuting the variables. For p C S(n) we have:
P_n( x_p(1), x_p(2). . .x_p(n)) = (sgn p) P_n (x_1, x_2…..x_n)
where sgn p = +/-1. If the sign is positive then p is called an even permutation, if the sign is negative then p is called an odd permutation. Thus: the product of two even or two odd permutations is even. The product of an even and an odd permutation is odd.
Back to transpositions!
We just saw:
[1 2 3]
[2 1 3]
The above permutation is actually a transposition 2 <-> 1 (leaving 3 fixed).
Now, let p' be the permutation:
[1 2 3]
[3 1 2]
Then pp' is the permutation such that:
pp'(1) = p(p'(1)) = p(3) = 3
pp'(2) = p(p'(2)) = p(1) = 2
pp'(3) = p(p'(3)) = p(2) = 1
It isn’t difficult to ascertain that: sgn (ps) = (sgn p) (sgn s)
so that we may write:
pp' =
[1 2 3]
[3 2 1]
Now, find the inverse p^-1 of the above. (Note: the inverse permutation, denoted by p^-1 is defined as the map: p^-1 : Zn -> Zn),
Since p'(1) = 3, then p ^-1(3) = 1
Since p'(2) = 1 then p^ -1(1) = 2
Since p'(3) = 2 then p^ -1(2) = 3
Therefore:
p^-1 =
[1 2 3]
[ 2 3 1]
Problem: Express
p =
[1 2 3 4]
[2 3 1 4]
as the product of transpositions, and determine the sign (+1 or -1) of the resulting end permutation.
Let T1 be the transposition 2 <-> 1 leaving 3, 4 fixed, so:
T1 p =
[1 2 3 4]
[1 3 2 4]
Let T2 be the transposition 2 <-> 3 leaving 1, 4 fixed, so:
T2 T1 p =
[1 2 3 4]
[1 2 3 4]
Then:
T2 T1 p = I (identity)
TWO transpositions (T1, T2) operated on p, so that the sign of the resulting permutation (to reach identity) is +1
The permutation is even.
Monday, December 15, 2008
Initial Conditions of the Big Bang?
In a recent issue (Oct.-Nov.) of the Intertel journal, INTEGRA, Ken Wear asks:
“Supposing the Big Bang theory is correct, what were the initial conditions that produced it?”
This can be approached in a more or less practical way by treating the ‘Big Bang’ as a solution to Einstein’s tensor (field) equations. (See, e.g. ‘Quantum Field Theory – A Modern Introduction’, by Michio Kaku, p. 643):
As per the 2.7K isotropic, microwave background radiation, we assume radial symmetry for the metric tensor – for which we adopt a Robertson-Walker form. This omits all angular dependence and leaves a function of form R(t) which sets the scale and defines an ‘effective radius’ of the universe.
We have:
ds^2 = dx^u g_uv dx^u = dt^2 – R^2(t) [ (dr^2/ 1 – kr^2) + r^2 d (S)^2]
where d(S)^2 is the solid angle differential and k = const.
Associate with this a fluid of average density rho(t) and internal pressure p(t)
The energy-momentum tensor becomes: T_o^0 = rho, T_I^I = -p
with all other components zero.
After inserting these into the Einstein field eqns.
(dR/dt /R)^2 = (8 pi)/ 3 (G_N rho) – k / R^2
whence:
(d^2R/ dt^2 )/ R = - 4 pi G_N (p + rho/3) + LAMBDA/ 3
After setting the cosmological constant (LAMBDA) = 0 and eliminating rho, one obtains as a solution for R (radius of universe as power law function).
R= (9/ 2GM)^1/3 [t ^2/3]
One can deduce from this (ibid, p. 645) that at the Planck energy of 10^19 GeV (giga -electron volts) of energy, the symmetries of gauge theory were still united in a single force. This is at a cosmic age of 10^-44 s.
This 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.
This continues as other symmetries ’break’ one by one, leading to the radiation dominated era. (Described by the Bose-Einstein distribution function, which perfectly applies to the expanding pure photon gas).
