Tuesday, April 30, 2013

Time Slips (3): Experiments in Time Travel?

Go back to November 22, 1963 and find out who was really in that 6th floor Depository window?

Hmmmm....an interesting proposition!

In the science fiction novel 'Lest Darkness Fall'  by L. Sprague de Camp,, the central character (Martin Padway) undergoes a time slip to 6th century Rome. The interesting aspect of this is that it is the Rome for which a definite history is known, since Padway used it to his advantage as he made his way in a strange environment. Hence, he knew what major political changes would occur, who was in charge and which factions were vying for control, including barbarians.

In other words, the template for his experience was not the same as the ones I've considered in the two earlier blog posts: an interphasing of two distinct parallel universes. As I conjectured, the experience of Charlotte Moberly and Eleanor Jourdain would be more a case of the women stepping into 1789 Versaille, but in an alternate universe. One briefly interphased with our own. The nature of their descriptions supported this hypothesis.

In the case of the fictional Padway, his memory and the ability to forecast events to unfold in 6th century Rome, disclosed that he didn't step into an alternate universe with an alternate past, but remained in this one, on the same Earth in fact. Otherwise the events that shaped ancient Rome would have been different and he'd not have been able to use his historical memory to any advantage

This brings up the questions, first, of whether time slips in this one universe (and Earth) are feasible, and  second, if so, are there experiments one might perform to exploit them - say to return to Dallas, in November, 1963 and interfere with the Kennedy assassination?

While Oxford physicist Michael Shallis, in his book 'On Time' doesn't elaborate at any length, he does provide a brief clue (p. 163-64) referring to "advanced waves moving back in time in counterpoint to their progressive and retarded partners."  He then goes on to write (ibid.):

"This interpenetration slips backward and forward in time simultaneously, seeming to defy the laws of matter and causality"

The notion of advanced and retarded waves, or potentials, is not new. In fact, every physics student taking his first Electricity and Magnetism course encounters them.  Indeed, from Maxwell’s E & M theory, we are fully enabled to make use of what are called “advanced potentials” defined in terms of:

V(r,ta) = f1(r, Ta) and A(r, ta) = f2(r, ta)

Where ta is the “advanced time”, ta = t + r/c

And the f1, f2 are functions of the electric potential and vector potential, respectively.   In the advanced time, we ascertain conditions for the future potentials V(r,ta)  based on the past, and are able to use them in appropriate calculations in the past. An evident violation of causality, though admittedly the sort of applications where these may be used are limited

What might be more directly relevant to time slips for the same universe involve the "offer" and "echo"waves proposed by John G. Cramer. The two interacting, interpenetrating wave forms might be expressed:

y(O)  + y(E) = Ö(2/π) e ωτ  +   Ö(2/π) e- ωτ

The use of such waves, say in a putative role for time slips, would demand using something called Minkowski space-time, Minkowski envisioned a kind of hyperspace in which events do not just 'happen'. Rather, they already are embedded in the space-time metric (geometry) and one comes across them, like towns along a highway (cf. Whittrow, G.J. 1972, The Nature of Time, Pelican Books, Great Britain, p. 103.)  For example, imagine the Minkowski temporal scale:


Past[-τ] <-------e1------e2--------e3-----> Future [+τ]

where e1, e2 and e3 are three events, say: e1 = Explosion of the Hindenburg dirigible, e2 = John F. Kennedy's assassination, and e3 = some future asteroid impact in the 21st century. In the Minkowski hyperspace these have always been on the timeline, which is traversed in the same way one would traverse a space. Thus, one encounters the various events on the timeline as s/he might encounter towns or villages along a highway.

Movement can occur in time or in space, and have a complementary (space or time) equivalent. For example, stay where you are and let one minute elapse on your watch. You have performed a 'movement in time' without a corresponding movement in space. We say you have traversed imaginary space. This imaginary space can easily be computed:

Im(x) = i(300,000 km/s x 60 s) = 18,000,000(i) km

That is, you have traversed 18 million imaginary kilometers or 11.25 million miles in imaginary space. (Im(x) is the symbolic representation for an imaginary space (x) transition). Now, think of a movement in real space, but none in time. Is this possible? Well, I can get out my telescope and observe the Moon instantly - bearing my consciousness upon it - without taking the time to travel there. For all intents and purposes I am there. In this case, an imaginary time interval is the result, and again can be computed:

Im(τ) = (i) 384,000 km/ 300,000 km/s = 1.28i sec

That is, 1.28 imaginary seconds to get there. I note here that this imaginary time interval is equivalent to a real space interval: 384,000 km (space distance to Moon) = 1.28 i seconds. Thus, imaginary time and real space are interchangeable. This has prompted at least one observer of the situation (to do with Minkowski spacetime) to observe (Whittrow, op. cit., p. 104.):

“In other words, the passage of time is merely to be regarded as a feature of consciousness that has no objective counterpart.”

