Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

What Makes the Hardest Equations in Physics So Difficult?

quantamagazine.org

Post reply on HN
Print view View original

31–40 of 75 posts

Re: What Makes the Hardest Equations in Physics So Difficult?

#31

Post by pixelpoet »

whatshisface wrote: post #15
jerf wrote: post #5

Earlier quoted context omitted.

Tone: Straight. I think you asked a reasonable question. What you are missing is that mathematicians are concerned about Navier-Stokes itself, as an independent entity in pure mathematics, not related to its physics correspondence. I think it would be safe to say that everybody believes that even if Navier-Stokes does have a singularity in it, that there won't be any way to manifest that singularity in the real unive…

One reason to think the physics would be interesting: it isn't every day that we can arrange macroscopic systems in ways where their small-scale behavior gets amplified enough for us to measure. Arranging a blowup in the Navier-Stokes equations would be a way to study atomic-scale physics on human scales - and, likewise, arranging a blowup (if one exists) in the QCD quark-gluon plasma equations would allow us to get…

A nice example of such a practical tool for microscopic analysis is X-ray crystallography, once you have the theory of Fourier transforms and lattices.

Re: What Makes the Hardest Equations in Physics So Difficult?

#32

Post by andrewflnr »

jerf wrote: post #5
andrewflnr wrote: post #4

So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. It seems obvious to me that Navier-Stokes can't be a perfectly accurate description of reality, so it should come as no surprise if they turn out to blow up or otherwise behave non-physically. Am I missing something? Why isn't it assumed that they're just a very nice approximation, like Newton's…

Tone: Straight. I think you asked a reasonable question. What you are missing is that mathematicians are concerned about Navier-Stokes itself, as an independent entity in pure mathematics, not related to its physics correspondence. I think it would be safe to say that everybody believes that even if Navier-Stokes does have a singularity in it, that there won't be any way to manifest that singularity in the real unive…

I guess if you're looking for pure mathematical abstraction, Navier-Stokes doesn't seem like the most interesting without the physics connection. But that's just me.

Re: What Makes the Hardest Equations in Physics So Difficult?

#33

Post by carterehsmith »

andrewflnr wrote: post #4

So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. It seems obvious to me that Navier-Stokes can't be a perfectly accurate description of reality, so it should come as no surprise if they turn out to blow up or otherwise behave non-physically. Am I missing something? Why isn't it assumed that they're just a very nice approximation, like Newton's…

>> So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist.

Atoms have structure, they consist of... whatever parts. And these parts have structure (like... quarks and whatnots). And... are we sure that quarks do not have structure themselves? Whatever the case is, it is not something that one should declare in a HN thread.

Even more interesting... 1+2+3+4... = -1/12

https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B...

And that result actually pops up in physics.

That kind of indicates continuity/infinite divisibility.

Re: What Makes the Hardest Equations in Physics So Difficult?

#34

Post by twiceaday »

carterehsmith wrote: post #33
andrewflnr wrote: post #4

So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. It seems obvious to me that Navier-Stokes can't be a perfectly accurate description of reality, so it should come as no surprise if they turn out to blow up or otherwise behave non-physically. Am I missing something? Why isn't it assumed that they're just a very nice approximation, like Newton's…

>> So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. Atoms have structure, they consist of... whatever parts. And these parts have structure (like... quarks and whatnots). And... are we sure that quarks do not have structure themselves? Whatever the case is, it is not something that one should declare in a HN thread. Even more interesting... 1+2…

There is a standard definition of what '=' means and your equation does not satisfy it.

https://www.youtube.com/watch?v=YuIIjLr6vUA

Re: What Makes the Hardest Equations in Physics So Difficult?

#35

Post by knight-of-lambd »

carterehsmith wrote: post #33
andrewflnr wrote: post #4

So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. It seems obvious to me that Navier-Stokes can't be a perfectly accurate description of reality, so it should come as no surprise if they turn out to blow up or otherwise behave non-physically. Am I missing something? Why isn't it assumed that they're just a very nice approximation, like Newton's…

>> So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. Atoms have structure, they consist of... whatever parts. And these parts have structure (like... quarks and whatnots). And... are we sure that quarks do not have structure themselves? Whatever the case is, it is not something that one should declare in a HN thread. Even more interesting... 1+2…

> Even more interesting... 1+2+3+4... = -1/12

What.. No. This sum diverges. It does not equal -1/12.

Now if you plug -1 into the Riemann zeta function, you get -1/12. One could interpret that to mean the sum 1 + 2 + 3 + .. can be mapped to -1/12.

But the sum has never, and will never equal -1/12. It diverges, simple as that.

Re: What Makes the Hardest Equations in Physics So Difficult?

