Using the force constant in equations

marcus · Mar 2, 2005

marcus · Mar 3, 2005

So far we have been fairly casual about the names we call the natural units.

The natural units themselves, which is the system we are using, have simply been called, for instance, "natural length unit", "natural energy unit", or sometimes just "energy unit", or (when the type of quantity was understood already) just saying "natural", for short.

Early on, I was trying to use a lot of "named powers of ten" which were humanscale practical-size power-of-ten multiples of the natural units----like "pound" for E8 mass unit, and "food Calorie" for E-5 energy unit. Even that, I am doing less now, tho still do it some (to help provide a picture of rough size of things).

So the basic units themselves have not (so far at least) been dignified with a rigamarole of names and symbols, as they do in metric international system: for instance with Joule energy, Pascal pressure, Newton force, etc.
At least so far we don't have names and symbols. Instead, we've done things informally and just called them what they are: energy unit, force unit, power unit, voltage unit, etc.

All the same, I was thinking that, in some circumstances if not all the time, it might help to have a standard way to "spell out" the units we are using, and be very explicit-----

I don't know if this is a good idea, but I am reluctant to introduce a lot of new symbols and it would be possible to efficiently "spell out" all the units (any that one wanted to, when it seemed appropriate) using only ONE new symbol, plus familiar things like c and hbar and electron charge e.

but one would have to get used to "reading" the units in this type of spelling. I mean with the natural frequency Z.

frequency is a number of events per time

so 1/Z is a way of writing the natural time unit. We really don't have to have Z a bold letter so I will just make it ordinary.

of course c is the unit speed, and multiplying unit speed by unit time gives unit length: c/Z.
So c/Z is a way of denoting the unit length ("planck length" in this variant of the Planck units)

and cZ is a way writing the natural unit of acceleration, unit speed per unit time

and so on. (one has the option of reading Z as "per unit time" when interpreting units written this way)

hbar is a natural ratio of energy to freq. If you take any freq. and multiply by hbar you get an energy. one might even say that's what hbar is all about.

So hbarZ is a way of writing the natural unit of energy

and hbarZ/c² is a way of writing the natural unit of mass

Maybe this would be useful. Have to try it out and see.

marcus · Mar 3, 2005

I guess the only thing to do is try and see if anyone understands and wants to reply.

My mass is 2E10 hbarZ/c²

does anybody want to reply and tell me (roughly approx. good enough), in more conventional terms, what that is? or describe some physical quantity at their end?

dont have to say your mass, can say the mass of something else not you, and there is linear dimension (c/Z is the unit and for convenience E34 c/Z is about 32 inches). Plenty of other types of quantity as well.

marcus · Mar 3, 2005

My wife and I just had supper---mostly it was rice and chicken breast with special orange sauce made with oranges off the tree.
Caloriewise supper, for me, was 1.5E-2 hbarZ.

thats how much food energy.

It would be nice if someone else would report a quantity or two in this notation.

BTW the point of the notation is that it is self-decoding. You only have to know the key which is that Z=3.7E42 per second and you can, if you want, find the metric equivalent of anything I say.

for instance as regards supper if you wanted to know what hbarZ is in joules (I am not proposing that you should want to know this, but if you did) you could just multiply the standard NIST value of hbar
which is 1.0545716E-34 by the metric value of Z which is 3.7E42
and that would give some number of metric Joules of energy----
and then 1.5E-2 of that, as I indicated, would be supper.

that is what i mean by the symbol being self-decoding.

nightcleaner · Mar 3, 2005

Hi Marcus
I think you are on the right track here, and I have been working over the natural units also, from a dimensional analysis point of view. For example, force seems to me to work down to inverse time. I should do more calculation, instead of just dimensional analysis, so I will try to work your mass problem.

Personally I am not fond of named units either, or of the ones scaled to human conventions. I am still working on relating units using Z to units using F. I'll let you know if anything interesting comes up.

h-bar Z cE-2 is the mass unit which I have as .434 E-8 kg, so
2E10 .434 E-8 = 2 x .434 E2 = 86.8 kg = 190 lbs.

Have you lost some weight? I thought I remembered from an earlier post that you weighed about 200lb?

Thanks,

Richard

nc

marcus · Mar 3, 2005

nightcleaner said:

...
I'll edit this with a reply to the mass problem.

good! it is pretty dull having a onesided discussion about something like mass (which is already not very exciting I fear)

if you have a dog, estimate his/her mass if you don't wish to reveal your own.

