Expressing second and its derivatives in terms of seven SI base units

In summary: FORMULA =...1sº = FORMULA =...1sº = FORMULA =...In summary, the conversation discusses time-oriented geometrized units and the conversion of second and its derivatives in terms of the seven SI base units. The speaker mentions using the speed of light, c, to express second in terms of meters and kilograms. They also mention wanting to convert other SI base units, such as ampere, Kelvin, mole, and candela, into second-derived units. They ask for help in obtaining the correct conversion formulas and constants for this conversion. The expert explains that the conversion factor from kilograms to seconds is c³/G, not G/c³, and provides a link
  • #1
TurricaN
12
0
Time-oriented geometrized units→Second and its derivates in terms of 7 SI base units

I expressed second in terms of meter and kilogram. For doing this I used:

For expressing second in meters:
1s¹ = c = 299792458 m

For expressing second in kilograms:

1s¹ = c³/G = 299792458³/0,0000000000667421 =
= 403703246037718000000000000000000000 kg

How to express ampere, Kelvin, mole and candela in terms of second-derived units, as sketched below?

I know dimension of these seven SI base units in geometrized units as follows:

D ³ →
D ² →
D ¹ → length, mass, time
D º → current, amount of substance, luminous intensity
Dˉ¹ → temperature
Dˉ² →
Dˉ³ →

I got this dimensional analysis by further distilling ST spacetime units from LUFE Matrix from here: http://www.brooksdesign-cg.com/Code/Html/Lm/LMqtySI.htm [Broken] into single geometrized D unit of distance (and its derivatives) along any of timespace dimensions as follows:

|Dˉ³|Dˉ²|Dˉ¹|Dº|D¹|D²|D³| ←D matrix that is simplified version of LUFE matrix

I want to obtain following result:

1sº = ¿ = ? A
1sˉ¹ = ¿ = ? K
1sº = ¿ = ? mol
1sº = ¿ = ? cd

¿ symbol denotes unknown converting formula with constants
? symbol denotes unknown result in target units

Which converting formulas and constants (not rounded, but exact values) use to express these second-derived units in terms of ampere, kelvin, mole and candela?
 
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  • #2
I'm not quite sure what you are doing, but it appears to be roughly similar to geometrized units (see http://en.wikipedia.org/wiki/Geometrized_unit_system) but not exactly the same.

However, geometrized units converts everything to meters (or perhaps cm), so one expresses seconds, kilogramts, etc. in meters. This is done by setting several fundamental constants equal to 1 (c, G and for charge related units, the coulomb force constant).

You might look at how geometrized units handle the cases you mentioned.
 
  • #3
Explanation

I'm wanting to do converting every of seven SI base units into seconds (or perhaps daynights) instead of meters, so I want expressing meters, kilograms, amperes, kelvins, moles and candelas in seconds and second-derived units such as seconds to minus one power and seconds to zero power, as I stated above. How exactly to do this? I couldn't find in Internet exactly needed formulas, I found only those for expressing MKS system in terms of seconds. I'm relatively new to physics related things. I didn't made anything physical since 2000 year, and because of losing by me my former physical experience, I need help. My approach differs from Wikipedia geometrized units in choosing second instead of meter, and due to this, Wikipedia formulas doesn't conform to my needs.
 
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  • #4
Here is a very quick answer:

1) converet everything into meters using the wikipedia formulas
2) Multiply the results by 1/c, the conversion factor from meters to seconds. (This has a value of unity since c is assumed to have a value of unity)

i.e.1 meter would be 1 meter x (1 second / 3e8 meters) = 1 meter / c.
 
  • #5
Note that c is a constant defined as exactly 299792458.
 
