2413: Pulsar Analogy

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Pulsar Analogy

Title text: The #2 cause of astronomer hand injuries is trying to do vector math when the second axis points off to the right.

Explanation

Pulsars are a kind of old, shrunken, fast-spinning star. They are usually neutron stars. They no longer shine in all directions, but instead produce beams of radiation out of their magnetic poles, which blip by us in rapid pulses as they spin.

Ponytail, an astronomer in this comic, explains a pulsar's fast rotation with an analogy about a tape measure retracting. The analogies that Ponytail picks are incredibly poor ones, as seen in 2094: Short Selling.

Since the analogy does result in something that spins, the reader might think that, while they don't immediately see how it helps in understanding pulsars, they're willing to reserve judgment to see what is then done with the analogy; Cueball's response may suggest this sort of wait-and-see attitude. However, the analogy is likely to be useless or misleading, as the tape measure starts to rotate because the retracting tape is not moving only in a radial (in/out) direction. As a star collapses into a pulsar, its natural rotation rate is greatly amplified by its shrinking moment of inertia.

Further elaborations of the analogy, rather than clarifying matters, are successively more surreal. More misleading than the tape-measure is the idea of a laser measure being "exactly" like the emissions of a pulsar, which, although both pulse, are produced in entirely different ways and are at best simply helping the mind hold the concept.

When a tape measure retracts, the part of the tape outside the tape measure is not going directly towards the tape measure's center but rather towards a hole in the side. This means the tape possesses some angular momentum relative to the tape measure. In addition, when the tape measure retracts, the part of the tape inside the tape measure rotates around a spool (which pulls the part of the tape outside the tape measure inside), so it also has angular momentum relative to the tape measure. When the tape is completely retracted, the tape can no longer rotate relative to the tape measure. Because of the conservation of rotational momentum, the tape measure will start spinning at this point.

While pulsars also rotate quickly due to the conservation of angular momentum, the exact mechanism is completely different. Pulsars are formed when stars collapse due to no longer performing enough fusion to produce enough heat and energy to cancel out gravity. This causes the star to contract, which causes its mass, on average, to be closer to its axis of rotation, which causes the rotational inertia (also called the moment of inertia) to decrease. If the star's angular velocity stayed constant, this would cause the angular momentum to decrease, so the star's angular velocity must increase in order to offset the decrease in rotational inertia, i.e. the star (which is now a pulsar) spins faster. This is demonstrated here. This method requires an initial rotation, which comes from the star. (The star's rotation comes from the dynamics of the gas cloud which forms the solar system in the first place.)

Some tape measures have a built-in laser line level and others have a built-in laser rangefinder. Pulsars emit electromagnetic radiation out of their magnetic poles, which is similar to a laser, but unlike the laser of a tape measure, the pulsar beam is emitted through the axis of the magnetic field. The pulsing nature of a pulsar comes from when the axis of rotation is not precisely aligned with the axis of the magnetic field, and the location of the viewer as the beam sweeps by. In the tape measure analogy the beam is at a right angle to the axis of rotation, so as long as the viewing angle isn't parallel with the rotation axis, the viewer would see the laser increase and decrease periodically as it the rotating tape measure points towards or away from the viewer.

While pulsars do demonstrate incredible starquakes and rotational glitches, neutron degeneracy is part of the mechanisms in which they are originally formed. During the formation of a neutron star, usually in the form of an initial inward implosion, the neutron degeneracy (basically the impossibility of neutron of occupying the same space because of fundamental constraints in physics that are studied by quantum mechanics) stops the implosion and redirects the shockwave outwards, thus producing a Supernova explosion. The analogy is with a tape measurer that hits a hand (the constraint) during its rapid rotation due to its retracting tape (the implosion) thus redirecting part of the energy towards the hand (the supernova energy is redirected outside).

However, astronomers do not usually let go of laser tape measures frequently, so they are probably not the top cause of any type of hand injuries, contrary to what Ponytail said.

The title text mentions the right-hand rule in three-dimensional space. In a typical 3D coordinate system the Y-axis will point counterclockwise to the X-axis when looking down from the positive Z-axis. In academia, students are often taught to remember a number of mathematical conventions by using their actual physical right and left hands to align the axes. When the axes are in a different order, the left hand can be used instead of the right, but there are a number of common operations in engineering and physics that use the cross product in systems where the first axis might point in absolutely any direction relative to the viewer. Using the hand rules, the thumb is aimed along the first axis, the forefinger along the second, and the middle finger along the third — all at ninety degrees. So, when the first axis points off to the right, the right wrist is torqued to its full extension to make the thumb point that way while the other two fingers don't. During exams, students can be seen performing this feat. People who learn cross products early in their life may develop other approaches for remembering these things, that don't stretch the hands as much, but then adopt the common approach once taught it. This rule has been previously mentionned in 199: Right-Hand Rule.

