Side by side Pendulums
We place 2 swinging pendulums (of equal length and mass) side by side on a wall. Initially, they are out of phase by
θ
=
0
. What would happen in an hour?
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1 solution
I didn't know this fact. I was trying to apply the principles of Classical Mechanics to solve the problem :/
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This effect remained a mystery for three and a half centuries, but the Royal Society has now published an explanation of the curious interaction Huygens observed, the result of a study done at the Georgia Institute of Technology...
There is more in the article.
According to Steven Strogatz, an applied mathematician at Cornell University, Huygens's discovery was the first-ever observation of what physicists call coupled oscillation—at least in inanimate objects. In the 20th century, coupled oscillators took on great practical importance because of two discoveries: lasers, in which different atoms give off light waves that all oscillate in unison, and superconductors, in which pairs of electrons oscillate in synchrony, allowing electricity to flow with almost no resistance. Coupled oscillators are even more ubiquitous in nature, showing up, for example, in the synchronized flashing of fireflies and chirping of crickets, and in the pacemaker cells that regulate heartbeats. "The theme of synchronization between coupled oscillators is one of the most pervasive in nature," Strogatz says.
I found @Michael Mendrin stating something similar in a recent discussion.
This is also something new : An international team led by Princeton University scientists has discovered an elusive massless particle theorized 85 years ago . I can recall a problem that I reported regarding similar topic.
:)
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Soumo, I had just heard about the discovery of Weyl Fermions. This is one reason why I find theoretical physics so fascinating--what starts out as a mathematical conjecture becomes a physical fact. Yet another example of Reality follows Mathematics. I thought maybe a Note should be written on Weyl Fermions and their discovery, but then I had the feeling it'd probably just get lost in here.
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@Michael Mendrin – I though of creating a note on "Huygens synchronization of two clocks", when I first read about. This was supposed to be my note on Brilliant after 3/4 weeks.
I didn't post a note.
I think you should create a note on "Weyl Fermions" It's something new. We can have a good discussion on it. If you don't, someone (perhaps Calvin :D) will post. But, why wait?
:)
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@Soumo Mukherjee – Let me think about how I could approach the subject of Weyl fermions. There was another topic I thought I'd post, a simpler one, Memristor , which was based on a conjecture "to fill a conceptual hole" (capacitor, resistor, inductor, and...?) that turned out to have a practical reality. Physicists often surprise themselves how well reality follows mathematical conjecture. It's something that happens again and again in the history of physics.
So, now we're looking at each other and saying, "hey, maybe somebody should be posting notes on these things".
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@Michael Mendrin – We can always ask Calvin. He is the Dumbledore of Brilliant.
"Help will always be given at Hogwarts," said Dumbledore, "to those who ask for it"
I thought it would be nice if it came from you. You have a rich background. You know so much about Physics as well as its history. While reading about a new discovery, you are more likely to spot related and useful topics, like you spotted "Coupled oscillators" in "Huygens's Clocks". Moreover, in case of Weyl fermions someone with an engineering background can surely help us to understand how it will affect electronics.
Whereas I can't help but get hooked into something irrelevant while venturing out into a new territory. i.e. into facts like: John von Neumann named his dog "Inverse". And, Rene Descartes named his dog "Monsieur Grat," which means "Mr. Scratch".
The concept of "memory of past voltages or currents" & "the device that remembers its history " sounds really interesting.
Have a good day Mr. Mendrin.
:)
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@Soumo Mukherjee – I think you're too kind in referring to my "rich background", and you mentioned "coupled oscillators" first. However, the significance of Weyl fermions goes way beyond what it can do for "electronics". As for poor Dumbeldore, there's only one of him, and he certainly can use a wand these days.
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@Michael Mendrin – I don't know anything about coupled oscillators. I mentioned that para because of the laser and superconductor thing which I am acquainted with.
So, why is Weyl fermions a particle? It's being referred to as mass-less particle, I want to know what qualifies something to be particle. And, does it occupy space?
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@Soumo Mukherjee – Right now, the "discovered" Weyl fermions are only quasi-particles that exist in certain semiconductors, i.e. it behaves just like "real Weyl fermions", which yet have to be discovered in free space. Too bad about that. But the promise these quasi-particle Weyl fermions have is that they can have quantum attributes such as charge, spin, chirality, but because of their particular spin attributes, they can travel, carrying a charge, through these specialized semiconductors, virtually without scattering. In short, superconductivity at room temperatures. What's more, some of the quantum attributes, such as chirality, can be "quantum teleported", which promises a bridge between conventional and quantum computation.
I sure see a lot of parallels now between the discovery of Weyl fermions in semiconductors and the discovery of memristors, even though the mathematics of the latter is considerably more elementary.
I was hoping to find that the discovery of such Weyl fermions, even only as quasiparticles, would be a boost for Supersymmetry theory, but it doesn't look like it. SUSY is still up in the air.
Read the paper. It does apply the principles of classical mechanics, though much more work is needed.
so classical mechanics fails to explains this phenomena????
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Classical mechanics is used to explain this phenomena. In fact, classical mechanics is even used to explain chaos theory as well. You don't need "weird probabilistic quantum mechanics" to explain either. See Calvin's earlier comment about this.
By the way, "chaos theory" isn't just about "oh, how easily things fall into disorder". It's also about emergent order in face of seeming chaos. The public gets the first part, we see this in the movies a lot, but the flip side of this is not as well publicized.
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@Michael Mendrin – Just like there are integers that are interesting and integers that are boring, there must be concepts (& devices) in Physics, interesting or boring, "that can be described in 19 words or less."
What say?
Space, Time, Force, Supersymmetry, Memristors, Dumbledore; wait not that..
=)
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@Soumo Mukherjee – How about "maximum entropy production = least action"?
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@Michael Mendrin – Kinda reminds me of me =D
frequency of suggesting/thinking up ideas > > frequency of making them happen
That's a great paper you cited on this phenomenon. I hadn't had the chance to find out how or why this works, exactly. "Coupled oscillators" was something I first learned about in undergraduate physics, but the text on it was far too elementary to be able to explain the Huygens synchronization.
This phenomenom is known as the Huygens synchronization of two clocks. When confined to rest in his room in 1665, he observed that the pendulums of two suspended clocks, hanging side by side from a common support, were swinging precisely in opposite phrase. He deliberately adjusted the motion os that they were no longer out of phrase, and realized that in 30 minutes, they were back to opposite phase motion.
This has puzzled physicists for 350 years. In the last week, there is a paper published in Nature , which provides a model that explains this phase opposition synchronization via single impacts like sound waves of the moving pendulum.