Black Holes Do Not Exist, claims Mersini-Houghton

Tom,

An infinite number of zeros is still zero.

Regards,

John M

Tom,

'covariant operations are nondegenerate near the singularity, because complex analysis substitutes lines for points in the underlying fundamental underlying geometry.'

May I ask for yet another math lesson? Firstly, I am assuming 'complex analysis' refers to operations with both real and negative values (?), and does substitution involve a transform of some sort or is it simply an assumed condition (mathematic) which eliminates singularity by virtue of the argument that two points can be infinitely close yet remain a real length?

Thanks for any elaboration. jrc

Jonathan,

An interesting article on biological feedback.

Regards,

John M

Jonathan, Tom,

Topology was introduced already in 1847 by Johann Benedict Listing. Pebble-set theory came up in the early 1870 decade. While C. S. Peirce in 1898 still nicely explained what he called the logic of continuity by speaking of the continuum as mere potentiality of the location of points, his reasoning included idealist views, and he failed to criticize that Dedekind's cut was at odds with his good old notion continuity.

Pebble-set theory requires to abandon this notion of continuity. There is not just one substitute for it but a huge amount of arbitrary chosen ones, all based on just nearby single pebbles. Instead of genuine continuity, pebble-set topology adds compactness (the property to be closed and bounded) and connectedness.

John M,

Your consider numbers like zero as a tangible pebble but infinity like an unreachable limit point. Mathematicians were and are also not consequent. Declaring division by zero forbidden, they don't likewise forbid multiplication with infinity.

John R,

I would be ready to translate some of the notions introduced by Tom if necessary. However, this would distract from my argument that real numbers are different from rational ones: With Euclid's good old notion, singular points in IR are measureless and accordingly definitely without a correlate in reality. That's why I consider Joy's compactification useless.

Eckard

It's probably more accurate to say that event horizons do not exist.

Eckard,

I think of numbers as sets. When you add 3 and 6 to get 9, you have added a set of three pebbles to a set of six peddles and now have a set of 9 pebbles. To "add" means to put together and you haven't actually put the pebbles together, but just put them in the same set. Consider adding flour, sugar, butter, etc, to make a cake. Then you have actually added them together. Or piles of sand. If you add them together, you have just one big pile of sand. Or apples. If you really add them together, you have apple sauce. So what you add with numbers, is the sets, to get one bigger set.

So zero is an empty set, while infinity is a set that doesn't close.

Now when you are dealing with multiplication, you are adding the numbers of sets of the multiplier and division is dividing the set by the divisor, like cutting the cake.

Regards,

John M

"An infinite number of zeros is still zero."

Once again, what does that have to do with your claim that infinity times zero is zero?

" ... I consider Joy's compactification useless."

It's not "Joy's compactification." It's elementary topology.

John R, points in complex analysis are lines, because the complex plane is fundamentally two-dimensional. A complex number, a ib, that describes a point of the complex plane, has real and imaginary parts. So dimensionless points native to the real line appear as lines native to the complex plane.

" ... does substitution involve a transform of some sort or is it simply an assumed condition (mathematic) which eliminates singularity by virtue of the argument that two points can be infinitely close yet remain a real length?"

Yes to the latter, and that's essentially what makes the complex Hilbert space suitable for quantum mechanics. Because quantum mechanics is founded on empirical phenomena (2-slit experiment) there is no way for singularities (defined as space collapsed to a point) to manifest -- the choice of space forbids it.

"Thanks for any elaboration. jrc"

No, John -- thank you, for asking real questions instead of making nonsense claims and saying, "that's math," when it ain't.

BTW, I think Barry Mazur's Imagining Numbers is a great introduction to appreciating complex analysis, rather than just calculating by rote.

That appears to be what Hawking and others are saying...

All the Best,

Jonathan

Tom,

1x0=0. 23x0=0. 5768x0=0. 200,456,326x0=0. At what point does it stop being 0?

Regards,

John M

To look a bit deeper...