Transcript

[Cueball and Ponytail are standing next to each other.]

Cueball: Why do pulsars spin so fast?

Ponytail: Hmm, let me think of an analogy...

[A tape measure is retracting above Ponytail's head. To the right of her head, a tape measure is spinning rapidly.]

Retracting tape measure: zzzzzzzzzzzzzzz

Spinning tape measure: SNAP

Ponytail: You know how when you retract a tape measure and let go, it leaves it spinning?

Ponytail: It's like that.

Cueball (off-panel): Oh, I see.

[A tape measure with a laser instead of a measuring tape is spinning slowly.]

Cueball (off-panel): And if the tape measure is the kind with a laser level, that's the beam of radiation?

Ponytail (off-panel): Exactly!

[Cueball and Ponytail are walking next to each other in silhouette.]

Ponytail: And when the tape whips around and smacks your hand, that's the neutron degeneracy shockwave.

Cueball: Sounds painful!

Ponytail: Top cause of astronomer hand injuries.

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Discussion

I tried applying the right-hand-rule with the y-axis pointing to the right. :( I hurt my hand. Avitzur (talk) 23:22, 18 January 2021 (UTC)

Rotate your paper then do the right hand rule :)

Hand joint exercises. Gentle motions with the wrist bent backwards, and bent forwards; 3-5 circles in both directions and both postures, twice a day. 162.158.62.41 00:48, 19 January 2021 (UTC)

172.69.35.149 23:38, 18 January 2021 (UTC)

The three-finger version of the right-hand rule actually isn't too bad in that case - pointing your right index finger to the right isn't too hard. Given that the alt text said "second axis", I assume the reference is to the "curling" version of the right hand rule: if you point your four fingers toward the first axis and then bend them toward the second axis then your thumb points in the direction of the cross product, and (at least in my opinion) it's a lot more painful to try to curl towards your right. 172.68.143.70 22:33, 22 January 2021 (UTC)

The analogy doesn't seem to be inaccurate in the way currently indicated. In both cases (tape measure and pulsar), conservation of angular momentum is what produces the result. With the tape measure, a small fast-spinning thing turns into a large slow-spinning thing; the opposite happens with a pulsar. 172.69.35.150 00:05, 19 January 2021 (UTC)

Isn't a tape measure bigger, not smaller, and slow-spinning, not fast-spinning, when it is elongated? This is very confusing. Thinking of how pulling the tape out stores energy. 162.158.62.41 00:49, 19 January 2021 (UTC)

A tape measure starts off not spinning. It's the acceleration of the tape as it moves in that starts the rotation, because the motion of the tape measure is not precisely radial. Same principle, different problem. Ltmauve (talk) 02:29, 19 January 2021 (UTC)

As the tape retracts, the tape inside the case is spinning. Once it is fully retracted, the case spins. Small spinny --> large spinny.

Of course, on a frictionless surface there's some slow retrograde rotation of the case + extended tape that speeds up as the tape retracts, but the case should completely stop spinning once the tape is fully retracted in that scenario, which is opposite of the analogy being drawn. 172.69.34.12 02:43, 19 January 2021 (UTC)

On a frictionless surface, it would never stop spinning. Once the case starts to spin, there's nothing to slow it down. --172.69.63.183 17:45, 19 January 2021 (UTC)

On a frictionless surface, before the extended tape measure is released, it has no net angular momentum. After it is released, the winding tape carries angular momentum, so the case+extended tape must spin in the opposite direction for the entire tape measure system to continue to have no net angular momentum. When the tape suddenly stops, it will no longer carry any angular momentum, so the case must stop spinning entirely for the system to continue to have no net angular momentum. Because of friction, we usually don't see the retro-rotation of the case until the tape is almost completely wound up. See also dlvozza's Impact Driver comment. 172.69.35.85 21:27, 19 January 2021 (UTC)

