Using the force constant in equations

marcus · Mar 7, 2005

it's a bright spring day, seems like the first really warm day for a long time.
as I sat in the sunlight my pocket thermometer went up
to 1.10E-29. a raven is building a nest at the top of a palm tree
half a block away, the tree is tall, like 4E35 (40 paces).
the bird sits at its building site and croaks and then it fetches another
treebranch.
it occurred to me that I am taking the conditions of life less for granted
these days

this sunlight---the brightness of the solar constant adjusted for slant attenuation. and the ambient pressure (which we can hardly sense and ignore much of the time.) if it weren't for ample surrounding pressure those of us composed of small bags of fluid would be having a difficult time, and our fishpond would probably be boiling.

I've gotten used to thinking of pressure E-107 as one PSI, and of the happy balance between heavy and light pressure around me as 14E-107 or 14 "PSI". Psi is just a temporary mental connection, a named power of ten to use until thinking E-107 gets easy.

they arent mere twigs either. ravens are big. it is funny to see the black silhouette glide overhead with a goodsize branch in its beak. they croak deeper than a crow which is how you tell

marcus · Mar 8, 2005

in the history of a planet there is the unique event when someone on the planet understands for the first time how the star works.

Hans Bethe figured out how the sun works. He died at age 98 late Sunday. essentially all the energy life on Earth uses is made in the core of the sun by the protonproton chain that Bethe and his collaborators found in 1938

we should write down the protonproton fusion process chain

Archimedes wanted a marker that was simply a stone with a diagram of a sphere inscribed in a cylinder. because he was proud of being the first human to figure out something about their area and volume ratio. writing down the fusion pathway Bethe found marks a moment in the growing up and coming of age of civilization on earth, a moment like when Ole Roemer in 1676 for the first time measured the speed of light. like the first time you shaved. rites of passage.

http://www.nytimes.com/2005/03/07/science/08cnd-bethe.html

in natural units the temperature at sun core is 5E-25, and at the surface it is 2E-28, the hotter in the center business keeps it from being squeezed down under the weight of its own gravity and the temperature difference keeps the energy percolating out to the surface where it radiates off to Earth and the other planets. so this process at the core is vital

I keep forgetting how it goes, and the terminology. this is a rough draft:

proton + proton -> deuterium + antielectron + neutrino

deuterium + proton -> helium3 + photon

helium3 + helium3 -> helium4 + proton + proton

the net energy released per helium4 nucleus formed is E-20 natural

it is just a nice accident that it comes out a round number like that, if we wanted to say it more accurately we could say 1.04E-20

marcus · Mar 8, 2005

here's some good stuff about the protonproton process

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/procyc.html

here is some more high school-level stuff with animations
http://www.windows.ucar.edu/tour/li...Fusion/Fusion_in_stars/H_fusion.html&edu=high

one source says the net energy production is 25 MeV and other says 26 MeV, but we use eQ-----electron quartervolts which are E-28 natural energy units each.

multiplying by 4 you get 100 MeQ
and that is 100 million E-28
which is E-20 energy.

so to produce one natural unit of energy
the sun has to make E20 heliums:
100 quintillion helium nuclei

or when I eat a 1000 Calorie meal that is E-2 natural (a hundredth of a unit) so that is E18 helium's worth. the sun had to make quintillion heliums to supply the energy I'm going to get from my vittles.

nightcleaner · Mar 18, 2005

Hi Marcus

One day Goat boy was crawling around a particularly steep outcrop of the crumbly brown rock on the hillside where he kept his goats. It was a perilous place and he knew it was foolish of him to be there. But from the top of the rock spur there was a particularly good view of the valley, and what's more, at a quick glance around he could see all of his hillside and easily count all of his goats without having to run up and down and sideways all afternoon. He had climbed the pinnacle almost every day since he had discovered it. That had been, what, two years and some months?

Goat boys don't have much reason to count time, and counting goats is chore enough, if you keep in mind that counting them also means that your count had better come out the same each day. There would be all kinds of trouble if it didn't. All the running about came from the fact that you couldn't see the whole hillside from anyplace on it, you had to climb up the steep rockface.

And the rockface keeps changing every day, falling down here, dripping gravel like water over there, sometimes collapsing where there was a path. So Goat boy climbed a different way each day the weather was clear enough to see. But from the top, breathless, he could count them all, and not only that, but have a good rest looking out on the farms and villages all down the mountain valley. So he spent his afternoons.

But today, hanging out in the particularly perilous spot, he found himself face to face with something he had never seen before. It was a strange kind of ball on a loop of fine chain, like ladies wear their jewelry, and it was stuck in a hole in the crumbly rock where he never would have seen it except for that little slip, and, well, at least he caught himself from falling. He found a hold for the toe which was still tingling from the sensation of that last rock suddenly not being there, and jamming it in, he got a hand free to reach in and grab the thing.

It was unusually heavy for it's size, as if it were made of some valuable metal, like gold, he thought, or silver, but he didn't know much about precious stuff. He slung it around his neck and the chain purred like a serpent. He didn't stop to look at it until he got off the outcrop and was back on the slope that led to the very top. Then he stole a glance at it as it swung up, he took a last few steps, he grabbed it, turned and sat down plop on the edge of the cliff, breathing heavily from the climb.

Black. It didn't look like metal at all. The chain was shiney, but the little ball that hung on it so heavy was black as the sky at night, and now that he had a closer look, he even saw stars in it. Stars. That's what they were.

"Well, you might even say thank you."

"HUH?"

"Intelligent as much as clever and good looking." She sniffed the air. "And sweet smelling? Why, from over here, you hardly have any odor at all." She held her nose delicately, turning her face to the side, but looking at him still with eyes that sparkled in their corners.

"Who are you?"