I will demonstrate the self-decoding feature of the notation for mass:
the mass unit is hbarZ/c²
If one doesn't want metric equivalents then one simply leaves it at that.
But if one wants metric equivalents then
hbar = 1.0545716E-34 joule second
Z = 3.7E42 per second
one multiplies those together and gets 3.9E8 joule
then one divides by square of speed of light, which is about 9E16 (m/s)²
and gets around 0.434 E-8 kilogram.

so, like if you have a dog, and the dog's mass is 2E9 hbarZ/c²,
and you have to describe the dog to a Frenchman who insists being
told kilograms
then you just multiply 2E9 by 0.434E-8 and get 8.6 kilograms.
or you tell the dog to bite the Frenchman on the leg and ignore the question
(but you can convert if you want to, it is built into
the notation for the mass unit hbarZ/c² itself)

marcus · Mar 3, 2005

nightcleaner said:

h-bar Z cE-2 is the mass unit which I have as .434 E-8 kg, so
2E10 .434 E-8 = 2 x .434 E2 = 86.8 kg = 190 lbs.

Have you lost some weight? I thought I remembered from an earlier post that you weighed about 200lb?

I think you must be kidding. No, obviously I lie about my weight!
It really is 200 well just a bit over, traditional American pounds.
But I call it 2E10 hbarZ/c^2 for round numbers.
Am I supposed to carry it out to two decimal places when I am sensitive about it anyway?

Let's talk about your dog. Do you have a dog?

nightcleaner · Mar 3, 2005

Yes, I do have a dog, or at least partial custody of a dog. His name is Tucker, a black lab, and he weighs in at very close to E10 mass units.

I myself am not svelte. I mass about 2.5E10M.

marcus · Mar 3, 2005

everybody please don't forget that the E notation is for powers of ten, as in a calculator.

if you want to write 1000 you can say E3

if you want to write c², then don't say cE2, say c^2.
cE2 would, I guess, stand for 100c.

Chronos and i were talking about this just 3 or 4 days ago. it is easy to confuse nE2 and n^2

nightcleaner · Mar 3, 2005

ok. noted. Probly one of the reasons I get confused easy. Thnks.

BTW, did you agree that F works down to dimensions of T^-1? and wouldn't these also be the dimensions of Z? Mass works down to dimensions of TL^-1, inverse velocity.

I have been trying to resolve all these units in terms of L, length, and T, time. Any ideas? Perhaps it is a useless endeavor.

Actually, I do find mass to be an interesting concept. I remember elsewhere working it down to T^-2 in dimensional units, and again elsewhere to inverse length, but I have too many notes and don't remember exactly how I got to those dimensions.

What do you think in general of the idea of using dimensional analysis to find the "meaning" of things like mass and energy? If I can get comfortable thinking of all physical quantities in terms of length and time, then I intend to use Einstein's spacetime equivalence to cancel out the universe. Sometimes I get tired of the universe. But then, I suppose, if I do find a way to cancel it all out, someone else will find a way to brew up a bunch of new ones. Oh well. And they say breaking mirrors is bad luck.

Oh, I was going to tell you, I read that the December 27 gamma burst was actually an expanding cloud of gamma, and the wavefront of the cloud was said to be moving at .3 c. So the Dec.24 event could have been a precurser after all. Perhaps a gravitational reaction to all those approaching gammas?

nc

marcus · Mar 3, 2005

nightcleaner said:

Yes, I do have a dog, or at least partial custody of a dog. His name is Tucker, a black lab, and he weighs in at very close to E10 mass units.

I myself am not svelte. I mass about 2.5E10M.

Great! this is my favorite PF post for the past couple of days, since whenever Kea wrote encouragements about the book. this is a great post.
I like black labs a lot. they are so beautiful and cute in a lumoxy way.
they can have enthusiasms too, like catching tennis balls in the air. they are enough dog that they have a distinct doggy smell. perhaps I should not generalize.

I am happy that Tucker mass is E10 mass units. that is like 43 kilogram so you do not pick that dog up lightly.