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  • #6
Specification

I have problem in transforming from to-meter conversion formulas placed here: http://en.wikipedia.org/wiki/Geometrized_unit_system at Wikipedia into to-second conversion formulas, because of different factors needed, which partially I don't know. For example, to make from Wikipedian kilogram-to-meter formula G/c^2 target kilogram-to-second formula c^3/G, I must multiply it by c^5/G^2. But while transforming second-to-meter c formula back into meter-to-second 1/c formula, I must multiply it by c^-2. As you see, each formula needs different transformation to get from to-meter into to-second conversion. Because to that, I would give from someone final conversion formulas as follows:

1sº = FORMULA = ? A (how many ampers fits in 1sº)
1sˉ¹ = FORMULA = ? K (how many kelvins fits in 1sˉ¹)
1sº = FORMULA = ? mol (how many moles fits in 1sº)
1sº = FORMULA = ? cd (how many candelas fits in 1sº)

I need this in this shape, knowing each exact final conversion formula, because I'm making simpler version of LUFE matrix, and subsequently system of units that is more consistent than SI, that uses only one time dimension instead of two or even seven base units, and I want to recalculate all myself using Windows ME calculator, that supports 32 decimal places, obtaining results in high precision. All needed constants and formulas I got from this PowerPoint presentation: http://web.mit.edu/8.01t/www/materials/Presentations/PPT_W01D3/PPT_W01D3_pc.ppt
 
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  • #7
Google calculator is your friend - or should be. It's quite handy for unit conversions.

G/c^3 is the correct conversion factor from kg into seconds, not c^3/G

This is because G/c^3 has units of

http://www.google.com/search?hl=en&q=G/c^3=

s/kg

Therfore kg * (G/c^3) = kg * (sec / kg) = sec

Examples:

1 kg * (G/c^3) = 2.5e-36 seconds

1 solar mass * (G/c^3) = 5 microseconds

Converting microseconds into meters (by multiplying by the speed of light, c) we get 1500 meters. This is correct, the Schwarzschild radius for 1 solar mass is 1.5 km

c^3/G is the conversion factor to go the other way.

I am assuming you are familiar with the standard pictorial method of unit conversion

N apples * (M oranges / apple) has units of oranges
You chose M so that the factor in the parenthesis is unity.

One must pick certain constants to set equal to unity to perform this conversion, the typical choice is the wikipedia choice, which includes setting the gravitational constant G equal to 1, and the speed of light c equal to 1.
 
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  • #8
MeJennifer said:
Note that c is a constant defined as exactly 299792458.

[tex]c=299,792,458 m/s^{-1} [/tex] due to the way meters and seconds have been defined.
 
  • #9
Gib Z said:
[tex]c=299,792,458 m/s^{-1} [/tex] due to the way meters and seconds have been defined.

It used to be like that, but now (since 1983) the metre is defined as the distance traveled by light in vacuum during a time interval of 1/299 792 458 of a second[1].

[1] http://en.wikipedia.org/wiki/Meter#Timeline_of_definition
 
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  • #10
explanation of c³/G

I used c³/G, instead of G/c³, because I wanted to convert seconds into kilograms, but not kilograms into seconds, which conversion I did from seconds into target units below:

1s¹ = c = 299792458 m
(299792458 meters are contained within 1s¹)
1s¹ = c³/G = 403703246037718000000000000000000000 kg
(403703246037718000000000000000000000 kilograms are contained within 1s¹)

Is this correct?

For these second-derived units listed below I too need four analogous formulas, that converts from second to various powers as below listed, into A, K, mol and cd.

1sº = FORMULA = ? A (how many ampers are contained within 1sº)
1sˉ¹ = FORMULA = ? K (how many kelvins are contained within 1sˉ¹)
1sº = FORMULA = ? mol (how many moles are contained within 1sº)
1sº = FORMULA = ? cd (how many candelas are contained within 1sº)

These units are units derived from second, as I got from simplifying abovementioned LUFE matrix. I want to derive all seven base SI units from second and abovementioned second-derived units, thus I need now only four factors, because first three I already know.

