Using the force constant in equations

[marcus]

... The "lines" therefore are artifacts brought about by the presence of the iron filings. The field lines are not really lines through empty space at all, but need the presense of material particles for definition, correct? ...

I agree.
field lines are a mathematical tool for drawing a field. they are not really there as material objects.

there are alternative ways to draw a field. those do not use field lines but they use other mathematical tools to depict or represent. these are also not there in material reality.

one can depict a field by first imagining the framework of Euclidean 3D space (like 3D graph paper) and at each point one imagines a little arrow.

the direction and length of the arrows gives the needed information about the field.

some fields are harder to imagine because you can't capture the information about the field simply by drawing field lines or bunches of little arrows. but why worry about that?

to understand QHE you just must picture the magnetic field as a thick bunch of arrows pointing straight up sticking thru the rectangular planar semiconductor sample----see the picture.

they make the electrons of the current going down the length of the sample want to "swerve" or veer over to one side-----so voltage builds up on one side versus the other.

 

[nightcleaner]

Superconductivity? Resistance falls to zero at some values of magnetic field.

The unit, h/e^2 n, uses h instead of h-bar? And why is it not presented as
n e^2/h? An integer number of squared charges per Planck? And on the other side of the graph, what is P_xx? and what is that unit, k omega per sq? Would that be square as in an area? So a ratio, of resistance to area? But xx isn't an area. So would it be a curve, the curve of the current j_x? So the resistance is the resistance to the curve? Curve means acceleration, and naturally charges resist acceleration.

 

[nightcleaner]

QH effect looks like it is geometric. I am playing with the numbers. Seems like mag field and amplitude of effect are roughly equivalent, with a factor of ten.

can QH effect be used to turn superconductivity on and off? Application in quantum computing? i am going to go play with the numbers some more. Magnetic resonance? What is sweeping? Is it like herding electrons with magnetic pulses?

I'll be back soon, if the dish doesn't run away with the spoon. Marcus, do you remember the Uncle Wiggley stories?

Be well, and many thanks

Richard

 

[marcus]

... And why is it not presented as
n e^2/h? An integer number of squared charges per Planck? ...

It IS presented that way sometimes. For example in the Wikipedia article.

In conventional physics talk and electrical engineering, the reciprocal of a resistance (a voltage-over-current ratio) is called a "conductance" (the word for a current per voltage, or current-over-voltage ratio)
So if it is to the author's liking to present it as you suggest, then he will talk about "Quantum Hall Conductance" which will be various values
e^2/h, or 2e^2/h, or 3e^2/h, or...

I think maybe aesthetically this is better.

However the NIST website lists the constant as 25,812.807 Ohm resistance.

If I want to be aesthetically better I have to talk about a constant which is
1/25812.807 "siemens" conductance.
many people have heard of Ohms of resistance but may not have heard of siemens of conductance. So I run the risk of losing them.

But I do not care all that much.
Ohm is just the metric name for "volt per amp" or volt/amp ratio.
and Siemens is the metric name for "amp per volt" or amp/volt ratio.
You prefer to talk about amp/volt ratio and you are reading this thread and the other people arent, so if you like to talk in terms of conductance, that is entirely to my liking.

You mentioned the h versus hbar thing.
Yes, this is a case where h is the preferred form of Planck constant. Physicists use hbar a lot (it has become pretty much the rule in the things I read) but whenever convenient they occasionally write h instead! It means you don't have to write 2pi

So e^2/h acts like a quantum of conductance in this situation
and you get multiples of this basic current-to-voltage ratio.

I will get the link to the Wiki article that discusses it that way.
http://en.wikipedia.org/wiki/Quantum_Hall_effect

 

[marcus]

I'll be back soon, if the dish doesn't run away with the spoon. Marcus, do you remember the Uncle Wiggley stories?

I can remember reading an Uncle Wiggley book, or books, when I was about 7 years old but I cannot remember any of the content. I remember a picture of a river and a riverboat and Uncle Wiggley, the rabbit, who was the hero, was on board the boat. Maybe he was steering, or maybe he was just riding passenger.

My memory of Uncle wiggley has faded. I know he was a rabbit though.

what about you, do YOU remember the uncle wiggley stories?

the dish running away with the spoon has nothing to do with it. I am sure you are aware that the dish-spoon escapade belongs to Mother Gooserhyme about cow jumped over the moon and is entirely extraneous (or so I believe) to stories about rabbits.

the metric unit of conductance (amps per volt) used to be the "mho"
which is Ohm spelled backwards, but the official body which governs the metric system renamed it "siemens". they play politics of honoring various national science role-models by naming units after them. they have great power over this department of our language. they are called CIPM "comité international des poids et mesures" or something like that: international committee on weights and measures If they decide to honor a German edison then even if you like Mho, Mho dies.
Eventually everyone goes along with decisions of the CIPM.

 

[marcus]

just to recall the short summary in post #121
https://www.physicsforums.com/showthread.php?p=457767#post457767

now what I want to condense into a post or so is a sampling of how the formulas look, which this thread has been illustrating

1. for a satellite in circular orbit
mass = 4 x period x speed³

e.g. a planet's year is E50 and its speed is E-4 (both very like Earth's)
how massive is its star?
4 E(50-12) = 4E38

e.g. a planet's mass is E33, its year is E50 and the speed of a synchronous satellite circling it is E-5 (similar to Earth case as well)
how many of this planet's days to a year?
4 period E-15 = E33, 4 period =E48, 400 days in a year.

e.g. you are orbiting a small planet at the speed of a run, 6.7 mph, and find that full circuit takes 1 and 7/8 hours. What is the planet's mass?
speed = E-8, 4 x period = 450 minutes = E47, E47 E-24 = E23

2. for black hole radius, area, temperature, evaporation time

radius = (1/4pi) mass
area = (1/4pi) mass²
temp = mass^-1
evaporation time = (80/pi) mass³

3. radiant energy density and brightness
(energy per unit volume, power per unit area)

energy density = (pi²/15) temp⁴
brightness = (pi²/60) temp⁴
...

that is the first three of the 8 items.

