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Frank DiMeglio: on 12/26/09 at 22:18pm UTC, wrote Hi Lawrence: How would your essay ideas account for/address the following? ...

Frank DiMeglio: on 12/5/09 at 20:04pm UTC, wrote Hi Lawrence, and how would your essay ideas account for this? Do you not...

Frank DiMeglio: on 12/5/09 at 19:03pm UTC, wrote Hello again Lawrence. Kindly consider the folliwing addition to my prior...

Author Frank Martin DiMeglio: on 12/5/09 at 18:44pm UTC, wrote Hi Lawrence. Think of how genius, dreams, memory, and art are possible. Now...

Lawrence B. Crowell: on 11/10/09 at 18:08pm UTC, wrote I didn't rate your essay a one. I can't remember what I did give it...

James Putnam: on 11/10/09 at 17:05pm UTC, wrote Dr. Crowell, Quoting you from Muiguzzi's forum: '...Of course I came in...

Lawrence Crowell: on 11/10/09 at 4:32am UTC, wrote Franklin Potter has some interesting ideas about discrete systems and...

Ray Munroe: on 11/10/09 at 1:09am UTC, wrote Dear Franklin, It appears that you and Lawrence had some interesting...

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CATEGORY: What's Ultimately Possible in Physics? Essay Contest (2009) [back]
TOPIC: Can we see into a black hole? by Lawrence B Crowell [refresh]

Author Lawrence B Crowell wrote on Sep. 1, 2009 @ 14:46 GMT
Essay Abstract

abs: This essay outlines a number of developments in physics that together permit an estimate of the cosmological constant. Through an examination of strings which enter a black hole, and connections to the Jordan exceptional algebra, are shown to exhibit properties similar to graphene and systems with quantum criticality. This permits an estimate of a renormalized cosmological constant due to quantum criticality. addend: This paper is a survey of a number of developments which linked together could lead to a better understanding of fine tuning. The quantum criticality may also bridge some physics between string theory and Loop quantum gravity. This paper is to be followed by a supplementary paper which a reader may access. This paper illustrates more completely the mathematical details behind this general essay. Notice and its website will be given on my personal essay FQXI blogsite. This paper is intended as one step in a general program to find an underlying structure to string/M-theory according to quantum error correction codes. This work illustrates aspect of the Jordan exceptional algebra, which is a step towards understanding a universal quantum error correction code for quantum gravity and cosmology.

Author Bio

I did my graduate work at Purdue University and have since worked in affiliation with the AIAS and industry. For the last several years I have been working to set up the problem which this paper is related. Quantum cosmology is a quantum error correction process.

Florin Moldoveanu wrote on Sep. 3, 2009 @ 00:49 GMT
Cheers Lawrence,

Nice to see your paper in this contest. I am still digesting it, I will come with questions later.

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Steve Dufourny wrote on Sep. 3, 2009 @ 09:16 GMT
Hi dear Lawrence ,

Indeed like says Florin ,it's very technical ,I am digesting it too .

You play easily with equations ,it's rare .Even if I don't work with strings and extra dimensions and E ,I agree your mathematical extrapolations are incredibles and interestings .

Sincerely

Steve

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Author Lawrence B Crowell wrote on Sep. 3, 2009 @ 12:40 GMT
This paper is actually the stripped down version of a more technical paper which outlines the details more fully. I will be giving reference to that here before long. I will also write some very generic posts which outline in qualitative fashions some of the physics here.

It is hard to discuss p-branes and the like without things getting a bit technical.

Cheers LC

Peter Jackson wrote on Sep. 3, 2009 @ 17:29 GMT
Could the quantum critical phenomonon be equilibrium Lawrence?

If we slice planet earth in half and stand on the cooling rock of one half at what once was the centre would we be crushed? or may we just feel lighter?

If we bring the 2nd half close and stand at the same position there would we be crushed more, or perhaps feel lighter still?

Were the 2 craft currently winging...

view entire post

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Author Lawrence B Crowell wrote on Sep. 3, 2009 @ 21:21 GMT
The Newtonian gravitational equation of importance is ∆φ = 4πρ, ∆ = ∂_i ∂^i, where φ is the gravitational potential and the gravitational force is ∂_iφ = -F_i, in the ith direction. The equation means that on a spherical surface that the divergence of the gravity field ∂_iF^I = -∆φ is given by the amount of mass energy in...

view entire post

Peter Jackson wrote on Sep. 4, 2009 @ 13:48 GMT
Thanks Lawrence, that clarifies it all - ok I admit I got lost at the 26th dimension and tachyons. I've never ventured beyond the 13th before and have recently reconfirmed my alliegence to the constancy of 'c'.

I might have agreed with it all a while ago, but I decided math may be as much a straight jacket as a tool, and there are better ways to proof. Have you read the excellent essay on new representational formalism? Dynamic evolving neurologically compatible concepts replacing static numbers. I've explored something similar and have found new 'Occams razor' pathways to real solutions.

Now if you just had some inductive evidence in there somewhere...?

Peter

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Author Lawrence B Crowell wrote on Sep. 4, 2009 @ 17:29 GMT
My take on consciousness issues is that we should try to avoid them as long as possible. It is possible that consciousness is ultimately the foundations of reality. I don't think that is the case, but I also don't know that with certainty. This is one problem with the anthropic principle, particularly the hard AP. It is an argument which borders on a type of theology.

We really don't know what consciousness is. This is certainly a big problem with invoking consciousness as a foundation to cosmology. At this time I think it preferrable to develop quantum gravity and cosmology with no such reference. Of course this might turn out to be an approximation, and ultimately consciousness is crucial. However, if we do come down to that phase it could be the end to the foundations of physics. It could just as well be argued that we are "lost." Ernst Fischer worte an essay which borders on this, which does suggest at some time we may end up with a lot of unanswerable questions.

Cheers LC

Steve Dufourny wrote on Sep. 7, 2009 @ 18:07 GMT
Hello all ,

Lawrence ,

I know you don't accept the anthropic principle.

But we can't deny the evidence about the universality and its evolution .

All our World ,our physical Universe shows us its evolution .If a system evolves thus the cause ,this unknew is an evidence .The universality in improvement is a reality without any doubt .The ubiquity is not our evidence but behind ,probably if I can say .We can't interpret our laws behind ,a sure thing all that is a big equation in the physicality where I repeat the ubiquity is not a reality ,it's the reason of the intelligence thus like a catalyser of this evolution ,thus it exists an aim .The informations and the fundamentals are our only tools .

The history is a evidence and our past shows us the diversification and complexification to create the lifes and the intelligence to optimise the interactions between mass .It's evident what the ultim entropy is in all things ,the equation of Einstein Lawrence shows that too ,the maximum entropy is everywhere with our limits and scales .

In my opinion ,the entropy is important to encircle our thermodynamic.

What do you think Lawrence?

Sincerely

Steve

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Author Lawrence B Crowell wrote on Sep. 8, 2009 @ 19:31 GMT
I think physics should pursue things as far as we can without invoking the anthropic principle. It would be nice to have a first order theory of quantum gravity and cosmology which does not require anthropic considerations. We might of course eventually find we are bereft of anything which serves as functional axioms and are forced into this tautological situation of the anthropic principle. I would just assume that situation is postponed as long as possible.

Cheers LC

Florin Moldoveanu wrote on Sep. 9, 2009 @ 02:09 GMT
Lawrence,

With the disclaimer that I am not a string expert, I do have a couple (maybe naïve) questions.

First regarding the AdS-CFT. How is this compatible with the no clone theorem of QM? Suppose I am an unfortunate physicist falling past the event horizon. To me nothing special occurred. After this and before my spaghettification and ultimate erase out of existence I solve the quantum gravity problem exactly thus creating new information. Is this information ever transferred outside during BH evaporation, or not? If yes, would this not be a copy of my quantum state violating the no clone theorem? If no, would this not violate the holographic principle?

Second question is about the singularity. The closed loop string folds and becomes an open string. But why is it not completely erased out of existence in a finite amount of time? For the newly created open string, does time continue to exist? Do its tachyonic properties give him a get out of jail free card?

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Author Lawrence B Crowell wrote on Sep. 9, 2009 @ 17:23 GMT
If one is watching a mass fall into a black hole the proper distance for dt = 0 is

∫dR = ∫dr/sqrt(1 - 2m/r) =

r*sqrt((r - 2m)/r) + m ln[r - m + r*sqrt((r - 2m)/r)].

This is evaluated from some large R' >> 2m to r = 2m which is

R =~ R' + m*ln(R') - {m*(m)} = R' + m*ln(R'/m),

which is finite. So the ruler distance to the event horizon is...

view entire post

Florin Moldoveanu wrote on Sep. 10, 2009 @ 00:39 GMT
Thanks Lawrence,

I understand your explanation, but it does not quite address my questions. For the no clone question I see that entanglement might offer a way out, but I think this is just a speculation at this point. Do you know of any paper addressing this? My second question was about the singularity: a far away observer never observes anything falling in, everything stops at the horizon, but from the falling object point of view, he reaches the singularity in a finite amount of time. So the string falls in and is changed from a closed to an open one, Fine, but why is not the string erased completely out of existence? Forget the quantum string, consider just a classical one.

PS: Get well.

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Steve Dufourny wrote on Sep. 10, 2009 @ 07:39 GMT
Hi Florin and Lawrence,

Lawrence ,I think really what this principle is so important in the thermodynamic .All equations are based on that ,the ultim equilibre.

Any mathematical extrapolation will be fundamenatl without this entropy in my opinion.

This order of sciences is essential to encircle this energy and its fractal .

All equations are correlated with this simple fact ,the antrhropic principle of balance betwen systems .

Of course many scientists think what it's not necessary but it's an error because all is unified in this anthropic principle .

This universality is different than a religion or a human invention .There a limit must be adapted too .

I can't extrapolate my equations without this evidence of ultim entropy ,unknew and physical .It's a personal choice of course but it implies easier way to calculate and link or unify all .

Best Regards

Steve

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Christian Corda wrote on Sep. 10, 2009 @ 17:00 GMT
Hi Lawrence,

I am not an expert of strings and black holes, but I have a general question on your interesting essay: which are the physical motivations for assuming that exp(-gamma) is a rapidity for black holes from their soft domain? I think this is crucial in your work.

Thanks,

Ch.

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Author Lawrence B Crowell wrote on Sep. 10, 2009 @ 18:52 GMT
Before I answer these question explicitly I first will lay down a little bit of background. I do this in hopes this will give some idea of the arguments I advance. The conservation of quantum information with BH's is argued for by putting the black hole in an AdS_4 spacetime. This is the BTZ black hole, which due to the odd structure of AdS is perfectly confined there and does not interact with...

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Florin Moldoveanu wrote on Sep. 13, 2009 @ 19:52 GMT
Lawrence,

Sorry to ask again, but I am still not clear. Let me frame the question in classical mechanics terms first. Classically, a BH has 2 problems. 1. There is a singularity at its center meaning that the general relativity equations break down. 2. an infalling object will reach this singularity in a finite amount of time and it will not only be spaggetified and crushed, but it will simply be erased out of existence as its time comes to an abrupt end (and also his information will simply vanish).

Now people assume those problems will be solved by the final quantum gravity theory. AdS-CFT solves the infomation paradox in a partiular case, and it is very credible that information is not lost even in general. But the other 2 problems remain: 1. does string theory still exibit a singularity (most likely it will not, but I am not an string expert) 2. would the infalling strings be erased out of existence? (I understand now that they get spaggetified and change from closed to open, but if this happens, why not they continue to fall toward the center and get erased out of existence?) Classically, there is this theorem that says that once inside the event horizon, an object can ony move towards the center; maybe quntification would make the strings behave like electrons inside the Fermy surface and freeze them as all lower energy levels are already filled, but I am only speculating now)

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Author Lawrence B Crowell wrote on Sep. 14, 2009 @ 13:00 GMT
The singularity at the center of a black hole is more than a point, and in the case of a Schwarzschild metric is actually a spatial hyperbolic 3-surface. It is a bit odd to think that this could “fit inside” a sphere, but the horizon is a boundary between two different spacetime regions. Near the event horizon the BH metric appears similar to the Rindler wedge for an accelerated observer...

view entire post

Steve Dufourny wrote on Sep. 14, 2009 @ 17:49 GMT
with basilicum and parmesello for me the spaghettis and an ultim carbon arrangement and the velocity of the electron is about 100000 *the actual velocity of the silicium hihihi humor is good for health .

To be serious ,do you know the pyroxens and the amphibols dear Lawrence,when I was at the FNDP in geology at Namur Belgium,,I studied the silicates ,Ino ,tecto ,phyllo...these architectures is very relevant .It's fascinating to see these minerals ,the geology is fantastic ,there too the complemenatrity and the evolution show us the anthropic principle where all particles are coded to arrange and polarise the particles in a spheroid mass system .

The carbon in time is incredible with the pression and the temperature where the thermodynamics of course are fundamentals.

These crystals and others polarisations are there for something like all .

Let's take the ecology too ,it's the same .

Just that to try to explain what the strings ,branes ,....are not necessary to find the truths of fundamenatls .

On other planet of our solar system ,I am persuaded what many crystals ,and systems ,secrets are to discover and that to accelerate our evolution and our complementarity with our systems .We are voyagers of the Universe and many systems are around us to make incredible things .It's the proof of the anthropic principle Lawrence I think.

What do you think ?

Regards

Steve

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Author Lawrence B Crowell wrote on Sep. 15, 2009 @ 00:07 GMT
Steve,

I must confess I have a hard time following your line of reasoning at times. I am not sure if you are trying to draw parallels with string or branes with other structures. There does appear to be some sort of self-similarity of structure. Strings encode information as does DNA, DNA binds onto higher dimensional structures such as ribosomes which result in peptides, and open superstrings attach to d-branes. Beneath this is what I think a solid state physics type of lattice system of Planck volumes or quantum-gravity-bits, which has parallels in crystals and viruses and so forth.

Cheers LC

Steve Dufourny wrote on Sep. 15, 2009 @ 09:15 GMT
hello Lawrence,

I confess you ,I have difficulties too to follow my line of reasoning hihih don't worry ,I am a little crazy hihih but I take my medicaments hihihi I am better after ,more quiet hihi.

About the information ,I don't beleive what the strings imply the informations,

If I take an adn torus ,the rotations of all these quantum spheres imply different systems where the attraction and repulsion permit to polarise and with their intrinsic code,the external system like protein,enzym give the information which is probably encoded in the main central quantum spheres in this torus .

