Using the force constant in equations

[marcus]

Frog and Toad went to a politically correct house of pleasure in Singapore. The house was owned and operated by the staff, all of whom were charming and imaginative.

Wow, said Frog, these women are attractive.
Yes Frog, said Toad, they are indeed fetching. And there is a room with zero gravity too.

Frog and Toad met two of the staff who happened to like amphibians and they all entered the zero gravity room. This was a room that a mad inventor had made impervious to the Earth's gravity, as a token of his appreciation. The Earth's gravity was turned off in this room.

Toad, do you notice anything strange about this room? said Frog, I think we are drifting up towards the ceiling.

You are right, Frog, said Toad, we seem to be falling upwards! Why could that be?


Question: Singpore is on the Earth's equator. The Earth's rate of rotation is 2E-47 (radians per nat. time unit) and its radius is 7.9E40. What is the acceleration experienced by the two friends and their companions?

 

[marcus]

eastertime and the wearing of swords

as Easter approaches one naturally thinks of Handel's Messiah which was written to be performed at Eastertime and was premiered in Dublin 1742 on April 13
http://tucsonsymphony.org/ProgramNotes/HANDELMessiah.html

from a Dublin newspaper of the day:

“The Stewards of the Charitable Musical Society request the Favour of the Ladies not to come with Hoops this Day to the Musick-Hall in Fishamble-Street; The Gentlemen are desired to come without their Swords.”

It was a benefit performance and they wanted to pack as many people into the hall as could conveniently fit, hence no swords.

So when you sing that piece, as so many people have, you are singing something that originated at a time when gentlemen normally wore swords when they went to the concert hall and theater.

Which reminds me that in Kyoto 1400 there was a famous performance of a Noh play which was attended by the Shogun and the chief of the Akamatsu Clan (one of the six noble clans of Japan at the time). The play was performed at the Akamatsu Palace to which the Shogun was invited as the guest of honor. Host and guest sat in the front row and both had their swords.
In the course of the evening, while they watched the play, Duke Akamatsu reached over with his blade and beheaded the Shogun. In Japanese History books this is referred to as "The Akamatsu Incident"

I have to go, back soon

 

[marcus]

...

You are right, Frog, said Toad, we seem to be falling upwards! Why could that be?
Question: Singpore is on the Earth's equator. The Earth's rate of rotation is 2E-47 (radians per nat. time unit) and its radius is 7.9E40. What is the acceleration experienced by the two friends and their companions?

What they are noticing is the downwards acceleration of the room itself and the satin-canopied, brass fourposter, which is bolted in place. you decide whether the fourposter is bolted to the floor or the ceiling. anything not tied down will be floating.

$$a = R \Omega^2 = 7.9E40 \times (2.0E\text{-}47)^2 = 3E\text{-}53$$

$$a = 3E\text{-}53$$

a gee is roughly E-50, so about 3 thousandths


the Earth's rotation rate is 1.9601E-47 but for simplicity we round 1.96 to 2.0 and call it 2.0E-47. The equatorial radius is 7.87E40 which we call 7.9E40.
If we used the more accurate figures we would get 3.0E-53 for the acceleration, but with the rounded ones it comes out slightly more: 3.2. In any case if you think of a gee as E-50 then it is around 3 thousandths of a gee

 

[marcus]

A certain king liked to compose war-songs, but his soldiers did not know how to sing. So he called Toad Robotics and ordered a truckload of robot soldiers with lovely tenor and baritone voices.

I want them to have swords, said the King, and to march in parade without making mistakes. And then they will stop, and raise their swords to the sky, and sing my song---whatever it is that day.

Uniforms? asked Toad. Empire, said the King, or Regency. Red and blue.
Gold braid and buttons? asked Toad. Yes, plenty of that, said the King.

Fine, said Toad, we will ship next Tuesday. Oh, facial hair? Muttonchops, said the King, and handlebars. All that. But the most important thing is that they sing on pitch with good portamento.

What about fighting? asked Toad. No problem, said the king, I have plenty of peasant boys to do the fighting. Concentrate on the other stuff.

Will do, said Toad, and he hung up.

The following Tuesday Frog, who drove a 12-wheeler semi rig for the company, got out on the road with a gross of singing robot soldiers stacked up in the trailer. They liked Verdi. After a while Frog stopped the truck and went back and turned them all off. He drove on in silence.