She smiled at him and leaned forward, almost enough to dislodge her from her perch on a neighboring ledge, perhaps twenty feet away on the other side of a deep ravine. But she caught herself in time and smiled delicately. "I am Lissa. And I have come here to be your friend. That's my friendship gift, that you have in your hand."

"What? What gift? This is mine. I found it."

"So you did, and who do you think put it there?"

"Not you."

"Oh." She sat back. "Ok." She smiled again, into herself this time. "Well, what if I tell you what it looks like, then?"

"What?" He turned and held the ball in his fist so she couldn't see it.

"It's called a Zoharrr." She held the 'r' longer than seemed necessary. "It is a dull black sphere, tiny points of light if you look close." She watched his face change pointedly. "And if you look close, you might see, that one of the stars is different from the others. Yes, look at it. There. It's a disk, you see, and the others are mere points. She held a thin finger out to show him. "And there," she said, "If you watch that smaller star, right there, you can see that it is going around."

He startled. She was standing right next to him! There was no way across that steep wash. "How? Who? What?" She plucked the ball from his fingers as easily as picking a berry off a bush.

"And this. Look at this." She held the ball in front of his eyes and did something with her fingers. The ball changed. Inside it now was a swirl of stars like a whirlpool. She turned it again and it changed again, into his own eyeball. She tossed it back at him and he caught it clumsily, stepping backward. He almost fell, but she grabbed him and pulled him to her face. "Listen, Goat boy. Don't you ever doubt me, do you hear? I will never, ever, lie to you. You must believe me, everything I say, everything I do. Got it?"

Her eyes were green fire and her fingers thin and hard as ice, and he thought he felt his toes rise off the ground in her grip, but she set him down, let go, patted and brushed his shoulders. "There, now. It's alright. I just get a little, passionate, at times." She smiled sweetly and he caught her scent, stangely mixed with his own. His was a deep toned musk, hers the light fluteing of night blooming flowers, and between them he knew the contratemps stattico of their two beating hearts.

He sat down hard again and she sat down beside him, both of them breathing heavy. He looked at her, felt startled, looked at the ball, looked startled again, but the two starts canceled each other and he suddenly felt very calm. She smiled at him, giggled a little, and then reached up to fix the silver clasp that held her long raven hair in a braided bun at the nape of her neck. Her shoulders were narrow as a bird's and her breasts nuzzled the light flowered fabric of her blouse. Her skin was soft ivory, with a faint undertone of olive. He felt that he had been looking at her for a very, very long time. But he knew they had just met. The difference didn't puzzle him. He was sure it would always be that way.

"So. Give me that, and I'll show you how it works. It isn't just a pretty bauble, you know. It does much, much more." He hardly hesitated to put it in her hand this time, but he held onto the chain, not for safety, but because he wanted the touch of it. "You turn this here, you see, and that's the scale, it makes it larger and smaller. And this, turn this and it moves left, right. Here is up down. This is forward and back. You see it? Try."

And he did. Turning as she showed him made the image in the ball grow or shrink, and he could move the center of the sphere among the stars in it at will.

"That one, there, go close to that one." It was the star with the small, dim partner going around. "Now on the small star, got it? Now close, closer, very close." The small point of light became a disk, an orb, and then it filled the ball completely, making it look like a marble of glowing colors. It was very beautiful.

"Go ahead, keep playing with it," she said. "There's lots of stuff in there to see. Later, when you get the hang of how to move around in it, I'll show you where we are. You will never have to be alone again. Unless you want to."

She looked at him with a pout, then a little frown. "Oh well, never mind. You are the strong silent type, arent you?" She patted his hand. "And young. But don't worry. You will soon catch up to me. And pass me, no doubt. But don't go too fast. Follow me for a while, then we'll go side by side. The day I call you father is a long, long way off." She pulled his arm to her and hugged it, raised his hand to her lips as if to kiss it, but he pulled away. She laughed. He liked it.

It was she who told me about this test for gravity waves. You take two massive objects, spheres is good, and polished smooth is better. You put them very close together, as close as you can get them to stay, but not quite touching. Then, between them, you pass a beam of coherant light. On the other side, you have an array of detectors. You can amplify the effect using whatever lenses you like, and interferometry.

As the light passes through the narrow spot, it is affected by the gravity of the two spheres. The gravity acts like a lense. The light is bent. It bends in proportion to the masses, and according to how close the photons pass to the center of gravity of the two masses. When a gravitic event sends waves though your region of space, the masses of the two spheres will temporarily change in relation to each other, and you will observe changes in the light as it passes through the gravitic lense.

She also told me about this. You make a small black hole and put it in a containment vessel. Normally it would expire in a very short time, due to quantum evaporation. But what you do, see, is you feed the small black hole a steady beam of energy, enough to match the rate of radiation. That way, it lives longer. If you do it just right, it might even live forever. Longer than you, anyway.

Ha ha ha ha ha ha ha ha. Mad, I tell you. but that's what she said to me. You can believe it or not. Personally, I never doubt her, but as for you, well, she has never held you in her icy grip, so what would you know about that?

But maybe you can tell me about these other things. Is she right? I'd be very interested to hear what you decide.

Richard.

marcus · Mar 18, 2005

a small typo, and suggested name

If you want to try submitting the shortstory to a magazine then you might want a name. A possible name is "The Orrery"

As you probably know an orrery is a working model of the solar system. Or of some other system of moving orbs.
It is named after Robert Boyle, fourth Earl of Orrery, who was born in 1676 about the time of Newton and within a year or so of the first measurement of the speed of light (by Ole Roemer in Paris). Apparently the Earl liked models of the planets that went around by gears and he had them built and they got his name attached to them. But I think that orreries go back to maybe the greeks. They have big ones sometimes at a Planetarium, that take up whole rooms, and humans are fascinated by them.