The ribosomes are on the RE and the spherical architecture and fields of polarisation are encoded too .This ARN and its macro proteins with the London interactions are relevant about the evolution point of vue and the increase of mass by very weak polarisation in these spherical architectures of quantum spheres .

Where are the strings ?? I don't see them really Lawrence ;even when two menbrans(nuclear...) are in contact ,it's always spheres and a +- polarisation where the informations is by contact ,what I find relevant is the difference with the volumes of quantum spheres and thus the kind of polarisation correlated with the weak polarizations of evolution and on the other side the polarisation of information by proteins,enzyms....the frequences and the velocity of rot more the different step of spherical field are essential to polarise in the same frequences ,without this spherical evidence ,the rationality is difficult to encircle in my line of reasoning .Even H20 is like that two poles in a spherical logic with their intrinsic code in evolution.

The strings are for me a lost of time.

I like read your mathematical method ,even if I don't agree with all ,I am impressed by your capacity to play with maths .Thus I read and don't agree but I learn in the same time too in math .

Sincerely

Steve

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Steve Dufourny wrote on Sep. 15, 2009 @ 19:18 GMT
I reread and here is an incredible confusion by me .But it's an interesting confusion.

I confounded the Anthropic principle and the ultim entropy ,

that's why I searched the real meaning ,I didn't seen the word Anthropology .

After I understand thus my confusion but if we extrapolate a little it's in fact the same after reflexions,

a non hasard because all is coded and...

view entire post

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Author Lawrence B Crowell wrote on Sep. 15, 2009 @ 23:46 GMT
Whether there is a need for consciousness in the universe is something for future generations to determine. It might well be that the universe exists because it gives rise to sufficient complexity so that aspects of the universe can observe and think about itself. At that point we might find consciousness is somehow at the ultimate foundations of the unvierse. Of course the problem is that we really don't know what consciousness is exactly and further if consciousness becomes the foundations of cosmology it might be the end of physical foundations.

Cheers LC

Steve Dufourny wrote on Sep. 16, 2009 @ 08:21 GMT
Hi Lawrence ,

I understand your point of vue .

But about the fact what "if consciousness becomes the foundations of cosmology it might be the end of physical foundations"

I don't understand ,the consciousness is a drinving force of the best experiments .

What I find very important is the difference with the harmony and the chaos ,the chaos is an error and a short instant ,like a instant .Thus there we can understand our actual global system .

The consciousness is there to harmonize the harmony if I can say and not to applicate some chaotics moments ,like a bomb for exemple ,this energy can be used in two roads ,to give electricity or to destroy .It's the same with all ,the consciousness is essential to encircle our fundamenatls and its enormous energy in all things .Like these words ,science without consciousness is ruin of soul ,simply .We can't do what we want ,it's only simple like that .

This reality increase the velocity of evolution.

The chaos is an human invention and can be aplly ,it's very sad and dangerous ,all chaos is short and return to the equilibrium .Thus is inutile and non universal .

I agree we are youngs and our consciousnes is still young too but we are in an Universal consciouness where the particles arranges and builds ,thus there is an ultim aim thus the consciousness is rational it seems to me.

At this moment on Earth we add chaotic systems and some eponentials are possibles thus our consciousness is to act to balance ,tha social and scientists responsability is essential to harmonize the chaotics affects due to our lack of consciousness .

Sincerely

Steve

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Steve Dufourny wrote on Sep. 16, 2009 @ 08:37 GMT

I am very intrigued by these BH ,they are there for several reasons .

Sometimes I say me what inside BH ,all becomes light ,thus their velocity of rot changes due to the specific properties of those BH .

Can we see inside ,in reality no ,in simulation yes if the good datas are encoded of course .

If we take the evolution point of vue ,thus we can consider what the polarisations aren't finish thus the light isn't still diffused in its maximum and for that if the light begins from the main central sphere towards systems thus a specific cycle between these centers is necessary.

If a BH takes that rediffuses it thus the quantity of light in the physical Universe decreases and the mass increases due to these kinds of vaccuums of equilibrium between mass systems in evolution .Let's imagine the orrientation and our place in our Universe and the link with the main central sphere where all has begun.Thus the Space and the supergravity can make a vaccuum of light link with centers .This connection between spheres is essential for me .The space with the gravity build its vaccum connected with the center and permit to have an ultim oscillation of evolution where the light become mass .It's a hypothesis of course .The galaxies are thus attaches with the center ,they turn ,probably what the ultim membran in the big limit dimension are a pure light too .It's the gauge without any doubt .

It's fascinating all that ,we are going to a beautiful sphere of mass and light .These spheres are linked by the light and evolve .

What do you think Lawrence ?

Sincerely

Steve

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Jayakar Johnson Joseph wrote on Sep. 16, 2009 @ 19:33 GMT
Dear Lawrence B Crowell,

As there is no absolute vacuum in a Coherent cyclic model of universe, the quantum-spaces that are extended matters in tensor fields as gravity; collapse into black holes that are also quantum-spaces. The black holes are clocks as quantum-spaces and void of matters that are causal for events and thereby no observables for exterior. The interconnected network of clocks that are black holes is the time surface for an evolved configuration of universe. Hawkins radiation may be the observables from another horizon through block hole.

Hence the string theory and braneworld scenario are descriptive for black holes in both the Inflationary and Coherent cyclic models of universe though there is certain degree of variations in formalism and manipulation rules. As a black hole evaporates with causality of multiple black holes, where the end of time of it is continued with the beginning of time in many, the universe has multiple origins in eternity with no beginning. I fully agree with Prof. Stephen Hawkins in that the universe is not inflationary in entirety and inflationary in locality with no beginning. Thereby the black holes represent the complexity of the universe to be explored by physics.

With best wishes,

Jayakar

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Author Lawrence B Crowell wrote on Sep. 16, 2009 @ 23:08 GMT
The connection between black holes and the cosmological constant is the duality of D1-branes and D5-branes. This is a bit of a complicated business to show but in involves something called T-duality. You might also think of it this way. Consider the D1-brane (string) as an open string which results from a closed string. The closed string (like a loop) is distended into an open string, think of stretching a rubber band so without breaking it is a double stranded appearing filament. The graviton modes wrap around the string clockwise and counter clockwise. Yet these two modes on the now open string merge into states corresponding to tachyon condensates. These tachyons are "glued" at their ends to the M2-brane like flies on fly paper.

With the big bang consider an elementary model of two three dimensional balls where surface points are identified with each other in a multiply connected manner. Now these two three dimensional balls form the interiors of two wormhole openings, and the surfaces of the two balls are horizons which connect the two. The two 3-d balls then form a three dimensional sphere. Now in this elementary model suppose a point in the 3-d sphere is removed and "sent to infinity." The result is the 3-dim sphere is converted to a three dimensional flat space. This spatial surface is the observable universe that evolves to foliate spacetime according to the cosmological constant, or equivalently inflation. The boundary point removed almost instantly are tachyons again. Now in this toy-ish model the tachyons are removed to infinity and removed from the RR sector, which is what the M2-brane does by gluing tachyons in a condensate state in black hole interiors. These two aspects of physics have a duality of sorts.

Cheers LC

Ray Munroe wrote on Sep. 17, 2009 @ 12:55 GMT
Dear Lawrence,

Are you familiar with the works of Claude Shannon? According to Shannon's Information Theory, we can model information content as N ln(N). Similary, entropy can be modelled as

$-\Sigma p^_i ln(p^_i)$

Apparently, some quantum information is conserved, and some may be converted into entropy. Are some of the quantum numbers (or "beables") of our system being conserved by higher-dimensional dynamics? If entanglement is a possible contributor in the conservation of these quanta, then we may be able to probe the Black Hole interior by observing entangled particles.

It appears that you are "renormalizing" the "bare" quantum critical point in a similar manner to QED's renormalization of the bare electron mass or charge. Certainly, from the Mass Hierachy problem, we expect the Planck and Higgs scales to be critical components of this renormalization.

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Sep. 17, 2009 @ 18:10 GMT
The quantum version of this is that entropy is S = -k Tr[ρ log(ρ)], for ρ the density matrix. Entropy amounts to some loss of knowledge about some submatrix of the density operator. Tracing over the unknown elements results in the loss of such data. So if we have a density matrix ρ = ρ’otimes ρ_{BH}, the black hole part of this might reflect the loss of information due to a quantum system being gravitationally coupled to the black hole. In the language of the Susskind stretched horizon, quantum bits are being stuck to the event horizon and lost.

To make this work with black hole complementarity the asymptotic observer and the infalling observer are observing string physics differently. The holographic string theory is a generalization of the S-matrix theory. The S-matrix requires a causal domain without any barriers. This is why the physics from the exterior is considered with tortoise coordinates where r* = r + 2m ln(|r – 2m|), and the horizon is at infinity. So this domain is different from the domain the infalling observer witness string physics as r - -> 0. The gravitational Doppler shifting of a string observed by the exterior observer as it approaches a BH as seen at a distance amounts to a choice of how one measures the eigenstates of the string. If this were a classical system approaching the BH there would be no such issue in particular. The observation by the asymptotic observer then adjusts the system according to a commensurate set of observables (complete set of commuting observables etc), which are the complement of another set of observables an observer would select for measurements further into the BH. The horizon then prevents any communication of there being simultaneous observations of the two sets of observables. If the BH is quantum mechanical, IOW the horizon is a distribution of null congruences determined by a quantum measure over a state space, the two sets of observables occur in a superposition. The distant or asymptotic observer who detects photons from the horizon is then measuring states which are in an entanglement with the BH.

If you are watching a particle or string approach a black hole you do so with auxiliary quanta that it is entangled with. Your partner decides to follow the particle or string all the way into the black hole. You both share an EPR pair that is entangled with the string. The loss of that entanglement is a measure of the entropy which is measured on the black hole. The entanglement phase across the horizon is lost, except for the case when the black hole is quantum mechanical. The entanglement phase becomes “tangled up,” if you will, similar to a blob of cream on the top of coffee that is stirred up and merged with the rest of the coffee. We lack the ability to track the fine grained details in how this happens, and so the entanglement phase is lost or buried away. This then counts into the entropy of the black hole.

Cheers LC

Jayakar Johnson Joseph wrote on Sep. 17, 2009 @ 23:42 GMT
Dear Lawrence B Crowell,

Thank you, I got the point. When two black holes collate there is causality of multiple black holes as they evaporate. This is describable by the T-duality of M2-brane and the emerging tachyons may provide background to resolve the paradox in speed of light, am I right.

Yours jayakar

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Author Lawrence B Crowell wrote on Sep. 18, 2009 @ 03:13 GMT
Jayakar,

I am almost done with the fuller version of this, which I can attach here. The matter involves a number of subtle connections. A crucial one is between S-duality of D1 & D5 branes and quantum homotopy or K-theoretic with something called Bott periodicity. This is where the M2-brane comes in. As I indicated the D1 branes can be tachyons which emerge from looped or closed strings by tidal forces into open string near the singularity. The tachyons are bunched together so they are no longer imaginary valued and faster than light, but are glued to this M2-brane. The M2-brane has physics simialr to what is found with graphene --- quantum critical phase transitions, quantum Hall effects and so forth. This is then dual to the D5-brane which is the outer portion we on the outside would call the black hole.

There is a lot here with holographic principles and so forth. This is an extension of the Susskind holographic principle, done in part to lend firmer support for a number of things such as AdS/CFT correspondence.

Cheers LC

Steve Dufourny wrote on Sep. 18, 2009 @ 08:59 GMT
Hi ,

This singularity is incredible .

If we consider a system which falls down inside the BH ,the function of mass is R= 2GM/c².

Like the similated collapse of our Earth and its about 1 cm of r .

Let's take the pulsars ,and the varible between 0 and R ,the potential energy liked is relevant and the cinetic relation thus .

E=G M m/R...with R =r of Scharzschild..and we can thus resume with E =G M²/R =1/2 M c²..2GM/c²R...

The potential shift is relevant and the evolution point of vue too I think where the mass increases.If we apply the rotation and its laws ,

It exists without any doubt a distribution of mass ,like in our galaxy near the center ,about 1000 pc of r .

Some datas show us this extrapolated mass of the center with 0.5 pc,the velocity of gas is relevant too .The mass is thus extrapolated M=V²R/G thus abot x millions of solar mass with variables .

This potential shift deforms the space probably in a vaccum of R diameter,this vaccum is a system of connection I think between light and diffusion by centers .What I find incredible in this singulatity ,is the balance between the galaxy and the vaccuum ,thus it's relevant about the sense of rotation and thus polarity of the light ,thus the difference between the linear velocity of the light and the stable particles and its rotations thus mass.

The curvature is relevant too and the mass which curves ....I prefer an space curved what an euclidian system .

Regards

Steve

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Ray Munroe wrote on Sep. 18, 2009 @ 13:18 GMT
Dear Lawrence,

On page 4, you introduce the Jordon algebra over the octonions, with three copies of octonions (the "O" terms or 8-dimensional E8's) and a three dimensional transform (the "z" terms) for a total of 27 dimensions. This looks like a generalization or expansion of Dray and Manogue's ideas. The difference is that Dray and Manogue are using one octonion and a two dimensional transform for a total of 10 dimensions. How many relevant combinations of Clifford divisor algebras (such as octonions and quaternions) and n-dimensional transforms exist?

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Sep. 18, 2009 @ 15:38 GMT
Dray and Manogue's work is essentially the same. The "O" in my matrix refers to elements from the octonions. It is any set of elements of the form

O = 1 + Σ_io_ie_i

where the sum is over 7 octonionic basis elements. I read one of Dray's papers the other day. He works out how to get eigenvalues from the Jordan matrix. The scalars "z," noted differently in dray's papers, enter into polynomial equations from which the eigenvalues and vectors are determined. In these analyses the three octonionic elements are different, and we of course might imagine assigning a "color index" to these which are a QCD-like element.

Cheers LC

Ray Munroe wrote on Sep. 19, 2009 @ 21:36 GMT
Dear Lawrence,

It is interesting to me that your Lagrangian is cubic in the octonion fields OO'O". Is this the equivalent of my deduction that fermion-boson-fermion interactions are three-legged Feynman diagrams? Perhaps I have an E8 octonion of initial state fermions, a different E8 Octonion of final state fermions, and a dual lattice (the dual to an E8 Octonion should be another E8 Octonion) of interaction bosons that connects these two fermion Octonions.

In another essay, Mohammed Sanduk asks "Is there a system beyond the particle?" The zero-dimensional "point" nature of a particle rightly bothers him and he proposes a Three Wave Hypothesis with a "Gear Model". Could his three gears be the three Octonions in the above paragraph? If these Octonions are "stringy lattices" as I modeled them in my upcoming essay, then "point particles" may be properly defined as the intersections of these "stringy lattices".