The fact that the ‘Big Bang’ can be obtained as a solution to one version of Einstein’s tensor equations, discloses that QM and GR equations certainly don’t ‘blow up’ and are impossible to use.
Mr. Wear then makes the assertion that it “would certainly be a violation of our concepts of cause and effect to say that suddenly, out of nothing….came this cataclysmic explosion”
But again, as I noted earlier, cause and effect notions are of little use. What we need instead are necessary and sufficient conditions for the event to occur - which by the way, is not an ‘explosion”! I refer Mr. Wear to ASTRONOMY magazine, May, 2007, ‘5 Things You Need To Know’, p. 31:
“The Big Bang wasn’t any kind of explosion. It was closer to an unfolding or creation of matter, energy, time and space itself. What would actually have been a much better name is ‘expanding universe theory’.”
As to how spontaneous cosmic inception can occur, this was referenced by T. Padmanabhan, 1983, ‘Universe Before Planck Time – A Quantum Gravity Model', in Physical Review D, Vol. 28, No. 4, p. 756.
To fix ideas, we are interested in first determining the gravitational action, and from this whether acausal determinism is more or less likely to apply. For any action S(g) if
S(g) < < h (the Planck constant)
where h = 6256 x 10^-34 J/s
we may be sure that classical causality is out the window and we are dealing with acausal determinism
If S(g) > > h
the converse holds.
To evaluate S(g) as Padmanabhan shows (op. cit.) , we need V the 4-volume of the space-time manifold for which we choose a de Sitter space, in the first approximation.
We have
S(g) = c^3/ (16 pi G) INT_V R(-g)^1/2 d^4x
where G is the gravitational constant, c is the speed of light, the integral (INT) is over the 4-volume V with the differential (d^4x) to match.
In the big bang model one takes V as the spatial volume enclosed by the particle horizon, and bounded by the time span (t) of the universe. Thus, at any epoch t for k = 0,
S(g) ~ t^1/2
The particle horizon is defined by
rS(g) = 2 ct
Einstein's gravitational equations (with cosmological term, for the sake of generality) are
R ( i k ) - (1 / 2) g ( i k ) R = T ( i k ) + lambda g ( i k )
where the ‘lambda’ denotes the cosmological constant. For de Sitter space it is equal to:
(n – 1)(n – 2)/ [2 a^2]
where a is a scale factor, and n denoted the dimension (4) of the volume under consideration. R(ik) is the Ricci tensor.
Now for S(g) ~ t^1/2, R (the scalar curvature of de Sitter space) = 0, so S(g) = 0
However, the above happens because the Einstein tensor (T_ik) has trace = 0 in the early universe. The ‘trace’ is the sum of the diagonal elements of a tensor, e.g.
Tr(M) = 0
where M =
[0 1 0 ]
[0 -1 0 ]
[0 0 1 ]
This means the limits must definitely be for acausal determinism, NOT classical – including classical causality.
Wear also alludes to a “sequence of oscillations” (ibid.) but this is egregious, since there will be no oscillations, as the universe is not only forever expanding but accelerating in its expansion.
Universes that re-collapse (decelerate), expand forever with zero limiting velocity (e.g. v uniform) or expand forever with positive limiting velocity (accelerate) are called in turn: 'closed' (can have curvature k = +1); 'critical' (k =0) or 'open' (can be k = -1), respectively
Now, to determine whether any F-R-W (Friedmann-Robertson-Walker) cosmological template leads to deceleration or not, we need to find the cosmic density parameter:
OMEGA = rho / rho_c
where the denominator refers to the critical density. Thus if:
rho > rho_ c
(c = critical)
then the cosmic density is able to reverse the expansion (e.g. decelerate it) and conceivably usher in a new cycle. (New Big bang etc.) The observations that help determine how large OMEGA is, come mainly from observing galaxy clusters in different directions in space and obtaining a density estimate from them.
Current data, e.g. from Boomerang and other satellite detectors shows that OMEGA ~ 0.3 or that:
rho = 0.3 (rho_c)
I.e. that rho < rho_ c, so there is no danger of the cosmos decelerating.
