joigus

1 hour ago, michel123456 said:

How do you describe this geometrically? if I expand, and you expand, at some time we will touch each other. In order to remain in place (relatively to each other) some displacement must take place. Otherwise it will look (from our expanding point of view) as if something was pushing us against each other.

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.

8 minutes ago, Markus Hanke said:

I don't think it is that simple. The duality we are referring to here is a duality between distinct types of physical theories - geometric theories of spacetime (on the bulk) on the one hand, and conformal field theories (on the boundary) on the other side. How does this relate to the FTC?

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.

23 minutes ago, michel123456 said:

But we are accelerated, through gravitation (see equivalence principle). And we do see a sea of particles around us (the universe). And it is impossible to stop. Our sliding in time cannot stop.

Exponentially-contracting universe, yes that crossed my mind but geometrically how do you make this? With one universal center of contraction? Or multiple centers? I was completely blocked by the incapacity of figuring the idea.

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.

1 hour ago, Airbrush said:

People will yell crude references to sex acts out of anger.  What does sex have to do with anger? 😲

https://www.youtube.com/watch?v=hBpetDxIEMU&t=381s

@ 20' 34'' - 40' 38''

Both hilarious and spot on.

1 minute ago, studiot said:

Last time I tried to write this out here, the site's crappy Latex defeated me.

I will have another go sometime.

It really is a wondrous thing that for many situations that actually concern us all the information about what is going on inside a closed boundary is available by just considering the boundary.

But yes this is tied up with Gauss, Stokes and Green's and Riemann.

Even better there is a digital or discrete version that is in great use as boundary elements v finite elements.

Let me help you. All of them are contained here,

\[\int_{M}d\omega=\int_{\partial M}\omega\]

1 hour ago, Markus Hanke said:

The result has already been replicated for deSitter space (dS/CFT correspondence), and even Kerr spacetimes (Kerr/CFT correspondence). It suggests that the duality itself is an expression of some deeper connection between bulk and boundary - I bet there is some form of underlying duality that relates the two for any kind of spacetime, independent of its specific geometry (or perhaps for some physically significant subset of geometries). Finding this would be a major breakthrough.

I wasn't aware of this. I must have been sleeping all these years. Thank you. +1

46 minutes ago, studiot said:

Indeed there is.

It's called the fundamental theorem of calculus.

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.

14 minutes ago, studiot said:

I choose isothermic because I consider this differential element to be all at one temperature.

 

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

1 minute ago, Markus Hanke said:

Ok, that's a good point, and I think I get what you mean. I looked at the situation only spatially, but not along the time line. So in that sense, as you explained it, it is indeed local - later measurement outcomes do not depend on distant parts of the system, since the statistical correlation has already been there from the beginning, and thus remains local at each branch of the experiment. So the situation does not in fact fulfil the non-locality definition you gave. That's a pretty self-consistent view on this, as it avoids any clashes with SR. This would seem to imply then that we have to let go of realism; it also implies that the spatiotemporal embedding of the underlying wavefunction that describes the system is non-trivial - it cannot be located anywhere in spacetime in any self-consistent way.

This is consistent with my own view which I keep exploring - that the underlying structure of reality is not in any way spatiotemporal in nature.

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.

29 minutes ago, MigL said:

Given that up to a third of the population of Europe died during the plague ( 1350s ), and that there wasn't much travelling or intermarriage outside of local towns, it is also possible that all of any one particular person's genes were completely wiped out.
Even those of Charlemagne.

Or am I over-analyzing ?

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.

3 minutes ago, studiot said:

My model is isothermal so doesn't depend on adiabatic walls.

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.

2 minutes ago, studiot said:

That cannot possibly be because heat must be transported down the temperature gradient.

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.

54 minutes ago, IDoNotCare said:

All philosophy is useless.

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.

1 hour ago, joigus said:

Are you assuming the tunnel also insulating, so we can guess only in (local) equilibrium with itself?

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.

2 minutes ago, Ken Fabian said:

I think the question is pressure for a lined borehole, a tunnel with walls that hold back the pressure. Or else the answer reverts to what is the pressure at Earth's core, sans borehole.

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?

4 hours ago, michel123456 said:

The Unruh effect: under the prism of what I posted you in PM, it may be (although I thought it would be impossible) that the observer under ridiculously high acceleration is "kicked out" of his own time line in such a way that he can observe particles of his own future (otherwise unobservable) or belonging to his own past, depending on the direction of acceleration.

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. 

On 8/11/2020 at 5:37 AM, Martoonsky said:

I was planning on using the ideal gas law but I now realize that deep inside the earth, the air would be heated to a plasma. 

Yeah, that doesn't work.

OK, punch a hole in the universe and go somewhere else. Good luck.

You cannot reach speed of light. Requires infinite energy for massive bodies. Period.

1 minute ago, fredreload said:

Cool, two points.

1. If you can fall through the universe why can you not move past the current universe. At light speed if the length of the universe becomes 0, then what lies beyond the universe at length 1? Wouldn't that suffice as a time machine?

2. It is simple to create a sphere eversion pattern energy with laser on mid air, you just etch the design in mid air as a plasma, but it would require a 1km radius of such plasma. With the Argon gas confinement you could compress the gas at some 500 atm to crunch the whole design in maybe less than 10 meters but it becomes harder for the plasma energy gas to follow the eversion pattern as compared to a laser = =. I am still working out on that part but for a variable magnetic field to twist and turn the plasma gas to shape the design seems kind of hard = =, or am I missing something?

First main reason is this:

32 minutes ago, Strange said:

You can't reach the speed of light. So your entire premise is false.

There are more.

1 minute ago, Strange said:

1. What evidence do you have that the universe is a sphere?

2. How on Earth do you plan to turn the entire universe inside out?

3. Why do you think that turning the universe inside out would lead to time travel?

4. Does sphere eversion work in 4 dimensions?

5. Why do you keep posting nonsensical ideas?

Fool through? 🙂

That could work too.  

5 minutes ago, iNow said:

Thanks for the visual help.