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Sep. 20, 2009 @ 14:09 GMT
Ray,

This involves IMO some matters involving quantum critical points and nonlnear behavior of Luttinger fluids. I attach an interesting in "Perspectives" article which introduces a main article published near the first of this year. The nonlinear interactions are of the sort not identified by a linear Feynman graph.

Cheers LC

attachments: when_infinity_does_not_count.pdf

Ray Munroe wrote on Sep. 21, 2009 @ 12:39 GMT
Dear Lawrence,

I understand renormalization and its Condensed Matter analogies - that wasn't the main point of my prior blog.

The point is: I think your three Octonions reflect my "3 Legged" and/ or Sanduk's "3 Geared" models, not a "3 Color" model.

In my theory, the initial state fermion is an 8-D Octonion in a 12-D framework. The interaction bosons have dimensionality ranging from one to eleven (excluding 8-D and 10-D), which implies that the final state fermion is a different Octonion in a different region of the 12-D framework. Curiously, an 11-D boson exists in a reciprocal (not necessarily dual) space to the fermions, and we now have 8+11+8=27 dimensions, with the bosonic degrees of freedom apparently represented by your middle octonion O' and your three transform dimensions, z's. My theory has four Electro-Color "colors" (not 3), and this seems to be part of the required "octality" symmetry of E8. Lisi already identified the only "triality" symmetry of E8 as Generations, so we can't use another triality symmetry like three colors.

I understand renormalization. I once considered Renomalized Group Theory (RGT) an "enemy" of my idea Quantum Statistical Grand Unified Theory (QSGUT - in my book). So I studied RGT with the intent of overthrowing it. I have since studied and applied RGT (I used RGT as part of my Thesis), and feel comfortable with it. I later decided that the Complementary Principle applies to RGT and QSGUT, and that realization led to Variable Coupling Theory (also in my book).

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Sep. 22, 2009 @ 03:18 GMT
I have finished this extension of my essay paper in a rough form. This is still a bit of an outline of things. As I push into this business I find it encompasses considerable depth. This extended version is attached here.

In reference to the three color problem, I attach a file with diagrams lifted from Lisi’s paper, since you made mention of it, which illustrates how three colors...

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attachments: jordan.pdf, 3color.GIF

Ray Munroe wrote on Sep. 22, 2009 @ 13:18 GMT
Dear Lawrence,

I'm not infallible. I could have made a mistake, but here is my reasoning.

Lisi uses a Pati-Salam Weak. Normally, Pati-Salam introduces a fourth color called violet. Lisi makes no mention of this color. In Lisi's Table 3 of a Gravitational D2G, he only has four fermion states fL^, fLv, fR^, and fRv. The only way that I know to make sense of this is if fL^=(uLr,g,b, e-barL), fLv=(dLr,g,b, nu-barL), etc.

From its Dynkin diagram, the symmetries of E8 are 240=8x(2x3x5). I interpret this as a single triality symmetry. Is this a triality of color or a triality of generations? Lisi says it is a triality of generations, but Distler says that Lisi is wrong about being able to place three generations of chiral fermions into a single E8. So maybe it is a triality of color?

But I digress. The question is "What do Lawrence's three Octonions represent?" I see at least three different answers. These three Octonions could represent three colors, or three generations, or three-legged Feynman diagrams. It isn't obvious to me - maybe it is to you.

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Sep. 23, 2009 @ 00:49 GMT
The basic triality is due to SO(8), where three of the roots in the Dtnkin diagram are at an angle of 2π/3 oridented around another root. However, triality can in general refer to any system of roots or elements which are related to each other by some operator where the cube of that operator is unity. There are a number of circomstances where this does happen.

I will have to look at...

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Leshan wrote on Sep. 24, 2009 @ 11:10 GMT
Dear Lawrence Crowell,

Since you are a black hole theorist, let's discuss the very similar objects – so-called holes in space-time (ST-holes). I have a deep suspicion that both objects may have the same nature.

Space-time holes appear in quantized theories of space-time. Imagine virtual quanta of space-time or an atom of space. This quanta appears and disappears continuously. If quanta of space-time disappear, it creates a hole in space-time or a vacant place in space-time. A hole is filled very quickly by environment. Since the speed of motion of environment is limited by the speed of light therefore the life-time of holes is non-zero. The holes are real objects and we can detect one using its properties. Inside of hole the abstraction and duration properties tends to zero due to a hole collapses quickly. Therefore if we increase the concentration of holes, the distance between every two points must decrease. In the limiting case when space consists of holes only the distance between every two points are equal to zero. Thus holes are accompanied always by time dilation and length contraction effects. Therefore we can detect the source of holes by detecting time dilation and length contraction effects. Thus I need two atomic clocks only to detect the source of holes. There is suspicion that some nuclear processes are able to create holes and I hope to detect one. What you think about it?

Sincerely, Leshan

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Author Lawrence B Crowell wrote on Sep. 24, 2009 @ 21:57 GMT
There are wormholes, which are similar to black holes. The difference is that at the horizon there is a thin shell of mass-energy or a quantum field which induces a curvature "jump" that is hyperbolic or defocusing. This is a Lanscoz junction. Gravity tends to focus spacetime paths (geodesics) if the spacetime geometry obeys the Hawking-Penrose energy conditions of positivity. This jump violates that which creates a multiply connected topology. The defocued rays have to diverge somewhere, and they do so around an identical opening in spacetime.

I have written a number of posts about these types of spacetimes. They tend to be pathological. One way of looking at this pathology is to think of the event horizon as a sort of capacitor. If I put a current source to the horizon and measure the impedance of the horizon I will find it is related to the impedance of free space ~ 440 Ohms. If I put this exotic field on the horizon and change the membrane configuration to make a wormhole then the impedence of free space is adjusted to a negative value. So from an electrical circuit perspective it would be a sort of "negative resistor," if I put a certain current on the "device" then from Ohm's law E = IR, I get a negative voltage drop across this "source." This is pathological in a way. I have used other examples to illustrate such pathology, such as with thermodynamics.

The wormhole might form a basis for Planck scale physics or so called quantum foam. Of course string theory is meant to valence the world from this chaos. The string “covers” the chaos of such physics on a scale smaller than the Hagedorn temperature or string length L = sqrt{8π}L_p. The work I am doing with illustrating how string physics is based on quantum error correction codes physics might be understandable on a scale about half this length. Beneath these scales as one approaches the Planck length the sort of chaos you mention might in fact take place, but this is a sort of troublesome area we really want nature to valence from observable physics.

Cheers LC

Author Lawrence B Crowell wrote on Sep. 25, 2009 @ 00:19 GMT
In reference to the above on G_2 group and the conformal approach to holographic principle:

The G_2 group acts on 7-manifolds as a system of three-forms. The G_2 group is then an holonomy with R^3 bundles over a quaterionic space. The G_2 group is a determined by space C^5, where for every point a ∈ C^5, let the 2-plane π_a exist in the tangent space T_aC^5. This means the...

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Anonymous wrote on Sep. 27, 2009 @ 21:32 GMT
This is to reference some post on other FQXI blog sites on quantions.

I have been giving the matter of quantions some study. I am not entirely decided about their status as yet. My sense is they are an interlinking between two complex number or quaternions in a way which defines norms differently. This might have something to do with S-matrix. So I will outline some aspects of S-matrix...

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Narendra nath wrote on Sep. 28, 2009 @ 05:48 GMT
i have ben losing my postings on your site because of Internet discoonections at my end. it seems you are lucky not to have some comments from me. i do appreciate your mathematical skill to work out the Physics and suggesting some innovative steps too. Somehow i get a recolllection of Einstein when he made remarks about the quantum mechanics being not a permanent theory for understanding Physics. he somehow seem to believe that the whole truth can not rest in probabilities. What about intellectual logic in the process of evolvement of any science. The present impasse in Physics is more due to lack of frsesh ideas and concepts. Once certain concepts get evolved and prove their success, one forgets that the same may be limiting us elsewhere. The best theory in Physics is one that involves the broadest of considerations encompassing as many phenomena as possible.

Presently i agree that we are able to understand the black holes through combining quantum and gravitational aspects. There has however been a recent exptal. report that has measured radiations coming out of one such object. Thus, we only are able to improve relative understandings in Physics and the finality is certainly not reached ever.

In my essay on this forum, i have hinted about an intense collaboration between physical and live sciences, towards a possible understanding about the human mind itsef. Everyone agrees that it is the basis for conceptualisation in Physics. This approach of evolving new Physics appears far superior to just relying on more mathematical jugglary. After all, maths. provides just a tool in Physics like the experimental data. The real thing is conceptualization in a better and better manner. Consciousness gets directly involved with the operation of the human mind. The total knowledge should be our aim and if it involves collaboration between humanity and sciences ( Physics is just one here)one should certainly give it a try.

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Lawrence B. Crowell wrote on Sep. 28, 2009 @ 18:35 GMT
I think that quantum mechanics is probably spot on, at least without gravitation. The think people need to realize is that quantum amplitudes obey perfectly deterministic wave equations. The modulus square of these amplitudes are interpreted as probabilities and according to the Born rule within the context of measurements. For basic QM the wave functions are complex numbers, determined by a Fourier series of such numbers, and a measurement is a destructive action which shifts this to a real number. In this perspective we might ask not whether quantum mechanics is fundamental, but rather why it is there exists a classical or macroscopic (non-quantal) world.

If you read some of my posts here, as well as my essay, the issue is ultimately how black hole complementarity preserves quantum bits. The AdS/CFT result and Susskind's analysis of BTZ black holes in AdS illustrate that quantum information is preserved. The next question is how. I will not claim to have solved this issue, but I think I have some suggestions for this and how this is connected to the problem of the cosmological constant.

Cheers LC

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Emile Grgin wrote on Sep. 29, 2009 @ 04:04 GMT
Dear Lawrence,

I read your paper and learned a great deal from it because I have not been following black hole research. I find your writing both clear and enjoyable.

This post is to keep the promise I made yesterday, but I have no questions.

Best regards, Emile.

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Author Lawrence B Crowell wrote on Sep. 29, 2009 @ 12:21 GMT
Emile,

The key point here is black hole complementarity involves two causal domains for the S-matrix. S-mtarix theory requires there to be causal domain of support without boundary. This is why Susskiind works with the tortoise coordinate for the xternal observer, where

r* = r - 2m ln|1 - 2m/r|

The causal domain for the observer on a commoving frame with an infalling string is different. The dstant exterior observer observes the time dilation effect on the infalling string and further how it covers the black hole horizon. Conversely the commoving observer witnesses none of this and records nothing particularly different from a string on a flat spacetime until the center of the black hole is reached. So the two observers witness the S-matrix according to quantum mechanically incommensurate observables.

Some features of quantions might aid in this if it can be worked for Jordan algebras. The metrical distance has Lorentzian features to it, which might provide a way of working how a string (or any general quantum field theoretic configuration) can exist in a superposed state with the interior and exterior basis of observables for the two S-matrix configurations.

Cheers, LC

Steve Dufourny wrote on Oct. 2, 2009 @ 11:57 GMT
Thank you very much .

It's very relevant in fact ,thus we can considered two systems or more thus two spheres systems like for the pulsars .

If the taxonomy ,the correct taxonomy is correlated with the spherical multipoles ,it becomes very relevant .

The moment in my opinion and the mass are correlated with the specific number and the specific entanglement,

with the...

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this post was moved here from a different topic

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Author Lawrence B Crowell wrote on Oct. 3, 2009 @ 01:48 GMT
I must confess I sometimes have trouble trying to figure out what you are saying here. You argue things are related to spheres in some way. The Lie algebra which has spherical geometry are the orthogonal rotation groups SO(n). These do get deformed in certain ways though. Also for relativity and AdS spacetimes there are SO(m, n) which have hyperbolic content.

Cheers LC

Narendra Nath wrote on Oct. 3, 2009 @ 14:51 GMT
My Sept 28 comments did not interest you to respond. may be i did n't enquire anything specific to your text. Being an experimentalist to the core, i feel fascinated by the conceptual pisture rather than the mathemetical applications to work the possible solution. i happen to note on Internet a news item on the daily galaxy website, that some radiation coming out of a distant black hole, some 12 billion years away, was detected against the normal expectation. Does black hole size has something to do with such a measurement if reliable. From what little i know, black hole is the last stage of a dead star/galaxy, as it starts attracting external mass and radiation on account of its intense gravitational field coupled with extremely high mass density too. To understand their behavior some attempts have also been made to introduce quantum gravitational approach. What are your expert opinion on these aspects?

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Lawrence B. Crowell wrote on Oct. 3, 2009 @ 17:17 GMT
I think I responded with my statement about quantum mechanics being exact, or nearly so, up to maybe quantum gravity.

My sense about mathematics is that it is an important way one works physics. I have an MS degree in mathematics, but don't consider myself to be a professional mathematician. IN what you say you indicate a greater interest in conceptual pictures. Yet mathematics are just those picture making elements. I don't advance the idea that mathematics is of greater importance than physical ideas. I think the two in a way can work together. A decent repertoire of mathematical knowledge helps in conceptualizing and formalizing things.

As for the distant black hole, this is rather interesting. There is this period called the reionization period about 400 million years after the big bang. About 400 thousand years into the universe the radiation dominated phase ended and luminous matter (ignoring dark matter) consisteded mainly of hydrogen, a little He and so forth. Gravitational clumping eventually gave rise to the first stars, which were strange population III stars that burned bright and exploded into supernova. These presumably gave rise to black holes and expelled matter somewhat richer in heavier elements. The generation of black holes is what is of interest. It appears as if these may have rapidly grown by coalescence or accretion of matter. This image is of a black hole of galactic proportions which existed about 1 billion years after the big bang.

This does feed into a question on why the early universe had such low entroy. It clearly was lower entropy than today, and it could not have been at some maximum entropy as well. A high entropy initial universe might have just generated lots of black holes to start with.

Cheers LC

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Steve Dufourny wrote on Oct. 4, 2009 @ 14:09 GMT
Hi ,

Lawrence ,I just try to convince you about the correct architecture .

For the Blach Holes ,there too it's a question of rotating spheres.

Like I said ,the Lie Algebra aren't sufficient ,too mathematical without real physicalities and reals numbers .This kind of symmetry is false because all quantum spheres are specifics in their volume,thus the symmetry is very very different .

Like I said with Florin ,you can see my writings ,a balance with the imaginaries and reals must be made .The complexification with naturals numbers from a multiplication of prime numbers must be physical .

If not the infinity is not encircled in fact and thus the real number too .