What you have in the story is, by analogy, a kind of orrery.

In the eighth paragraph from the bottom there is a typo "parter" instead of "partner"

nightcleaner said:

And he did. Turning as she showed him made the image in the ball grow or shrink, and he could move the center of the sphere among the stars in it at will.

"That one, there, go close to that one." It was the star with the small, dim parter going around. "Now on the small star, got it? Now close, closer, very close." The small point of light became a disk, an orb, and then it filled the ball completely, making it look like a marble of glowing colors. It was very beautiful.

"Go ahead, keep playing with it," she said. "There's lots of stuff in there to see...

marcus · Mar 19, 2005

I would like to know the circular orbit speed around a black hole
at the distance 3R
where R is the schw. radius.
this is the minimum stable orbit
http://casa.colorado.edu/~ajsh/approach.html

it is assumed to be the inner edge of the accretion disk, if the hole has an accretion disk.

I would also like to know the circular orbit speed at 2R. this is the "zero kinetic energy at infinity" orbit. A thing that is almost not moving and very far away could fall and spiral into this orbit. It is unstable in the sense that a tiny boost that slows or speeds you up will greatly perturb it.

I think Andy Hamilton is discussing a nonrotating hole here

but I mainly would like the formula for the circular orbit speed at 3R (minimum stable orbit). Can anyone help out?

hmmm I see Andy gives a speed for the 2R orbit as perceived by observers who are themselves 2R out:
"Relative to an observer at rest at 2 Schwarzschild radii (i.e. at rest with respect to the distant stars), our velocity is sqrt(1/2)c = 0.707c, where c is the speed of light. Relative to an observer freely falling radially inward from rest at infinity, our velocity is 3/4c."

so if you spiral down into that unstable 2R orbit then you will see that you are going around 70 percent of speed of light
http://casa.colorado.edu/~ajsh/orbit.html

but I guess an observer very far away would judge your speed to be slower than that. maybe I should specify I want to know the speed from a standard viewpoint of someone far away

marcus · Mar 19, 2005

Andy Hamilton says that the kepler formula is exact for circular orbits around black holes

for convenience let us call Period/2pi = "radian time"
it is the time to go one radian. these things are going to be measured as they would be to an observer a long distance away, or at "infinity", to provide a kind of standard point of view (since the speed and gravity well would distort stuff for people actually involved in it).
also the orbit radius is measured as 1/2pi times the circumference, which is normal for black hole calculations since it is well-defined whereas the distance out from the singularity is more problematical.

kepler formula

GM (radian time)^2 = radius^3

so now I can say something about the speed at distance 3R!

GM = radius x speed^2

GM = 3R x speed^2

beta = sqrt(1/6)

I wonder if either I or Andy has made a mistake.
I also get that in the unstable circular orbit at 2R, the speed (from the distant perspective) is beta = 1/2. that is much slower than the 0.7 c which Andy says is measured by people actually involved.

check my calculation, anyone who wants, and refer to
http://casa.colorado.edu/~ajsh/orbit.html
if you want

this is kind of interesting. we should be able to get natural units examples out of these orbits around black holes

marcus · Mar 19, 2005

there are now two ravens living in the top of this very tall palm tree
a couple of lots over from us

nightcleaner · Mar 19, 2005

Hi Marcus.

Thanks for the word, Orrery. I got Zoharrr out of my vague memories, and should have googled it before using it. I see that it is already taken by Kaballah, and I have no conscious intention of indicating that use here. Actually, I was afraid I had stolen the name from the movie Big, where Tom Hanks puts a coin in an amusement arcade fortune telling machine and gets a wish. I was thinking maybe the name on the machine was "the amazing Zoharrr" or something like that. Maybe it was the Amazing Zantec. My memories are full of vague notions like that, which plague me. So I will change the word to Orrery, as you suggest.

work tonight, more study monday.

Thanks, Richard

ps rats, I see I have lost the edit option. Oh well. In future, then. R

marcus · Mar 20, 2005

what can we say about the sky?

Richard, i didnt realize you had a name for your shortstory already. I suggested you try "The Orrery" as a descriptive title. I don't know if that title has ever been used for a SciFantasy story. but only try it if you like it and want to. calling the story "Zoharr" would be OK too.
=============

this thread is supposed to be mainly about "test-driving" that new set of natural units that John Baez proposed a couple of years ago (and which I see used in QG research)-----trying the units out by examples.

however I don't mind wandering from the straight and narrow topic since it often produces ideas, and why not?

getting back to main topic, though, can we say anything about the way the sky looks? such an obvious part of our experience. can natural units have any bearing?

well the main thing is that airmolecules can scatter light. or else it the sky on a clear cloudless day would be black.
once you have that they scatter at all you can worry about why they scatter MORE BLUE than green or red.
there is the famous Rayleigh scattering thing that the probability that a molecule will scatter a visible photon depends on the fourthpower of the frequency so the higher the frequency of the incoming photon the more likely it is to scatter.

red-end freq is 7E-28 and blue-end freq is 13E-28, with green right in the middle
so we can say the ratio is 13/7 and raise that to fourth power is about 12
so a photon at the top-end is about 12 times more apt to scatter than one at the bottom end
but also the lower ones are somewhat more numerous and to be conservating let's just say that blue is about 9 or 10 times more likely to scatter than red
http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html
which is how hyperphysics site explains that normal sky-color is blue and sunset color (which has the blue scattered out of it by the time it gets to you) is red.