This is important!  It suggests that although we might formulate an apparently real "temporal highway" - i.e. the Minkowksi timeline, that the reality is we can't use it in any objective fashion, say analogous to changing locations on an actual physical highway.  In this case, the only "time travel" one would be able to do is a limited form based on displaced consciousness. Since quantum mechanics fuses the role of observer with that observed, then a quantum displacement affecting consciousness could conceivably "transport" one to another time, say perhaps the day of Kennedy's assassination.

The problem is one would only access it as a conscious observer, as if watching passively from a TV screen, not as a participant. Moreover, to make it work it seems likely the inception would have to commence in the brain itself - say at a synapse- for which we already know the dimension of the synaptic cleft (200- 300 nm) is arond the scale for the Heisenberg Uncertainty principle to operate. From an initial energy emergence, say based on the energy-time uncerainty relation:

DE  Dt  £    ħ

One might then arrive at adequate energy, i.e.

DE     »   ħ/ Dt 

to initiate a temporal cascade or 'push' to displace one's conscious in time. Following this in a more comprehensive way would require using some kind of operator to generate variation in time as experienced by consciousness. David Finkelstein ( Quantum Sets and Clifford Algebras, in International Journal of Theoretical Physics, Vol. 21, Nos. 6/7, p. 489 ) has created an operator explicitly to vary time via ‘bracing’. The operator is called ‘the brace operator’, Br. To see how it works on an elementary level, select a quantum unit set (say of cardinality 1) over some sub-module S (1) of the Clifford algebra S, with basis B(1). Then it follows from application of Br, and its conjugate Br*:

Br* Br = 1 Br Br* = [unit] Br* Br - Br Br* = [non-unit]


A more graphic way to see this is as follows:

After 1 τ, Br = { }

After 2 τ, Br = { { } }

After 3 τ, Br = { { { } } }

where we define:   10-43  s < τ <   10-23 s

And we see that for the smaller values on the left side, for which Dt = D τ

enormous energy would be released.   Notice that the brace creation increases arithmetically as the unit tau increases. The operation Br, equivalent to C(b) in Grassman space, generates an elemental tau (τ) each time, starting from some initial fluctuation.   Might this fluctuation be willed? Perhaps, but more than likely it would be spontaneous. All of this is of course highly speculative, but one thing which isn't is the clear impossibility of actual physical time travel, by time slip or otherwise. 

 Yes, I'd originally planned to travel to Dachau sometime in the next 2 months, to attempt a time slip experiment. But I don't believe it would be wise to try it, even slipping into a parallel universe with Dachau on another Earth!  But it might yet be feasible to attempt a quantum -based displacement of consciousness - say back to Nov. 22, 1963.

Reefer Madness Redux: Exploding Mike's Delusions About Amendment 64

ReeferMadnessPoster.jpgMany readers may recall, or perhaps have seen,  the film "Reefer Madness" - a 1936  propaganda exploitation effort revolving around the melodramatic events that ensue when high school students are lured by pushers to try marijuana.  Their travails extend from a hit and run accident, to manslaughter, suicide, attempted rape, and descent into madness.

The obvious purpose was to scare the living bejeezus out of any kid to not even think of trying "demon weed". The message was it would wreck young lives leaving them broken husks - much like modern Xtian fundamentalism has wrought on too many minds these days.

Anyway, the film was directed by Louis Gasnier and starred a cast composed of mostly unknown bit actors.

Originally it had been financed by a church group (Wouldn't ya know?) under the title "Tell Your Children". Its primary mandate was circulation and screening to parents as a  putative morality tale, attempting to teach them about the dangers of any cannabis use by their kiddies. Perhaps two decades later, any viewing of this dreck became so laughable that it emerged as a cult film - shown to audiences primarily as joke material. Which is rightly the niche to which it belongs.