John Baez is skimming around a planet of pure gold. How long does it take him to make one complete orbit?

 

[marcus]

Over centuries, the planet's generations of craftsmen have carved ornamental figures on its surface. Mostly they are figures of naked women, as do often occupy the artistic mind, but there are also those of monkeys and elephants engaged in sportive activity. The entire surface of the planet has been worked ornamentally in this way and Baez admires it as he skims along in low orbit.

By diligent study Baez has acquired the ability to judge brightness in the infrared (which the unenlightened cannot see) and he notices that the planet's surface glows with brightness 2E-117

what is the temperature of the planet?

 

[marcus]

just to recall the short summary in post #121
https://www.physicsforums.com/showthread.php?p=457767#post457767
...
John Baez is skimming around a planet of pure gold. How long does it take him to make one complete orbit?

item 6 of that list mentioned that in low orbit, limiting case,
radiantime² = 6/density

our densities of materials are on the E-91 scale and gold is 23 some.
Call it 23E-91.
radiantime² = 6/(23E-91) = 2.6E90
radiantime = 1.6E45
multiply by 2pi to get time for full orbit, remember E45 = 4.5 minutes
it seems that one circles a solid gold planet very quickly regardless of whether (within reason) it is large or small.

item 3 said
brightness = (pi²/60) temp⁴
so if the brightness is 2E-117 all one needs do is multiply 2E-117 by 60/pi² and take fourth root.

as a humanscale handle on it 2E-117 is like two 160 watt litebulbs on a square pace area: one litebulb power is E-49 and the area is E68, and the ratio of that power to area is E-49/E68 = E-117. Two bulbs is twice.

(60/pi²)2E-117 = 1.21E-116

(1.21E-116)^1/4 = 1.05E-29

 

[nightcleaner]

Hi Marcus

Does a cyclotronic cat rotate?

 

[marcus]

the cyclotron frequency of the proton

this is partly in reply to richard. the cyclotron frequency of basic particles like electron and proton has been an important frequency to know in experimental physics over the years, especially in the design of ring accelerators (like cyclotrons) and detectors (like cloud and bubble chambers). the spiral paths one sees in detector photographs are due to there being a vertical magn field so the particles come in and go splat and the pieces that are charged go in spirals.

however I have introduced this idea using charged cats instead of charged particles because more people are cat-conscious than proton-conscious

... they have special cats which are highly tolerant of electric charge. It is possible to charge one of these cats up to E19 a truly amazing charge equal, in conventional terms, to 1.6 metric Coulombs!

A large magnetic room has been built to discover the cycloton frequency of fully charged cats.

A cat of charge E19 and mass E9 (about 10 pounds) is launched into a uniform vertical field of strength E-53 (in conventional terms one Tesla). The cat is observed to travel in a circle with a fixed constant angular frequency determined by its mass m, charge q, and the strength B of the field

frequency = qB/m = E19 x E-53/E9 = E10 x E-53 = E-43.

This constant frequency is called the "cyclotron frequency of the cat"
...

However let us now calculate the cyclotron frequency of the proton in a 1 Tesla magnetic field

It is very easy to do in natural units because the field B = E-53, the charge q=1 and the reciprocal mass 1/m= 2.6E18 (this is a number you have already seen dozens of times in this thread)

frequency = qB/m = 1 x E-53 x 2.6E18 = 2.6E-35

to get a humanscale handle on this frequency, recall that the musical pitch D on the treble clef (a note that sopranos and altos sing) is E-39.

so we are talking something that is 10,000 times higher frequency---which would be E-35----and then some, a little factor of 2.6.

[edit: Note about the previous post. One can easily determine that cats are stable with regard to rotation. Simply drop a cat from a convenient height. You will observe that the cat only rotates as much as it has to so that it lands rightside up. The question is not relevant to the problem but no, the cats in the cyclotron do not rotate.]

[edit: NOTE about next post. It is on the round number planet where gravity is a neat E-50 instead of around 0.9E-50 the way it is here. the air, which is a comfortable temperature and good to breathe, offers no resistance to motion]

 

[marcus]

Batman is in his batbed, sipping a cup of warm batmilk.
It is his sleepytime and he has a hard day of fighting injustice tomorrow.
King Kong reaches in through the window and, seizing Batman, hurls
him upwards at angle 45 degrees from the horizontal at a speed
of 7E-8.
How far does Batman travel before he goes bump on his batbottom?

 

[marcus]

In 1873 the two poets Verlaine and Rimbaud went to Belgium. They were 29 and 19 years old.
Verlaine shot Rimbaud with his pistol, giving him a non-fatal wound.
The mass of the bullet which Verlaine shot at Rimbaud was E7
and the speed was E-6.

As a consequence Verlaine had to sit in jail for 2 years during which time he wrote this poem:

Le ciel est, par-dessus le toit,
Si beau, si calme!
Un arbre, par-dessus le toit,
Berce sa palme.


La cloche, dans le ciel qu'on voit,
Doucement tinte,
Un oiseau sur l'arbre qu'on voit,
Chante sa plainte.


Mon Dieu, mon Dieu, la vie est là,
Simple et tranquille.
Cette paisible rumeur-là
Vient de la ville.


-Qu'as-tu fait, ô toi que voilà
Pleurant sans cesse,
Dis, qu'as-tu fait, toi que voilà,
De ta jeunesse?

What was the momentum of the bullet?

 

[marcus]

I just made this rhymed translation of the Verlaine poem:

The sky above the roofs,
so clear and calm!
And higher than the roofs,
there sways a palm.

From steeples on that sky
a chime comes faint,
and from the tree outside
a bird's complaint.

