Stringy interior of non-rotating black hole
On May 7, 2006, at 5:28 PM, Paul Zielinski wrote:
I'm not sure what you mean here. In the SSS spacetime, r > 2M is simply a scaled radial coordinate.
"r" is defined so that the area of spherical surface concentric with the event horizon surface is 4pir^2 when r > 2m. This meaning is lost when r < 2m. I don't know what "scaled radial coordinate" means?
...
This idea that the curvature singularity at Hilbert r = 0 somehow fills a "spacelike hypersurface" makes no sense to me. As far as I can see it is at most a 4D line.
It's actually effectively a 2D world sheet since the transverse polar and azimuthal directions close up analogous to a Cerenkov radiation cone as the speed of the charge --> infinity.
From Hawking & Ellis: Note that in Appendix B pp 371-2 the NAIVE interior vacuum solution r < 2m is Eq. (A8)
with t -> r and r -> t
ds^2 = - dr^2/(2m/r - 1) + (2m/r - 1)dt^2 + r^2(d@^2 + sin^2@d&^2)
So that in these NAIVE coordinates one "sees" what the spacelike singularity "means" when r -> 0
The hypersurface of constant r, i.e. dr = 0 has the SPACELIKE 3D metric
3^ds^2 = (2m/r - 1)dt^2 + r^2(d@^2 + sin^2@d&^2)
With the effective interior proper radial differential
dR = (2m/r - 1)^1/2dt ---> infinity as r ---> 0 singularity
If you integrate along dt
R(2) - R(1) = (2m/r - 1)^1/2(t2 - t1)
So this is a "radial" stretch or dilation as r -> 0. It's as if the two transverse directions are getting compactified into a mini Kaluza-Klein "hose pipe" (with S2 instead of S1).
That is, the effective interior RADIAL "space" is warped to infinity with infinite tidal stretch-squeezed ripping-apart curvature. Therefore, when Penrose uses "centre" he is speaking LOOSELY, i.e. the NAIVE "Euclidean" INFERENCE of the OUTSIDE r > 2m observer.
OK, as r --> 0, one can ignore the transverse angular @, & terms relative to the "radial" dt term. The celestial sphere gets swallowed up, i.e. the effective solid angle of the in-falling observer's future light cone shrinks to a point. Of course he is long dead before he can notice! ;-)
Therefore, in a sense, the interior space morphs to a string as the infinite curvature a = J/m = 0 space-like singularity is approached, i.e. a 2-D world sheet in the (r,t) plane
Jack Sarfatti wrote:
That is, the physical meaning of "r" as Area of spherical surface about spatial center of symmetry = 4pir^2 only is true for r > 2M.
On May 7, 2006, at 2:19 PM, Jack Sarfatti wrote:
Quick note to Zielinski
re: SSS black hole
Strictly speaking one should only use the Schwarzschild radial coordinate r outside the event horizon 2M (G = c = 1) and use Eddington-Finkelstein coordinates inside the event horizon. The overlap of the two patches is important at the event horizon. As stated before, if one insists on using r inside it is no longer a space coordinate, but a time coordinate, with the spacelike singularity of infinite curvature at r = 0 being an entire spacelike hypersurface.
String Theory Scandal?
In the course of citing Polchinski & Witten that superstring theory at ~ Planck scale is the only game in town to explain "quantum gravity" Penrose says that his reaction, and that of his "close colleagues" is "Very negative." He gives several excellent technical reasons. By analogy string theorists have to posit Ricci flatness Rab = 0 in 10 Dim. No wonder they cannot explain dark energy ~ /\zpf that would be more like
Rab - (1/2)gab/\zpfgab = 0 in 10 Dim
But that is the least of the problems. There are too many degrees of freedom and string theory is basically perturbative (violating the generalized no action without reaction) although the duality arguments partially fix that - except in the important middle.
Sunday, April 30, 2006
Penrose severe on Polchinski & Witten
pp.892 - 897 basically Penrose implies that string theorists are hyping what in Silicon Valley is called "vaporware." That the claim that string theory predicts gravity is bogus - citing Polchinski & Witten as if they are used car salesmen in Tiajuana selling Mercedes with a Yugo engine under the hood. ;-)
pp.892 - 897 basically Penrose implies that string theorists are hyping what in Silicon Valley is called "vaporware." That the claim that string theory predicts gravity is bogus - citing Polchinski & Witten as if they are used car salesmen in Tiajuana selling Mercedes with a Yugo engine under the hood. ;-)
String Theory Vaporware
On Apr 30, 2006, at 8:45 PM, Jack Sarfatti wrote:
bcc
On Apr 30, 2006, at 8:08 PM, Mcmahon, David M wrote:
Don't recall if you noticed this.
http://arxiv.org/abs/physics/0603112
Thanks. It looks good. I am reading Penrose Ch. 31 On the Road to Reality ;-) on the same topic right now as a matter of fact. Actually, I am formulating an argument for old hadronic string theory without extra space dimensions.
c^4/G* ~ 1 Gev/fermi
No problem with point-like quarks and electrons from large space-warp in which the effective radius R ~ h/mc is much larger than circumference over 2pi.
R >> C/2pi
i.e.
2pi >> C/R ~ "scattering size of string"/Compton wavelength ---> 0 (point limit) as the scattering momentum transfer increases - until of course a little strong finite-range G* blackhole forms with Hawking radiation that we see as all sorts of particles coming out of the collision.
Strings and black holes are sort of dual to each other anyway. Wheeler's geons as elementary particles made out of "marble" Weyl curvature works for Lp* ~ 1 fermi. The Weyl gravity energy is NONLOCAL - with a twistor basis. Micro-geons are Bohm's hidden variables. This is strong-short range macro-quantum geometrodynamics powered by dark energy that comes in two forms i.e., attractive positive and repulsive negative pressure.
Abdus Salam invited me to ICTP in 1973 when I published a paper suggesting Kerr black hole microgeon explanation for universal slope Regge trajectories with Lp* ~ 1 fermi and massive strong graviton - f-meson spin 2.
-----Original Message-----
From: Jack Sarfatti [mailto:sarfatti@pacbell.net]
Sent: Sun 4/30/2006 5:17 PM
To: Waldyr Jr.; RKiehn2352@aol.com
Subject: Super-algebra of Cartan Forms?
Each element of the super-algebra is of the form
a(p+1) + db(p)
a is a p + 1 form
b is a p-form
d = Cartan exterior derivative that is nilpotent
d^2 = 0
Addition law
[a(p+1) + db(p)] + [c(p+1) + de(p)] = [a(p+1) + c(p+1)] + d[b(p) + e(p)]
Exterior multiplication law
[a(p+1) + db(p)]/\[c(p+1) + de(p)]
= a(p+1)/\c(p+1) + d[a(p+1)/\e(p) + b(p)/\c(p+1)]
In n-dim space the largest non-zero p-form is an n-form.
Is this well-known or did I just invent it?
Ref. p. 877 "The Road to Reality" by Roger Penrose
On Apr 30, 2006, at 8:45 PM, Jack Sarfatti wrote:
bcc
On Apr 30, 2006, at 8:08 PM, Mcmahon, David M wrote:
Don't recall if you noticed this.
http://arxiv.org/abs/physics/0603112
Thanks. It looks good. I am reading Penrose Ch. 31 On the Road to Reality ;-) on the same topic right now as a matter of fact. Actually, I am formulating an argument for old hadronic string theory without extra space dimensions.
c^4/G* ~ 1 Gev/fermi
No problem with point-like quarks and electrons from large space-warp in which the effective radius R ~ h/mc is much larger than circumference over 2pi.
R >> C/2pi
i.e.
2pi >> C/R ~ "scattering size of string"/Compton wavelength ---> 0 (point limit) as the scattering momentum transfer increases - until of course a little strong finite-range G* blackhole forms with Hawking radiation that we see as all sorts of particles coming out of the collision.
Strings and black holes are sort of dual to each other anyway. Wheeler's geons as elementary particles made out of "marble" Weyl curvature works for Lp* ~ 1 fermi. The Weyl gravity energy is NONLOCAL - with a twistor basis. Micro-geons are Bohm's hidden variables. This is strong-short range macro-quantum geometrodynamics powered by dark energy that comes in two forms i.e., attractive positive and repulsive negative pressure.
Abdus Salam invited me to ICTP in 1973 when I published a paper suggesting Kerr black hole microgeon explanation for universal slope Regge trajectories with Lp* ~ 1 fermi and massive strong graviton - f-meson spin 2.
-----Original Message-----
From: Jack Sarfatti [mailto:sarfatti@pacbell.net]
Sent: Sun 4/30/2006 5:17 PM
To: Waldyr Jr.; RKiehn2352@aol.com
Subject: Super-algebra of Cartan Forms?
Each element of the super-algebra is of the form
a(p+1) + db(p)
a is a p + 1 form
b is a p-form
d = Cartan exterior derivative that is nilpotent
d^2 = 0
Addition law
[a(p+1) + db(p)] + [c(p+1) + de(p)] = [a(p+1) + c(p+1)] + d[b(p) + e(p)]
Exterior multiplication law
[a(p+1) + db(p)]/\[c(p+1) + de(p)]
= a(p+1)/\c(p+1) + d[a(p+1)/\e(p) + b(p)/\c(p+1)]
In n-dim space the largest non-zero p-form is an n-form.
Is this well-known or did I just invent it?
Ref. p. 877 "The Road to Reality" by Roger Penrose
Cartan Form Exterior Super Algebra
Each element of the super-algebra is of the form
a(p+1) + db(p)
a is a p + 1 form
b is a p-form
d = Cartan exterior derivative that is nilpotent
d^2 = 0
Addition law
[a(p+1) + db(p)] + [c(p+1) + de(p)] = [a(p+1) + c(p+1)] + d[b(p) + e(p)]
Exterior multiplication law
[a(p+1) + db(p)]/\[c(p+1) + de(p)]
= a(p+1)/\c(p+1) + d[a(p+1)/\e(p) + b(p)/\c(p+1)]
In n-dim space the largest non-zero p-form is an n-form.
Is this well-known or did I just invent it?
Ref. p. 877 "The Road to Reality" by Roger Penrose
Each element of the super-algebra is of the form
a(p+1) + db(p)
a is a p + 1 form
b is a p-form
d = Cartan exterior derivative that is nilpotent
d^2 = 0
Addition law
[a(p+1) + db(p)] + [c(p+1) + de(p)] = [a(p+1) + c(p+1)] + d[b(p) + e(p)]
Exterior multiplication law
[a(p+1) + db(p)]/\[c(p+1) + de(p)]
= a(p+1)/\c(p+1) + d[a(p+1)/\e(p) + b(p)/\c(p+1)]
In n-dim space the largest non-zero p-form is an n-form.
Is this well-known or did I just invent it?
Ref. p. 877 "The Road to Reality" by Roger Penrose
Greg Benford's Time Scape
Subject: Re: Communicating Backward in Time with Tachyons? No. Real on-mass-shell imaginary rest mass tachyons do not SEEM to exist. When a spin 0 Higgs field has an effective imaginary rest mass it forms a macro-quantum coherent vacuum state whose Goldstone phase quanta have zero mass and whose conjugate Higgs amplitude quanta have positive mass. If there is a massless spin 1 gauge field, the spin 0 massless Goldstone phase quantum becomes the longitudinal polarization of the gauge field which then gets a positive rest mass. This is essentially the Meissner effect in superconductors and how the weak bosons get their mass - all this needs to be permitted by the various charge conservation laws.
Signal nonlocality, as in Dick Bierman's "presponse data" and the remote viewing data is completely different from the above.
On Apr 29, 2006, at 6:18 PM, yuzhou@pacbell.net wrote:
To:
Jack Sarfatti
From:
Richard D.K. Johnson
aka Dick Johnson
aka Richard Baird (pen name)
President, SF2 (San Francisco Science Fiction Society/
Golden Gate Futurians)
Date:
Marsday, 25 April 2006
(Cosmic Note: Sunday=Sunday,
Moonday=Monday, Marsday=Tuesday,
Mercuryday=Wednesday, Jupiterday=Thursday,
Venusday=Friday, Saturnday=Saturday)
You mention Gregory Benford's Timescape (1976) as
being about signalling backward in time. However, in the story they
don't use the quantum non-local connection (as you know, Bell's theorem
was not proven until the Aspect experiment of 1981), but
tachyons.
Last October, I e-mailed you about James Blish's science fiction story
Beep (1954) in which communication backward in time is
effected via device called a Dirac Communicator that
uses deBroglie waves. (Neither of you e-mailed
me back a comment on this e-mail.)
So, thinking about communication backward in time by
science fiction writers goes all the way back to
1954, not just to 1976.
Your friend always.
Richard
Jack Sarfatti wrote on 29 April 2006 at 12:45PM:
I know George Chapline since 1966 at UCSD La Jolla and Cal Tech. We were both part of the scene that Greg Benford describes in his Sci Fi novel "Timescape" about messages from the future, i.e. SIGNAL NONLOCALITY that I am working on NOW although that concept was UNKNOWN back in the 1960's & even 70's!
I have written George about this and will see what he says.
I have not yet considered the URLS in detail. Kip Thorne & Ray Chiao should be asked. It is so difficult to detect ELF gravity waves so is the claim here that the detection & generation of HFGW more efficient?
Even if it was, I do not understand the motivation for this approach because far field radiation is like a leak in the water tank when you are trying to conserve water!
That is, we want to use the MACRO-QUANTUM NEAR VIRTUAL GRAVITY FIELDS ~ 1/r2 in the whole (frequency-wavevector space) etc. that do not propagate away to infinity in the form of gravity radiation. That is the gravity induction type fields (off-mass-shell) are more important for practical metric engineering of warp and wormhole than the gravity waves ~ 1/r (on-mass-shell where frequency = (speed of light)(wavenumber) locus in frequency-wavevector space).
What you wrote makes no sense to me. The basic idea is simple. You use dark zero point energy with negative pressure & w < - 1/3 BEHIND the ship. This dark energy's induced gravity repulsion expands space behind the ship and makes a counter-intuitive reverse Dopper gravity BLUE SHIFT of all signals coming from the expanding space at the stern. You do opposite in front i.e. positive pressure zero point energy causing contraction of space that gives a counter intuitive gravity red shift from the bow.
You do this by inhomogeneous phase-locking of the vacuum's Goldstone phases to a control Goldstone phase in thin-film high Tc anyon condensate modulated by tiny perpendicular magnetic field flux quanta - all at micro->nanoscale. That's my rough current intuition on how it basically works.
http://arxiv.org/abs/gr-qc/0602022
Richard D.K. Johnson wrote on 18 October 2005 at 7:05PM:
To: Jack Sarfatti and Nick Herbert
From Richard D.K. Johnson
aka Dick Johnson
aka Richard Baird (pen name)
President, San Francisco Science Fiction Society
Date: Tue. 18 October 2005
I was wondering if either or both of you have read
an interesting science fiction story called
Beep by James Blish. It was published in 1954.
It is in volume II of the anthology Galactic Empires,
published in 1976. I just re-read the story today.
I read it for the first time in 1982, synchronistically,
at the same time that you (Jack Sarfatti) gave me
the plans for your FTL communicator.
It is about an FTL communications device
just like the "Future Machine" that you (Jack Sarfatti)
were working on. In science fiction this kind of device--
an communications device that can send signals
faster than light--is usually called a Subspace Radio or Ansible.
In this story it is called a "Dirac Communicator".
The way it works in the story is like this:
"We'll go on Dirac's assumption--and it works very well,
and always has--that a positron in motion through a
crystal lattice is accompanied by deBroglie waves
which are transforms of the waves of an electron
in motion somewhere else in the Universe. Thus
if we control the frequency and path of the positron,
we control the path of the electron--we cause it to
appear, so to speak, in the circuits of a communicator
somewhere else. After that, reception is just a matter of
amplifying the burst and reading the signal."
(Page 95, Galactic Empires,
Volume II)
This sounds like the quantum non-local connection.
Would that be correct?
