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There have been some developments along these lines which may give support for my thesis here. The paper Black Holes: Complementarity or Firewalls? by Almheiri, Marolf, Polchinski, Sully raises an important point. This points out an inconsistency with the holographic principle. They focus on the suggestion that postulate #2; Outside the stretched horizon of a massive black hole, physics can...

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There have been some developments along these lines which may give support for my thesis here. The paper Black Holes: Complementarity or Firewalls? by Almheiri, Marolf, Polchinski, Sully raises an important point. This points out an inconsistency with the holographic principle. They focus on the suggestion that postulate #2; Outside the stretched horizon of a massive black hole, physics can be described to good approximation by a set of semi-classical field equations, is to be "relaxed." I take it that this relaxation focuses on the issue of "massive" as the mass approaches around 10^3 to 10^4 Planck units of mass. This still makes the black hole massive when compared to the masses of elementary particles.

In discussions with Stoica on singularities I suggested the following metric with 1 – 2m/r = e^u. so then

ds^2 = e^udt^2 – e^{-u)dr^2 + dΩ^2.

We now have to get dr from

dr = -2me^u/(1 – e^u)^2du.

Now the metric is

ds^2 = e^udt^2 + -2m[e^u/(1 – e^u)^4]du^2 + dΩ^2.

The singularity is at u = ∞, where the dt term blows up, and the horizon coordinate singularity at u = 0 is obvious in the du term. My rational was that the singularity had been removed “to infinity” in these coordinates. This makes the black hole metric similar to the Rindler wedge coordinates, which does not contain a singularity. In the accelerated frame or Rindler wedge there is singularity. The treatment of the Schwarzschild metric in the near horizon approximation Susskind uses is one where the singularity is sufficiently removed so that field in the Rindler wedge may be continued across the horizon without concerns. In this metric of mine the singularity is at infinity so the analytic functions for fields in the Rindler wedge are replaced with meremorphic functions with a pole at infinity.

Stoica made the observation that this runs into trouble with Hawking radiation. The singularity at infinity causes trouble with the end point of the radiance process for it has to "move in" from infinity. The final quantum process of a black hole is a problem not well known in any coordinates. Your objection does have a certain classical logic to it. However, by the time the black hole is down to its last 10^4 or 10^3 Planck mass units the black hole itself is probably quantum mechanical. In my coordinates (assuming they are unique to me, which is not likely) the singularity at infinity may not have to “move” from infinity. There may be some nonlocal physics which causes its disappearance without having to move at all. This nonlocality is a correspondence between states interior to a black hole and those on the stretched horizon. The Susskind approach does not consider the interior, and he raises this as a question towards the end of his book "The Holographic Principle."

This nonlocaity would be a relaxation of the postulate #2. The issue of unitarity comes into play. If the theory is replaced with meremorphic functions, say analytic in a portion of the complex plane, then fundamentally quantum fields in curved spacetime or quantum gravity is not unitary but modular.

Unitarity is represented by a complex function e^{-iHt} and so forth, which is analytic. The loss of unitarity does not mean there is a complete loss of everything; in particular quantum information can still be conserved. A simple analytic function of this sort describes standard quantum physics. Gravity as we know is given by a hyperbolic group, such as SO(3, 1) ~ SL(2,C), where the latter has a map to SL(2,R)^2. The functions over these groups have posed difficulties for quantum gravity, for they are explicitly nonunitary. The trick of performing a Wick rotation on time or with τ = it is a way of recovering the compact groups we know in quantum physics.

It does turn out I think that we can think directly about quantum gravity by realizing that the SL(2,R) is related to a braid group with Z --- > B --- > PSL(2,Z), and that the braid group is contained in SL(2,R). Braid groups have correspondence with Yang-Baxter relations and quantum groups. The group SL(2,Z) is the linear fractional group, which is an elementary modular form. An elementary modular function is

f(z) = sum_{n=-∞}^{n=∞}c(n)e^{-2πi nz}

which in this case is a Fourier transform. In this case we are safely in the domain of standard QM and QFT. In general modular functions are meromorphic (analytic everywhere but infinity) and analytic condition is held on the upper half of the complex plane.

