Black Holes Do Not Exist, claims Mersini-Houghton

"Imagine a measure quantifying for instance the length L of a body. Is then a difference between (L) and [L]?"

I think you actually mean to say [a,b] and (a,b), referring to closed and open intervals. There's no length without interval. Your sets (L) and [L] are dimensionless.*

"Why cannot point-set topology perform a cut A|B between IR and IR- without an arbitrary choice between -)[, -](, -), 0, (, or undecided? Neither of these variants deserves to be called a symmetrical cut."

With due respect, Eckard, I don't think you understand Dedekind cuts. The interval of successive integers is most certainly symmetric. I tried to explain this by the example that in Dedekind cuts, there exist two definite numbers that when multiplied together equal the square root of 2. This is by way of proving that "the least of the most and the most of the least" in the continuum have boundary of length 1 and measure of zero -- since we cannot say what the two numbers are.

* I touched on this in my ICCS 2006 paper. First paragraph of 7.0, the discussion section: "The positivity requirement (5.11.1) and the infinite variety of state spaces made available by the Hilbert space -- along with the constructed continuity that unites real and complex analysis in a backward-forward projection between S^1 and S^3 suggests the preservation of equilibrium on the intervals (0,1) and [0,1] in a true transformation of an indefinite and continuous measure space to a discrete counting function symmetric about the complex plane axis." (Ray, 2002)

I didn't say that gravity attracts to infinity, did I?

Tom,

Obviously it would only attract to the boundary with the adjacent fields, because then their influence would predominate, just as all light doesn't radiate for billions of years.

Regards,

John M

"Obviously it would only attract to the boundary with the adjacent fields ..."

Obvious to whom? The field is continuous. So what adjacent fields are you talking about?

John,

The process seems fractal, as Jonathen identifies but a 'dynamic mechanism'. I wouldn't say "more" of one or the other, but the smaller the fractal the shorter the cycle.

Have you noticed our AGN getting more powerful by the month? 50 years ago we didn't even have one! (lol). But it looks like we have another 5Gyr to ship out to another galaxy, a halo satellite galaxy should be safe. But at our current rate of intellectual evolution it looks like we may miss the boat. Perhaps next time round!

PJ

Peter,

Looking at the markets and Ebola, it looks like we might be falling into our own little cosmic vortex.

Top down world order seems to be falling and the bottom seems to be falling out of the bottom.

Things only get more interesting.

Regards,

John M

Tom,

Your responses seem a bit distracted.

For instance, something within the earth's field is going to be attracted more to it, than say Venus.

I think there is an interesting point someone, not necessarily you, might find interesting to consider; That of the consequences of expansion versus contraction at an essential level.

For instance, contraction necessarily coalesces to a unit. Be it an atom, or a planet, a distinct entity is formed and surface tension makes it as efficiently formed as possible. I would even posit that light as a photon is a form of contraction, as opposed to a wave.

On the other hand, expansion radiates outward. Even possibly to the point of all material from the original source being shed, such that it no longer exists. In a sense then, it is like the proverbial wave. Like one washing through rocks on the beach, or out from a stone in the water, it spreads out and fills in the gaps between all the more solid and discrete forms.

So as gravity and mass contract and coalesce, there are not going to be particles drawn from outside the primary fields of influence, so mass is very much a global and globalizing effect, light travels everywhere it can, even washing past intervening galaxies, for billions of lightyears.

We could examine this relationship in any number of ways, such as even human affairs. for instance, liberalism tends to be like light, expanding out over and illuminating everything, but without much gravitas, while conservatism is like mass, quite solid, but loath to extend much beyond its range. One could say the Ebola virus is quite liberal in its reach, but also very conservative in the consequences it could have on humanity.

While I realize you will offer up the usual so what, I just wanted to show these discussions cause my brain to exercise itself and for that I am grateful.

Regards,

John M

Tom,

I didn't speak of sets [L] and (L) but of a physical body of length L assumed as continuous in the sense explained by C. S. Peirce and without any obligation for referring it numerically to a particular unit. The body is imagined to extend from a to b. A second one extends from b to c. I don't see any reason to attribute the point b to either the first or the second body. Only point-sets give rise to do so and distinguish between open, closed, or even clopen. The reason is perhaps obvious: Pebble-like numbers are demanded to be unique. Moreover, measure-based (Euclidean) numbers fit better to physics, where there is often no natural zero available, than do coordinate systems.

While Dedekind cut claims to create irrational numbers, I see it just an infertile method to constructively describe the separation of the continuum of real numbers into the rational and the necessarily always only implicitly given irrational numbers - or the other way round a justification of putting rational and irrational numbers by means of an axiom under the common umbrella of the continuum of real numbers. Dedekind followed Stiefel when he guessed that there are much more irrational than rational numbers instead of accepting the different quality of what Stiefel called fog and Weyl called sauce. I see them failing to accept the incomparability of quantity and quality.

I see Dedekind cut a crossing mark rather than a cut in the usual sense of a knife separating two parts. It depends on the chosen measure one whether an interval is of rational or irrational quality.

Moreover, D's cut denotes the position of a point, not of the absence of a position. Hence the word cut is a bit misleading.