Flash forward to today, and we still behold would-be propagandizing clowns - like a certain under-educated goober- who don't even bother to do minimal reearch before shooting from the hip concerning another state's MJ laws.   In this case, it seems like my dumb turd wannabe Rebel bro didn’t take long to take umbrage at my post about his MJ bloviations 3 days ago. True to his bellicose nature he came out firing…..but alas…..all scattershot, ending up hitting himself in his own fat ass.

I am not about to reference all his assorted BS, but focus in particular on two aspects:   1) His citation of lengthy recycled bollocks from a known anti-MJ crusader link about the “ill effects” of MJ on youth,  and (2) His claim that (in yesterday's blog post) I was "comparing apples and oranges" in highlighting the ill-effects, fatalities for DUI in FLA, over MJ -induced auto fatalities in Colorado.

Regarding (1), it doesn't take much Google searching even by a lamebrain to dredge up multiple anti-MJ sites (e.g. 'Smart Colorado'), then recycling their hogwash into a blog. That was essentially how Mikey consumed over two thirds of his last blog, by parroting one site and its "warnings" and  how MJ will  "tarnish" Colorado in multiple ways. All of these are exaggerated  fear- mongering Agitprop -much like "Reefer Madness"- and all have been shot down by MJ legalization backers and groups. Multiple times.  In Colo. we know such anti-MJ groups existed even before Amendment 64 became law, and I even referenced the efforts of Patrick Kennedy to form one of his own for a national campaign to halt any further state legislation to allow MJ, see: http://brane-space.blogspot.com/2013/01/patrick-kennedy-useful-idiot-for-big.html  

I further noted that in taking this route Kennedy effectively became a useful idiot for Big PhrMA- much like Mike has become (albeit unconsciously) with his laughable anti-MJ, anti-Amendment 64 blogs. As far as the “risks” to teens, young people I cited a letter in the Denver Post which nailed such a red herring:  

“There are many freedoms adults often enjoy that are illegal for kids, including gambling, drinking, smoking, investing, driving, getting piercings and tattoos, getting married, staying out all night, going to many concerts, working a double shift, etc. Granted, many of these freedoms could be considered bad for adults, too, but the “bad for kids” trope is nothing more than a cudgel designed to stifle honest debate. An unregulated black market is most assuredly more harmful to kids than a regulated honest market, and Colorado enjoys many economic advantages from the tax revenue these freedoms bring when adults enjoy them responsibly”    

Of course, such points are way too subtle for a hammerhead like Mike! This stubborn tool- or more like a half tool and half fool, will always twist semantics to what suits his specious fundie agenda,  and bring in irrelevancies and red herrings since he lacks any argumentative ballast.

This brings up his second issue for which I insert here his nutso response from his blog, for reference:

"The FACT is that any would-be traveler is much more likely to be killed by a drunk in Florida than even sideswiped by an MJ user here in Colorado."

Hey, DUMBASS! That statement is true in any state! Why? DUHHHH....you idiot! Because alcohol has been legalized where MJ has NOT! When prohibition was in effect, deaths via drunk drivers were miniscule! Once it was repealed and made "legal," as time went by, alcohol-related motor vehicle crashes and deaths SOARED! As did overall crime (e.g., domestic violence, robberies, murders, etc!). Y'all wanna see MORE of something negative from an abusive substance? JUST LEGALIZE IT!

Hence, if your Libtard Guv and other politicians in CO decide to keep MJ "legal," keep an eye on your state's impaired driving deaths and injury stats THEN! Okay? Then let me know what ya find! (oh yeah, toss in the stats on the overall crime rate as well)


Well, leave it to a brain damaged (at Parris Island) fucktard to restate the point I’d already made! I.e.

“Yes, the basis analog for the argument is different, but then he brought it on himself by harping on all the “ills” of pot use in Colorado – while neatly overlooking that marijuana is not the culprit in ANY state, rather alcohol is. “

But missing the boat as to the reason why! At the risk of getting even more subtle beyond his comprehension level, let me make this finer point: The WHOLE basis for Amendment 64 was the regulation of marijuana LIKE alcohol. The reason that the amendment surpassed (by a long way) the requisite number of petition signatures to get on last November's ballot -  was because intelligent people, prospective voters saw the value in this equivalent regulation, despite the fact MJ has not caused one CO fatality (all Mike’s speculations aside or taking biased factoids from his anti-MJ sites). Indeed, the virtues of pot, in NOT creating analogous DUI-type havoc on the roads, or other crimes, were largely what drove young voter turnout in the state and 2 to 1 votes for the Amendment!  In other words, DOH!!! - So long as alcohol consumption is legal in Colorado (and other states), criminalizing marijuana is fucking absurd!