My god that's Life out there:
so settled down--
the peaceful noise I hear
comes from the town.

"Hey you down there! the one
with all the tears:
Say, what have you done
with your young years?"

Le ciel est, par-dessus le toit,
Si beau, si calme!
Un arbre, par-dessus le toit,
Berce sa palme.


La cloche, dans le ciel qu'on voit,
Doucement tinte,
Un oiseau sur l'arbre qu'on voit,
Chante sa plainte.


Mon Dieu, mon Dieu, la vie est là,
Simple et tranquille.
Cette paisible rumeur-là
Vient de la ville.


-Qu'as-tu fait, ô toi que voilà
Pleurant sans cesse,
Dis, qu'as-tu fait, toi que voilà,
De ta jeunesse?

this poem is about looking out of the jailhouse window
and regretting one's lost youth.
we've all had this experience, or will sometime.

 

[marcus]

Verlaine carves a wooden cat

Verlaine carves a wooden cat.
He inserts a screw-eye so he can tie a string to the cat
and suspend it like a pendulum from the ceiling.

Then he shoots the cat with his pistol.

The famous poet has aimed precisely at the cat's center of mass, the slug buries itself deep in the heart of the wooden carving. This causes the cat to swing.

How much momentum does the cat acquire at impact?

 

[marcus]

Batman is in his batbed, sipping a cup of warm batmilk.
It is his sleepytime and he has a hard day of fighting injustice tomorrow.
King Kong reaches in through the window and, seizing Batman, hurls
him upwards at angle 45 degrees from the horizontal at a speed
of 7E-8.
How far does Batman travel before he goes bump on his batbottom?

Batman flies 50 paces, that is a distance of 50E34 = 5E35 natural.
solution: vertical speed = horizontal speed = 5E-8,
gee = E-50
time of flight = 2 x 5E-8/E-50 = E43
distance of flight = E43 x 5E-8 = 5E35

as a rough estimate, a pace is 2 and 1/2 feet, so 50 paces is about 125 feet.

 

[marcus]

Rimbaud measures the angle of deflection of the cat

Verlaine carves a wooden cat.
He inserts a screw-eye so he can tie a string to the cat
and suspend it like a pendulum from the ceiling.

Then he shoots the cat with his pistol.

The famous poet has aimed precisely at the cat's center of mass, the slug buries itself deep in the heart of the wooden carving. This causes the cat to swing.

How much momentum does the cat acquire?

The carved wooden cat is suspended by a string from the ceiling at a distance of 2 paces, or 2E34 natural.
the mass of the slug is a tenth of a pound----E7 mass units----and the muzzle velocity of Verlaine's pistol is E-6, roughly the speed of sound.
Therefore the slug's momentum is 10 natural units of momentum.

the mass of the cat is about 10 pounds----E9 mass units----so for it to acquire 10 units of momentum it must have the speed E-8 (in familiar terms 6.7 mph).

What is the kinetic energy of the cat immediately after impact?

KE = (1/2) m v² = (1/2)E9 x (E-8)² = (1/2)E-7 natural energy units.

Rimbaud, who is the lab assistant, measures the maximum angle of deflection from the verticle attained by the pendulum.

What swing angle does Rimbaud measure?

 

[marcus]

How the Gypsies stole the Moon (revised)

How the Gypsies stole the Moon

Some gypsies were roaming this part of the galaxy. On their way thru the solar system they stole the moon and replaced it by a black hole of the same mass

Dont worry, said the gypsies (when the people complained) you will still have tides and everything will be the same because the black hole we put in has the same mass----1.7E31 units---as the moon.

The people appointed John Baez the noted explorer to negotiate.

Give us back our moon, Baez told the gypsies, this black hole you gave us will eventually evaporate. It is not a fair exchange, you have cheated us.

The gypsies thought about it some. then they said "All right, we will give you one chance. If you can tell us how long the black hole will take to evaporate we will swap the moon in for the black hole and take our black hole away with us!"

John baez cubed 1.7E31 to get 4.9E93

then he multiplied by 80/pi to get 125E93

he knew gypsies like to use units based on the Force, so he said "Evaporation will take 1.25E95 natural."

Very good, said the gypsies, but you are from Earth and measure time in years. Tell us the time in years so we can know you really understand.

John Baez knew that a year is close to E50 natural units of time, so that the answer would be close to 1.25E45 years. In fact a year is 1.17E50 natural, so he divided 1.25 by 1.17 to get 1.07 and said
"1.07E45 years"

All right said the gypsies and they swapped their black hole out and the real moon back into orbit.

 

[nightcleaner]

The carved wooden cat is suspended by a string from the ceiling at a distance of 2 paces, or 2E34 natural.
the mass of the slug is a tenth of a pound----E7 mass units----and the muzzle velocity of Verlaine's pistol is E-6, roughly the speed of sound.
Therefore the slug's momentum is 10 natural units of momentum.

the mass of the cat is about 10 pounds----E9 mass units----so for it to acquire 10 units of momentum it must have the speed E-8 (in familiar terms 6.7 mph).

What is the kinetic energy of the cat immediately after impact?

KE = (1/2) m v² = (1/2)E9 x (E-8)² = (1/2)E-7 natural energy units.

Rimbaud, who is the lab assistant, measures the maximum angle of deflection from the verticle attained by the pendulum.

What swing angle does Rimbaud measure?

5E-8 ML2T-2 E50t2L-1=5E42ML;
5E42ML E-9M = 5E33L

The cat is lifted 5E33, the rest is trig.

secant theta = 20E33 1/15 E-33 = 20/15 = 1.5
cos theta = .75
theta= about 41 degrees

 

[marcus]

The cat is lifted 5E33, the rest is trig.

right on target nightcleaner!
the pendulum swing is just enough to lift the cat a distance 5E33
exactly as you say

one way to do the trig (for anybody reading the thread who likes trig)
is to say (since the length Richard calculated, 5E33, is a quarter of the length of the pendulum) we want to find angle A such that:
1- cos A = 1/4
cos A = 3/4
A = 41.4 degrees angle

so the pendulum swings some 41 degrees converting KE to PE and then it stops and turns around and swings back.

