2646: Minkowski Space

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Minkowski Space

Title text: My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.

Explanation

Faster than light travel, an impossibility in our universe, is often portrayed in science fiction by having spaceships enter (or "jump") into some different realm, termed "hyperspace" or similar technobabble, where superluminal travel can occur before returning to the ordinary universe. In this comic, a spaceship is being chased by an enemy ship and the crew attempt to escape by jumping into Minkowski space which is actually just conventional 3-D space together with time combined into a mathematical object called a manifold used in special relativity. Because Minkowski space is merely a representation of real physical spacetime, "jumping" into it is meaningless and offers no benefit for escaping pursuit, providing the humor of the comic's absurdist joke.

The visual depiction of the spaceships skewed diagonally is based on the graphical Minkowski diagram representation of objects in Minkowski space, where the world line of matter is bounded inside its diagonal light cone.

The mention of distance depending on the observer's frame of reference refers to distances changing when measured in different inertial frames of reference, a concept called the relativity of simultaneity. Here are some videos intended to explain that concept. The skewing depicted changes the distance between the spaceships in such a way that the tip of the pursuer comes closer to the pursued spaceship, but their centers move further apart. So the question of whether they have come closer is indeterminate for the reader of the comic.^{[citation needed]}

The title text is a status report from someone in the pursuing spaceship to their leader (whom they call "my liege.") Following the spaceship to Minkowski space was not a problem, but the pursued ship subsequently jumped to Hilbert space and could now be anywhere. Hiding in Hilbert space is much easier because Hilbert spaces (of which there are many very different varieties, unlike Minkowski space) can have an infinite number of dimensions, and are thus much more complicated than four-dimensional Minkowski spacetime.

As in the Sea Chase comic, there was also more than one type of space to jump to here.

Transcript

[A spaceship is being pursued by another spaceship. Both ships have a black part in the front representing a window. They are the same size but different designs. The pursued spaceship to the right has two engines below and a big engine behind. The pursuing spaceship to the left has a V-shaped rear end, and what seems like two weapons on either side pointing forward. At least two persons inside the pursued spaceship are talking to each other, and their text comes out from two starburst on top and bottom of the spaceship.]

Voice 1: The enemy ship is right behind us!

Voice 2: Prepare to jump to Minkowski space on my mark.

[Same setting, with star burst above only. The sound coming from the pursued spaceship is written inside a burst of small lines below the spaceship. Voice 2, by context, is the same as in panel 1.]

Voice 2: Three... two... one... mark!

Click

[Both spaceship are tilted upwards and becomes distorted so they become longer and thinner.]

[The tilting increases and the distortion is now so pronounced that the spaceships are almost unrecognizable, almost just lines with structure. The distance between the tip of the pursuing spaceship and the pursued becomes shorter in the last two panels, but the distance between their center parts becomes larger. Up to three distinct voices are shown, here, which may include those seen in Panel 1 but with no clear relation.]

Voice 3: Are they still getting closer?

Voice 4: I can't tell.

Voice 5: I think it depends on your frame of reference.

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Discussion

I still don't get it. 172.69.33.163 03:06, 16 July 2022 (UTC)

It's definitely not in the top ten all-time funniest ever, but there are probably more than a few academic physicists it got a grin out of. 172.70.210.233 03:38, 16 July 2022 (UTC)

It's been a long time since I had any sort of dealing with Minkowski diagrams, but it definitely got me chuckling... I suppose you just have to appreciate Randall's particular slant. 172.70.86.10 04:45, 16 July 2022 (UTC)

You were just bound to make that kind of joke, weren't you? 162.158.146.57 05:33, 26 July 2022 (UTC)

I don't think checking in to Hilbert's Hotel provides any comfort at all. After all you are required to pack up your belongings and move to a new room a possibly infinite number of times, thus leaving you no chance to get any sleep. MAP (talk) 05:46, 16 July 2022 (UTC)

I agree, and removed "The fugitives of the first ship may enjoy a more comfortable getaway if they check into Hilbert's Hotel." because the hotel paradox has nothing to do with Hilbert space or anything else in the comic. I also think the subsection should be removed as misleading, but I'm waiting on someone to perhaps proofread it as maybe it's just poorly drafted. 172.70.210.233 06:06, 16 July 2022 (UTC)

If the pursuer knows what the prefered "move and insert" algorithm is (and 'arrival number(s)' used in that), then they can go immediately to the pursued's room, without bothering to book in themselves. So maybe that's a danger. But I'd rather be in a hotel room (that is an unknown one amongst a countably infinite whole) than in a quite obvious maybe-reachable tin can in the openness of space.