the secret of the fourthpower is that the air molecule is resonant at a frequency or frequencies up in the UV, so that is where the scattering probability has a maximum. and the visible range is near that. so the sharp increase with frequency in the visible is the behavior of approaching a resonant peak response. (BTW there is a polarization thing here too)

that's fine but there is still the bit about why does an air molecule scatter any visible light at all? of whatever color
It is much smaller than a visible wavelength, so how apt is it to scatter?
http://farside.ph.utexas.edu/teaching/jk1/lectures/node85.html
http://farside.ph.utexas.edu/teaching/jk1/lectures/node86.html

I will see if the brightness of the sky can supply an example for us.

marcus · Mar 20, 2005

thomson scattering cross-section of electron

earlier I was making lists of like a dozen or so basic constants
that are used so much they are worth remembering

the REALLY basic constants are all one, in this system, so they are not hard to remember

but then there is the next layer, like the mass of the electron is 2.1E-22 mass units

even that is not so bad because the rest-energy of the electron is the same number...2.1E-22 energy units.
and the Compton wavelength is just the reciprocal of that
1/(2.1E-22) length units.

well there is something called the "Classical Radius of the Electron"
which is just 1/137 times the Compton.

so it is something I can calculate just from knowing 1/137 and 2.1E-22

and the THOMSON crosssection which tells the probability that an electron left to its own devices will scatter some light is simply

\sigma_{\text{Thomson}} = \frac{8\pi}{3}(\text{classical radius})^2

I am having trouble getting the LaTex to work so for redundancy I will just type out what I was trying to write

sigma-sub-Thomson = 8pi/3 x (classical radius)²

once you have the thomson crosssection then (as that U. Texas link shows) you have to tack on a term that shows how the resonant frequency of the molecule affects the scattering probability, but the basic thing that there is any scattering at all comes from the Thomson, which is just 8pi/3 times the square of the classical radius.

It isn't important but I might as well calculate the thomson scattering crosssection

the radius is
1/(137 x 2.1E-22) = 3.48E19 natural length units

squaring and multiplying by 8pi/3 gives
1.01E40 natural area units.

wow. that is weird. the interaction of an electron with light is a little area which in these units comes out to right around E40 area units.

just as a check I converted that to metric and it was about 6.6E-29 sqmeters. wow again. that is what the U.Texas website on this gives!
getting the answer their conventional way involves looking up constants and multiplying a lot of stuff together because the formulas are more complicated but comes to the same thing.

marcus · Mar 20, 2005

I like the E40 area
when i walk out into the garden on a bright morning
I see the temperature of the sun is 2E28 natural
(and that is very close: has a couple of decimalplaces unstated precision)

and in the sky each molecule is holding out a card with this area E40
which shows the probability that a photon passing thru will bump it

and the rayleigh scattering section showing dependence on the photon frequency is just that E40 area units multiplied by

the fourth power of the freq. ratio-------(omega_photon/omega_resonant)⁴

so the blue overhead is talking about a small area with a simple formula namely

(\frac{\omega_\text{photon}}{\omega_{\text{resonant}}})^4 E40 \text{ natural units}

marcus · Mar 21, 2005

marcus said:

when i walk out into the garden on a bright morning
I see the temperature of the sun is 2E28 natural
...

I guess it has become a custom with me (might be too much to say an observance or a kind of mantra)

to go outside in the morning, or if it's raining wait tlll the sun comes out, and
be aware of some numbers that go along with the experience

first thing is the sun (you can tell by the color it glows) is really hot 2E-28
and our speed going around it is E-4
and a year is E50

and the thomson area E40 that makes the sky scatter light
(which when you correct with the fourthpower rayleigh factor explains the blue)

and the colors red-end 7E-28, green 10E-28, blue-end 13E-28
these being frequencies (photon energies, same number) that you would expect to get from something the sun's temperature

and the leaves look green because they are eating the red and blue but not the green in between.

the temperature of the air around me is like E-29, and inside me it's 1.1E-29

and that thomson area E40 comes straight from the mass of the electron 2.1E-22 and the number 1/137

and there is sound, like birds and maybe some distant freeway noise,
maybe I played the treble D on the piano just before I stepped outside E-40

and the speed of sound, which relates the pitch of a bird's call to the size of its throat and governs all kinds of resonance like that...

and then there is breakfast to think about... taking on a little energy...

marcus · Mar 21, 2005

brunch might be a hundredth of a natural energy unit
since the sun is out there and I feel its warmth I might remember
that it has to make E20 helium atoms in order to release one natural unit of energy.

i am vaguely aware that i am standing on a sphere. its girth at the equator is about 50E40

standing in the garden I feel a force of E-40 on the sole of each foot.

(telling me something about the Earth's mass and mine)

it was really windy yesterday, today it's calm, which says something about the temperature gradient and the threshold for convection

I should say that the mass of a proton is 1836 x 2.1E-22
and the mass of an air molecule is 29 x 1836 x 2.1E-22.
that will tell me the threshold for wind: it is 2/7 times the weight of a molecule of air.

time to take a walk up the hill in back of campus.
idleness punctuated by numerical musing

marcus · Mar 22, 2005

In natural units the Unruh temperature that goes along with an acceleration a is very simple

T_\text{unruh} = \frac{a}{2\pi}

You just have to get the acceleration that something experiences, expressed in natural units, and divide by 2pi. That gives the temperature of the thermal radiation seen in the accelerated frame.

Unruh temperature = acceleration/2pi

in the RHIC, heavy ion collider, stuff is decelerated from the speed of light down to zero in a distance they put at 0.2E-15 meter, which is 2.5E18 natural length units.
that means it is taking about 5E18 time units to come to a stop, from the speed of light.

Order of magnitude, the acceleration is 2E-19 natural units, so divide by 2pi and you get a Unruh temperature of 3E-20

this around a 100 million electron volts. basically what the RHIC people say.
http://www.bnl.gov/rhic/black_holes_kharzeev.htm

compare this Unruh temp to the surface of the sun which is 2E-28.
it is about 100 million times hotter than the solar surface.
so there is some thermal radiation which the experimenters have evidence of. I don't know if they are interpreting their findings right or not. I calculate the same Unruh temperature they do but I can't vouch that this is what is going on.