I like read your extrapolations ,be sure but unfortunally the physicality and its fundamenatals aren't the main piece of your extrapolations ,too much complexs implies a complexification of the mind .I think .

It's probably the reason why I don't understand your words

you say

"A high entropy initial universe might have just generated lots of black holes to start with."

I don't encircle this meaning ,could you develop please?

ps you dislike really my little and poor spheres hihihi ??

Best Regards

Steve

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Author Lawrence B Crowell wrote on Oct. 4, 2009 @ 19:00 GMT
The highest entropy a lump of mass can have is when it is packed into a black hole. So an early universe with lots of black holes would have a higher entropy. Yet this does not appear to be the state of the early universe. It started out with an unusually low entropy.

Infinity is not really a number. It is more a set, or a label given to a set with some unber of elements which are not finitely countable.

Cheers LC

Steve Dufourny wrote on Oct. 6, 2009 @ 17:09 GMT
Yes indeed but the prime are limited and the naturals ,products of the multiplication of primes are unlimited in the multiplication of the human and its mind ,like the complexification .

It's just this difference what I say between math and physic .A physical system without limit hasn't any thermodynamics laws in my opinion .

If the pression ,the volume ,the density ,the temperature ,the mass ,the energy ,the evolution point of vue and its increasing of mass ,the probable specific dynamic of our Universe ......all that must be coordonnated ,with a real topology in evolution .There without limit ,it's impossible .

Some fundamentals like the mass and the limits are essentials No ?

Best Regards

Steve

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Narendra nath wrote on Oct. 7, 2009 @ 04:17 GMT
Dear Lawrence,

i read your response to my posting appreciatively. However, the first stars formed only around 400 million years after Big Bang. The dead star to have reached Dark hole status could not have been such a coalescing star as you picture. i suspect that we do not know yet all about the dark holes. There may well be variety amongst them that differ in behavior. Cosmology is an open field thus far and we also need to keep our minds wide open for fresh ideas. I for one do not feel convinced about quantum gravity as it is not showing any signs of unification with the other three interaction fields. The latter three have no problems with quantum mechanics but i do find gravity requires much more understanding before it may be unified with Quantum mechanics. Further, as per Einstein often stated belief that Q.M. may be replaced by another theory as he did not like that physical processes are entirely governed by randomness, as logic does have a place in the design that our Universe has evoleved. If it has been random then many other evolutionary pictures could have come in. Thus multiverses idea for our universe may not be ruled out completely. Multi dimensionality will also cause problems for applying quantum mechanics to gravity. The latter may have components that conform and do not conform to multi-dimensional and multi-verses ideas.

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Author Lawrence B Crowell wrote on Oct. 7, 2009 @ 12:55 GMT
There is this dark age period after the end of the radiation dominated phase of the universe. It largely ended around 400 million years later with the gravitational accretion of matter into the earliest stars. These population III stars are not entirely understood. Pure hydrogen has a low opacity, and os it is not well understood how they maintained a nuclear fusion in a thermal-hydrodynamic equilibrium. These stars did result in two things. They produced a huge amount of radition which reionized the universe. The other is that in their death they produced the first large black holes in the universe. These appear to have grown by feeding off matter which coalesced into the earliest quasars or galaxies.

Quantum gravitation requires some new ways of thinking about quantum mechanics. The approach I take is by looking at the how the basis for the S-matrix is incommensurate for the two classes of observers with respect to a black hole. The distant observer who remains outside the black hole and the observer who falls into the black hole respectively observe different stringy physics. This is because the S-matrix, the simplest example being the Veneziano amplitude and the Euler β function which results, is a flat spacetime version of the string/M holography.

Cheers LC

Ray Munroe wrote on Oct. 7, 2009 @ 13:13 GMT
Dear Lawrence,

Mathematics is one of the cornerstones of physics.

Regarding the use of mathematics in physics, I used math in my own ideas. I am not opposed to Emile and Florin's use of quantions - I simply have not yet been convinced that we cannot accomplish similar things (even though I know that the mathematical structures are different) with Pauli and Dirac matrices, but I scored both of their papers well, and remain open-minded regarding their ideas. I truly would like to see a quantion theory with interactions.

If I understand quantions properly, they are an effectively two dimensional algebra in competition with the Pauli sigma matrices. Just as we can build twistors (an equivalent to Dirac gamma matrices) out of pairs of Pauli spinors, we should be able to build relevant 4-D structures out of pairs of quantions. That should be relevant for 4-D spacetime.

BUT, we are also dealing with an AdS 2-D M2-brane. Is the rule of algebra in these dimensions based on quantions or on Pauli matrices? We also anticipate anyons in these bizarre dimensions. Would one algebra be more likely to yield this feature than the other?

K12' has a G_2 of color buried deep within (see Lisi's paper or Ref [11]). Regarding the G_2 holonomy, Gordon Kane also referred to this mathematical structure. I was originally distracted by the similarities between K12' and Klein's Chi(7), and thought I was working with an I_2(7) seven/fourteen-fold symmetry. But now I realize that I may be working with a Lambda_{10}, and NOT a Chi(7). If it is a Lambda_{10} (Conway & Sloane "Sphere Packings, Lattices and Groups" - Laminated Lattices), then it would have the same five/ten-fold symmetries as the G_2 holonomy. I think this five-fold symmetry is important to Supersymmetry, where we might expect five fundamental particle multiplets: scalar bosons (spin-0), matter fermions (spin 1/2), vector bosons (spin-1), gravitino fermions (spin-3/2), and tensor bosons (spin-2).

Ray Munroe

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Author Lawrence B Crowell wrote on Oct. 7, 2009 @ 18:12 GMT
Quantions are a sort of two-way map from complex valued coordinates, where one way determine a sum of bar-z_i*z_i as a quantum probability, and the other map which determines a metric distance. This is a bi-fibration system, one from the Hilbert space to the projective Hilbert space and the other to a metric space, If the complex coordinates are spinor valued (which quantions appear implicitly to be) then the two maps can well enough be defined. It is not a wrong or bad idea, but honestly I don't find that it has the power Grgin and other seem to think. This idea is pretty closely related to twisters, due to the bi-fibration structure. To be honest given the relative coverage given to twistors vs quantions I would recommend considering twistors. Witten a few years ago illustrated some aspects of twistor valued D-branes, which has put some wind back in Penrose's sails.

The G_2 holonomy is given by the tangent plane on C^5 with the action of a 2-plane. This determines G_2 as having 7 complex dimensions, or with two representations in 7 and 14 dimensions. I have a fairly long piece above dated Sep. 25, 2009. The G_2 is an automorphism of the Jordan exceptional algebra, and it is a holonomy over the three octonions in the matrix. The largest subgroup of G_2 is the SU(3), which suggests this structure is related to an AdS_3 ~ QCD type of model. I would say that the I_2(7) symmetry or the related OP^2 (Moufang plane) structure is more likely on tack here. The roots of the G_2 are related within this system to the 7-elements of the Fano or Moufang planes.

The quantions seem to be a way of representing a set of states with a bilinear map, which in curved spacetime leads to nonunitary equivalent fields according to Bogoliubov elements. This then appears to be really a holonomic system of some type, which for an extended group might result in a description of quantum gravity, or field in curved spacetime. Under a trace of elements it should then reduce I think to thermalized fields such as Unruh or Hawking radiation.

I will try to write more on this later. One reason for posting essays here is to increase connections with various people. Christian Corda and myself have an interesting exchange on the physics of detecting gravitational waves. So I ahve a number of new irons in the fire here.

Cheers LC

Jonathan J. Dickau wrote on Oct. 7, 2009 @ 18:22 GMT
Greetings Lawrence,

I have started reading your paper and will likely return for more soon. I read through to the end of Exceptional Nature, then skimmed ahead looking for familiar concepts and conclusions. I'll need to get back to it, having reached my limit. I have several questions and comments already, though, so here I am looking for clarification. Bear with me if I ask a stupid question or re-state something obvious. At this point it looks like you are making a strong case for the utility of the Jordan exceptional algebra, but I haven't fully grasped your meaning yet.

First some foundations. I find that whenever invoking the Holographic principle, I am wise to mention and cite 't Hooft's paper on dimensional reduction arXiv:gr-qc/9310026. I'm looking forward to seeing him speak next month at FFP10 about black hole/information questions. And wasn't it Maldacena's contribution that we could move either up or down dimensions, at a dimensional boundary, with the same generalization? Next; are the Black Holes embedded in AdS space-time the same as the BTZ Black Holes Witten talks about in arXiv:0706.3359?

It seems as though your formulation's proof hinges on the closed string becoming an open string at the black hole's event horizon, so I'll start there. It seems as though a tidally distended string could have a time retarded portion and a portion in advancing time, to keep the loop open, making the stretched loop into a pair of facing cobordisms, as the 'string' is really a flux tube. Is the fact that it is flattened against the event horizon (making it 2-d plus 1 for time) the key here? Are the tidal forces of the Weyl curvature the factor which causes it to stretch and shear? Are we accepting on faith that it 'must' become 2-d conformal in order to pass through the event horizon?

I may believe you are on the right track, and enjoy seeing if your analysis bears out when we see more quantum Black Holes in the accelerator experiments, but I don't claim to understand why your formalism should work yet.

More Later,

Jonathan J. Dickau

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Jonathan J. Dickau wrote on Oct. 7, 2009 @ 19:38 GMT
Hello again,

I think I answered my own question, as to what causes the loop to collapse. It is the shear between the most time-retarded point and the most time-advancing point on the closed loop which accomplishes the task, because these become the endpoints of the open string. I imagine that with the stretching, the string tension is increased until the two sections of the loop are less than the string dimension apart, at which point they effectively merge.

Is this correct? If so, I'll go on to other questions next time.

Regards,

Jonathan

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Author Lawrence B Crowell wrote on Oct. 7, 2009 @ 20:04 GMT
Jonathan,

Thanks for your questions and in reading my paper. It is not entirely complete, and there are a few open questions with it at this time. The main point is this. If you have a string fall onto a black hole there are two ways one can choose to observe this. The smart observer reamins far removed from the black hole and watches the string fall in. The dumb observer sets...

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Author Lawrence B Crowell wrote on Oct. 7, 2009 @ 20:07 GMT
Yes that is the case. The open string under the tidal forces or shearing is like a rubber band stretched out from opposite points so it becomes effectively a single rubber thread.

LC

Author Lawrence B Crowell wrote on Oct. 7, 2009 @ 20:11 GMT
PS: I have tried to make the arguments at the early stage and later stage of the essay as physical as possible. There is quite a bit here about K-theory and Fermi surfaces. Much of this is to advance the theory of how the cosmological constant is due to a breakdown of Landau-fermi fluids.

LC

Jonathan J. Dickau wrote on Oct. 8, 2009 @ 02:07 GMT
Checking back,

Thanks for the clarification and encouragement. I'll read the rest of your essay soon, starting from the top of Exceptional Nature, so I'm sure I have my bearings.

All the Best,

Jonathan

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Author Lawrence B Crowell wrote on Oct. 8, 2009 @ 17:43 GMT
Take your time. And if you have criticisms I would prefer to read them directly than to get a silent 1 or 2. Real feedback is important.

LC

Frank Martin DiMeglio wrote on Oct. 11, 2009 @ 16:27 GMT
In reading/considering your essay, I have some very important questions for you. They are very relevant to string theory and "black holes".

1) Why is it NOT your position that it is plain and simple common sense that the known mathematical unification of Einstein's theory of gravity (general relativity) with Maxwell's theory of light (electromagnetism) that is achieved by the addition of a...

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Frank Martin DiMeglio wrote on Oct. 11, 2009 @ 16:38 GMT
Hi Lawrence, I add the following to what I had written about astronomical/telescopic observations in my prior post to you.

Consider the blackness of outer space, the position of red light on the visible light spectrum, and transparent/clear space. Consider this in relation to the black and clear/invisible spaces of the eye. Kindly consider all of this in relation to visibility/black holes and "dark matter/"dark energy". How would your essay account for, or refute, this?

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Author Lawrence B Crowell wrote on Oct. 12, 2009 @ 01:16 GMT
I will try to answer these question as best I can:

Frank Martin DiMeglio:

1) Why is it NOT your position that it is plain and simple common sense that the known mathematical unification of Einstein's theory of gravity (general relativity) with Maxwell's theory of light (electromagnetism) that is achieved by the addition of a fourth dimension of space to Einstein's theory must be...

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Author Lawrence B Crowell wrote on Oct. 12, 2009 @ 01:20 GMT
I am anonymous above! Forgot to log in. Here are more thoughts on where this is going, which I have posted elsewhere on FQXI

-----------------------

I am working on a problem involving octonionic black holes, or a way to use the heavenly phere structure of the Jordan exceptional algebra as local systems of 26 dimensional Lorentz spaces. The identification between the three...

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attachments: 1_octonionic_curved_space.JPG

Frank Martin DiMeglio wrote on Oct. 12, 2009 @ 03:10 GMT

1)You said that you did not quite understand the following:

The fundamental union of gravity and electromagnetism/light necessarily/ideally involves balancing scale by making gravity repulsive and attractive as electromagnetic energy/light? If we consider photons/electromagnetism/light AS gravity, is this not what we would get (or like to get,...

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Frank Martin DiMeglio wrote on Oct. 12, 2009 @ 03:24 GMT
The [relative] repulsiveness of gravity in outer space is not separate from that fact that there is no [feeling of gravity] there, as compared to the [relative] attraction of objects on/in relation to the Earth. See how this relates to my last post? The dream balances/adjusts space, temperature, visibility, energy, scale/distance, and invisible/visible space electromagnetically/gravitationally.

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Author Lawrence B Crowell wrote on Oct. 12, 2009 @ 16:05 GMT
The absense of gravity in free space is related to why a freely falling frame has not gravity as well. This is the falling elevator issue. A person on a falling elevator is not able to determine locally if they are in free space or falling in a gravity field. This is the essense of the Einstein equivalence principle. Now of course the freely falling frame may have some spatial extent and so the radial dependency of a gravity field will result in small deviations in motion between distributed masses. This is the Weyl curvature or tidal accelerations.

Cheers LC

Author Lawrence B Crowell wrote on Oct. 12, 2009 @ 22:12 GMT
I am not terribly educated in psychology, and so I can't comment on dreams too much. It is my understanding that dreams are ways the brain processes information at a time when glycogen stores are restored by oligoastrocytes.

One might say in some sense that models are mental ideations similar to dreams. I have a certain speculation that beneath what I think is the ultimate theory of everything, based on the monster group, there might at the Planck scale exist self-referential states which are similar to Liebniz's monads, or the Indra net of the Uppanishads. In that loose sense the universe might ultimately be something similar to the eternal dream of Vishnu.