 

[nightcleaner]

Hi Marcus

Some gypsies were traveling through Switzerland and they lost a trinket. A goat boy found it and tried to pry it open but couldn't. He took it to his grandmother, who was a wise woman, and she said he shouldn't play with it.

But she was very curious about what was inside the trinket and so she took it along with her to a meeting of her friends at Solstice. They always had a good time at Solstice and the old woman drank quite a bit of blackberry cordial. When she got home again, she had a good sleep, and after a few days she unpacked her bags, discovering that the trinket was gone.

Then she began to worry. Those darn Gypsies. They were always going to far places and bringing strange things back with them. What if what was in the trinket were dangerous? Some of her friends might be silly enough and yet smart enough to open the trinket. Then what might happen?

She went deep into a cave and had a long think. Now, wise women have certain mystical abilities, and one of them is to be able to see things and places that their eyes can't ordinarily visit. She should have used this before, but she was busy getting ready for the Solstice gathering and hadn't had time, before, to sit in a cave.

Now she used her mystical ability and found that things with the trinket were worse than she first imagined. Inside the trinket was a very very hungry worm. If it were released from it's magical case, it would fall to the center of the earth, swallowing everything in its path. Then, it would keep on going through the center, and come out almost all the way to the other side. Then it would fall back again, swallowing everything in its path. Eventually, given enough time, it would swallow up everything in the earth, leaving only a hollow shell. She didn't think this was a good idea.

She was about to set out to retrace her steps to search for the trinket, and had just put on her coat and hat, when she saw a gypsy caravan passing by on the road just beyond her gate. A young girl was sitting in the window of the caravan. She was wearing the trinket on a chain around her neck, and she held it up to show it to the old woman, giving her a dirty look.

She might have felt much better that the gypsies had recovered their trinket on their own, but she didn't trust gypsies. She spit three times on the path and turned around twice before going back in her cottage. The whole episode left her with an uneasy feeling. Next time she saw the goat boy, she gave him a good swat to the back of the head.

And if the dish doesn't run away with the spoon, or the teacup fall into the soup kettle, I will be back tomorrow for another bedtime story.

Thanks for being here,

nc

 

[marcus]

And if the dish doesn't run away with the spoon, or the teacup fall into the soup kettle, I will be back tomorrow for another bedtime story.

so will I, and i will expect another story from you!

 

[marcus]

we could try utilizing the Josephson effect, in a story or problem.
Here is the Wiki article:
http://en.wikipedia.org/wiki/Josephson_effect

it explains that there are several effects, or several parts to the Jos. eff.
1.The AC Jos. effect amounts to a perfect voltage to frequency converter
(Wiki says) in other words you put a constant voltage across the junction and a current flows but the current RIPPLES and the frequency of the ripple is propor'nl to the voltage. In our units the constant is simply the number 2.

if the voltage put across the junction is E-31 (in conventional terms, a quarter of a millivolt)
then the ripple frequency resulting will be 2E-31 (remember that soprano D is E-39 so we are talking something a hundred million times higher than a soprano)
the impressive thing to me is not that it is a high frequency but that the ratio is just the number 2 regardless of how you build the device---it is an absolute universal proportion between voltage and frequency

every voltage has a particular "pitch"

2. The Inverse Jos. Effect this is a perfect frequency-to-voltage converter (Wiki says).
If you have a known frequency microwave source you can set the junction up someway that allows you to "shine" the microwave signal on the junction and GET A VOLTAGE produced which is proportional to the frequency.
Here the constant is just the inverse of 2, namely 1/2.

Wiki says that the Inverse Jo. is used by the metric system people to standardize the volt.

Maybe it used to be that if you wanted to know what a volt was you called them on the phone and they would come over with a standard one volt chemical battery (or something equally ridiculous) and show it to you and say "DAS IST VUN FOLT!" and they would let you hook up things to it and callibrate your volt gauges and so on. But now they don't do that.

Now I suppose if you call them the metric people will still come to your house but they don't bring their old chemical battery (which wasnt very reliable) instead they bring a superstable microwave zinger. They come in and immediately ask "WO IST DER CHUNKTSHUN??" and you show them your Jo. junction and they point their zinger at it and zap it with their precise standardized frequency and it gives a little squeak and makes a perfect one volt potential. And they say "Das ist vun folt," and go away.

In other words WHAT HAS NOW BEEN STANDARDIZED IS NOT THE VOLT ANYMORE BUT THE FREQUENCY THAT PRODUCES ONE VOLT in a Josephson junction.

Or so it seems to me anyway. Maybe someone has more detailed knowledge of contemporary standards.

 

[marcus]

when I discuss frequencies I prefer to consistently use angular format (radians per unit time) instead of cyclic format (cycles per unit time) to talk about them.
Ordinarily physicists don't stick to one format and switch easily back and forth.

the letter they use for frequency (in angular format) is small omega looking like a small rounded w.

the letter for the other format could be a nu sometimes or an f.

in the Wiki article you can see both formats being used
----------------

when you put a steady voltage across a Jo junction it is a little bit like blowing a whistle
(except it is a special whistle where the harder you blow the higher the pitch gets, proportional to the pressure)

with a whistle blowing makes the air stream thru the whistle but it is a steady stream with a flutter or ripple superimposed on it. there is a basic "DC" current of air but on top of that there is an AC flutter.
-----------
a commercial company Theva also has stuff on web about Jo junction
http://www.theva.com/super/josephson.html
http://www.theva.com/super/ac_josephson.html

they seem to use omega angular format frequency more consistently than Wiki but I haven't looked it over enough to recommend it. they have several related pages. talk a little about SQUIDs and such.

if anyone has a good link for Josephson effect please share it!

