Classical Physics:
Classical physics refers to the physics whose
foundation was laid by Newton's determinism. According to Newton's determinism,
given the initial parameters of any physical system, the future state of the
physical system can be uniquely determined. For example, if we have an object
and we know its velocity (v) displacement vector (r) and all the forces acting
on that object, we can predict its path and future values of its velocity and
position vector as given by Newton's second law of motion F = m*a. Thus,
classical physics claims that given correct initial conditions of any physical
system its future is completely deterministic. Giving rise to a phenomenon what
we call as Newton's determinism.
This deterministic phenomenon was working quiet
well until it hit a wall, when we started observing on microscopic world.
Quantum Mechanics:
In the context of quantum mechanics, particles
also exhibit wave properties and can be expressed as a wave function corresponding
to that particular particle waves. When a particle exhibits wave
characteristics, we cannot apply Newton's determinism since its wave function cannot
be localized in space unlike an macroscopic object. This is where the classical
physics deterministic phenomenon fails to predict or explain the physical
system in terms of its initial conditions.
Double-Slit Experiment:
Double slit experiment is perhaps the most
famous experiments in the foundation of quantum mechanics. What is this double
slit experiment? It is an arrangement in which we have a source which lights up
a double slit film and behind this thin film is a screen collecting the results
passing through the film.
Case 1:
Film has a single slit and the source is a
source of light, what happens is what exactly we expect. When we throw a beam
of light on a film with a single slit, we get a pattern of waves on the screen
since light is passing through that slit. When we add another slit i.e. double
slit experiment, we get an interference pattern and experiments show that:
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| Equation of non-equivalence. |
where I1 is the intensity of
light that passes through slit 1 and I2 is the intensity of light from slit 2. We get
an interference pattern (both constructive and destructive) where some areas
are much brighter than others, as we predict and expect from wave-theory. Figure
below shows how waves behave in above scenario.
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| Figure 1: Source of waves in double slit experiment |
Case 2:
As seen
is case 1, nothing is weird and different from classical physics, because the
waves behave exactly as we predict according to wave theory, but when we try
the same above double slit experiment by using a source of micro-particles,
things start to bizarre and unexpected.
Now, in
the same above experiment if we use a source of electrons instead of photons,
with a single slit we have a dot on a screen. When we add another slit what we
predict is we should get two distinct spots that are summation of intensities
of both slits since particles do not interfere with each other. But experiments
shows that even with electrons we get an interference patterns as if electrons
were waves instead of particles and were passing through both slits at the same
time. These results raised a lot of questions on predictions given by classical
physics. As shown in figure below we can see that electrons (particles) behave
same as light (waves), as if a single electron is passing through both slits
simultaneously.
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| Figure 2: Electron source in double slit experiment |
Scientists were
intrigued by these mysterious results, so everyone jumped in to solve this
mystery. Experiments done by different researchers confirmed that electrons
does behave like waves when passed through slits, another experiment was setup
to check that an electrons passes through which slit, because it was being
theorized that electron passes through both which was against the concept of
particles. A light counter was setup on each slit such that the counter will
give a signal if electron passes through that slit. With this setup, when the
same experiment was repeated, instead of interference pattern we again a simple
summation of intensities as if electrons are now behaving as particles. As
shown in figure below:
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| Figure 3: With setup of testing which slit electron passes |
After the above experiment, thing were even more
strange than before as if electron knew when it was being observed. If electron
was not observed, it behaved like a wave but if we add some observer into the
experiment, electron starts to behave as an ordinary particle.
The above mystery ended Newton’s determinism,
that given initial conditions, a physical system can be uniquely determined at
any point in time. The experiments were totally in contradiction of classical
physics. This laid the foundation of Quantum mechanics and also The Heisenberg’s
principle.
Heisenberg's Uncertainty Principle:
What happens when we place an observer in the experiment that makes the electron change its path and behavior? Quantum mechanics explains that particles and wave are complementary to each other. When we try to measure the position of electron in double slit experiment we use a source of light or a photon whose wavelength and energy is comparable to that of an electron. This photon when interacts with the electron changes its momentum or position disturbing the physical system (as an external force is acting on the system). Heisenberg stated that we cannot accurately determine the position and momentum of quantum particle, when we try to accurately measure position the momentum changes and trying to take the momentum effects the position of electron. According to Heisenberg's uncertainty principle, there will always be an inaccuracy in measuring momentum and position given by following equation:
where x denotes position, p denotes momentum and ℏ is Planck's constant.