Of particular interest to me are the Eisenstein series of modular functions or forms. These define an integer partition function, which is an acceptable partition function or path integral for a stringy black hole. I include a graphic here illustrating an Eisenstein function. This has a certain self-similar structure to it, or what might be called an elementary form of a fractal. In this picture unitarity is replaced with modularity. In this more general setting the transformation do no promote a field through time by some operator, but that the operator simply computes the number of states or degrees of freedom in a way that is consistent. Unitarity is then a special case of this, which happens to fit into our standard ideas of causality.

The Eisenstein series describes a partition function or path integral for a black hole. The theory is not one of unitary evolution, but simply one of counting states or degrees of freedom on the horizon. In effect physics is more general than unitarity, where unitarity is a necessary condition to describe the semi-classical states in postulate #2.

Cheers LC

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The Britto, Cachazo, Feng, Witten (BCFW) recursion relationship is a way in which a complex scattering process can be decomposed into tree level diagrams. The picture attached describes the process

A set of gluon momenta entering a region (we set those leaving as the negative of entering as done in the STU symmetries) may be written as the sum of products of two diagrams. To start one...

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The Britto, Cachazo, Feng, Witten (BCFW) recursion relationship is a way in which a complex scattering process can be decomposed into tree level diagrams. The picture attached describes the process

A set of gluon momenta entering a region (we set those leaving as the negative of entering as done in the STU symmetries) may be written as the sum of products of two diagrams. To start one chooses two gluons, here the k and n lines bolded. The sum is over all cyclically ordered distributions of gluons on each sub-amplitude (one with k and the other with n mometa) and one sums further over the helicities of the internal gluon.

To formulate this requires the use of bispinors, or what are in effect twistors. BCFW recursion is a development in Witten’s “twistor revolution” in string theory. The momenta for a gluon, a null momenta as it is massless, is written as p_{aa’} = λ_aω_{a’}. This exterior product is a form of twistor, and the two spinors for the inner products (λ, λ’) = ε_{ab}λ^aλ^b, [ω, ω’] = ε_{a’b’}ω^{a’}ω^{b’}. (I use parentheses because carrot signs cause trouble with this blog) There is a notation convention that one spinor type has ( ) as an inner product and the other a [ ] inner product. This is the convention that has emerged and is here to stay. If we have two momenta p_{aa’} = λ_aω_{a’} and q_{aa’} = λ’_aω’_{a’} then

p•q = λ_aω_{a’}λ’_bω’_{b’}δ^a_b&#
948;^{a’}_{b’}

= = λ_aλ’_bω_{a’}ω’_{b’}δ^a_b&#
948;^{a’}_{b’}

= (1/2)ε^{ab}λ_aλ’_bε^{a’b’}ω_{
a’}ω’_{b’} = ½(λ, λ’)[ω, ω’]

A tree level amplitude A(1,2,…,n-1,n) of n cyclically ordered gluons. Each gluon has momenta p_i^{aa’} = λ_i^aω_i^{a’} corresponding to the two spinors. We pick out our two gluons of interest and define a momentum

p_k(z) = λ_k(ω_k - zω_n},

p_n(z) = (λ_n + zλ_k)ω_n

which are forms of the twistor equations. The momenta of the other gluons remain unchanged p_j(z) = p_j, for j =/= k or n. This theory involves then the transformations on the two elements of the bispinor as

ω_k --- > ω_k - zω_n

λ_n --- > λ_n + zλ_k.

Now examine the amplitude under this transformation

A(z) = A(p_1, p_2, …, p_{k-1}, p_k(z), … p_{n-1}, p_n(z)),

Now a complex function of z. This amplitude is on shell for all z and momenta are all conserved.

Breaking up the “blob” into these two parts is then equivalent to writing this amplitude as

A_k = sum_{ij}A_{j+1}(1/P_{ij}^2)A_{k – i+1}

The momentum flowing through a tree diagram is equal to the sum of external momenta. This sum in the propagator is the sum of momenta in adjacent external lines, where here the index j stands for k and n P_{ij}(z) = p_i(z) + …+ p_j(z) = sum j_j + p_k(z) + p_n(z). By the construction above it is clear this turns out to be independent of z. In the summation we let k lie within the range i,j and n in the range j+1 … .

