
#1
Aug510, 06:40 PM

P: 751

About 6 minutes ago I thought of this, and I want to check if it is true.
Is the kilogram and the second a basis for all units in existence? That is, can all units be derived from these two? I can't think of any other units that are independent. 



#2
Aug510, 06:44 PM

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mass kg
length m time s current A substance mol intensity of light cd Temperature K fundamental quatities You use these base units to derive all others. 



#3
Aug510, 09:12 PM

P: 751

length  not needed since the meter is defined as the distance traveled by light in X amount of time.
current  based of coulombs and seconds. Not a fundamental unit. substance  included in KG. Mol is just a number, not a unit. intensity of light  energy density, energy is derived from kg*(m/s)^2 and meter is derived as stated above. temperature  in an ideal gas it is derived from the RMS speed of the gas molecules, in m/s; meters derived as above, seconds fundamental. For solids temperature is defined as T1=T2 if heat=zero when two bodies are in thermal contact (one body is the ideal gas). then there are others: magnetic field  derived from kg and sec, since the volume integral of the magnetic field is directly proportional to energy, and energy again is derived from kg and sec. electric field  derived from magnetic field by maxwell's equations or from the coulomb. coulomb  since charge is fundamental, it can be directly related to the kilogram (1kg of charged particles = x coulombs) or it can be derived from the electric field/magnetic field/ speed of light I can't think of any other units that can be questionable. 



#4
Aug510, 10:46 PM

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P: 2,156

KG and SEC as the basis of all units?It sounds like you're taking the view that, if you can multiply a unit of X by some combination of fundamental physical constants to get a unit of Y, then Y is a derived quantity. For example, multiplying the second (a unit of time) by the speed of light (a fundamental constant) gives you the lightsecond (a unit of length), thus length is a derived quantity. With that view, then yes, the kilogram and second will allow you to derive all other units. But you can go further than that  you don't need any base units at all. The fundamental constants automatically suggest a particular set of base units, called the Planck units. They're awfully tiny quantities, though, so they're really inconvenient to use for anything except highenergy theoretical work (string theory and the like). That's why we define things like the kilogram, meter, second, etc., so that we have a set of units that corresponds more closely to the quantities we encounter in everyday life. 



#5
Aug610, 01:22 AM

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P: 6,925

Possible alternative from wiki article:
A coulomb is then equal to exactly 6.24150962915265 × 10^{18} positive elementary charges. Combined with the present definition of the ampere, this proposed definition would make the kilogram a derived unit. http://en.wikipedia.org/wiki/Coulomb#Explanation 



#6
Aug610, 01:27 AM

P: 751

yes but the "elementary charges" can have different masses (mass of proton is not equal to mass of electron). Also there is high uncertainty in the mass (in kg) of a proton/electron which still makes it a bit difficult to make the kilogram a derived unit.
Personally I don't like the idea of having a block in Paris and saying "this is 1.0000000000000000... kg". Why can't we just define it "mass of X number of hydrogen atoms"? 



#7
Aug610, 02:05 AM

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#8
Aug610, 03:16 AM

P: 76

N carbon atoms weigh 1K when subject to X gravitational force. 



#9
Aug610, 06:10 AM

P: 178

The choice of the units you consider fundamental should depend on the practical accuracies as well. Well, at least if you want to use them for measuring things and deriving other units. Post #53 in http://www.physicsforums.com/showthr...=418112&page=4 has a bit on this when it comes to the kilogram. Likewise the SI system takes the current over the charge, since it's easier to measure accurately.




#10
Aug610, 02:34 PM

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P: 6,925

1 A = the constant current which will produce an attractive force of 2 × 10^{–7} newtons per metre of length between two straight, parallel conductors of infinite length http://en.wikipedia.org/wiki/Ampere Ampere would be derived from the definition of coulomb and second. 1 A = 1 coulomb / second 1 second = the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. http://en.wikipedia.org/wiki/Second So 1 newton would be a force derived based on the derived value of 1 amp. Then 1 kg would be the amount of mass accelerated at 1 m / s^{2} by a force of 1 newton. 1 kg = 1 N s^{2} / m 1 meter = the length of the path travelled by light in vacuum during a time interval of 1 ⁄ 299792458 of a second http://en.wikipedia.org/wiki/Metre 



#11
Aug610, 05:15 PM

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#12
Aug610, 05:41 PM

P: 5,462

what sort of light?? 



#13
Aug610, 07:27 PM

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#14
Aug710, 03:20 AM

P: 5,462

Or is it an additional axiom? 



#15
Aug710, 12:18 PM

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#16
Aug710, 12:35 PM

P: 5,462

For instance is there any proof for EM wavelengths equal to or greater than the the measurement distance? To be fundamental it would have to work for all possible wavelengths including unusual ones. 



#17
Aug710, 08:17 PM

P: 751

It works through Maxwell's equations, I don't know if you have studied that.
If Maxwell's equations aren't correct, then we're not in the position to derive any units until it has been figured out. 



#18
Aug710, 08:20 PM

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P: 6,213

But it seems that the second is further defined as a certain number oscillations and so on. As far as basic physics for engineering is concerned, those fundamental quantities are fine. Perhaps if you are studying atoms and quantum physics, they may not be. 


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