# My kid stumped me with a question about the speed of lightSeptember 22, 2014 4:49 PM   Subscribe

On a car trip yesterday my kid posed a hypothetical question. I was blown away, and I have no idea how to answer it. This is what she said. "So light takes 90 minutes to go from Saturn to Earth. What if, instead of shining a light on Saturn, you had a long metal chain that stretched from Saturn to Earth. A person on Saturn pulls on the chain. How long would it take the person on Earth to feel that pull?"

Dude. Like, whoa.

So I talked about elasticity for a while, and she made it clear that we are to assume the metal doesn't stretch and the chain is taut.

My (limited) understanding of this is that the pull wouldn't be felt for at least 90 minutes, because that's how long it takes light to travel the distance. If the pull were any faster, we could just (stay with me here) establish chain-pulling morse code interplanetary communications to beat the speed of light, which isn't possible.

So, how do I explain this to her?
posted by spikeleemajortomdickandharryconnickjrmints to Science & Nature (32 answers total) 21 users marked this as a favorite

The speed of sound in the chain. Depends on the density (mass per unit length) of the chain and the tension in the chain. (And you can't make an unstretchable chain for the exact reason that then the pull on the chain would travel faster than the speed of light.)
posted by BrashTech at 4:51 PM on September 22, 2014 [13 favorites]

A tug on a chain would propagate that the speed of sound in the medium - that's basically how fast an atom could let the atom next to it know that it was coming through.

However, given the mass of a chain of that length, you would need a substantial tug to get the other end to notice it over the noise, even without stretching.
posted by Pogo_Fuzzybutt at 4:53 PM on September 22, 2014 [3 favorites]

I'm not a physicist, but I think once you've discounted elasticity, your entire premise is wrong. Basically, what you have when you have a chain or even a rod or string or whatever is a structure of atoms connected by electromagnetic forces, and that electromagnetic force operates at exactly the speed of light.
posted by Aleyn at 4:53 PM on September 22, 2014 [2 favorites]

I should also clarify that my answer means that the speed of light would also be the upper bound of the speed the tug would propagate. The above answers about the speed of sound in that medium are likely much more correct about what would actually occur.
posted by Aleyn at 4:57 PM on September 22, 2014 [2 favorites]

Aside from elasticity, your hypothetical doesn't seem to be considering the way that we'd span a taut chain or pole between objects that are all moving and spinning independent of each other.
posted by a box and a stick and a string and a bear at 4:58 PM on September 22, 2014 [3 favorites]

It would take about a million hours to feel the tug, very roughly (ignoring all the complicated stuff.)
posted by michaelh at 5:00 PM on September 22, 2014 [2 favorites]

A million hours being 120 years.
posted by ambrosen at 5:06 PM on September 22, 2014

I think you should suggest she write to an astrophysicist at the nearest university with this question.
posted by chapps at 5:09 PM on September 22, 2014 [22 favorites]

Speed of sound in the chain is correct. A helpful analogy might be the way earthquakes take time to travel through the earth; the effect is the same (if you gloss over the issue of different speeds for S waves and P waves).

There is nothing wrong with this premise. It's a very reasonable question. "electromagnetic force operates at the speed of light" is kind of misleading. The carriers of the force (photons) travel at that speed, but we're talking about a wave in a solid, and to propagate that you need to move atoms. Moving the atoms is what slows down the process. That is, if I pull on Atom #1, sure its force on Atom #2 travels fast, but accelerating Atom #2 so that it starts to pull on Atom #3 takes time.
posted by kiltedtaco at 5:10 PM on September 22, 2014 [8 favorites]

c is the upper bound, the speed limit for transmitting information across this here universe, whether you're using a chain, fishing line or whatever.
posted by bruce at 5:11 PM on September 22, 2014 [2 favorites]

The other thing to add here which might make this more understandable to your budding scientist is that even a solid rod is composed of mostly empty space between the atoms. You push on the first row of atoms, it pushes on the second, which pushes on the third, and so on until the last row (located at Saturn) feels the push. Sound is just a pressure wave in a material which is very roughly what we just described with our series of pushes. This is why the tug (or push) would move through the rod, chain, etc. at the speed of sound in that material.

Also note that the speed of sound varies as a function of the material it propagates through... with propagation through metal being much faster than say air.

You could then follow up with the question: "Is there sound in space?"
posted by NoDef at 5:11 PM on September 22, 2014 [5 favorites]

Or she could write Quirks and Quarks for their listener questions episode.
posted by chapps at 5:14 PM on September 22, 2014 [1 favorite]

The speed of sound is the right way to go. You can actually demonstrate this by striking a hammer on train tracks: someone far away will hear two distinct bangs, the first conducted through the metal rail and a second through the air.
posted by d. z. wang at 5:18 PM on September 22, 2014 [4 favorites]

So we did some math, talked about units, and came up with 8.4 years to feel the pull of the chain if it were steel, assuming speed of sound in steel to be 6100m/s.

I think you should suggest she write to an astrophysicist at the nearest university with this question.