Meanhippy provided the original link for this:
http://www.bnl.gov/rhic/black_holes.htm

"Horatiu Nastase, a member of the high-energy physics theory group at Brown University, has written a paper, posted on the preprint website arxiv.org, in which he claims that collisions at Brookhaven’s Relativistic Heavy Ion Collider (RHIC) produce the analog of a black hole..."

They are not talking about Hawking radiation from a black hole, they are talking about Unruh radiation from acceleration which is ANALOGOUS to Hawking radiation from a black hole.
Bill Unruh at UBC Vancouver discovered his temperature and his radiation right around the same time as Hawking discovered the other kind.
The two formulas are very similar.

Here is the technical article by Nastase that goes with the news item.
http://arxiv.org/abs/hep-th/0501068

marcus · Mar 23, 2005

in conventional nuclear engineering and physics there is the familiar blue light in the tank of water----the cerenkov effect light.

you can tell the energy of a beam of electrons going thru water by the cerenkov angle, the angle that the light diverges from the direction of the beam.

the cerenkov rays make a cone of directions at a fixed angle from the direction of the beam

if you tell a physicist the angle, he or she will tell the energy of the electrons in MeV, or eevee.

we have to use electronQUARTERvolts, or "eQ" pronounced "eekyoo"

because E-28 of the natural voltage unit is a quarter of a conventional
and E-28 of the natural energy unit is a quarter of a conventional eevee
too bad the historically accidental metric volt is 4 times too big tough luck that is just how the cookie crumbled

so here is a problem, to keep in practice with natural units:
suppose there is a beam of electrons in water and the cerenkov angle turns out to be 30 degrees
what is the kinetic energy of one of the electrons?

\cos \theta = \frac{\text{speed of light in water}}{\text{speed of electron}}

I guess the best would be to first find the speed.

the speed of light in water is 0.75 natural units

marcus · Mar 23, 2005

This summary description of the units needs to be brought forward periodically, to keep it accessible. the latest copy is post #245, which is a ways back. So I will reproduce it here:

the force F = c⁴/(8piG) is the main constant in Gen Rel, the prevailing theory of gravity since 1915. The constant in the Einstein equation is not Newton's G, but rather F. In Quantum Gravity one often uses units in which |F| = 1
(this can come about by stipulating that |8piG|=1, since normally one already has adjusted the units so |c|=1)

the moment one sets
|F|= |c|=|hbar|=|k|=|e|=1
one has a fairly universal set of units and it is interesting to see what some familiar quantities come out to be.

Another way (suggested by a Kea post) to define the same units is to make the unit angular frequency be 3.7E42 per second. Call it Z, just to have a symbol. Adjusting the units to make the value |Z| = 1 gives the same set of units as setting |F| = 1.

I am trying out this version of natural units to see how they work. In order to try out the units one must keep a list of rough sizes of things handy----to use the units for practical purposes one must have a sense of scale. Here are some rough sizes of familiar things expressed in the units.
I periodically bring this list forward to keep it handy.

rough sizes:

Code:

q'ty expressed in nat.     approximate size
E8 mass             pound
E50 time units       year
E33 length           handbreadth (3.2 inch, 8.1 cm)
E34 length           pace
E37 length           half mile
E50 length           lightyear
E-5 energy           food Calorie 
E-8 energy            lab calorie 
E-28 voltage          quarter volt 
E-28 energy          quarter eV
10E-28 energy        typical photon energy for green light
E-53 electmagn.field unit     tesla 
E-57 field unit             gauss
E-29 temperatrure     average Earth surface temp
E-9 speed           2/3 mph
E-7 speed             67 mph
E-6 speed             speed of sound (cold air)
E-107 pressure      conventional PSI on airgauge
14E-107               normal atmospheric pressure
E-39 (ang. format) frequency   D on treble staff
E-50 acceleration   one "gee"
E-40 force          weight of 50 kg sack of cement, traditional "hundredweight"
E-49 power        144 watt bulb

some constants (approx.):

reciprocal proton mass 2.6E18
electron mass 2.1E-22
Hubble time 1.6E60
Lambda 0.85 E-120
rho-Lambda 0.85 E-120
rho-crit (critical density) 1.16 E-120
more exact Earth year 1.1676 E50
more exact lightyear 1.1676 E50
avg Earth orbit speed E-4
earth mass 1.38 E33
earth radius 7.86 E40
sun mass 4.6 E38
solar surface temp 2.0E-28
sun core temp 5E-25
solar constant 6.2E-117
CMB temperature 9.6E-32
earth surface air pressure 1.4E-106
earth surface gravity 0.88E-50
fuel energy released by one O₂ 17E-28
density of water 1.225 E8/E99

timescale:
3.700E42 rad per sec 1 (the unit frequency)
1/222 of a minute E42
4.5 minutes E45
As a handle on the natural timescale, imagine counting out loud rapidly at the rate of 222 counts a minute, each count is E42 natural time units. A thousand counts is 4 and 1/2 minutes. It just happens that one year is roughly E8 counts, or E50 natural.

marcus · Mar 23, 2005

marcus · Mar 23, 2005

about the cerenkov problem earlier

...suppose there is a beam of electrons in water and the cerenkov angle turns out to be 30 degrees
what is the kinetic energy of one of the electrons?