Yes I am not svelte either we don't have to be precise about these personal things.

marcus · Mar 3, 2005

let us estimate Tucker's energy intake per day

like my daily food energy intake is 3E-2 hbarZ
that is 0.03 hbarZ.
(I know it is more congenial to be informal and say "0.03 energy unit" but I am trying out the notation)

does he eat dry food (kibble) or can food or other?

------
btw about collapsing units all down into one unit (or two), it can be done.
by setting stuff equal to one it is possible to reduce all units to one unit and all types of quantity down to one type. but this may actually be counterproductive. I like to keep the different types of physical quantity distinct----speed differnt from force, different from voltage, different from acceleration, different from density. But it is in some way a matter of taste. One tries to be consistent.

when I say |c| = 1 what I mean is that the value of c is one, expressed in these units. in other words that c = 1 length unit per time unit.

there is a subtle difference between this and saying baldly flat-out c = 1.
If you say c=1 it is like there are no units in the picture at all! c is just a number, the number 1. Or maybe it means that length and time are measured with the same unit! But that is too radical for me, so I say |c| = 1 meaning that there is a time unit and a length unit and they are distinct. but related so that c = 1 unit length per unit time.

that is the idea behind conventional Planck units too. Planck length and Planck time are two different things. And Planck mass is different, and so on. You can DO physics with all the units collapsed into one, and I believe somepeople like to do this. but I am very reluctant to take that step.

nightcleaner · Mar 3, 2005

marcus said:

let us estimate Tucker's energy intake per day

like my daily food energy intake is 3E-2 hbarZ
that is 0.03 hbarZ.
(I know it is more congenial to be informal and say "0.03 energy unit" but I am trying out the notation)

does he eat dry food (kibble) or can food or other?

He eats 3 cups of kibble each day, and numerous treats. I don't give him treats, just lots of pats and rubs and one-way conversation. My ex, now a very good friend, gives him p-nut butter in a Kong, sometimes five or more tbsp each day. And he gets table scraps, not from me of course. I take him for a run almost every day. He runs about a mile, then he has had enough. He is overweight, and gets scolded by the vet every time we take him in.

He smells very good. I even like to smell his paws. He is a very affectionate dog, but spoiled horribly, by my ex, of course. He doesn't like other dogs but he is crazy for attention from people. Any passer-by will do. He has to stay leashed when outdoors except when I take him out for a run. Then we go out in the deep woods where we never see other dogs or people.

I edited the post before this some. Maybe you didn't see it.

I was having some confusion about the mass unit. I have it variously as dimensions E c^-2, h-bar Z c-2, and sqrt (h-bar F c^-3.) Do you concur with these?

nc

nightcleaner · Mar 3, 2005

marcus said:

btw about collapsing units all down into one unit (or two), it can be done.
by setting stuff equal to one it is possible to reduce all units to one unit and all types of quantity down to one type. but this may actually be counterproductive. I like to keep the different types of physical quantity distinct----speed differnt from force, different from voltage, different from acceleration, different from density. But it is in some way a matter of taste. One tries to be consistent.

when I say |c| = 1 what I mean is that the value of c is one, expressed in these units. in other words that c = 1 length unit per time unit.

there is a subtle difference between this and saying baldly flat-out c = 1.
If you say c=1 it is like there are no units in the picture at all! c is just a number, the number 1. Or maybe it means that length and time are measured with the same unit! But that is too radical for me, so I say |c| = 1 meaning that there is a time unit and a length unit and they are distinct. but related so that c = 1 unit length per unit time.

that is the idea behind conventional Planck units too. Planck length and Planck time are two different things. And Planck mass is different, and so on. You can DO physics with all the units collapsed into one, and I believe somepeople like to do this. but I am very reluctant to take that step.

Yes, I understand your reluctance, but I have been working on this for some time and have actually a better reason in mind than the one about cancelling all appointments forever. It does seem that every time I get down to one or two base units, I lose track of the meaning. It is kind of a Tantulus myth. Just when I think I am making progress, the well dries up.

And after all, the base units of length and time are not absolutes anyway. There seems to be no Planck to hold onto in the swell of the sea of relitivity. Sometimes I think I should develop an interest in hockey instead. Things there at least are unequivocal.

marcus · Mar 3, 2005

nightcleaner said:

He eats 3 cups of kibble each day...
I edited the post before this some. Maybe you didn't see it.

