New more precise natural units at nist.gov

[marcus]

The National Inst. of Standards and Technology NIST has a
fundamental physical constants website
http://physics.nist.gov/cuu/Constants/

and until sometime this year what they posted were the
1998 CODATA recommended values
(same as those in Physics Today August 2000, or the CRC Handbook of Chemistry and Physics, or a bunch of other places)

CODATA is an international committee whose job is to establish the world's best current values for the constants, and estimate the uncertainties.

Now CODATA has come out with the official 2002 recommended values and the NIST site has changed over. I just noticed this, don't know when it happened.

Planck units are gradually creeping into CODATA
1998 was the first year they had them, and they just listed 3:
planck mass
planck length
planck time

in the 1998 listing the uncertainty given was 7.5E-4 (same for all three)

Now the uncertainty has been reduced to 7.5E-5 (order of magnitude improvement) and a new one has been added: Planck temperature.

Here are the 2002 CODATA rec. values (numbers in parenthesis show the std. deviation in last two digits)

planck mass 2.17645(16) E-8 kilogram
planck length 1.61624(12) E-35 meter
planck time 5.39121(40) E-44 second
planck temperature 1.41679(11) E32 Kelvin

A good thing to know in connection with natural units is that the Planck mass is 13E18 times the proton mass. Thirteen quintillion.
Frank Wilczek had a series of articles about this number in Physics Today a year or two ago---"Scaling Mount Planck". Its a basic number, basic to how the universe is.

The proton mass is 1/(13E18) natural mass units.

Wilczek was trying to explain how it happens that number is as small as it is.

sorry if this strikes anyone as foolish but these are the units built into nature so I want to know what is an ordinary temperature----like outdoors on today 28 December----in those terms. And what is the average mass of an air molecule in these terms.

Well temperature here is 2E-30
An air molecule has an average of 29 nucleons
each contributing 1/(13E18) of the Planck mass,
so an average molecule of air is 29/(13E18) natural mass units.

OK I confess, I'm crazy about Planck units. Can PF stand another off-beat enthusiast? Probably won't even notice. So I want to calculate the speed of sound in Planck units. That is, as a fraction of the speed of light since the Planck speed unit is c.

$$\sqrt{\frac{7}{5}*\frac{T}{29/N}}$$

$$\sqrt{\frac{7}{5}*\frac{NT}{29}}$$

Plug in 2E-30 for T, the temperature. Boltzmann k = 1, so kT is 2E-30 natural units of energy. Numerator is an energy, denominator is mass, so the fraction is the square of a velocity and sqrt gives speed.
Plug in 13E18 for N, a multipurpose number in natural units contexts.
you should get about a millionth----more exactly 1.1E-6---because that's the speed of sound in air at today's temperature of 2E-30 natural.
the 7/5 is the ratio of specific heats for a biatomic gas---good chance anyone reading this knows that already and is familiar with the formula, though maybe not in a Planck units context

Well I checked when the new values for the fundamental constants became available and it turns out it was just this month.
The 2002 CODATA values were issued December 2003 and they incorporate the experimental data available as of 31 December 2002
http://physics.nist.gov/cuu/Constants/bibliography.html

 

[marcus]

A propos Planck units, this can serve as an alternative "numerology" thread.

the temperature gradient required to cause convection in dry air
$$\frac{2}{7}*\frac{29}{13E18*5.67E50}$$

in these units k=1 and kT is identified with T, so temperature is rated on an energy scale and what the formula gives is an energy gradient with altitude. The 2/7 that shows up here is the reciprocal specific heat of a biatomic gas. 5.67E50 is the reciprocal of normal Earth surface gravity.

Here is the Chandrasekhar limit for a star core which is half protons.

$$\frac{\pi}{4}*(13E18)^2$$

This is a mass limit (a threshold for collapse into neutron matter, in effect) and the proton fraction, typically a half or less, is squared---which is where the 4 comes from in the formula. It is remarkable, I think, that the dependence on fundamental constants (like G, hbar, proton mass, c) is simply through the square of the number 13 trillion.

The Chandrasekhar mass limit is here expressed in the natural, or Planck, mass unit.

 

[marcus]

Here, slightly edited, is part of something I posted in "numerology" thread:

Let us start with three numbers given only approximately (to 3 or 4 significant figures)
1/137
1836
13E18

these are the finestructure constant, the proton/electron mass ratio (as you mentioned) and the proton compton (in Planck)
or if preferred think of 13E18 as the ratio of Planck unit mass to the proton mass.

the bohr radius turns out to be $$137*1836*13E18$$

the electron compton turns out to be $$1836*13E18$$

the electron's classical radius is $$\frac{1836*13E18}{137}$$

I guess we should be able to get electron cyclotron frequency (in ratio to magnetic field strength) and also Thomson scattering cross-section, and a bunch of stuff like that. The main wavelengths of the hydrogen spectrum---the atom's "colors"---should be easily calculated from these numbers

Also the masses of the proton and electron----expressed in Planck mass units----are easy.

