If that wasn’t clear, here is the same demonstration done with Microwaves and using wax as a prism:
The reason why this happens is because the incident wave does not abruptly stop when it hits the end of the prism.
Some of the waves seep out with the intensity of the wave decaying exponentially outside the first prism.
But this changes when you place another prism closer to the first one.
Does this even matter?
You might be tempted to think that this would make no difference on the macro-scale.
One possible application involving TIR and Tunneling are Optical Fibers. Loss of photons (or information) through the cladding layer of an optical fiber due to tunneling is a major concern. Therefore when they are designed the cladding layer thickness is such that the probability of tunneling to occur in such a system is extremely low.
And that’s how Tunneling, Electrodynamics and Optics are interwoven in nature.
**In case you wanted to learn more about this in rigorous manner,most standard graduate level electrodynamics such as Jackson dwell into the mathematics of Evanescent waves. Do take a look at them!
You might have seen animations like this that show an electron undergoing a transition from a lower energy to a higher energy state and vice versa like so:
There is something really important about this image that one must understand clearly.
The diagram represents the transition in energy of an electron BUT this does not mean that the electron
is magically jumping from one position and respawning at another
The electron’s position is NOT doing this i
If you want to know about the probability of finding an electron around the nucleus at a certain energy level, you look at its wavefunction and not at the energy diagram.
Here is the wavefunction of a hydrogen atom and each stationary state defines a specific energy
level of the atom.
The electron makes a transition between these wavefunctions by the absorption/emission of photons. *
This might not sound like a big deal but one might be surprised to know that there are a lot of people who think that the electron is magically transported from energy level to another which, most certainly is not true.
.“While the founding fathers agonized over the question “particle or “wave” de Broglie in 1925 proposed the obvious answer “particle” and “wave”.. This idea seems so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was generally ignored”
– John Stewart Bell from Bell’s Theorem
Now having taken this grand tour in pilot-wave hydrodynamics, one must also be aware of the ongoing controversy that has wrapped around pilot-wave theory over the years.
De Broglie: The pioneer of Pilot wave theory
In the eyes of De Broglie, all this would be a trip down memory lane. In 1927, he proposed an alternate interpretation for quantum mechanics – The pilot wave theory by saying that all particles are accompanied by a pilot wave.
What on earth does that mean?
Here is the analogous version of it. Observe this animation carefully:
At first, you just see a wave propagating outwards like when you drop a pebble on a pond.
But when a vibrational excitation is given, that wave is split into two traveling waves moving in opposite directions.
And as you know when two waves traveling in opposite directions are set up just right, you obtain a standing wave pattern.
This is known as a pilot wave (or) wave that pilots/guides the droplet where to go.
How does it ‘pilot’ the droplet?
At each bounce, if the droplet is made to land on the ‘incline’ of a standing wave, it would propel the droplet forward at different rates based on the level of incline.
Think of a ball hitting an inclined plane for reference
If it were to land on a flat plane, of course, it would just bounce in the same place forever like so:
All this is essential because:
De Broglie said that all particles (electrons, protons, etc) like the droplet are accompanied by physical waves that act like a pilot to guide the particle along the trajectories.
And that the pilot waves spans the entire universe.
In the 1950s Bohm took this interpretation and made it even stronger. This came to be called as pilot wave theory or Bohm-de Broglie theory or just Bohmian Mechanics.
It offers determinism that Bohr’s theory doesn’t
The most satisfying thing about this theory is that it is deterministic, i.e., one can extract sufficient information to plot a particle’s path, something that is not allowed in Bohr’s interpretation of quantum mechanics.
Bohmian interpretation applied to the Double slit experiment. Notice that the path of the particles is clearly defined and none of the particle paths cross one another but yet one obtains the same interference pattern.
For the droplet these trajectories looked like this :
All weirdness that encapsulates quantum mechanics such as wave-particle duality, wave function collapse and the paradox of Schrodinger’s cat can be avoided by using Bohmian mechanics (because it is deterministic) BUT there is a catch – nonlocality.