Let's eventually find out how to convert that 3 cups to Calories.
I just now saw the expanded edited version of the previous post.
I will provide some input to that process but I will not venture in that direction myself. It can get confusing when units are folded up into each other, one can lose track. So I personally refrain from it. but AFAIK anyone can do anything they want along those lines if they can manage to be consistent.

I was having some confusion about the mass unit. I have it variously as dimensions E c^-2, h-bar Z c-2, and sqrt (h-bar F c^-3.) Do you concur with these?

E c^-2, h-bar Z c-2, I agree. the other one I have to check. Yes, I concur with all three (the other one too)

nightcleaner · Mar 3, 2005

ok. He gets science diet lite, and say 1/4 cup pnut butter a day. Maybe about five dog biscuits. And the table scraps, which don't really amount to much. I can't tell you about the caloric value of the foods, because I am at my house and Tucker usually eats over at my ex. It is reduced fat pnut butter.

Marcus, I am tired tonight and have to retire early. Thanks for your conversation.

As always,

Richard

marcus · Mar 3, 2005

nightcleaner said:

Yes, I understand your reluctance, but I have been working on this for some time and have actually a better reason in mind than the one about cancelling all appointments forever. It does seem that every time I get down to one or two base units, I lose track of the meaning. It is kind of a Tantulus myth. Just when I think I am making progress, the well dries up.

And after all, the base units of length and time are not absolutes anyway. There seems to be no Planck to hold onto in the swell of the sea of relitivity. Sometimes I think I should develop an interest in hockey instead. Things there at least are unequivocal.

I laughed out loud when I read that in icehockey
"things are at least unequivocal"

the tantalus picture is very descriptive of what i remember experiencing with possibly similar investigations which can be very exciting for a moment but in the end one clutches air

montaigne invented the essay, where one combines a thoughtful reflective attitude towards one's own life with just the right amount of philosophy balanced with humor.
selfAdjoint would know if it was really montaigne. if it was, then maybe I should read montaigne.
what you just wrote, the post about icehockey, was a bit like an essay.
where does wisdom come from except from shared reflection and honestly reported experience

Marcus, I am tired tonight and have to retire early. Thanks for your conversation.

thanks likewise. I won't bug you again about the Tucker calories (dumb idea). well enough. good night

marcus · Mar 3, 2005

the unit of electric current can be written Ze
(flow of electrons at rate of 3.7E42 electrons per second)
and the unit of voltage can be written as hbarZ/e
(unit potential energy per unit charge, i.e. per electron)

Ze current is 6E23 amps and hbarZ/e voltage is 2.4E27 conventional volts.

so when you multiply the current and voltage units together (which must give the power unit hbarZ²) you get
6E23 amps x 2.4E27 volts = 14.4E50 watts.
which I got earlier for the unit power. just checking.

I want to scope out what it might be like to use
Ze for current
hbarZ/e for voltage.

this lightbulb over my shoulder is drawing 120 volts and about 0.6 amps so what is it drawing in natural units?

E-24 current units = E-24 Ze

480 quartervolts (about) so 480E-28 = 4.8E-26 voltage units.
Let's round it to 5E-26 voltage units = 5E-26 hbarZ/e

that's what the lightbulb should have written where the specs are on the top: E-24 Ze and 5E-26 hbarZ/e.
and for the wattage it would be 5E-50 hbarZ²

marcus · Mar 4, 2005

Richard mentioned googlephobia the aversion to extreme numbers and I find it comes and goes in fits. sometimes quantities in terms of natural units seem too extremely small or large to assimilate.

(assimilate often means to find something similar)

the pressure unit can be denoted hbarZ⁴/c³
(which maybe deserves some explanation, why is that the unit force per unit area?)

and by coincidence
E-107 hbarZ⁴/c³ = about 1 PSI
(actually 1.06 PSI but still close enough to say that when I check the tires on the car I put in 30E-107 pressure)

we seem to be near the edge of what I can tolerate by way of extreme numbers, but anyway why is this how you spell the natural unit pressure?

because unit length is c/Z and area is (c/Z)²
and unit force (being energy/length) is hbarZ/(c/Z) = hbarZ²/c

so unit force over unit area is hbarZ²/c divided by (c/Z)², and that is

hbarZ⁴/c³

If you work it out in metric (using 3.7E42 per second, and metric values of hbar and c) and by the way I don't see why you should think you need to, then it comes to 7.335E111 Pascal. Pascal is the sanctioned alias for "Newton per square meter"

so if you ride a bicycle and put 60 PSI in the tires then you are
riding on the pressure 60E-107 natural.

