Category: tumblr series

Pilot Wave Hydrodynamics: Series Wrap-up This week FYP in…

Pilot Wave Hydrodynamics: Series Wrap-up

This week FYP in collaboration with FYFD brought to you an exclusive Tumblr series.on Pilot Wave Hydrodynamics. In case you had missed it out, here’s an overview:

1) We started with Chladni & inverse Chladni patterns – Basically normal modes of vibration on a plate with a subtle twist.

image


2) But what happens if the vibrating medium was water? This lead to a discussion on  Faraday instability;

image


3) Along the way, we discovered that at the right excitation, droplets placed atop a vibrating bath could be made to walk & bounce.

image

4) Using many of these bouncing droplets one could form extremely stable complex lattices

image


5) Then we started to subject the system to quantum experiments such as the single and double-slit experiments,

image

6) And found that they formed similar diffraction and Interference patterns with the bouncing droplets as well..

image

                                                   Source


7) Maybe it was luck, so we tried quantum tunneling.

image

8) But even that was reproduced on the macroscopic scale using these bouncing droplets

image

             

9) Absolutely fascinated by what we had seen thus far, we then explored Pilot wave theory in its raw essence and its potential as an interpretation for Quantum mechanics

image


10) Hoping that this fascinated you, we left you with a treasure of useful resources to aid you in your ecstatic adventure. 

We hope you enjoyed this journey that spanned almost two centuries’ worth of scientific discoveries, feel free to share with us your thoughts, comments, and questions on this series.

Have a great weekend!

FYP! & FYFD

Particle and wave: A dichotomy

.“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

image

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:

image

At first, you just see a wave propagating outwards like when you drop a pebble on a pond.

image

But when a vibrational excitation is given, that wave is split into two traveling waves moving in opposite directions.

image

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.

image

                    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.

image

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 :

image

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.

image

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 the event.

The cost of observing

In the series, we talked about the double-slit experiment. But here’s the deal: When you observe each electron as they are passed through the slit, the interference pattern disappears.

image

            Disappearance of the interference pattern when 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.

image

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.

image

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 will be posting a list of useful resources that we compiled, do take a look at that.

Through a Quantum Tunnel

The phenomenon of quantum tunneling is best explained with a narrative:

You are at the bottom of a hill and need to roll a ball up the hill and down the other side.

Classically, the only option is to push the ball all the way up and roll it down. This would be a test of endurance and not to mention physically taxing.

image

But if you are in the quantum world you can dig a virtual hole and “probably” get to the other side of the mountain without expending as much energy as the classical ‘you’. 

This behavior is called ‘tunneling’.

image

The reason why you would be able to pull this off in a quantum system is that there is a small probability of finding the particle in a certain location that extends to the other side of the hill.

Or if one were to put it more formally:

The wavefunction of the particle is a continous function and it cannot abruptly just collapse near the mountain/wall/barrier.

Instead it decays exponentially inside the barrier and extends onto the far side of the barrier as well.

This implies that there is a finite probability for the particle to tunnel through the barrier and get to the other side.

image

How big can the mountain be?

Since the wavefunction decays exponentially inside the barrier, it is no surprise that thinner the mountain, the better the chances for the particle to tunnel through.

image

                                  Dependence on Barrier width

Can humans be tunneled through a barrier?

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.

image

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’.

image

Okay so maybe not the best way to break out of jail if you are a human I suppose.

But if you were a bouncing droplet, there might still be some hope. Check out the latest FYFD post on Hydrodynamic Quantum tunneling.


In case you had missed out, here are the previous posts on this collaborative series on Pilot wave Hydrodynamics with FYFD 1) Introduction; 2) Chladni patterns; 3) Faraday instability; 4) Walking droplets; 5) Droplet lattices; 6) Quantum double-slit experiments, 7) Hydrodynamic Single and Double slit experiments

“If you place a small droplet atop a vibrating pool, it will…

“If you place a small droplet atop a vibrating pool, it will happily bounce like a kid on a trampoline”. And when lots of these droplets are placed in a lattice, their behavior as a collective is absolutely fascinating.

In this series of gifs, you can see the evolution of complex lattices from simple droplets eventually leading to an instability that drives them apart.

Now a key thing to note is that when you have 7 droplets, you will not obtain a hexagonal lattice configuration per se. Those lattices had to be obtained artificially but can be very stable after they are formed.

image
image

Source: Archimedean lattices in the bound states of wave interacting particles

The key point of distinction when one talks about lattice in this vernacular is that in solid state physics, a crystal lattice is the depiction of three-dimensional solid as points.

And one obtains these crystalline solids through crystallization.

image

In contrast, when we are talking about lattices in pilot wave hydrodynamics, they are formed by the standing waves of the bouncing droplets.

In the upcoming posts, we will take a dive into some quantum mechanical experiments and their pilot wave hydrodynamic counterparts.

In case you had missed out, here are the previous posts on this collaborative series on Pilot wave Hydrodynamics with FYFD : 1) Introduction; 2) Chladni patterns; 3) Faraday instability, 4) Bouncing droplets

Chladni patterns

Chladni was a German physicist and a trained musician and is best known for inventing a technique to visualize the various modes of vibration of a rigid surface.

image

Take a flat metal plate, fix it at any point (say at the center) and sprinkle some fine sand particles on it.

Using a violin bow, gently excite any edge of the plate to witness beautiful normal mode patterns (known as Chladni patterns/figures).

image

Notice that by pinching the plate at different points one gets different patterns.

image

                               Gif source video: Steve Mould

Inverse Chladni plates

There is much more than what meets the eye in this experiment as the patterns that emerge are dependent on the size of the particles that one chooses and the acceleration of the resonating plate.

Bigger particles ( > 0.15 micrometers ) – tend to accumulate at the nodes of the vibrating plate – Chladni figures.

Smaller particles ( e.g Lycopodium powder ) – tend to accumulate at the anti-nodes of the vibrating plate – Inverse Chladni figures.

image

                   Source : “Air-induced inverse Chladni patterns

What causes them?

Although the traditional Chladni patterns are discussed extensively in the context of solid mechanics and normal modes of vibration in engineering.

image


But that’s NOT where the story ends.

Michael Faraday argues in his remarkable paper that the ‘inverse Chladni patterns’ that one observes are not a run of mill mechanics problem with a secondary mode of vibration.

Instead, he demonstrates that the vibrating plate induces air currents on top of it, which drags the fine particles along to the antinode. This is completely counterintuitive since one doesn’t expect the air to play such a pivotal role in these patterns.

image

A plot of the velocity profile above the Chladni plate.  Notice the air currents that are caused by the vibrating plate. This phenomenon is often referred to as “Rayleigh streaming”.

Thus far we have merely considered a plate vibrating in air.

image

But what if we were to look at water atop a vibrating plate? For that, check out the accompanying FYFD post and stay tuned for more tomorrow.

Pilot Wave Hydrodynamics – A Tumblr seriesNext week, FYP! in…

Pilot Wave Hydrodynamics – A Tumblr series

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.

Stay Tuned!