3317: Gravitational Square Wave

Gravitational Square Wave

|< < Prev #3317 (October 28, 2026) Next > >|

Title text: Depending on the energy deposition I can manage, it might also be a fun prank on the rest of the Earth.

|< < Prev Random explanation Next > >|

Explanation

This is one of 64 incomplete explanations: This page WAVED HELLO recently. Don't remove this notice too soon. The insert with the cubes should be explained in detail. Some have already made a good attempt in the discussion, but this should be included in the explanation. Also, briefly explain what gravitational waves are. You can help by editing the explanation!

This is a comic in the My Hobby series. While Randall's other hobbies are often realistic to have, this one is not!

Gravitational waves were predicted by general relativity many years before scientists were able to directly observe them. Gravitational waves large enough to be found by current detectors can only be created by very heavy objects like neutron stars or black holes moving very quickly, such as when two of them spiral in to each other and merge as shown in the comic. Oscillations from such an event create sine waves, which are smooth.

The French mathematician Joseph Fourier famously proved that sine waves of various amplitudes, frequencies, and phases can be summed to approximate any periodic function, including square waves. Summing sine waves to get a square wave requires sine waves that oscillate faster and faster at lower and lower amplitudes; this is achieved in the comic with more and more, but smaller and smaller, pairs of merging black holes/neutron stars. As depicted by the series of rectangular cuboids, the square gravitational wave would cause spacetime to oscillate between the the 'tall' and 'wide' states in sharply changing zones as the gravitational wave passes, as opposed to the smooth transitions from sine waves. Square wave gravitational waves would be very unlikely to be found naturally, due to the requirement that multiple independent waves interact in exactly the right way, so observing such waves would greatly surprise scientists. The gravitational waves from the objects are emitted three-dimensionally, so the requirement that they combine in a very precise way means that it would only appear as a square wave to those directly on the line of 'aim'; observers in most other locations would see a wave with differently timed (and possibly suppressed) harmonics, depending on their position relative to the line. The effect only works if the merging objects are lined up, and only along that line. If very precise positions/timings are maintained, something very similar to the square wave may also propagate in the reverse direction.

The amount of energy required to manipulate black holes or neutron stars in the way illustrated in the comic is astronomically large, as they usually have masses larger than the Sun. Doing so in a manner to produce a gravitational wave with the level of accuracy to functionally work as a square wave would require energy many tens of orders of magnitude larger than humanity has ever produced. In addition, creating a perfect square wave would require an infinite number of merging stars, which is not possible in our (presumably) finite universe, though increasingly close approximations of a square wave would be possible with increasing numbers of stars.

The title text implies that the waves could be given enough energy to destroy or otherwise significantly affect the Earth.

Transcript

This is one of 41 incomplete transcripts: Don't remove this notice too soon. You can help by editing the transcript!

[A diagram shows a sinusoidal gravitational wave emitted by two merging black holes being progressively modified into a square wave using a line of progressively smaller pairs of merging black holes and neutron stars. After the wave has become a square wave, a diagram is shown of six alternately 90°-turned flat rectangular blocks, presumably showing the square gravitational wave propagating through space. Then the wave reaches Earth, where people are puzzled by it, as indicated by "???!".]

[Caption below the panel:]

My Hobby: Arranging binary black holes and rotating neutron stars to produce a gravitational square wave, as a prank on gravitational wave astronomers

  Add comment 

Discussion

I think those pesky astronomers have a bigger thing to worry about. King Pando (talk) 02:49, 29 October 2026 (UTC)

randall out here pushing black holes and neutron stars billions of light-years away from earth GreyFox (talk) 03:50, 29 October 2026 (UTC)

POV Beret Guy is affected by this and just blurs into 2 beret guys This isn't a good name (talk) 03:57, 29 October 2026 (UTC)

If there's someone arranging neutron stars and black holes, I'm going to salute them. The amount of energy required for such a feat is... high enough on the Kardashev scale that it's best not thought about too closely. We wouldn't want there to be two Beret Guys. -2A10:D586:3E93:0:D00:1F9E:F1D7:74FA 08:29, 29 October 2026 (UTC)

I'm confused by the string of blocks. What does this represent? SystemParadox (talk) 09:47, 29 October 2026 (UTC)

I think it's indicating that space is alternately being squished 'short and wide' and then 'tall and thin'. 86.22.132.121 10:04, 29 October 2026 (UTC)

Perhaps these are the "dice" that God does not play with. Mad Marie (talk) 10:38, 29 October 2026 (UTC)

It's likely attempt at showing that squished and stretched cubes exist next to one another (at one given time). The act of stretching and squishing is what happens normally (at ultra-miniscule scale), Randall's "square wave" results in space jumping between the two extremes instantly, there is no stretching, space just becomes stretched and becomes squished. Seeing this would indeed confuse astronomers, and at some (insane) energy would be very "funny" to experience. Maur11cio (talk) 10:58, 29 October 2026 (UTC)

Imagine a square cross-section, perpendicular to the source of particularly polarised gravitational waves. As a 'beam' of oscillations moves along that axis of propagation, it makes space-time squash in one cross-sectional direction and stretch in the other. (Note: I think that 'standard' waves squish and stretch both perpendicular directions relative to the axial dimension that stretches and squishes, but I stand to be corrected... and maybe it depends entirely upon the orientation of the gravitational-binaries relative to the observer's direction, so edge-on orbiting does as described.)

For a sinusoidal variation (given the above stipulation) the nominal 'square' will flex taller and thinner and then shorter and wider and back. Viewing the 'box' that is this cross-section across the axial length looks very much like some particularly pretty forms of decorative ironwork bars. But, with a perfect square wave, it'll look like a series of boxes, lined up, alternating tall-and-thin with short-and-wide.