She wrote a letter to NASA to ask them if a sparkler would work in space.
posted by spikeleemajortomdickandharryconnickjrmints at 5:18 PM on September 22, 2014 [16 favorites]

d.z. wang, we talked about how the speed of sound is faster in cold air than hot, and then how it's super fast in steel, and a train track was the analogy I used.

Thanks to all from both of us.
posted by spikeleemajortomdickandharryconnickjrmints at 5:20 PM on September 22, 2014

There can be no rigid bodies in relativity. That was one of Einstein's fundamental insights.
posted by alms at 5:32 PM on September 22, 2014 [15 favorites]

Different frequencies will move at different speeds. So your square wave impulse won't get there all at the same time! Try stretching out a slinky, putting a plastic cup in one end, and tapping the other end. It will sound like a laser zap - and the sound will last a lot longer than the tap did. Similarly the tug will be smeared out.
posted by aubilenon at 5:34 PM on September 22, 2014 [1 favorite]

BOOM! Thanks, alms, that's perfect.
posted by spikeleemajortomdickandharryconnickjrmints at 5:35 PM on September 22, 2014 [2 favorites]

She wrote a letter to NASA to ask them if a sparkler would work in space.

And what did they say? I'm on the edge of my seat here!
posted by Faint of Butt at 5:58 PM on September 22, 2014 [4 favorites]

I'll let you know !
posted by spikeleemajortomdickandharryconnickjrmints at 6:33 PM on September 22, 2014 [1 favorite]

If you want more than AskMeFi can offer, I think you should submit this to Randall Munroe's What If?. Even if you don't get a new answer, it will be much wittier than ours.
posted by brianogilvie at 6:45 PM on September 22, 2014 [14 favorites]

Good thought, brianogilvie. This sort of question is right up Munroe's alley.
posted by Faint of Butt at 7:29 PM on September 22, 2014

write to an astrophysicist
Just an FYI - an astrophysicist deals with the nuclear reactions inside stars.
posted by HiroProtagonist at 8:00 PM on September 22, 2014

And I love how many people here can answer this.
posted by chapps at 12:02 AM on September 23, 2014 [3 favorites]

I'm thinking sparklers would work in space because they work when you plunge them underwater.

Yes, I realise this is a poor comparison, but the point is that sparklers release their own oxygen, just like rocket fuel does. See here.
posted by Decani at 3:29 AM on September 23, 2014 [1 favorite]

Just an FYI - an astrophysicist deals with the nuclear reactions inside stars.
We deal with all sorts of things, not just that. Generally not steel chains though.

On aubilon's comment, obligatory slinky Star Wars sound effect video.

Another point - there'll be attenuation I guess, so you may well not get any detectable tug at the other end of a chain that long, unless you pull really hard. But I think that's 'legitimately' ignorable for the purposes of the question in my opinion, unlike the limits on rigidity of materials
posted by edd at 4:22 AM on September 23, 2014 [1 favorite]

On the bike ride to school this morning we talked more about it, and I explained how when you pull on the chain, you'r really pulling on the first link, which pulls on the second link, which pulls on the third link, etc etc. And then we talked about how when you pull on the links, the first layer of atoms in the link pull on the next layer of atoms in the link, and on and on, and that's why elasticity can't be ignored in this situation.
posted by spikeleemajortomdickandharryconnickjrmints at 6:19 AM on September 23, 2014 [2 favorites]

Just an FYI - an astrophysicist deals with the nuclear reactions inside stars.

Astrophysicist and astronomer are used pretty interchangeably these days. The joke is, if someone asks you what you do, if you want to talk to them, you tell them you're an astronomer. If you don't want to talk to them, you tell them you're an astrophysicist.

Some astronomers/astrophysicists study nuclear reactions in stars. Some study other things. They've all taken a physics class where relativity was covered.
posted by Anne Neville at 6:21 AM on September 23, 2014 [6 favorites]

Aleyn: and that electromagnetic force operates at exactly the speed of light.
Although we've established it's the speed of sound, not the speed of light, that matters here, it's worth noting the speed of light in a medium (not in a vacuum) is always less than c (3e8 m/s).

IIRC, the speed of light in copper (as an example metal) is typically two orders of magnitude lower (slower). The implication is that, if you turn off the light in a room, the light hits the opposite wall before the reverse EM pulse stops the flow of electrons from that wall. There's no practical application for this, per se; it's just a thought experiment.
posted by IAmBroom at 11:21 AM on September 23, 2014

Assuming no elasticity is like assuming a spherical cow. Now you've got something new and fun to talk about after you talk about the speed of sound traveling through the chain. Find more metaphorical spherical cows; they're fun.
posted by nobeagle at 11:36 AM on September 23, 2014 [2 favorites]

Exactly! Cows become increasingly spherical and less elastic as they approach the speed of light, but they can never be perfectly spherical or perfectly rigid, because they can't ever reach the speed of light.

Hence E=MC^2, otherwise known as Elasticity=Moo*Cows^2.
posted by alms at 5:02 PM on September 23, 2014 [2 favorites]

alms: Hence E=MC^2, otherwise known as Elasticity=Moo*Cows^2.
The classic equation, first deduced by Albert Holstein.
posted by IAmBroom at 9:34 AM on September 24, 2014 [2 favorites]

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