It's professor Dave, let's learn about
the Heisenberg uncertainty principle.
Once Schrodinger and pals had
sufficiently developed the brand new
field of quantum mechanics, some
perplexing implications arose. For one, in
classical mechanics an object will have
a precise value for its position and
momentum at all times. In quantum
mechanics, this was no longer the case.
If a quantum particle were to have precise
values for position and momentum it
would simply be a particle, but all
particles are also waves, so this kind of
determinism no longer applies. Instead, as
we saw with the Schrodinger equation, the
quantum realm is probabilistic in nature.
This brought about the issue of how to
describe the position and momentum of
the electron. Under the Copenhagen
interpretation of quantum mechanics, an
electron simply does not possess precise
values for both of these parameters at
the same time, so when we take a measurement,
the result is randomly drawn from a
probability distribution. An electron
will seem to be in a particular location
if and only if we measure its location.
However, if we know its location we can
no longer know its precise momentum, or
what it's doing, and this notion is
summarized in Heisenberg's uncertainty
principle. This states that when looking
at complementary variables like position
and momentum, the more precisely one
parameter is known, the less we know
about the other. Here, delta x represents
the uncertainty in position, while delta
p is the uncertainty in momentum, and
their product must be greater than h
over 4 pi. If the uncertainty in one
parameter decreases, the uncertainty in
the other must increase, and if one
becomes known with total certainty, the
other becomes unknowable. The important
thing to realize is that this has
nothing to do with our measuring instruments.
This is a fundamental quality of matter.
We can't reduce an electron to particle
like determinacy, as it is also a wave, as
was demonstrated by the double slit
experiment. Furthermore, this forces us to
examine what it is to make an
observation. To know the location of an
object, to see it, at least one photon
must hit our eyeballs. But if a quantum
system interacts with even just one
photon such that it can be seen, that
interaction itself will alter the state
of the system. So the seemingly innocent
act of observation has a concrete impact
on the system. When this problem of
measurement emerged, the scientific
community was in total confusion.
This notion, and the idea that nature was not
deterministic but rather probabilistic
on the most fundamental level, had
incredible philosophical implications
and many scientists developed thought
experiments to elucidate the absurdity
of a probabilistic universe. The most
famous of these thought experiments was
developed by Schrodinger himself, as he
could not accept the Copenhagen
interpretation. It is called
Schrodinger's cat, and it focuses on the
bizarre concept of quantum superposition.
The idea is that if the Copenhagen
interpretation is correct, a quantum
system can exist in a number of
different states, and until the system is
observed it exists in a superposition of
all these states. Once observed, it
collapses into one of the definite
states according to its probability.
Schrodinger did not like this, and he
came up with a paradox. He supposed that
there was a box containing a single
radioactive atom. At any given moment
this atom has the potential to decay,
emitting a high-energy particle. Inside
the box there is also a cat, a flask of
poison, and a device with the ability to
detect radiation.
If the device detects that the atom has
decayed, it will trigger a mechanism that
breaks the flask of poison and the cat
will die. If it does not detect this, it
won't, and the cat will be alive.
The problem arises when we isolate this
system from observation. According to the
Copenhagen interpretation, the atom is in
a superposition of decaying and not
decaying, which seems pretty abstract and
harmless, but because of the mechanism in
the box, that means that the cat must be
in a superposition of dead and alive.
Only once you open the box and look
inside will you observe the cat as being
one or the other.
Schrodinger meant for this paradox to
discredit the Copenhagen interpretation
but there are many camps that believe
that this dead/alive superposition is a
concrete reality. This thought experiment
remains a classic, and it is frequently
referred to when comparing different
interpretations of quantum mechanics.
But enough about cats, let's finish up with Heisenberg.
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