The device is described as "an instantaneous communicator
based on deBroglie wave inversion." (Page 103)
The device assumes a deterministic universe like
you (Dr. Sarfatti) believe in, as opposed to the
many worlds interpretation of quantum mechanics:
"There were no alternatives, no fanciful
'branches of time', no decision points that
might be altered to make the future change.
My future....like everyone else's, was fixed."
(Page 102)
So the Earth Secret Service of the
Terran Galactic Empire of 2400 CE used
the Dirac Communicator to get messages
from the future. All the messages were
kept secret among the agents of the
Earth Secret Service. Earth had a
great advantage because it could
assemble a fleet of spaceships in
advance of any other alien race
opposing it because it knew their
battle plans in advance. An important
restriction was that the future death of
any agent of the Earth Secret Service
was never to be revealed to them.
They also had a slower device that was
not instantaneous called the Ultrawave
that could travel not instantaneously
but at "only" four times the speed of
light. This device used the phenomenon
described by you (Nick Herbert) in your
book Faster Than Light called the phase
velocity of a wave of light (like the undulations
of a caterpillar) to send messages. (Of course
in the real world we know this is impossible.)
Finally, in the story they had starships which
could travel through hyperspace at 40 times
the speed of light to deliver physical letters.
This is pretty advanced for 1954!
Did either of you know about or read
this story before I told you about it?
What do you think about the
Dirac Communicator?
Best wishes, Richard
Quotation from Gregory Benford's Timescape (1976)
taken from
http://www.phys.uregina.ca/sparro/huber/timescape.html
From ``Timescape'', by Gregory Benford. Published by Pocket Books, New York, 1980.
They had both more drinks when Peterson said, ``Look, it's Sir Martin who's really the technical type on the British delegation. I'm a nonspecialist, as they call it. What I want to know is, how in hell do you get around this grandfather paradox bit? That fellow Davies explained about the discovery of tachyons right enough, and I accept that they can travel into our past, but I still can't see how one can logically change the past.''
Markham sighed, ``Until tachyons were discovered, everybody thought communication with the past was impossible. The incredible thing is that the physics of time communication had been worked out earlier, almost by accident, as far back as the 1940s. Two physicists named John Wheeler and Richard Feynmann worked out the correct description of light itself, and showed that there were two waves launched whenever you tried to make a radio wave, say.''
``Two?''
``Right. One of them we receive on our radio sets. The other travels backward in time -- the `advanced wave,' as Wheeler and Feynmann called it.''
``But we don't receive any message before it's sent.''
Markham nodded. ``True -- but the advanced wave is there, in the mathematics. There's no way around it. The equations of physics are all time-symmetric. That's one of the riddles of modern physics. How is it that we perceive time passing, and yet all the equations of physics say that time can run either way, forward or backward?''
``The equations are wrong, then?''
``No, they're not. They can predict anything we can measure -- but only as long as we use the `retarded wave,' as Wheeler and Feynmann called it. That's the one that you hear through your radio set.''
``Well, look, surely there's a way to change the equation round until you get only the retarded part.''
``No, there isn't. If you do that to the equations, there's no way to keep the retarded wave the same. You must have the advanced wave.''
``All right, where are those backward-in-time radio shows? How come I can't tune into the news from the next century?''
``Wheeler and Feyrunann showed that it can't get here.''
``Can't get into this year? I mean, into our present time?''
``Right. See, the advanced wave can interact with the whole universe -- it's moving back, into our past, so it eventually hits all the matter that's ever been. Thing is, the advanced wave strikes all that matter before the signal was sent.''
``Yes, surely." Peterson reflected on the fact that he was now, for the sake of argument, accepting the ``advanced wave'' he would have rejected only a few moments before.
``So the wave hits all that matter, and the electrons inside it jiggle around in anticipation of what the radio station will send.''
``Effect preceding a cause?''
``Exactly. Seerns contrary to experience, doesn't it?''
``Definitely.''
``But the vibration of those electrons in the whole rest of the universe has to be taken into account. They in turn send out both advanced and retarded waves. It's like dropping two rocks into a pond. They both send out waves. But the two waves don't just add up in a simple way.''
``They don't? Why not?''
``They interfere with each other. They make a criss-cross network of local peaks and troughs. Where the peaks and troughs from the separate patterns coincide, they reinforce each other. But where the peaks of the first stone meet the troughs of the second, they cancel. The water doesn't move.''
``Oh. All right, then.''
``What Wheeler and Feynmann showed was that the rest of the universe, when it's hit by an advanced wave, acts like a whole lot of rocks dropped into that pond. The advanced wave goes back in time, makes all these other waves. They interfere with each other and the result is zero. Nothing.''
``Ah. In the end the advanced wave cancels itself out.''
Suddenly music blared over the Whim's stereo: ``An' de Devil, he do de dance whump whump with Joan de Arc-''
Peterson shouted, ``Turn that down, will you?''
The music faded. He leaned forward. ``Very well. You've shown me why the advanced wave doesn't work. Time communication is impossible.''
Markham grinned. ``Every theory has a hidden assumption. The trouble with the Wheeler and Feynmann model was that all those jiggling electrons in the universe in the past might not send back just the right waves. For radio signals, they do. For tachyons they don't. Wheeler and Feynmann didn't know about tachyons; they weren't even thought of until the middle '6os. Tachyons aren't absorbed the right way. They don't interact with matter the way radio waves do.''
``Why not?''
``They're different kinds of particles. Some guys named Feinberg and Sudarshan imagined tachyons decades ago, but nobody could find them. Seemed too unlikely. They have imaginary mass, for one thing.''
``Imaginary mass?''
``Yes, but don't take it too seriously.''
``Seems a serious difficulty.''
``Not really. The mass of these particles isn't what we'd call an observable. That means we can't bring a tachyon to rest, since it must always travel faster than fight. So, if we can't bring it to a stop in our lab, we can't measure its mass at rest. The only definition of mass is what you can put on the scales and weigh -- which you can't do, if it's moving. With tachyons, all you can measure is momentum -- that is, impact.''
``You have a complaint about the food, sir? I am the manager.''
Peterson looked up to find a tall man in a conservative gray suit standing over their table, hands clasped behind him military style. ``Yes, I did. Mostly I preferred not to eat it, in view of what it did to that lady a short while ago.''
``I do not know what the lady was eating, sir, but I should think your -- ''
``Well, I do, you see. It was certainly close enough to what my friend here ordered to make him uncomfortable.''
The manager bridled slightly at Peterson's manner. He was sweating slightly and had a harried look. ``I fail to see why a similar type of food should -- ''
``I can see it quite plainly. A pity you can't.''
``I am afraid we shall have to charge you for -- ''
``Have you read the recent Home Office directives on imported meats? I had a hand in writing them.'' Peterson gave the manager the full benefit of his assessing gaze. ``I would say you probably get much of your imported meat from a local supplier, correct?''
``Well, of course, but -- ''
``Then you presumably know that there is a severe restriction on how long it can be kept before use?''
``Yes, I'm sure ... '' the manager began, but then hesitated when he saw the look on Peterson's face. ``Well, actually I haven't read much of those lately because -- ''
``I think I would take more care in future.''
``I am not sure the lady actually ate any imported meat whatever -- ''
``I would look into it, if I were you.''
Abruptly the man lost some of his military bearing. Peterson looked at him with assurance.
``Well, I think we can forget the misunderstanding, sir, in light of -- ''
``Indeed.'' Peterson nodded, dismissing him. He turned back to Markham. ``You still haven't got round the grandfather thing. If tachyons can carry a message back to the past, how do you avoid paradoxes?'' Peterson did not mention that he had gone through a discussion with Paul Davies at King's about this, but understood none of it. He was by no means assured that the ideas made any sense.
Markham grimaced, ``It's not easy to explain. The key was suspected decades ago, but nobody worked it out into a concrete physical theory. There's even a sentence in the original Wheeler-Feynmann paper -- `It is only required that the description should be logically self-consistent.' By that they meant that our sense of the flow of time, always going in one direction, is a bias. The equations of physics don't share our prejudice -- they're time-symmetric. The only standard we can impose on an experiment is whether it's logically consistent.''
``But it's certainly illogical that you can be alive even after you've knocked off your own grandfather. Killed him before he produced your father, I mean.''
``The problem is, we're used to thinking of these things as though there was some sort of switch involved, that only had two settings. I mean, that your grandfather is either dead or he isn' t.''
``Well, that's certainly true.''
Markham shook his head. ``Not really. What if he's wounded, but recovers? Then if he gets out of the hospital in time, he can meet your grandmother. It depends on your aim.''
``I don't see -- ''
``Think about sending messages, instead of shotgunning grandfathers. Everybody assumes the receiver -- back there in the past -- can be attached to a switch, say. If a signal from the future comes in, the switch is programmed to turn off the transmitter -- before the signal was sent. There's the paradox.''
``Right.'' Peterson leaned forward, finding himself engrossed despite his doubts. There was something he liked about the way scientists had of setting up problems as neat little thought experiments, making a clean and sure world. Social issues were always messier and less satisfying. Perhaps that was why they were seldom solved.
``Trouble is, there's no switch that has two settings -- on and off -- with nothing in between.''
``Come now. What about the toggle I flip to turn on the lights?''
``Okay, so you flip it. There's a time when that switch is hanging in between, neither off nor on.''
``I can make that a very short time.''
``Sure, but you can't reduce it to zero. And also, there's a certain impulse you have to give that switch to make it jump from off to on. In fact, it's possible to hit the switch just hard enough to make it go halfway -- try it. That must've happened to you sometime. The switch sticks, balanced halfway between.''
``All right, granted,'' Peterson said impatiently. ``But what's the connection to tachyons? I mean, what's new about all this?''
``What's new is thinking of these events -- sending and receiving -- as related in a chain, a loop. Say, we send back an instruction saying, `Turn off the transmitter.' Think of the switch moving over to `off.' This event is like a wave moving from the past to the future. The transmitter is changing from `on' to 'off.' Now, that -- well, let's call it a wave of information -- moves forward in time. So the original signal doesn't get sent.''
``Right. Paradox.''
Markham smded and held up a finger. He was enjoying this. `But wait! Think of all these times being in a kind of loop. Cause and effect mean nothing in this loop. There are only events. Now as the switch moves towards `off,' information propagates forward into the future. Think of it as the transmitter getting weaker and weaker as that switch nears the `off' position. Then the tachyon beam that transmitter is sending out gets weaker.''
``Ah!'' Peterson suddenly saw it. ``So the receiver in turn gets a weaker signal from the future. The switch isn't hit so hard because the backward-in-time signal is weaker. So it doesn't move so quickly toward the `off' mark.''
``That's it. The closer it gets to `off,' the slower it goes. There's an information wave traveling forward into the future, and -- like a reflection -- the tachyon beam comes back into the past.''
``What does the experiment do then?''
``Well, say the switch gets near `off,' and then the tachyon beam gets weak. The switch doesn't rnake it all the way to `off', and -- like that toggle controlling the lights -- it starts to fall back toward on.' But the nearer it gets to `on,' the stronger the transmitter gets in the future.''
``So the tachyon bearn gets stronger,'' Peterson finished for him. ``That in turn drives the switch away from `on' and back towards `off.' The switch is hung up in the middle.''
Markham leaned back and drained his stout. His tan, weakened by the dim Cambridge winter, crinkled with the lines of his wry smile. ``It flutters around there in the middle.''
``No paradox.''
``Well ...'' Markham shrugged imperceptibly. ``No logical contradictions, yes. But we still don't actually know what that intermediate, hung-up state means. It does avoid the paradoxes, though. There's a lot of quantum-mechanical formalism you can apply to it, but I'm not sure what a genuine experiment will give.''
``Why not''
Markham shrugged again. ``No experiments. Renfrew hasn't had the time to do them, or the money.''
Peterson ignored the implied criticism; or was that his imagination? It was obvious that work in these fields had been cut back for years now. Markham was simply stating a fact. He had to remember that a scientist might be more prone simply to state things as they were, without calculating a statement's impact. To change the subject Peterson asked, ``Won't that stuck-in-the-middle effect prevent your sending information back to 1963?''
``Look, the point here is that our distinctions between cause and effect are an illusion. This little experiment we've been discussing is a causal loop -- no beginning, no end. That's what Wheeler and Feynmann meant by requiring only that our description be logically consistent. Logic rules in physics, not the myth of cause and effect. Imposing an order to events is our point of view. A quaintly human view, I suppose. The laws of physics don't care. That's the new concept of time we have now -- as a set of completely interrelated events, linked self-consistently. We think we're moving along in time, but that's just a bias.''
``But we know things happen now, not in the past or future.''
``When is `now'? Saying that `now' is `this instant' is going around in circles. Every instant is `now' when it `happens.' The point is, how do you measure the rate of moving from one instant to the next? And the answer is, you can't. What's the rate of the passage of time?''
``Well, it's -- '' Peterson stopped, thinking.
``How can time move? The rate is one second of movement per second! There's no conceivable coordinate systern in physics from which we can measure time passing. So there isn't any. Time is frozen, as far as the universe is concerned.''
``Then ... '' Peterson raised a finger to cover his confusion, frowning. The manager appeared as though out of nowhere.
``Yes sir?'' the man said with extreme politeness.
``Ah, another round.''
``Yes sir.'' He hustled off to fill the order himself. Peterson took a small pleasure in this little play. To get such a response with a minimum display of power was an old game with him, but still satisfying.
``But you still believe,'' Peterson said, turning back to Markham, ``that Renfrew's experiment makes sense? All this talk of loops and not being able to close switches ... ''
``Sure it'll work.'' Markham accepted a glass dark with the thick stout. The manager placed Peterson's ale carefully before him and began, ``Sir, I want to apol-- ''
Peterson waved him into silence, impatient to hear Markham. ``Perfectly all right,'' he said quickly.
Markham eyed the manager's retreating back. "Very effective. Do they teach that in the best schools?''
Peterson smiled. ``Of course. There's lecture, then field trips to representative restaurants. You have to get the wrist action just right.''
Markham saluted with the stout. After this silent toast he said, ``Oh yes, Renfrew. What Wheeler and Feynmann didn't notice was that if you send a message back which has nothing do with shutting off the transmitter, there's no problem. Say you want to place a bet on a horse race. I've resolved that I'll send results of the race back in time to a friend. I do. In the past, friend places a bet and makes money. That doesn't change the outcome of the race. Afterward, my friend gives me some of the winnings. His handing over the money won't stop me from sending the information -- in fact, I can easily arrange it so I only get the money after I've sent the message.''
``No paradox.''
``Right. So you can change the past, but only if you don't try to make a paradox. If you try, the experiment hangs up in that in-between state.''
Peterson frowned. ``But what's it like? I mean, what does the world seem like if you can change it round?''
Markham said lightly, ``Nobody knows. Nobody's ever tried it before.''
``There were no tachyon transmitters until now.''
``And no reason to try to reach the past, either.''
``Let me get this straight. How's Renfrew going to avoid creating a paradox? If he gives them a lot of information, they'll solve the problem and there'll be no reason for him to send the message.''
``That's the trick. Avoid the paradox, or you'll get a stuck switch. So Renfrew will send a piece of the vital information -- enough to get research started, but not enough to solve the problem utterly.''
``But what'll it be like for us? The world will change round us?''
Markham chewed at his lower lip. ``I think so. We'll be in a different state. The problem will be reduced, the oceans not so badly off.''
``But what is this state? I mean, us sitting here? We know the oceans are in trouble.''
``Do we? How do we know this isn't the result of the experiment we're about to do? That is, if Renfrew hadn't existed and thought of this idea, maybe we'd be worse off. The problem with causal loops is that our notion of time doesn't accept them. But think of that stuck switch again.''
Peterson shook his head as though to clear it. ``It's hard to think about.''
``Like tying time in knots,'' Markham conceded. ``What I've given you is an interpretation of the mathematics. We know tachyons are real; what we don't know is what they imply.''
Back to the Eclectic Quotation Index.