Frog is barreling down Highway 5 at speed E-7 with 25,000 pounds of robot soldiers. E-7 (a ten-millionth of the speed of light) is 67 mph which is what everybody drives on that stretch of the road. The truck has mass too: let's take it to be 25,000 pounds as well.

What is the momentum of 25,000 pounds of truck and 25,000 pounds of robot going that speed?
well the pound we use is E8 natural, so the total mass is
50E11 = 5E12, and the speed is E-7.
momentum = 5E12 x E-7 = 5E5 units.

Getting up to speed is quite an effort for the engine. Even on the level it has to supply 5E5 units of momentum. It takes Frog a couple of minutes, about 5E44 time units, to get the rig up to highway speed.

What is the effective power of the rig's engine and drivetrain, neglecting friction and air resistance.

Answer: Recall E45 time units =4.5 minutes. the truck takes half of that time, 5E44, to get up to speed. when it is going E-7 the kinetic energy is (1/2)mv² = 2.5E12 x E-14 = 2.5E-2.
Energy/time = 2.5E-2/5E44 = .5E-46 = 5E-47. this is only about 100 horsepower (E-48 is two horsepower). That may seem puny for a truck engine but there are inefficiencies including loss in getting the power from the engine to the rubber on the road. I am not the local trucking expert but it seems like a reasonable first approximation. (obviously the truck has a lot more power than 100 hp, but it gets dissipated in friction and air resistances and drive train and things like that)

 

[marcus]

It looks to me like one could do a rather nice primer of genrul fizix using natural units.
the version of the units that we've been using in this thread (8piG = 1) is especially handy for a bunch of reasons (that don't apply to the original G=1 Planck set).

E-50 acceleration is about one gee
E8 mass is about a pound
E-53 field strength is a tesla and E-57 is a gauss
E-91 is near the density of human body, somewhat less than water
E-28 is a quarter volt
E37 length is half a mile (which makes E34 a pace)
global average temperature is around E-29
sun surface is approximately 2E-28
green photon energy is 10E-28 = E-27 (middle of visible range)

and there are other coincidences that make the units handy to use, which I am forgetting or not bothering to list. oh, like E99 volume and E-5 energy are roughly a pint and food Calorie, respectively,
and E-40 force is roughly the weight of 50 kg in normal Earth gravity.

of course the main convenience is things like having the speed of light and Planck's constant be one, in fact a considerable number of important basic constants take simple values in these terms.

another thing is that in a general physics text the main thing you learn by reading it is how to solve problems using SYMBOLS like F and m and a and v and K.E. and P.E. etc. So it does not matter all that much what underlying set of units the book is using. As a rule you are supposed to solve things using symbols, get the answer expressed in symbols, and then only at the end do you evaluate the answer in terms of some units. So if that's the normal operating proceedure then the units are not playing a very critical role and you might as well have them be natural.

So I am trying to project how a small book would look, using QG units.

 

[marcus]

Batman and his Hovercraft(TM) Aircushion vehicle

Batman is cruising Hollywood Boulevard in his one-ton hovercraft, equiped with a 360-degree inflatable bouncy bumper
(this is advisable since it it next to impossible to drive straight in this model).

He has come to a momentary stop so that he can scope out a Mexican Restaurant. Arnold Schwarzenegger, in his new five-ton hovercraft, rear-ends Batman at a speed of 4E-8

What is Batman's speed after this elastic collision with Schwarzenegger?


note: it doesn't much matter what a ton is, think of it as 2E11 mass (2000 pounds) if you like. 4E-8 speed is 27 mph. treat it as an air track problem ( linear collision)

 

[marcus]

the ballerina on the asteroid

a ballerina is scheduled to perform on an asteroid.
she inquires as to the escape velocity. she does not want to hop too vigorously or she will sail off into space.

the asteroid mass is only a millionth of the Earth's mass and its radius is E39 (a hundred half miles, in other words 50 miles)

what is escape velocity?

sqrt(2GM/R) = sqrt (2 x 1.38E27/25E39) = 3.3E-7

It is explained that this is about 222 mph so she can rest secure.

Now the ballerina is performing and she takes a very tiny hop, leaving the surface at just 5.5E-9 speed. How long before she reaches the highpoint?