The P_{ij}(z) = P_{ij} + z_kλ_n so the square is then P_{ij}^2(z) = P_{ij}^2 – z(λ_k|P_{ij}|ω_n], here evaluated on both pairs of spinors. Thus we have

1/P_{ij}^2(z) = 1/(P_{ij}^2 – z(λ_k|P_{ij}|ω_n]) =

(1/P_{ij}^2)(1/(1+z(λ_k|P_{ij}|ω_n])/P_{ij}^2)

or as

A(z) = sum_{ij}ρ_{ij}/(z – z_{ij}), for z_{ij} = z(λ_k|P_{ij}|ω_n]/P_{ij}^2

This then has simple poles at z = z_{ij} where the residues ρ_{ij} are evaluated with ∫A(z)dz/z. The residues correspond to internal lines which are placed on shell.

This then in general corresponds to the recursion relationship, where we set

A_k = sum_{ij}sum_hA^h_{j+1}(1/P_{ij}^2)A^{-h}_{k – i+1},

where now I have included the sum over helicity states. The recursion relationship is evident where the two terms in the numerator may be further decomposed. This procedure with P_{ij}(z) = P_{ij} + z_kλ_n evaluated at the pole reduces all off-shell processes in the “blob” on the left hand side of the diagram to an on-shell process in the evaluation of residues.

Cheers LC

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If locality and unitarity are not fundamental it means there is a huge reduction in the number of fundamental degrees of freedom in the universe. In fact if you read my paper referenced in my essay you see that the number of degrees of freedom on a brane are boost dependent, and are thus not fundamental. The huge number of elementary particles we observe in the universe are just the same type...

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If locality and unitarity are not fundamental it means there is a huge reduction in the number of fundamental degrees of freedom in the universe. In fact if you read my paper referenced in my essay you see that the number of degrees of freedom on a brane are boost dependent, and are thus not fundamental. The huge number of elementary particles we observe in the universe are just the same type of particle under multiple copies of emergent spacetime configuration variables This means there is fundamentally only one electron, one down quark, one Z particle, one Higgs particle, one photon and so forth. We observe any of these single particles under a huge number of “projections,” if you will, which are due to the emergence of configuration variables on a spatial manifold.

I think that quantum gravity is not unitary, but that it probably conserves quantum information. The issue I raised on your essay blog with coordinate change with the singularity removed to infinity connects with this. The quantum wave functions are not unitary, but with the appearance of a pole they are meromorphic. These functions are then more fundamentally modular functions, or modular forms, which operate on lattices. These lattices are E_8 or the Leech lattice Λ_{24}, which are quantum error correction codes.

I am not very happy with how this is turning out. First off I am not garnering the type of attention I would prefer to see. Secondly my essay is languishing at #46, where 10 to 15 of the essays ahead of mine are TOTLSHT. About an equal number I fail to see as better than mine. In fact the paper by Fischer that has been near the top is basically wrong; he uses a static matter solution (the TOV equation of state) for a dense star to prove that a collapsing body (not static mind you) does not form a singularity. Thirdly, since I had to re-edit my essay, due to the fact it went over a bit to page 10, it was later hosted but I was not given a voting code. My attempts to rectify this situation have failed.

In the near future I will try to rattle some people’s cages to see if I can get more attention, and maybe a few votes that buoy me upwards a bit. I have been rather busy and frankly a bit depressed about how this seems to be turning out.

Cheers LC

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Lawrence,

You wrote: "Einstein changed Newton's laws by adjusting the first and third laws, motivated by the locality of electromagnetic fields predicted by Maxwell's equations."

Einstein did not adjust anything - he just introduced two postulates the second of which was false. In 1887 the Michelson-Morley experiment had refuted the light postulate and had confirmed the variable...

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Lawrence,

You wrote: "Einstein changed Newton's laws by adjusting the first and third laws, motivated by the locality of electromagnetic fields predicted by Maxwell's equations."

Einstein did not adjust anything - he just introduced two postulates the second of which was false. In 1887 the Michelson-Morley experiment had refuted the light postulate and had confirmed the variable speed of light predicted by Newton's emission theory of light. It is time for you, Lawrence, to stop claiming that Banesh Hoffmann, John Norton and John Stachel are wrong:

http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoff
mann/dp/0486406768

"Relativity and Its Roots" By Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

http://www.aip.org/history/einstein/essay-einstein-re
lativity.htm

John Stachel: "An emission theory is perfectly compatible with the relativity principle. Thus, the M-M experiment presented no problem; nor is stellar abberration difficult to explain on this basis."

http://www.philoscience.unibe.ch/documents/kursarchiv/SS07/N
orton.pdf

John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

http://philsci-archive.pitt.edu/1743/2/Norton.pdf

John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

Pentcho Valev pvalev@yahoo.com

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Hello Lawrence

Thank you for your essay. It gives the clearest presentation I have yet come across of what seems to be a fundamental muddle pervading the subject. It appears in the notion which you describe very clearly on your page 3:

"The light cone at any point is subject to quantum fluctuations. Consequently the point where all null rays pass through is indeterminate; null rays...

