Constants

[The Rebel]

On the topic of constants has there been any research into linking all the constants together.

 

Speed of light c, Planck constant h, Constant of Gravitation G, Magnetic constant u0, Electric constant e0, avogrado constant NA, Boltzman constant k, stefan-Boltzman constant, pi, e, magic number etc.

 

All these appear to have been derived and refined through experimentation but there must be a link between them all. Perhaps this will verge on unified theories, but it bugs me that we have all these constants that have appeared.

 

All I can find is u0 = 4pi x 10^-7 and u0e0C^2 = 1

 

There must be a link between all this natural phenomena somewhere.

[noz92]

On the topic of constants has there been any research into linking all the constants together.

 

Speed of light c' date=' Planck constant h, Constant of Gravitation G, Magnetic constant u0, Electric constant e0, avogrado constant NA, Boltzman constant k, stefan-Boltzman constant, pi, e, magic number etc.

 

All these appear to have been derived and refined through experimentation but there must be a link between them all. Perhaps this will verge on unified theories, but it bugs me that we have all these constants that have appeared.

 

All I can find is u0 = 4pi x 10^-7 and u0e0C^2 = 1

 

There must be a link between all this natural phenomena somewhere.[/quote']

Could you explain what those constants are? Some of them I've seen before, but never actually understood what they are. For example, Plank constant [math]h[/math].

[bloodhound]

i think its something to do with the quantisation of energy packets.

[JaKiri]

On the topic of constants has there been any research into linking all the constants together.

 

That's something that string theory is hoping to deal with.

 

There almost certainly has to be a link between the constants of the fundamental forces, but beyond that things become less clear.

[Guest julz]

if you are still wondering about Planck's constant, it actually has to do with quantum theory. It is used in Plank's blackbody radiation law wich is E=hv were (E) is the energy of a quantum, (v) is fequency, and (h) is a constant (Planck's constant).

 

I was also wondering about radians, i am doing a project on radian measure. This may sound like a stupid question, but does only the unit circle have a circumfrence of 2pi? becasue if not, then the radius changes and we no longer can substitute 1 in for the radius, wich then changes the circumfrence.

[Guest julz]

also, can you give me some natural circumstances were radians would be used

[echo]

I've been getting some resistance to these results, but if anyone is interested in the following calculations, please read the attachment.

Super G111.doc

[JaKiri]

also, can you give me some natural circumstances were radians would be used

 

Everything involving some sort of angle.

[Martin]

On the topic of constants has there been any research into linking all the constants together.

 

Speed of light c' date=' Planck constant h, Constant of Gravitation G, Magnetic constant u0, Electric constant e0, avogrado constant NA, Boltzman constant k, stefan-Boltzman constant, pi, e, magic number etc.

 

All these appear to have been derived and refined through experimentation but there must be a link between them all. Perhaps this will verge on unified theories, but it bugs me that we have all these constants that have appeared.

 

...[/quote']

 

About pi look at

 

http://mathworld.wolfram.com/RiemannZetaFunction.html

scroll 3/5 of the way down the page to equation (53) and (54)

 

--------

We know to expect pi to turn up in geometry (circles, spheres, areas, volumes.

 

We know to expect pi to turn up in trigonometry----radian is the natural measure of angle that works when you actually calculate what sine and cosine are using the simplest (powerseries) formulas----pi is 180 degrees, pi/2 is 90 degrees, pi/3 is 60 degrees.

 

But pi also turns up in TOTALLY DIFFERENT situations like studying the prime numbers and doing number theory with the Riemann Zeta Function, which is not about trigonometry.

 

So pi is pretty weird. pervasive. into all sorts of things.

==============

 

About the Stefan Boltzmann constant sigma

 

[math]\sigma = \frac{\pi^2 k^4}{60 \hbar^3 c^4}[/math]

 

so clearly you CAN express it in terms of the others.

 

that is typical

there is a small set of constants that are really basic and that we dont know how to express in more basic terms

 

and then there are hundreds of constants that you find listed at the

NIST constants website which can be expressed in terms of the small set of basic ones.

 

http://physics.nist.gov/cuu/Constants/

 

the NIST website will give you the formulas for expressing the less basic ones, like the Rydberg constant, StefanBoltzmann, ionization potential of hydrogen atom etc etc. in terms of the more basic.

you just put the mouse on the constant and hold down the button and you will get the formula, like I wrote for Stef Boltz.

 

===========

about Planck's hbar

first it seems better on the whole not to use h but to use hbar which is h/2pi. the farther you go in physics the more h will tend to drop out.

 

and hbar is very pervasive and has many many roles

 

here is just one role it plays: it is the ratio between a photon's energy and its (angular-format) frequency. this has already been said several times in this thread and in many other threads.