In addition, people saw the economic benefits! If MJ is indeed regulated like alcohol then taxes would provide additional revenues! In a state drowning in debt because of too low state taxes, this is a godsend. In the case of Colorado Springs, for example, our medical marijuana businesses brought in nearly $1m in extra local tax revenues last year – enough to keep assorted gov’t functions going, including upkeep of parks and trails cleaned, street lights on and a few more schools open- as well as maintained. Does this matter? Ask the people who live here! One thing we DO know is that bringing in more military - as based at Ft. Carson- hasn't made a significant difference to state coffers! The drain on our schools, highways, hospitals has more than countered any tax revenue largesse.

Thus, the point this terminal idiot doesn’t grasp is that OF COURSE one is more likely to be killed in any state via DUI from excess alcohol BUT THAT IS EXACTLY WHY EQUIVALENT REGULATION OF BOTH – AS DRUGS- SHOWS THERE IS LESS REASON TO BAN MJ THAN ALCOHOL! In other words, when both (legal) alcohol and MJ are forced under the same regulatory standards, then MJ wins the benefits column by a mile! (And I won't even belabor the proven benefits of cannabis for cancer patients, i.e. in finding their appetities after chemotherapy!)

But trying to explain this to a dumb, Bars 'n stars- toting wannabe Confederate (he was actually born in Milwaukee- a fact he can never change)  is like trying to explain differential calculus to ‘Sparky’ – wifey's and my  favorite backyard squirrel.

He also commits the logical fallacy of "slippery slope" when he claims if MJ is legalized across the nation, like alcohol  after prohibition – then we will all be on the highway to Hell with even more "evils", "abuses" etc.. We will have crazy MJ dopers running amuck just like drunks. But the stats again don’t support his fear mongering. We have had medical MJ for over five years now and no one is going nuts on the streets, despite the fact many more citizens likely avail themselves of it than really need it, i.e. for cancer or severe pain. But so WHAT?

As for the federal war on drugs and their prohibitions of a ‘schedule 1 substance’ even the most avid right wingers agree that all it has done is filled our prisons and at great cost, which we can no longer afford. This is also why a consistent majority of Americans support legalization for the nation. (By almost 55% to 45%)

The last irksome element of his endless gibberish is the nonsensical one that I am not entitled to be taken seriously if I cite links or info from state DMV urls to do with drunk driving stats, crimes, arrests! The reason? I never worked in law enforcement, or was a cop (like he was- though he spent most of his time beating in the heads of poor black sugar cane cutters in South Bay). But what does that have to do with the price of tea?

 In fact, the argument is as fucking stupid and deranged  as arguing that I have no right to blog on the Vietnam War, the wrongful way it was started or the atrocities committed, because I never served in the military. In like manner- though Mike is too dumb and blind to see it- his own pseudo-logic and arguments militate against him citing links to MJ from Colorado despite the fact he's: a) never been a lobbyist in the state, or b) has never been a legislator and doesn't know beans about the basis of Amendment 64. (Though again, he could learn and justify his blogs! But as in the case of evolution, the Big Bang, etc. he never does.)

In the end it's useless to try to argue or debate this character because he is totally ignorant of the basic parameters  that apply to the content of any worthwhile argument. In this case, it's the Amendment 64 basis and legalization framework - to regulate MJ like alcohol has been.  This being the case, there'll be no further engagements until he can show he can pass a basic test in logic, for which I provide a link here:


My bet is that, like the biblical exegesis test, he will punk out. It's much easier, after all, to spout endless rubbish, ignorance and bullshit than it is to show he can truly engage on the same intellectual "battle field". Perhaps he ought to stick to the battlefields to which he's accustomed, i.e. bat and bottle fights in bars and .....with rogue gators in Lake Panosoffkee, FL.

Monday, April 29, 2013

Solutions to Bessel Function Problems

We now look at the solutions to the last group of math problems:

1) Compute the Bessel functions for Jo(x)  and J1(x) with x = 1 and then compare with the values obtained from the graph shown at top.


Use the truncated series:

Jo(x) = 1 - x2/ 22 (1!)2 + x4/ 24 (2!)2 - x6/ 26 (3!)2 +…..