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Hello Lawrence

Thank you for your essay. It gives the clearest presentation I have yet come across of what seems to be a fundamental muddle pervading the subject. It appears in the notion which you describe very clearly on your page 3:

"The light cone at any point is subject to quantum fluctuations. Consequently the point where all null rays pass through is indeterminate; null rays in the region are not connected to a unique point."

To start with, the term "light cone" is an unfortunate misnomer. Light consists of waves. It does not travel along lines in cones.

The quoted passage does not say what the Heisenberg uncertainty principle asserts. Heisenberg's idea implies that any attempt to observe the region where null rays converge will produce fluctuating answers. This is not the same as asserting that there is no point where these rays converge. The uncertainty principle just says that we can't see it clearly; in fact, any physical phenomenon can't be relied on to behave as if there were such a point because of the modern equivalent of Newton't third law. If an event occurred at that point and had an effect on some physical phenomenon then the phenomenon whould have an equal and opposite effect on whatever caused that event, and knock it off that point.

It would be foolish to speculate how theoretical physicists think. However, maybe one can outline a sequence of mental conceptions which lead in the direction of this muddle.

Conception 1: an event occurs when two or more particles bounce off each other.

Conception 2: we see a thing by detecting particles which have been bounced off that thing.

Conception 3: particles are wave-like, and fuzzy, in accordance with QT.

Conception 4: our faculties and intellects are not fuzzy. If it is impossible for us to see something then it isn't there.

The problem lies in Conception 4. We are fuzzy, and we can't escape this fact precisely because we are huge lumps of interacting wave-like particles. The muddle occurs because we are reluctant to admit our own limitations.

I think this is the root cause of the notion that space-time is granular, not a smooth continuum, and all the consequent hassle.

Best wishes

Alan H.

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Lawrence

I was very pleased to be able to understand your essay, until page 6, and the problem of frame boundaries expressed in the conflict of Maxwell's equations/CSL and classical mechanics. I found your resume clear and logical, up to that point. I congratulate you for that and am sure the problem after then was mine.

I wonder if you might use your obvious deep understanding of...

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Lawrence

I was very pleased to be able to understand your essay, until page 6, and the problem of frame boundaries expressed in the conflict of Maxwell's equations/CSL and classical mechanics. I found your resume clear and logical, up to that point. I congratulate you for that and am sure the problem after then was mine.

I wonder if you might use your obvious deep understanding of QFT to comment on my slightly different suggestion, where the wave equation itself is conserved but the geometry does not commute due to delta lambda. localisation giving quantization is almost instantaneous but the process of charge takes non zero time, so evolves lambda, deriving delta f (Doppler shift). (The light cone IS distorted, as my essay last year). In terms of your text, my essay gives an underlying mechanism, of how Maxwell/CSL and CM can; "...fit into a single theory..." also; "The underlying structure" does NOT require; "...the abandonment of locality and unity."

Though well supported, and consistent with foundations discussed a number of other essays, I'm not sure the ontological construction had the rigorous additional falsification I was hoping for. It is of course only a glimpse of the whole ontology, which I've found has precisely the same structural framework as truth propositional logic; a hierarchical mutually exclusive nested sequence of local compound propositions, none of which has any relevance to any but their local neighbour. Maxwell's near/far field term transition zone forms the turbulent magnetohydrodynamic boundary, working as a fluid dynamic coupling (as ALL scales) via re-scattering at c. A cross section through one such boundary found by the Cluster probes (ion bow shock as non-rotating ECI frame to rotating ECRF) is shown in the Kingsley-Nixey essay Fig 2 with the same logical re-interpretation.

I was very pleased Tom assimilated the set of assumptions and effects of more logical interpretation, which encourages me to believe you may now also do so (beneath the theatrical metaphors). I very much hope you are able. Well done for your own good work, which honestly clarified the limitations of other current approaches. I'm sorry to discuss mainly mine here, but have no criticism of yours.

Many thanks, and best wishes

Peter

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Dear Lawrence B. Crowell,

In the past contest I have found flaws and errors in ~ 20 essays, including leading essays. However, in this contest'2012 I decided not to judge any essays because Brendan recommended avoiding the judgment atmosphere. Nevertheless, since Dr. Crowell estimates my essay, I also have the right to estimate his essay.

