One significant application of the wave equation in pre-quantum physics occurred when Maxwell was able to derive, from the electromagnetic theory he was developing, a wave equation having solutions in which electromagnetic waves propagate at the speed of light.
Is pretty much everything described by those two classes?
Any third-order differential equations in physics?
First & second order covers most cases, third order applications include things with 'jerk', sticky flows through small channels, ..
There are other examples offered here:
https://www.researchgate.net/post/Are_there_examples_of_thir...
https://www.quora.com/Why-dont-differential-equations-of-phy...
https://math.stackexchange.com/questions/2167292/are-there-e...
No, we don't. There is enough misinformation and woo surrounding QM already. There is absolutely no reason to entertain the notion that there is some deep connection between QM and any macroscopic phenomenon simply because both inolve a wave equation. That's just stupid.
I'm with you here. Lot of ground for certain people to pick the sentence and use it out of context to augment their systematic bullshit.
This is not a description of the scientific process, but a description of tribalism, polarization and confirmation bias. People who prefer their team to end up right (or even worse, their goal is for the other team to end up wrong regardless of merit) by bending reality to fit their view, rather than bend themselves to perceive reality as it is, end up wrong.
Things tend to fall into patterns in physics, chemistry, ecosystems, societies, information technology. If they didn't, math would be useless, as it's the abstract description of such patterns and the quantitative relationships of measurable variables within them.
And these patterns will be constantly rediscovered, often by different people, under different names, with different levels of sophistication, and many of those people won't have the best of intentions or wisdom how to use what they found, or guessed about. We can't simply reject every concept, simpy because someone we don't like happens to subscribe to it. This is an outright childish way of looking at the world.
The science done in the article is fine science. Drawing parallels between the models is good and not woo
The question that started this thread is:
>Aren't quantum effects supposed to disappear in the macroscopic world
Which is just a straightforward misreading of the article.
Nobody is trying to "supress an actual scientific discovery" they are trying to clarify what has actually been discovered.
In fact such attitudes tend to hold back science for an entire generation, until all those stubbornly persistent in ignoring the obvious start passing away.
From previous discussions, I think he understand. We have a few disagreements, but in most cases we agree.
For me, the problem is in the title of the article:
> Quantum physicists explained earth’s oscillating weather patterns
It's too easy to misinterpret it and think that the Quantum Physicists used Quantum Mechanics at the whole Earths. They actually used some mathematical tools first discovered to solve QM problems and repurposed them to solve climate patterns.
That confused the person that made the comment at the top of this thread.
> Aren't quantum effects supposed to disappear in the macroscopic world? How is this explained?
The answer to this question is: yes, quantum effects generally disappear in the macroscopic world. There are some exceptions, like rainbows and transistors, but in general macroscopic phenomena can be completely explained by classical approximations to QM, notwithstanding that they are in fact quantum systems "under the hood". To be technically precise, in macroscopic phenomena, and in particular in thermalized systems (like the planet's climate) decoherence causes all of the interesting effects of QM (and specifically all of the non-local effects) to become unmeasurably small. In thermalized macroscopic systems, the classical approximation is 100% in agreement with observation, and so any suggestion that because some of the math of QM is applicable to climate that there might be a new physical phenomenon waiting to be discovered and that this phenomenon has something to do with quantum mechanics can be dismissed out of hand. Supporting such a claim would require a lot more than just some similar-looking equations.
But I didn't feel like getting quite so long-winded about it.
There are some aspects of our day-to-day lives that are governed by QM, like rainbows and transistors. But not weather or climate. Those are purely classical phenomena.
But everything is quantum even if you don't see weirdness. Certainty of probability and other "non-quantum" effects still fall within QM.
For examples of macro scale quantum effects, see e.g. the Casimir effect and the HBT experiment. There are many of them and scale doesn't really enter into it whatsoever. The key factor that underlies your question mainly is entanglement.
Underlying is the question though, why does this equation apply to the earths wheather? There seem to be parallels in the quantum and "macro" model, like windings of electron and wheather currents. Maybe the right view to modeling the earth is about dynamics as much as it is about topoligical phenomenons. After all, topology is used for solving gravitational problems, too.
Then why can the earth can be treated as a topoligical insulator and what implications does this have? Can we learn something from it that can be applied to other wheather phenomenons? Or maybe even to the earths core?
I am missing something here. Topology is a field of mathematics that studies the properties of objects that do not change under continuous deformations. So before asking why can Earth be treated as a topological something - one should specify what topology he is looking at, that is what continuous deformations of Earth he is talking about.
So - what continuous deformations of Earth are you talking about?
Well, the description of a topological insulator does use a tiny bit of topology.
So when you cut a topological insulator in half to expose the non-conducting inside, that exposed surface becomes conducting again.
So… I remain puzzled ((
It’s similar to the layman view of an atom as a miniature solar system. There are some similarities, but also very significant differences and not all knowledge is transferable from one to the other.
It is not particularly surprising that we would find new solutions to Navier-Stokes equation applied at the level of a whole planet, these things are very complex and far from completely understood.
> Then why can the earth can be treated as a topoligical insulator and what implications does this have?
That’s jumping to conclusions a bit. Again, they have found similarities in atmospheric flows and magnetic currents in topological insulators. It does not mean that the Earth is one, or that all properties of topological insulators also applies to the Earth.
> Or maybe even to the earths core?
There is bound to be some similarities, as with any fluid flow (assuming we’re not talking about the solid inner core). There are also significant differences in things like viscosity, compressibility, etc. So yeah, that’s a possibility, but as in the atmosphere, that would not make the outer core a particularly quantum object.
I think this is the wrong way of looking at this, quantum physics does not really have anything to do with this. Both systems, the oceans and topological insulators, share some of their structure and dynamics which means that the same mathematical models can be used to describe some aspects of both systems.
Large groups of people or animals can, to a certain extend, be described with fluid dynamics equations as they have some common structure, i.e. being composed of many particles interacting with each other locally. But the link is not from fluids to groups of people or the other way around, the link is a similar structure underlying both systems which makes mathematical models transferable between the two.