Then for x = 1:

Jo(1) = 1 – (1)2/ 22 (1!)2 + (1)4/ 24 (2!)2 – (1)6/ 26 (3!)2 +…

Jo(1) =  1 – ¼   +  1/ 64  -  1/2304  =  0.765

Compare to graphical value: Jo(1) =   0.8


J1(x) = x/ 2 - x3/ 23 ·1! 2! + x5/ 25 ·2!3! - x7/ 27 ·3!4! - .....

Then for x = 1:

J1(1) = 1/ 2 – (1)3/ 23 ·1! 2! + (1)5/ 25 ·2!3! – (1)7/ 27 ·3!4! - .....

J1(1) =  ½  -  1/16  +  1/ 384  - 1/ 18432  =   0.44

Compare to graphical value: J1(1) =   0.45

2) Find the twist in a solar loop (take it to be a magnetic tube) if: B q (r)= 0. 1T and B z (r) = 0.2T. Take the radius of the tube to be r = 104  km and the length L =108  m. Is the tube kink unstable or not? (Kink instability is said to obtain when: T(r) >2 p

Solution: the “twist” is defined:

   T(r)  =  (L B q(r))/  (r  B z (r))

Where: B q(r) = 0.1 Tesla and B z (r)  = 0.2 Tesla

Also: r =  104  km  = 107  m   and L = 108  m

Therefore: B q(r))/  (B z (r))  = (0.1)/ (0.2) = 0.5  and L/r = (108)/ (107) = 10


T(r)  = (L/r) (0.5)  =   10 (0.5) = 2.0

The tube is not kink unstable since that requires: T(r) > 2p  = 6.28

3) Compute the intensity for the azimuthal magnetic field component (i.e. B q (r)   ) of a large sunspot, if its equilibrium magnetic field Bo = 0.01 T and the value of  J1(ar) conforms to a = 0.4 and r = 40.

Solution: By definition: B q (r)  =  Bo J1(ar)

If a = 0.4 and r = 40 then ar = (0.4)(40) = 16

From the graph: J1(ar) = J1(16))  » 0.17


B q (r)  =  Bo J1(ar)  = 0.01T (0.17) =  0.0017 Tesla

FACT: You’re More Likely Dead from a Drunk Driver in FLA Than From an MJ User in Colorado!

Well, let's get it out into the open: Fact-based reality is a challenge for most repukes and Southern Tea party types in the best of times. In times of political upheaval especially with the North-South divide increasing due to hatred of Obama, it goes over the top. Especially for a certain blogger who yaps a lot but is unable to even pass a relatively simple test in his self-proclaimed area of expertise.

Enter then a recent, semi-serious blog in which he holds Florida up as an exemplar “vacation spot” (along with other formerly Rebel enclaves like MS, AL) while dissing all the “Yankee” states- i.e. north of the Mason-Dixon line- as well as Colorado. In the latter case he bloviates about the prospective traveler’s likelihood of getting killed – maybe run down or whatever- by a pot-crazed lunatic, given our state has passed Amendment 64 to allow recreational use of pot.

Of course, this is as much codswallop as his obsession over a non-existent "salvation" and  its schizoid driving forces: “Satan” and “Hell”. So one must wonder if those puerile, phantasmagorical ideations formed some kind of embolism in his deteriorating brain leading him to write so much crap about Colorado and marijuana!   The FACT is that any would-be traveler is much more likely to be killed by a drunk in Florida than even sideswiped by an MJ user here in Colorado. But don’t believe me, check out the state of Florida’s own statistics from a state site:  http://www.dmvflorida.org/florida-dui.shtml
Therein we learn:

"According to Florida DMV records there were 33,625 DUI convictions in Florida in 2011. Of the 55,722 DUI tickets issued in Florida in 2011 - 9,328 were issued by the FHP, 23,649 were issued by police departments in Florida, and 21,868 were issued by Florida Sheriffs departments.”