There are conditions for which Relativity breaks down, because its premises are violated. Specifically; one must have a condition where objects with independent centers and discrete surfaces exist, which can move relative to one another, for Relativity to operate. In a Quark Gluon Plasma; this is no longer the case, as individual quarks display asymptotic freedom within a region where sufficient density of energy is maintained. In other words; they are seen to partially or completely overlap their neighbors - a property which in my model is caused by their being topologically incomplete, until a sufficient volume of space allows them to link up.

This becomes greatly important in the inner region of an ECO, but somewhat outside where a horizon would form, and this is the subject of Mitra's 2010 paper with Glendenning.

All the Best,

Jonathan

To be clear...

The violation of the premises of Relativity is evident in the QGP, because the individual quarks do not behave like distinct objects with independent centers. And the 2010 Mitra and Glendenning paper deals with some of the complications arising thereby.

Regards,

Jonathan

Jonathen,

Have you considered this model, consistent with fractals;

1. Imagine you can shrink or grow to ANY size scale, from below Planck to greater than our universe.

2. Whatever size you decide to be you find spinning bodies (OAM) also describing a helical path (which may be ellipticised) as they translate (or orbit) as they spin. This is indeed the spin/orbit relation of light, Birkland currents etc.

Certainly our planet and sun do so through the galaxy, etc etc right up to the CMB helicity. At quark scale the 'hyperfine spin' state is consistent with the same pattern, of positive and negative charges orbiting the greater body. Certainly 'hyperfine' spin states are ubiquitous in optical science, parallel with Gell-Mann's 'fine grain' decoherence mechanisms. Way down smaller we may even find the same as a 'phase transition' to dark energy (ether?)

Peter

Yes, John, to overcome the "crisis of understanding" the fundamental knowledge requires a comprehensive synthesis, compression all information accumulated by mankind and construction of "the general framework structure". Need more profound dialectic than the "Yin-Yang" deeper ontological eidos of the Universum - eidos of "coincidence of opposites", pulling together all the meanings of the "LifeWorld" (E.Gusserl), all the ultimate meanings and values of the Universum. New heuristics and understanding of the Universum can only give the deepest philosophical ontology.

Sincerely,

Vladimir

Steve,

This latest finding confirms the quasar luminosity variability issues showing why redshift is the safest distribution function;

"Introduction; Luminosity variability is a common feature of quasars (QSOs), and active galactic nuclei (AGN) in general, throughout the electromagnetic spectrum from X-rays to radio wavelengths and on time-scales from several hours to many years. Various models have been postulated to explain this variability, such as accretion disc instabilities (e.g. Rees 1984; Kawaguchi et al. 1998), variation of accretion rates (e.g. Li & Cao 2008; Zuo et al. 2012), supernova explosions or starbursts (e.g. Terlevich et al. 1992; Kawaguchi et al. 1998), and gravitational microlensing (e.g. Hawkins 1993; Alexander 1995).

Several studies of quasar variability in the optical bands have explored relations between variability amplitude and important parameters such as time lag, luminosity, rest-frame wavelength and black hole mass. The amplitude of variability is found to correlate with time lag, increasing until it seems to flatten at longer time-scales (e.g. Hook et al. 1994; Trèvese et al. 1994; Cristiani et al. 1996; di Clemente et al. 1996; Vanden Berk et al. 2004, hereafter VB04; Bauer et al. 2009; Kelly, Bechtold & Siemiginowska 2009).

A number of studies have also found an anticorrelation of the variability with the luminosity of quasars, with more luminous quasars varying less (e.g. VB04; Hook et al. 1994; Trèvese et al. 1994; Cristiani et al. 1996; Wilhite et al. 2008; Bauer et al. 2009; Zuo et al. 2012). Furthermore, evidence of an increase of the amplitude of variability with decreasing rest-frame wavelength (bluer) is seen in the part of the spectrum ranging from the UV to the near-infrared..." etc.

