joigus

Any arguments, or are you after founding a new religion and we're supposed to nod and follow you?

Very poorly thought, IMO. Did the differently-beaked finches interbreed? (Darwin's-time criterion for speciation).

I tested it and it doesn't work for me. Plus there's a considerable amount of looping. Could account for the remaining 5%. I need a clicking tutorial. The thing is it kind of make sense to me that philosophy is an attractor.

Thank you for anticipating your ideas. +1 I'm in no hurry, in case you're wondering. I'm just interested. The problem is quite academic, but interesting nonetheless. Somewhat out of my scope. I think that's the route to solving it. Slicing the tube into infinitesimal slices of constant thermodynamic conditions. And let the gas equilibrate with itself. The only thing I don't see is the temperature. But maybe you've got that into account for later.

Allow me to answer, and Markus, feel free to correct mistakes/imprecissions and/or add info as you see fit. The AdS/CFT dualities are more sophisticated. For example: On the inside (bulk) you have a gravitational theory, which has a metric connection (a rule to parallel-transport vectors from a metric). On the boundary you have a gauge theory (a non-metric connection or affine connection, which stands on its own). They are completely different animals, and there is no simple way to relate the degrees of freedom. Also, some solutions of the theory without metric may be completely devoid of meaning as solutions of the theory in the bulk. There are topological aspects in the spectrum of solutions on the boundary that have no easy interpretation (or non at all) in the bulk. And so on... People who work on these type of dualities generally speak of a dictionary (a set of rules to translate boundary conditions, etc. from one theory to the other). Edit: x-posted with @Markus Hanke . I think you have an extra circle there. It'd be, \[\int_{M}d\omega=\oint_{\partial M}\omega\] I personally prefer not to use the circle because there's no simple way to iterate the operation. So, for example, if you want to express Hodge duality's simple result "the boundary of a boundary is empty": \[\int_{M}d^{2}\omega=\int_{\partial^{2}M}d\omega\] \[d^{2}\omega=0\Rightarrow\partial^{2}M=\textrm{Ø}\] The boundary of a boundary has no points. Edit: And the \partial symbol already implies you're looping around. But that's a matter of taste.

Spaces with intrinsic curvature can expand or contract without any coordinate points touching each other, like when you paint dots on a balloon and start to blow. They separate but they never touch. Exactly. "Remindful of", "suggestive of". And that's the reason. +1 Unless anybody comes up with a closer analogy that one theory is like an exterior differential of the other in some sense.

Well, Maldacena's initial idea wasn't motivated by a realistic model of the universe. So the so-called AdS (anti-DeSitter Space) was not meant to represent the real universe. Although the AdS space-time is an exact solution of the Einstein field equations. But exponentially expanding or contracting universes don't have to have a center. Our universe is a DeSitter universe (exponentially expanding) AFAWK and it's not doing it around any particular point. Everything is expanding with respect to everything else.

https://www.youtube.com/watch?v=hBpetDxIEMU&t=381s @ 20' 34'' - 40' 38'' Both hilarious and spot on.

Let me help you. All of them are contained here, \[\int_{M}d\omega=\int_{\partial M}\omega\]

I wasn't aware of this. I must have been sleeping all these years. Thank you. +1 Mmmm... Remindful of, suggestive of, rather than equal. Reminds more of Cauchy's integral theorem of complex calculus. And even more of Stokes' theorem for differential forms. Because we always use analytic functions, things on the inside are determined by things on the surface. But I'm getting hopelessly vague and metaphorical. Although the FTC is a particular case.

Aaaah. Now I understand much better what you're trying to do. Thanks for careful explanation. +1

Oh, my, you're sharp, Hanke! I may be going nowhere, but you understand exactly what I mean. +1 You're worth 10 points here. In fact, there is a kind of non-locality in my view, but it has nothing to do either with space nor with time. It's abstract, internal-space. The functions you're trying to measure are not point-to-point (eigenvalue-to-eigenvalue) functions of one another. What some analysts call "non-local operators". Maybe the expression filtered out from there. Same way x is non-local operator in p-eigenstates (it depends on all the spectrum) and vice-versa.

You can have a plague, massive wiping out of genes, but the smallest sample get amplified by the founder effect later. And what previously was a Charlemagne differential gene (I suppose Charlemagne had genes for cellular respiration too) get amplified to almost universal proportions. It's kind of a mix, filter, mutate and stretch kind of dynamics.

Mmmm. But temperature must go up as you go down the hole, irrespective. Gravitation always heats up any stuff as you go down towards the core. Never mind gravity field going down to zero. Pressure builds up --> temperature goes up. It's not temperature coming from Earth's core transferring it to the gas. It's the gas' own internal energy/volume that does it. Say, I may have misunderstood something. I must confess I'm a bit confused about this one. If you want to solve the problem, the only thing you can do is let the air in the hole acquire temperature from its own pressurization, so to speak, as it builds up weight on top. The Earth can't touch it, either thermally or pressure-wise. I've just done a lookup and the Van der Waals eq. is not good enough to deal with this either.