 

[marcus]

...He has come to a momentary stop so that he can scope out a Mexican Restaurant. Arnold Schwarzenegger, in his new five-ton hovercraft, rear-ends Batman at a speed of 4E-8

What is Batman's speed after this elastic collision with Schwarzenegger?

standard elastic collision with masses M, m
initial velocities V_i, v_i
final velocities V_f, v_f
extra assumption v_i = 0 (Batman is momentarily stopped on the boulevard)

one applies conservation of energy and momentum and find
v_f = (2M/(M+m))V_i = (10/6)4E-8 = 6.7E-8
so Batman is abruptly accelerated to nearly 45 mph.

 

[marcus]

...Now the ballerina is performing and she takes a very tiny hop, leaving the surface at just 5.5E-9 speed. How long before she reaches the highpoint?

The mass of the asteroid is one millionth of earth's, so M = 1.38E27 mass.
Radius R = E39 length
so surface gravity is GM/R² = 1.38E27/25E78 = 5.5E-53 acceleration
she jumps off the surface at speed 5.5E-9
the time to reach the highpoint of her jump is 5.5E-9/5.5E-53 = E44 time units.
this is about half a minute
the whole jump lasts roughly 0.9 minute before she lands back on the surface again.

note: E-9 speed is 0.67 mph so the speed with which she takes off, namely 5.5E-9, is somewhat less than 4 mph.

 

[marcus]

the traditional rollercoaster problem

A rollercoaster is being built on a distant planet where the balmy, hibiscus-scented air offers no resistance. We are not told the mass of the planet---it is supposed to be somewhere between that of Earth and that of Mars. Friction there is negligible, especially at amusement parks.

The track is to have a circular loop 20 paces high with a brief experience of zero gravity at the top.
In other words there is to be a vertical loop with radius E35, at the top of which riders will be upside down in their seats and feel no gravity.
Cars approaching the loop start from a higher altitude so that the car will have sufficient speed.

How much higher than 2E35 off the ground must the car start rolling?

 

[marcus]

the harmonic oscillator

Giant chickens from outer space have seized Locksley castle and hold Maid Marion captive. Robin Hood and his men have put on chicken suits and deceived the guard at the castle gate into letting them enter.
They discover that the sportive aliens are bungee jumping from a tower in the inner courtyard.
The Captain of the Chickens has just gotten buckled into harness and his weight causes the cord to stretch an extra 10 paces (E35 length units).
To testing the cord, the Captain bounces up and down and notes the bounce frequency of 3E-43.

Robin pulls off his fake chicken head, revealing his identity, and draws his sword. I challenge you calculate the gravity of this planet! cries out the famed outlaw.

 

[marcus]

parachute: terminal falling speed

Giant chickens have invaded Earth and are living in a castle where they hold Robin Hood's girlfriend captive. The chicken's leader has insisted that Maid Marion promise to be his bride. Otherwise, he says, he will blow up the planet.

Robin is deperate so that night he and his men dress up in chicken suits to deceive the enemy and parachute into the castle. They surprise the foe and drive them from the land. Maid Marion is free!

The problem is how big are the parachutes.
The force of a typical venison-fed outlaw's weight is 1.6E-40
and the density of Earth's atmosphere is 1.6E-94
assume the drag coefficient is one

The outlaws wish to land gently, at a speed of E-8, so as not to wake the chickens. Therefore they use extra large parachutes. (E-8 speed is 6.7 mph)

force = air density x area x (terminal speed)²/2
1.6E-40 = 1.6E-94 x E-16 x A/2
2E70 = A

a square pace area is E68, so this is 200 sq paces. an 8 pace radius circle

 

[marcus]

... there is to be a vertical loop with radius E35, at the top of which riders will be upside down in their seats and feel no gravity.
Cars approaching the loop start from a higher altitude so that the car will have sufficient speed.

How much higher than 2E35 off the ground must the car start rolling?

gh = (1/2)v²
v²/R = g
h = (1/2)R
the car must start 5 paces higher, 5E34 units.

 

[marcus]

...Which reminds me that in Kyoto 1400 there was a famous performance of a Noh play which was attended by the Shogun and the chief of the Akamatsu Clan (one of the six noble clans of Japan at the time). The play was performed at the Akamatsu Palace to which the Shogun was invited as the guest of honor. Host and guest sat in the front row and both had their swords.
In the course of the evening, while they watched the play, Duke Akamatsu reached over with his blade and beheaded the Shogun. In Japanese History books this is referred to as "The Akamatsu Incident"
...