Precision measurements of the cosmic microwave background (CMB), including data from the Wilkinson Microwave Anisotropy Probe (WMAP), have recently provided further evidence for dark energy. The same is true of data from two extensive projects charting the large-scale distribution of galaxies - the Two-Degree Field (2DF) and Sloan Digital Sky Survey (SDSS).
The curves from other data with corrected apparent magnitude v. redshift (z) give different combinations of OMEAG_dark to OMEGA_matter over the range. However, only one of the graph combinations bests fits the data:
OMEGA_dark = 0.65 and OMEGA_matter = 0.35
Corresponding to an expansion accelerating for the last 6 million years- with much more dark energy involved (~ 0.65) than ordinary matter.
When the predictions of the different theoretical models are combined with the best measurements of the cosmic microwave background, galaxy clustering and supernova distances, we find that:
0.62 < OMEGA_dark < 0.76,
where OMEGA_dark = rho_dark/ rho_c, and -1.3 < w < -0.9.
In tandem, the numbers show unequivocally that dark energy is the acceleration agent, and in addition that dark energy comprises the lion’s share of what constitutes the cosmos (~ 73%).
In addition, all of this data is firmly backed up by earlier Boomerang (balloon) data that – when plotted on a power spectrum- discloses two adjacent ‘humps’ one a bit higher than the other. The “first acoustic peak” and the “second acoustic peak” fit uncannily to the sort of spherical harmonic function that describes a particular plasma condition. In this case, one that conforms to the supernova-derived values of OMEGA (d, m). (See: ‘Balloon Measurements of the Cosmic Microwave Background Strongly Favor a Flat Cosmos’, in Physics Today, July 2000, p. 7 and 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003, p. 53)
Lastly, astronomers make no “claim” that galaxies are moving apart with increasing velocities. We have actual data that this is so, and it’s based on the basic physics of the Doppler effect.
-----------------------! L1 -------! L2----
---!----------!------------------
L1(o) L2(o)
Thus, in the above pictograph, lines L1(o) and L2(o) are the observed, redshifted (by some number of nanometers) spectral lines for some distant object such that:
v = cz
Where V denotes the velocity of recession, c is the speed of light, and z is the red shift
z = {L2(o)/ L2} - 1
Note again that L2 is the (lab-emission) standard line and L2(o) the observed line wavelength. If z > 0 we say the line is Doppler-effect redshift and receding.
To illustrate, say the hydrogen alpha line (emitted at 656.3 nm, e.g. L2 = 656.3 nm) is redshifted in some distant object to 666 nm (L2(o)). Then we have:
z = 1.015 – 1.000 = 0.015
This translates to a recessional velocity: v = (3 x 10 8 m/s) (0.015) = 4.5 x 10^6 m/s
As to Wear’s claim that it “may be difficult to place credence in such observations over a comparatively brief interval of time”, perhaps, but this “brief interval” is all we have to work with. What, will he dismiss all our painstakingly obtained date (including from the new CERN large hadron collider) because they were obtained over brief intervals? This isn’t the way a Realist works, but it is certainly the modus operandi for an Idealist.
“Supposing the Big Bang theory is correct, what were the initial conditions that produced it?”
This can be approached in a more or less practical way by treating the ‘Big Bang’ as a solution to Einstein’s tensor (field) equations. (See, e.g. ‘Quantum Field Theory – A Modern Introduction’, by Michio Kaku, p. 643):
As per the 2.7K isotropic, microwave background radiation, we assume radial symmetry for the metric tensor – for which we adopt a Robertson-Walker form. This omits all angular dependence and leaves a function of form R(t) which sets the scale and defines an ‘effective radius’ of the universe.
We have:
ds^2 = dx^u g_uv dx^u = dt^2 – R^2(t) [ (dr^2/ 1 – kr^2) + r^2 d (S)^2]
where d(S)^2 is the solid angle differential and k = const.
Associate with this a fluid of average density rho(t) and internal pressure p(t)
The energy-momentum tensor becomes: T_o^0 = rho, T_I^I = -p
with all other components zero.
