System of base units

francisco

can you imagine a system of base units* in which time was not included?

*the system of base units is the following:

quantity----------------------------name-----------symbol
time--------------------------------second----------s
length------------------------------meter------------m
mass-------------------------------kilogram----------kg
amount of substance----------------mole-------------mol
thermodynamic temperature---------kelvin-------------K
electric current---------------------ampere-----------A
luminous intensity-------------------candela----------cd

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rbj

francisco said:
can you imagine a system of base units* in which time was not included?
no, but i sure as hell can imagine a system of base units in which "amount of substance", "thermodynamic temperature", and "luminous intensity" are not included (they can be derived from the base units) and one where electic charge replaces electric current as a base unit.

rbj

actually, now that i think about it: base units, if there is a unit speed (or some other rate of change physical quantity) that one makes into a base unit, then time can be a derived unit.

i think that conceptually, time, length, mass, and charge are the "base" dimensions of physical quantity of which nearly every other dimension of physical quantity can be derived from.

francisco

i was thinking of defining the second as a specified length (299,792,458m)
of the path travelled by light in vacuum.

so that 1s = 299,792,458m

the meter of course would then be difined (as it is currently defined) as
the length of the path traveled by light in vacuum in 1 / 299,792,458 of a
second.

currently the second is defined as the duration of 9,192,631,770 vibrations
of a (specified) radiation emitted by a (specified) isotope of the cesium
atom.

vibration or a periodic oscillation of the radiation emitted by the isotope
is a periodic movement to and fro between two points. let the length of a
single movement to and fro between two points of the radiation emitted by
the isotope = L.

does this mean that 9,192,631,770L = length = 1s?

how fast is one oscillation?
what is the length of L?
if the speed of one oscillation = c, does that mean that 9,192,631,770L =
299,792,458m?

lightgrav

Homework Helper
>does this mean that 9,192,631,770L = length = 1s?"

No.

>vibration or a periodic oscillation of the radiation emitted by the isotope
>is a periodic movement to and fro between two points. let the length of a

These are not oscillations of the location of an object - they are
oscillations of the strength and orientation of an E-field vector.

But you've already defined length, you don't need to do it again.
just use speed "c" as one of your base units, like the meter.
If anybody asked me (oh, you did?) I'd use atomic mass unit (not kg).

momentum would have units [uc] ; Force would be [uc^2/m].
and electric current would be q/t in [em/c] , derived from the proton charge.

HallsofIvy

Homework Helper
That depends upon what you mean by "included". It is not uncommon for scientists to use a "natural" set of units based on natural constants. Of course, the "base" units have to change:

speed: the speed of light, c

action: Planck's constant, &lambda;

Not sure what to call it: the graviational constant, G.

While time is not directly a base unit, it is included in the speed unit.
Using these base units, the unit of distance is the "diameter of an electron" and the unit of time is the time it takes light to cross that distance.

pervect

Staff Emeritus
francisco said:
can you imagine a system of base units* in which time was not included?
In a way. There exists a system of units where c=1, and time is formally measured in centimeters (cm). Usually one makes the gravitational constant G=1 as well, in which case mass can also be measured in cm (via the factor G/c^2). These are known as "geometric units" and are useful for studying gravity.

One can get rid of units altogether by going to Planck units, where everything is a number, by setting the value of more constants to 1 and adjusting the size of the base unit.

See http://en.wikipedia.org/wiki/Planck_units for the details, one starts with c=g=1 as in geometric units, and sets the values of the following constants in addition:

h-bar =1
permittivity of space = 1/4pi
k (Boltzman's constant) = 1

However, there is always some way to represent time in any useful system of units, because it is a useful quantity. It may be measured in cm, or as a pure number, but there is some way to measure it.

rbj

HallsofIvy said:
That depends upon what you mean by "included". It is not uncommon for scientists to use a "natural" set of units based on natural constants. Of course, the "base" units have to change:

speed: the speed of light, c

action: Planck's constant, ?

Not sure what to call it: the graviational constant, G.

While time is not directly a base unit, it is included in the speed unit.
Using these base units, the unit of distance is the "diameter of an electron" and the unit of time is the time it takes light to cross that distance.

this is interesting, Halls. actually Barry Taylor and Peter Mohr (of NIST) have proposed a redefinition of the kilogram as such:

The kilogram is the mass of a body at rest whose equivalent energy equals the energy of a collection of photons whose frequencies sum to 135639274 x 1042 hertz.
with the speed of light already defined, this would have the the effect of defining Planck's constant rather than measuring it. this is a good idea, in my opinion.

however, i believe that using G to ultimately define the unit time is less accurate and robust and repeatable and portable than how it is defined now:

The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
i *do* truely believe that "Nature" (whomever she is) is likely more attuned to the Planck units (or an adjustment to them with factors of $$\sqrt{4 \pi}$$) as the units of quantity that nature operates with, but for experimental physicists, they need a better time base than they could get from G.

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lightgrav

Homework Helper
> kilogram from light with total 135639274 E42 oscillations/sec !?

Who's going to count the 10^30 photons needed for this?
Where are we supposed to collect and store them meanwhile?

As for the "second being portable" - isn't this frequency different
at different gravitational potentials?

rbj

lightgrav said:
> kilogram from light with total 135639274 E42 oscillations/sec !?

Who's going to count the 10^30 photons needed for this?
Where are we supposed to collect and store them meanwhile?
wow, i can't find a free copy of this pdf online anymore:

http://ois.nist.gov/nistpubs/technipubs/recent/search.cfm?dbibid=6661

edit: i think you can get a copy at http://ejde.math.txstate.edu/conf-proc/04/m1/abstr.html

the mechanism they suggest is with a watt balance:

Mohr&Taylor: "The Planck constant can be measured by comparing a watt of mechanical power expressed in terms of the meter, kilogram, and second to a watt of electrical power expressed in terms of the Josephson constant and von Klitzing constant..."
instead of using the kilogram prototype and measuring Planck's constant, the idea is to use the same setup with a defined value of Planck's constant and then to use that device to define the kilogram.

As for the "second being portable" - isn't this frequency different at different gravitational potentials?
dunno. i s'pose they mean at a point at infinity (with no gravitational field).

do you think that the current kilogram prototype in Paris makes a better standard of the unit mass?

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