Double Slit Experiment

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: 

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.

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. 

 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:

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.