UFT Part Two: Geomechanics

To keep in line with that last post,
If we throw out the idea of frictionless vacuum,
A lot of other things we take for granted go out the window with it.

The Earth, The Sun, all the other stars, and maybe more importantly, all the atoms,
Will stop spinning without some mechanism propelling them.
Not slowly over aeons as thermodynamic entropy suggest, but very quickly.
That's not what we observe, so there must be something driving them.
An engine that keeps everything functioning normally.

What is that?
How does it work?

In order to find a source, first we have to establish the nature of the mechanism itself.
Atoms are too small to get a close look at... Stars are too far away...
I think the planet we're standing on is the best place to start.

Earth has a molten inner mantle. We're all used to that, right?
Probably don't stop to think about why it's hot enough to stay molten all the time.
It takes a lot of energy to keep rock molten all day and night.
The weirdest part is that the core of Earth is NOT molten.
And neither is the crust.

So let’s try throwing some math at this:
Earth's iron/nickel core, based on seismological estimates, has a radius of 1,220 km,
Giving it a volume of ≈ 7,606,210,000 km^3 at an estimated temperature of 5,430 °C.
Close to the temperature of the surface of the sun.
The mantle has a thickness of 2,886 km, so if we calculate that sphere and the subtract the core,
We get ≈ 93,081,790,000 km^3

Keep in mind these are all rough approximates just to get a ballpark of the energy we're dealing with,
And that we can't really measure the weight or precise density of these components, because Earth is in free fall.

According to Louie, J. (1996). "Earth's Interior". University of Nevada, Reno. Retrieved 2007-12-24:
"In the mantle, temperatures range between 500 to 900 °C at the upper boundary with the crust to over 4,000 °C at the boundary with the core. "
And Turcotte, DL; Schubert, G (2002). "4". Geodynamics (2nd ed.). Cambridge, England, UK: Cambridge University Press. pp. 136–7. ISBN 978-0-521-66624-4:
"The geothermal gradient of the mantle increases rapidly in the thermal boundary layers at the top and bottom of the mantle, and increases gradually through the interior of the mantle."

It is obvious the heat source for the mantle is not any external force, such as solar heating,
Otherwise the crust would be molten too, and we would all be extremely dead.
That heat has to be coming from the core, as evidenced by the gradient.
What can a big ball of iron and nickel do to produce that much heat?

It can spin!
How fast does it spin?
Surely not the same speed as the crust...
It must be spinning much faster. How much faster?

For that I'll need to very roughly approximate some friction coefficients.
I wish I had more precise figures, but unfortunately nobody has a probe that can actually journey to the center of the Earth... And even if they did, that's not a controlled laboratory condition, so I'm going to work with what I have:
“Metals in contact with glass in vacuum exhibit the same friction behavior as glass in contact with glass. Because glass transfers to metals (e.g. aluminum, iron, and gold,) glass is essentially sliding on itself.”

• Friction Behavior Of Glass And Metals In Contact With Glass In Various Environments, Donald H. Buckley, Lewis Research Center

This system is not in a vacuum, quite the opposite, it's under extreme heat and pressure the likes of which would be very difficult to replicate in a lab environment... But this is a place to start, and I've got to start somewhere.

The Engineering Toolbox (https://www.engineeringtoolbox.com/friction-coefficients-d_778.html)
Says glass on glass has a coefficient of 0.9-1.0
So we'll call it that for now.
Pressure at the boundary of Earth's core is estimated at 330-360 gigapascals.
One pascal is equivalent to one newton (1 N) of force applied over an area of one meter squared (1 m2). That is, 1 Pa = 1 N.

https://en.wikipedia.org/wiki/Inner_core
https://en.wikipedia.org/wiki/Mantle_(geology)
https://en.wikipedia.org/wiki/Thermal_history_of_the_Earth
https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget

delta_T=(7800muWabv)/(J(k1+k2))
delta_T = rise in temperature
mu = coefficient of friction
Wab = surface energy of adhesion
v = sliding speed
J = mechanical equivalent of heat
k1, k2 = heat conductivity of the two materials

These formulas are all designed to operate in linear systems.
When you try and wrap them around a sphere without a start and end point,
The only thing that spins in your head.

