Talk:Geometrized unit system

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1 Title?
2 8πG = 1?
3 Students beware
4 MKS Charge units
5 Edits
6 more edits
7 LUFE Matrix and unit conversion
8 Unit conversion
9 Getting from second to ampere, mole and candela
10 Conversion factors between meter, kilogram, second, coulomb and kelvin

[edit] Title?

Should this be moved to geometrized unit (singular)? Sometimes the plural is appropriate in an article title; is this such a case? Michael Hardy 15:46, 18 Dec 2003 (UTC)

I moved it to geometrized unit system, for in this case the plural was used to identify a category. Thanks for the comment.

[edit] 8πG = 1?

Isn't sometimes 8πG set to 1? --Pjacobi 11:05, July 31, 2005 (UTC)

There actually are several different systems involved here. Your "sometimes" and the "sometimes" starting the second paragaph of the article are clues to that fact. Gene Nygaard 11:16, 31 July 2005 (UTC)

Yes, 8πG is another common convention, as is 16πG=1. This is problematic. My impression is that the most common modern convention is 8πG=1, but I could be mistaken. –Joke137 18:10, 2 October 2005 (UTC)

But what about Wald, General relativity, Appendix F, which uses c = G =1? This is probably the most widely used graduate textbook on general relativity in the English-speaking world. Can anyone cite a major textbook which used either of the other two conventions mentioned by Joke137? ---CH (talk) 01:33, 3 October 2005 (UTC)

[edit] Students beware

I extensively edited the August 2006 version of this article and had been monitoring it for bad edits, but I am leaving the WP and am now abandoning this article to its fate.

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.

Good luck in your search for information, regardless!---CH 23:52, 30 June 2006 (UTC)

[edit] MKS Charge units

I beleive there should be a entry for converting SI charge units in the official conversion table.

Using google calculator, I get for the conversion constant:

$\sqrt{G / 4 \pi \epsilon_0 c^4}$ = sqrt(G / (4 * Pi * electric constant * c^4)) = 8.61667791 × 10-18 m / coulomb

question: what source should be used for constant values?

Pervect 23:09, 22 July 2006 (UTC)

[edit] Edits

I've made the edits indicated above, having gotten no comments. The conversion table from Wald is for cgs units, unfortunately. This would only matter for charge and related electrical units. I've marked up the table to indicate it's a cgs table as the simplest course of action to fix the issue.

consistincy checks:

1 statcolumb * sqrt(G)/c^2 -> 2.87 * 10^-25 cm = 2.87* 10^-27 m

1 coulomb -> 8.62 * 10^-18 m (from MKS table)

1 statcolumb / 1 coulomb = 3.33*10^-10

consistent with http://en.wikipedia.org/wiki/Statcoulomb This is incosistent with the wiki cgs page, however!

more consistency checks:

charge of electron = 1.381*10^-34 cm (MTW back cover)

charge of electron = 1.60*10^-19 coulomb * 8.62*10^-18 m/coulomb = 1.38*10^-36 m = 1.38*10^-34 cm

Pervect 22:41, 29 July 2006 (UTC)

[edit] more edits

I went through and added the SI units and conversion factors to the table (a major edit at least in terms of work).

I cross-checked the conversion formulas for SI units with google calculator. Examples (cut and paste the following formula into google calc). epsilon_0 is "electric constant" in Google.

(amps)* (sqrt (G / (4 * pi * electric constant))) / c^3=

(tesla) * (sqrt(G * (4 * pi * electric constant) ) / c) =

(volts) * (sqrt(G * (4 * pi * electric constant) ) / c^2) =

[edit] LUFE Matrix and unit conversion

I recently added unidimensional version of LUFE Matrix to Geometrized unit system article, and too documenting reference to less simplified original duodimensional LUFE Matrix. I ask, how to convert meter, kilogram, second, ampere, kelvin, mole and candela to second, using cross-consistent converting formulas that too will retain cross-consistency in converting between meter, kilogram, second, ampere, kelvin, mole and candela, giving cross-consistent results? Which formulas are needed to perform this conversion task, directly from these units to seconds and second-derivations as follows:

from meter to second to one power
from kilogram to second to one power
from second to second to one power
from ampere to second to zero power
from kelvin to second to minus one power
from mole to second to zero power
from candela to second to zero power

After removing from article I moved to discussion both reference of this duodimensional LUFE Matrix by Reginald Brooks that simplifies non-geometrized units to space and time dimensions, and too unidimensional LUFE Matrix that simplifies non-geometrized units to only one dimension, that can be either linear space or linear time dimension. It is a simplification of Brooks's one. Maybe it will be useful for someone?