97.09.19 / Garth Hube
About deBroglie Waves--taken from
http://regentsprep.org/Regents/physics/phys05/bdebrogli/default.htm
deBroglie Waves - Matter Waves
Based on an intuitive feeling that nature is symmetrical, Louis deBroglie (de-broy-lee) made an argument in 1924 that if waves have a particle nature, then particles must have a wave nature.
He began with the formula for momentum of a photon, solved it for wavelength, then replaced momentum with mv (particle momentum).
For any particle with even a small amount of mass, the wavelength is very small. Even the electron has a very small wavelength. Protons or Neutrons have even smaller wavelengths since they have more mass. Theoretically, any moving matter has wave characteristics. However, the wavelength of any life-size particle, like a golf ball, is so small that it is immeasurable.
Subject: Re: Communicating Backward in Time with Tachyons? No. Real on-mass-shell imaginary rest mass tachyons do not SEEM to exist. When a spin 0 Higgs field has an effective imaginary rest mass it forms a macro-quantum coherent vacuum state whose Goldstone phase quanta have zero mass and whose conjugate Higgs amplitude quanta have positive mass. If there is a massless spin 1 gauge field, the spin 0 massless Goldstone phase quantum becomes the longitudinal polarization of the gauge field which then gets a positive rest mass. This is essentially the Meissner effect in superconductors and how the weak bosons get their mass - all this needs to be permitted by the various charge conservation laws.
Signal nonlocality, as in Dick Bierman's "presponse data" and the remote viewing data is completely different from the above.
On Apr 29, 2006, at 6:18 PM, yuzhou@pacbell.net wrote:
To:
Jack Sarfatti
From:
Richard D.K. Johnson
aka Dick Johnson
aka Richard Baird (pen name)
President, SF2 (San Francisco Science Fiction Society/
Golden Gate Futurians)
Date:
Marsday, 25 April 2006
(Cosmic Note: Sunday=Sunday,
Moonday=Monday, Marsday=Tuesday,
Mercuryday=Wednesday, Jupiterday=Thursday,
Venusday=Friday, Saturnday=Saturday)
You mention Gregory Benford's Timescape (1976) as
being about signalling backward in time. However, in the story they
don't use the quantum non-local connection (as you know, Bell's theorem
was not proven until the Aspect experiment of 1981), but
tachyons.
Last October, I e-mailed you about James Blish's science fiction story
Beep (1954) in which communication backward in time is
effected via device called a Dirac Communicator that
uses deBroglie waves. (Neither of you e-mailed
me back a comment on this e-mail.)
So, thinking about communication backward in time by
science fiction writers goes all the way back to
1954, not just to 1976.
Your friend always.
Richard
Jack Sarfatti wrote on 29 April 2006 at 12:45PM:
I know George Chapline since 1966 at UCSD La Jolla and Cal Tech. We were both part of the scene that Greg Benford describes in his Sci Fi novel "Timescape" about messages from the future, i.e. SIGNAL NONLOCALITY that I am working on NOW although that concept was UNKNOWN back in the 1960's & even 70's!
I have written George about this and will see what he says.
I have not yet considered the URLS in detail. Kip Thorne & Ray Chiao should be asked. It is so difficult to detect ELF gravity waves so is the claim here that the detection & generation of HFGW more efficient?
Even if it was, I do not understand the motivation for this approach because far field radiation is like a leak in the water tank when you are trying to conserve water!
That is, we want to use the MACRO-QUANTUM NEAR VIRTUAL GRAVITY FIELDS ~ 1/r2 in the whole (frequency-wavevector space) etc. that do not propagate away to infinity in the form of gravity radiation. That is the gravity induction type fields (off-mass-shell) are more important for practical metric engineering of warp and wormhole than the gravity waves ~ 1/r (on-mass-shell where frequency = (speed of light)(wavenumber) locus in frequency-wavevector space).
What you wrote makes no sense to me. The basic idea is simple. You use dark zero point energy with negative pressure & w < - 1/3 BEHIND the ship. This dark energy's induced gravity repulsion expands space behind the ship and makes a counter-intuitive reverse Dopper gravity BLUE SHIFT of all signals coming from the expanding space at the stern. You do opposite in front i.e. positive pressure zero point energy causing contraction of space that gives a counter intuitive gravity red shift from the bow.
You do this by inhomogeneous phase-locking of the vacuum's Goldstone phases to a control Goldstone phase in thin-film high Tc anyon condensate modulated by tiny perpendicular magnetic field flux quanta - all at micro->nanoscale. That's my rough current intuition on how it basically works.
http://arxiv.org/abs/gr-qc/0602022
Richard D.K. Johnson wrote on 18 October 2005 at 7:05PM:
To: Jack Sarfatti and Nick Herbert
From Richard D.K. Johnson
aka Dick Johnson
aka Richard Baird (pen name)
President, San Francisco Science Fiction Society
Date: Tue. 18 October 2005
I was wondering if either or both of you have read
an interesting science fiction story called
Beep by James Blish. It was published in 1954.
It is in volume II of the anthology Galactic Empires,
published in 1976. I just re-read the story today.
I read it for the first time in 1982, synchronistically,
at the same time that you (Jack Sarfatti) gave me
the plans for your FTL communicator.
It is about an FTL communications device
just like the "Future Machine" that you (Jack Sarfatti)
were working on. In science fiction this kind of device--
an communications device that can send signals
faster than light--is usually called a Subspace Radio or Ansible.
In this story it is called a "Dirac Communicator".
The way it works in the story is like this:
"We'll go on Dirac's assumption--and it works very well,
and always has--that a positron in motion through a
crystal lattice is accompanied by deBroglie waves
which are transforms of the waves of an electron
in motion somewhere else in the Universe. Thus
if we control the frequency and path of the positron,
we control the path of the electron--we cause it to
appear, so to speak, in the circuits of a communicator
somewhere else. After that, reception is just a matter of
amplifying the burst and reading the signal."
(Page 95, Galactic Empires,
Volume II)
This sounds like the quantum non-local connection.
Would that be correct?
The device is described as "an instantaneous communicator
based on deBroglie wave inversion." (Page 103)
The device assumes a deterministic universe like
you (Dr. Sarfatti) believe in, as opposed to the
many worlds interpretation of quantum mechanics:
"There were no alternatives, no fanciful
'branches of time', no decision points that
might be altered to make the future change.
My future....like everyone else's, was fixed."
(Page 102)
So the Earth Secret Service of the
Terran Galactic Empire of 2400 CE used
the Dirac Communicator to get messages
from the future. All the messages were
kept secret among the agents of the
Earth Secret Service. Earth had a
great advantage because it could
assemble a fleet of spaceships in
advance of any other alien race
opposing it because it knew their
battle plans in advance. An important
restriction was that the future death of
any agent of the Earth Secret Service
was never to be revealed to them.
They also had a slower device that was
not instantaneous called the Ultrawave
that could travel not instantaneously
but at "only" four times the speed of
light. This device used the phenomenon
described by you (Nick Herbert) in your
book Faster Than Light called the phase
velocity of a wave of light (like the undulations
of a caterpillar) to send messages. (Of course
in the real world we know this is impossible.)
Finally, in the story they had starships which
could travel through hyperspace at 40 times
the speed of light to deliver physical letters.
This is pretty advanced for 1954!
Did either of you know about or read
this story before I told you about it?
What do you think about the
Dirac Communicator?
Best wishes, Richard
Quotation from Gregory Benford's Timescape (1976)
taken from
http://www.phys.uregina.ca/sparro/huber/timescape.html
From ``Timescape'', by Gregory Benford. Published by Pocket Books, New York, 1980.
They had both more drinks when Peterson said, ``Look, it's Sir Martin who's really the technical type on the British delegation. I'm a nonspecialist, as they call it. What I want to know is, how in hell do you get around this grandfather paradox bit? That fellow Davies explained about the discovery of tachyons right enough, and I accept that they can travel into our past, but I still can't see how one can logically change the past.''
Markham sighed, ``Until tachyons were discovered, everybody thought communication with the past was impossible. The incredible thing is that the physics of time communication had been worked out earlier, almost by accident, as far back as the 1940s. Two physicists named John Wheeler and Richard Feynmann worked out the correct description of light itself, and showed that there were two waves launched whenever you tried to make a radio wave, say.''
``Two?''
``Right. One of them we receive on our radio sets. The other travels backward in time -- the `advanced wave,' as Wheeler and Feynmann called it.''
``But we don't receive any message before it's sent.''
Markham nodded. ``True -- but the advanced wave is there, in the mathematics. There's no way around it. The equations of physics are all time-symmetric. That's one of the riddles of modern physics. How is it that we perceive time passing, and yet all the equations of physics say that time can run either way, forward or backward?''
``The equations are wrong, then?''
``No, they're not. They can predict anything we can measure -- but only as long as we use the `retarded wave,' as Wheeler and Feynmann called it. That's the one that you hear through your radio set.''
``Well, look, surely there's a way to change the equation round until you get only the retarded part.''
``No, there isn't. If you do that to the equations, there's no way to keep the retarded wave the same. You must have the advanced wave.''
``All right, where are those backward-in-time radio shows? How come I can't tune into the news from the next century?''
``Wheeler and Feyrunann showed that it can't get here.''
``Can't get into this year? I mean, into our present time?''
``Right. See, the advanced wave can interact with the whole universe -- it's moving back, into our past, so it eventually hits all the matter that's ever been. Thing is, the advanced wave strikes all that matter before the signal was sent.''
``Yes, surely." Peterson reflected on the fact that he was now, for the sake of argument, accepting the ``advanced wave'' he would have rejected only a few moments before.
``So the wave hits all that matter, and the electrons inside it jiggle around in anticipation of what the radio station will send.''
``Effect preceding a cause?''
``Exactly. Seerns contrary to experience, doesn't it?''
``Definitely.''
``But the vibration of those electrons in the whole rest of the universe has to be taken into account. They in turn send out both advanced and retarded waves. It's like dropping two rocks into a pond. They both send out waves. But the two waves don't just add up in a simple way.''
``They don't? Why not?''
``They interfere with each other. They make a criss-cross network of local peaks and troughs. Where the peaks and troughs from the separate patterns coincide, they reinforce each other. But where the peaks of the first stone meet the troughs of the second, they cancel. The water doesn't move.''
``Oh. All right, then.''
``What Wheeler and Feynmann showed was that the rest of the universe, when it's hit by an advanced wave, acts like a whole lot of rocks dropped into that pond. The advanced wave goes back in time, makes all these other waves. They interfere with each other and the result is zero. Nothing.''
``Ah. In the end the advanced wave cancels itself out.''
Suddenly music blared over the Whim's stereo: ``An' de Devil, he do de dance whump whump with Joan de Arc-''
Peterson shouted, ``Turn that down, will you?''
The music faded. He leaned forward. ``Very well. You've shown me why the advanced wave doesn't work. Time communication is impossible.''
Markham grinned. ``Every theory has a hidden assumption. The trouble with the Wheeler and Feynmann model was that all those jiggling electrons in the universe in the past might not send back just the right waves. For radio signals, they do. For tachyons they don't. Wheeler and Feynmann didn't know about tachyons; they weren't even thought of until the middle '6os. Tachyons aren't absorbed the right way. They don't interact with matter the way radio waves do.''
``Why not?''
``They're different kinds of particles. Some guys named Feinberg and Sudarshan imagined tachyons decades ago, but nobody could find them. Seemed too unlikely. They have imaginary mass, for one thing.''
``Imaginary mass?''
``Yes, but don't take it too seriously.''
``Seems a serious difficulty.''
``Not really. The mass of these particles isn't what we'd call an observable. That means we can't bring a tachyon to rest, since it must always travel faster than fight. So, if we can't bring it to a stop in our lab, we can't measure its mass at rest. The only definition of mass is what you can put on the scales and weigh -- which you can't do, if it's moving. With tachyons, all you can measure is momentum -- that is, impact.''
``You have a complaint about the food, sir? I am the manager.''
Peterson looked up to find a tall man in a conservative gray suit standing over their table, hands clasped behind him military style. ``Yes, I did. Mostly I preferred not to eat it, in view of what it did to that lady a short while ago.''
``I do not know what the lady was eating, sir, but I should think your -- ''
``Well, I do, you see. It was certainly close enough to what my friend here ordered to make him uncomfortable.''
The manager bridled slightly at Peterson's manner. He was sweating slightly and had a harried look. ``I fail to see why a similar type of food should -- ''
``I can see it quite plainly. A pity you can't.''
``I am afraid we shall have to charge you for -- ''
``Have you read the recent Home Office directives on imported meats? I had a hand in writing them.'' Peterson gave the manager the full benefit of his assessing gaze. ``I would say you probably get much of your imported meat from a local supplier, correct?''
``Well, of course, but -- ''
``Then you presumably know that there is a severe restriction on how long it can be kept before use?''
``Yes, I'm sure ... '' the manager began, but then hesitated when he saw the look on Peterson's face. ``Well, actually I haven't read much of those lately because -- ''
``I think I would take more care in future.''
``I am not sure the lady actually ate any imported meat whatever -- ''
``I would look into it, if I were you.''
Abruptly the man lost some of his military bearing. Peterson looked at him with assurance.
``Well, I think we can forget the misunderstanding, sir, in light of -- ''
``Indeed.'' Peterson nodded, dismissing him. He turned back to Markham. ``You still haven't got round the grandfather thing. If tachyons can carry a message back to the past, how do you avoid paradoxes?'' Peterson did not mention that he had gone through a discussion with Paul Davies at King's about this, but understood none of it. He was by no means assured that the ideas made any sense.
Markham grimaced, ``It's not easy to explain. The key was suspected decades ago, but nobody worked it out into a concrete physical theory. There's even a sentence in the original Wheeler-Feynmann paper -- `It is only required that the description should be logically self-consistent.' By that they meant that our sense of the flow of time, always going in one direction, is a bias. The equations of physics don't share our prejudice -- they're time-symmetric. The only standard we can impose on an experiment is whether it's logically consistent.''
``But it's certainly illogical that you can be alive even after you've knocked off your own grandfather. Killed him before he produced your father, I mean.''
``The problem is, we're used to thinking of these things as though there was some sort of switch involved, that only had two settings. I mean, that your grandfather is either dead or he isn' t.''
``Well, that's certainly true.''
Markham shook his head. ``Not really. What if he's wounded, but recovers? Then if he gets out of the hospital in time, he can meet your grandmother. It depends on your aim.''
``I don't see -- ''
``Think about sending messages, instead of shotgunning grandfathers. Everybody assumes the receiver -- back there in the past -- can be attached to a switch, say. If a signal from the future comes in, the switch is programmed to turn off the transmitter -- before the signal was sent. There's the paradox.''
``Right.'' Peterson leaned forward, finding himself engrossed despite his doubts. There was something he liked about the way scientists had of setting up problems as neat little thought experiments, making a clean and sure world. Social issues were always messier and less satisfying. Perhaps that was why they were seldom solved.
``Trouble is, there's no switch that has two settings -- on and off -- with nothing in between.''
``Come now. What about the toggle I flip to turn on the lights?''
``Okay, so you flip it. There's a time when that switch is hanging in between, neither off nor on.''
``I can make that a very short time.''
``Sure, but you can't reduce it to zero. And also, there's a certain impulse you have to give that switch to make it jump from off to on. In fact, it's possible to hit the switch just hard enough to make it go halfway -- try it. That must've happened to you sometime. The switch sticks, balanced halfway between.''
``All right, granted,'' Peterson said impatiently. ``But what's the connection to tachyons? I mean, what's new about all this?''
``What's new is thinking of these events -- sending and receiving -- as related in a chain, a loop. Say, we send back an instruction saying, `Turn off the transmitter.' Think of the switch moving over to `off.' This event is like a wave moving from the past to the future. The transmitter is changing from `on' to 'off.' Now, that -- well, let's call it a wave of information -- moves forward in time. So the original signal doesn't get sent.''
``Right. Paradox.''
Markham smded and held up a finger. He was enjoying this. `But wait! Think of all these times being in a kind of loop. Cause and effect mean nothing in this loop. There are only events. Now as the switch moves towards `off,' information propagates forward into the future. Think of it as the transmitter getting weaker and weaker as that switch nears the `off' position. Then the tachyon beam that transmitter is sending out gets weaker.''