Comparable statistics in all categories for MJ users in COLORADO : O

We also learn the following DUI stats for assorted arrests in Florida counties:

· Hillsborough County (Tampa) - 3,256

· Miami-Dade - (Miami) - 2,274

· Duval County - (Jacksonvile Area) - 2,222

· Pinellas County (St Petersburg) - 1,824

· Palm Beach County (West Palm Beach) - 1,561

· Orange County (Orlando) - 1,383

· Brevard County (Melbourne) - 1,072

· Broward County (Fort Lauderdale) - 985

Comparable driving-related stats for MJ users in COLO, for all counties: Zero

We also learn about fatalities from this site: http://www.dui-usa.drinkdriving.org/Florida_dui_drunkdriving_statistics.php

For which we find:

717 fatal accidents in Florida where at least one driver had a BAC (Blood alcohol content) of 0.08% or above

803 people were killed in Florida in accidents where at least one driver had a BAC of 0.08% or above

154 people were killed in Florida in accidents where at least one driver had a BAC between 0.01% and 0.07%

These are startling stats! Look at them! That is a total of  957 deaths from drunken drivers! There are also likely hundreds of shooting incidents, including accidents, engendered by too high a BAC but the state (fortuitously) keeps no records on those. Meanwhile, the comparable stats for marijuana users in Colorado? Zero!

The hard truth, which this bozo seems not to process, is that you’re much more likely to lose your life from a drunken driver in FLA than from an MJ user in Colorado. Yes, the basis analog for the argument is different, but then he brought it on himself by harping on all the “ills” of pot use in Colorado – while neatly overlooking that marijuana is not the culprit in ANY state, rather alcohol is. It leads to more DUI deaths, more accidents – including by use of weapons- than MJ does in any parallel universe.

The guy’s fact base is so distorted that he actually impugned Gov. John Hickenlooper of CO despite the fact he was never a fan of Amendment 64. Indeed, in the wake of its passage, he was the one that  snarkily warned voters they’d best “not get high on Cheetos”.

Hickenlooper was also the one that proposed, after 64’s passage, a way to get MORE Federal oversight- working with the U.S. Attorney Gen. ! This so outraged many that Denver Post columnist Vincent Carroll was driven to write a column ('Come On, Governor, Defend 64!' , Nov. 8, 2012, p. 21A) to steer the Guv to the side of the angels. (Alas, he's gone more to the side of the 'devils'- as in recently drinking a glass of allegedly "fracked" water and declaring it "tastes fine, has no ill effects".)

Sadly, what all of this shows is that “Mr. Johnny Reb Blogger” has no clue what goes on in this state, nor the comparable damage done by alcohol relative to MJ. But then why be surprised when he earlier shot his yap off about Chicago being the the No. 1 city for homicides in the USA, when FBI uniform crime stats disclosed Detroit! Or, being totally unaware that the Vietnam conflict was started on a pretext, or that the ‘Amazing Race’ episode he calumniated was not about “forcing contestants to learn a communist song” but rather matching different symbols on posterboards.

But after all, why be surprised? This is the same character that wouldn’t even attempt a test in his own proclaimed specialty area, biblical exegesis, i.e. http://brane-space.blogspot.com/2013/04/can-pastor-mike-pass-basic-test-on.html

This despite being given unlimited time to take it!

Perhaps, before  Mr. 'Goober' next blogs on MJ or Colorado, he might learn a bit more from other subjects. Say like: Sociology, crime statistics, American history......oh, and basic English.  Maybe at his FLA Smokehouse Bible College, assuming there are any offerings besides "bible study" and watching Woody Woodpecker cartoons!

Sunday, April 28, 2013

Looking at Bessel Functions & Applications

Plot of Bessel function of the first kind, Jα(x), for integer orders α = 0, 1, 2.

Among the most important special functions is the Bessel function. In the field of solar physics, for example, it's of inestimable importance in the analysis of solar magnetic fields and their evolution. One very key equation is the Helmholtz, viz.

1/ r  [/ r  ( r  / r)] B  +  (a)2 B = 0

where r is the radial coordinate, B  the magnetic field intensity, and a a quantity called the "force free parameter". Then the axially symmetric (i.e.- in cylindrical coordinates r, z, q) Bessel function solutions are

B z (r)    =   Bo Jo(a r)  

B q (r)  =  Bo J1(ar)

where the axial (top) and azimuthal magnetic field components are given, respectively, and  Jo(a r) is a Bessel function of the first kind, order zero and J1(ar) is a Bessel function of the first kind, order unity. (See graphs at the top for Bessel functions of the orders 0, 1 and 2).

The Bessel functions are mathematically defined (cf. Menzel, 'Mathematical Physics', 1961, p. 204):

Jm (x) = (1/ 2m m!) xm [1 -  x 2/ 22 1! (m + 1)  +  x4/ 242! (m + 1) (m + 2) -  ….(-1)j x2j / 2 2j j! (m + 1) (m + 2)…(m + j) +  …]

which we terminate with second order terms.