The Akamatsu Palace had a mass of 70,000 pounds and was very grand, consisting of beautifully carved and painted wood.

After Duke Akamatsu sliced off the head of the guest of honor he waited to see if anyone would object. The actors stopped performing their Noh play and also waited. The guests were scandalized at the Duke's bad manners and all went home.

For two days the noble clans of Kyoto stayed in their various mansions wondering what was going on. They each suspected that the other clans were part of a plot and wanted to be careful.

The Akamatsu, having waited in the quiet capital for two days, lined up outside their palace and set it on fire. Then they marched off to their comfortable castle in the country taking the women and children with them, as well as some of the furniture. The palace burned to the ground.

How much energy was released when the Palace of the Akamatsu burned?

 

[marcus]

this version of the Akamatsu Incident (1441) was told me by a member of the family, it differs in some details from versions available on the web

http://www.samurai-archives.com/mitsusuke.html

this version says that it was not a Noh play they were watching but a performance of dance.

 

[marcus]

The Akamatsu Palace had a mass of 70,000 pounds and was very grand, consisting of beautifully carved and painted wood.

...
How much energy was released when the Palace of the Akamatsu burned?

One thousand natural units of energy were released.

Whether it's to burn or eat
The Oh-Two count will tell the heat.
On the average each Oh-Two
Releases seventeen eekyoo.

eekyoo (electron-quartervolt) is a nickname for E-28 energy unit.
Burning 7E9 mass of dry wood releases about one natural unit.
One can check this using the rhyme, as follows

typical piece of cellulose polymer is CH₂O with
12+2+16 = 30 baryons and therefore a mass of 30/2.6E18 natural.
In burning it consumes one Oh-Two molecule and releases
accordingly about 17E-28 in energy.

the energy from 7E9 mass units (70 pounds) can be reckoned as
7E9 divided by 30/2.6E18 and multiplied by 17E-28. That comes to 1.03,
or approximately one.

 

[marcus]

reliable conversion factors: metric equivalents from NIST

http://physics.nist.gov/cuu/Constants/
the NIST provides a useful table of conversion factors
http://physics.nist.gov/cuu/Constants/energy.html
(click on "table(gif)" or "table(PDF)")

Finally you get the table itself:
http://physics.nist.gov/cuu/Constants/factors.html

This table makes it especially simple to get metric equivalents of our natural units

to illustrate, suppose we take the angular frequency 3.7E42 (that Kea pointed out) and want to convert it successively to
mass
energy
voltage
temperature

all we have to do is divide by 2pi and then go along the "Hz" row in the table multiplying by one of the following
7.372E-51 kg
6.626E-34 joule
4.135E-15 eevee
4.799E-11 kelvin
I have left off the many decimal place accuracy they have in the table because i just want to convey the idea.

It is a way of getting very accurate values for the natural units. for instance

3.7E42 divide by 2pi multiply by 7.372E-51 kg gives 0.434E-8 kg, and this is the natural unit of mass, (I have dropped off the precision just to show the basic idea, you can recover the precision if you want by doing the calculation yourself)

and so one gets highly precise values, if desired, for the natural units of mass (as shown) and also energy, voltage, and temperature.

 

[marcus]

Giant chickens from outer space have seized Locksley castle and hold Maid Marion captive. Robin Hood and his men have put on chicken suits and deceived the guard at the castle gate into letting them enter.
They discover that the sportive aliens are bungee jumping from a tower in the inner courtyard.
The Captain of the Chickens has just gotten buckled into harness and his weight causes the cord to stretch an extra 10 paces (E35 length units).
To testing the cord, the Captain bounces up and down and notes the bounce frequency of 3E-43.

Robin pulls off his fake chicken head, revealing his identity, and draws his sword. I challenge you calculate the gravity of this planet! cries out the famed outlaw.

stationary stretch = E35 (ten paces)
bounce frequency = 3E-43

frequency² = g/stretch

g = stretch x frequency² = E35 x 9E-86 = 0.9E-50

this is the correct value for Earth surface gravity to the indicated precision
so the leader of the Chickens has the necessary data should he choose to take up the challenge

 

[nightcleaner]

Hi Marcus and Kea.

Just wanted to let you know I am still lurking.

