# Planck’s Constant Day

My nerdery really knows no bounds.  That is to say, it is not limited to mathematical or statistical nerdery.  I’m also a fan of computer science, chemistry, biology, and physics.  Today’s post is all about the latter of these.

Specifically, today’s post is all about Planck, er, well, Planck’s Constant.

What is Planck’s constant?  Well, Planck’s constant can be written as the ratio of the energy of a photon (denoted $E$) and its electromagnetic wave frequency (denoted $\nu$).  That is

$h=\frac{E}{\nu}$

But why, all of a sudden are we talking about Planck’s constant?  Well that is because today, May 1, is known as Planck’s constant day.  Or maybe more accurately as Reduced Planck’s Constant Day.

Wait, what?  Reduced Planck’s constant?  What is that?

Simply, Reduced Planck’s constant is the regular old Planck’s constant $h$, but divided by $2\pi$ and denoted by $\hbar$ (h bar).  It is used in place of $h$ whenever the frequency $\nu$ has units of radians per second.

But what is the value of $h$ or $\hbar$?  Well, that all depends on the units.  I found the following summary on the all-powerful Wikipedia.

Values of h Units
6.62606896(33)×10−34 J·s
4.13566733(10)×10−15 eV·s
6.62606896(33)×10−27 erg·s
Values of ħ Units
1.054571628(53)×10−34 J·s
6.58211899(16)×10−16 eV·s
1.054571628(53)×10−27 erg·s

The most important thing to note here is the magnitude of the constant.  That is, depending on the units the constant is really, really tiny.  So tiny, that Planck’s constant would not be registered by our typical everyday human observation.  But, this constant is essential if we want to describe the physical world around us.  In very simple terms, the constant represents a tiny jump from one level of physical action to the next, where action is measured in units of energy by time (i.e., $J\cdot s$).  This means that at the particle level, physical action cannot take on just any value (contrast this with our everyday world where we can make things just a little bit longer, or heavier, or hotter – that is, this restriction doesn’t seem to exist).  Instead, physical action can occur at particular levels.

Consider it this way; if we standardized all the levels of physical action, we would have the set of non-negative integers.  We could jump from level 1 to level 2, or level 2 to level 3, but we couldn’t jump to level 1.2, or 2.7.  In the everyday world, this doesn’t seem to be the case.  But that is because our world exists on a scale that is magnitudes larger than that where Planck’s constant acts.

But why do we celebrate this constant today?  Note the value of h bar:

$\hbar\approx 1.05\times 10^{-27}$.

Or, for some people, the 1st of May.  And now you know.

Happy Planck’s Constant Day, all y’all.