 

photons all over the universe have this basic proportionality in common

 

with any photon its energy is proportional to its frequency, so the faster the vibration the more energy in the package. And the ratio of energy to frequency is planck constant----somehow this universal proportion is built into things

 

greek architecture, greek temples, have proportions

so does the universe

I'm think there is no way around it with planck's constant, one has to acknowledge it is an awe-inspiring mystery that there is this proportion

 

hbar is one of the basic ones

==============

 

also you should distinguish between dimensionless pure numbers on the one hand (like 1836 the ratio of proton mass to electron mass, and like 1/137 the fine structure constant)

and dimensioned physical quantities which are not numbers but are instead AMOUNTS (like the speed of light and the charge on the electron)

 

Someday it might be possible to explain the pure dimensionless numbers and to say why 1836 does happen to be that.

 

But maybe there are some basic quantities like the speed of light that are not explainable because they themselves are the very dimensions of our experience in terms of which we measure and explain the rest.

 

============

so yes very many constants can be written out like StefBoltz in terms of others but there is a kind of tough gnarly core in nature that resists.

[noz92]

Here's what I found:

 

[math]\sqrt{2}[/math], or Pythagoras' constant, is equal to about [math] 1.41421356237309504880168872420969807[/math],

 

[math]\sqrt{3}[/math] is about [math]1.732050807568877293527446341505[/math]

 

[math]Y \thickapprox 0.57721566490153286060651209008240243[/math]

 

[math]\beta \thickapprox 0.70258[/math]

 

[math]\sigma \thickapprox 4.66920160910299067185320382046620161[/math]

 

[math]\alpha \thickapprox 2.50290787509589282228390287321821578[/math]

 

[math]C_2 \thickapprox 0.66016181584686957392781211001455577[/math]

 

[math]M_1 \thickapprox 0.26149721284764278375542683860869585[/math]

 

[math]B_2 \thickapprox 1.9021605823[/math]

 

[math]B_4 \thickapprox 0.8705883800[/math]

 

[math]\Delta > -2.7 \times 10^{-9}[/math]

 

[math]B'_L \thickapprox 1.08366[/math]

 

[math]\mu \thickapprox 1.451369234883381050283968485892027[/math]

 

[math]E_B \thickapprox 1.606695152415291763[/math]

 

[math]\lambda \thickapprox 0.3036630029[/math]

 

[math]\theta \thickapprox 1.30637788386308069046[/math]

 

[math]F \thickapprox 2.8077702420[/math]

 

[math]L \thickapprox 0.5[/math]

 

Most of these I've never even heard of, but those are all of the constants I was able to find.

[The Rebel]

also you should distinguish between dimensionless pure numbers on the one hand ... and dimensioned physical quantities which are not numbers but are instead AMOUNTS

 

I did start to write a thread especially on these basic constants we see around in physics as a fundamental constant, which unfortunately got lost.

 

It basically listed all the constants, which can be found at the same address I came across that you mentioned.

 

http://physics.nist.gov/cuu/Constants/

 

I made a point of trying to stay away from quantites such as electron charge, rest mass and avogrado's constant. I was also insecure in presenting c as a constant, but left it due to its popularity as a constant in so many formulae. I also wanted to avoid mathematical constants that could be specific to our numbering system. even though pi, natural log e and the magic number are so pertinent in our world.

 

I had come up with three formulae I found. One day I might repeat the thread in the hope that ideas could be brought together to link the constants we have defined but not yet explained.

 

[math]e_{0}u_{0}c^{2}=1[/math]

[math]e^{\pi i}=-1[/math]

[math]u_o=4\pi * 10^{-7}[/math]

 

---

 

On radians I should imagine they are in themselves natural. Afterall there are pi number of radians in a circle. Degrees are probabily an earily man made inventation based on clocks (i.e. degrees, minutes and seconds)

[noz92]

I think clocks are more based on degrees. I havn't checked this, but I think 1' is the time it takes for the sun to move 1' across the sky. It's probably that or similar.

[Martin]

also, can you give me some natural circumstances were radians would be used

 

I think you mean some circumstance where it would be MORE natural to talk about angles in radians

than to evaluate them in degrees.

 

suppose you have a physics problem in which you have to keep track of rotation of a wheel, and you have angle as a function of time

 

theta (t)

 

[math]\Theta (t)[/math]

 

by time t the angle it has rotated is that theta(t) and then the

distance a point on the wheel has traveled is

 

[math]R \Theta (t)[/math]

 

it is cleaner to write formulas with radians

 

Often one must use the small angle approximation for trig functions and

then THE SINE OF AN ANGLE IS THE ANGLE ITSELF

 

for small angles theta it is a very good approx

 

[math]sine ( \Theta) = \Theta[/math]

 

this is not true if you make the mistake of using degrees for angles!

The sine of 3 degrees is nowhere near 3!

 

the sine of 2 degrees is nowhere near 2!

 

But if everything is in radians then it is very nearly precise to say

 

sin(0.03) = 0.03

 

sin(0.02) = 0.02

 

this makes trig very much simpler sometimes. you just dont bother with the sine you just use the angle itself!

astronomers do this with parallax angles all the time.