After inserting these into the Einstein field eqns.
(dR/dt /R)^2 = (8 pi)/ 3 (G_N rho) – k / R^2
whence:
(d^2R/ dt^2 )/ R = - 4 pi G_N (p + rho/3) + LAMBDA/ 3
After setting the cosmological constant (LAMBDA) = 0 and eliminating rho, one obtains as a solution for R (radius of universe as power law function).
R= (9/ 2GM)^1/3 [t ^2/3]
One can deduce from this (ibid, p. 645) that at the Planck energy of 10^19 GeV (giga -electron volts) of energy, the symmetries of gauge theory were still united in a single force. This is at a cosmic age of 10^-44 s.
This 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.
This continues as other symmetries ’break’ one by one, leading to the radiation dominated era. (Described by the Bose-Einstein distribution function, which perfectly applies to the expanding pure photon gas).
The fact that the ‘Big Bang’ can be obtained as a solution to one version of Einstein’s tensor equations, discloses that QM and GR equations certainly don’t ‘blow up’ and are impossible to use.
Mr. Wear then makes the assertion that it “would certainly be a violation of our concepts of cause and effect to say that suddenly, out of nothing….came this cataclysmic explosion”
But again, as I noted earlier, cause and effect notions are of little use. What we need instead are necessary and sufficient conditions for the event to occur - which by the way, is not an ‘explosion”! I refer Mr. Wear to ASTRONOMY magazine, May, 2007, ‘5 Things You Need To Know’, p. 31:
“The Big Bang wasn’t any kind of explosion. It was closer to an unfolding or creation of matter, energy, time and space itself. What would actually have been a much better name is ‘expanding universe theory’.”
As to how spontaneous cosmic inception can occur, this was referenced by T. Padmanabhan, 1983, ‘Universe Before Planck Time – A Quantum Gravity Model', in Physical Review D, Vol. 28, No. 4, p. 756.
To fix ideas, we are interested in first determining the gravitational action, and from this whether acausal determinism is more or less likely to apply. For any action S(g) if
S(g) < < h (the Planck constant)
where h = 6256 x 10^-34 J/s
we may be sure that classical causality is out the window and we are dealing with acausal determinism
If S(g) > > h
the converse holds.
To evaluate S(g) as Padmanabhan shows (op. cit.) , we need V the 4-volume of the space-time manifold for which we choose a de Sitter space, in the first approximation.
We have
S(g) = c^3/ (16 pi G) INT_V R(-g)^1/2 d^4x
where G is the gravitational constant, c is the speed of light, the integral (INT) is over the 4-volume V with the differential (d^4x) to match.
In the big bang model one takes V as the spatial volume enclosed by the particle horizon, and bounded by the time span (t) of the universe. Thus, at any epoch t for k = 0,
S(g) ~ t^1/2
The particle horizon is defined by
rS(g) = 2 ct
Einstein's gravitational equations (with cosmological term, for the sake of generality) are
R ( i k ) - (1 / 2) g ( i k ) R = T ( i k ) + lambda g ( i k )
where the ‘lambda’ denotes the cosmological constant. For de Sitter space it is equal to:
(n – 1)(n – 2)/ [2 a^2]
where a is a scale factor, and n denoted the dimension (4) of the volume under consideration. R(ik) is the Ricci tensor.
Now for S(g) ~ t^1/2, R (the scalar curvature of de Sitter space) = 0, so S(g) = 0
However, the above happens because the Einstein tensor (T_ik) has trace = 0 in the early universe. The ‘trace’ is the sum of the diagonal elements of a tensor, e.g.
Tr(M) = 0
where M =
[0 1 0 ]
[0 -1 0 ]
[0 0 1 ]
This means the limits must definitely be for acausal determinism, NOT classical – including classical causality.
Wear also alludes to a “sequence of oscillations” (ibid.) but this is egregious, since there will be no oscillations, as the universe is not only forever expanding but accelerating in its expansion.