The universe might then be some ultimate self-referential wholeness, and what we consider to be physical principles are various accidents, spontanous emergences or (fill in the blank) which come about. Human consciousness might then be some sort of recherche or mirror of this. It might then possibly be said that our capacity to abstract the nature of the universe is some mirror or similar process by which it came about.

Cheers LC

Ray Munroe wrote on Oct. 14, 2009 @ 15:06 GMT
Dear Lawrence,

If information content scales as N ln(N), and entropy can be modelled as

S = -k Tr[p log(p)], for p (rho) the density matrix, then we may have information being converted into entropy. What are the possibilities of this information being reconstituted into an equivalent amount of information on the AdS M2-brane?

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Oct. 15, 2009 @ 12:13 GMT
The AdS/CFT result indicates that quantum information is not really destroyed. The AdS spacetime turns out to be a bottle that can hold a black hole, since the hyperbolic curvature (Gaussian curvature ~ -1) means the boundary of the spacetime is repelling. Geodesics are great arcs, where a two dimensional version is the Poincare disk, or the Escher disks tessellated by stylized fish or bats vs birds, angels vs devils etc, which leave the boundary at high energy and return at near zero energy. A black hole placed in the spacetime is guaranteed to not hit the boundary. The equivalency between conformal fields and the boundary of the spacetime, and further the holographic principle on field theoretic information on the black hole horizon and the spacetime illustrates that information is preserved.

Information is then never really destroyed, where here we are referring to quantum information. Hence the entropy S = -k*ρln(ρ) is constant and the entanglements between EPR pairs or n-tuples is never destroyed. Such information might be hidden, such as if one particle in an EPR pair approaches a black hole, while the other particle remains at asymptopia, but the decoherence means entanglement phase has been lost. That entanglement phase is not destroyed, but in a manner similar to chaotic dynamics in classical physics, it has become distorted and folded into the environment in ways which are hard to dynamically predict. The domains of causality of the S-matrix for the two entangled states are not equivalent, and this results in the apparent loss of entanglement between the two states. It is also why Susskind says you will see an object, or its string-field theoretic content, suspended on the stretched horizon while at the same time the black hole will emit radiation from that string-field theoretic information (Hawking radiation) which burns up the fields on the stretched horizon. Working this problem out is one of the purposes of the sketch I wrote in my FQXI paper. The two domains of S-matrix causality for the two entangled states are related to each other by modular structure which ultimately preserves quantum information. This is also one basis for quantum error correction codes.

Cheers LC

Ray Munroe wrote on Oct. 16, 2009 @ 15:25 GMT
Dear Lawrence,

I think our ideas have significant compatibility, but I'm also studying your fundamental assumptions.

On page 2, you say "For the 26 dimensional bosonic string, two dimensions are vacuum tachyon modes and the remaining 24 dimensions define an SO(24) group." I think this is a good foundation for a theory. I think the two dimensions of vacuum tachyon modes could be Higgs. After all, the Minimal Supersymmetric Standard Model (MSSM) has two complex Higgs doublets (not 1 like the Standard Model). In my models, I usually equate rank with dimension. I haven't produced a mathematical proof of this, but if it is a reasonable assumption, then you may have a 24 dimensional SO(24)xSO(24). This gives enough theoretical framework for spin-up and spin-down, or maybe Supersymmetry. Furthermore, my 12 dimensional models aren't so wierd because an SO(24) could be 12 dimensional.

What do you think?

Ray Munroe

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Author Lawrence B Crowell wrote on Oct. 16, 2009 @ 18:56 GMT
The SO(24) comes from the three representations on the algebraic level 8 (+) 8 (+) 8 of the Jordan exceptional algebra, here (+) means “oplus.”. One of these gives the vector terms in the J^2(O) 2x2 matrix and the other are for the supersymmetric pairs θ θ-bar. So for elements in the vector portion there is the framing

Φ = v + ξ-bar θ + ξθ-bar + ξξ-bar F

of a superfield, for ξ the anticommuting Grassmannian.

This exercise is meant to build up to the Leech lattice which has F_4 automorphism as does the J^3(O). Then the Leech system can be decomposed into a pure N = 8 supergravity multiplet of 32 supersymmetries with a Bloch lattice like system as [E_8xE_8] x[H_4]^2. The H_4 stands for the 120/600 cells with Coxeter group H_4, [3,3,5] and Coxeer-Dynkin diagram *-5-*--*--* . SO(12) is a D_6 group which has the Dynkin diagram

*\

~~*--*--*--* Here the ~ means “space” since the editor does not like them.

*/

So how might we pull SO(12) from H_4? The H_4 emerge from E_8 in the Weyl group diag[H_4,H_4], where there are additional cyclic permutations of 8 letters. This is unless we get creative and do something like

*\

~~*--*--*--* + *-5-* =

*/

*\

~* --* + *-5-*--*--*

*/

which is almost a group theory “chemical reaction” on the algebraic level

so(12) (+) h_2 = so(8) (+) h_4

where h_2 is the algebra for the pentagonal group *-5-*.

In order to do this it requires a complete E_8 to construct this. So for this to work, where we have the above decomposition, I think we need to work in the domain of octo-octonions, or E_8-octonions. There is a whole lot of work to do before we get their. Yet this is not entirely impossible.

Cheers LC

Ray B Munroe wrote on Oct. 16, 2009 @ 19:25 GMT
Dear Lawrence,

I like E8's - they are beautiful and challenging. My fermion multiplet is basically an E8 transcribed inside of a K12'. I like octonions - I think they have the structure for a quantum gravity. I'm just not sure which front to attack first...

I also agree on the importance of H4 and G2. F4, D4 and H2 may play minor roles.

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Oct. 16, 2009 @ 23:17 GMT
E_8 is of course interesting, as the most complex of the ADE groups. There are of course the sporadic groups which stretch from the Mathieu _{24} group to the monster. There things get really crazy.

F_4 is the automorphism group of the Jordan matrix. G_2 is the automorphism of the octonions. The J^2(O) is the spin factor J^2(O) = O(+)R [(+) = oplus] and the J^3(O) is the extended spin factor

J^3(O) = J^2(O)(+)R = ([O(+)R](+)R.

There is then an interplay here between G_2 and F_4. The spin factor define light cone structure in 11 dimensions, and we can certainly consider physics where this is a local frame. A curved space analogue of this can be examined according to the transformation roles of F_4 and G_2, which reduces the complexity of the problem.

Cheers LC

Ray B Munroe wrote on Oct. 19, 2009 @ 18:51 GMT
Dear Lawrence,

I just read your new paper "Exceptional Black Holes" for the second time. Much of the content is in prior papers, but you did break out the 10-D transformation in more detail. I find it interesting that your J3(O) posses an SO(8) triality. Have you read my book? Section 7.2 has some potentially important SO(8) symmetries based on a simple FCC lattice.

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Oct. 19, 2009 @ 22:39 GMT
I am writing up more explicit results with this. I sent an early phase of this to you last week. The purpose is to compute a general Born-Infeld action from this, which is the cornerstone of M-theory.

Cheers LC

James Putnam wrote on Oct. 20, 2009 @ 00:37 GMT
Dear. Dr. Lawrence B Crowell,

The thrust of your essay depends upon the existence of, at the least, Black Holes. Before I evaluate and vote of this essay, can you please say something about the empirical evidence for the existence of Black Holes. I am not asking for a theoretical explanation. I want to know if there is empirical evidence that clearly distinguishes the existence of a black hole from an otherwise very massive object?

James

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Author Lawrence B Crowell wrote on Oct. 20, 2009 @ 01:29 GMT
I don't know how knowledgable you are on the subject. A sort of general source can of course be found at Wikipedia:

http://en.wikipedia.org/wiki/Black_holes

The main point of evidence lies with accretion disk and quasar jets which are observed. Black holes are the only known power source which can generate these enormously high energy events. Attempts with phenomenology of hyperstars and other putative sources have failed to theoretically work, nor do they satisfy observational data.

Another source is with the motion of stars near the center or the Milky Way galaxy. The UCLA astronomy dept has their research posted at the UCLA Galactic Center Group

http://www.astro.ucla.edu/~ghezgroup/gc/

The animation of stars is from data taken by tracking the motion of galactic center stars about nothing visible, but yet based on basic calculations must be around 10 million solar masses.

My paper really discusses quantum black holes more than large astrophysical black holes. Yet quantum black holes should also exist, and amplitude signatures for them have appeared in RHIC data.

http://arxiv.org/abs/0805.3579

Yet it has to be admitted that as yet the data is not solid or conclusive.

Cheers LC

James Putnam wrote on Oct. 20, 2009 @ 02:22 GMT
Dr. Crowell,

Thank you for your quick response. In rereading my message just now, I think I should make it clear that my rating does not depend upon what I think about your answers. I have no intention of giving someone with your skills a poor rating. I have high respect for your knowledge. It is the case that, because of my own work which is not nearly as sophisticated as yours, I do not believe in Black Holes. I think perhaps I was not as specific as I needed to be when asking my question. I will rephrase it: Is there empirical evidence that distinguishes between equal masses one of a Newtonian view and one of an Einsteinian view? I am phrasing it this way because you responded by referring to a 'power source'. In other words, is there empirical evidence that can distinguish between two power sources of equal mass, one of which is Newtonian and one of which is Einsteinian?

James

James

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Author Lawrence B Crowell wrote on Oct. 20, 2009 @ 13:12 GMT
I am not sure if you disbelief in black holes is due to a rejection of relativity and general relativity, or if it is due to your opinion that matter should prevent the complete implosion of stuff into a black hole.

Newtonian mechanics, without relativity, indicates that the energy of a system is given by

E = (1/2)mv^2 – GMm/r,

A body dropped from infinity with E = 0 will reach different radii from the center with velocity v^2 = 2GM/r, or equivalently that velocity is reached once the particle reaches a radius r = 2GM/v^2. So it does not take much to set v = c, the speed of light, to get r = 2GM/c^2, which is the same horizon result of general relativity for the Schwarzschild solution. This is the Newtonian black hole, though it is a bit different from that of relativity. It differs from the general relativity result in that if I send a particle towards the gravity field with E > 0 or E < 0 I can adjust the radius at which it reaches a velocity v, which includes v = c. Relativity requires that the speed of light is an invariant of the universe, so that no observer can exist on a frame where electromagnetic radiation is observed traveling at a velocity different from c = 2.99e5km/sec (approximately).

The question might refer to whether there must exist a solid surface with some gravity fields identified as black holes. There are two reasons to think it is highly unlikely this can be the case. The first reason is that bodies with a solid surface interact with in-falling material with a “slash.” The stuff crashes onto the surface and there are distinct signatures for that. This is found with neutron stars and white dwarf stars. Objects identified as black holes lack this signature. The black hole at the galaxy center has been observed to tidally rip an orbiting star that gets close and rip material off of it. No splash was observed. Another reason to doubt the existence of a solid material surface is that even in the Newtonian case, where you predict a black hole of sorts, there are no known materials which can resist gravitational implosion or collapse at the radius near r = 2GM/c^2. Also for a solid surface at this radius the solid surface would have to be made of material which can resist collapse by permitting sound or pressure waves to travel through it at velocity v > c. This is not permitted within the context of relativity theory.

It must be understood of course that in science we never really prove things, but only support theories and their predictions with a body of evidence. So in some sense we have not proven that black holes exist. It is however the case that astronomic evidence presents growing support for the existence of black holes.

Cheers LC

James Putnam wrote on Oct. 20, 2009 @ 15:25 GMT
Dr. Lawrence B Crowell,

Thank you for that response. It is helping me reform my question. With regard to what I think about relativity theory: No I don't accept it as real. Even the proofs put forward appear to me to miss their mark. Its not my own opinion that I am trying to get at. However, the definition of a black hole does rely upon relativity theory. It is that distinction that I wish to isolate and question.

I have no question with regard to what happens physically to matter when it is that dense. You wrote about strings, their curvature of spacetime, and the effects upon them when they reach a black hole. Speaking about space and time, it seems to me that those are the properties that relativity theory uses to establish when a black hole forms. You gave a helpful response in your last message; however, you did not refer directly to space or time.

It seems to me that determining whether or not the super massive object is a black hole depends upon some evidence that includes effects upon space and time. I wanted to avoid taking your time by discussing relativity theory in general. I also was hoping to avoid an answer of the type: Time is relative or GPS work not work. That kind of answer appears to me to miss its mark. So, when I asked if there was empirical evidence to distinguish a black hole from an equally massive object of matter, I was wondering if there is any evidence that can be put forward that does not depend upon a prior belief in relativity theory. For example: If a traveler, who knew nothing about Einstein's theory, came upon a black hole, is there anything empirically known about black holes that would help him to determine that something extroardinary has happened to space and time.

I'm sorry, but I don't feel that I am succeeding in making my point. I think it sounds as if I am asking for more explanations about the details of relativity theory and the standard proofs put forward in defense of it. I am not. I am asking about empirical knowledge that clarifies the existence of a black hole without referring back to relativity theory itself. If you believe that I am lacking the understanding necessary to appreciate the reality of black holes, you can say so without offending me. There is no need to write a lengthy lesson type response. I think I have taken enough of your time on this question. I appreciate the responses you gave.

James

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Ray Munroe wrote on Oct. 20, 2009 @ 16:58 GMT
Dear James,

I used to work with NASA, and later taught College-level Astronomy. I understand that many people don't believe in Black Holes.

The concept of a Black Hole does not require General Relativity. It only requires that we can define a speed of light, c, and an

escape velocity, and that we can determine a mass and radius such that the escape velocity is greater than c.

Black Holes are a strange phenomena in that their properties make them impossible to directly observe. We infer the existance of Black Holes based on indirect observations such as the rotation speeds of stars near a galactic center. If a star is orbiting the center of a galaxy at a much faster speed than what we expect from counting bright stars within its orbit, then we know there is invisible mass present. Is this Dark Matter or a Black Hole? The normal assumption is that Black Holes exist at galactic centers. You may want to check out these

NASA

If String theory/ M-theory is correct, we should expect strings to be distorted by intense gravitational fields, and follow these gravitational field lines. If a Black Hole is a quantum phenomena, we might expect an abrupt quantum break in these strings, and thus closed string loops become open strings. If a Black Hole is a non-quantum event, then we should expect these field lines to asymptotically approach infinity as an infinite collection of parallel (but never quite touching) lines.

Have Fun!