``Ah!'' Peterson suddenly saw it. ``So the receiver in turn gets a weaker signal from the future. The switch isn't hit so hard because the backward-in-time signal is weaker. So it doesn't move so quickly toward the `off' mark.''
``That's it. The closer it gets to `off,' the slower it goes. There's an information wave traveling forward into the future, and -- like a reflection -- the tachyon beam comes back into the past.''
``What does the experiment do then?''
``Well, say the switch gets near `off,' and then the tachyon beam gets weak. The switch doesn't rnake it all the way to `off', and -- like that toggle controlling the lights -- it starts to fall back toward on.' But the nearer it gets to `on,' the stronger the transmitter gets in the future.''
``So the tachyon bearn gets stronger,'' Peterson finished for him. ``That in turn drives the switch away from `on' and back towards `off.' The switch is hung up in the middle.''
Markham leaned back and drained his stout. His tan, weakened by the dim Cambridge winter, crinkled with the lines of his wry smile. ``It flutters around there in the middle.''
``No paradox.''
``Well ...'' Markham shrugged imperceptibly. ``No logical contradictions, yes. But we still don't actually know what that intermediate, hung-up state means. It does avoid the paradoxes, though. There's a lot of quantum-mechanical formalism you can apply to it, but I'm not sure what a genuine experiment will give.''
``Why not''
Markham shrugged again. ``No experiments. Renfrew hasn't had the time to do them, or the money.''
Peterson ignored the implied criticism; or was that his imagination? It was obvious that work in these fields had been cut back for years now. Markham was simply stating a fact. He had to remember that a scientist might be more prone simply to state things as they were, without calculating a statement's impact. To change the subject Peterson asked, ``Won't that stuck-in-the-middle effect prevent your sending information back to 1963?''
``Look, the point here is that our distinctions between cause and effect are an illusion. This little experiment we've been discussing is a causal loop -- no beginning, no end. That's what Wheeler and Feynmann meant by requiring only that our description be logically consistent. Logic rules in physics, not the myth of cause and effect. Imposing an order to events is our point of view. A quaintly human view, I suppose. The laws of physics don't care. That's the new concept of time we have now -- as a set of completely interrelated events, linked self-consistently. We think we're moving along in time, but that's just a bias.''
``But we know things happen now, not in the past or future.''
``When is `now'? Saying that `now' is `this instant' is going around in circles. Every instant is `now' when it `happens.' The point is, how do you measure the rate of moving from one instant to the next? And the answer is, you can't. What's the rate of the passage of time?''
``Well, it's -- '' Peterson stopped, thinking.
``How can time move? The rate is one second of movement per second! There's no conceivable coordinate systern in physics from which we can measure time passing. So there isn't any. Time is frozen, as far as the universe is concerned.''
``Then ... '' Peterson raised a finger to cover his confusion, frowning. The manager appeared as though out of nowhere.
``Yes sir?'' the man said with extreme politeness.
``Ah, another round.''
``Yes sir.'' He hustled off to fill the order himself. Peterson took a small pleasure in this little play. To get such a response with a minimum display of power was an old game with him, but still satisfying.
``But you still believe,'' Peterson said, turning back to Markham, ``that Renfrew's experiment makes sense? All this talk of loops and not being able to close switches ... ''
``Sure it'll work.'' Markham accepted a glass dark with the thick stout. The manager placed Peterson's ale carefully before him and began, ``Sir, I want to apol-- ''
Peterson waved him into silence, impatient to hear Markham. ``Perfectly all right,'' he said quickly.
Markham eyed the manager's retreating back. "Very effective. Do they teach that in the best schools?''
Peterson smiled. ``Of course. There's lecture, then field trips to representative restaurants. You have to get the wrist action just right.''
Markham saluted with the stout. After this silent toast he said, ``Oh yes, Renfrew. What Wheeler and Feynmann didn't notice was that if you send a message back which has nothing do with shutting off the transmitter, there's no problem. Say you want to place a bet on a horse race. I've resolved that I'll send results of the race back in time to a friend. I do. In the past, friend places a bet and makes money. That doesn't change the outcome of the race. Afterward, my friend gives me some of the winnings. His handing over the money won't stop me from sending the information -- in fact, I can easily arrange it so I only get the money after I've sent the message.''
``No paradox.''
``Right. So you can change the past, but only if you don't try to make a paradox. If you try, the experiment hangs up in that in-between state.''
Peterson frowned. ``But what's it like? I mean, what does the world seem like if you can change it round?''
Markham said lightly, ``Nobody knows. Nobody's ever tried it before.''
``There were no tachyon transmitters until now.''
``And no reason to try to reach the past, either.''
``Let me get this straight. How's Renfrew going to avoid creating a paradox? If he gives them a lot of information, they'll solve the problem and there'll be no reason for him to send the message.''
``That's the trick. Avoid the paradox, or you'll get a stuck switch. So Renfrew will send a piece of the vital information -- enough to get research started, but not enough to solve the problem utterly.''
``But what'll it be like for us? The world will change round us?''
Markham chewed at his lower lip. ``I think so. We'll be in a different state. The problem will be reduced, the oceans not so badly off.''
``But what is this state? I mean, us sitting here? We know the oceans are in trouble.''
``Do we? How do we know this isn't the result of the experiment we're about to do? That is, if Renfrew hadn't existed and thought of this idea, maybe we'd be worse off. The problem with causal loops is that our notion of time doesn't accept them. But think of that stuck switch again.''
Peterson shook his head as though to clear it. ``It's hard to think about.''
``Like tying time in knots,'' Markham conceded. ``What I've given you is an interpretation of the mathematics. We know tachyons are real; what we don't know is what they imply.''
Back to the Eclectic Quotation Index.
97.09.19 / Garth Hube
About deBroglie Waves--taken from
http://regentsprep.org/Regents/physics/phys05/bdebrogli/default.htm
deBroglie Waves - Matter Waves
Based on an intuitive feeling that nature is symmetrical, Louis deBroglie (de-broy-lee) made an argument in 1924 that if waves have a particle nature, then particles must have a wave nature.
He began with the formula for momentum of a photon, solved it for wavelength, then replaced momentum with mv (particle momentum).
For any particle with even a small amount of mass, the wavelength is very small. Even the electron has a very small wavelength. Protons or Neutrons have even smaller wavelengths since they have more mass. Theoretically, any moving matter has wave characteristics. However, the wavelength of any life-size particle, like a golf ball, is so small that it is immeasurable.
Saturday, April 29, 2006
From the last episode of this Scientific Mystery Thriller
It is so difficult to detect ELF gravity waves so is the claim here that the detection & generation of HFGW more efficient?
Even if it was, I do not understand the motivation for this approach because far field radiation is like a leak in the water tank when you are trying to conserve water!
That is, we want to use the MACRO-QUANTUM NEAR VIRTUAL GRAVITY FIELDS ~ 1/r^2 in the whole (frequency-wavevector space) etc. that do not propagate away to infinity in the form of gravity radiation. That is the gravity induction type fields (off-mass-shell) are more important for practical metric engineering of warp and wormhole than the gravity waves ~ 1/r (on-mass-shell where frequency = (speed of light)(wavenumber) locus in frequency-wavevector space).
Also one needs to consider all 5 polarization states of the near gravity field off mass shell (light cone) not only the two leaky radiation polarizations + & - helicity. For now assume a weak warp field on flat Minkowski background. Will that suffice for saucer flight? The strong field self-dual/anti self-dual "nonlinear gravitons" have a chiral asymmetry like parity non-conservation in the weak force - that may be an important clue. We need to use the 5D O(4,1) deSitter space momentum-energy Cartan 1-form prior to local gauging of O(4,1):
Pa = -i{[1 - (r^2 - t^2)/R^2]^-1&a + (x^bMab/R^2)]}
/\zpf = 1/R^2
R ~ 10^28 cm
s^2 = r^2 - t^2
{Mab} = Lie algebra of O(3,1)
Note that DeSitter O(4,1) is a subgroup of O(4,2) basic to Penrose's twistor theory.
d = dx^a&a = Cartan exterior derivative with
d^2 = 0
observer at r = t = 0 = location of ship
P = dx^aPa = -ihd + /\zpf (stuff)
Note if
P ~ ihd
Then
P^2 = 0 fundamentally, i.e. massless field
On the other hand, when dark energy density ~ /\zpf
P^2 =/= 0.
On Apr 29, 2006, at 1:14 PM, Jack Sarfatti wrote:
The propulsion part seems dubious. The rest not. Ray Chiao has a better idea IMO.
On Apr 29, 2006, at 12:45 PM, RON STAHL wrote:
I haven't read about Baker in a year or two but the concept is based upon oscillating mass.
Ray Chiao has another idea.
When it gets a jolt, it releases HFGW's in the GHz range His devise is designed to produce coherent waves that don't attenuate when passing through matter.
Problem is signal strength.
I had heard that he was working with the Chinese on a communications scheme--call your subs, have your cell phone contact anyone on the planet at any time, etc. I had also heard I think, that a year ago at STAIF he was saying that he had more confidence in communications apps than in propulsion.
That's what I told you.
Now I pop onto the web site and find projections for propulsion. Well color me crazy but WHERE ARE THE AMERICAN INVESTORS?!!!
If there is anything to it - it's classified is my guess financed by UAE. ;-)
On Apr 29, 2006, at 12:20 PM, Jack Sarfatti wrote:
I know George Chapline since 1966 at UCSD La Jolla and Cal Tech. We were both part of the scene that Greg Benford describes in his Sci Fi novel "Timescape" about messages from the future i.e. SIGNAL NONLOCALITY that I am working on NOW although that concept was UNKNOWN back in the 1960's & even 70's!
I have written George about this and will see what he says.
I have not yet considered the URLS in detail. Kip Thorne & Ray Chiao should be asked. It is so difficult to detect ELF gravity waves so is the claim here that the detection & generation of HFGW more efficient?
Even if it was, I do not understand the motivation for this approach because far field radiation is like a leak in the water tank when you are trying to conserve water!
That is, we want to use the MACRO-QUANTUM NEAR VIRTUAL GRAVITY FIELDS ~ 1/r^2 in the whole (frequency-wavevector space) etc. that do not propagate away to infinity in the form of gravity radiation. That is the gravity induction type fields (off-mass-shell) are more important for practical metric engineering of warp and wormhole than the gravity waves ~ 1/r (on-mass-shell where frequency = (speed of light)(wavenumber) locus in frequency-wavevector space).
On Apr 29, 2006, at 11:57 AM, RON STAHL wrote:
the good old boys are out of their minds. . .look at the 20 year projection at the first link
http://www.gravwave.com/docs/Chinese&GRAVWAVE%20Joint%20HFGW%20Project.pdf
http://www.gravwave.com/docs/Dr%5B1%5D.%20George%20Chapline%27s%20Comments.pdf
Jack, as you probably know, this propulsion concept is based upon creating a singularity through constructive interferance of HFGW's. Set aside whether you think Baker can succeed at this and tell me, with the projectors attached to a ship, which is falling toward the singularity, which is receeding as the ship draws near. . .a moving gravity well. I don't see a reason to suppose this would be limited to subluminal travel, do you?
What you wrote makes no sense to me. The basic idea is simple. You use dark zero point energy with negative pressure & w < - 1/3 BEHIND the ship. This dark energy's induced gravity repulsion expands space behind the ship and makes a counter-intuitive reverse Dopper gravity BLUE SHIFT of all signals coming from the expanding space at the stern. You do opposite in front, i.e. positive pressure zero point energy causing contraction of space that gives a counter intuitive reverse gravity red shift from the bow. Note observations of rapidly changing colors of saucers. Those color patterns should correlate with the motion of the saucer if my idea is correct. See Jacques Vallee's "Fastwalker" for a fictional version as well as my Super Cosmos. Are Skinwalkers inside Fastwalkers? ;-)
You do this by inhomogeneous phase-locking of the vacuum's Goldstone phases to a a control Goldstone phase in thin-film high Tc anyon condensate modulated by tiny perpendicular magnetic field flux quanta - all at micro->nanoscale. That's my rough current intuition on how it basically works.
http://arxiv.org/abs/gr-qc/0602022
It is so difficult to detect ELF gravity waves so is the claim here that the detection & generation of HFGW more efficient?
Even if it was, I do not understand the motivation for this approach because far field radiation is like a leak in the water tank when you are trying to conserve water!
That is, we want to use the MACRO-QUANTUM NEAR VIRTUAL GRAVITY FIELDS ~ 1/r^2 in the whole (frequency-wavevector space) etc. that do not propagate away to infinity in the form of gravity radiation. That is the gravity induction type fields (off-mass-shell) are more important for practical metric engineering of warp and wormhole than the gravity waves ~ 1/r (on-mass-shell where frequency = (speed of light)(wavenumber) locus in frequency-wavevector space).
Also one needs to consider all 5 polarization states of the near gravity field off mass shell (light cone) not only the two leaky radiation polarizations + & - helicity. For now assume a weak warp field on flat Minkowski background. Will that suffice for saucer flight? The strong field self-dual/anti self-dual "nonlinear gravitons" have a chiral asymmetry like parity non-conservation in the weak force - that may be an important clue. We need to use the 5D O(4,1) deSitter space momentum-energy Cartan 1-form prior to local gauging of O(4,1):
Pa = -i{[1 - (r^2 - t^2)/R^2]^-1&a + (x^bMab/R^2)]}
/\zpf = 1/R^2
R ~ 10^28 cm
s^2 = r^2 - t^2
{Mab} = Lie algebra of O(3,1)
Note that DeSitter O(4,1) is a subgroup of O(4,2) basic to Penrose's twistor theory.
d = dx^a&a = Cartan exterior derivative with
d^2 = 0
observer at r = t = 0 = location of ship
P = dx^aPa = -ihd + /\zpf (stuff)
Note if
P ~ ihd
Then
P^2 = 0 fundamentally, i.e. massless field
On the other hand, when dark energy density ~ /\zpf
P^2 =/= 0.
On Apr 29, 2006, at 1:14 PM, Jack Sarfatti wrote:
The propulsion part seems dubious. The rest not. Ray Chiao has a better idea IMO.
On Apr 29, 2006, at 12:45 PM, RON STAHL wrote:
I haven't read about Baker in a year or two but the concept is based upon oscillating mass.
Ray Chiao has another idea.
When it gets a jolt, it releases HFGW's in the GHz range His devise is designed to produce coherent waves that don't attenuate when passing through matter.
Problem is signal strength.
I had heard that he was working with the Chinese on a communications scheme--call your subs, have your cell phone contact anyone on the planet at any time, etc. I had also heard I think, that a year ago at STAIF he was saying that he had more confidence in communications apps than in propulsion.
That's what I told you.
Now I pop onto the web site and find projections for propulsion. Well color me crazy but WHERE ARE THE AMERICAN INVESTORS?!!!
If there is anything to it - it's classified is my guess financed by UAE. ;-)
On Apr 29, 2006, at 12:20 PM, Jack Sarfatti wrote:
I know George Chapline since 1966 at UCSD La Jolla and Cal Tech. We were both part of the scene that Greg Benford describes in his Sci Fi novel "Timescape" about messages from the future i.e. SIGNAL NONLOCALITY that I am working on NOW although that concept was UNKNOWN back in the 1960's & even 70's!
I have written George about this and will see what he says.
I have not yet considered the URLS in detail. Kip Thorne & Ray Chiao should be asked. It is so difficult to detect ELF gravity waves so is the claim here that the detection & generation of HFGW more efficient?
Even if it was, I do not understand the motivation for this approach because far field radiation is like a leak in the water tank when you are trying to conserve water!
That is, we want to use the MACRO-QUANTUM NEAR VIRTUAL GRAVITY FIELDS ~ 1/r^2 in the whole (frequency-wavevector space) etc. that do not propagate away to infinity in the form of gravity radiation. That is the gravity induction type fields (off-mass-shell) are more important for practical metric engineering of warp and wormhole than the gravity waves ~ 1/r (on-mass-shell where frequency = (speed of light)(wavenumber) locus in frequency-wavevector space).