D^-3	D^-2	D^-1	D⁰	D⁺¹	D⁺²	D⁺³
amount of substance concentration	angular acceleration, electric charge density, mass density	acceleration, electric field, electric field reluctance, electric field strength, electric flux density	conductance, velocity of light	capacitance, length, wavelength	angular momentum, Boltzmann constant, entropy, heat capacity, magnetic moment, Planck constant, universal gas constant	moment of inertia, quadropole moment
	electric current density	activity, angular frequency, angular velocity, frequency, magnetic flux density, temperature	current, magnetomotive force	charge, electric flux, mass	area	volume
	energy density, modulus of elasticity, pressure, stress	heat flux, spring constant, surface tension, thermal conductance	dose, potential difference, specific energy	energy, heat, internal energy, moment of force, torque, work	center of mass, electric moment
	heat flux density, irradiance, radiance, radiant flux density, sound intensity	Josephson frequency volt quotient	energy, power, radiant flux conduction	impulse, momentum	specific volume
	luminance	magnetic field intensity, magnetic field strength, magnetization, viscosity	force, tension, thermal conductivity	inductance, permeance	Stefan Boltzmann constant
		Rydberg constant	impedance, reactance, resistance	magnetic flux, specific heat, thermal diffusivity
			permeability of the vacuum	resistivity, temperature coefficient resistance, thermal expansion coefficiency, time

Source: LUFE Matrix

83.19.52.107 07:21, 29 March 2007 (UTC)

I rather hate to say this after all the work this user has put in, but I think that the LUFE matrix is not a good Wikipedia reference, as per http://en.wikipedia.org/wiki/Wikipedia:Reliable_sources, specifically WP:SPS

I'll take the liberty of quoting the relevant section

---<quote begin>---

Self-published sources Shortcut: WP:SPS WP:SELFPUB

Main article: Wikipedia:Attribution

A self-published source is a published source that has not been subject to any form of independent fact-checking, or where no one stands between the writer and the act of publication. It includes personal websites and books published by vanity presses. Anyone can create a website or pay to have a book published, and then claim to be an expert in a certain field. For that reason, self-published books, personal websites, and blogs are usually not acceptable as sources (see Exceptions below).

---<quote end>---

I haven't been terribly active on Wikipedia recently, or I would have mentioned this much earlier.

Unfortunately this suggests that a major revert is in order.... Pervect 18:47, 29 March 2007 (UTC)

If you find out something new, even a new way of presenting it, Wikipedia isn't the right place to publish it. Encyclopedias aren't for creative work. And I'd consider something new, as long as not taken up in textbooks or at least review papers. There is some middle ground, where nasty long-going arguments may arise (as happened regarding Entropy), but the case of the LUFE matrix seems rather clear to me. So I revert now. --Pjacobi 22:24, 29 March 2007 (UTC)

[edit] Unit conversion

What's with conversion from all base SI units to seconds? How to convert from these units to second to various power as stated below and deduced from abovementioned LUFE Matrix?

from meter to second to one power
from kilogram to second to one power
from second to second to one power
from ampere to second to zero power
from kelvin to second to minus one power
from mole to second to zero power
from candela to second to zero power

83.5.0.83 16:32, 31 March 2007 (UTC)

See the table in "Definition" which lists the more important cases. Perhaps the conversion factor of "1" for length should be explicitely added. Current and voltage may be added, mole and candela I would leave out. --Pjacobi 16:38, 31 March 2007 (UTC)

Can you update definition table in article to cover all seven SI base units, even mole and candela, and reorient table's conversion to converting from these units into second to various power, or at least provide in discussion all needed conversion formulas that fits my need of converting from seven SI units into second? I don't know all needed conversion factors for these, and those placed there converts into meters, but not into seconds.83.5.0.83 16:42, 31 March 2007 (UTC)

A mole is just a certain number of particles - it shouldn't need any conversion. I don't know how to handle candela offhand. To convert to seconds rather than meters, convert to meters and multiply by 1/c, which has units of seconds/meter.

As far as powers go, there is a standard rule for handling unit conversions, which is that if you square the units, you square the conversion factor. Example: 1 foot = 12 inch, 1 foot^2 = 144 square inches. There should be articles on how to do general unit conversions that explain this. However, dimensional analysis, the logical place for this, doesn't seem too detailed. So there is room for improvement in the Wikipedia, but the improvement should probably go into the dimensional analysis article. Pervect 02:23, 1 April 2007 (UTC)

After aplying your tips I got:

for conversion from meter to second to one power - c defining how many meters are in one second
for conversion from kilogram to second to one power - c³/G defining how many kilograms are in one second
for conversion from second to second to one power - no conversion factor, because 1s=1s¹
for conversion from ampere to second to zero power - no conversion factor, because it is dimensionless number
for conversion from kelvin to second to minus one power - c⁵/(G*k) defining how many kelvins are in one second

(not in second to minus one power, because LUFE Matrix has contradiction at kelvin position between "°K" and "per °K" between these tables: [1] [2])

for conversion from mole to second to zero power - no conversion factor, because it is dimensionless number
for conversion from candela to second to zero power - no conversion factor, because it is dimensionless number

I cross-checked these conversion factors by converting from obtained from second these values of both meter and kilogram back to kelvin, both using direct conversions from second to kelvin, and too from meter to kelvin multiplying by (c⁴/(G*k)) [K/m] and from kilogram to kelvin multiplying by (c²/k) [K/kg], and finally obtained the same results as in direct conversion from second to kelvin. That means that this set of conversion formulas is fully cross-consistent.