and regular atmospheric is 14E-107.

nightcleaner · Mar 4, 2005

I suppose this is why self-Adjoint cautioned me about reductionism. I have come this far to see the land where there is only unity and separation, and unity is removed in time as separation is removed in distance. The universe is very flat here, unmarked in all directions from where I stand to the horizon, and the sky is unmarked also from horizon to azimuth. The sky is a mirror, and so is the ground, so the horizon here is quite invisible. If I look straight down, I see only my own face stareing back at me. Why have I come to this place? To find myself. I would turn and go, but there is no turning here. Mach was right.

Well, I am strangely satisfied. Now that all the universe has come down to me and my feet, I remember, as an infant, the insane discovery of toes. That's me, out there, but how can that be? For this is me, in here. I can't be out there, and in here, both, can I? And if that is really me, what are these eyes?

Now there is the space between stacked mirrors. The Casimir force, and the degeneracy of protons in a neutrino beam. Why, exclusion is attractive, and neutrinos count the aeons in a proton life. I am amazed by these things and filled with a renewed sense of wonder.

marcus · Mar 4, 2005

nightcleaner said:

I suppose this is why self-Adjoint cautioned me about reductionism. I have come this far to see the land where there is only unity and separation, and unity is removed in time as separation is removed in distance. The universe is very flat here, unmarked in all directions from where I stand to the horizon, and the sky is unmarked also from horizon to azimuth. The sky is a mirror, and so is the ground, so the horizon here is quite invisible. If I look straight down, I see only my own face stareing back at me. Why have I come to this place? To find myself. I would turn and go, but there is no turning here. Mach was right.

Well, I am strangely satisfied. Now that all the universe has come down to me and my feet, I remember, as an infant, the insane discovery of toes. That's me, out there, but how can that be? For this is me, in here. I can't be out there, and in here, both, can I? And if that is really me, what are these eyes?

Now there is the space between stacked mirrors. The Casimir force, and the degeneracy of protons in a neutrino beam. Why, exclusion is attractive, and neutrinos count the aeons in a proton life. I am amazed by these things and filled with a renewed sense of wonder.

intense essay. the brinkmanship of introspection.
I am becoming a fan. I will supply some outlandish looking Z-symbols for various types of physical quantity like the energy-density with appears to cause curvature (the unit of the stress-energy tensor)

I walk up the hill nearly every day. it is aerobic for about half hour and very important. Have you run the mile with Tucker today?

marcus · Mar 4, 2005

these Z symbols for the units are alienating and a bit scary, while the informal casual nomenclature is comfortable and easy.

it is very easy to say "E10 mass units" or "E10 natural" for the dog's mass.

it is off-putting to say E10 hbarZ/c²

but I think I should check it out anyway:

the natural unit of brightness (power radiating per unit area) is the
extreme brightness of
hbarZ⁴/c²

compare the surface of the sun, power radiating per unit area
it is roughly 3E-112 hbarZ⁴/c²

or compare the brightness of direct sunlight at Earth's distance from sun
6E-117 hbarZ⁴/c²

the point is the extreme difference between what I think of as very bright, like the brightest sunlight I ever see on earth, or like the face of the sun if you could look at it up close, and this universal unit brightness

they differ by over a hundred orders of magnitude, it is primordial
------------------

now what about curvature and energy density
the unit of area is (c/Z)² and the unit of curvature is the reciprocal (Z/c)²

the force is hbarZ²/c

If you multiply an observed curvature by this force then you get the density of energy needed to produce that amount of curvature (main eqn. of GR)

try multiplying curvature x force units
(Z/c)² x hbarZ²/c = hbarZ⁴/c³

and in fact what is on the righthand side is the natural unit of energy density------in other words one unit of energy density produces one unit of curvature and it is proportional

any actual energy or mass density one would encounter would be much much less than unit density, and any real observed curvature would be proportionally less than unit curvature too.

still just trying the notation out, poking around so to speak (btw pressure and energy density have the same unit---as in metric: Newton per sq. meter is algebraically the same thing as joule per cubic meter)