On Apr 29, 2006, at 11:57 AM, RON STAHL wrote:
the good old boys are out of their minds. . .look at the 20 year projection at the first link
http://www.gravwave.com/docs/Chinese&GRAVWAVE%20Joint%20HFGW%20Project.pdf
http://www.gravwave.com/docs/Dr%5B1%5D.%20George%20Chapline%27s%20Comments.pdf
Jack, as you probably know, this propulsion concept is based upon creating a singularity through constructive interferance of HFGW's. Set aside whether you think Baker can succeed at this and tell me, with the projectors attached to a ship, which is falling toward the singularity, which is receeding as the ship draws near. . .a moving gravity well. I don't see a reason to suppose this would be limited to subluminal travel, do you?
What you wrote makes no sense to me. The basic idea is simple. You use dark zero point energy with negative pressure & w < - 1/3 BEHIND the ship. This dark energy's induced gravity repulsion expands space behind the ship and makes a counter-intuitive reverse Dopper gravity BLUE SHIFT of all signals coming from the expanding space at the stern. You do opposite in front, i.e. positive pressure zero point energy causing contraction of space that gives a counter intuitive reverse gravity red shift from the bow. Note observations of rapidly changing colors of saucers. Those color patterns should correlate with the motion of the saucer if my idea is correct. See Jacques Vallee's "Fastwalker" for a fictional version as well as my Super Cosmos. Are Skinwalkers inside Fastwalkers? ;-)
You do this by inhomogeneous phase-locking of the vacuum's Goldstone phases to a a control Goldstone phase in thin-film high Tc anyon condensate modulated by tiny perpendicular magnetic field flux quanta - all at micro->nanoscale. That's my rough current intuition on how it basically works.
http://arxiv.org/abs/gr-qc/0602022
Wednesday, April 26, 2006
On Apr 26, 2006, at 11:04 AM, Jack Sarfatti wrote:
On Apr 25, 2006, at 10:43 AM, Waldyr A. Rodrigues Jr. wrote:
1) You got the idea...In a de Sitter world you can exchange angular momentum and what appears to be "linear momentum", the Phi_mu, which is indeed angular momentum.
2) Take notice: the formula for the Phi_mu that I wrote is valid only instereographical coordinates. It is important to emphasize this point. In other coordinate systems you (of, course) will find different formulas.
On Apr 26, 2006, at 9:33 AM, RKiehn2352@aol.com wrote:
Hi
I hate to get embroiled in this dd -> 0 argument,
but I would like you both to know my opinion on a point, which I think is important.
Thanks Robert.
I think Waldyr is saying that d^2 = 0 always, consistent with it's non-metrical topological origin that you emphasize.
However, the metrical Pu from the 10 Killing vector field isotropies in deSitter O(4,1) have the form (non-rigorously heuristically here)
D = dx^uPu ~ topological pre-metrical Cartan d + metrical stuff proportional to /\zpf
/\zpf = 1/R^2 ~ dark energy density of our pocket universe
R is the 5D constant curvature parameter.
In Susskind's theory R^2/4Lp^2 is the Holographic Universe BIT content of our pocket universe confined to the observer-dependent de-Sitter horizon on the inflation bubble.
In any case I made the analogy of
D = dx^uPu ~ topological pre-metrical Cartan d + de Sitter metrical stuff proportional to /\zpf
to
D = d + A/\ in EM & Yang-Mills
&
D = d + W/\ in GR with W as the spin-connection
Now this has important ramifications.
The existence of positive dark energy density /\zpf > 0 on cosmic scale means we formally live in a 5D deSitter space-time. Since the dark energy density is small this closely approximates 4D space-time's Poincare group.
When we locally gauge all of the 10-parameter deSitter group O(4,1) we get NEW compensating gauge field potentials and this allows /\zpf to be a local scalar field rather than Einstein's cosmological constant from 1915 GR which is an approximation to what we are talking about now that includes torsion fields of course.
Then, it's a long story, I think we can locally amplify /\zpf "harness cosmic energy" on a small scale both positive and negative for propellantless geodesic propulsion (Alcubierre type) like we see in the "alien ET flying saucers."
This sounds crazy, but is it crazy enough to be true? (Bohr)
Some flaky URLS (disinfo also has some true info)
http://www.ancientx.com/nm/anmviewer.asp?a=65&z=1
http://www.indiadaily.com/editorial/tech_default.asp
On Apr 25, 2006, at 10:43 AM, Waldyr A. Rodrigues Jr. wrote:
1)You got the idea...In a de Sitter world you can exchange angular momentum and what appears to be "linear momentum", the Phi_mu, which is indeed angular momentum.
2)Take notice: the formula for the Phi_mu that I wrote is valid only instereographical coordinates. It is important to emphasize this point. In other coordinate systems you (of, course) will find different formulas.
-----Mensagem original-----
De: Jack Sarfatti [mailto:sarfatti@pacbell.net]
Enviada em: terça-feira, 25 de abril de 2006 14:26
Para: Waldyr A. Rodrigues Jr.
Assunto: Re: OK now I understand Waldyr's statement & ZPF anyonic propellantless propulsion
Pa = -i{[1 - (r^2 - t^2)/R^2]^-1&a + (x^bMab/R^2)]}
= -i{[1 - /\zpfs^2]^-1&a + /\zpf(x^bMab)]}
where
s^2 = r^2 - t^2
G = h = c = 1
/\zpf = 1/R^2 > 0 ~ dark vacuum energy density
take the weak field linear approximation
[1 - /\zpfs^2]^-1 ~ 1 + /\zpfs^2
-i&a is the MECHANICAL KINETIC MOMENTUM OPERATOR pa in quantum mechanics
The analogy is to EM
P = p + (e/c)A
P is the canonical momentum, (e/c)A is the EM field momentum, e.g.
Feynman Vol III
So in the linear approximation
Pa ~ (1 + /\zpfs^2)pa - i/\zpf(x^bMab)]
In NR quantum theory, the Hamiltonian for a neutral test particle of
mass m moving in this weak dark energy field is
H ~ pa^2/2m ~ (Pa - /\zpfs^2pa - i/\zpf(x^bMab))^2/2m
With curious NEW nonlinear couplings between the deSitter Lie algebra
"charges" (Killing isometries) translations and space-time rotations
that are mediated/catalysed by the dark energy field - suggesting
propellantless propulsion. Again this is a linear approximation for
temporary convenience.
This is analogous to a charge in an external EM field
H ~ (P - (e/c)A)^2/2m
Now if you confine the test particle to a nanolayer 2D film, then you
may get ANYON fractional quantum statistics in which /\zpf is
manipulated to act like the normal magnetic field.
Also one wants to do strong field case with large localized /\zpf
vacuum zero point energy density.
On Apr 24, 2006, at 5:52 PM, Jack Sarfatti wrote:
> Waldyr says that for the deSitter O(4,1) group
>
> Pa = -i{[1 - (r^2 - t^2)/R^2]^-1&a + (x^bMab/R^2)]}
>
> Therefore, lim Pa as R -> infinity is i&a.
>
> /\zpf = 1/R^2
>
> OK, so what I meant was
>
> D = dx^a(Pa/i)
>
> as the GENERALIZED d for O(4,1)
>
> This D^2 =/= 0 when /\zpf =/= 0
>
> Limit of D when /\zpf ---> 0 is the Cartan d
>
> Therefore, this D is analogous to a covariant exterior derivative
> with the extra stuff as a connection.
On Apr 26, 2006, at 9:33 AM, RKiehn2352@aol.com wrote:
Hi
I hate to get embroiled in this dd -> 0 argument,
but I would like you both to know my opinion on a point, which I think is important.
IMO the operator d is a differential concept, not a derivative concept.
*
My topology base is self -taught, and most of it - that which I truely understand - comes from point set topology.
I was impressed by Kuratowski, especially his ideas on a "Closure Operator = K" as being
something which would allow the construction of a topology, for then my imagination led
me to believe that the {Identity-union-the-exterior-differential-d} = K= {I + d}, appeared to satisfy the Kuratowski Closure axioms.
It was then exciting to comprehend that the exterior differential acting on p-forms created the limit sets of the p-form.
*
From early physics training, this fit in well, for from the postulate that dJ = 0, one can dervice the Maxwell-Ampere PDE's.
dG = J
which implies that
div D = rho.
Hence, as taught in EM 2.01, the D field lines orignate and end on charges.
These endpoints ( the charges) are the "limit points" of the field lines.
*
IN an abstract manner, it then became apparent to me that the exterior differential was a generalized limit point generator, indeed.
*
This idea was later justified by the development of Cartan Topological Structure for an arbitrary 1-form.
It is possible to construct (what I called) a Cartan topology form any 1-form of Action,
and in 4D, show that the exterior differential indeed generated the limit sets of all sets in the Cartan topology.
(See pdf attachment.)
*****************************************************************************
Before 1991, when the ideas of a Cartan topological structure was presented at Santa Barbara, and for several years afterwards,
I used the words exterior derivative, ( and even in the article math-ph/0101033),
but it slowly became apparent to me that this was a philosophical error that should be corrected. Since 2002 or so I have tried to be careful and use
the words "exterior differential" ( not exterior derivative) which do not explicity fix the definition of a limit.
***************************************************************************************************************************
The words exterior derivative imply that a limit process has been chosen such that
dx/dt = V.
I have called this topological constraint: "Kinematic Perfection"
Written as an exterior differential form, dx -V(x,y,z,t)dt = w,
if w = 0, the statement is in effect a severe topological constraint formulated by the differential system, dx -V(x,y,z,t)dt = 0 .
it would follow that
dw = -dV^dt
and
w^dw = 0^dw = 0,
which implies that the system is integrable (in the sense of Frobenius).
In fact, V =V(t) not V(x,y,z,t).
**
But if w is not zero, then
w^dw = dx^dV^dt,
and to be integrable, V must be a function of x and/or t alone.
For otherwise, dx^ (Vy dy^dt+Vz dz^dt) = w^dw is not zero and
there does not exist a unique integral equivalent. (Frobenius theorem)
*
HOWEVER IMO
The exterior differential is much more general than a derivative concept.
The exterior differential does not require Kinematic Perfection, and permits a
formulation of topological fluctuations about the guiding lines of Kinematic Perfection, which are possible
integrable solutions assuming NO topological fluctuations.
*
**
That is in 4D, for example,
dx - V(x,y,z,t) dt = a topological fluctuation 1-form = w = w(x,y,z,t,dx,dy,dz,dt)
**
Cartan was well aware of this idea, for he often would substitute the 1 - form (dx - V(x,y,z,t) dt) into expressions for dx, in order to prolong his original expressions.
For example, if
dx - U(x,y,z,t) dt =0,
dy - V(x,y,z,t) dt = 0,
dz - W(x,y,z,t) dt = 0,
was substituted into the expression for a 3D differential volume,
then
d(3Vol) = dx^dy^dz = Udt^Vdt^Wdt which is zero !!!
In other words, Kinematic perfection is not compatable with a differential volume element.
**
I now use the algebraic definitions of the exterior derivative and the Lie derivative as being the dominant ideas.
The limits of Kinematic perfection are treated as special sub cases,
that do not apply to problems of systems far from equilibrium,
interactions that involve cubic curvature (such as pressure and temperature),
and to processes that exhibit thermodynamic irreversibility.
**
By the Way, Just where are the cubic interaction curvatures in EGR?
regards
RMK
On Apr 25, 2006, at 10:43 AM, Waldyr A. Rodrigues Jr. wrote:
1) You got the idea...In a de Sitter world you can exchange angular momentum and what appears to be "linear momentum", the Phi_mu, which is indeed angular momentum.
2) Take notice: the formula for the Phi_mu that I wrote is valid only instereographical coordinates. It is important to emphasize this point. In other coordinate systems you (of, course) will find different formulas.
On Apr 26, 2006, at 9:33 AM, RKiehn2352@aol.com wrote:
Hi
I hate to get embroiled in this dd -> 0 argument,
but I would like you both to know my opinion on a point, which I think is important.
Thanks Robert.
I think Waldyr is saying that d^2 = 0 always, consistent with it's non-metrical topological origin that you emphasize.
However, the metrical Pu from the 10 Killing vector field isotropies in deSitter O(4,1) have the form (non-rigorously heuristically here)
D = dx^uPu ~ topological pre-metrical Cartan d + metrical stuff proportional to /\zpf
/\zpf = 1/R^2 ~ dark energy density of our pocket universe
R is the 5D constant curvature parameter.
In Susskind's theory R^2/4Lp^2 is the Holographic Universe BIT content of our pocket universe confined to the observer-dependent de-Sitter horizon on the inflation bubble.
In any case I made the analogy of
D = dx^uPu ~ topological pre-metrical Cartan d + de Sitter metrical stuff proportional to /\zpf
to
D = d + A/\ in EM & Yang-Mills
&
D = d + W/\ in GR with W as the spin-connection
Now this has important ramifications.
The existence of positive dark energy density /\zpf > 0 on cosmic scale means we formally live in a 5D deSitter space-time. Since the dark energy density is small this closely approximates 4D space-time's Poincare group.
When we locally gauge all of the 10-parameter deSitter group O(4,1) we get NEW compensating gauge field potentials and this allows /\zpf to be a local scalar field rather than Einstein's cosmological constant from 1915 GR which is an approximation to what we are talking about now that includes torsion fields of course.
Then, it's a long story, I think we can locally amplify /\zpf "harness cosmic energy" on a small scale both positive and negative for propellantless geodesic propulsion (Alcubierre type) like we see in the "alien ET flying saucers."
This sounds crazy, but is it crazy enough to be true? (Bohr)
Some flaky URLS (disinfo also has some true info)
http://www.ancientx.com/nm/anmviewer.asp?a=65&z=1
http://www.indiadaily.com/editorial/tech_default.asp
On Apr 25, 2006, at 10:43 AM, Waldyr A. Rodrigues Jr. wrote:
1)You got the idea...In a de Sitter world you can exchange angular momentum and what appears to be "linear momentum", the Phi_mu, which is indeed angular momentum.
2)Take notice: the formula for the Phi_mu that I wrote is valid only instereographical coordinates. It is important to emphasize this point. In other coordinate systems you (of, course) will find different formulas.
-----Mensagem original-----
De: Jack Sarfatti [mailto:sarfatti@pacbell.net]
Enviada em: terça-feira, 25 de abril de 2006 14:26
Para: Waldyr A. Rodrigues Jr.
Assunto: Re: OK now I understand Waldyr's statement & ZPF anyonic propellantless propulsion
Pa = -i{[1 - (r^2 - t^2)/R^2]^-1&a + (x^bMab/R^2)]}
= -i{[1 - /\zpfs^2]^-1&a + /\zpf(x^bMab)]}
where
s^2 = r^2 - t^2
G = h = c = 1
/\zpf = 1/R^2 > 0 ~ dark vacuum energy density
take the weak field linear approximation
[1 - /\zpfs^2]^-1 ~ 1 + /\zpfs^2
-i&a is the MECHANICAL KINETIC MOMENTUM OPERATOR pa in quantum mechanics
The analogy is to EM
P = p + (e/c)A
P is the canonical momentum, (e/c)A is the EM field momentum, e.g.
Feynman Vol III
So in the linear approximation
Pa ~ (1 + /\zpfs^2)pa - i/\zpf(x^bMab)]
In NR quantum theory, the Hamiltonian for a neutral test particle of
mass m moving in this weak dark energy field is
H ~ pa^2/2m ~ (Pa - /\zpfs^2pa - i/\zpf(x^bMab))^2/2m
With curious NEW nonlinear couplings between the deSitter Lie algebra
"charges" (Killing isometries) translations and space-time rotations
that are mediated/catalysed by the dark energy field - suggesting
propellantless propulsion. Again this is a linear approximation for
temporary convenience.