It seems to me like the reason the full tape measure spins is somewhat similar to an Impact Driver. Shooting slow motion videos of retracting my tape measure I see a small rotation in the opposite direction of the rotation in the end (likely due to the device maintaining angular momentum as the spring inside spins up) and then a quick snap when the tape is fully retracted, followed by the tape spinning very quickly in the opposite direction. As for my comparison to an impact, this reminds me a lot of how those work, with some inner barrel spinning at a very high speed, and then mechanically imparting that energy onto the body of the driving head, causing it to turn with a high torque. Typically when you start an impact spinning you can feel a small torque opposite to how the driver end spins because of the inner barrel spinning up. In the tape measure the inner spinning barrel is the tape itself and the spring to retract it, the driver head is the outer shell of the tape measure. dlvozza (talk) 19:48, 19 January 2021 (UTC)

Currently the description starts off “Pulsars are dead stellar cores” and that phrase seems very bizarre to me, since all stellar objects are dead. Do astronomers routinely anthropomorphize to such a degree as to call some stars alive and others dead? I would think more literal language like “A pulsar is the very compact and highly magnetized remains of a star after a nova or supernova explosion” but if the acceptable astronomical parlance is to say “dead star” far be it for me to demand a change162.158.63.94 05:26, 19 January 2021 (UTC)

I find the "dead star" also odd. Sure, I know what is meant, but in the same way I know what is meant by the tape measure analogy. Neither is accurate. Side note: I removed the part about the measures' lifespan and how you could repair it as this gives no benefit for the explanation and is totally irrelevant. Elektrizikekswerk (talk) 10:18, 19 January 2021 (UTC)

The word "dead" can be used to refer to inactivity in an object that was never classically alive. i.e. dead volcanoes --188.114.102.60 15:55, 19 January 2021 (UTC)

Humans aren't the only things that can be alive or dead, so calling it anthropomorphization is way off mark. But besides that, stellar objects aren't all "dead", they're non-living. You have to be alive and then die to be dead, in the biological sense. But in this case, it's called a "dead stellar core" because it no longer has sustained fusion reactions which is what stars are known for, just like a battery that's used up all of its charge is called "Dead" - not because we're assigning human qualities, but because it doesn't do what it's supposed to. Same with any non-living thing that doesn't function as expected being referred to as dead. --172.69.63.183 17:41, 19 January 2021 (UTC)

Astronomers also biomorphise stars by talking about when they are "born" – the moment sustained fusion starts in the core. 172.69.35.7 21:34, 19 January 2021 (UTC)

I think stars are alive! They're not biological but they have histories and stories and communities, they just have to do with unimaginably large atomic behaviors and orbiting patterns and stuff instead of fast food and mobile phones. 108.162.219.80 20:33, 20 January 2021 (UTC)

The increased angular velocity as the star shrinks is analogous to the way an ice skater's rotational velocity changes as they draw their arms in and out, no? Barmar (talk) 23:59, 19 January 2021 (UTC)

Just in, no pulsar ever managed to do "out" ... and yes, that's the analogy usually used, because it's easier to understand and considerably more fitting. Well, at least for someone who ever saw ice skating ... -- Hkmaly (talk) 06:24, 20 January 2021 (UTC)

Though they didn't use that analogy here, as they needed one that could be extended in a really ridiculous way to make the joke. It's not supposed to be the best possible analogy, but the follow up is supposed to be much worse.--108.162.216.118 17:51, 20 January 2021 (UTC)

Currently, the explanation doesn't say anything about the last panel, and should probably emphasize the core of the joke in that the explanation starts out kind of reasonable, albeit imperfect, but then gets progressively much worse when it is elaborated on in the last 2 panels (the initial analogy is a lot more reasonable than the stuff about the laser, and the fourth panel is just nonsense.)--162.158.74.85 05:01, 20 January 2021 (UTC)

Is it possible this is a reference to the anecdote in "Surely You're Joking, Mr. Feynman", in chapter "Lucky Numbers" (page 176 in my copy), in which Feynman tells a brief story about hurting his hand with a tape measure while playing with it? Nosrednayduj (talk) 03:17, 23 January 2021 (UTC)

Currently the explanation states "As a star collapses into a pulsar over unimaginably many years, its natural rotation rate is imperceptibly and eventually greatly amplified by its shrinking moment of inertia". This is not true; pulsars are formed by supernovae over the course of minutes. 108.162.246.124 17:24, 25 March 2022 (UTC)

Fixed Jkshapiro (talk) 17:57, 25 March 2022 (UTC)