Answer 1:
Units can be deceptively tricky, depending on
the unit convention being used. In fact, despite
being in research to study all sorts of physical
phenomena, I find one of the trickiest things to
calculate are actual quantities for materials
properties that make physical sense. So an
excellent question, indeed!
You may be familiar with the SI unit
system (e.g., meters, seconds, kilograms).
There are other conventions like CGS units
that defines quantities in terms of centimeters,
seconds, and grams. Planck units are yet
another kind of unit convention. In physics,
you will come across quantities that are
universal constants. These are the
gravitational constant G, Coulomb constant
K_{c} , Boltzmann constant
K_{B} , speed of light c,
and reduced Planck constant ℏ.
Each of these
constants are associated with fundamental theories
in physics like thermodynamics, electromagnetism,
and quantum mechanics.
For example, the reduced Planck constant is a
quantity that appears everywhere in quantum
mechanics and can be considered a measure for the
scale at which quantum mechanical phenomena begin
to be observed. It turns out that you can group
these five universal constants in various ways to
get the Planck time, Planck length, and Planck
energy, which frequently occur in many physics
equations.
By definition, these five universal
constants are
set to 1. Part of the reason for this convention
is convenience (you can leave them out in
derivations) and for ease of calculations (you can
do unit conversion to whatever convention you need
at the very end).
Other interesting tidbit about units: what is
considered a kilogram or second was not always
well defined. In fact, a definition for what
physical thing constitutes exactly a kilogram is
is still a major challenge today. You can read
more about what physical metrics are used to
standardize the basic SI units and their histories
here .
Best,
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