 

[marcus]

Astronuc just posted about a bright flash witnessed in December 2004
http://www.everything-science.com/index.php?option=com_content&task=view&id=111&Itemid=2
see his post "brightest explosion ever observed"
https://www.physicsforums.com/showthread.php?t=64274

some co-authors of the Nature article are
Bryan Gaensler (Harvard-Smithsonian Center for Astrophysics)
Rob Fender
Maura McLaughlin

“This is a once-in-a-lifetime event. We have observed an object only 20 kilometres across, on the other side of our Galaxy, releasing more energy in a tenth of a second than the Sun emits in 100,000 years,”

"The next biggest flare ever seen from any soft gamma repeater was peanuts compared to this incredible December 27 event. Had this happened within 10 light years of us, it would have severely damaged our atmosphere and possibly have triggered a mass extinction. Fortunately there are no magnetars anywhere near us."
-----------
Let's estimate the energy release in natural units of energy, and also gauge the power output during that tenth of a second.
A year is E50 and 100,000 years is E55.
I looked up the power output of the sun and it seems to be 2.7E-25 (have to double check this)
So the energy the sun puts out in 100,000 years is 2.7E-25 x E55 = 2.7E30.
A tenth of a second is about 4E41. So the power of the flash during that tenth of a second was 27E29/4E41 = 6E-13. Just preliminary estimates that we can check when their paper comes out. I'm having a bad arithmetic day, will double check this after coffee.

Yes, I need to double check more. Back a ways I was trying to get a humanscale handle on the natural unit of power and made a rough calculation that E-49 was like a 160 watt litebulb. Just checked that and it came out to 144 watts instead. Embarrassment
Fortunately not very much later stuff depended on that, it was a rough calculation to provide a way to visualize the solar constant or brightness of direct sunlight.

 

[marcus]

the solar constant is 6.2E-117
instead of the 5.7E-117 which I reckoned earlier
and I still visualize it as around 6 litebulbs in a square pace area
but they are 6.2 bulbs which are 144 watts each
instead of 5.7 bulbs which are 160 watts each.
drat. nothing to do but check more carefully

 

[marcus]

Astronuc just posted about a bright flash witnessed in December 2004
http://www.everything-science.com/index.php?option=com_content&task=view&id=111&Itemid=2
see his post "brightest explosion ever observed"
https://www.physicsforums.com/showthread.php?t=64274
...

Here's a NASA link that goes with that. It has an animation of the flare and some photographs of the aftermath taken in the optical range.
http://www.nasa.gov/vision/universe/watchtheskies/swift_nsu_0205.html

It says that for a tenth of a second the power of the explosion was E40 watts.
the natural unit of power is 1.444E51 watts, so roughly 100 billion time brighter still.
In case anyone is curious and wants to calculate the natural power unit for themselves it is really easy, you just need to know c and G
the power unit is just c⁵/(8piG)

so you put in 299792458, raise it to the fifth,
then you divide by 8pi,
then you divide by 6.6742E-11 (what NIST gives for G)
and that's it

at this point I believe you have 1.444E51 watts.

this is the number that I somehow goofed with and got 1.6E51
in a rough calculation a couple of weeks ago. too much in a hurry
or just careless

 

[nightcleaner]

Hi Marcus

Goat boy's gramma wonders if the bright flash could have had anything to do with the Christmas Tsunami? I told her, probably not, but then got to thinking about it. The CT event was several days before the flash, and the flash traveled at speed of light, so no particle or energy could have preceded the flash.

However, the flash was on the far side of the galaxy, and the galaxy curves space, so the light flash had to travel in a curve to get here. In fact, if the galaxy is roughly a hundred thousand lightyears across, it took a hundred thousand years to get here. What if spacetime distortions, gravitational waves if you like, take a straighter path? Maybe gravitational waves could outpace the light flash by a few days in a hundred thousand years?

Don't tell gramma about this. She has enough on her mind as it is.

Richard

 

[marcus]

Once there was a Taoist sage who had a special tooth that allowed him to listen to programs on the airwaves. His dentist had accidentally made the filling in his first bicuspid act like a crystal radio set. The sage could receive two stations, one when he was wearing his spectacles and one when he was not.

That would have been wonderful enough but something even more amazing was true. The sage could test batteries by LISTENING TO THE VOLTAGE. If the pitch was high enough it meant that the battery had enough voltage.

The way it worked was that his upper and lower bicuspids served as contacts and when he bit the battery just right he could hear a kind of humming or whistling and this tone, which he could hear by virtue of senses heightened by years of spiritual discipline, was exactly a trillion times lower than Josephson frequency for the same voltage

For instance if he heard the pitch "A440" when he bit the battery (that's the note orchestras often tune by) then it meant the battery was only putting out 0.91 conventional volts.

But if the battery was a fresh Dragon class Alkaline Power-cell delivering a perky 1.53 volts, the he would hear the Soprano High G. This is the G right above the treble staff. It is only a few notes down from the High C which is sometimes said to fracture fine crystal.

Question: My rechargeables put out 1.23 conventional volt which is around 5 quartervolts. We've been using "quartervolts" in this thread to stand for E-28 on the natural voltage scale. What pitch would correspond to 5E-28 natural?

 

[marcus]

...
Question: My rechargeables put out 1.23 conventional volt which is around 5 quartervolts. We've been using "quartervolts" in this thread to stand for E-28 on the natural voltage scale. What pitch would correspond to 5E-28 natural?

Answer: to convert any voltage to its Josephson frequency (see the post about the AC josephson effect) you simply multiply by 2.

Since the voltage is 5E-28, the Jo frequency must be 2 x 5E-28 = E-27.

But by virtue of the tooth, what he hears is a trillionfold (E12) lower frequency instead:
E-27 x E-12 = E-39
And E-39 is the D on the treble staff.