For m = 0 and m = 1 forms one gets:

Jo(x) = 1 - x2/ 22 (1!)2 + x4/ 24 (2!)2 - x6/ 26 (3!)2 + ......


J1(x) = x/ 2 - x3/ 23 ·1! 2! + x5/ 25 ·2!3! - x7/ 27 ·3!4! - .....

The equations in B z (r),  B q (r),  with the special Bessel functions at root, are critical in describing the respective magnetic fields for a magnetic tube. For a cylindrical magnetic flux tube (such as a sunspot represents viewed in cross-section) the “twist” is defined:
T(r)  =  (L B q(r))/  (r  B z (r))

Where L denotes the length of the sunspot-flux tube dipole and r, the radius. If the twist exceeds 2p then the magnetic configuration may be approaching instability and a solar flare.

Problems for the Math Maven:

1) Compute the Bessel functions for Jo(x)   and  J1(x)  with x = 1 and then compare with the values obtained from the graph shown at top.

2) Find the twist in a solar loop (take it to be a magnetic tube) if: B q(r) = 0. 1T and B z (r) = 0.2T. Take the radius of the tube to be r = 10 4  km and the length L = 10 8  m.   Is the tube kink unstable or not? (Kink instability is said to obtain when: T(r) > 2p)

3) Compute the intensity for the azimuthal magnetic field component (i.e. B q (r) ) of a large sunspot, if its equilibrium magnetic field Bo = 0.01 T and the value of  J1(ar) conforms to a = 0.4 and r = 40.

TIME SLIPS (2): Flights of Fancy or Temporal Displacements Based on Real Physics?


In the diagram directly above there appears a two-slit  diffraction pattern  and also an associated intensity pattern showing the relative light intensity for the pattern -obviously with the central portion amplitude above the rest.

David Deutsch's arguments on p. 44 of his monograph ('The Fabric of Reality") basically contend that:

"there is no intrinsic difference between tangible and shadow photons: each photon is tangible in one universe and intangible in all the other parallel universes"

In his representation on p. 41 (Fig. 2.7), we see a similar pattern to the one given above, along with an additional pattern in which the dark interference fringes are much wider. He infers that "something must be coming through the second pair of slits (bear in mind two, 2-slit arrangements are set up in sequence) to prevent the light from the first pair reaching X? But what? We can find out with further experiments."

After a lengthy bit of reasoning, including successive tweaking of thought experiments, Deutsch arrives at "shadow photons from a parallel universe". He infers (p. 44) for at least one arrangement "at least a trillion shadow photons accompanying each tangible one."

He also is careful to distinguish the respective properties: (ibid.)

"Thus, we have inferred the existence of a seething, prodigiously complicated, hidden world of shadow photons. They travel at the speed of light, bounce off mirrors, are refracted by lenses, and are stopped by opaque barriers or filters of the wrong color. Yet they do not trigger even the most sensitive detectors. The only thing in the universe that a shadow photon can be observed to affect is the tangible photon it accompanies. That is the phenomenon of interference. Shadow photons would go entirely unnoticed were it not for this phenomenon."

In light of the above, we now return again to the experience of Charlotte Moberly and Eleanor Jourdain in experiencing a time slip transferring them from the year 1901 to 1789. (Previous blog). Moberly described a flat and lifeless terrain in her report and most importantly declares: "There were no effects of light and shade, and no wind stirred the trees".  What do we infer?

If there really were "no effects of light and shade" then it must mean that their surreal domain was in fact an inter-phased one for two parallel universes. In this domain we surmise that if they could have performed the sequential two slit diffraction experiment cited by Deutsch they'd have found instead a central large dark area and bright fringes. As opposed to a central bright region and dark fringes. In addition, we may infer this interphased domain was dominated by shadow photons over tangible ones but at different angles.  This is why "everything suddenly looked unnatural, therefore unpleasant; even the trees behind the building seemed to have become flat and lifeless ".

It is important to reiterate here, that according to the standard multiverse theory (based on cosmic inflation), there are basically an infinite number of parallel universes. In the hyper-toroid geometry (graphic shown in the previous blog)  these separate universes can be regarded as lines of longitude, since an infinite number of them can be fit around the circumference of the hyper-sphere.  If say, one somehow for some reason briefly overlapped another, one would expect an interphase condition. This then would permit a time slip to occur but it would not be between times in the same universe (say for the Brit pair between the 1901 and 1789 Earth as we know it) but between TWO distinct parallel universes. That is, they'd have slipped from 1901 in this universe with the Earth as it exists therin, to another (parallel) universe with the Earth as it existed in 1789.