This is analogous to a charge in an external EM field
H ~ (P - (e/c)A)^2/2m
Now if you confine the test particle to a nanolayer 2D film, then you
may get ANYON fractional quantum statistics in which /\zpf is
manipulated to act like the normal magnetic field.
Also one wants to do strong field case with large localized /\zpf
vacuum zero point energy density.
On Apr 24, 2006, at 5:52 PM, Jack Sarfatti wrote:
> Waldyr says that for the deSitter O(4,1) group
>
> Pa = -i{[1 - (r^2 - t^2)/R^2]^-1&a + (x^bMab/R^2)]}
>
> Therefore, lim Pa as R -> infinity is i&a.
>
> /\zpf = 1/R^2
>
> OK, so what I meant was
>
> D = dx^a(Pa/i)
>
> as the GENERALIZED d for O(4,1)
>
> This D^2 =/= 0 when /\zpf =/= 0
>
> Limit of D when /\zpf ---> 0 is the Cartan d
>
> Therefore, this D is analogous to a covariant exterior derivative
> with the extra stuff as a connection.
On Apr 26, 2006, at 9:33 AM, RKiehn2352@aol.com wrote:
Hi
I hate to get embroiled in this dd -> 0 argument,
but I would like you both to know my opinion on a point, which I think is important.
IMO the operator d is a differential concept, not a derivative concept.
*
My topology base is self -taught, and most of it - that which I truely understand - comes from point set topology.
I was impressed by Kuratowski, especially his ideas on a "Closure Operator = K" as being
something which would allow the construction of a topology, for then my imagination led
me to believe that the {Identity-union-the-exterior-differential-d} = K= {I + d}, appeared to satisfy the Kuratowski Closure axioms.
It was then exciting to comprehend that the exterior differential acting on p-forms created the limit sets of the p-form.
*
From early physics training, this fit in well, for from the postulate that dJ = 0, one can dervice the Maxwell-Ampere PDE's.
dG = J
which implies that
div D = rho.
Hence, as taught in EM 2.01, the D field lines orignate and end on charges.
These endpoints ( the charges) are the "limit points" of the field lines.
*
IN an abstract manner, it then became apparent to me that the exterior differential was a generalized limit point generator, indeed.
*
This idea was later justified by the development of Cartan Topological Structure for an arbitrary 1-form.
It is possible to construct (what I called) a Cartan topology form any 1-form of Action,
and in 4D, show that the exterior differential indeed generated the limit sets of all sets in the Cartan topology.
(See pdf attachment.)
*****************************************************************************
Before 1991, when the ideas of a Cartan topological structure was presented at Santa Barbara, and for several years afterwards,
I used the words exterior derivative, ( and even in the article math-ph/0101033),
but it slowly became apparent to me that this was a philosophical error that should be corrected. Since 2002 or so I have tried to be careful and use
the words "exterior differential" ( not exterior derivative) which do not explicity fix the definition of a limit.
***************************************************************************************************************************
The words exterior derivative imply that a limit process has been chosen such that
dx/dt = V.
I have called this topological constraint: "Kinematic Perfection"
Written as an exterior differential form, dx -V(x,y,z,t)dt = w,
if w = 0, the statement is in effect a severe topological constraint formulated by the differential system, dx -V(x,y,z,t)dt = 0 .
it would follow that
dw = -dV^dt
and
w^dw = 0^dw = 0,
which implies that the system is integrable (in the sense of Frobenius).
In fact, V =V(t) not V(x,y,z,t).
**
But if w is not zero, then
w^dw = dx^dV^dt,
and to be integrable, V must be a function of x and/or t alone.
For otherwise, dx^ (Vy dy^dt+Vz dz^dt) = w^dw is not zero and
there does not exist a unique integral equivalent. (Frobenius theorem)
*
HOWEVER IMO
The exterior differential is much more general than a derivative concept.
The exterior differential does not require Kinematic Perfection, and permits a
formulation of topological fluctuations about the guiding lines of Kinematic Perfection, which are possible
integrable solutions assuming NO topological fluctuations.
*
**
That is in 4D, for example,
dx - V(x,y,z,t) dt = a topological fluctuation 1-form = w = w(x,y,z,t,dx,dy,dz,dt)
**
Cartan was well aware of this idea, for he often would substitute the 1 - form (dx - V(x,y,z,t) dt) into expressions for dx, in order to prolong his original expressions.
For example, if
dx - U(x,y,z,t) dt =0,
dy - V(x,y,z,t) dt = 0,
dz - W(x,y,z,t) dt = 0,
was substituted into the expression for a 3D differential volume,
then
d(3Vol) = dx^dy^dz = Udt^Vdt^Wdt which is zero !!!
In other words, Kinematic perfection is not compatable with a differential volume element.
**
I now use the algebraic definitions of the exterior derivative and the Lie derivative as being the dominant ideas.
The limits of Kinematic perfection are treated as special sub cases,
that do not apply to problems of systems far from equilibrium,
interactions that involve cubic curvature (such as pressure and temperature),
and to processes that exhibit thermodynamic irreversibility.
**
By the Way, Just where are the cubic interaction curvatures in EGR?
regards
RMK
Tuesday, April 25, 2006
Nonlocality & Susskind's Blackhole Complementarity
"The views of space and time that held sway during most of the 20th century were based on locality and field theory ... The most fundamental object was the space-time point or better yet, the event. Although quantum mechanics made the event probabilistic and relativity made simultaneity non-absolute, it was assumed that all observers would agree on the usual invariant relationships between events. This view persisted even in classical general relativity. But the paradigm is gradually shifting. It was never adequate to deal with the combination of quantum mechanics and general relativity. ... In order to reconcile the equivalence principle with the rules of quantum mechanics the rules of locality have to be massively modified ... an unprecedented mix of short distance and long distance physics. Radical changes are called for. The new paradigm ... is based on four closely related concepts ....
The first is Black Hole Complementarity. This principle is a new kind of relativity in which the location of phenomena depends on the resolution time available to the experimenter who probes the system. An ... example .. Alice, falling into an enormous black hole with Schwarzschild radius of a billion years, according to the low frequency observer, namely Alice herself ... nothing special is felt at the horizon. The horizon is harmless ... she or her descendants can live for a billion years before being crushed at the singularity.
In apparent complete contradiction, the high frequency observer who stays outside the black hole finds that his description involves Alice falling into a hellish region of extreme temperature, being thermalized, and even eventually re-emitted as Hawking radiation ... the key to black hole complementarity is the extreme red shift of the quantum fluctuations as seen by the external observer."
Any signal sent from near the event horizon outward to the distant observer is red shifted, but any signal coming inward the opposite way from the distant observer is blue shifted. It's the latter Susskind is talking about. The energy E of a geodesic infalling "FREFO" particle of rest mass m seen by a locally coincident hovering non-geodesic accelerating (rockets firing propellant radially inward toward the event horizon) fiducial observer "FIDO" at FIXED r,theta,phi, using local Schwarzschild coordinates is
E ~ 2mc^2e^ct/2rs 1.7.37 p. 23
"Locally, the relation between the coordinates of(LIF) Frefos and (LNIF HOVERING) Fidos is a time-dependent boost along the radial direction. ... The Fidos see all matter undergoing Lorentz contraction into a system of arbitrarily thin 'pancakes' as it approaches the horizon. According to classical physics, the infalling matter is stored in 'sedimentary' layers of diminishing thickness as it eternally sinks toward the horizon. ... The Frefos of course see the matter behaving in a totally unexceptional way."
There is also the Infrared/Ultravioler duality followed by the holography principle and then the surface entropy principle.
When gravity come into to play, the more energy you pump into a small region decreases the resolution rather than increases it as in the old Heisenberg uncertainty principle because of the formation of an extended event horizon with Hawking radiation that can be strong at tiny scales. Holography is that the non-redundant geometrodynamic degrees of freedom are on the surface boundary of an enclosed 3D volume 1 c-bit per Planck area. The final entropy principle, really conjecture, is that black holes are huge tangled strings.
On Apr 24, 2006, at 8:28 PM, Jack Sarfatti wrote:
Memorandum for the Record
Subject: http://www.serpo.org disinformation?
Hal Puthoff's PV model is not consistent with Einstein's principle of equivalence, which is the essential reason I reject it as a viable USG DOD/DOE strategy for the metric engineering of practical warp drive and star gates to SERPO et-al for advanced space vehicles.
"The views of space and time that held sway during most of the 20th century were based on locality and field theory ... The most fundamental object was the space-time point or better yet, the event. Although quantum mechanics made the event probabilistic and relativity made simultaneity non-absolute, it was assumed that all observers would agree on the usual invariant relationships between events. This view persisted even in classical general relativity. But the paradigm is gradually shifting. It was never adequate to deal with the combination of quantum mechanics and general relativity. ... In order to reconcile the equivalence principle with the rules of quantum mechanics the rules of locality have to be massively modified ... an unprecedented mix of short distance and long distance physics. Radical changes are called for. The new paradigm ... is based on four closely related concepts ....
to be continued.
On Apr 24, 2006, at 6:20 PM, Jack Sarfatti wrote:
No Paul you do not understand what they mean by "Black holes have no hair."
Generically the best model we have for astrophysical black holes is the Kerr solution. We can forget net charge. So the only issue is whether we can have a > m where a = J/m
http://home.case.edu/~sjr16/media/stars_blackhole_anatomy.jpg
On Apr 24, 2006, at 5:03 PM, Paul Zielinski wrote:
Head in sand.
Penrose clearly states that it can be objected that the Kerr-Newman solutions with event horizons are "somewhat special".
I sent you the paper. I gave you the quotes.
Jack Sarfatti wrote:
I don't care what you allege Penrose said in 1969 that I bet you pulled out of context to come to a screwy conclusion.
On Apr 24, 2006, at 2:00 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
I mean of course NAKED FUTURE SINGULARITIES in gravitationally collapsing matter
i.e. a > M ---> J > M^2 extreme rotation
This allows time travel to past p. 78 Matt Visser "Lorentzian Wormholes"
mod quantum objections of the alleged infinite blue shift explosion at the critical point of time travel to the past (Ground Hog Day photons) - that Gott says can be averted.
On Apr 24, 2006, at 11:13 AM, Paul Zielinski wrote:
Jack Sarfatti wrote:
I have not misunderstood you. Apart from Chapline's model there ARE no alternatives within GR.
I've given you one -- a naked collapsed mass. You haven't shown me anything that rules this out in the case of the "best candidate" offered by Penrose.
Paul if there were any evidence at all of a very fast rotating black hole that blew off its outer event horizon you can be sure it would be front page news!
Then why does Penrose say that the solutions that are known to feature event horizons are "somewhat special in that..."?
You've turned this around so that it is the solutions without event horizons that are "somewhat special". That is not what
Penrose was saying in 1969.
r+- = M +-(M^2 - a^2)^1/2
a = J/M
Note the extremal Kerr black hole is
M = a
i.e. J = M^2
like the universal slope Regge trajectories of hadronic resonances as if
G* ~ 10^40G on scale of 1 fermi.
".. somewhat special ..." - R. Penrose.
Penrose argues against a *material surface*. There is no material *surface* either for a complete black hole or for a naked collapsed source, according to his own argument as actually stated.
It's not clear BTW whether Chapline's quantum critical surface at the event horizon is "material" or not.
Good question.
There will be dark energy in the interior, i.e. /\zpf(dark star) >> /\zpf(cosmological) > 0
That we know.
But I am now thinking he really means that the collapsed mass is swallowed up and removed from the physical universe by the singularity that results from gravitational collapse -- a Rabbit Hole within a Rabbit Hole!
Yes, that's what he means.
As I said, a Rabbit Hole within a Rabbit Hole.
However, from POV of outside observers the in-falling mass piles up near outside the infinite redshift surface g00 = 0 and NEVER gets there in any finite time.
*Appears* never to get there in a finite amount of time, due to the infinite redshift of light transmitted outward from the horizon.
Not *appears* they never get the signals - objectively.
That's not the same as saying certain events don't occur in a finite time.
No, Paul you do not understand Susskind's "black hole complementarity" - later I will quote Susskind.
Does the in-falling matter reach the infinite redshift surface according to any objective measurement of the outside hovering LNIF observer in any finite time? NO!
Does the in-falling matter reach the infinite redshift surface according to any objective measurement of the in- falling geodesic observer in any finite time? YES!
Of course, time observed near the event horizon is not the same as time observed remotely -- due to the traditional Einsteinian conflation of what is immediately observed here with what is actually out there.
Not even wrong. Einstein has a good theory of measurement showing what actual detectors measure.
Of course for in- falling detectors they will see nothing at the event horizon if it was only a thin shell of in-falling matter and they fall in afterward. They will be killed of course if the black hole is small.
I have to say I am having a hard time taking this kind of thing seriously. This is even nuttier than Penrose's literal belief in the non-local character of gravitational vacuum energy, IMHO.
So who are the real "crackpots" here? It's getting hard to tell.
Together with
dT(P*) = [gu'v'(P*)dx^u'dx^v']^1/2 = 0
INVARIANTLY for all choices of local coordinates
If you're right that g_00 (r_s) = 0 in all CSs, then this is a very interesting property of the SSS metric that must reflect some deep aspect of the symmetry of the problem.
No, you miss the point here. It's not true that g_00(r_s) = 0 in all CSs! What's true is that dT(r_s) = 0 in all CSs!
Strange that such an invariant inflection boundary should appear at r = 2M, out in the SSS vacuum.
It doesn't.
The g_00 = 1 - rs/r
is true only in that special class of HOVERING LNIF detectors OUTSIDE the event horizon!
But the invariant proper time differential dT(rs) = 0 is local CS invariant!
"The views of space and time that held sway during most of the 20th century were based on locality and field theory ... The most fundamental object was the space-time point or better yet, the event. Although quantum mechanics made the event probabilistic and relativity made simultaneity non-absolute, it was assumed that all observers would agree on the usual invariant relationships between events. This view persisted even in classical general relativity. But the paradigm is gradually shifting. It was never adequate to deal with the combination of quantum mechanics and general relativity. ... In order to reconcile the equivalence principle with the rules of quantum mechanics the rules of locality have to be massively modified ... an unprecedented mix of short distance and long distance physics. Radical changes are called for. The new paradigm ... is based on four closely related concepts ....
The first is Black Hole Complementarity. This principle is a new kind of relativity in which the location of phenomena depends on the resolution time available to the experimenter who probes the system. An ... example .. Alice, falling into an enormous black hole with Schwarzschild radius of a billion years, according to the low frequency observer, namely Alice herself ... nothing special is felt at the horizon. The horizon is harmless ... she or her descendants can live for a billion years before being crushed at the singularity.
In apparent complete contradiction, the high frequency observer who stays outside the black hole finds that his description involves Alice falling into a hellish region of extreme temperature, being thermalized, and even eventually re-emitted as Hawking radiation ... the key to black hole complementarity is the extreme red shift of the quantum fluctuations as seen by the external observer."
Any signal sent from near the event horizon outward to the distant observer is red shifted, but any signal coming inward the opposite way from the distant observer is blue shifted. It's the latter Susskind is talking about. The energy E of a geodesic infalling "FREFO" particle of rest mass m seen by a locally coincident hovering non-geodesic accelerating (rockets firing propellant radially inward toward the event horizon) fiducial observer "FIDO" at FIXED r,theta,phi, using local Schwarzschild coordinates is
E ~ 2mc^2e^ct/2rs 1.7.37 p. 23
"Locally, the relation between the coordinates of(LIF) Frefos and (LNIF HOVERING) Fidos is a time-dependent boost along the radial direction. ... The Fidos see all matter undergoing Lorentz contraction into a system of arbitrarily thin 'pancakes' as it approaches the horizon. According to classical physics, the infalling matter is stored in 'sedimentary' layers of diminishing thickness as it eternally sinks toward the horizon. ... The Frefos of course see the matter behaving in a totally unexceptional way."
There is also the Infrared/Ultravioler duality followed by the holography principle and then the surface entropy principle.
