The Ring of Steel | Hacker News Reader

The Ring of Steel

solipsys.co.uk

29 pointsColinWright16 comments

This reminds me of a similar problem I came across whilst studying quantum mechanics in my undergrad. The problem is stated as follows 'imagine a perfectly upright pencil balancing on its perfectly sharpened tip. How long does it take to fall over?'. At first this seems surprising. Classically speaking, the pencil would never fall over, but knowing that we live in a quantum world, we can conclude that it would in fact fall over. The reason for this is the famous Heisenberg Uncertainty Principle which says that the product of the uncertainty in a particle's momentum and its position is always greater than or equal to hbar/2. You can derive a similar expression for uncertainty in angular momentum and angular position.

Now, these expressions don't imply it's impossible for the angle (theta) and angular momentum (L) both to be simultaneously zero, just that it's infinitely improbable. If you plug in reasonable values for both parameters, say by assuming that Δtheta = ΔL = sqrt(hbar) and that the actual values took a figure corresponding to an expected value assuming these uncertainties, you can work out that the pencil will actually fall over in a few seconds.

I don't find this quantum argument convincing.

We know that the better you isolate an atom, the longer it takes for an excited electron to come back to ground state. The issue is that the electron must dump a full quantum of energy, and it tends to do so as part of an exchange with the outside world.

If you isolate an atom really well, that electron can take a really long time to decay.

See: "Collective Electrodynamics" https://mitpress.mit.edu/books/collective-electrodynamics

Brownian motion and standard thermodynamics almost certainly makes a stronger case.

I was literally repeating to myself “The Ringworld Is Unstable” as I read the article, glad to see the last section where he mentions Niven’s book.

As you say, the Ringworld is unstable. This was always something I had known, and accepted, but never really knew why. This article came from the problem Bill presented, and then in understanding that better, and making the connection with the Shell Theorem, meant that I can see why it's morally true, and not just a result of "doing the sums."

As lmilcin[0] says[1], the Ringworld was kept stable by artificial means, and that's the major plot point/device in the sequel.

[0] https://news.ycombinator.com/user?id=lmilcin

[1] https://news.ycombinator.com/item?id=19165894

The Ringworld was kept stable artificially if I remember.

Also it rotated extremely quickly which prevented it from getting squashed like the steel ring in the article. The rotation was so high that it created artificial gravity and so was also high enough to counteract star's gravity. In effect, the ringworld was in constant tension.

Since it was made from some pretty exotic stuff it is difficult to say anything about the tensile strength of the material.

I believe this is pretty impractical, the required velocity was relativistic and created too much tension for any plausible material.

For reference, using the Earth as a measure, we are about 150 x 10^9 metres from the Sun, acceleration due to gravity is about 10 m/s^2, and a=v^2/R.

So the speed required is about sqrt( 10 x 150 x 10^9 ) which is about 1.22 x 10^6 m/s. Light speed is about 3 x 10^8, so this is about 0.4% of c.

So yes, we're coming into the realm of relativity.

> What happens next?

It falls to the ground, of course. At the scale of something that long steel isn't any more rigid than rope is.

Not sure why your comment is being downvoted. It is obvious that the shell theorem only applies to Earth and not the steel ring (it's not the ring that is within a shell) and only to the plane of Earth that is in the plane of the ring.

While the single plane (crossection) of Earth would not see gravitational gradient from the ring it is only because each part of that crossection of Earth is being attracted to all parts of the ring in a way that all forces cancel each other.

For the ring itself, each part of the ring is being attracted by the Earth that is beneath it. There is no magic, the Earth is not a shell around that part of the ring and and full force of attraction is felt.

The compressive force on the steel would just squash it immediately. No known material would be strong enough to support itself in this configuration.

Think about an arch that is 5 feet high standing on the Earth. Now start making the span wider while keeping its height. The arch gets shallower and shallower until the radius of the arch is the same as radius of Earth. The wider the span and the shallower the arch the stronger the material needed and the less force it can carry.

The idea is that we're in "Puzzle World". This is one of the things that most people take for granted, that the way this is set up has the ring being rigid, even though that's not genuinely feasible. We assume that in the same way as we are assuming that the Earth is a perfect, homogeneous sphere.

I might add a note to that effect - thanks for highlighting this.

Added in edit: I've now added a note to the page to address this question/issue. And when I say "address", I really mean "try to avoid".

There's nothing wrong with an infeasible thought experiment. Frictionless surfaces and spherical cows are a staple of learning physics. The problem is when the author describes them as "greased surfaces" or "watermellon shaped cows" and asks you to treat them as perfectly frictionless or spherical.

Describing the rope as being "steel" instead of "rigid" is just needlessly confusing.

If you're inside the world of physics, "rigid" carries exactly the meaning you say it has. But it's a code word, it's got a technical meaning, and for people not in the world of physics, using the word "rigid" would, I think, be confusing.

So I've updated the side-box to try to make it clearer. You might like to check it out to see what you think.

Yep, sometimes a good puzzle needs a spherical chicken to be tractable.

I think you mean spherical cow ...

But yes.

To avoid adding yet another semi-off-topic comment in the thread I'll add this here: Yes, absolutely, "Spherical [cow|chicken|horse|other]." Cheers!

There are variants of the joke for both spherical cows and chickens going back decades.

> "Postulate a spherical chicken ...", as presented in a 1973 letter to the editor of the journal Science titled A Spherical Chicken.

Turing discussed spherical horses even earlier :).

Never heard of the Shell Theorem, great way to explain it With a very simplified example: a picture frame

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