 

[marcus]

we just went for a walk up the hill and looked at the lights of the bay area

they are mostly sodium pinkish orange. apparently sodium lights make especially efficient use of electricity

the basic sodium yellow is actually a pair of frequencies
8.64E-28
and 8.63E-28
these both come from the transition 3p down to 3s
most of the light comes from the 8.64E-28 (the higher of the two frequencies----the shorter of the two wavelengths) but both are quite strong.

you may recall that 10E-28 is green and over 10 gets into blue and violet
8E-28 on the other hand is red. So it makes sense that 8.6E-28 should be orange or yellow.

Here's a web source about sodium that shows the electron transition and stuff. It shows how you can plug a salty pickle into housecurrent and it will glow yellow from the sodium lines
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodium.html

[edit: we went up the hill again tonight and I asked my wife what color she thought the East Bay streetlights were and she said gold. That is right. It is a gold with a slightly reddish tinge to it]

 

[marcus]

anyone who wants to can convert back and forth between conventional visible wavelengths in nanometers and frequencies in natural.

you just divide 5091 by the conventional wavelength and that gives the frequency in E-28 terms, or likewise the photon energy.
so if you know that conventional wavelength 650 is red, 500 is green, 430 is blue then you calculate the frequencies as 5091/650 for red,
and 5091/500 for green, and 5091/430 for blue (and multiply each by E-28)

but that is a bit cumbersome so I have just gone ahead and learned the visible range in natural frequency terms is from 7 to 13, with 10 in the middle for green. I mean from 7E-28 to 13E-28 with 10E-28 in the middle.

Now this whole planet full of life survives mostly by eating red and blue photons.
the fact is that "Chlorophyl A" the main thing that eats sunlight here, can only absorb and utilize red photons around 7.6-7.7
and blue photons around 11.6-11.8.

Chlorophyl A is a very picky eater. It gets some help from "Chlorophyl B" which can absorb some little bit more of the blue and red and transfer energy to Type A. but there is a big gap from 8.2 to 10.4 which hardly get used at all.

7.6-7.7 YUM! delicious red photons *smack* *slurp*

8.2-10.4 YUK! nasty yellow and green, spit it out!

11.6-11.8 CHOMP! SLURP! yummy blue photons

what impresses me is that I just went out to the kitchen and got a bowl of granola and sliced a banana onto it and all that energy that I just ate came from a narrow range of red and a narrow range of blue photons
Red and blue light is my phood ----- I just eat the energy second or third hand.

[edit afterthought: it's strange that life hasnt evolved to make better use of photons in the frequency/energy range 8E-28 to 11E-28.
If it did then leaves would be black. Common knowledge that the reason leaves are green is they don't absorb and utilize much light in that central 8-to-11 section of the visible spectrum, so it gets reflected back to us.]

 

[marcus]

Markers in the visible range 7-13 eekyoo

The numbers stand both for photon energies and for (angular format) frequencies. Think of them all multiplied by E-28, which I'm sometimes to lazy to write.
Below 7E-28 light is infrared, above 13E-28 it is ultraviolet.
By good luck it turns out that a typical green frequency 10E-28 is right in the middle of the visible range. So the three main landmarks are 7--10--13.

Low end of visible 7

Chlorophyl red peak 7.7

Sodium street lights ("D-lines") 8.64

Middle green 10

Chlorophyl blue peak 11.7

High end of visible 13

Suppose you needed to know the conventional (cyclic format) wavelength in nanometers for some reason. Just divide 5091 by any of these numbers. Like 5091/10 = 509.1 nm is the conventional wavelength for the "middle green" I'm using as a landmark color.
My source on the endpoints of the human visible range is Campbell's Biology, a modern textbook. He gives two decimal places compared with only one in the Handbook of Chemistry and Physics. Presumably the boundaries vary from person to person and are only approximately known.

 

[marcus]

Batman in Zero Gee

Batman is at Burger King enjoying a tasty batburger.
The plate glass beside him shatters and a giant hand reaches in.
It is King Kong again!

King Kong's arm is 10 paces long----E35 in natural length units.
He does a circular windmill-style pitcher's windup, preparing to throw Batman a long distance.

At the top of Kong's windup arc, Batman feels no gravity! It must be that the planet's normal E-50 gravity is canceled by "centrifugal force"!

What is Batman's speed?

 

[marcus]

Giant chickens have invaded from outer space and are living in a castle.
They are holding Robin Hood's girlfriend captive.

Robin sneaks into the castle and appears suddenly in the grand dining hall.
He surprises the chickens by singing the Queen of the Night Aria from Mozart's Magic Flute.

This is one of the great coloratura arias of all time and it goes up to the high E-flat above the soprano's high C. Even professionals can often only make a kind of indeterminate squeak for this E-flat.

The chickens are alarmed and flee to their ships. Maid Marian is free!

What is the frequency of Robin Hood's high note on the natural scale?

Listen to a midifile of the Queen of the Night aria:
http://www.geocities.com/Vienna/Strasse/2915/flute2.mid
the very high passage starts when the aria is about 1/3 of the way thru

 

[marcus]

The celebrated opera singer Kiri Te Kanewa once went to a masquerade party as Minny Mouse. Her friends persuaded her to an make an impromptu performance and she sang Donna Elvira's aria Ah! Chi mi dice mai.

Some hydrogen-breathing aliens from outer space were at the party and the prince of a distant planet fell in love with her. He therefore commissioned skilled doll-makers to create a copy of the famous Diva for him to take home. The doll was to be life size, able to sing several Mozart arias, and satisfy the desires of the prince.

When the masterful reproduction of the Diva was delivered to the prince's hotel, however, it was rejected scornfully. The prince declared that they had put the wrong head on the singer by mistake. She was supposed to have large round black ears, he said, and a pointed nose.

