Physics Units

So a little while back I decided that I would actually start getting serious about Physics again. To this end I started looking at Superconductivity. A subject that I once knew a little about. I did a couple of posts on this and then got down to some serious research. The idea being that I would then move forward on this subject with the ultimate goal of posting a valid theory of high temperature Superconductivity. You have to think big, right?

Now four or five months have passed since my last post, what have I been doing?

Well... reading, reading, reading and pondering. It was while I was pondering that I got to thinking about units. There are loads of them in Physics, energy has Joules, power has the Watt, electrical resistance the Ohm, pressure the Pascal, force the Newton, electricity the volt, current the amp and on it goes, Hertz, Coulomb, Candela, Farad, Tesla, Weber, Henry, Becquerel, Siemen. We haven't even mentioned the second, the meter or the kilogram.

There are lots of posts on SI units, why they have the values they do, why we decided on this measurement and so on, so I will not bother discussing that here. What this post is about is the base units. There are seven SI base units;

length - m
mass - kg
time - s
electric current - A
thermodynamic temperature - K
the amount of substance - mole
luminous intensity - candela

All the other units in physics are derivatives of these seven.

Does this tell us anything? can we gain anything from knowing this?  For example, the unit of pressure is the Pascal (Pa), for energy density (the amount of energy per cubic meter) it is Joules/(meter cubed). Can looking at the base units tell us anything about pressure and energy density? Pa and J/m³?

Take the Joule, the unit of energy, this also as the units of Newton.meters, which can in turn be shown to be, kg m² s^-2. Think of kinetic energy, kinetic energy is energy and is measured in Joules. It is given by

KE = 1/2 m v²

m = kg
v = m/s

so J = kg m² s^-2.

Reducing units to the base units can open up some wonderful surprises and may offer some insights into the nature of the universe. In the next post I am going to go into something called Planck's units, but for now have a look at this. By definition

Electrical Power = Volt x Current

the unit of power is the Watt (W). The unit of Voltage is the volt (V), current is the Amp (A).

Current = amount of charge / second, units = C/s

so, W = V C /s

so, W s = V C

but W s is the same a energy, the Joule, because

Energy = Power x time = W s

so Energy  =  Volt x Charge.

so a Volt = Energy / Charge

but the unit of energy is the Joule, and Charge is A.s so a Volt can be viewed as J/A.s, replacing J with the value we got for kinetic energy earlier

J = kg m² s^-2.

V = kg m² s^-2/A.s

The Volt has units of m²·kg·s^-3·A^-1 ! Think about that! The Volt unit is actually made up of area, mass, time cubed and current! This is also same as Newton.meter/Coulomb, which is the same as J/C.

Similarly there is electric field strength who's units are Volts/meter, which is just Newton/Coulomb.

Coming back to energy density, this is measured in joules per cubic meter, but we know the joule is just  kg m² s^-2, so energy density units are kg m^-1 s^-2 .

Now, take the Pascal, the unit of Pressure, a Pascal is the same as N / m² , which is  kg m^-1 s^-2 ! the exact same units as energy density.

Energy density and pressure have the same units and we can go further and say that energy density can act as a pressure!

This brings me to the point of this post. It is not obvious that pressure and energy density share the same units and can be seen as synonymous. It is not clear that a Pascal is the same as  J/m³, yet they are. We come to this realization when we look at the base units.

While units are a great short hand and aid to understanding. It should not be forgotten that they are based on more basic units and information can be gained from looking at the base units.

In the next couple of posts I am going to take a look at angular momentum, the gravitation constant and Planck units from the point of view of base units. There are some fantastic surprises.

Unlike my previous posts some of those that are coming do contain a fair amount of calculations. Most of this is relatively straight forward and can be managed with people who did maths until they were 16 years old.