I have been trying to understand Kea's Z number and have gotten lost, somehow, diverted into studying the fine structure constant . Still working on it. You say it is the natural unit of frequency? I havn't come on any references to it. Can you or Kea tell me where this comes from?

I have noticed that the values for natural units you calculated using Z in post 204 of this thread do not match those given by the NIST. Am I missing something?

Thanks,

Richard

 

[Kea]

fine structure constant?

...diverted into studying the fine structure constant. Still working on it.

Hi Richard

What are you studying about the fine structure constant?

Kea

P.S. If you look at page one here, you will see where Marcus discusses 'counts' and this indicates how to calculate the factor.

 

[marcus]

Hi Marcus and Kea.

Just wanted to let you know I am still lurking.

Hi Richard, good to see you! hope Kea drops in too.

I have been trying to understand Kea's Z number and have gotten lost, somehow, diverted into studying the fine structure constant . Still working on it. You say it is the natural unit of frequency? I havn't come on any references to it. Can you or Kea tell me where this comes from?

It is good to be diverted into studying fine structure alpha constant.

So as not to embarrass Kea, I should take responsibility for highlighting this frequency quantity and naming it "Z".

there are more interesting physical quantities than letters in the alphabet so there are probably other things denoted by Z, don't get confused

WHENEVER there is a unit of time, whether it is a metric unit or a Planck unit or other kind, there is always the corresponding unit of frequency which is the reciprocal of the unit of time. Like in metric s^-1, or "one event per second".

So if you have a natural unit of time (some unit which comes from nature) then the corresponding frequency of "one event per unit time" is the natural frequency unit belonging with it.

Note however that people have different habits and conventions about what events they count. Angular format frequency counts radians of phase----1/2pi of a full cycle. Cyclic format counts cycles.

I have noticed that the values for natural units you calculated using Z in post 204 of this thread do not match those given by the NIST.

That's right that is the whole point of the thread, as I explained at the start. The conventional Planck units are defined by setting
|G| = |hbar| = |c|= 1.

But G although it is very important and plays a central role in Newtonian gravity is not the coefficient in the Einstein equation. The coeff. in Einstein main equation of Gen. Rel. is a force, call it F. Our units are defined by setting

|F| = |hbar| = |c|= 1.

this is the same as defining the units by setting

|8piG| = |hbar| = |c|= 1.

this means that our natural units will be different from the traditional Planck ones (that NIST lists) by factors of either 8pi or the square root of 8pi.

It happens that 8pi is very nearly 25, so for practical purposes the units differ by factors of either 25 or 5 (the sqrt).

A couple of years back John Baez pointed this out and suggested that the traditional Planck units should be replaced by these, that I am trying out here. I did not at first understand this. However more and more i see QG papers use variants of Planck units like these here, which are different from the customary ones (that NIST lists). So at a certain point I decided to take these clues seriously and seriously consider that the original definition of Planck units in 1899 by Planck might have not have been the best, and may have come about thru an historical accident, and that Baez suggestion of a variation of the units might make a more useful system.

 

[marcus]

Hi Richard

What are you studying about the fine structure constant?

Kea

P.S. If you look at page one here, you will see where Marcus discusses 'counts' and this indicates how to calculate the factor.

Hi Kea! good to see a post from you! Yes I was wondering about Richard studying alpha.
In these (planck variant, natural) units the alpha number is first of all just the value of the Coulomb constant when expressed in these units.
It is used when one calculates the electric or the magnetic field, and when one calculates force between charges. But of course it is famously also the basic constant in Quantum Electrodynamics.

 

[marcus]

Hi Marcus and Kea.

Just wanted to let you know I am still lurking.

I have been trying to understand Kea's Z number and have gotten lost, somehow, diverted into studying the fine structure constant ...

several possible approaches to understanding the role of alpha

here is one. (maybe it is not the best, maybe kea has a better that she will supply, but this is at least one simple handle on it)


suppose you have two tennisball size balls suspended by thread and all safely protected and insulated so you can't get a shock

suppose each ball has a trillion extra electrons

what is the force between, if you dangle them close together?