Indeed he had fallen in love with Kiri while she wore a mouse mask and had no idea she had any other face.

This oversight was quickly remedied and the prince departed happily accompanied by his vocally talented paramour with the long eyelashes and big ears.

When they arrived at the prince's home planet, trouble immediately developed. It was found that the doll would now only sing Mozart's arias two octaves too high. It was like fingernails scraping on slate and gave everyone a very bad impression. What caused this to happen?

 

[Kea]

hello

When they arrived at the prince's home planet, trouble immediately developed. It was found that the doll would now only sing Mozart's arias two octaves too high. It was like fingernails scraping on slate and gave everyone a very bad impression. What caused this to happen?

Perhaps when they changed the heads, the mouse thought it was really
supposed to be singing arias from the The Tales of Hoffmann?

Wouldn't the mouse have trouble breathing hydrogen?

 

[marcus]

...Wouldn't the mouse have trouble breathing hydrogen?

I was thinking of Tales of Hoffmann too

It was a doll, like the kind that runs on NiCad batteries, or you have to wind up, so it didnt have any metabolic trouble with the planet's hydrogen atmosphere.
But the doll's vocal apparatus was analogous to flutes and woodwinds, so she had the same problem that a flute would have if someone tried to play it in a hydrogen atmosphere. The speed of sound is almost four times faster.

I think you thought of that and that is why you mentioned breathing hydrogen.

Kea I would really love it if you would deign to work some of the simple problems in this variant of Planck units. Like the Batman problem I just posted, or the one about the chickens.

 

[marcus]

There were seven dwarves who lived in a old Victorian in San Francisco and operated a bed-and-breakfast. For extra cash flow these dwarves had a mailing business where they pack and ship things for you. They had all the materials ready--the right size crates and boxes, the plastic bubbles-- and it saved time to let them do it.

One time the Stanford Board of Trustees got tired of Leonard Susskind and they decided to have him shipped to an alternative universe, so they called Dwarves We-Send-It and the dwarves came and got Susskind and packed him up. What a lot of fussing he made about it!

Then the most disagreeable dwarf, whose name was Stinky, put the address on. He wrote

Deliver to:

alpha = 1/138
Lambda = 0.9E-120

At last they wheeled the crate out onto the loading dock and it disappeared.

The reason Stinky wrote that address was because of the Anthropic Principle, he wanted to send Leonard Susskind where he could be happy because the basic parameters were close to ours. We have alpha = 1/137.036... and this leads to a nice big periodic chart of elements, rich chemistry, stable long-lived stars etc. So Stinky made the alpha be near ours, but slightly different just to make sure they really got rid of Susskind.

Again just to be on the safe side, he made the cosmological constant Lambda be slightly different from our Lambda, which is 0.85E-120.

If its Lambda is too small a universe will short-lived and collapse, but if Lambda is too big it will be rather vacuous: space will expand so fast that galaxies and stuff never have a chance to collect and condense.
Stinky judged that having a wee bit more vacuousness would suit Susskind which was why he made it 0.9.

 

[Kea]

Batman and King Kong

King Kong's arm is 10 paces long----E35 in natural length units. He does a circular windmill-style pitcher's windup, preparing to throw Batman a long distance. At the top of Kong's windup arc, Batman feels no gravity! It must be that the planet's normal E-50 gravity is canceled by "centrifugal force"!

What is Batman's speed?

About 3E-8 in natural units. In other words, speed squared = gravity times armlength = E-15.

Assuming a pace is roughly 0.25 metres, in metric the speed is 5 m/s.

Batman was visiting a Wellington Burger King, so he screamed out to Peter Jackson, who was scoffing burgers at the next table, to ask King Kong to let him down, which King Kong did so that there could be a next episode.

 

[Kea]

Giant Chickens

Giant chickens have invaded from outer space and are living in a castle. They are holding Robin Hood's girlfriend captive. Robin sneaks into the castle and appears suddenly in the grand dining hall. He surprises the chickens by singing the Queen of the Night Aria from Mozart's Magic Flute.
This is one of the great coloratura arias of all time and it goes up to the high E-flat above the soprano's high C. Even professionals can often only make a kind of indeterminate squeak for this E-flat. The chickens are alarmed and flee to their ships. Maid Marian is free!

What is the frequency of Robin Hood's high note on the natural scale?

High E-flat is about 1.25 KHz. Using a speed of sound of 343 m/s, the wavelength of high E-flat is about 0.27 metres. Converting to natural units, the frequency is

f = \frac{1250}{3.7 E42} = 3.4E-40

Fortunately this is quite a bit smaller than the visible frequencies above.
Analogously to the visible case, we talk in terms of E-40 for musical notes.
In these terms the conversion factor k in

\frac{k}{\lambda} = \nu

for wavelength in metres and frequency in natural units E-40, is k = 0.92.

The chickens weren't happy because Maid Marion had been treating them to a few arias by Handel, who died only 3 years after Mozart was born, and the chickens immediately thought Mozart was a postmodern anarchist, and they left in disgust to join Susskind in another universe.

 

[marcus]

About 3E-8 in natural units. In other words, speed squared = gravity times armlength = E-15.

Assuming a pace is roughly 0.25 metres, in metric the speed is 5 m/s.

Batman was visiting a Wellington Burger King, so he screamed out to Peter Jackson, who was scoffing burgers at the next table, to ask King Kong to let him down, which King Kong did so that there could be a next episode.

Yes yes yes! THANK you Kea, you are very kind. that is exactly right for the speed. It is sqrt(E-15) = about 3E-8

I am glad that you have arranged to keep Batman around. We all admire his style and his relentless battle against the wicked


as for metric conversions the speed unit in this system is c, so that E-8 is 3 meters/second, sqrt(E-15) is around 9.5 m/s
the pace is E34 times the (variant) Planck length or around 81 cm.
but the metric conversion part is totally non-essential, what is a balm to my spirit is when someone works the problem companionably with me in natural units and gets the answer in those terms

 

[marcus]

... a postmodern anarchist, and they left in disgust to join Susskind in another universe.

is right!