Some contestants invented a fast method that...

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Dear Lawrence B. Crowell,

In the past contest I have found flaws and errors in ~ 20 essays, including leading essays. However, in this contest'2012 I decided not to judge any essays because Brendan recommended avoiding the judgment atmosphere. Nevertheless, since Dr. Crowell estimates my essay, I also have the right to estimate his essay.

Some contestants invented a fast method that allows producing quickly many senseless essays in order to make money in FQXi. Meanwhile, I observed that many professionals use this technology. In fact, this fast "technology" allows creation of many high level essays that looks "very scientifically". In order to produce such a story-essay, you must simply retell the accepted physics from textbooks and internet but using your own words. Therefore, it is not the copy/paste operation because the author simply changes the words, but he repeats the generally known information from accepted physics.

Dear Crowell, what means this proposition from your essay: "The acceleration is directly proportional to a force applied to it. The momentum of a body is its mass times its velocity p = mv as determined by an inertial observer'? It is the statements copied from a textbook - the author only changed the words. Or another proposition: "D-branes are composed of strings in a way similar to a Fermi-electron surface in a crystal' - it is a statement copied from brane theory. In the same way, I can show that the most part of Crowell's essay repeats the generally known information. You see, it is the retelling of the generally known information by using other words. In this way, you can prepare hundreds of different essays simply by retelling GR, quantum mechanics and other accepted theories. For example: 'The coupling constant G of general relativity (GR) with units of area, or G1=2 with units of inverse mass, while quantum field theories (QFT's) are unitless coupling constants in naturalized units'. You see, it is simply a story that repeats GR using other words.

Does such essay-story that repeats the generally known information deserve any prize? I can produce 10 such essays-stories like Crowell's essay during a week.

Besides, it is a collection of propositions without any logical connection between them. What logical connection is between Newton, QCD and string (brane) theory?

Since experimentation at Plank scales is not possible, many scientists, including Crowell, publish their free fantasies about Plank scales because they know that all these fantasies cannot be proved or disproved because experimentation at Plank scales is not possible.

Thus, Crowell tells us about Newton and Einstein, then about GR and QFT, quantization of spacetime, QCD, Feynman's rules, then string theory… In my view, Crowell simply tries to fill his essay with generally known information that "looks scientifically". I quote: "Cardenas proposed inflation preserves the holographic principle. In [10] it is demonstrated how a closed FLRW spacetime cosmology with k = 1 upon turn around to recollapse exceeds the entropy bound of Bekenstein and the holographic principle. Crowell [11] proposed from this quantum cosmologies".

You see, it is a collection of random fragments and propositions; Yes, it looks 'scientifically' but it is simply the retelling of accepted physics.

However, the question of essay contest is 'Which of Our Basic Physical assumptions are Wrong'. I do not see any wrong physical assumptions found by Crowell. 'The foundations are not foundations' is not wrong assumption, I can also write that physics is not physics. Why this essay was accepted? It is simply the retelling of known information. The contribution of Crowell is simply that he RETELLS (copy) the accepted physics (even if he copies the SENSE but not copy/paste).

Does this collection of random propositions and fragments of text that repeats the generally known information deserve any prize? I repeat that I can produce 10 such "high level" essays during a week.

For example, first I'll copy the fragments of text from academic papers about Lorentz symmetry, Heisenberg uncertainty, GR, Feynman diagrams. Then I change the words and formulae, and the new essay is ready for publication! Pay attention that it is not a copy/paste because I changed the words! Therefore the essay appears to be 'original' whereas it actually repeats the accepted physics. For example, Crowell wrote: 'The coupling constant G of general relativity (GR) with units of area, or G1=2 with units of inverse mass, while quantum field theories (QFT's) are unitless coupling constants in naturalized units'. You see, it is simply a story that repeats GR and other theories using other words. The contribution of Crowell is simply that he RETELLS the accepted physics but not copy/paste.

If Dr. Crowell will receive a prize for his collection of copied random stories then this (above) new-produced essay also deserve a prize.

It is very difficult to create an original research with Unique information, but is very easy to create the stories about generally known information like Crowell's essay. I propose to eliminate all such stories from contest, it is a fraud only; In such a way professionals make money.

Sincerely,

Constantin

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