In natural units the charges are E12 and E12 (the unit is the electron itself and E12 is a trillion)

and say the distance is 2E33 center to center (that is two handbreadth)

$$\text{force} = \frac{1}{137}\frac{E12 \times E12}{(2E33)^2}$$

THE FORCE IS ALWAYS 1/137 TIMES THE TWO CHARGES MULTIPLIED TOGETHER, DIVIDED BY THE SQUARE OF THE DISTANCE

so let's see how much it turns out to be, I didnt calculate it in advance.


$$\text{force} = \frac{1}{4 \times 137}\frac{E12 \times E12}{E66} = \frac{1}{548}E\text{-}42 \text{ natural force unit}$$

roughly speaking E-42 of natural force unit is about a "poundforce" (dont confuse with pound mass!) or the weight-force in normal Earth gravity of half a kilogram.
So this calculation says the force between the two tennisballs is extremely delicate, it is 1/548 of the weight of a pound of butter taken out of the fridge.

And I don't mean 1/137, I mean the real number 1/137.036...

But anyway, in very concrete terms that is a story of how 1/137 enters into our life. You dangle the two tennisballs close together and they repel with a delicate force. And the force is reckoned by the number 1/137 and knowing how many extra electrons (a trillion) on each ball

the natural force unit is ultimately what this thread is about. what happens if you actually use it as your unit... what kind of system of units do you get then and how does the system behave in uses.

I know the natural force unit mainly because when I stand still the force I feel on each sole of my feet is E-40 (this is a "hundredweight" force or the weight of a 50 kilo sack of something) My mass is about 200 pound and my weight-force is about 200 "poundforce". so on each footsole I feel E-40.

When I compare E-42 with the heft of a pound of butter, i am basically just dividing that E-40 that i know by a hundred and comparing it to something.
And that is how i get some idea of the force of repulsion between the two charged tennisballs.

[REPLY TO NEXT POST, ADDED IN EDIT: Hi Richard. I was delighted to hear about 8piG, in the next post. The whole post is very interesting. I'm answering just minimally and out of order here so as not to cover it up. I wish some other people like selfAdjoint would respond to it. several good perceptions and/or interesting ideas]

 

[nightcleaner]

Hi Marcus. I moved the Alpha post to a new thread, because I want to work on it some more and I don't want to clog up this thread with extraneous matter. Thanks for the encouragement.

nc

 

[marcus]

Hi Marcus. I moved the Alpha post to a new thread, because I want to work on it some more and I don't want to clog up this thread with extraneous matter. Thanks for the encouragement.

nc

that post was really interesting, raised a lot of things that wd be valuable to go into.
I will follow it in the new thread you have made, and maybe pick up some stuff I can use here

[edit REPLY TO NEXT POST question about mass: Richard the issue about mass is fascinating but i cannot tell you why the masses of non-composite particles are so small. Frank Wilczek was speculating about this, perhaps even answered. but it is a bigleague question.

I think that Planck mass IS OR OUGHT TO BE an upper limit on mass of pointlike particles because at that mass a pointlike particle would turn into a black hole.

the compton wavelength (localizability) gets smaller as the mass gets bigger until finally the compton shrinks down to the size of the schwarzschild radius and its own gravity collapses it to something we don't know what is but used to be called a singularity

so Planck mass is the limit mass that space or nature can endure that a pointparticle should have

but the mystery which wilczek discusses is why the real things have mass which is so much LESS than this theoretical upper limit.

the electron is pointlike in the sense that it is not made up of other stuff the way a proton is, and look how tiny!

the electron mass is 2.1E-22 natural mass unit!

and you mention stuff that is several GeV or several hundred GeV, well that is still tiny.

remember that an "eekyoo" electronquartervolt is E-28 natural
(sun surface temp is 2E-28, green photon energy is 10E-28, we use E-28 energy as analog to normal physicist saying eV)
so natural energy unit is (1/4)E28 eV
that is 0.25E19 GeV = 2.5E18 GeV

so the natural mass unit is 2.5 quintillion GeV

so when someone talks a couple hundred GeV that is still tiny mass.]

 

[nightcleaner]

Hi Marcus.

I found a Wiki artical, disputed, but interesting, about a German physicist named Burkhard Heim who seemingly may have cracked the unified theory. For some reason my browser has changed and no longer displays links, so I cannot easily post one here, however if you are interested just google his name. The claims are rather astonishing, which redlines my B-meter, but it may be worth watching.

Meanwhile, I have been thinking about the constants which we have reduced to unity in this thread. It seems to me that some of them are very large, like c, and some are very small, like h-bar. Then there is mass. The mass constant is roughly human scale, or at least visible to a human. Why is that?