 

[marcus]

... we talk in terms of E-40 for musical notes.

Exactly! Let me clarify: the units are defined by |8piG| =|hbar| = |c| = 1
and that has the outcome that the D right above middle C (near the top of my range) is 0.50E-39 = 5.0E-40

The frequency E-39 is an octave up so it is the note D on the treble staff (up in soprano/alto range)

So this E-flat the Queen of the Night sings, that is one halfstep up from a still higher D: 2E-39.

The D which is an octave above the D on the treble staff is 2E-39

and since the dreaded E-flat is a halfstep up from there, I have to multiply by 1.06------and it is 2.12E-39

(I should mention that I am using angular format for wavelengths and frequencies unless stated otherwise, as in the case with conventional cyclic wavelengths in nanometers for light)

 

[marcus]

\frac{...}{3.7 E42}

I am going to focus on just one thing in Kea's post #190, the number
3.7E42 that she divided by in one of her equations

this is the natural unit of angular frequency expressed as radians per second. (in these units we have |hbar| = 1 so it makes sense to work consistently in angular format for freq. and wvlength.)

It is a really good number to remember. Also it has latent (undeclared) accuracy.
According to current estimates of the fundamental constants you could say that the fundamental frequency, or natural frequency unit, is
actually 3.700E42.

So we can copy Kea's approach and get frequency equivalents like this.

The A that orchestras use to tune by is 880pi radian/second.
All we need do is divide by 3.7E42 and we will know the frequency of A in natural terms!

\omega_A = \frac{880 \pi }{3.7 E42} = 7.472E\text{-}40

So the A they tune by is 7.472E-40
The D on the treble staff is 5 musical halfsteps above that so one just needs to multiply the frequency by 2^5/12 = 1.335.

So the D on the treble staff is 1.335 x 7.472E-40 = 1.00E-39

this is so close that one could tune by setting D = E-39 and not know the difference.

So using this number 3.7E42 (natural unit of ang. freq.) that Kea supplied is a good way to explain why, for instance, the D right above the soprano's high C has frequency 2E-39

and the E-flat a halfstep up from that high D has frequency 2.12E-39.

we could call this the "Kea number" and go back and define the whole set of natural units on the basis of that exact frequency of

\omega_{kea} = \sqrt{\frac{c^5}{8\pi G \hbar}} = 3.7 E42 \text{ per second (exact)}

If there were some reason to do it over it might not be such a bad way to proceed.

 

[marcus]

Giant chickens have invaded from outer space and are living in a castle.
They are holding Robin Hood's girlfriend captive.

Robin sneaks into the castle and appears suddenly in the grand dining hall
with half of a Kentucky Fried Chicken in a paper bag. He consumes this delicious fast food at the Invaders' victory banquet, thoughtfully sucking each bone clean before tossing it into their punch bowl.

The chickens are sickened with disgust and flee to their ships moaning and barfing. Maid Marian is free!

What fraction of a natural unit of energy did Robin consume at the banquet?

Anne Collins lists the Calories in Kentucky Fried Chicken piece by piece here:
http://www.annecollins.com/calories/calories-fried-chicken.htm
WING 135
BREAST 370
DRUMSTICK 140
THIGH 360
One can easily see that half a bird is 1000 Calories.

 

[marcus]

Giant chickens have invaded from outer space and are living in a castle.
They are holding Robin Hood's girlfriend captive.

Robin sneaks into the castle and appears suddenly in the grand dining hall
with half of a Kentucky Fried Chicken in a paper bag. He consumes this delicious fast food at the Invaders' victory banquet, thoughtfully sucking each bone clean before tossing it into their punch bowl.

The chickens are sickened with disgust and flee to their ships, barfing and moaning. Maid Marian is free!

What fraction of a natural unit of energy did Robin consume at the banquet?

Anne Collins lists the Calories in Kentucky Fried Chicken piece by piece here:
http://www.annecollins.com/calories/calories-fried-chicken.htm
WING 135
BREAST 370
DRUMSTICK 140
THIGH 360
One can easily see that half a bird is 1000 Calories.

with other food problems in this thread we've been using a crude approximation that one natural energy unit is 100,000 food Calories.
So clearly Robin consumes 1/100 of a natural unit.

But just for a change let's be real precise and use Kea's value for the natural frequency expressed in conventional radian-per-second terms.


\text{energy unit = hbar x frequency unit} = \hbar \times \omega_{kea} = 1.05457E\text{-}34 \times 3.7 E42 = 3.90E8 \text{ joules} \approx E5 \text{ food Calories}

 

[marcus]

This summary needs to be brought forward periodically.
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 omega_nat and set its value equal one, instead of F. Same result.

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:

pound E8
year E50
handbreadth E33
pace (32 inch) E34
halfmile E37
lightyear E50
food Calorie E-5
lab calorie E-8
quartervolt E-28
tesla E-53
green photon energy 10E-28
average Earth surface temp E-29
2/3 mph E-9
67 mph E-7
cold air speed of sound E-6
D on treble clef E-39
one "gee" acceleration E-50
weight of 50 kg sack of cement E-40
power of 144 watt bulb E-49

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.

 

[Kea]

Marcus

Where is everybody?

 

[marcus]

Marcus

Where is everybody?

Hi Kea, I went to a friends house this afternoon to practice singing Brams Liebeslieder Waltzes. they are fun. bouncy. and with nice harmony.

I just got back. I don't notice fewer or more people than usual. I hope you check in soon and tell me who is missing.

 

[Kea]

Hi Marcus

It's great that you sing. I guess you're right about it being as busy as
usual. I have been talking to Urs on the Coffee Table lately.

Kea