Let's now explore the dynamics more closely, using the diagram shown at the very top, for two spaces in  algebraic homology:

T = S1 X S1

The first (space) is the circle all the way around the middle of the 'donut's body. The second (time) is the circle around a section of the donut itself. Here (diagram), the respective spaces (circles S1) define two dimensions for what we will call the global state space GL. Thus, we have:

GL = S1 X S1 = (SPACE) X (TIME)

The line marked 'Axis' defines the center of the toroidal space we are looking at. The important point is that the time cycle is mapped all along the (single) S1 cycle of space. The space cycle therefore defines all hyperdimensional cosmic time cycles that ever have, or will, exist. Evidently, there are an infinite number of such cycles, since an infinite number of points can be mapped onto the space cycle as well.

All cycles are identical in the infinite series (Σi Θi) but also different. Identical, since each cycle goes from 0 through 360 degrees, folding back on itself so that a particular beginning (Big Bang = 0) and ending (Big Crunch = 360°) for each universe occurs at one and the same point (0° = 360°). Hence the same initial and final coordinates apply to all cosmic cycles. Θ is thus a fixed dimension of the Young-model ‑hypertorus, much like time in the Minkowski universe. Indeed, in the hypertorus overview, any position can be fixed by two coordinates (φ, Θ) where the φ is used for space and Θ for time. In fact, since both are circles, it makes sense to assign them angles: one (φ) for space, the other (Θ) for time.

Consider now, the mapping for the phase space volume we called the global state space. It is the (topological) space of all possible times and all possible spaces, for all possible universes. Thus, it is an imaginary (in the mathematical sense!) space. Two possible events in this global state space might be designated:

Ξ = (φ, Θ) AND Ξ' = (φ',Θ')

By way of example, Ξ could be the assassination of Hitler, and Ξ' the event wherein Hitler escapes assassination. Either one is possible but not both simultaneously in the same cosmic cycle or universe! We already know we inhabit the cycle for which Ξ' holds, so the other (Ξ) cannot. The "pasts" are thus mutually exclusive, which further reinforces Hawking's "temporal censorship" postulate that one cannot go back and change the past.. The topological space of the hypertorus cosmos can therefore be represented by the global state space, a product of absolute hypertorus coordinate time (Θ) and 'all-space'(φ):

GL = Θ X φ

Now, the set of specific times t_i C Θ_i, and the set of specific 4-dimensional spaces R_i C φ_i, so the space of all local states, L is the product space of four dimensional spaces and specific times:

L = R X t

We now need to look at is how L and GL are related, and the space and time sets within them:  L Ì GL That is, the local state space L is contained within the global state space GL, but can never be equal to it The same applies to the subsidiary spaces: R in relation to φ, and the specific times: t in relation to Θ.

For example, for Θ, there is some spatio-temporal matrix M with generalized dimensional indices {x0, x1, x2, x3}. No one of these is 'time' specifically and uniquely. Rather, "time" arises when the three space indices have been assigned (i.e. if φ= {x1, x2, x3}, then Θ = {x0}. In effect, as S. Auyang observes: "the structure M is too primitive to confer special meaning on the time dimension. M is not in time, it is all times." (How is Quantum Field Theory Possible?, Oxford University Press, 1995, p. 169). By contrast, 't carries the load of temporal significance'. (Note here that when the 4 dimensional indices for each parallel universe are defined, then it becomes possible to more rigorously separate the parallel universes, i.e. in terms of their respective physical constants, specific times of origin, and duration.)

"Time" then is by no means as straightforward as often assumed, especially if one can plausibly have both time and space uncertainty - i.e. the Heisenberg Indeterminacy principle applicable to each. If this be so, then one can conjecture unusual conditions in which both space and time indeterminacy for two adjacent parallel universes allow for brief interphasing. If a sentient person, human, happens to be at such a location when this indeterminacy of space and time occurs, he can experience a "time slip".

Again, we cannot say the person or persons are really "going back in time". Instead, only that they have transitioned from a current coordinate Θ1 in one universe to Θ2 in other. While Θ2 appears to be "backward" in time by the reckoning of the person at Θ1 it is not really in relation to their own universe.

Part 3: Can I do a time slip to take me to the Kennedy assassination in any universe?