(And any given insertion of new residents needs only a single move at a time, no matter how many nested infinities of arrivals/transports/etc. So moving every now and then isn't so onerous, so long as housekeeping has an infinite number of staff to clean and prepare each new room each time, which they probably can with evenly distributed live-in staff alone.)

That said, it seems to be more the ubiquity of Hilbert in mathematical constructs than a direct link, him seemingly having an infinite number of fingers in an infinite number of infinite-pies. Probably no loss. 162.158.159.137 12:14, 16 July 2022 (UTC)

An infinite housekeeping staff would either be able to so easily keep up with the rooms that the hotel could give them infinite paid vacation, or they'd all be working 24 hours a day and still getting farther and farther behind on the cleaning, depending on how the housekeeping staff's infinity is defined. Dansiman (talk) 21:19, 18 July 2022 (UTC)

On position alone, "Closer?" could be Voice 1, "Reference" is Voice 2 (both from the cockpit) and "Tell" a new voice (from further behind, passenger/engineer?). Which matches (and adds to) the original dialogue, with Voice 2 being the experienced captain reacting to the more worried copilot/operator next to him, etc. Except that Voice 2 says "On my mark" but then their presumed "Mark" emits elsewhere (to leave room for the actual click, which I'd expect Voice 1 to make). I have sympathy with Randall, if he actually wanted to put this story down in accurate visuals and yet positionally keep to conventions (having a top-down reading experience) he'd need to either wrap speech-lines around the nose of the craft or (...might need some intermediate frame showing some 'acrobatic' drawing...) have the evading craft flip inverted for the current second frame. Could get more complex than 'necessary', just to leave us with less of a voice-ID mystery where it probably matters very little in the long run. 172.70.162.155 12:51, 16 July 2022 (UTC)

Hilbert space sounds like the Infinite Probability Drive. 108.162.238.16 13:46, 16 July 2022 (UTC)

How long should I wait before getting worried about not returning to normality? 15635176 (talk) 15:30, 18 July 2022 (UTC)

At first I wondered if this was a reference to the Wolf 359 podcast ([1]), which has a couple of characters named Minkowski and Hilbert. But it's likely that those names are references to these different kinds of space. ShifterCat (talk) 16:30, 16 July 2022 (UTC)

that was what I thought too, then I had the same train of thought. At least I wasnt the only one lol 172.69.71.30 03:28, 18 July 2022 (UTC)

I disagree with the explanation! We are not living in the Minkowski space but in the Minkowski spacetime. This little detail lead into misunderstanding of the joke. In Minkowski space there is one cordinate with different signature to others. We use this in relativistic physics for the time coordinate to explain many phenomenons in relativistic physics. But in this comics we swap into Minkowski SPACE. It is even more obvious from pictures that strange deferomation happens when we are closer to the diagonal direction. We know this deformation on the spacetime diagram but this one displays whole ship in its spece-like character. So it is not trivial to do such a jump into Minkowski space and it changes the situation! On top of that the distance is usually invariant and indepenedent on reference frame for the given geometry. So the last frame may be a bit strange becouse it looks like a false statement. But it makes sense if you think about it. If we think about "reference frame" in common comics language the reference frame in comics language basically means mention of different frames we picture. And we changed the goemetry between frames. So the geometry itself may cause that distance is independend on reference frame but the fact that we changed the geometry between frames causes that the distance of both ships may depend on such a thing as reference frame. The joke is ingenious! But for completely different reasons that are presented in here.MBas (talk) 10:29, 20 July 2022 (UTC)

I really wish I understood what you're trying to say. Is there a source which explains the distinction between Minkowski space and Minkowski spacetime you're trying to draw? Even 1-D Minkowski space is always taken to mean a 2-D spacetime, isn't it? 172.70.211.90 06:03, 24 July 2022 (UTC)

As a mathematician, jumping to "Hilbert space" is a weird comment is a weird comment as there's multiple Hilbert spaces. In fact, any finite dimensional space is Hilbert (a fact that's taught in math undergrads at R1s). Even if take it to mean that it's infinite dimensional, there are infinitely many Hilbert spaces, so the only joke to infer is the one referring to number of dimensions.