Dr. Cosmic Ray

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Author Lawrence B Crowell wrote on Oct. 20, 2009 @ 17:40 GMT
I have to say that relativity theory has been confirmed to extraordinary levels. Special relativity is well understood and more used than researched. The patching together of local regions of space that are flat enough for special relativity is what gives general relativity. General relativity has also passed all the experimental tests put to it. The last test was the Gravity Probe B, which was sent to detect the frame dragging effects of a rotating gravitating body. The rotation drags space around with it. The Gravity Probe B is documented in:

http://en.wikipedia.org/wiki/Gravity_Probe_B

The data analysis is ongoing, due to the fact the measurement was of a very small effect due to the small curvatures induced by Earth's weak gravity field. Another test is the Rebka-Pound experiment which demonstrated Doppler shift of light be gravity, as predicted by general relativity. The Taylor-Hulst observation of two neutron stars in a mutual orbit indicated how the orbit is decaying at a rate exactly predicted by the general relativistic emission of gravity waves.

So relativity is pretty well substantiated. Virtually everybody in physics accepts it as the realistic theory of spacetime and gravitation. The matter is not hotly disputed. So I can only leave the relativity issue at this point. It is a bit like Darwinian evolution. Again scientists regard it as the unifying theory for the relatedness and structure of life. Yet there are those who adamantly call it a falsehood in favor of creationist ideas.

When it comes to black holes and the direct detection of spacetime curvature near them, the data is somewhat sparse. There are Doppler shift measurements on radiation emitted by accretion disks around black holes, which conform to a general relativistic understanding of gravity. The problem is that telescope resolution is not sufficient at this time to image the region right around the black hole. There are some "super-scopes" in the works which might be able to do just this. The optical characteristics of spacetime around the galactic black hole at the Milky Way center might be directly observed. It will take another 15 years for that data to come forth.

I will say that I wonder why it is that people with an interest in science will end up rejecting some of its central pillars. Yet there are those who elect to do this. I can only suggest that you do some of the reading and research required on basic relativity. General relativity is of course incomplete, and that problably occurs with quantum physics of black holes or maybe with the very large scale structure of the universe. Yet to be honest if you reject relativity in favor of a purely Newtonian idea of things then you will simply fail to understand things properly.

Cheers LC

James Putnam wrote on Oct. 20, 2009 @ 18:00 GMT
Dr. Cosmic Ray,

Thank you for your response. So may I conclude that when NASA reports finding black holes that they are not offering them as evidence of General Relativity. It may or may not be interpreted that way depending upon the belief system of the scientist? I have found that it is very difficult to discuss black holes without getting into debates about the correctness of relativity theory. I would like to think that black holes are being evaluated without the prejudice of existing theory. They may teach us a great deal if we allow the door to open.

James

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James Putnam wrote on Oct. 20, 2009 @ 18:18 GMT
Dr. Lawrence B Crowell,

Thank you your response. Quoting you:

"Yet to be honest if you reject relativity in favor of a purely Newtonian idea of things then you will simply fail to understand things properly."

I do not agree that relativity theory has been confirmed. I do agree that it has been mathematically designed to fit empirical evidence. Relativity theory is not the only way to mathematically model that empirical evidence. Newton's work did need some refinement. Rejecting relativity theory actually results in new equations that also accurately model empirical evidence and that return us to a universe of three spatial dimensions and the independence of time. I will leave this subject alone now. I just was interested in what you had to say in support of your essay. I'll leave my opinions for my forum. Thank you for your time.

James

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Ray Munroe wrote on Oct. 20, 2009 @ 18:28 GMT
Dear James,

The original concept of a "Black Hole" was conceived by John Michell in 1783 - way before Einstein, although the terminology Black Hole was coined by John Archibald Wheeler.

The only "problem" I personally have with General Relativity is that it is not Quantum General Relativity. But Lawrence is talking about Quantum Black Holes, and Lawrence and I are both interested in String Theory/ quantum gravity applications. Even though my essay dropped out of the top 16 last night, I still have hope for a unified theory.

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Oct. 20, 2009 @ 18:37 GMT
Certainly special relativity works. The time delay of muon decay was an early measurement of this. Particles which are acclerated to enormous energy would surpass the speed of light by a thousand fold if the world were completely Newtonian with Galilean transformation properties.

Cheers LC

James Putnam wrote on Oct. 20, 2009 @ 19:10 GMT
Dr. Lawrence B Crowell,

I didn't say that relativity theory did not work. I said that I do not agree that it has been confirmed. The equations that replace those of relativity theory do not accelerate particles passed the speed of light. Newton's work did need to be refined to take into account the properties of light. That refinement does not lead to relativity theory unless the theorist makes it happen that way as Einstein did. I understand that relativity theory is a successful pillar of today's theoretical physics. I understand why it would be believed. I just happen to think that throughout the development of physics theory decisions had to be made. I think that each of those decisions should be challenged for the purpose of rooting out misdirections. I find that pursuit rewarding. I do not insist that others should agree with me.

James

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Author Lawrence B Crowell wrote on Oct. 20, 2009 @ 20:19 GMT
I would suspect that if you patch worked Newtonian mechanics in a way to make it fit with data which supports special relativity that you would end up in fact with special relativity --- of sorts. As for general relativity and gravitation, that might be harder or problematic.

Science never proves theories. All that science does is to measure and observe things in nature to determine if these are consistent with the implications or predictions of a certain theory. So theories are falsifiable, and a bad theory is falified right away if it has no domain of prediction. A good theory might also be falisified if it begins to fail outside some domain of observation where it really applies. This in fact happened with Newtonian physics. It began to fail to account for physically observed phenomenon. On a small scale it was supplanted by quantum mechanics and for large velocities and large gravity fields it was replaced with general relativity. General relativity is likely to be incomplete when quantum physics enters the picture. This is the problem of quantum gravity.

I will just say that special relativity states that in order for the speed of light to be an invariant, or is always measured to be the same in all frames of reference, that space and time must transform into each other. Just as the x and y coordinates in ordinary space transform into x' and y' under a rotation, it turns out that time and spatial variables also transform into each other in this more general setting. This is why you get some of the odd results of relativity, such as time dilation. This "rule" is extended for gravitation where spacetime curvature is on a small region sufficiently flat that special relativity holds. The curved spacetime then results by patching together these flat region, with connection coefficients and a calculus limit. This part gets a bit abstract and requires Riemannian geometry to address.

Cheers LC

James Putnam wrote on Oct. 20, 2009 @ 22:06 GMT
Dr. Lawrence B Crowell,

Quoting you:

"I would suspect that if you patch worked Newtonian mechanics in a way to make it fit with data which supports special relativity that you would end up in fact with special relativity --- of sorts. As for general relativity and gravitation, that might be harder or problematic."

Why would you use the word patchwork? I presume you are intent...

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Author Lawrence B Crowell wrote on Oct. 21, 2009 @ 00:31 GMT
James Putnam wrote, "No one has ever conducted an experiment on time."

Of course we perform experiments on time. Atomic clocks at different floor levels at NIST will measure different time intervals due to gravitational time dilation. You mentioned GPS and relativity. That was something I worked on for a while in connection with Lageos. Again time synchorization involves experiments with time and applies general relativity. These count as experiments in time because clocks measure time.

Experiments don't prove theories, but they will confirm the predictions of a theory and support it with a preponderance of evidence.

I suppose the problem is that if you are adamant in rejecting special relativity then things are at an impass. Some years ago I ended up having a web argument with someone who ardently upheld geocentrism --- the Earth is the center of the universe or solar system. Of course this individual rejects virtually all of physics since Copernicus, Galileo and Kepler. You don't go that far back in time, but you are rejecting something which is pretty canonical in physics. You are not likely to get many physicists to agree with you on this, but I suppose you are not likely to be pursuaded by physicist either.

Cheers LC

James Putnam wrote on Oct. 21, 2009 @ 02:42 GMT
Dr. Lawrence B Crowell,

"Of course we perform experiments on time. Atomic clocks at different floor levels at NIST will measure different time intervals due to gravitational time dilation. You mentioned GPS and relativity. That was something I worked on for a while in connection with Lageos. Again time synchorization involves experiments with time and applies general relativity. These count...

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Author Lawrence B Crowell wrote on Oct. 21, 2009 @ 14:00 GMT
Saying a measurement of time intervals is not of time but in time can be applied to everything in a sense. A ruler could be argued to not measure units of spatial distance but units of distance in space. The same can be applied to any measurement. It can well enough be said we don’t measure electric charge, or an electric field, but rather motion in putative ideas of such. There are those inclined to the philosophy of science who get tied into knots over these things. I tend to avoid these matters honestly for I think they lead nowhere.

It can be said that in special relativity everything is moving at the speed of light. Even if you are sitting still relative to a frame on Earth you are moving at the speed of light. You are moving along a fourth dimension at the speed of light, with x_4 = ct, where t is time of course and c the speed of light. Now if a particle is moving along some spatial direction with respect to some frame this distance becomes a general distance or interval

s^2 = (ct)^2 – x^2 – y^2 – z^2

At the coordinate origin with x = y = z = 0 the distance is s = ct. If the particle is moving along x = vt then this gives

s^2 = (ct)^2 – (vt)^2 = (c^2 – v^2)t^2

= c^2(1 – (v/c)^2)t^2.

We instantly have the time dilation result! That is all there really is to all of this. Of course a more general frame transformation is really needed, but this will suffice.

I can understand being skeptical of string theory or membranes. Extra dimensions are pretty canonical, for it is well enough understood since the work of Hermann Weyl back in the 1930s that a gauge potential is something which defines a transformation on an internal bundle of vector spaces. In the case of electromagnetism this internal space is a circle. So that does give, at least in a model perspective, an internal extra dimension.

At any rate, relativity theory (particularly special relativity) is well buttressed by experimental evidence. The situation is much the same for biological evolution, yet clearly there are millions how reject that science. Of course there are some theological issues involved with this rejection. Yet anyone familiar with the scientific community knows that biology is effectively unified through evolution. Much the same occurs with relativity theory. I am aware there are people out there who think it is all wrong and the like. Yet frankly I think they have just removed themselves from the intellectual process.

Cheers LC

James Putnam wrote on Oct. 21, 2009 @ 16:19 GMT
Dr. Lawrence B Crowell,

I will have to return and write a second message in response to time dilation. Here are some quick thoughts about your last paragraph:

"At any rate, relativity theory (particularly special relativity) is well buttressed by experimental evidence."

Yes it is.

"The situation is much the same for biological evolution, yet clearly there are millions how reject that science. Of course there are some theological issues involved with this rejection. Yet anyone familiar with the scientific community knows that biology is effectively unified through evolution."

I think it depends upon the speakers's meaning. If the meaning is that no form of intelligence potential or existing, simple or complex was involved in inanimate matter combining together to become highly intelligent life, then I think the speaker as a lot of work to do to explain how that is possible. That state of affairs is not a given, it is not an intellectually defendable position, regardless of the determination of the speaker to insist that it is.

"Much the same occurs with relativity theory. I am aware there are people out there who think it is all wrong and the like. Yet frankly I think they have just removed themselves from the intellectual process."

I understand the strength of your commitment to relativity theory. However, relativity theory is not the standard for intellectual analysis and inquiry. I say that it is the prudent scientific and intelligent thing to do to challenge it and any other theoretical invention that is forced onto the otherwise clean equations that model the patterns observed in empirical evidence.

James

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Author Lawrence B Crowell wrote on Oct. 21, 2009 @ 17:05 GMT
There are two issues here with evolution. Biological evolution is the theory on the relatedness of species. The question of how life came about to start is an open question at this time, and is not germane to biological evolution. An understanding of how life came about involves issues of self-organizing chemistry and the conditions required for that. At this time we are largely ignorant about this problem.

When it comes to intelligence, this appears to refer to intelligent design (ID). Darwin made reference to the problem of irreducible complexity (IC), though he did not call it that. IC is the cornerstone idea to ID. If something is found which absolutely is not reducibly complex then the theory of evolution is falsified. So IC is a statement on the falsifiability of a theory. So far none of the structures proposed to be IC, flagellum, eyes etc, have been demonstrated to be irreducibly complex. A statement on the falsifiability of a theory is not a theory itself. In fact IC can't ever be itself falsified. It can be demonstrated to be false for specific examples, but it can't in general be shown to be false. A scientific theory is by definition falsifiable, so IC fails to serve as a scientific theory.

Again, when it comes to the origin of life, or how self-organizing biochemistry emerged, that is an open question. What ever processes were involved have been either destroyed or seriously buried away. So as yet that is an open question. Maybe evidence for this exists on Mars or the other planetary bodies. Only the future will tell.

Cheers LC

James Putnam wrote on Oct. 21, 2009 @ 17:41 GMT
Dr. Lawrence B Crowell,

Lets see how this flies:

Well I don't think I am moving at the speed of light in a fourth dimension. I will wait for empirical confirmation of that idea. However, the equation you give can be formed without using that approach. And, the time dilation equation follows from it. There is one challenge to the interpretation of that equation that I can maybe adequately make in this forum setting. So, here it is:

The time dilation equation is actually the t dilation equation. The t in physics equations is a measure in time (some duration of some physical activity) and not of time (as in a testable property in itself). All activity is measured with respect to a standard of activity. That standard can be chosen by virtue of its exhibiting as stable as practical cyclic activity. For example, if one wished to measure the rate of cyclic activity A, one would compare it to the standard for cyclic activity. Both of these cyclic activities are material in nature and are therefore subject to effects brought upon them by other material objects. In other words, they both are variable.

We use the name seconds for the unit of measurement in physics equations: however, in the most fundamental sense, the units of t should be referred to as cycles of the standard chosen. So, by measuring cyclic activity A against the standard cyclic activity B, The true fundamental form of the units for both of them is (#cyclesA)/(cycleB). The property of time is no more affected by this action than it is by the hands of my watch. All activity requires time to occur. The time taken is a duration in time simply because time is passing during the activity. Time itself is not a physcial property that can be sliced up, contained, or molded into a new form.

James

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Jonathan J. Dickau wrote on Oct. 21, 2009 @ 20:48 GMT
Hello Lawrence,

I just finished reading your essay from Exceptional Nature to the end, having digested the set-up before. It was remarkably lucid, considering how complex some of the Math is, and how greatly your skills with it exceed my level of sophistication. It seems that quantum criticality, resulting from the graphene-like behavior on the M2 brane, is the crucial point to understand.

I like the way this results in fractal-like scaling of cosmic structures. That's pretty neat. From what I can grasp, it's almost like the quantum phase transitions are occurring on a 2-d sheet. I agree there are congruent connections to pursue which unite the Stringy and Braney theories with LQG. It may indeed be a matter of how we deal with the duality of an 8-dimensional (Octonion) framework with the lower dimensional (2 + 1) space.