But how transform this conversion factor c⁵/(G*k) to change its dimension from kelvins per second to one power (K/s¹) into kelvins per second to minus one power (K/s^-1) ? 83.5.72.232 10:44, 1 April 2007 (UTC)

Boltzman's constant converts kelvins into energy units. A higher temperature means more energy. In geometric units, energy, mass, time, and length all share the same unit - the meter or centimeter in most variants. Therfore kelvin units, as a measure of energy, are not equivalent to hertz, but rather to meters or seconds. Think about linear dimensions. Feet are not equivalent to 1/feet and feet are not equivalent to square feet. Feet, 1/feet, and in general feet^n are all different units for different values of n and cannot be equated. Pervect 17:23, 1 April 2007 (UTC)

Thus if kelvin equals to meters or seconds, why LUFE Matrix treats temperature as dimension to minus one power as is stated in aboveplaced table and in LUFE Matrix subpage placed here:http://www.brooksdesign-cg.com/Code/Html/Lm/LMunitSI.htm ? With all other ratios LUFE Matrix dimensionally agrees with pink-titled conversion table in Wikipedia article about geometrized units. That suggests that possibility of changing dimension of abovementioned ratio from K/s¹ into K/s^-1 that you, Pervect denied, can exist. Please explain why there is contradiction between LUFE Matrix and your judging? 83.5.72.232 19:05, 1 April 2007 (UTC)

LUFE Matrix treats temperature as dimension to minus one power instead of dimension to one power, because it has contradiction at kelvin position between "°K" and "per °K" between these tables: [3] [4] Additionally, because c⁵/(G*k) [K/s] is consistent with other conversion factors, while h/k [K/Hz] is not consistent with other conversion factors, LUFE Matrix is in error at Kelvin position, while Wikipedia set of conversion factors is valid. That fact finally denies possibility of changing dimension of abovementioned ratio from K/s¹ into K/s^-1.83.19.52.107 07:32, 4 April 2007 (UTC)

Finally our discussion about septenary geometrized units was crowned by releasing by me principles and creation process of such system in article placed here: http://www.internet-encyclopedia.org/index.php/Septimalisation 83.19.52.107 07:06, 16 April 2007 (UTC)

[edit] Getting from second to ampere, mole and candela

I now need to go into geometrically dimensionless SI base units, and because of geometrical dimensionessness of ampere, mole, and candela, I think that some visualisations are needed:

For ampere: Because 1A = 1 C/s, and because 1s equals 3.47921161E25C from this expression: c^3/((G/(4*pi*(electric constant)))^0.5) [C/s]=[A], verifiable here: Google I can visualize resultant dimensionless unit of current as one second of space that equals 3.47921161E25C and 299792458m, that flows in one second of time. Due to this, I will rather consider coulomb as next base unit, because it has dimension of distance, and was not present in previous set of units such as meter, kilogram, second and kelvin.

For mole: Because 1mol= 1NA, I can visualize one mole as 6.0221415E23 dimensionless units, thus I will discard it completely, because it is not even ratio of two dimensionful units.

For candela: Because 1cd is 1/683 [W/sr], I will rather consider lumens to discard dimensionless steradian that is a dimensionless ratio of areas. 1 lm equals 1/683 [W], that equals [J/s] and [kg*m^2/s^3], and because ratio of length*mass^2 to time^3 is the same as ratio of distance^3 to distance^3, I can visualize lumen as dimensionless ratio of volumes, which makes lumen in its parts and its wholeness a totally dimensionless unit, consisted of ratios of dimensionful units such as meter, kilogram, and second which all have dimension of distance. Because lumen contains no additional units besides meter, kilogram, second, coulomb and kelvin, I will discard it completely.

Source: Human vision

[edit] Conversion factors between meter, kilogram, second, coulomb and kelvin

Here you have all needed conversion factors that covers all SI base units, and if not possible, their unique elements:

into m

G/c^2 [m/kg]
c [m/s]
((G/(4*pi*(electric constant)))^0.5)/c^2 [m/C]
(G*k)/c^4 [m/K]

into kg

c^2/G [kg/m]
c^3/G [kg/s]
1/(G*4*pi*(electric constant))^0.5 [kg/C]
k/c^2 [kg/K]

into s

1/c [s/m]
G/c^3 [s/kg]
((G/(4*pi*(electric constant)))^0.5)/c^3 [s/C]
(G*k)/c^5 [s/K]

into C

c^2/((G/(4*pi*(electric constant)))^0.5) [C/m]
(G*4*pi*(electric constant))^0.5 [C/kg]
c^3/((G/(4*pi*(electric constant)))^0.5) [C/s]
(k*(G*4*pi*(electric constant))^0.5)/c^2 [C/K]

into K

c^4/(G*k) [K/m]
c^2/k [K/kg]
c^5/(G*k) [K/s]
c^2/(k*(G*4*pi*(electric constant))^0.5) [K/C]

All these units represents nothing else than distance along dimension, that makes SI redundant in comparison to geometrized units. I added all these abovementioned factors after proper formatting to article. They can be verified in Google calculator. Wikinger 16:46, 19 September 2007 (UTC)

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