[edit: added on reflection. I'm thinking this Z notation is not reader-friendly enough.
it has the advantage of being explicit: definite and self-defining. but it is too cold and outlandish. maybe it could be used for sporadic marginalia and footnotes]

marcus · Mar 4, 2005

despite the downside outlandishness, to continue testdriving the Z notation, let's use it in calculating the number of CMB photons in a cubic mile of space.

the natural temperature unit is hbarZ/k

hbarZ is the energy unit and k is the Boltzmann constant which NIST lists
(if metric equiv needed hbarZ/k = 2.826E31 kelvin)
CMB temperature is 0.96E-31

first let's do it informally without Zees and calling pi²/15 =2/3

then the energy density of the microwave background is just 2/3 times the fourth power of the temp. let's be sloppy and call the temp E-31 so the fourth power is E-124.
so in natural units the energy density of the CMB is just (2/3) E-124
and the average photon energy is 2.7 times the temp, so 2.7E-31
we divide the total by the average to get the number of photons:
(1/2.7)(2/3)E-93
now a halfmile is E37 natural and a cubic halfmile is E111 volume units
so the number of photons in a cubic halfmile is (1/2.7)(2/3)E18

and a cubic mile is 8 cubic halfmiles. so multiply by 8 and we get that
the number of CMB photons in a cubic mile is 2E18

hey, nice. Two quintillion of these very old photons, that left home a few hundredthousand years after the Bang.
====================

now let's do it with the Zees, in a more uptight regular way.

the radiation is blackbody thermal, and the volumetric energy density of blackbody radiation depends on the temperature:
it is pi²/15 (times a constant which has value one and is just there to take care of the units) times the fourth power of the temp

the constant with value one is k⁴/(hbar³c³)
you can see it has value one because everything it is made of has value one (it wouldn't if you were working in metric so then you would need to multiply out or look up in book), because here
|k|=|hbar|=|c|=1

and in thermal radiation the average photon energy is 2.701kT

(1/2.701kT)(pi²/15)(k⁴/(hbar³c³)T⁴

and one of the Tees cancels, so it is only T³ now, and I will put in what the temperature of the CMB actually is: T=0.96E-31 hbarZ/k and get

(1/2.701)(pi²/15)( k³/(hbar³c³) (0.96E-31 hbarZ/k)³

I am jumping thru all this hoops and the number answer is going to be the same. this may diminish one's pleasure slightly. Anyway when you put all the constants in you find that almost all cancel, because they were there mainly to take care of (unnatural) units.

(1/2.701)(pi²/15)(0.96E-31)³ (Z/c)³

and that (Z/c)³ is the reciprocal of the unit volume(c/Z)³ means per unit volume
so it is a number per unit volume (a number of photons per unit volume) like we said in the first place.

marcus · Mar 7, 2005

Casimir force in natural units

https://www.physicsforums.com/showpost.php?p=398364&postcount=18

formulas are often simpler and easier to remember in natural units and the formula for the Casimir force is no exception

between two conductive plates the attractive force per unit area is:

force/area = (pi²/240) (1/separation)⁴

so it's simple you just put sep in and square twice to raise it to the fourth,

and the number in front is basically just 1/24
because pi-square is about 10.

marcus · Mar 7, 2005

the challenge is often just to get comfortable with the large numbers
which is mainly a business of practice with examples
so like E33 length units is a handbreadth (3.2 inch or 8.1 cm)
and a convenient area is E66 (roughly palmsize)

so suppose we want to know the Casimir attraction force on a palmsize E66 area where the separation is E30

the main thing is just raise sep to the fourth and get the reciprocal E-120
then we divide by 24 and that's the casimir force!

actually it is the force per area, so we multiply by our sample area E66
and get
(1/24)E-54
and that is the force felt by the palmsize area, expressed in natural force unit. we're done!

but then how do you imagine this delicate force? Well I always relate forces to what I feel on the sole of my foot when I am standing quietly in the garden. On each foot I feel E-40 force
(traditionally it would be called a "hundredweight")
and a hundredth of that is E-42 and it's the weight of a pound of butter.
But everybody probably has their own way of connecting to the force scale.
Anyway that E-54 force you see up there, for me it would be a trillionth of the weight of a pound of butter. that is: E-12 x E-42 = E-54
And it is astonishing to me that they can measure forces that delicate in the lab. but they do. the casimir force e.g. between two gold spheres has been measured and found to agree with formula. humbling thought.

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.

Using the force constant in equations

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