In Causal Dynamical Triangulation, their basic building block is the 4-simplex, and they do a Monte Carlo simulation where timelike edges of adjoining blocks must line up, which is what makes it causal. They find it describes a universe that is 2-d near the Planck scale - that evolves through fractional dimensions to become 4-d spacetime for macroscopic volumes. I have wondered, since reading about this and after seeing the paper by Baez and Barret on the 10-j symbols, if perhaps what needed to be considered is how we deal with defining basic concepts like dimensionality and orthogonality.

People doing Loop Quantum Gravity like the idea of a universe that's 2-d near the Planck scale, but String Theory people like 10 dimensions to play with. Well; if our humble 4-simplex can be flattened into 2-d (yielding a 5-pointed star in pentagon representation) or unfolded into a 4-d object, that's pretty neat. But if the granularity of space is 2-d near the Planck scale, and the 10 faces of the simplex are viewed as mutually independent projected directions in space (i.e. - by re-defining orthogonality near the Planck Scale), there is perhaps another road to exploring the duality between the spaces in which LQG and String Theory operate.

In any case, I enjoyed your paper. It seems likely the quark-gluon plasmas at RHIC have generated some quantum black holes already, although the results appear inconclusive. It will be interesting to see whether future experiments confirm your expectations of what we will find inside a black hole. It is likely that the mini ones we observe in the lab will yield more information than cosmic ones, but we'll have to see.

All the Best,

Jonathan

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James Putnam wrote on Oct. 21, 2009 @ 22:02 GMT
Dr. Lawrence B Crowell,

"When it comes to intelligence, this appears to refer to intelligent design (ID). Darwin made reference to the problem of irreducible complexity (IC), though he did not call it that. IC is the cornerstone idea to ID. If something is found which absolutely is not reducibly complex then the theory of evolution is falsified. So IC is a statement on the falsifiability of a theory. So far none of the structures proposed to be IC, flagellum, eyes etc, have been demonstrated to be irreducibly complex. A statement on the falsifiability of a theory is not a theory itself. In fact IC can't ever be itself falsified. It can be demonstrated to be false for specific examples, but it can't in general be shown to be false. A scientific theory is by definition falsifiable, so IC fails to serve as a scientific theory."

I do not argue from a creationist viewpoint. I do not agree with the IC viewpoint. I do not have a religion. What I do have is the understanding that dumbness cannot evolve into intelligence. Even Darwin stepped away from addressing this challenge. The properties offered to us by theoretical physicsts, in general, represent dumbness, purposelessness, toatally inanimate properties from which to construct this universe. This does not work out. The alternative is to look for the real properties, not yet known or admitted to, that can logically give rise to intelligent life. Call it intelligent design if you wish; however, this problem has nothing to do with the book of Genesis. It has to do with scientifically explaining the real universe.

James

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James Putnam wrote on Oct. 21, 2009 @ 22:50 GMT
Dr. Lawrence B Crowell,

"Biological evolution is the theory on the relatedness of species."

I should have addressed this. If this is all that biological evolution is, then it, I think, it remains at the level of the minor evolutionist. Darwin extended this concept to a general evolutionary process for all lifeforms by appealing to our imaginations. I remember reading his push for accepting this concept and experiencing a feeling similar to when religious groups try to win new converts. "I know that you too will come to believe if you allow yourself to be immersed over time in these ideas." Those aren't his words. I agree with his conclusion that all of life evolved. However, he didn't have enough empirical evidence available to prove his case. He had to rely on reason. However, he recognized where reason met its match.

I respect his decision to not speculate about the development of intelligence. I think today's concept of Evolution goes far beyond the relatedness of species. The modern view appears to me to be driven by a desire to find a way out of including intelligence in the evolution of the universe. If intelligence can be dismissed as a necessary property, then God is removed from consideration. Now, I don't know about God, but, I do know that modern evolutionary theory is often used for unscientific purposes.

I think the theory of evolution must address the evolution of intelligence or it remains, conceptually, much like the level that Darwin left it. I think if Darwin were still alive today he would be working as hard as he could to find the means to include the evolution of intelligence in coordination with the evolution of biological forms. Perhaps he would have believed that dumb mechanical type fundamental properties could evolve into highly intelligent life, but, I like to think that he would have chosen to move us forward toward learning the real story.

James

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Author Lawrence B Crowell wrote on Oct. 22, 2009 @ 00:15 GMT
James,

A cyclically occurring system is essentially a clock. We use clocks to measure time, or in an operational sense time is what a clock reads out. I am not going to get into philosophical hair splitting of measuring in time or of time. That is almost like homoousios versus homoiousious. Time in classical mechanics is a one dimensional space, or is modeled as such. The motion of particles is parameterized by this one dimensional space with some fiducial or initial time and condition. I agree that time is not something you can isolate in a chamber like molecules, but you can’t really do that with space either --- if you think about it. So in relativity theory the one dimensional time space is unified with the space of three dimensions according to a set of transformations or a symmetry.

Whether time, or for that matter space, are real in a standard sense. They can be thought of as purely model systems, which we perceive according to how matter and energy behave. The problems which faced physics in the late 19 th century were solved by doing this, and some of the consequences of relativity were confirmed. They have been consistently confirmed.

I could go on a whole lot about time, in particular with the different notions of quantum time and relativistic time. But my time right now is limited and I will spare that for later.

When it comes to evolution, the imposition of intelligence is not likely to ever fly in the biological community. The idea means there are elements of will or choice in the nature of life which is not identifiable in science.

Cheers LC

James Putnam wrote on Oct. 22, 2009 @ 00:23 GMT
Dr. Lawrence B Crowell,

I understand. Thank you for your time.

James

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Author Lawrence B Crowell wrote on Oct. 22, 2009 @ 01:23 GMT
Jonathan

Thanks for the good review. I did not break out fractal geometry in this, but it lurks in the wings. I indicate first what underlies this structure and then indicate how this leads to fractal geometry. I will get to loop variables and related systems at the end.

The underlying construction here involves the Leech lattice. The 27 dimensional Jordan exceptional algebra...

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Author Lawrence B Crowell wrote on Oct. 22, 2009 @ 03:10 GMT
James,

My sense is that you need to study some of these issues further. Some study of relativity is probably advised. Special relativity is 104 years old and general relativity is 91. The basic concepts there are essentially old hat really. In terms of age it is comparable to the maturity of Newtonian mechanics when Adams or Jefferson were President of the US. Relativity theory is pretty much old stuff these days.

Cheers LC

James Putnam wrote on Oct. 22, 2009 @ 03:44 GMT
Dr. Lawrence B Crowell,

I think you could have said something more responsive to my messages. If this message is supposed to make it clear that relativity theory is truth and any modern phycisist or any up-to-date scientifically inclined, well read, layman would understand this then so be it. I will continue to spend my time cleaning up the misdirections of the last 104 years. I will move on now. You are very generous with your time and knowledge, and, you are to be commended for this. Best of luck in the essay contest.

James

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Author Lawrence B Crowell wrote on Oct. 22, 2009 @ 13:11 GMT
Of course in science all we support theories as tentatively true, not absolutely true in the sense of mathematical proofs. This not only holds for relativity theory, but Newtonian mechanics as well. In relativity and Newtonian mechanics there are also clearly model structures, such as in Newtonian mechanics there are those radial lines of force or gravity field, which can be argued to be model structures. So I am not arguing that relativity is the absolute truth, but as a tentatively true physical system of understanding it works very well.

Cheers LC

Ray Munroe wrote on Oct. 25, 2009 @ 02:01 GMT
Dear Frank,

Have you explained the long-range attractive behavior of Gravity (I understand you have attractive and repulsive Gravity)? Have you unified the nuclear forces? Have you explained the origin of mass? Can you explain why we only observe 4 dimensions?

Lawrence's next paper contains ideas that may challenge Relativity as we know it. Lawrence and I are working on a TOE that follows much of the accepted mathematical formalism of Physics.

I've had an out-of-body experience and defied Gravity in a dream. I do believe in the power of the mind and soul. Perhaps dreams are an insight into the powers of the mind and soul. Even so, if we don't/ can't understand the full power of a dream/ mind/ soul, then using this as the basis for a TOE will be incomplete. As a simple example, if your mind doesn't comprehend the unseen nuclear forces (that we know must be real - the like-charged protons of an atomic nucleus would fly apart without the strong nuclear force to hold them together), then how can your soul or dreams incorporate these forces into a TOE and utilize the power of these forces?

I'm not asking you to stop working on your ideas. I'm sure you think you are on a fertile path, even though I think you're way off base. Maybe you'll accomplish your mission some day. I just think you are a little too pushy, and you need new material. Data and math would be good...

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Oct. 25, 2009 @ 21:25 GMT
Frank Martin DiMeglio wrote: Hi Lawrence. The following proves that sting theory is a waste of time.

Maybe sting theory is a bit more limited than string theory. I work on a number of problems. One of them involves the physics of insect flight. If you caught one of my early posts on my blog I related how I helped my son map out anthills. I have alsways found insects interesting --- they will outlast us by a billion years. So sting theory might refer to the physics of the flight of bees and wasps. If you do enough hands on work there you get stung a bit by the buggers. The physics of insect flight is rather tough, and I got into a while back when I heard again the phrase about how physics can't understand the flight of a bumblebee --- Rimsky Korsakov besides.

Cheers LC

Ray B Munroe wrote on Oct. 26, 2009 @ 15:05 GMT
Dear Lawrence and Frank,

I have plenty of ants, wasps and bees in my yard if you want to expand your studies of Sting Theory. Those insects thrive nearly year-round here in Florida. If you prefer to study String Theory, I'm sure we could find a ball of yarn.

Have Fun!

Ray Munroe

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Steve Dufourny wrote on Oct. 27, 2009 @ 11:59 GMT
Hello Lawrence ,Ray ,Frank,James ,all ,

It's well that ,you speak about the hymenoptera ,the ants ,the apis ,the vespas don't sting ,only if you aren't in harmony with them in your ecosystem.They are our friends these hymenopteras ,very interesting this sociability .I have selected several plants for the polinisation .They disaper our bees ,ants and others ,it's catastrophic really .Don't be afraid about their stings .But let's help them to re born .

Dear Ray ,I don't think what these insects are on the good road ,they disapear in Florida due to an add of chaotics systems and utilisations .(Phytopharma products ,insecticids ,fongicids ,foods for soil chemicals,more a decrease of the vegetal mass ,more an increase of towns ,more the consummation of their honney thus like (a+b)²=a²+2ab+b² ....thus conclusion ,it's time to act very very quickly .

They need helps these hymenopteras,but too ,the coleopteras,the odonates,the lipedopteras ,and many others friends .They are a part of the complemenatrity .

All is linked and the soil is the key with the multiplication of plants more the composting and the harmonisation .

Just a thought

Best Regards

Steve

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Author Lawrence B Crowell wrote on Oct. 29, 2009 @ 03:08 GMT
News flash: I kept saying these ideas of frequency dependencies, such as from LQG, on the speed of light were wrong. Well read ‘em and weep

http://www.nasa.gov/home/hqnews/2009/oct/HQ_09-254_Fermi
_anniversary.html

http://arxiv.org/ftp/arxiv/papers/0908/0908
.1832.pdf

String theory makes a nice prediction that the quantum foam which produces this effect is valanced or renormalized out from observable physics.

I have been having long hard arm wrestling sessions over this. This makes me absolutely giddy! Bye bye loop quantum gravity breaking of the Lorentz group at small scales — YIPEEE!!! There are litterally thousands of theory papers now which are worth less than toilet paper. God it feels good. :-)

This pretty much does rule out some quantum gravity theories. Various models of quantum gravity, except string/M theory , have spacetime broken into struts and links near the Planck scale. This results in the breaking of Lorentz symmetry (spacetime symmetry of relativity) at very short scales. These models include LQG and Dynamical Triangulated Causal Nets and so forth, have these features. The one alternative to string theory which fly through this problem is twistor theory, which in what I am working on with string/M-theory does emerge. These various models are going to have to be either seriously revised or scrapped.

Loop Quantum Gravity is not dead though. In fact I have been working, rather unsuccessfully to be honest, on how LQG could be a system of constraints which exist in a map from the string/M-theory AdS_5 spacetime to the physical (the real universe) de Sitter spacetime. String theory works on the anti-de Sitter spacetime, but that is not the universe. It maps to the de Sitter spacetime under a Wick rotation. A BTZ black hole on AdS spacetime makes this rotation-map difficult, but I think the BPS charge of that black hole maps to the LQG constraints on physical spacetime. This problem has proven to be abominably difficult though. But I think something like this has to happen. String/M-theory stuck forever in the AdS domain does not do as much good for understanding this universe.

Lawrence B. Crowell

Steve Dufourny wrote on Oct. 30, 2009 @ 17:37 GMT
Hello dear Lawrence ,

It's always a pleasure to read your explainations .This one is very well written and well thought .

Lawrence ,what do you think about Feynman diagrams ?

Regards

Steve

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Ray Munroe wrote on Nov. 1, 2009 @ 01:53 GMT
Dear Frank,

I am not your enemy. I agree that the Physics community does need paradigm changes. Admittedly, I also have a bias that one should give serious study to areas that one chooses to overthrow. Don't be surprised by that. I can assure you that there are many PhD physicists who would simply choose not to respond to your persistent and repetitive blogs. It is effort to counter a proposal.

I had the original idea for Quantum Statistical Grand Unification (QSGUT - in my book) in 1979 as a 20 year-old Senior in Physics at Florida State University. My friends told me that I should show the idea to Paul Dirac, who was an Emeritus Professor at FSU at the time. I chickened out. What if he took the idea? What if he laughed at the idea? For decades, only my closest friends ever got to see my "crazy" idea. One of my graduate school professors called it a "Nobel Effort", but wasn't interested in helping me finish it. I purposely studied the Standard Model and Renormalization in graduate school hoping to overthrow them one day. A funny thing happens when you study something that you once thought was mysterious. You understand its mysteries and how to apply them. Rather than trying to overthrow Renormalization (after all - it is weird to divide an infinite number by another infinite number to get a finite one), I used the Complementarity Principle to marry Renormalization with QSGUT and create Variable Coupling Theory.

The Standard Model (SM) is very ugly, but it works. Any unification must contain the SM as a subset. If you have unified Gravity and Electromagnetism, then your model must include Maxwell's Equations, General Relativity, and Quantum Electrodynamics as a minimum requirement. One would naturally expect many of the other theories and mysteries of the Universe to fall out somewhere along the way. I compare Unification (whether we call it GUT or TOE) to adding fractions by finding the Least Common Denominator:

$1/2+1/3+1/6=3/6+2/6+1/6=6/6=1$

and the apparently complicated becomes simple (but contains all of the components of the original idea).