\cos \theta = \frac{\text{speed of light in water}}{\text{speed of electron}}

I guess the best would be to first find the speed.

the speed of light in water is 0.75 natural units

I think it is clear that the electrons are traveling at 0.866 speed unit.
so an electron's total energy is twice its energy at rest
which is 2.1E-22

so the kinetic energy is 2.1E-22 we don't have to convert that to "eekyoo"
but since an eQ is E-28 this amount would translate to 2.1 million eQ.
(around half a conventional MeV, if you like it so)

if anyone is following the thread and wants more detail on this please say, would be happy to provide it

marcus · Mar 26, 2005

One reason I had for practicing with these variant Planck units, in a thread like this, is because of a feeling that they are replacing conventional Planck units in QG research.

this is illustrated by what you can see martin bojowald doing in his most recent Loop Quantum Cosmology paper.
http://arxiv.org/gr-qc/0503020

On page 3 right after equation (8) he simply defines the Planck length by

l_P = \sqrt{8 \pi G \hbar}

so he is not walking on tiptoe he just flat-out explictly says "the Planck length is such and such" and it turns out to be the very same thing I have been calling "natural length unit" in this thread

it comes out to 8.1E-33 centimeter.
(c is already understood to have value unity)

I believe I must have seen that before but just wasnt sensitized to it.

well so the width of my palm is E33 Planck length, and I don't have to say E33 "natural length units" all the time, to keep reminding that these are variants of the older Planck units.

marcus · Mar 27, 2005

In another thread Fibonacci was asking what is the matter density in space
https://www.physicsforums.com/showthread.php?p=505249#post505249
and there were several answers offered depending on if he meant the overall average density of (visible? baryonic?) matter in the universe, or should it just be the amount of stuff in the space between stars in our part of the galaxy, or what?

I have to try answering this is natural units terms. the critical density, needed for the observed flatness, is the usual benchmark and it is
order of magnitude E-120

but if we need accuracy then 1.16E-120

and visible or baryonic matter is ordinarily estimated to be 4 percent of critical, so around 5E-122.

we need to imagine some volume, let's take an 81 cm step, roughly 2 and a half feet-----E34 natural length units----and consider the "cubic pace" volume which is E102 natural.
then the ordinary matter in the universe averages out to 5E-20 mass units inside that cubic pace volume.

a proton mass is about 4E-19. so in that cubic pace the average is roughly a tenth of a proton, order of magnitude.

In the space between stars in our galaxy it might be tenfold larger or one proton mass per cubic pace, just as a rough guess. but this estimate is overall including galaxies and the empty space between them, all averaged out

marcus · Mar 27, 2005

one thing I'm trying to do is sort out a small set of essential numbers which if you have them on a piece of paper by the computer can tell you the rest

for example I remember that in natural units the Hubble radius is 1.6E60
and in anybody's system of units the visible or baryonic matter is 4% of critical

that is enough to answer a wide range of questions:
the Hubble time is 1.6E60
the Hubble parameter H₀ is the reciprocal of that, namely (1.6E60)^-1
critical density is 3 times the square of the Hubble parameter
so if I ever forget it I can just go 3/1.6² and see that
critical is around 1.16E-120
I can take 4 percent of that and get the density of ordinary matter.
Or take other well known percentages to find the densities of other stuff like dark matter and the hypothetical dark energy.

So it comes down to remembering that the Hubble time is 1.6E60 natural time units (or, since it is the same number, that the Hubble length is 1.6E60 length units)

marcus · Mar 27, 2005

marcus said:

One reason I had for practicing with these variant Planck units, in a thread like this, is because of a feeling that they are replacing conventional Planck units in QG research.

this is illustrated by what you can see martin bojowald doing in his most recent Loop Quantum Cosmology paper.
http://arxiv.org/gr-qc/0503020

On page 3 right after equation (8) he simply defines the Planck length by

l_P = \sqrt{8 \pi G \hbar}

so he is not walking on tiptoe he just flat-out explictly says "the Planck length is such and such" and it turns out to be the very same thing I have been calling "natural length unit" in this thread

it comes out to 8.1E-33 centimeter.
(c is already understood to have value unity)

I believe I must have seen that before but just wasnt sensitized to it.

well so the width of my palm is E33 Planck length, and I don't have to say E33 "natural length units" all the time, to keep reminding that these are variants of the older Planck units.

The same pattern again, this time with a worldclass cosmologist in a survey article summarizing the state of his field. He just comes right out and says that the Planck mass is equal to the new value: 2.4E18 GeV.
check out page 9 of this definitive overview of current status of cosmology

http://arxiv.org/abs/gr-qc/0503107
Understanding Our Universe: Current Status and Open Issues
T. Padmanabhan
To appear in "100 Years of Relativity - Space-time Structure: Einstein and Beyond", A.Ashtekar (Editor), World Scientific (Singapore, 2005); 30 pages; 4 figures

"Last couple of decades have been the golden age for cosmology. High quality data confirmed the broad paradigm of standard cosmology but have thrusted upon us a preposterous composition for the universe which defies any simple explanation, thereby posing probably the greatest challenge theoretical physics has ever faced. Several aspects of these developments are critically reviewed, concentrating on conceptual issues and open questions. [Topics discussed include: Cosmological Paradigm, Growth of structures in the universe, Inflation and generation of initial perturbations, Temperature anisotropies of the CMBR, Dark energy, Cosmological Constant, Deeper issues in cosmology.]"

Padmanabhan does not mess around, on page 9, when it comes time to, he just says

M_P = (8\pi G)^-^1 \approx 2.4E18 GeV

apparently Ashtekar's nickname for Thanu Padmanabhan is "paddy"

lets double check that Padmanabhan figure for Planck mass is correct.
for us the eekyoo or electron quartervolt is E-28 of Planck energy, so Planck energy is E28 eQ
which is roughly 0.25E28 eV = 2.5E27 eV = 2.5E18 x E9 eV = 2.5E18 GeV.
OK Padmanabhan is right. actually an eekyoo is 0.24 eV, it is only approximately a quarter, it is really 0.24 instead of 0.25.

marcus · Mar 27, 2005

Just an aside about Ashtekar's book "A Hundred Years of Relativity" to be published by World Scientific this year.