This is really heavy shit, and it doesn't make sense to me - the math is extremely intimidating. But I'm sharing it with you because laymen are not indoctrinated, and thing that don't make sense generally don't make sense to them. In that sense, you're perfect for this!

I have a question for you:

"Narrator: And the deeper you go, the hotter it is, right?

Marc: That's right. Although it's very difficult to find out the temperature at great depths, the core may be between about 7,000 and 12,000 degrees Fahrenheit. To appreciate how hot that is, the surface of the Sun is about 10,000 degrees, so our planet's core might be hotter than the surface of a star!

Narrator: OK . . . well, how did it get that way?

Marc: Our planet formed from many smaller bits of rock that collided and stuck together when the solar system was developing more than four and a half billion years ago. As each piece of rock fell onto the forming planet, it added a little bit of energy, which caused the growing Earth to heat up. So our home had a hot beginning."

Does that make sense to you?

Next question:
"Narrator: But after billions of years, why hasn't it cooled off?

Marc: Good question. A brilliant 19th century physicist, William Thomson, who we know better as Lord Kelvin, asked a similar question. He assumed Earth had begun in a molten state and then calculated how long it would take to cool to its present conditions without any other source of internal energy. He returned to this problem many times over the decades, and his final estimate at the end of the century was that Earth must be only about 20 to 40 million years old. His conclusion disagreed with findings from geology and biology, both of which showed that Earth was much older than that.

Narrator: Why were his calculations so far off? Was there a problem with his method?

Marc: Kelvin's method was good, but 19th century scientists didn't know about radioactivity. At the beginning of the 20th century, when they recognized that decaying atoms released tremendous amounts of energy, scientists understood that Earth has not simply been cooling off since its formation. Now we know that radioactive elements that take billions of years to decay have kept Earth's interior hot. " Could Lord Kelvin have been right?

"Now we know that radioactive elements that take billions of years to decay have kept Earth's interior hot."
How do we know that?

Upon review - we don't.
We can't measure the amount of radioactive material in the core, or the mantle.
We just assume there must be enough, because it's real hot down there, and we don't have any other explanation.

Quote Source: https://spaceplace.nasa.gov/review/podcasts/transcripts/090302_earths_core.html

Somebody on Quora asked
"If the terrestrial core and magma are hot due to radioactive elements decay, then why doesn't each volcanic eruption make a nuclear disaster far worse than Chernobyl?"

There weren't any great answers, but it's a really good question: the eruption of magma from Earth's mantle should give us a good approximation of the radioactive content present. If there were enough isotopes present to generate the type of heat we're talking about (5700K for 4.5 billion years is A LOT) one could reasonably expect lava not to cool off very quickly, and to possess a potentially dangerous amount of radiation. But it does cool off quickly, and it's not dangerously radioactive.

The arguments made in favor of the current theory are that lots of rock is a good insulator, and that it's small releases of heat from radiation accumulating over time. I'm not buying it without some really solid mathematical proofs, and I can’t find any.

I've been trying to break my own model all morning, and all of the math is very challenging... But what I find funny is that the guys on the opposite side of this argument are very serious physics guys, way better than I am at all kinds of math... They should have done these calculations already, to prove their own theory, and I can't find it anywhere.
The roughness of their approximations does not constitute anywhere near the level of certainty they possess when pressed on for explanations.

Neither do mine - I'm not sure I'm right - I'm not sure they're wrong.
But they're so sure they're right that it's unscientific.
Do the math first, bitches!
"Show your work" or STFU.

"...many smaller bits of rock that collided and stuck together" do not account for temperatures that may be in excess of the surface of the sun 4.5 billion years later. No fuckin' way.

FUCK LINEAR DYNAMICS! FUCK THEM RIGHT IN THEIR LINEAR ASSHOLE!
Goddammit. I've hit a wall. You can't find thermal exchange from friction without a start and end point and a nice straight line using any of the existing mechanics. They just don't work for this.
I have to make up new physics, and I have no experimental apparatus or funding.

!@$&%#$ $#@#, @$$!

Me today:

Why won't it break? My head is very hard!

My mind hurts now. I'm taking a break.