If you want the Physics community to follow your idea, you will need better than what you have done thus far. Am I stuck in my own biases? Are people like Jonathan Dickau and James Putnam, who know some theory but are not as constrained with biases, more or less likely to overthrow the system than people like Lawrence and I, who have studied our individual fields and asked questions on the fringes? I don't have the answer. And believe it or not, I am cheering you on to a deeper understanding of your goal.

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Nov. 1, 2009 @ 13:16 GMT
I tend to get a little annoyed when ever people throw around the world “paradigm.” There has been a lot of heat generated over Thomas Kuhn’s “Scientific Revolutions” over the years. I of course read this many years ago, and I don’t think it is completely without merit, but it also puts too much emphasis on the social aspects of science. People who often throw around the idea they are “making a new paradigm,” often have little to back it up. Oldershaw is raising up the heat and entropy over his new paradigm on the article section “Tying up the universe with strings,” about the Andre Linde work, here on FQXI, but his actual physics is a bit low on content IMO.

There exists a range of scientific work according to its impact on our basic understanding. It is not as if there are these blockbuster paradigm shifts which occur every century or so which punctuates otherwise normal science. There is a range of importance to how discoveries and theoretical work changes our understanding of things. In physics there have been in the last several of decades a number of major developments, such as the standard model or the AdS/CFT correspondence. These might not rank with the size of Einstein’s relativity or the development of quantum mechanics. Further, quantum physics was developed by a number of physicists who for the most part did ground breaking work, but maybe not on the scale of Einstein’s relativity achievements. Then of course maybe the really great paradigm shifter was Newton, but of course there were a fair number of subsequent considerable developments in subsequent time, Lagrange, Euler, Gauss, Faraday, Carnot, Helmholtz, Hamilton, Maxwell, Boltzman, Gibbs, … , before the so called modern physics. We might then go back to Galileo, who really started the whole idea of physics

Cheers LC

Ray B Munroe wrote on Nov. 2, 2009 @ 14:09 GMT
Dear Lawrence,

I think this essay contest is experimental evidence for the existence of paradigms. As part of our core belief systems, you and I are open-minded to concepts such as Black Holes, Strings and GUT's/ TOE's. But we have also encountered people in this contest who have the opposite opinions as part of their core belief systems. We have both received many 1's with only a few negative comments. Did they dislike our math or our paradigms? It is natural to have biases. Many people have favorite sports teams, or favorite political parties. Some people purposely support the underdog. Some people even define themselves in terms of which "team" they support.

As I understand paradigm shifts, if a concept is finally proven or dis-proven, then the "losing team" acknowledges the fact and accepts the now dominant paradigm (that may have existed beforehand but did not dominate). We could consider Special Relativity a paradigm shift that solved the aether problem (that existed beforehand). But a paradigm shift can be more subtle. Often, the losing team never quits fighting, and you literally have to wait for an entire generation to die off before a paradigm shift is fully realized.

Love it or hate it - Biases are a part of science. And the situation is compounded by the fact that experiment hasn't caught up with theoretical speculation.

Have Fun!

Ray Munroe

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Lawrence B. Crowell wrote on Nov. 2, 2009 @ 19:04 GMT
I agree up to a point. However, I get a bit irritated when people start throwing around the idea of a paradigm shift, or that they have the paradigm shift. DiMeglio in bold type has declared on one of the FQXI general blog site he will "win the Nobel Prize." I suppose Jack Kevorkian can win the Nobel Prize in Physiology and Medicine as well.

Cheers LC

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Ray Munroe wrote on Nov. 3, 2009 @ 13:57 GMT
Dear Lawrence,

I think your G2 automorphism is related to the triality symmetry of E8, as I demonstrated in this article. Could your F4 automorphism be similarly related to the pentality symmetry of E8?

Have Fun!

Ray Munroe

this post has been edited by the forum administrator

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Lawrence B. Crowell wrote on Nov. 3, 2009 @ 21:14 GMT
Ray,

I guess I have to have some access to get this paper. I must confess I have to punt when it comes to the pentality. E_8 is a complex system on 2, 3, 5 and 6 fold symmetries. I will see what I can work up or research. The G_2 group is an holonomy on M^7 or S^7 constructed from a tangent 2-plane on C^5.

Frank,

I suppose I have to agree with Ray in many ways. The problem is that physicists don't cast about saying that "dreams are unification" and the like. This is not a particularly standard way to proceed. Theoretical physics involves some hard work and usually rather advanced mathematical work. The inner subjective experience of a person is not a good guide from which to argue scientific theories or facts.

Cheers LC

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Lawrence B. Crowell wrote on Nov. 3, 2009 @ 21:16 GMT
I hit a 6 and the above should read "... 2, 3, 5 and 8 fold symmetries."

LC

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Ray Munroe wrote on Nov. 3, 2009 @ 21:34 GMT
It was an accident, but 6=2x3 is applicable as well. Lisi and I are Facebook friends. At one point, he posted that he was working on a 6-fold symmetry.

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Frank Martin DiMeglio wrote on Nov. 4, 2009 @ 05:01 GMT
Lawrence,

Dreams are not an "inner subjective experience". You incorrectly assume that we all have the same "outer" experiences. ALL of our experiences (including those of dreams) are different Lawrence. That is quite obvious. Again, you lack the very basics regarding properly understanding what is the interactive nature of being, experience, space, and thought. The integrated extensiveness of being and experience go hand-in-hand. Your distinctions/objection of "inner" and "subjective" experience do not fly. Dreams do have a common and shared general structure.

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Author Lawrence B Crowell wrote on Nov. 4, 2009 @ 13:01 GMT
Frank Martin DiMeglio,

The problem is that nobody proceeds this way in science. We do not know what consciousness is exactly, and what its relationship is to the exterior world. For this reason I keep a firewall between questions of the physical universe and the murky world of conscious experience.

Cheers LC

Jonathan J. Dickau wrote on Nov. 4, 2009 @ 14:56 GMT
Hello again Lawrence,

I got back and read what's here, and I appreciate the detailed response to my comments. It's great to see the connections you enumerate spelled out, because while I knew those things were interrelated (with fractals 'waiting in the wings'), the details were kind of fuzzy - and your explanation provides much clarity. I must say that your love of Math and the enthusiasm of your sharing comes through quite clearly. It sounds like fun, coming from you, and I sense that you must have a lot of fun entertaining some of these ideas yourself. Your enjoyment is infectious!

I read about the Fermi results, cited above and on Ray Monroe's page, and I'm glad I found out now. I've also downloaded the expanded version (jordan dot pdf) of your paper, which I will be examining more fully for the complete picture of your theory. I shall be quite interested in understanding your quantum error correction procedure - as I am impressed with what you can derive thereby. It will be very interesting to see what further research will reveal about Black Hole interiors, and it's very cool to be able to speculate with such amazing detail. I hope the experiments bear out - in affirming some of your theorizing.

All the Best,

Jonathan

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Author Lawrence B Crowell wrote on Nov. 4, 2009 @ 21:20 GMT
I was looking at my Jordan paper a couple of weeks ago. I found I accidently copied in a paragraph twice.

I have done a whole lot of work on this. My essay paper is just a sketch. I have found an explicit representation for the quasi-particle states which result in the cosmological constant renormaliaation, and how they define p-branes and the rest. I honestly wish this essay contest had started in the fall and ended in January as it did last year. I would have a much superior product to offer.

This essay started with an idea I had about a string falling into a black hole along the two coordinate frames of observation: distantly removed and comoving with the string. I saw what appears to be correlations with electrons on graphene, and then wrapped that into my previous idea about quantum criticality.

Cheers LC

Franklin Potter wrote on Nov. 9, 2009 @ 23:56 GMT
Dear Lawrence,

(1) I want to thank you for your article in this contest and for commenting on mine at various intervals. Your perturbations have encouraged me to flesh out more details of my geometrical approach, although I have been waiting since 1992 for the b' quark to show before continuing with all the gory details, since I now have a gravitational lab experiment in process that requires much time.

(2) I wish that I had more to say about your sophisticated Lie group approach, but there is a good possibility that we will end up along the same road to the truth about Nature at the Planck scale.

(3) If the b' quark doesn't show itself at the LHC between 65 GeV and 80 GeV, then I'll know that I've been on the wrong road considering finite groups instead of Lie groups. I'll be disappointed, but I can adjust to however clever Nature proves to be. I simply want to know the truth!

Frank Potter

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Ray Munroe wrote on Nov. 10, 2009 @ 01:09 GMT
Dear Franklin,

It appears that you and Lawrence had some interesting conversations on your blog site. I apologize that I didn't read your paper sooner (there were so many, and your paper is so short).

I am not opposed to new generations. Certainly, we know that if new neutrinos exist, then they must be greater than half the Z mass. But we also know that neutrinos have mass, and this idea is not impossible.

I explored the possibility of five generations of matter in my book. The reason why I prefer five generations over four is that my Lie Algebras have pentality, not tetrality, symmetries. If "E14" (K14?) is the 14-dimensional TOE, then it would have 5 generations of matter. This was not my preferred model. K12' was my favorite model, but the two models may be related.

Have Fun!

Ray Munroe

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Author Lawrence B Crowell wrote on Nov. 10, 2009 @ 04:32 GMT
Franklin Potter has some interesting ideas about discrete systems and Jacobi theta functions, or j-functions. I am less clear about his idea of a pure discrete symmetry for a fourth generation of quarks, but then again ... experiment will tell.

Cheers LC

James Putnam wrote on Nov. 10, 2009 @ 17:05 GMT
Dr. Crowell,

Quoting you from Muiguzzi's forum:

'...Of course I came in at a 3.4 or so, so I did not enter the winner circle. ...'

If I read the rules correctly, I am not certain what to expect. They take the top 30 satisfying a minimum number of ratings. If the minimum is 20 ratings then many of us drop out. Its possible you might make it by tying with a few others. They will take ten of so more for their own reasons. Then it is up to the judges.

'...I can't remember what score I gave yours, which was a month ago or so. ...'

It wouldn't have mattered if I knew you gave me a one. I can see why some would rate me that low. I still would have rated yours high. I don't judge others by whether or not they agree with me. Your essay was clearly representative of advanced modern theory looking toward the future. Good luck. The results aren't in yet.

James

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Lawrence B. Crowell wrote on Nov. 10, 2009 @ 18:08 GMT
I didn't rate your essay a one. I can't remember what I did give it though. I doubt I will win anything though. My essay is really a sort of sketch of something I had started to work on about a month before. So I will have to admit it does not have the sort of integral unity that some other essays have.

Cheers LC

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Author Frank Martin DiMeglio wrote on Dec. 5, 2009 @ 18:44 GMT
Hi Lawrence. Think of how genius, dreams, memory, and art are possible. Now think of this in keeping with this enormously important fact:

The ability of thought to describe OR reconfigure sense is ultimately dependent upon the extent to which thought is similar to sense.

Emotion, thought, feeling, and sensory experience are all fundamentally interactive Lawrence. Dreams add to (or improve upon) what is the integrated extensiveness of being, experience, and thought. Dreams conceptually/actually unify gravity and electromagnetism/light. It is that simple.

Note the transparent space/sky around the larger and red [setting] sun.

(Telescopic/astronomical observations make the object larger, or they could not be seen at all.) Importantly, isn't the increased transparency/invisibility of space, in relation to the blackness of night/outer space, the requirement of seeing farther?

Of huge importance, isn't the increasing transparency/invisibility of space the reason for the redshift?

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Frank Martin DiMeglio wrote on Dec. 5, 2009 @ 19:03 GMT
Hello again Lawrence. Kindly consider the folliwing addition to my prior post:

Think of how genius, dreams, memory, and art are possible. Now think of this in keeping with this enormously important fact:

The ability of thought to describe OR reconfigure sense is ultimately dependent upon the extent to which thought is similar to sense.

Emotion, thought, feeling, and sensory experience are all fundamentally interactive. Dreams add to (or improve upon) what is the integrated extensiveness of being, experience, and thought. Dreams conceptually/actually unify gravity and electromagnetism/light. It is that simple.

Note the transparent space/sky around the larger and red [setting] sun.

(Telescopic/astronomical observations make the objects larger, or they could not be seen at all.) Importantly, isn't the increased transparency/invisibility of space, in relation to the blackness of night/outer space, the requirement of seeing farther?

LARGER OBJECTS, IN A RELATIVELY SMALLER SPACE -- COMPARABLE TO THE EARTH -- WOULD HAVE HIGHER GRAVITY, WOULD THEY NOT -- CONSIDERING THAT THE INVISIBILITY/TRANSPARENCY OF [THE SPACE] IS INCREASED?

Of huge importance, isn't the increasing transparency/invisibility of space the reason for the redshift?

How would your essay account for this?

FQXi -- DO NOT DELETE THIS POST.

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Frank Martin DiMeglio wrote on Dec. 5, 2009 @ 20:04 GMT
Hi Lawrence, and how would your essay ideas account for this?

Do you not agree that telescopic/astronomical observations are "activating" -- similar to dreams -- what would otherwise be the waking/ordinary visual experience of the stars?

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Frank Martin DiMeglio wrote on Dec. 26, 2009 @ 22:18 GMT

This goes to the core of cosmology, physics, gravity, thought, and electromagnetism/light. My essay (and essay page) discusses this further.

Thanks. Have a nice day. Frank

The increased invisibility/transparency of space is a requirement of these astronomical/telescopic observations. Importantly, there is a "telescoping"/narrowing of vision in dreams too. (Dreams make thought more like sensory experience in general, including gravity and electromagnetism/light.)Astronomical/telescopic observations have significant similarities with dream vision. Dream vision is constantly active/shifting/variable. Similarly, telescopic/astronomical observations are "activating " what would otherwise be the [basically] unmoving stars at night (as seen by the unaided eye). Astronomical/telescopic observations are interactive creations of thought to a significant extent. Red borders black and transparent. Supernovas and the red sun both only last so long, as well. Witness the clear space around the red [larger] setting sun. Telescopes are known to function as a sort of "big eye". Note the clear and black parts of the eye. Astronomical/telescopic observations make objects larger, or they could not be seen. Yet they are in a smaller space, and dreams are in/involve a smaller space. The earth may also be considered to be in a smaller (and transparent) space. THINK! Dreams involve how a larger space is made smaller, and also how a smaller space is made larger.

FQXi -- stop delecting my posts.

Essay Author Frank Martin DiMeglio

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