Universes that re-collapse (decelerate), expand forever with zero limiting velocity (e.g. v uniform) or expand forever with positive limiting velocity (accelerate) are called in turn: 'closed' (can have curvature k = +1); 'critical' (k =0) or 'open' (can be k = -1), respectively
Now, to determine whether any F-R-W (Friedmann-Robertson-Walker) cosmological template leads to deceleration or not, we need to find the cosmic density parameter:
OMEGA = rho / rho_c
where the denominator refers to the critical density. Thus if:
rho > rho_ c
(c = critical)
then the cosmic density is able to reverse the expansion (e.g. decelerate it) and conceivably usher in a new cycle. (New Big bang etc.) The observations that help determine how large OMEGA is, come mainly from observing galaxy clusters in different directions in space and obtaining a density estimate from them.
Current data, e.g. from Boomerang and other satellite detectors shows that OMEGA ~ 0.3 or that:
rho = 0.3 (rho_c)
I.e. that rho < rho_ c, so there is no danger of the cosmos decelerating.
Precision measurements of the cosmic microwave background (CMB), including data from the Wilkinson Microwave Anisotropy Probe (WMAP), have recently provided further evidence for dark energy. The same is true of data from two extensive projects charting the large-scale distribution of galaxies - the Two-Degree Field (2DF) and Sloan Digital Sky Survey (SDSS).
The curves from other data with corrected apparent magnitude v. redshift (z) give different combinations of OMEAG_dark to OMEGA_matter over the range. However, only one of the graph combinations bests fits the data:
OMEGA_dark = 0.65 and OMEGA_matter = 0.35
Corresponding to an expansion accelerating for the last 6 million years- with much more dark energy involved (~ 0.65) than ordinary matter.
When the predictions of the different theoretical models are combined with the best measurements of the cosmic microwave background, galaxy clustering and supernova distances, we find that:
0.62 < OMEGA_dark < 0.76,
where OMEGA_dark = rho_dark/ rho_c, and -1.3 < w < -0.9.
In tandem, the numbers show unequivocally that dark energy is the acceleration agent, and in addition that dark energy comprises the lion’s share of what constitutes the cosmos (~ 73%).
In addition, all of this data is firmly backed up by earlier Boomerang (balloon) data that – when plotted on a power spectrum- discloses two adjacent ‘humps’ one a bit higher than the other. The “first acoustic peak” and the “second acoustic peak” fit uncannily to the sort of spherical harmonic function that describes a particular plasma condition. In this case, one that conforms to the supernova-derived values of OMEGA (d, m). (See: ‘Balloon Measurements of the Cosmic Microwave Background Strongly Favor a Flat Cosmos’, in Physics Today, July 2000, p. 7 and 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003, p. 53)
Lastly, astronomers make no “claim” that galaxies are moving apart with increasing velocities. We have actual data that this is so, and it’s based on the basic physics of the Doppler effect.
-----------------------! L1 -------! L2----
---!----------!------------------
L1(o) L2(o)
Thus, in the above pictograph, lines L1(o) and L2(o) are the observed, redshifted (by some number of nanometers) spectral lines for some distant object such that:
v = cz
Where V denotes the velocity of recession, c is the speed of light, and z is the red shift
z = {L2(o)/ L2} - 1
Note again that L2 is the (lab-emission) standard line and L2(o) the observed line wavelength. If z > 0 we say the line is Doppler-effect redshift and receding.
To illustrate, say the hydrogen alpha line (emitted at 656.3 nm, e.g. L2 = 656.3 nm) is redshifted in some distant object to 666 nm (L2(o)). Then we have:
z = 1.015 – 1.000 = 0.015
This translates to a recessional velocity: v = (3 x 10 8 m/s) (0.015) = 4.5 x 10^6 m/s
As to Wear’s claim that it “may be difficult to place credence in such observations over a comparatively brief interval of time”, perhaps, but this “brief interval” is all we have to work with. What, will he dismiss all our painstakingly obtained date (including from the new CERN large hadron collider) because they were obtained over brief intervals? This isn’t the way a Realist works, but it is certainly the modus operandi for an Idealist.
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