It will have a chapter by Martin Bojowald too!

looks like it might be a very good book, with a definitive chapter on cosmology by Padmanabhan and a definitive chapter by Bojowald on current state of quantum cosmology (LQC)

Towards the end of paddy chapter he has some questions to ask of quantum gravity, basic things that cosmology needs to know, he does not give QG such a good report card. On page 25, he says:

"The second question is: How (and why!) was the universe created and what happened before the big bang? The cosmologist giving the public lecture usually mumbles something about requiring a quantum gravity model to circumvent the classical singularity - but we really have no idea!. String theory offers no insight; the implications of loop quantum gravity for quantum cosmology have attracted a fair amount of attention recently [45] but it is fair to say we still do not know how (and why) the universe came into being."

[EDIT] sorry about the unfortunate confusion over the words "was created"! I should have realize that could suggest a conscious creator and eliminated the words. What Padmanabhan more likely meant is how he pHrased it the second time "came into being". That is more impersonal and more in keeping with scientific inquiry in general and cosmology in particular. When i posted the quote it did not occur to me that anyone would read it as suggesting anything other than simply "came into being".[/EDIT]

nightcleaner · Mar 28, 2005

Hi Marcus

Assumption: the universe was created. (whoooo boy, hot topic. I pray we not get into a creationist debate.)

Assumption: there was time and space before the "big bang" (well there has to be if there is going to be a creator going around creating stuff?)

an idea: the "creation" is ongoing and can be observed right now by investigating conditions at very small scales. This is a generalizing reformulation of the concept from Biology that ontology recapitulates ontogeny. If I remember it right, ontology is the study of how organisms form from reproductive cells. A single cell becomes an entire organism. Ontogeny is the study of how species evolve from simpler species (cheese! crossing the creationists again.)

Well we can watch a single cell become an organism. The idea is that the single cell retraces the steps that the species went through in evolving. First it is like an amoeba, then it is like a worm, then it is like a fish, then like a reptile, then like a mammal, and so on. It isn't a very exact process. Lots of the steps can be left out without losing anything, so eventually the genetic instructions for those steps are deleted.

I am surprised to see a world class cosmologist asking this how and why question.

Thanks for the conversation.

nc

selfAdjoint · Mar 28, 2005

nightcleaner said:

Hi Marcus

Assumption: the universe was created. (whoooo boy, hot topic. I pray we not get into a creationist debate.)

Well, honestly, nightcleaner, if you assume a creator you're going to get static from those who, like Laplace, have no need for that assumption.

Assumption: there was time and space before the "big bang" (well there has to be if there is going to be a creator going around creating stuff?)

Not necessarily. The Bible says "without form and void", and some of the causal triangulations proposals could fulfill this. To mathematicians and some physicists, fully metric spacetime is a very special idea that could be preceded by several more general states.

an idea: the "creation" is ongoing and can be observed right now by investigating conditions at very small scales. This is a generalizing reformulation of the concept from Biology that ontology recapitulates ontogeny. If I remember it right, ontology is the study of how organisms form from reproductive cells. A single cell becomes an entire organism. Ontogeny is the study of how species evolve from simpler species (cheese! crossing the creationists again.)

You're thinking of ontology (development of the individual embryo) and philogeny (evolution of the species). There was a nineteenth century belief that "Ontogeny recapituates philogeny" which is what you are stating here, but it's false! Ontogeny does go through stages reminiscent of earlier forms, but each species does that in a slightly differnet way, and the stages that are displayed do not by any means include all the evolutionary stages. A human embryo spends some time looking a lot like a frog, but no time looking like a chimp.

Well we can watch a single cell become an organism. The idea is that the single cell retraces the steps that the species went through in evolving. First it is like an amoeba, then it is like a worm, then it is like a fish, then like a reptile, then like a mammal, and so on. It isn't a very exact process. Lots of the steps can be left out without losing anything, so eventually the genetic instructions for those steps are deleted.

And I needn't have worried, you got there on your own! (as usual). But what does this have to do with continuous creation? Continuous creation was a hot idea in the 1950s. It seemed to be refuted by the discovery of the microwave background, but with modern theories of "episodes" of inflation, however caused, the continuous creation idea might stage a comeback.

I am surprised to see a world class cosmologist asking this how and why question.

Suprised how? That a cosmologist would ask how and why questions?

Thanks for the conversation.

Thank YOU!

nightcleaner · Mar 28, 2005

Hi selfAdjoint

You are correct, and have new information for me, both much appreciated. I am pleased that there are ideas out there about what the universe might have looked like before there was time to look, or anything to look at. How entertaining. I would certainly like to know more about these ideas.

"The second question is: How (and why!) was the universe created and what happened before the big bang?" Marcus posted this sentance, a quote from Padmanabhan I believe.

I was trying to point out that there are some assumptions here. If the universe is said to be created, then one must assume that the speaker invokes some person or principle as a creator. I do not personally treat the idea of a creator as an assumption. Within my internal cosmology, the creator holds an honored and beloved position, but I wouldn't presume to insist anyone else require this belief. And I do not appeal to my belief, either, in trying to understand the universe. Laplace had some wrong ideas about inheritance of traits but was right, I think, in leaving the creator out of human attempts at understanding. "Because God made it that way, now go to sleep," was not a comfort to me, but a source of insomnia.

Philogeny. How embarassing. I knew I should have googled that up.