When gravity come into to play, the more energy you pump into a small region decreases the resolution rather than increases it as in the old Heisenberg uncertainty principle because of the formation of an extended event horizon with Hawking radiation that can be strong at tiny scales. Holography is that the non-redundant geometrodynamic degrees of freedom are on the surface boundary of an enclosed 3D volume 1 c-bit per Planck area. The final entropy principle, really conjecture, is that black holes are huge tangled strings.
On Apr 24, 2006, at 8:28 PM, Jack Sarfatti wrote:
Memorandum for the Record
Subject: http://www.serpo.org disinformation?
Hal Puthoff's PV model is not consistent with Einstein's principle of equivalence, which is the essential reason I reject it as a viable USG DOD/DOE strategy for the metric engineering of practical warp drive and star gates to SERPO et-al for advanced space vehicles.
"The views of space and time that held sway during most of the 20th century were based on locality and field theory ... The most fundamental object was the space-time point or better yet, the event. Although quantum mechanics made the event probabilistic and relativity made simultaneity non-absolute, it was assumed that all observers would agree on the usual invariant relationships between events. This view persisted even in classical general relativity. But the paradigm is gradually shifting. It was never adequate to deal with the combination of quantum mechanics and general relativity. ... In order to reconcile the equivalence principle with the rules of quantum mechanics the rules of locality have to be massively modified ... an unprecedented mix of short distance and long distance physics. Radical changes are called for. The new paradigm ... is based on four closely related concepts ....
to be continued.
On Apr 24, 2006, at 6:20 PM, Jack Sarfatti wrote:
No Paul you do not understand what they mean by "Black holes have no hair."
Generically the best model we have for astrophysical black holes is the Kerr solution. We can forget net charge. So the only issue is whether we can have a > m where a = J/m
http://home.case.edu/~sjr16/media/stars_blackhole_anatomy.jpg
On Apr 24, 2006, at 5:03 PM, Paul Zielinski wrote:
Head in sand.
Penrose clearly states that it can be objected that the Kerr-Newman solutions with event horizons are "somewhat special".
I sent you the paper. I gave you the quotes.
Jack Sarfatti wrote:
I don't care what you allege Penrose said in 1969 that I bet you pulled out of context to come to a screwy conclusion.
On Apr 24, 2006, at 2:00 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
I mean of course NAKED FUTURE SINGULARITIES in gravitationally collapsing matter
i.e. a > M ---> J > M^2 extreme rotation
This allows time travel to past p. 78 Matt Visser "Lorentzian Wormholes"
mod quantum objections of the alleged infinite blue shift explosion at the critical point of time travel to the past (Ground Hog Day photons) - that Gott says can be averted.
On Apr 24, 2006, at 11:13 AM, Paul Zielinski wrote:
Jack Sarfatti wrote:
I have not misunderstood you. Apart from Chapline's model there ARE no alternatives within GR.
I've given you one -- a naked collapsed mass. You haven't shown me anything that rules this out in the case of the "best candidate" offered by Penrose.
Paul if there were any evidence at all of a very fast rotating black hole that blew off its outer event horizon you can be sure it would be front page news!
Then why does Penrose say that the solutions that are known to feature event horizons are "somewhat special in that..."?
You've turned this around so that it is the solutions without event horizons that are "somewhat special". That is not what
Penrose was saying in 1969.
r+- = M +-(M^2 - a^2)^1/2
a = J/M
Note the extremal Kerr black hole is
M = a
i.e. J = M^2
like the universal slope Regge trajectories of hadronic resonances as if
G* ~ 10^40G on scale of 1 fermi.
".. somewhat special ..." - R. Penrose.
Penrose argues against a *material surface*. There is no material *surface* either for a complete black hole or for a naked collapsed source, according to his own argument as actually stated.
It's not clear BTW whether Chapline's quantum critical surface at the event horizon is "material" or not.
Good question.
There will be dark energy in the interior, i.e. /\zpf(dark star) >> /\zpf(cosmological) > 0
That we know.
But I am now thinking he really means that the collapsed mass is swallowed up and removed from the physical universe by the singularity that results from gravitational collapse -- a Rabbit Hole within a Rabbit Hole!
Yes, that's what he means.
As I said, a Rabbit Hole within a Rabbit Hole.
However, from POV of outside observers the in-falling mass piles up near outside the infinite redshift surface g00 = 0 and NEVER gets there in any finite time.
*Appears* never to get there in a finite amount of time, due to the infinite redshift of light transmitted outward from the horizon.
Not *appears* they never get the signals - objectively.
That's not the same as saying certain events don't occur in a finite time.
No, Paul you do not understand Susskind's "black hole complementarity" - later I will quote Susskind.
Does the in-falling matter reach the infinite redshift surface according to any objective measurement of the outside hovering LNIF observer in any finite time? NO!
Does the in-falling matter reach the infinite redshift surface according to any objective measurement of the in- falling geodesic observer in any finite time? YES!
Of course, time observed near the event horizon is not the same as time observed remotely -- due to the traditional Einsteinian conflation of what is immediately observed here with what is actually out there.
Not even wrong. Einstein has a good theory of measurement showing what actual detectors measure.
Of course for in- falling detectors they will see nothing at the event horizon if it was only a thin shell of in-falling matter and they fall in afterward. They will be killed of course if the black hole is small.
I have to say I am having a hard time taking this kind of thing seriously. This is even nuttier than Penrose's literal belief in the non-local character of gravitational vacuum energy, IMHO.
So who are the real "crackpots" here? It's getting hard to tell.
Together with
dT(P*) = [gu'v'(P*)dx^u'dx^v']^1/2 = 0
INVARIANTLY for all choices of local coordinates
If you're right that g_00 (r_s) = 0 in all CSs, then this is a very interesting property of the SSS metric that must reflect some deep aspect of the symmetry of the problem.
No, you miss the point here. It's not true that g_00(r_s) = 0 in all CSs! What's true is that dT(r_s) = 0 in all CSs!
Strange that such an invariant inflection boundary should appear at r = 2M, out in the SSS vacuum.
It doesn't.
The g_00 = 1 - rs/r
is true only in that special class of HOVERING LNIF detectors OUTSIDE the event horizon!
But the invariant proper time differential dT(rs) = 0 is local CS invariant!
Monday, April 24, 2006
Memorandum for the Record http://www.serpo.org disinformation?
Hal Puthoff's PV model is not consistent with Einstein's principle of equivalence, which is the essential reason I reject it as a viable USG DOD/DOE strategy for the metric engineering of practical warp drive and star gates to SERPO et-al for advanced space vehicles.
"The views of space and time that held sway during most of the 20th century were based on locality and field theory ... The most fundamental object was the space-time point or better yet, the event. Although quantum mechanics made the event probabilistic and relativity made simultaneity non-absolute, it was assumed that all observers would agree on the usual invariant relationships between events. This view persisted even in classical general relativity. But the paradigm is gradually shifting. It was never adequate to deal with the combination of quantum mechanics and general relativity. ... In order to reconcile the equivalence principle with the rules of quantum mechanics the rules of locality have to be massively modified ... an unprecedented mix of short distance and long distance physics. Radical changes are called for. The new paradigm ... is based on four closely related concepts ....
to be continued.
On Apr 24, 2006, at 6:20 PM, Jack Sarfatti wrote:
No Paul you do not understand what they mean by "Black holes have no hair."
Generically the best model we have for astrophysical black holes is the Kerr solution. We can forget net charge. So the only issue is whether we can have a > m where a = J/m
http://home.case.edu/~sjr16/media/stars_blackhole_anatomy.jpg
Hal Puthoff's PV model is not consistent with Einstein's principle of equivalence, which is the essential reason I reject it as a viable USG DOD/DOE strategy for the metric engineering of practical warp drive and star gates to SERPO et-al for advanced space vehicles.
"The views of space and time that held sway during most of the 20th century were based on locality and field theory ... The most fundamental object was the space-time point or better yet, the event. Although quantum mechanics made the event probabilistic and relativity made simultaneity non-absolute, it was assumed that all observers would agree on the usual invariant relationships between events. This view persisted even in classical general relativity. But the paradigm is gradually shifting. It was never adequate to deal with the combination of quantum mechanics and general relativity. ... In order to reconcile the equivalence principle with the rules of quantum mechanics the rules of locality have to be massively modified ... an unprecedented mix of short distance and long distance physics. Radical changes are called for. The new paradigm ... is based on four closely related concepts ....
to be continued.
On Apr 24, 2006, at 6:20 PM, Jack Sarfatti wrote:
No Paul you do not understand what they mean by "Black holes have no hair."
Generically the best model we have for astrophysical black holes is the Kerr solution. We can forget net charge. So the only issue is whether we can have a > m where a = J/m
http://home.case.edu/~sjr16/media/stars_blackhole_anatomy.jpg
Waldyr Rodrigues formula for deSitter space
Waldyr says that for the deSitter O(4,1) group
Pa = -i{[1 - (r^2 - t^2)/R^2]^-1&a + (x^bMab/R^2)]}
Therefore, lim Pa as R -> infinity is i&a.
/\zpf = 1/R^2
OK, so what I meant was
D = dx^a(Pa/i)
as the GENERALIZED d for O(4,1)
This D^2 =/= 0 when /\zpf =/= 0
Limit of D when /\zpf ---> 0 is the Cartan d
Therefore, this D is analogous to a covariant exterior derivative with the extra stuff as a connection.
Waldyr says that for the deSitter O(4,1) group
Pa = -i{[1 - (r^2 - t^2)/R^2]^-1&a + (x^bMab/R^2)]}
Therefore, lim Pa as R -> infinity is i&a.
/\zpf = 1/R^2
OK, so what I meant was
D = dx^a(Pa/i)
as the GENERALIZED d for O(4,1)
This D^2 =/= 0 when /\zpf =/= 0
Limit of D when /\zpf ---> 0 is the Cartan d
Therefore, this D is analogous to a covariant exterior derivative with the extra stuff as a connection.
Sunday, April 23, 2006
Note that in our pocket universe in the cosmic landscape populated by eternal chaotic inflation
r = 10^28 cm
The number of BITS of our universe as a COMPUTER SIMULATION is
~ 10^56/10^-66 ~ 10^122 BITS
On Apr 23, 2006, at 9:56 PM, Jack Sarfatti wrote:
Kaku says very simply on p. 562 of "Introduction to Superstrings and M Theory"
"Let us define the derivative operator as
d = dx^aPa (A.3.3)"
Now here I take h = c = 1
Pa = i&a
"Notice that because the derivatives commute
[Pa,Pb] = 0 (A.3.4)
so therefore
d^2 = 0 (A.3.5)
What could be simpler formally without jillions of excess formulae? Clearly the factor of i does not matter.
Then on p 549
"then the only commutator that changes" relative to the Poincare group
[Pa,Pb] = 1/r^2Mab
for DeSitter group O(4,1)'a Lie algebra
Then on p. 550
"r is called the de Sitter radius"
I define the dark energy density /\zpf ~ 1/r^2
"Notice that if r goes to infinity, we have the Poincare group. Thus, r corresponds to the radius of a five-dimensional universe such that if r goes to infinity" (i.e. the dark energy density /\zpf = 1/r^2 goes to zero in the UNBROKEN supersymmetry limit) "it becomes indistinguishable from the flat four-dimensional space of Poincare. Letting the radius go to infinity is called the Wigner-Inonu contraction and will be used extensively in super gravity theories. After the contraction, the de Sitter group becomes the Poincare group." p. 550 Kaku
From this I infer that
1. The physical observation of dark energy Omega ~ 0.73 means we live in 5D DeSitter space approximately on the large scale of cosmology.
2. Therefore the local basis invariant
d^2 = (1/2)[Pa,Pb]dx^a/\dx^b = /\zpfMabdx^a/\dx^b =/= 0 when /\zpf > 0
where {Mab} = Lie algebra of Lorentz group O(3,1).
Now this seems obvious physically. So we need to see if the excess mathematical baggage Waldyr provides in rebuttal is really physically relevant? Perhaps, but his point is not obvious to my mind.
"As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality." Einstein
r = 10^28 cm
The number of BITS of our universe as a COMPUTER SIMULATION is
~ 10^56/10^-66 ~ 10^122 BITS
On Apr 23, 2006, at 9:56 PM, Jack Sarfatti wrote:
Kaku says very simply on p. 562 of "Introduction to Superstrings and M Theory"
"Let us define the derivative operator as
d = dx^aPa (A.3.3)"
Now here I take h = c = 1
Pa = i&a
"Notice that because the derivatives commute
[Pa,Pb] = 0 (A.3.4)
so therefore
d^2 = 0 (A.3.5)
What could be simpler formally without jillions of excess formulae? Clearly the factor of i does not matter.
Then on p 549
"then the only commutator that changes" relative to the Poincare group
[Pa,Pb] = 1/r^2Mab
for DeSitter group O(4,1)'a Lie algebra
Then on p. 550
"r is called the de Sitter radius"
I define the dark energy density /\zpf ~ 1/r^2
"Notice that if r goes to infinity, we have the Poincare group. Thus, r corresponds to the radius of a five-dimensional universe such that if r goes to infinity" (i.e. the dark energy density /\zpf = 1/r^2 goes to zero in the UNBROKEN supersymmetry limit) "it becomes indistinguishable from the flat four-dimensional space of Poincare. Letting the radius go to infinity is called the Wigner-Inonu contraction and will be used extensively in super gravity theories. After the contraction, the de Sitter group becomes the Poincare group." p. 550 Kaku
From this I infer that
1. The physical observation of dark energy Omega ~ 0.73 means we live in 5D DeSitter space approximately on the large scale of cosmology.
2. Therefore the local basis invariant
d^2 = (1/2)[Pa,Pb]dx^a/\dx^b = /\zpfMabdx^a/\dx^b =/= 0 when /\zpf > 0
where {Mab} = Lie algebra of Lorentz group O(3,1).
Now this seems obvious physically. So we need to see if the excess mathematical baggage Waldyr provides in rebuttal is really physically relevant? Perhaps, but his point is not obvious to my mind.
"As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality." Einstein
Saturday, April 22, 2006
Gravity as a gauge theory and Dark Energy
The only difference between the electro-weak-strong force standard model of leptons and quarks with weak parity violation and Einstein's theory of gravity is that in the former it is internal compact continuous unitary symmetry groups SU(N) that are locally gauged with subgroup symmetries hidden (Meissner-Higgs effect), and in the latter it is the non-compact continuous orthogonal space-time symmetry groups O(n,n'). The local Einstein equivalence principle is simply the minimal coupling assumption use of locally gauge covariant derivatives applied to space-time symmetries rather than internal symmetries. The Cartan exterior derivative d is nilpotent, i.e. d^2 = 0, only for the 10-parameter Poincare group not for the 10-parameter DeSitter group with anti-gravity dark zero point energy density ~ /\zpf > 0 for G = c = h = 1 unit convention. Therefore, Wheeler's "boundary of a boundary vanishes" is violated by dark energy in DeSitter space because of homology/cohomology duality. The exterior derivative is dual to the boundary operator.
The Cartan exterior derivative operator is
d = dx^a&a
Where dx^u is a basis of forms and &u is a dual basis of co-forms (tangent vectors)
In general
F = dA = (1/2)(&aAb - &bAa)dx^a/\dx^b
the "/\" here is the antisymmetric exterior product not to be confused with /\zpf.
In particular let A = d, therefore
d^2 = (1/2)(&a&b - &b&a)dx^a/\dx^b
But this depends on the group structure!
For the Poincare group T4*O(3,1) = 4DTranslations*4DSpace-Time Rotations
(&a&b - &b&a) = 0
However, for the 5D DeSitter group O(4,1)
&a ~ Q5a
a,b = 0,1,2,3
(&a&b - &b&a) = /\zpfO(3,1)ab
The SUPERSYMMETRY limit of ZERO DARK ENERGY /\zpf --> 0 (positive side) is the Wigner-Inonu space dimension contraction of constantly curved 5D DeSitter space-time to globally flat 4D Poincare space-time.