The pilot wave idea gives up on locality: meaning that every experiment can only be understood in the context of the entire universe. The “pilot wave” brings information from all over the entire universe to influence an event’s outcome.
The cost of observing
In the series, we talked about the double-slit experiment. But here’s the deal: IF you observe each electron as they make their way through the slit, then the interference pattern disappers.
Disappearance of the interference pattern when electrons are observed
The way one explains this through the Bohmian interpretation is that the act of observing must obviously interfere/disturb the wave field. This, as a result, destroys the interference pattern.
Why isn’t Bohmian mechanics popular?
Sadly, the reason why Bohmian mechanics is not popular is NOT that it is scientifically inaccurate. It is able to perform equally well as other interpretations out there.
This answer by Thad Roberts does a really good job of explaining why people don’t subscribe to Bohmian mechanics. The major argument is that “It hasn’t produced anything new or predicted something better than the other interpretations.” among other critical factors.
The future for pilot-wave hydrodynamics
The droplet wave experiments remain as spectacular analogs of the pilot-wave theory at the macroscale.
But thus far, there has been no seminal evidence of pilot waves at the quantum scale.
In addition, the analogs are only capable of describing the simplest of interactions, and phenomena such as quantum entanglement are still an area of active research.
How does one weave together all of these experimental revelations that we have unearthed so far? Is there a much bigger picture of how nature manifests itself that we are yet to comprehend or are we staring at the end of a barrel?
Only time will tell.
Thank you for joining us this week on this amazing journey as we explored the essence of pilot wave hydrodynamics.
If you are thirsty to know more, FYFD has posted a list of useful resources that we compiled, do take a look at that.
All this while, our discussion was primarily for simple quantum mechanical entities such as electrons, protons and so on.
And even for these systems merely increasing the barrier width would drastically bring down the probability.
Now if we were to scale this up to a system as complex as ours with billions and billions of atoms trying to tunnel through a wall couple of centimeters thick, nature just says ‘Sorry dude, Not gonna happen’.
Okay so maybe not the best way to break out of jail if you are a human I suppose.
How could a light source behave like that? So you call upon your friend Dr. Tonomura (actual physicist) to conduct this experiment with photons or electrons in his laboratory to see if this behavior is consistent.
He decides to conduct it with electrons and invites you to watch. And to your astonishment, as electrons start hitting the screen you get a pattern similar to the one you got at home.
Results of a double-slit-experiment performed by showing the build-up of an interference pattern of single electrons.
Numbers of electrons are a) 11, b) 200, c) 6000, d) 40000, and e) 140000.
The pattern( known as an interference pattern ) is mysterious but similar to ones you’d seen before.
The other day when you were at the Arboretum you noticed that ripples caused by rocks thrown in the pond behave in the same way and produced the same pattern.
So what is going on?
This double slit experiment supports the idea that light is a wave since in the classical sense that you would never see such a behavior from a particle.
But then you also have experiments like the photoelectric effect which is predicated on the particle view.
So are electrons and photons behaving like a wave or a particle? Well… it’s both!
Albert Einstein wrote:
It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.
The interference pattern that we saw earlier was first observed by Thomas Young in the early 1800s. When physicists continued to study the results of the double slit, its variants and other experiments, it lead them to a bizarre new world underlying everyday reality – The quantum world. (A story for another day)
Next week, FYP! in collaboration with FYFD is bringing you an exclusive Tumblr series on Pilot wave hydrodynamics. There will be a new post on FYP! and FYFD all through next week (Jan 8 – 12) exploring pilot wave hydrodynamics.
This has been the topic of spectacular experimental investigations and revelations (and controversies too) in Fluid Dynamics & Quantum Mechanics in recent times.
On Monday, we begin this journey in the labs of Michael Faraday and Chladni; And then embark on an exciting adventure through decades of research to arrive at where we are today.