You mentioned identical intervals between succeeding integers. I focus on something quite different: mirror-symmetry in particular between positive and negative in IR. Incidentally, Dedekind used R for the body of rational numbers.

Writing "symmetric about the complex plane axis" you confused me. Did you mean the real axis, the imaginary one, or what else?

Your "the least of the most and the most of the least in the continuum have boundary of length 1 and measure of zero" sounds to me also like an unnecessary play with confusing words.

Eckard

" ... something within the earth's field is going to be attracted more to it, than say Venus."

Right. All physics is local.

Distractedly yours,

T

Sorry, Eckard, I can't make sense of what you are saying. This isn't going anywhere.

Tom,

The question is whether physics is cyclical.

Is what contracts in, eventually being radiated out and what is radiated out eventually cool off to the degree of coalescing back together, rather than linear assumptions, where gravity contracts to a singularity and light radiates to infinity, without apparent relation.

It would seem the premise of this forum topic is that what contracts in does radiate out, so when would the other side of this relation be considered, given that the possibility doesn't involve any current conflict between established theories and the subject fields seem too narrowly defined for anyone to consider it as a big picture consequence.

Insistently,

John M

"It would seem the premise of this forum topic is that what contracts in does radiate out ..."

That's not how Hawking radiation works, John. It's a quantum effect at the black hole event horizon. If the event horizon doesn't exist, then we can speak of how to describe the effect in terms of a local theory, i.e., the behavior of classical wave mechanics near the singularity. That's why the topic is foundationally important.

Jonathan,

Tom wrote: "It's a quantum effect at the black hole event horizon. If the event horizon doesn't exist, then we can speak of how to describe the effect in terms of a local theory, i.e., the behavior of classical wave mechanics near the singularity."

That's why my Figures 1-4 might be unwelcome and Tom has no chance but to blindly reject them: Bogoljubov was son of a priest, Bog means God, Ljubov means love. Not just Bogoljubov transformation is based on the firm belief that reality is ruled by the mathematics at hand. Of course, tan(90°) is actually infinite. However...

Eckard

Tom,

"Mersini-Houghton and Hawking both agree that as a star collapses under its own gravity, it produces Hawking radiation. However, in her new work, Mersini-Houghton shows that by giving off this radiation, the star also sheds mass. So much so that as it shrinks it no longer has the density to become a black hole. Before a black hole can form, the dying star swells one last time and then explodes. A singularity never forms and neither does an event horizon. The take home message of her work is clear: there is no such thing as a black hole.""

Reading between the lines, it would seem political cover to say it is Hawking radiation, because Hawking radiation theoretically exists on the edge of black holes and this says there is never enough density for black holes to form in the first place.

Regards,

John M

Tom,

"the behavior of classical wave mechanics near the singularity."

Which gets back to the point I made above and what Eckard is mentioning, as to whether gravity is really a mathematical projection from the surface of the sphere, to the center, or whether it is an attractive element of mass.

The difference being whether there is that singularity at the center, or whether at the center, all the attraction is surrounding it.

Regards,

John M

The center is everywhere, John.

Jason,

Logic shows we can't discount anything. Max Tegmark and others appeared in the TV prog shown again last night in the UK; "Are all our theories..wrong?" all saying sensible things (as opposed to the often stomach turning Discovery channel dross). Conclusion? (Tom look away now); Yes of course. Unfortunately ghosts didn't appear Jason, but 'lack of proof' is not.. etc' One step at a time perhaps?

Jonathen,

That also opens the way a little more for quantum-classical convergence. I'm in an interesting discussion on Quantum Entanglement at present on Linked-In APS where the exact issue is well specified. If anyone didn't understand my route to convergence I'm about to describe it concisely there by invite. Do look in, even if only to help falsify.

Best wishes

Peter

John,

1+1=2 posits the dynamical process of addition to arrive at the answer.

You are absolutely right! 2 is only the final answer. A planet acquires mass by pulling more mass closer ... and on its surface. Addition in nature is a geometrical operation. Also, addition means that one or more properties of what is being added DO add up: more mass, more light, more charges BUT the basic addition is about something that exists.

Bests,

Marcel,

Since several issues were raised..

I'll begin with this; while Hawking radiation is a quantum effect, it is founded on the principles of thermodynamics. Specifically; black body radiation was found to act differently from the Classical interpretation, where energy is emitted in continuous ranges, but is well explained if we assume that it is a spectral phenomenon. This is then interpreted as evidence the system is quantum mechanical - radiating only in discrete units of a specific frequency.

However; the question of what constitutes Hawking radiation is considerably more complicated. Strictly speaking; Mersini-Houghton uses the term incorrectly, because the way it is defined Hawking radiation is a phenomenon that occurs once an event horizon has formed - and M-H is positing that it does not. So there is definitely an issue with calling it that. But I think that Hawking's own recent paper opens the door to redefinition by focusing on the fact that an event horizon's location is sufficiently indefinite that a physical system could never evolve to that state.

However; this would also suggest that Dr. Mitra is correct in his main arguments, because the crux of the Hawking paper is that non-linear classical dynamics can trump quantum mechanical effects by amplifying quantum uncertainty to a point where trying to define a specific state near where the event horizon would be becomes like forecasting the weather.

All the Best,

Jonathan