Let {Qab,Q5a} be the 10 Lie algebra "charges" Q@, where @ = 0,1,2,3,4,5,6,7,8,9 infinitesimal generators of the DeSitter group O(4,1) in an obvious reassignment of labels that I do explicitly in my archive paper. I locally gauge this entire group to get the curved-torsioned Yang-Mills gravity tetrad 1-form
A = Au^@Q@dx^u
Where now {Q@} is the Lie algebra of the 5D dark energy DeSitter group O(4,1)
The FOUR curved tetrad potentials are the SUBSET
A^a = Au^adx^u
where a = 0,1,2,3 = (5,0),(5,1),(5,2), (5,3) i.e. @ = 0,1,2,3
Einstein's 1915 GR metric tensor field is
guv = (Iu^a + Au^a)(Minkowski)ab(Iv^a + Au^b)
In the limit /\zpf --> 0
In addition, in the archive paper I relate A^a to the 8 Goldstone phases of the inflation vacuum ODLRO field - that is a separate conceptual module.
In general we need to locally gauge O(4,1) for /\zpf =/= 0 and hide 6 symmetries of the 10 to get the 10^500 Calabi-Yau spaces.
*In this more general case d^2 = 0 is not true!
That is main NEW INSIGHT here.
The only difference between the electro-weak-strong force standard model of leptons and quarks with weak parity violation and Einstein's theory of gravity is that in the former it is internal compact continuous unitary symmetry groups SU(N) that are locally gauged with subgroup symmetries hidden (Meissner-Higgs effect), and in the latter it is the non-compact continuous orthogonal space-time symmetry groups O(n,n'). The local Einstein equivalence principle is simply the minimal coupling assumption use of locally gauge covariant derivatives applied to space-time symmetries rather than internal symmetries. The Cartan exterior derivative d is nilpotent, i.e. d^2 = 0, only for the 10-parameter Poincare group not for the 10-parameter DeSitter group with anti-gravity dark zero point energy density ~ /\zpf > 0 for G = c = h = 1 unit convention. Therefore, Wheeler's "boundary of a boundary vanishes" is violated by dark energy in DeSitter space because of homology/cohomology duality. The exterior derivative is dual to the boundary operator.
The Cartan exterior derivative operator is
d = dx^a&a
Where dx^u is a basis of forms and &u is a dual basis of co-forms (tangent vectors)
In general
F = dA = (1/2)(&aAb - &bAa)dx^a/\dx^b
the "/\" here is the antisymmetric exterior product not to be confused with /\zpf.
In particular let A = d, therefore
d^2 = (1/2)(&a&b - &b&a)dx^a/\dx^b
But this depends on the group structure!
For the Poincare group T4*O(3,1) = 4DTranslations*4DSpace-Time Rotations
(&a&b - &b&a) = 0
However, for the 5D DeSitter group O(4,1)
&a ~ Q5a
a,b = 0,1,2,3
(&a&b - &b&a) = /\zpfO(3,1)ab
The SUPERSYMMETRY limit of ZERO DARK ENERGY /\zpf --> 0 (positive side) is the Wigner-Inonu space dimension contraction of constantly curved 5D DeSitter space-time to globally flat 4D Poincare space-time.
Let {Qab,Q5a} be the 10 Lie algebra "charges" Q@, where @ = 0,1,2,3,4,5,6,7,8,9 infinitesimal generators of the DeSitter group O(4,1) in an obvious reassignment of labels that I do explicitly in my archive paper. I locally gauge this entire group to get the curved-torsioned Yang-Mills gravity tetrad 1-form
A = Au^@Q@dx^u
Where now {Q@} is the Lie algebra of the 5D dark energy DeSitter group O(4,1)
The FOUR curved tetrad potentials are the SUBSET
A^a = Au^adx^u
where a = 0,1,2,3 = (5,0),(5,1),(5,2), (5,3) i.e. @ = 0,1,2,3
Einstein's 1915 GR metric tensor field is
guv = (Iu^a + Au^a)(Minkowski)ab(Iv^a + Au^b)
In the limit /\zpf --> 0
In addition, in the archive paper I relate A^a to the 8 Goldstone phases of the inflation vacuum ODLRO field - that is a separate conceptual module.
In general we need to locally gauge O(4,1) for /\zpf =/= 0 and hide 6 symmetries of the 10 to get the 10^500 Calabi-Yau spaces.
*In this more general case d^2 = 0 is not true!
That is main NEW INSIGHT here.
Tuesday, April 18, 2006
Cornell physics e-print archive papers of note
Note that Waldyr has significantly toned down his initial comments made under duress from some "dozen important physicists" who did not particularly "like" him and who allegedly threatened the funding of his students. Note also that Waldyr explicitly mentions his pattern of critiquing other physicist's archive papers for what he considers mathematical errors.
http://arxiv.org/abs/gr-qc/0602022
General Relativity and Quantum Cosmology, abstract
gr-qc/0602022
From: Jack Sarfatti [view email]
Date (revised v12): Tue, 18 Apr 2006 20:18:39 GMT (998kb)
Emergent Gravity: String Theory Without String Theory
Authors: Jack Sarfatti
Comments: This 12th version adds a remark about DeSitter Space and Cartan forms. The formal math objections raised by Waldyr Rodrigues about the first version of this paper that I did not have 4 tetrads and 6 spin connections were based on his misreading of my notation. Professor Rodrigues wrote me that he has made similar formal objections about "twenty" other physicist's papers. Needs Acrobat 6 or later to read
I derive the Einstein 1915 classical field theory of gravity with what resembles both a massive torsion field and the Calabi Yau degrees of freedom from a conjectured eight Goldstone phases of the cosmic inflation field provided that the full Poincare group is locally gauged and its Lorentz subgroup is spontaneously broken in the vacuum. What looks like both the t Hooft Susskind world hologram conjecture of volume without volume and the quantization of area in Planck units given by Bekenstein and Hawking seem to be natural consequences of the conjecture. Just as the Michelson Morley experiment gave a null result, this model predicts that the LHC will never find any viable dark matter exotic particles as a matter of fundamental principle, neither will any other conceivable dark matter detector. The Cambridge IofA dark matter virial speed of 9km/sec is questioned. A way to detect pocket universes in the cosmic landscape beyond all types of horizons bounded by null geodesics is suggested based on the work of Antony Valentini.
http://arxiv.org/abs/gr-qc/0602111
General Relativity and Quantum Cosmology, abstract
gr-qc/0602111
From: Waldyr A. Rodrigues Jr. [view email]
Date (v1): Mon, 27 Feb 2006 12:17:17 GMT (20kb)
Date (revised v2): Mon, 27 Mar 2006 10:57:06 GMT (20kb)
A Comment on Emergent Gravity
Authors: Waldyr A. Rodrigues Jr
Comments: 21 pages. In this version some misprints have been corrected, two new references have been added and some (eventual) offensive observations have been deleted
This paper is a set of notes that we wrote concerning the first version of Emergent Gravity [gr-qc/0602022]. It is our version of an exercise that we proposed to some of our students. The idea was to find mathematical errors and inconsistencies on some recent articles published in scientific journals and in the arXiv, and we did.
Note that Waldyr has significantly toned down his initial comments made under duress from some "dozen important physicists" who did not particularly "like" him and who allegedly threatened the funding of his students. Note also that Waldyr explicitly mentions his pattern of critiquing other physicist's archive papers for what he considers mathematical errors.
http://arxiv.org/abs/gr-qc/0602022
General Relativity and Quantum Cosmology, abstract
gr-qc/0602022
From: Jack Sarfatti [view email]
Date (revised v12): Tue, 18 Apr 2006 20:18:39 GMT (998kb)
Emergent Gravity: String Theory Without String Theory
Authors: Jack Sarfatti
Comments: This 12th version adds a remark about DeSitter Space and Cartan forms. The formal math objections raised by Waldyr Rodrigues about the first version of this paper that I did not have 4 tetrads and 6 spin connections were based on his misreading of my notation. Professor Rodrigues wrote me that he has made similar formal objections about "twenty" other physicist's papers. Needs Acrobat 6 or later to read
I derive the Einstein 1915 classical field theory of gravity with what resembles both a massive torsion field and the Calabi Yau degrees of freedom from a conjectured eight Goldstone phases of the cosmic inflation field provided that the full Poincare group is locally gauged and its Lorentz subgroup is spontaneously broken in the vacuum. What looks like both the t Hooft Susskind world hologram conjecture of volume without volume and the quantization of area in Planck units given by Bekenstein and Hawking seem to be natural consequences of the conjecture. Just as the Michelson Morley experiment gave a null result, this model predicts that the LHC will never find any viable dark matter exotic particles as a matter of fundamental principle, neither will any other conceivable dark matter detector. The Cambridge IofA dark matter virial speed of 9km/sec is questioned. A way to detect pocket universes in the cosmic landscape beyond all types of horizons bounded by null geodesics is suggested based on the work of Antony Valentini.
http://arxiv.org/abs/gr-qc/0602111
General Relativity and Quantum Cosmology, abstract
gr-qc/0602111
From: Waldyr A. Rodrigues Jr. [view email]
Date (v1): Mon, 27 Feb 2006 12:17:17 GMT (20kb)
Date (revised v2): Mon, 27 Mar 2006 10:57:06 GMT (20kb)
A Comment on Emergent Gravity
Authors: Waldyr A. Rodrigues Jr
Comments: 21 pages. In this version some misprints have been corrected, two new references have been added and some (eventual) offensive observations have been deleted
This paper is a set of notes that we wrote concerning the first version of Emergent Gravity [gr-qc/0602022]. It is our version of an exercise that we proposed to some of our students. The idea was to find mathematical errors and inconsistencies on some recent articles published in scientific journals and in the arXiv, and we did.
Monday, April 17, 2006
Dark Energy, DeSitter Space & Catan's Forms
note go to discussion forum at
http://stardrive.org/title.shtml
for more current up-dates
This is starting something very new! Uncharted territory. Before Waldyr jumps on this:
"Anyone who has never made a mistake has never tried anything new." Einstein
I. Relation of DeSitter Group to Poincare Group
First, Klein 1872 groups define geometries.
Second, orthogonal groups of nxn matrices have n(n - 1)/2 parameters.
The invariant is x^2 = xi^2 (summation convention), xi real, i = 1 ... n
The anti-gravtating w = -1 (no boundaries) dark energy density ~ /\ > 0 corresponds to a global DeSitter group O(4,1) with invariant of Kaluza-Klein type 4 + 1 space-time with one extra space dimension.
x1^2 + x2^2 + x3^2 + x4^2 - x0^2
n(n - 1)/2 = 5x4/2 = 10
The "charges" of the Lie algebra are the 4x3/2 = 6 space-space rotations Mij = - Mji, i,j = 0,1,2,3 and the 4 space-time rotations Pi = Mi4, i = 0,1,2,3
The commutator of interest is
[Pi,Pj] = /\zpfMij
The other commutators
[Pi,Mjk] and [Mij,Mkl] are exactly the same as the Lie algebra of the 10 parameter Poincare group T4*O(3,1) in 3 + 1 space-time.
When the CONSTANT dark energy density vanishes /\zpf ---> 0 in the fermion-boson supersymmetry limit of 3 + 1 space-time then this "Wigner-Inonu contraction is from constantly curved 4 + 1 space-time to globally flat 3 + 1 Minkowski space-time, so that [Pi,Pj] = 0 where Pi is the total Energy-Momentum of 3+1 flat space-time.
Relationship to Cartan's forms.
d = dx^iPi = exterior derivative 1-form, h = c = 1 for now
d^2 = 0
means
d/\d = 0
That is only true when
[Pi,Pj] = 0
Therefore, when /\zpf =/= 0 we can no longer assume that d/\d = 0 in a 3 + 1 space-time with a dark energy density.
Note "/\" = Cartan exterior multiplication of forms
"/\zpf" is scalar constant curvature of 4 + 1 DeSitter space-time.
d/\d = dx^iPi/\dx^jPj = dx^i/\dx^j[Pi,Pj] = dx^i/\dx^j/\zpfMij
So for example suppose
B = dTheta
Theta is a 0-form
B is a 1-form
Therefore
dB = d^2Theta = d/\d = dx^i/\dx^j/\zpfMijTheta =/= 0
This will create ANOMALIES.
For example, Maxwell's EM equations
F = dA
dF = d^2A = dx^i/\dx^jMij/\zpfA =/= 0
This begins to look like the Meissner effect in superconductors ? and also magnetic monopoles!
dF = 0 when /\zpf = 0 corresponds to
curlE + Bt = 0 i.e. induction
divB = 0 no magnetic monopoles
Then also second half of Maxwell's equations
d*F = *J
d^2*F = d*J = dx^i/\dx^jMij/\zpf*F =/= 0 current anomaly
When /\zpf = 0 this is Ampere's law with displacement current
curlH + D,t = j
divD = rho
and Gauss's law.
This is before we get /\zpf as a local dark energy/matter field including /\zpf < 0 by locally gauging all of O(4,1).
note go to discussion forum at
http://stardrive.org/title.shtml
for more current up-dates
This is starting something very new! Uncharted territory. Before Waldyr jumps on this:
"Anyone who has never made a mistake has never tried anything new." Einstein
I. Relation of DeSitter Group to Poincare Group
First, Klein 1872 groups define geometries.
Second, orthogonal groups of nxn matrices have n(n - 1)/2 parameters.
The invariant is x^2 = xi^2 (summation convention), xi real, i = 1 ... n
The anti-gravtating w = -1 (no boundaries) dark energy density ~ /\ > 0 corresponds to a global DeSitter group O(4,1) with invariant of Kaluza-Klein type 4 + 1 space-time with one extra space dimension.
x1^2 + x2^2 + x3^2 + x4^2 - x0^2
n(n - 1)/2 = 5x4/2 = 10
The "charges" of the Lie algebra are the 4x3/2 = 6 space-space rotations Mij = - Mji, i,j = 0,1,2,3 and the 4 space-time rotations Pi = Mi4, i = 0,1,2,3
The commutator of interest is
[Pi,Pj] = /\zpfMij
The other commutators
[Pi,Mjk] and [Mij,Mkl] are exactly the same as the Lie algebra of the 10 parameter Poincare group T4*O(3,1) in 3 + 1 space-time.
When the CONSTANT dark energy density vanishes /\zpf ---> 0 in the fermion-boson supersymmetry limit of 3 + 1 space-time then this "Wigner-Inonu contraction is from constantly curved 4 + 1 space-time to globally flat 3 + 1 Minkowski space-time, so that [Pi,Pj] = 0 where Pi is the total Energy-Momentum of 3+1 flat space-time.
Relationship to Cartan's forms.
d = dx^iPi = exterior derivative 1-form, h = c = 1 for now
d^2 = 0
means
d/\d = 0
That is only true when
[Pi,Pj] = 0
Therefore, when /\zpf =/= 0 we can no longer assume that d/\d = 0 in a 3 + 1 space-time with a dark energy density.
Note "/\" = Cartan exterior multiplication of forms
"/\zpf" is scalar constant curvature of 4 + 1 DeSitter space-time.
d/\d = dx^iPi/\dx^jPj = dx^i/\dx^j[Pi,Pj] = dx^i/\dx^j/\zpfMij
So for example suppose
B = dTheta
Theta is a 0-form
B is a 1-form
Therefore
dB = d^2Theta = d/\d = dx^i/\dx^j/\zpfMijTheta =/= 0
This will create ANOMALIES.
For example, Maxwell's EM equations
F = dA
dF = d^2A = dx^i/\dx^jMij/\zpfA =/= 0
This begins to look like the Meissner effect in superconductors ? and also magnetic monopoles!
dF = 0 when /\zpf = 0 corresponds to
curlE + Bt = 0 i.e. induction
divB = 0 no magnetic monopoles
Then also second half of Maxwell's equations
d*F = *J
d^2*F = d*J = dx^i/\dx^jMij/\zpf*F =/= 0 current anomaly
When /\zpf = 0 this is Ampere's law with displacement current
curlH + D,t = j
divD = rho
and Gauss's law.
This is before we get /\zpf as a local dark energy/matter field including /\zpf < 0 by locally gauging all of O(4,1).
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