The proton mass:
$$\frac{1}{13E18}$$

The electron mass:
$$\frac{1}{1836*13E18}$$

The Rydberg energy----the ionization energy of the hydrogen atom (expressed in Planck energy units)-----should be easy.

what makes all these things easy to calculate is that we express the answer in natural units. so few inputs and conversion factors are involved

 

[marcus]

The Rydberg energy, that amount of energy required to
ionize a hydrogen atom in its ground state
$$\frac {1}{2}*\frac {1}{137^2}*\frac {1}{1836}*\frac {1}{13E18}$$

Remember this is hydrogen's ionization potential expressed in the natural, or Planck, unit of energy (planck mass times speed of light squared). It needs all that stuff in the denominator because it has to be quite a small number----since Planck unit energy is rather big.
some 2 gigajoules.

the Rydberg frequency expressed as a fraction of the natural frequency, is the same number

Hydrogen's colors are gotten by multiplying Rydberg energy (or frequency) by terms of the form

$$\frac {1}{m^2}-\frac {1}{n^2}$$

in particular for the balmer lines set m = 2

$$\frac {1}{2^2}-\frac {1}{n^2}$$

 

[marcus]

Rovelli's parable of the whale

You may not see the relevance of this immediately.
In "Quantum Gravity" on page 7, Rovelli says

"It is as if we had observed in the ocean many animals living on an island: animals on the island. Then we discover that the island itself is in fact a great whale. Not anymore animals on the island, just animals on animals. Similarly, the universe is not made by fields on spacetime; it is made by fields on fields. In this book we study the far reaching effect this conceptual shift has on quantum field theory."

Einstein established in 1915 that the gravitational field is the geometry of spacetime.
Like the animals on the whale, the other fields live (not on some absolute fixed spacetime) but on the gravitational field.
If one is to quantize the gravitational field one must quantize the geometry. If the gravitational field is to be dynamic and arise from interaction with other fields, then the underlying geometry must be dynamic likewise.

I want to have a way to communicate at a basic level my feeling that
we may someday have an explanation of why these numbers 1836 and 1/137 and 13 quintillion are what they are
And these numbers (and a few others in the standard model like them) are the underpinnings of our existence
there are many examples of how many things can be calculated (in terms of the system of units built into nature) from these 3 numbers and a few others like them.
These numbers are the island, the solid ground. But in time we may discover that they are the whale, and can swim around and change.

And so these few numbers, the fundamental physical constants expressed in natural units, are an important indicator of where we are now, how far we have come, and where the next change must happen. They define for us a kind of frontier.

 

[marcus]

a lot of fundamental constants are calculable
(in natural units) from these three numbers I mentioned or less
for example the reciprocal Josephson constant, by which I mean the characteristic
voltage/angular frequency ratio of a Josephson junction

It is just
$$\frac{1}{2}$$
because if you adjust the voltage across the junction so
that the angular frequency (radians per Planck time unit)
is some number $$\Phi$$
then the voltage (planck energy units per elementary charge)
will automatically be half that number:
$$\frac{1}{2}*\Phi$$

the Josephson constant is one of those listed among the fundamental]
physical constants at the NIST site. I forget what its CODATA recommended value is in metric.

 

[marcus]

Stefan-Boltzmann constant

another example of a fundamental physical constant that can be calculated without using any of the three basic numbers mentioned earlier is the fourth-power law Stefan-Boltzmann constant which is just

$$\frac{\pi^2}{60}$$

If the temperature of a black body is T (in natural) then the number

$$\frac{\pi^2}{60}*T^4$$

is the radiant power per unit area (planck energy units per unit time per unit area)
Maybe an example is in order. At the Earth's distance from the sun, the brightness of direct sunlight is E-119---this is the solar constant in natural units (0.98E-119 if needed more accurately) So imagining a patch of sunlight at the equator under absolutely clear sky gives some notion of that quantity of incoming power per unit area.
A common temperature at the Earth's surface (around 10 celsius or 50 fahrenheit) is 2E-30. Things that temperature radiate considerably more feebly than E-119 as can be seen by raising to the fourth (16E-120) and multiplying by Stefan-Boltzmann constant (approximately 1/6).

 

[8LPF16]

Marcus,

Commonality?:

137/pho = 1781.00178100178100178100...

1836/pho = 23868.0238680238680238680...

13E-18/pho = 1.69000169000169000169000169000E-16

Products contain repeating values through the decimal point. Value can be said to have "burst" quality - on, on, on, etc.


137/13 = 10.538461538461538461...

1836/13 = 141.230769230769230769...

Alternating values create on, off, on, off, on, etc. (polarity)


13E-18/13 = 0.000000000000000001
(13E-18*pho = 0.000000000000000000999999)
(to avoid dividing by self)

13 produces these patterns regardless of size. 13E+4, 13E-34, etc.
Pho is the quantum product of 13. (1/13)
Quantum products are "the relationship a number has with itself".

Please see my threads in theory development.


LPF

 

[marcus]

At last, a real Numerologist!

Hello LPF
you seem to be a real numerologist not just the harmless
ersatz sort.

Did Pythagoras not forbid the eating of beans?

 

[8LPF16]

Marcus,

Yes, no beans. No foods that produce flatulence. Vegetarian too (imagine a no bean vegen). Women equal. Respect animals. Don't pour libations with your eyes closed. Don't pee into the Sun.

So, not all of their rules are crazy.


Numbers is as numbers does. Life is a box of numbers...

I'm just a toddler playing with numbered cubes.


LPF