Above: Diagram showing the fundamental units of the S.I. (International System of Units) - inner circle, which in a new endeavor will be defined by the seven fundamental constants occupying the outer circle.
Table showing fundamental constants and their role in the universe, current values.
Fundamental constants, units and dimensional analysis lay the groundwork for physics, since above all physics is a science of measurement and obtaining correct values while recognizing the associated errors is essential. We begin with the base and derived units for the S.-I. system given in the link below:
These are now all in the process of being updated, revamped (by 2018), based on use of fundamental constants as opposed to clumsy, arcane and too abstract ways of definition. For example, up until 1983, the meter - the fundamental unit of length - was defined:
"The length that is exactly 1,650, 763,73 time the wavelength of the orange light emitted when a gas consisting of the pure krypton nuclide of mass number 86 is excited in an electrical discharge."
That was recognized as too unwieldy and so since 1983 the new definition is in terms of the fundamental constant c, the speed of light in a vacuum:
"The meter is the distance light travels in a vacuum in 1/ 299, 792, 458th of a second ."
The string of digits in the denominator merely reflects the current high precision value of c , or c = 299, 792, 458 meters per second. The other base S.I. units also need to undergo similar redefinitions.
For example, the kilogram (basic unit of mass) is:
"the mass equal to the mass of the International Prototype of the Kilogram (IPK, also known as "Le Grand K" or "Big K"), currently housed as a 137-year old chunk of platinum -iridium metal in a vault outside Paris".
How weird is that? Also, what if a reckless bug were to somehow climb onto it and get permanently affixed and altered the mass by one millionth of a kg? No big deal? Wrong! A big deal because then the whole standard mass is thrown off.
Then there is the Kelvin, the unit of temperature, currently defined as referenced to the temperature and pressure (standard) at the "triple point of water" or where it exists concurrently as solid, liquid and gas. A totally arbitrary definition that gives more physicists indigestion than you'd like to believe and need to be changed to a more rational basis.
Add in now the ampere which is currently defined:
"The current produced that - when flowing through two infinitely long parallel wires one meter apart- would produce a force between them".
This is also somewhat of an arbitrary and wacky definition given it is impossible to manufacture two infinitely long copper wires (or other) and hence to create a current that can be measured realistically.
So all these units are now in the process of revision, updating. The next one up is the kilogram which will be revised based on refining Planck's constant- which we've seen multiple times before - e.g. in the posts on Quantum Mechanics I did in the late summer of 2014.
The value of the Planck constant is currently:
h = 6.62607 x 10-34 kilograms time meters squared per second
Or writing in shorter form:
h = h = 6.62607 x 10-34 kg m 2/ s
To get h to the point it can be used to redo the kilogram physicists (actually a specific subset called metrologists) need to get the measurement accuracy to two millionths of a percent, or at least out to seven decimal places. Further, several measurements, preferably from different sources, need to be done and all need to agree.
Once that hurdle is crossed, the value of the Planck constant can first be fixed, then the kilogram:
So if we have h fixed, then:
kg = h/ (m 2/ s )
The meter is already defined in terms of c, as shown above, and the unit for time, the second, is given as independent of varying astronomical time, or:
"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 cesium 133 atom."
While that sounds nerdy and clumsy too, it is defined to a specific atomic transition event, and is measurable. It also - as I said - removes the definition from solar observations, and the vagaries introduced by Earth's varying rotation rate.
Several teams are now working on the Planck aspect. One is using a device called the watt-balance to compare the electromagnetic force to the force exerted by gravity. This may sound difficult if not impossible, but thanks to new quantum mechanical methods of producing voltages it's no big deal. An object's mass can be directly related to the Planck constant.
In another method, physicists are making use of exact (perfectly formed) spheres of silicon. Since atoms in the sphere are placed in a 3D crystal grid, the number of atoms can be deduced from the volume of the sphere. The result is the Avogadro constant, e.g. from the table shown above:
NA = 6.022140857 x 10 23/ / mole
Other constants will also need to be reworked, and one of these - the fine structure constant - poses particularly hairy challenges, and will be the sole topic of a future post.
For now, we are confident by late next year a new set of fundamental units - based on 7 fundamental constants- will be ready for application.
Once this threshold is crossed, we can be more confident in our calculations requiring actual physical quantities. Remember, a physical quantity is comprised of basic units which have one of the dimensions (M, L, T, etc.).
Velocity or speed is defined: L T - 1
Or length (L) per unit time
Similarly, an acceleration would be: L T - 2
And a volume would be: L3
Force would be expressed: M L T -2
Or, simply mass (M) times acceleration ,( L T -2) according to Newton's 2nd law, F= ma.