#36

Post by kazinator »

carterehsmith wrote: post #33
andrewflnr wrote: post #4

So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. It seems obvious to me that Navier-Stokes can't be a perfectly accurate description of reality, so it should come as no surprise if they turn out to blow up or otherwise behave non-physically. Am I missing something? Why isn't it assumed that they're just a very nice approximation, like Newton's…

>> So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. Atoms have structure, they consist of... whatever parts. And these parts have structure (like... quarks and whatnots). And... are we sure that quarks do not have structure themselves? Whatever the case is, it is not something that one should declare in a HN thread. Even more interesting... 1+2…

> 1+2+3+4... = -1/12

Only through a derivation which involves some cute but unsound pseudo-algebra on infinite series.

See, in the same page, the remark "Generally speaking, it is incorrect to manipulate infinite series as if they were finite sums".

Re: What Makes the Hardest Equations in Physics So Difficult?

#37

Post by carterehsmith »

twiceaday wrote: post #34
carterehsmith wrote: post #33

Earlier quoted context omitted.

>> So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. Atoms have structure, they consist of... whatever parts. And these parts have structure (like... quarks and whatnots). And... are we sure that quarks do not have structure themselves? Whatever the case is, it is not something that one should declare in a HN thread. Even more interesting... 1+2…

There is a standard definition of what '=' means and your equation does not satisfy it. https://www.youtube.com/watch?v=YuIIjLr6vUA

You say "your" and yet, this has nothing to do with me. I pointed to the wikipedia article. BTW this result is not exactly new, and it has specific confirmation in physics.

You cannot argue that with high-school math. There is more to it.

Re: What Makes the Hardest Equations in Physics So Difficult?

#38

Post by Retric »

SAI_Peregrinus wrote: post #29
Retric wrote: post #24

Earlier quoted context omitted.

The other side of this is cells are also really fast. Modeling even 0.01 seconds could be very useful.

Much of the action inside cells is done via proteins. It's taken a huge amount of distributed computing power just to figure out a reasonable hypothesis for how they fold (only one part of the movement) and €1.22 billion to build the XFEL and have a way to image them on the required timescales: 1-2 femtoseconds. 0.000000000000001 seconds. 0.01 seconds is an eternity, calculating that long would take an utterly enormo…

You can spend similar amounts of processing power (or vastly more) modeling a single atom over much shorter time scales from quantum mechanics. Protean folding while important results on fairly stable configurations and you don't need the same granularity after that point.

PS: Also of note protean folding simulations don't even simulate the water surrounding the protean and are again very simplified.

Re: What Makes the Hardest Equations in Physics So Difficult?

#39

Post by carterehsmith »

knight-of-lambd wrote: post #35
carterehsmith wrote: post #33

Earlier quoted context omitted.

>> So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. Atoms have structure, they consist of... whatever parts. And these parts have structure (like... quarks and whatnots). And... are we sure that quarks do not have structure themselves? Whatever the case is, it is not something that one should declare in a HN thread. Even more interesting... 1+2…

> Even more interesting... 1+2+3+4... = -1/12 What.. No. This sum diverges. It does not equal -1/12. Now if you plug -1 into the Riemann zeta function, you get -1/12. One could interpret that to mean the sum 1 + 2 + 3 + .. can be mapped to -1/12. But the sum has never, and will never equal -1/12. It diverges, simple as that.

What is the argument here? There are certain ways of assigning a number to the divergent (by partial sums) sum. If they are well-defined, they all arrive at the same number. In this case, -1/12. There is nothing to argue here, that shit has been around for 200 years or more.

And, there are some results in physics that actually measure close to the number -1/12, from something that looks like a sum of 1+2+3... and that's kind of telling us that the whole construction is not just some math sleight-of-hand, it actually has some meaning in the real world.

Example: Casimir effect

So my point is... that kind of suggests the smoothness, or continuity, or differentiability, or whatever we want to call it, of the underlying function. The opposite of discrete. Is what my point was.

Re: What Makes the Hardest Equations in Physics So Difficult?

#40

Post by carterehsmith »

kazinator wrote: post #36
carterehsmith wrote: post #33

Earlier quoted context omitted.

>> So, Navier-Stokes assumes infinite divisibility in the fluid it models, right? Which we know is not the case: atoms exist. Atoms have structure, they consist of... whatever parts. And these parts have structure (like... quarks and whatnots). And... are we sure that quarks do not have structure themselves? Whatever the case is, it is not something that one should declare in a HN thread. Even more interesting... 1+2…

> 1+2+3+4... = -1/12 Only through a derivation which involves some cute but unsound pseudo-algebra on infinite series. See, in the same page, the remark "Generally speaking, it is incorrect to manipulate infinite series as if they were finite sums" .

>> some cute but unsound pseudo-algebra on infinite series.

Sure it looks like that, but, amazingly, there is a physical meaning to that number.

I replied here: https://news.ycombinator.com/edit?id=16164915

Post reply on HN