https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&feed=atom&action=history2646: Minkowski Space - Revision history2024-03-28T10:00:01ZRevision history for this page on the wikiMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=338088&oldid=prev1234231587678 at 00:42, 25 March 20242024-03-25T00:42:35Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The title text is a status report from someone in the pursuing spaceship to their leader (whom they call "my {{w|Homage (feudal)|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 {{w|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.  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The title text is a status report from someone in the pursuing spaceship to their leader (whom they call "my {{w|Homage (feudal)|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 {{w|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.  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">As </del>in <del class="diffchange diffchange-inline">the </del>[[2577:_Sea_Chase<del class="diffchange diffchange-inline">|Sea Chase</del>]] <del class="diffchange diffchange-inline">comic</del>, <del class="diffchange diffchange-inline">there was also more than one type </del>of space to <del class="diffchange diffchange-inline">jump </del>to <del class="diffchange diffchange-inline">here</del>.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">A similar situation happened </ins>in [[2577:_Sea_Chase]], <ins class="diffchange diffchange-inline">where instead </ins>of <ins class="diffchange diffchange-inline">jumping from </ins>space to <ins class="diffchange diffchange-inline">space, ships jumped from map projection </ins>to <ins class="diffchange diffchange-inline">map projection</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Transcript==</div></td></tr>
</table>1234231587678https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=331212&oldid=prev141.101.98.63: /* Transcript */ Meant to remove the 'repeated' info (originally broke the description flow). Also meant to redefine the lower engines as nacelles (could be propulsion, floats/landing-gear or anything else, depending upon in-universe 'mechanics').2023-12-20T17:55:49Z<p><span dir="auto"><span class="autocomment">Transcript: </span> Meant to remove the 'repeated' info (originally broke the description flow). Also meant to redefine the lower engines as nacelles (could be propulsion, floats/landing-gear or anything else, depending upon in-universe 'mechanics').</span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Transcript==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:[A spaceship is being pursued by another spaceship of similar size but <del class="diffchange diffchange-inline">subtly </del>different design. Both ships have a black part in the front representing a window<del class="diffchange diffchange-inline">. They are the same size but different designs</del>. The pursued spaceship to the right has two <del class="diffchange diffchange-inline">engines </del>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.]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:[A spaceship is being pursued by another spaceship of similar size but <ins class="diffchange diffchange-inline">distinctly </ins>different design. Both ships have a black part in the front representing a window. The pursued spaceship to the right has two <ins class="diffchange diffchange-inline">nacelles </ins>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.]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Voice 1: The enemy ship is right behind us!  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Voice 1: The enemy ship is right behind us!  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Voice 2: Prepare to jump to Minkowski space on my mark.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Voice 2: Prepare to jump to Minkowski space on my mark.</div></td></tr>
</table>141.101.98.63https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=331211&oldid=prev141.101.98.62: /* Transcript */ Meaningful that they are different. Similar enough in size/type (c.f. "shuttlecraft") that velocities won't really be vastly different, but not identical thus suggesting either opposing sides in a conflict or maybe police/etc vs. civilian2023-12-20T17:51:21Z<p><span dir="auto"><span class="autocomment">Transcript: </span> Meaningful that they are different. Similar enough in size/type (c.f. "shuttlecraft") that velocities won't really be vastly different, but not identical thus suggesting either opposing sides in a conflict or maybe police/etc vs. civilian</span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Transcript==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Transcript==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:[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.]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:[A spaceship is being pursued by another spaceship <ins class="diffchange diffchange-inline">of similar size but subtly different design</ins>. 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.]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Voice 1: The enemy ship is right behind us!  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Voice 1: The enemy ship is right behind us!  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Voice 2: Prepare to jump to Minkowski space on my mark.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Voice 2: Prepare to jump to Minkowski space on my mark.</div></td></tr>