I recently found using Google calculator, that in one second fits 2.62844382 e+75K, because: http://scholar.google.com/scholar?hl=en&lr=&q=(c^5)/(G*k)&btnG=Search. Thus factor from seconds to kelvins is (c^5) / (G * k). How to transform this factor for making converting from reciprocal seconds to kelvins, because of reciprocal second being dimension of temperature?
 
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  • #11
Thats what I meant lol. I was saying c being defined as 299292458ms^-1 is due to the fact the meter is defined and seconds are defined. It is deducible from the definition you posted that c is defined as such.
 
  • #12
Gib Z said:
Thats what I meant lol. I was saying c being defined as 299292458ms^-1 is due to the fact the meter is defined and seconds are defined. It is deducible from the definition you posted that c is defined as such.
Yes and that was my whole point as well. :smile:
 
  • #13
Help needed

Can anyone, even mentor give me correct conversion factors from second and second-derived units into each of seven SI base units as I described above, and when necessary tell me where I'm wrong in my factors, of course confirming what is good?
 
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  • #14
MeJennifer said:
Yes and that was my whole point as well. :smile:

I know and I am sorry if you got the impression I thought you didnt know, its just that I run into a lot of people who think its amazing that c is exactly 299792458, they won't think its so amazing when they find out the definitions...
 
  • #15
Conversion

How to transform (c^5)/(G*k) expressed in K/s to make it expressed in K*s that is equal to K/Hz ? I now need to know how many kelvins fits into one hertz.
 
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  • #16
conversion from hertzes into seconds solved

I found that to get how many kelvins fits into one hertz I must use formula h/kB, which tells me that into one hertz fits 0.00000000004799237 K.

Proof here:
http://www.google.pl/search?hl=en&q=h/k&btnG=Szukaj+w+Google&lr= which equals needed units of K/Hz: http://www.google.pl/search?hl=en&q=1K/1Hz&btnG=Search

Good conversion table suitable for my task is here:
http://ptf.fuw.edu.pl/stale/stale_fiz.pdf [Broken] - please look at nearly lowest section, where is header with J kg mˉ¹ Hz and K eV u Eh symbols. It helped me very much, because of lack of any further help from any forum members.
 
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  • #17
masudr said:
It used to be like that, but now (since 1983) the metre is defined as the distance traveled by light in vacuum during a time interval of 1/299 792 458 of a second[1].

[1] http://en.wikipedia.org/wiki/Meter#Timeline_of_definition

but i think the point is the need of units attached to the 299792458 number for c. in SI, c is not dimensionless, even if it is defined constant.

if it were Natural Units (Planck or something else) then it is meaningful to define the speed of light in vacuo as either 1 (Planck units and most other systems) or sometimes as [itex]\alpha^{-1}[/itex] = 137.03599911 (Atomic units). so it can make sense that c can be either of those two dimensionless numbers, but not the dimensionless number: 299792458.
 
  • #18
Gib Z said:
[tex]c=299,792,458 m/s^{-1} [/tex]
I'm waiting for a pot of water to boil, so I'll just nitpick some silly mistakes until the water's ready for my spaghetti. :smile: I'm sure you didn't really mean meter-seconds, so you should have written [itex]ms^{-1}[/itex] or [itex]m/s[/itex].
 
  • #19
rbj said:
but i think the point is the need of units attached to the 299792458 number for c. in SI, c is not dimensionless, even if it is defined constant.

if it were Natural Units (Planck or something else) then it is meaningful to define the speed of light in vacuo as either 1 (Planck units and most other systems) or sometimes as [itex]\alpha^{-1}[/itex] = 137.03599911 (Atomic units). so it can make sense that c can be either of those two dimensionless numbers, but not the dimensionless number: 299792458.

I don't see the disagreement here. I've never claimed c was dimensionless: only in units where displacements in space and displacements in time are measured by a common unit (sometimes they are) is c dimensionless.
 