But heat transport can happen even though the situation does not depend on time. Heat transfer must have reached a stationary regime (I'm not saying heat doesn't flow). Also, they're assuming perfectly isolating walls... Maybe I got the premises wrong.

Agreed. Language of itself can mislead you. Maths too. Experiments without theoretical analysis are devoid of meaning. Sheer observation can be a crook. It's a network of interrelationships, cross checks, that makes it all solid. Narrowing down the chances of being mistaken. Cladking doesn't even seem to know what a cat is. Most people have no problem with this.

The problem with this is that is sounds sooooo much like a particular philosophy... You simply can't escape philosophy. Break down the word into etymological pieces and you'll understand why.

Some days ago I learnt from @Strange that most Europeans are descended from Charlemagne. I've learnt many other things from him. But this one got me thinking (and still is) about the likely regular Jacks and Susans, and Joes and Marys, who were especially successful in the reproductive sense, but not particularly notorious, and got their genes pushed forward in human history.

Sorry, I didn't read carefully above. You're assuming that.

Your nom de plume is indeed faithful to the workings of your mind. Gave some points to the brave soldiers.

Very good point! +1 Answer in jest: That's cheating! Answer in earnest: I think you're right that constraints are needed to make the problem well-defined. Are you assuming the tunnel also insulating, so we can guess only in (local) equilibrium with itself?

Or for just any acceleration. It is not a crazy idea at all that non-locality/non-causality are present at a very small scale that cannot have consequences farther away than a certain tiny range. So you could have both pre-images and post-images of your local universe that your mind integrates in a "solid picture", so to speak. I think that's possible. But the priority, I think, is to understand where temperature comes from in GR (what degrees of freedom it's talking us about) and obtaining a generalisation of QFT workable for general coordinate systems (what's called in the lingo diffeomorphism-invariant). See how temperature arises in both contexts, then understand what both temperatures mean and relate them. Easier said than done... Keep in mind that whenever you have a temperature, it means that there are dynamical degrees of freedom that are not in your description, so your description is averaging over them. Then you've got Maldacena's mind-blowing mathematical result that gravity inside a ball is describing classical gauge field theory on the surface of that ball, but at the price of having the metric be anti-DeSitter (something like an anti-universe or exponentially-contracting universe). This strongly suggests that any new physics should be capable of relating inside-outside quantities for any observers (that naturally perceive some kind of inside-outside distinction), which is what I was trying to connect with before. More tame speculations later...

Even if air at centre is not a plasma, certainly the equation of state to be used would have to be a power series in the density, extending the way that the Van der Waals eq. deals with the first terms. \[P=a\left(T\right)+b\left(T\right)\rho+c\left(T\right)\rho^{2}+\cdots\] This is very general for real gases even in conditions of high pressure, very far from ideal gases. High temperatures makes it behave more gas-like. But estimating the T-dependent coefficients is another story... Ideal gases doesn't cut it because already for Van der Waals you have 3rd power of density essential to account for phenomenology. Using the tools of my trade what I would do if I were desperate to solve it is depart from a simplified molecular model and calculate the partition function. And from there to the equation of state. The thing that I see difficult from first principles is that the way I see it you must have an enormous reservoir of air to fill in the hole while at the same time have the air compensate for the enormous pressures of the solid/plasma, hot Earth material, that would tend to squeeze the borehole to a mathematical line. I'm reading also @Ken Fabian and @studiot's ideas, as the OP. See if I can relate them to my reasoning... The comment I want to make is that it is entirely possible that the parametrics of the problem becomes ridiculously impossible. After all, we're asking the atmosphere to hold the Earth in place, which wants to recover this hole by squeezing it out. Does that make any sense to any of you? ------- PD: The thing that makes me very suspicious is that assuming exponential atmosphere with T at centre given by known temperature at centre of the Earth returns numbers so out of whack that I'm confused. The whole thing could have an implicit assumption that makes it thermodynamically rotten at its core (pun intended). Totally agree with comments by @Martoonsky and @Ken Fabian that situation is static (local equilibrium). Everything must grind to a halt.

I'd say human skin and sweat are the major factor in evacuating heat. Evaporation of water is the most efficient way for us humans to get rid of heat. It's no coincidence that we've evolved that. It's been proven that human skin is our trump card with respect to furry animals, allowing humans to use persistence hunting in very intense heat until prey die of heat exhaustion. Interesting studies by Harvard anthropologist Daniel Lieberman.* Colour is not nearly as efficient, although I would recommend white for reflectivity. *About persistence hunting and adaptation to running. There are other studies more directly related to skin. Edit: Also pick up anything by Nina Jablonski on human skin. There's a lot on the web.

Yeah, that doesn't work.