 

RADIANS WERE INVENTED BY NATURE to describe angles but

 

DEGREES WERE INVENTED BY THE BABYLONIANS

 

they are the ones to blame. they really liked the number 60 and they

had almost a fetish about the number 360

so they were very weird

but they were the best astronomers of that time so when the greeks

learned to count and read and write they picked up all the Babylonian

habits. And that is how we got the 360 degree circle

Of course for the Babylonians it had something to do with the number of days in the year because they believed in "intelligent design" and were very in to making calendars.

however screw the babylonians. Use a radian every day!

[noz92]

Found some more constants:

 

Velocity of light: [math]c = 2.99793 \times 10^8m \times sec^{-1}[/math]

 

Elementery charge: [math]e = {^{1.60219}_{4.80325} \times 10^{-19}c[/math]

 

Electron rest mass: [math]me = 9.10956 \times 10^{-31}kg[/math]

 

Proton rest mass: [math]mp = 1.67261 \times 10^{-27}kg[/math]

 

Neutron rest mass: [math]mn = 1.67261 \times 10^{-27}kg[/math]

 

Plank's constant: [math]h = 6.6262 \times 10^{-34}J \times sec[/math]

 

Here's one I don't really understand:

[math]\frac{h}{2\pi}[/math]: [math]h = 1.05459 \times 10^{-34}J \times sec[/math] Apperantly this one is [math]h[/math] too. It seems to be related to planks constant.

 

Boltzmann constant: [math]k = 1.38062 \times 10^{23}J \times K^{-1}[/math]

 

Avogadro constant: [math]NA = 6.02217 \times 10^{23} \times mol^{-1}[/math]

 

Faraday constant: [math] F = 9.64867 \times 10^4C \times mol^{-1}[/math]

 

Molar gas constant: [math] R = 8.31434J \times mol^{-1} \times K^{-1}[/math]

 

Molar volume of ideal gas at [math]STP^{_c}: Vm = 2.24136 \times 10^{-2}m^3 \times mol^{-1}[/math]

 

Ice point of water in absolute temperature scale (1 atm): [math]To = 273.15\degree K[/math]

 

Mechanical equivalent of heat: [math]J = 4.184 J \times calc^{-1}[/math]

 

Permittivity constant: [math]\Eta 0 = 8.85419 \times 10^{12}C \times c^{-1} \times m^{-1}[/math]

 

Gravitational constant: [math]G = 6.6732 \times 10^{-11} N \times m^2 \times kg^2[/math]

 

Acceleration of gravity: [math]g = 9.80665 m \times sec^{-2}[/math]

[Martin]

Here's one I don't really understand:

[math]\frac{h}{2\pi}[/math]: [math]h = 1.05459 \times 10^{-34}J \times sec[/math] Apperantly this one is [math]h[/math] too. It seems to be related to planks constant.

--------------------

 

this is hbar

h with a bar thru it

 

it was Planck's original planck's constant (1899) and the trend is to use it more----especially as one moves into junior and senior college physics courses, grad courses

 

and to use h less

one can always recover h since it is simply hbar multiplied by 2pi

 

[math] h = 2 \pi \hbar [/math]

 

non-physicists, like Electrical Engineers and the like, may very well favor h,

but the tendency in theoretical physics is to favor hbar because it seems to be the one nature wants----the one that makes more formulas come out simpler

[Martin]

Found some more constants:

 

Velocity of light: [math]c = 2.99793 \times 10^8m \times sec^{-1}[/math]

 

Elementery charge: [math]e = {^{1.60219}_{4.80325} \times 10^{-19}c[/math]

 

....

 

This is a good list.

I do not understand how the 4.803 gets into your expression of the elementary charge.

I think it is just plain 1.602 x 10^-19

 

I'm glad to see such a list here though.

 

do you know the NIST fundamental constant website?

it gives the latest best estimates of the values of these things

as settled on by an international committee for scientific constants called

CODATA

 

if not you might want to check it out

just google "fundamental constants"

and the NIST site will come up first

 

their list of "universal constants" is very good

it is their short list

 

they also have a longer more inclusive list of

"frequently used constants"

 

DO YOU KNOW WHAT PLANCK UNITS ARE

they are included in modern lists of universal fundamental constants

they are nature's units, basically, built into the universe as vital proportions

 

NIST lists the planck mass unit, the length unit, the time unit and the temperature unit

[noz92]

I was coppying off the back of my calculator. It has a constants list. But could you give me the address of the site you mentioned?

[Martin]

I was coppying off the back of my calculator. It has a constants list. But could you give me the address of the site you mentioned?

 

very happy to

 

the NIST constants site:

http://physics.nist.gov/cuu/Constants/

 

the NIST category "universal constants"

http://physics.nist.gov/cgi-bin/cuu/Category?view=html&Universal.x=65&Universal.y=9

 

on that list, if you click on the name of a constant you will get a page with its symbol and its measured value (with current experimental uncertainty)

 

if you then click on the symbol, you will usually get a formula relating

that constant to others, if it has some good connection with others on the list. they did a pretty thorough job. check out some of the other categories too, besides universal.

[noz92]

Thank you.