  • #20
I saw that between h/kB [K/Hz] and (c^5)/(G*k) [K/s] exist inconsistency in converting, because if 1Hz=1s, then conversions should be the same, but I give http://www.google.pl/search?hl=en&q=h/k&btnG=Szukaj&lr= and http://www.google.pl/search?hl=en&q=(c^5)/(G*k)&btnG=Search that are not even their reciprocals. Because of this mish-mash in formulas, I need from anew help in converting seconds and second-derived units into meters, kilograms, seconds, amperes, kelvins, moles and candelas as follows:

1s¹ = FORMULA = ? m (how many meters fits in 1s¹)
1s¹ = FORMULA = ? kg (how many kilograms fits in 1s¹)
1s¹ = FORMULA = ? s (how many seconds fits in 1s¹)
1sº = FORMULA = ? A (how many ampers fits in 1sº)
1sˉ¹ = FORMULA = ? K (how many kelvins fits in 1sˉ¹)
1sº = FORMULA = ? mol (how many moles fits in 1sº)
1sº = FORMULA = ? cd (how many candelas fits in 1sº)
 
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  • #21
masudr said:
I don't see the disagreement here. I've never claimed c was dimensionless: only in units where displacements in space and displacements in time are measured by a common unit (sometimes they are) is c dimensionless.

no big deal. it's just that GibZ corrected a possible oversight of MeJennifer (i thought correctly, c is not simply the number 299792458) and i thought you were correcting GibZ. i dunno. i'll just watch.
 
  • #22
I made working formula from seconds to kilograms in form:
((1 second)*(c²/h))-¹
Both second and (c²/h) are to -¹ power.

Thus I transformed it to:
(1 second)-¹*(c²/h)-¹

But how to transform it further to make bare (1 second) on left side of multiplication (or division if needed) sign, and appropiate transformation on right side of multiplication (or division if needed) sign, that too converts from seconds to kilograms, and has only one instance of second on left?
 
  • #23
[c] = L T-1
[h] = M L2 T-1

[c2/h] = L2 T-2 M-1 L-2 T1 = M-1 T1 = T/M.

Therefore, in SI units:

1 second = c2/h * 7.372 -51 kg
1 kg = h/c2 * 1.356 x 1050 second

EDIT: oops! forgot to put in the conversion factors.
 
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  • #24
masudr said:
[c] = L T-1

1 second = c2/h * 7.372 x 10-51 kg
1 kg = h/c2 * 1.356 x 1050 second

I deduced that these factors:

7.372 x 10-51
1.356 x 1050

are derived from:
h/c2
and
c2/h

but unit dimension doesn't match, because of introducing of dimensionless unit made by multiplication by inversion. Thus how finally these two expressions:

1 second = c2/h * 7.372 x 10-51 kg
1 kg = h/c2 * 1.356 x 1050 second

are formulated using combination of constants only?
 
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  • #25
You can't do those without constants in the SI system: these factors are not chosen so that they are normalised. Of course, you are free to use any other standard.
 
  • #26
I want to do it of course with constants, but how these expressions:

1 second = c²/h * 7.372 x 10-51 kg
1 kg = h/c² * 1.356 x 1050 second

are expressed using symbols of constants, but not digits to plus and minus ten power?
 
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  • #27
I finally avoided this ugly contradiction, by choosing another conversion factor for temperature, thus 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)
*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) ?
 
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  • #28
Boltzman's constant converts degrees kelvin 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.
 
  • #29
TurricaN said:
I now need to go into dimensionless SI base units, and because of dimensionessness of ampere, mole, and candela,

there are no such thing as dimensionless SI base units.

and since all geometrized units do are normalize c and G, there are a zillion different ways to define geometrized units. i have no idea what this exercise in arithmetic polishing of the knob is about.
 
  • #30
This thread is degerating into absurdity, and it has nothing to do with SR/GR. So it is DONE.

Zz.
 

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