The speed of light, c, can be found by a ratio of space and time units which are themselves very small. As far as I know, there is only one kind of velocity, or maybe two, possibly three. Energy on the contrary occurs at different scales as different kinds of things...mass, atomic nuclei, em radiation, even sound and heat. Energy obeys quantum law, so one might think that mass should also. So shouldn't the mass unit be a discrete irreducible quantity, like length and time, or else made up of some combination of irreducibles, in a way similar to the way c can be found by taking the ratio of length to time?

Well the mass unit doesn't seem small enough to be a discrete irreducible unit. As Frank Wilczek commented, the question is, not why the mass unit is so large, but why is the proton mass so small? String theory suggests masses are small because they are spread out in ten dimensions so not much is left to affect our puny three. I seem to remember that Wilczek suggested that some sort of shielding is going on, like the shielding NIST says affects electrostatic charges due to, possibly, vacuum fluctuations or virtual particles. I personally am currently speculating that the mass unit size might be explained in the same sense as the speed of light, as a ratio or other combination of small discrete irreducible units.

In this case we might see a continuum of mass values as we see a continuum of velocities. Masses of fundamental particles would not have to obey discrete rules if they are composed of some ratio or other combination of much smaller units, in the same way that c is composed of the ratio of length to time.

If the mass unit is a unit like c, one might expect that it would be an upper limit to the masses of truly fundamental particles, as c is an upper limit to velocity. I am wondering if there is any evidence for this idea. Perhaps you will know if the rest masses of any fundamental particles are thought to be larger than the mass unit. I know some of the SUSY particles are predicted to be very massive, but I am not sure how to translate values of GeV into our mass unit. And what about gluons? They are thought to be very massy also.

I am looking for numbers in the literature now, and will try to post some here, if I find any interesting. Perhaps you would favor me with some of your light on this subject.

As for kinds of velocity, there is linear velocity and orbital velocity, as governed by SR, and then it seems to me there is another kind of velocity which is governed by GR. If gravity is an acceleration, what is accelerating? And if there is an acceleration, is there not an integral, and wouldn't that integral be a kind of velocity? I don't want to stir up any FTL fanatics, but we have been accelerating at one g for quite a while now. Just how fast are we going, anyway? Not that we would notice, since we all seem to be on the same train.

One more thing for this post. I was trying on the force units and I noticed this relationship:

F=ma
P=Fc=mac
EE=Ph=Fch=mach

Silly, I guess, but it made the relationship between force, power, and energy come clear for me in a new way. Maybe Ernst Mach would have liked this.

sleep well,

nc

 

[nightcleaner]

This paper lists simulated sparticles with masses between 100 and 200 GeV

http--www.fys.uio.no-~borgeg-Gjelsten2004Nov10EvMeet.pdf

 

[marcus]

steering back towards Quantum Gravity units

the main thing I want to be doing (but we are all encouraged to digress) is to practice using the QG units that I see cropping up in QG papers and to test them out. just a variant of the traditional Planck units. but with the factor of 8pi or its sqrt appearing now and then.

specifically we set the coefficient in the main equation of GR equal one,
instead of the coefficient in the Newtonian equation for gravity (called G)

so we make the Force equal one, and that has the result that 8piG =1
instead of G =1 (and Planck units are slightly differnt)

So then QED topics come up, or just plain E&M (electricity and magnetism) and what can we say? The topic of Alpha comes up.

Well, in natural units, something to remember is the massenergy of the
electron is 2.1E-22 energy units.

Of course the mass of the electron is the same number 2.1E-22 of mass units.

the electron compton wavelength (among other things an index of the size of the electron) is just the reciprocal 1/(2.1E-22) length units.

instead of having a lot of numbers about electron to remember (how many eevee energy, how many kilograms mass, what corresponding frequency, how many meters wavelength, how many joules if you like joules, and so on) instead of all these different numbers describing electrion there is just this one number 2.1E-22

I want to draw one of several possible connections to that number, and to the number alpha:
the energy needed to ionize an H atom is 1/2 x alpha² x 2.1E-22 energy unit

that means that the voltage to ionize H is also 1/2 x alpha² x 2.1E-22 voltage unit

it also means that the frequency of the UV photon that can just ionize the atom is
1/2 x alpha² x 2.1E-22 frequency unit

and the wavelength of the light that energetic enough to ionize H is simply the reciprocal
1/(1/2 x alpha² x 2.1E-22) length unit

because if you are working in QG natural units then all THESE numbers are the same too. You don't have to remember a lot of numbers (in eevee or joules or kelvin or meters or Herz) about ionizing the hydrogen atom. just the one.