</table>141.101.98.62https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=331208&oldid=prev172.69.214.29: /* Explanation */ The deleted comment made no sense as Euclidean 3-dimension is a Hilbert space, and we most definitely represent physical objects there.2023-12-20T17:36:47Z<p><span dir="auto"><span class="autocomment">Explanation: </span> The deleted comment made no sense as Euclidean 3-dimension is a Hilbert space, and we most definitely represent physical objects there.</span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The mention of distance depending on the observer's frame of reference refers to distances changing when measured in different {{w|inertial frame of reference|inertial frames of reference}}, a concept called the {{w|relativity of simultaneity}}. Here are [https://www.youtube.com/watch?v=asW78vToNLQ some videos] intended [https://www.youtube.com/watch?v=Xrqj88zQZJg 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.{{cn}}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The mention of distance depending on the observer's frame of reference refers to distances changing when measured in different {{w|inertial frame of reference|inertial frames of reference}}, a concept called the {{w|relativity of simultaneity}}. Here are [https://www.youtube.com/watch?v=asW78vToNLQ some videos] intended [https://www.youtube.com/watch?v=Xrqj88zQZJg 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.{{cn}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The title text is a status report from someone in the pursuing spaceship to their leader (whom they call "my {{w|Homage (feudal)|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 {{w|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<del class="diffchange diffchange-inline">. However, Hilbert space is a mathematical construct used to describe objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it would be very unusual for a physical object to be represented in Hilbert space. Quantum states can be represented as vectors in Hilbert spaces, so it might relate to the {{w|uncertainty principle}} concerning how the escaped spaceship could be anywhere</del>.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The title text is a status report from someone in the pursuing spaceship to their leader (whom they call "my {{w|Homage (feudal)|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 {{w|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.  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>As in the [[2577:_Sea_Chase|Sea Chase]] comic, there was also more than one type of space to jump to here.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>As in the [[2577:_Sea_Chase|Sea Chase]] comic, there was also more than one type of space to jump to here.</div></td></tr>
</table>172.69.214.29https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=297941&oldid=prev172.70.218.167: /* Explanation */2022-11-01T17:00:50Z<p><span dir="auto"><span class="autocomment">Explanation</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Explanation==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Explanation==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{w|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 {{w|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 {{w|Minkowski space}} which is actually just conventional 3-D space together with time combined into a mathematical object called a {{w|manifold}} used in {{w|special relativity}}. Because Minkowski space is merely a representation of real physical {{w|spacetime}}, "jumping" into it is meaningless and offers no benefit for escaping pursuit, providing the humor of the comic's absurdist joke.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{w|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 {{w|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 {{w|Minkowski space}} which is actually just conventional 3-D space together with time combined into a mathematical object called a {{w|manifold}} used in {{w|special relativity}}. Because Minkowski space is merely a representation of real physical {{w|spacetime}}, "jumping" into it is meaningless and offers no benefit for escaping pursuit, providing the humor of the comic's absurdist joke.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>172.70.218.167https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=293683&oldid=prev162.158.178.27: Undo revision 293343 by 172.70.207.8 (talk) Having the omniscience to say that so definitively must be nice.2022-08-29T21:53:23Z<p>Undo revision 293343 by <a href="/wiki/index.php/Special:Contributions/172.70.207.8" title="Special:Contributions/172.70.207.8">172.70.207.8</a> (<a href="/wiki/index.php?title=User_talk:172.70.207.8&action=edit&redlink=1" class="new" title="User talk:172.70.207.8 (page does not exist)">talk</a>) Having the omniscience to say that so definitively must be nice.</p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{w|Faster than light travel}}, an impossibility, is often portrayed in science fiction by having spaceships enter (or "jump") into some different realm, termed "hyperspace" or similar {{w|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 {{w|Minkowski space}} which is actually just conventional 3-D space together with time combined into a mathematical object called a {{w|manifold}} used in {{w|special relativity}}. Because Minkowski space is merely a representation of real physical {{w|spacetime}}, "jumping" into it is meaningless and offers no benefit for escaping pursuit, providing the humor of the comic's absurdist joke.