Yes, it is a flawed idea, in biology, for the reasons you mention, and others. I was just putting it up here for wallpaper, and maybe as a little friendly tickle for the creationists. Flawed as the idea is, it has value in understanding how things are done in biological evolution. The idea I am more interested in today is that conditions and events in the first instants of the big bang may be recapitulated on a microscopic scale all around us.

Long, long ago, far, far away, and very, very tiny. Irresistable.

The truth is I am still not comfortable with the expansion implied by gravity. The evidence seems irrefutable. But the windows on this elevator are all painted shut. My monkey and his gramma are never, ever going to accept that we have been accelerating all this time, and still can't tell we are going anywhere. How fast are we going now anyway? Four and a half billion years at one G...I refuse to calculate it. It wouldn't make any sense anyway.

Ok, Marcus Help! I am being kidnapped by logic. Four and a half billion c! No. That is just plain silly. And people argue about phase shift!

We are huge and expanding much faster than can possibly make any sense. Hence, the past is a tiny little homunculus hidden deep within us. We are expanding so fast that no ordinary perceived velocity will ever allow us to escape ourselves. We each of us carry the entire history of the universe in our bowels. What a concept.

So, if we look at things that are very very tiny, we should see our own universe as it was very, very long ago.

I have to tell the truth, it is a curse and I know I would be better off to keep my mouth shut. Here it is. It is easier to believe in an old guy with a long white beard, a bathrobe, and a magic finger than to accept this bill of lading for a load of manure. What does an optimist do with a load of crap except make fertilizer?

Anyway the idea should totally be falsifiable. All we have to do is compare very tiny stuff with very old stuff. If the two don't look the same, bingo.

For example: Very early universe, very high energy. Very small scale, very high energy. So far so good.

Darn, I wish I could find my copy of "The First Three Minutes."

Any help here? Anyone?

Inside the atom: gravity, then strong force, then weak force, then em. Is this like, inflation, quarkonium, neutronium, and let there be light? What was that about the ultraviolet catastrophe? I really have to find that book. I can see the cover: Stephen Hawking, grinning like the cover of Mad Magazine.

Heck with it. I am going to go get another copy.

Be well,

Richard.

selfAdjoint · Mar 28, 2005

nightcleaner said:

Hi selfAdjoint

You are correct, and have new information for me, both much appreciated. I am pleased that there are ideas out there about what the universe might have looked like before there was time to look, or anything to look at. How entertaining. I would certainly like to know more about these ideas.

The most mature paper on causal triangulations, is Ambjorn, Jurkievich, and Loll, which has received a lot of attention from the physics community. Marcus has linked to it a couple of time, as have I. The "Why" question seems to presume causality if nothing else ("Why? Because!"). To me, this doesn't require a mind, since causality is expressed as geometry in relativity ("Light-cones"). This is the attitude of the AJL paper.

"The second question is: How (and why!) was the universe created and what happened before the big bang?" Marcus posted this sentance, a quote from Padmanabhan I believe.

AAH! Light dawns. My apologies!

I was trying to point out that there are some assumptions here. If the universe is said to be created, then one must assume that the speaker invokes some person or principle as a creator. I do not personally treat the idea of a creator as an assumption. Within my internal cosmology, the creator holds an honored and beloved position, but I wouldn't presume to insist anyone else require this belief. And I do not appeal to my belief, either, in trying to understand the universe. Laplace had some wrong ideas about inheritance of traits but was right, I think, in leaving the creator out of human attempts at understanding. "Because God made it that way, now go to sleep," was not a comfort to me, but a source of insomnia.

It was Lamarck who taught inheritance of acquired traits. This seems like an awfully snotty comment of mine, but I have all these useless facts in my head!

Philogeny. How embarassing. I knew I should have googled that up.

What's in a name? You had the concept right on.

Yes, it is a flawed idea, in biology, for the reasons you mention, and others. I was just putting it up here for wallpaper, and maybe as a little friendly tickle for the creationists. Flawed as the idea is, it has value in understanding how things are done in biological evolution. The idea I am more interested in today is that conditions and events in the first instants of the big bang may be recapitulated on a microscopic scale all around us.

Marcus will tell you that Bojowald's LQG cosmology takes the universe back through the BB to the other side, where it has an "arithmetically negaive" mirror development. So in a sense in this approach it comes in from negative infinity (of age-of-universe, a simpler thing than time), does a minimal volume flip at BB time, and goes off to positive infinity. So the physicists are actively working on these concepts; the string folks have their clashing brane models too. Google on ekpyrotic for some of those. The name means "from the pyre" a reference to the myth of the phoenix.

nightcleaner · Mar 28, 2005

Rats! I am going to have to quit relying on this old creaky memory entirely. Lamarck indeed. Well a mark is a place, isn't it. I suppose the nursery rhyme about three blind mice and a farmer's wife has nothing to do with either of them, too. Humpf.

Anyway I edited my last post while you were adding your last post. Honestly I checked before I started and you were offline then. I really am going to go get that Hawking book.

Thanks,

Richard

ps that would be Stephan Weinberg. The Hawking book, of course, is A Brief History. I have had both volumes, but neither is on my bookshelf tonight. Instead, I came home with The Cambridge Handbook of Physics Formulas. Pure heroin for physics junkies.

nc

marcus · Mar 29, 2005

nightcleaner said:

... but neither is on my bookshelf tonight. Instead, I came home with The Cambridge Handbook of Physics Formulas. Pure heroin for physics junkies.

I must say i started laughing out loud when I read that.

I didnt find Hawking "Brief" readable. My mother-in-law didnt either so she gave her copy to me thinking that I would. it has sat idle on the shelf ever since.

never looked at the Cambridge Handbook of Heroin for Physics Junkies,
could be great fun!

Have been enjoying your conversation with spicerack. Now I regret having butted in. It was better talk when it was just you and her

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