The ensemble optical variability of type-1 AGN in the Sloan Digital Sky Survey Data Release 7

It's in the the November issue (early access alert) but may be out on arXiv. A group of other 'anomalous' findings in that issue also appear to only be consistent with a cyclic model with significant re-ionizing outflows. I'm analysing them now.

Abhas does seem rather churlish entirely ignoring the physical evidence. Seems a bit like studying monkeys from 3rd hand descriptions when we have real monkeys to study! If he'd rather call outflows 'Gorillas' I suppose it's ok, but it seems to miss the point rather. Has he actually responded to anyone?

Best wishes

Peter

Tom,

Please comment on my Fig. 3 if you are able to do so without resorting to unnecessarily confusing utterances as "points are lines". A point in a 3D physical space or in a 2D plane, including the complex one, should also be understood as something zero-dimensional, something that has no parts although its position is described by 3 or 2, respectively measures.

You will of course feel sure when you are blaming me for lack of understanding in topology. Be cautious. I am merely arguing that topology suffers from Cantor's ill-founded set-theory. Just substitute the notion set by continuum. and understand that the distinction between open and closed only applies for rational numbers, not for really real ones.

Let me try and answer instead of you the naive question by John M:

- Being perfectly zero is the fictitious quality of being unreachable by division and accordingly representing no measure at all; being perfect infinite is the fictitious quality of being an unreachable by addition and accordingly neither enlargeable nor exhaustible measure. Therefore, functions that are leading to indefinite expressions like 0*oo, 0/0, oo/oo, oo-oo, 0^0, oo^0, 1^oo can at best be treated with the rule by Bernoulli and l`Hospital.

John M,

The abacus with pebbles instead of measures was already very popular for at least a millennium before Euclid. Dedekind and Cantor were just populists when they reintroduced the pebbles instead of measures. There are however several imperfections, e.g.:

- Imagine pebbles for ... -2, -1, 0, 1, 2, 3, ... with red color for negative but green color for positive pebbles. What about the pebble zero? Is it positive, negative, can we choose it arbitrarily, or may we use a split number? - While the problem cannot be satisfactory resolved with pebble-set theory, the continuum of measures does not need a pebble zero.

-In other words, a cut that is thought to separate two pebbles cannot be simultaneously located at one of them. Pebble-set theory based topology cannot even perform what every child is in principle able to perform: a symmetrical cut between positive and negative.

- With enough pebbles one can in principle represent any rational number but not the variety of the mere potentialities called real numbers. As many pebbles as you like cannot exactly represent irrational measures.

- The superiority of measures over pebbles is quite understandable as a result of dealing with length in geometry and belonging logical foundation by those like Euclid and Galileo in contrast to use of abacus.

- Peirce's Tychism corresponds to an uncertainty: the ultimate absence of distinction between individual points.

Eckard

Vladimir,

Yin and yang is a very simple model, but using it as a counter-example to linear narrative is a way to express how there are profoundly different paradigms taking precedence for different people. Being able to first develop some common denominator of understanding in order to have the necessary conversation requires some basic models and relationships. Probably a more explicit example would be along the lines of feedback loops and thermodynamics.

Now the larger goal might well be to have more than just a pleasant conversation and trading of insights and to genuinely get humanity thinking about what it wants for the future of this planet, as the prior contest asked and that requires strategy, not just modeling.

The only way that would arise from these discussions is if the coming paradigm shift in physics can be used as a lever to raise questions about many of the other facets of society and civilization which could use reconsideration. That was somewhat the intent in my own entry, but I didn't state it explicitly, just reviewed some of those broader issues which could use a different perspective.

While this may seem far-fetched in our current situation, change does happen and if a generation raised on such ideas as the Big Bang theory were to suddenly find it was just a passing intellectual fad, they might be much more open to re-consideration of other sacred cows. Now you wouldn't think such a thing possible, given how set these particular conversations can be, but that might well be due to many of us being middle aged or older. Who knows what the world will look like in even just another ten years. Certainly the political map looks like it will have significant changes in assumptions and relationships. Not all for the good, but some good will arise from the coming chaos.

Regards,

John M