 

[marcus]

Richard I had an idea, there should probably be a book called "A Primer of Natural Units"

equip any novice to understand the basics

plus how to convert back and forth to GeV, if desired, and things like that

stuff you've encountered could help give me ideas of what needs explaining

 

[nightcleaner]

Marcus

I like your idea for a book very much. I didn't comment on it before because my wrestling with angels keeps me very modest about such things. But it does seem to me that it would be useful in my sort of study. Especially, I would like to see the index and appendices to such a book, which in my imagination would form a reference work for those, like myself, whose memories are often confounded by imaginary results.

It happens that I have been assembling a notebook for my own use with information, mostly, from this thread. I am doing it in paper because I don't have access to my computer at work and often find myself needing to refresh my memory about one thing or another. Ideally it should be done in some form of database. I don't carry my computer to work with me because it is a precious object to me and I fear my clumsies.

Anyway, Marcus, I owe you a debt as my most patient and attentive teacher to date. Please feel free to use anything I post in this forum as you like, with the sole reservation that I would like to know about it beforehand and not come on it unawares in a dark alley some night. If I can be of any assistance to the project, I would be enthused.

Richard T. Harbaugh
Nightcleaner

 

[Kea]

Hi Marcus and Richard

I had an idea, there should probably be a book called "A Primer of Natural Units"

Marcus, yes! You've already written a fair bit of it. Perhaps it should be illustrated? I'm not volunteering as an artist. My chickens would look like my Maid Marions.

Cheers
Kea

 

[marcus]

Richard and Kea,
thank you both. Both your replies are very heartening.
If the project were to go ahead I would definitely not
use your posts without telling you, Richard,
and would only do so with prior permission.

Kea, what point or use do you see for a thin book about
this variant of the Planck units?

To get an audience would it have to discuss both conventional
(G=1) Planck units and this variant (that seems to appeal to
relavitivists and QG people and has 8piG = 1)?

Is there a point in a QG grad student's career when he or she
might enjoy such a book or get something out of it?

Or would "A Primer of Natural Units" inevitably be an eccentric adventure
of no real usefulness besides a few people's amusement?

(that last possibility does not mean I would refuse to write it
because i actually think the natural units are beautiful and i like
to look at nature thru them as lenses----but if it is apt to be
of very limited appeal to others I would like to know).

so if you don't mind giving an opinion, I'd appreciate it.

I'd actually prefer to avoid conventional Planck units and focus on these,
if that approach could be made to work

 

[Kea]

a book

To get an audience would it have to discuss both conventional (G=1) Planck units and this variant (that seems to appeal to relavitivists and QG people and has 8piG = 1)?

Is there a point in a QG grad student's career when he or she might enjoy such a book or get something out of it?

Or would "A Primer of Natural Units" inevitably be an eccentric adventure of no real usefulness besides a few people's amusement?

I don't see why you would need to clutter up the book with 'conventional' Planck units. Personally, with a little editing, I think it would be an excellent first year level physics text. Physics should be taught in appropriate units, surely. To be honest I don't think a grad student would actually buy it. They don't have any money. But I have certainly enjoyed the entertainment. Much better than the illustrated wonderwoman knot book that recently appeared in my library.

Cheers
Kea

 

[marcus]

I don't see why you would need to clutter up the book with 'conventional' Planck units. Personally, with a little editing, I think it would be an excellent first year level physics text. Physics should be taught in appropriate units, surely. To be honest I don't think a grad student would actually buy it. They don't have any money. But I have certainly enjoyed the entertainment. Much better than the illustrated wonderwoman knot book that recently appeared in my library.

Cheers
Kea

This is really encouraging. Thanks, Kea. Yes, physics should be taught in appropriate units! (what could be more appropriate?) I have been visualizing a small thin book, a "primer", and I like it more and more. Haven't got a picture of the table of contents yet

 

[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 Z, just to have a symbol. Adjusting the units to make the value |Z| = 1 gives the same set of units as setting |F| = 1.

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

rough sizes:

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

some constants (approx.):

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

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