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.
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.
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.
It kind of depends on what you consider to be a derivation. 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 light-second (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 high-energy 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.
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
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"?
There's exactly the same uncertainty in the value of Avogadro's number, but that doesn't stop us from using it to define the mole as a derived unit. You try counting out 10^{27} hydrogen atoms without losing track of a few trillion along the way People actually are trying to do this, though: there's a project to create a new standard definition of the kilogram, as the mass of some integer number of carbon atoms. The exact number will have to be decided on before they finish, because we don't know exactly how many carbon atoms would equal the mass of the current standard kilogram.
Mass is a fixed quantity, weight (kilogram) is determined by gravitational force; hence the number of carbon atoms that = 1K depends on the G force. The true fundamentals are internal force (energy) and external force (force). N carbon atoms weigh 1K when subject to X gravitational force.
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 https://www.physicsforums.com/showthread.php?t=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.
The mass of the protons and/or electrons wouldn't be a part of the derivation of kg. Instead it would be based on the force between 2 wires carrying 1 amp of current and a rate of acceleration. 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
No, the kilogram is a unit of mass, abbreviated kg. The concept of weight doesn't enter into my argument at all.
There have been many experimental observations which support that conclusion. For instance, pulses of different kinds of EM radiation coming from distant stars and galaxies arrive at Earth-based telescopes in perfect synchronization.
Yes I am not disputing that, I am just observing that if you want to claim something as fundamental and underlying other things then the basis has to be stronger than just support for a theory. 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.
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.
How then do you measure the the distance then without a unit of length? If I remember the definition properly, a mole relates the amount of a substance to C-12. 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.
Kroenecker's comment Is relevant to attempts to minimise basic quantities. It really is a deep comment. You can for instance define a time unit as the duration of one complete cycle of the light emission of a particular atom. You can define a length unit as the distance travelled by this cycle. You can even stick with whole numbers (integers) by specifying a number of cycles. But I am not convinced you can get away from the old MLTC[tex]\theta[/tex] setup, without equivalents being substituted. A good deal of thought went into deciding the minimum set. @Curl Yes I am aware of Maxwells equations, but consider this. Maxwell theory is predicated upon there being sensibly no reduction in field strength over the length of one cycle. The theory does not discuss what happens when the wavelength is so large that the diminution of intensity becomes significant over the lenght of a single cycle.
The wavelength doesn't matter. The "speed of light" is actually a misnomer, it is more like the "speed of space" because all electric/magnetic fields are limited at this speed (this information is too) so it doesn't matter if there is a wave or not or if the wave is changing in wavelength. The space (which hosts the field) can only carry the field at this rate. Similar to the speed of sound and speed on a string, etc. You don't need a unit of length. You already know what length is, and you say "the light traveled this far in this amount of time, therefore this is the unit of length".