Professor Dave again, let's continue
discussing the Heisenberg uncertainty principle.
We know that the
Heisenberg uncertainty principle limits
what can be simultaneously known about
the position and momentum of a quantum
particle like an electron, but there is
another set of complimentary variables
that abide by this principle, so we must
also investigate how the uncertainty
principle relates to energy and time.
We can restate the principle mathematically
just as we did before, but instead of x
and p, let's put E and t, leaving the rest
the same. What this says now is that the
uncertainty in the energy of a particle
in a certain state times the uncertainty
in the interval of time that the
particle inhabits that state is greater
than or equal to h over 4 pi. If the
uncertainty in one of these parameters
is very small, that is to say if one of
the two values is very certain, the other
becomes increasingly uncertain, so if we
know the precise energy of a particle, we
don't know how long it has that energy.
If we know precisely how long a particle
exists in a certain state, we don't know
how much energy it possesses.
An immediate ramification of this concept
brings us possibly the hardest pill to
swallow in all of modern physics, the
idea of quantum fluctuation. Since it is
the case that the shorter the lifetime
of a particle, the greater the
uncertainty in the energy of the
particle, it becomes possible for
particles to come into existence from
nothing, completely without cause,
provided that they exist for
inconceivably short durations of time.
We call these virtual particles. While it
seems like this just can't be true, that
it violates causality and everything we
thought we knew about the universe,
quantum fluctuation of virtual particles
is necessary to explain a number of
observations, such as the Casimir effect.
When two completely neutral plates are placed
in a complete vacuum just a tiny distance
away from one another, they will
eventually be pushed together.
This can't be due to gravity or the
electromagnetic force. Instead, we must
understand that there are more virtual
particles coming into existence on
either side of the plates and imparting
some force onto them than there are
between the plates, so the net force
pushes the plates together. Virtual
particles arise all the time, everywhere
in the universe, subsisting on borrowed
energy that is returned when they
annihilate a tiny fraction of a second
later. Through this phenomenon, we
realized that empty space is not empty
at all, it is actual substance unto
itself. We call this property of space
the quantum foam, a sea of probability
from which virtual particles manifest
and froth. Because of this, empty space
actually has measurable energy. This is
called the zero-point energy, and it
sheds some additional light on the third
law of thermodynamics. In classical
physics, we understood that any system,
including the universe, can never be cooled
to absolute zero in a finite number of
steps, essentially meaning that absolute
zero, a complete absence of kinetic
energy, can't be reached. Now we know why.
Because there will always be the tiny
amount of energy irrevocably contained
by space itself, preventing us from
peeling away those last few thousandths
of a Kelvin. By now you should feel
sufficiently confused, possibly on the
brink of existential crisis. If this
isn't the case, you may not have been
paying attention, so you'd better go back
and watch again. If you do indeed feel
reality spinning away from you,
congratulations, you have a small window
of insight into how it felt to be a
physicist in the early 20th century.
It's incredible to think that in just a few
decades we went from thinking physics
was essentially complete to having the
entire field turned on its head, leaving
even the most brilliant people in the
field, like Albert Einstein
unable to know what to make of it.
But before all of this quantum insanity
there were those three quintessential
papers by Einstein in 1905. It was the
one on the photoelectric effect that
started this mess, but there was another
regarding special relativity that is
also crucial. Let's talk about that next.
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