You could also consider a nominally circular cross-section, for either form, which is actually composed of ovals varying/alternating the major and minor axis. The main point is the way this smoothly/sharply transitions, rather than what arbitrary cross-section shape you use, but square/rectangular cross-sections match the square/rectangular 'through-sections' you might also decide to view from sidelong to the 'aimed' gravity-wave.

But it's perhaps harder to describe than visualise. And I'm not sure how I'd be able to do it visual justice better than how the comic displays it. 81.179.198.128 20:06, 29 October 2026 (UTC)

this feels like an answer to a what-if question that was never asked. Lettherebedarklight (talk) 15:37, 29 October 2026 (UTC)

RIP what if 107.1.219.44 16:15, 29 October 2026 (UTC)

Lightbulb idea. Are there any universe simulator visualizations/games to test this? If not, xkcd just petitioned all of us to want one! Is there a Universe Creator, like Kerbal, SimCity or Roller Coaster Tycoon? One that I can play with silly physics stuff to see what cosmic phenomenae I can create. An Arcade mode would be for the newbies with gamification of goals ("Kill The Dinosaurs" or "Trigger a Supernova by a Cosmic Deadline" or "Create a Gravity Square Wave"), and a Scientist/Astronomer mode would let me dive deep into things like these. The compute would be extreme, but we now have black hole simulators running in a browser today that looks better than Interstellar (100 hours/frame) running at 10 frames per second on my 5080 GPU. A simplified universe simulation might be possible with clever multi-zoom-levels architecture, combined concurrentyl with the "minimum possible compute" necessary to do this simulation with all kinds of tricks like scientific-neural models and raymarching that is reportedly to dramaticaly speed up simulation. Zoom in, you simulate more (e.g. star has millions of variables) zoom out, you simulate less (e.g. a star might be one variable) at least for a sub-scale "arcade simulation" model sufficient to play with phenomenae like this. And for some of the gamification (dopamine arcade style stuff), you'd have floating measurement windows (energy levels) depending on what you clicked, and you can click Home (which can can have alert icons) to "Observation Lab" on Earth when things are discovered, changes or meets goals, like the discovery of a new planet or a gravity wave or extreme event. We can optimize our math cannons (GPUs). The physics don't have to be perfect. Just want to blow things up that's not typical DOOM games. We don't necessarily need to play with ~10^80-10^85 particles to have something fun that's better than doomscrolling. GDouglas (talk) 20:46, 29 October 2026 (UTC)

Does anyone have a closed or non-closed form expression for this wave function? Thanks. ~~ItsMeAMario~~ 169.150.218.79 (talk) 22:44, 29 October 2026 (UTC) (please sign your comments with ~~~~)

Whatever form you like it as, imagine adding together an infinite series of odd-integer harmonic sine wave. With some magnitude reduction, at each stage, of course. 81.179.198.128 23:02, 29 October 2026 (UTC)

Lucky enough to be working on square waves today...and... this looks not quite right. The binaries should only be at fundamental spacing. Each would be at an odd harmonic. (NASA engineer) 156.68.251.33 02:32, 30 October 2026 (UTC) 02:30, 30 October 2026 (UTC)

Wait - NASA is engineering square waves with black holes?? 86.22.132.121 10:22, 30 October 2026 (UTC)

This clearly and simply shows how a square wave is constructed out of the sum of sine waves https://youtu.be/SpzNQOOBeRg?si=cXoByzkO98v75-6g 2600:1700:25b1:700:88d9:c212:49d2:caf6 (talk) 23:33, 30 October 2026 (UTC) (please sign your comments with ~~~~)

IIUC all the gravitational waves we have detected so far are "chirps" and not steady state waves, so generating a square wave would also be time dependent, and probably not possible since different frequency chirps have different durations and other characteristics. Also IIUC the hopes to detect much weaker longer duration steady states require averaging over many periods and could not distinguish a square wave from a sine wave. There is a general problem that the evolution of a system depends on the rate at which it loses energy, so strong detectable waves will tend to be short lived. Randall needs a different hobby.76.180.39.133 17:31, 31 October 2026 (UTC)

I, for one, wouldn't argue with anyone who even could try to have this hobby. I'm not going to tell them that they'd need to try harder to do it correctly. :P 2.98.68.172 21:19, 31 October 2026 (UTC)

Since we don't have infinitely precise instruements, can someone try working out how many sets of blackholes and neutron stars you'd need to have a perfect square wave by the standards of our best gravitational wave instruments? Sorry if I worded that horribly. RG (talk) 13:00, 1 November 2026 (UTC)

The known events that create gravity waves use up the masses involved. The emitted waves use up energy and then things fall together and then that source can't generate more gravity waves. So the square wave can't go very long. Also, the image seen is going to depend on the location of the viewer, so the perpetrator of this has to know the Earth is special a long time in advance. 104.251.240.78 13:43, 1 November 2026 (UTC)

Fun fact! This isn't mathematically quite possible; a series of waves can never accurately approximate a square function. A Fourier series will converge exponentially if approximating a *smooth* function, but a square function isn't smooth. Instead, the approximation will always have some "ringing" at the discontinuity, and the amplitude of that ringing converges to around 9%. See: The Gibbs Phenomenon. BenWinchester (talk) 15:21, 2 November 2026 (UTC)

Another comic about unlikely weaponization of wave phenomena: 967: Prairie 67.0.30.15 21:42, 2 November 2026 (UTC)
        Add comment