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{w|Faster than light travel}}, an impossibility <ins class="diffchange diffchange-inline">in our universe</ins>, is often portrayed in science fiction by having spaceships enter (or "jump") into some different realm, termed "hyperspace" or similar {{w|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 {{w|Minkowski space}} which is actually just conventional 3-D space together with time combined into a mathematical object called a {{w|manifold}} used in {{w|special relativity}}. Because Minkowski space is merely a representation of real physical {{w|spacetime}}, "jumping" into it is meaningless and offers no benefit for escaping pursuit, providing the humor of the comic's absurdist joke.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The visual depiction of the spaceships skewed diagonally is based on the graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}.  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The visual depiction of the spaceships skewed diagonally is based on the graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}.  </div></td></tr>
</table>162.158.178.27https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=293343&oldid=prev172.70.207.8: /* Explanation */ wat2022-08-24T06:47:19Z<p><span dir="auto"><span class="autocomment">Explanation: </span> wat</span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 06:47, 24 August 2022</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{w|Faster than light travel}}, an impossibility <del class="diffchange diffchange-inline">in our universe</del>, is often portrayed in science fiction by having spaceships enter (or "jump") into some different realm, termed "hyperspace" or similar {{w|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 {{w|Minkowski space}} which is actually just conventional 3-D space together with time combined into a mathematical object called a {{w|manifold}} used in {{w|special relativity}}. Because Minkowski space is merely a representation of real physical {{w|spacetime}}, "jumping" into it is meaningless and offers no benefit for escaping pursuit, providing the humor of the comic's absurdist joke.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{w|Faster than light travel}}, an impossibility, is often portrayed in science fiction by having spaceships enter (or "jump") into some different realm, termed "hyperspace" or similar {{w|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 {{w|Minkowski space}} which is actually just conventional 3-D space together with time combined into a mathematical object called a {{w|manifold}} used in {{w|special relativity}}. Because Minkowski space is merely a representation of real physical {{w|spacetime}}, "jumping" into it is meaningless and offers no benefit for escaping pursuit, providing the humor of the comic's absurdist joke.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The visual depiction of the spaceships skewed diagonally is based on the graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}.  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The visual depiction of the spaceships skewed diagonally is based on the graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}.  </div></td></tr>
</table>172.70.207.8https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=290896&oldid=prev162.158.107.30: /* Explanation */ not sure; perspective and choice of projection play big roles2022-07-27T09:45:33Z<p><span dir="auto"><span class="autocomment">Explanation: </span> not sure; perspective and choice of projection play big roles</span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 09:45, 27 July 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l14" >Line 14:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The visual depiction of the spaceships skewed diagonally is based on the graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}.  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The visual depiction of the spaceships skewed diagonally is based on the graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}.  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The mention of distance depending on the observer's frame of reference refers to distances changing when measured in different {{w|inertial frame of reference|inertial frames of reference}}, a concept called the {{w|relativity of simultaneity}}. Here are [https://www.youtube.com/watch?v=asW78vToNLQ some videos] intended [https://www.youtube.com/watch?v=Xrqj88zQZJg 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.  </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The mention of distance depending on the observer's frame of reference refers to distances changing when measured in different {{w|inertial frame of reference|inertial frames of reference}}, a concept called the {{w|relativity of simultaneity}}. Here are [https://www.youtube.com/watch?v=asW78vToNLQ some videos] intended [https://www.youtube.com/watch?v=Xrqj88zQZJg 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.<ins class="diffchange diffchange-inline">{{cn}}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The title text is a status report from someone in the pursuing spaceship to their leader (whom they call "my {{w|Homage (feudal)|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 {{w|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. However, Hilbert space is a mathematical construct used to describe objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it would be very unusual for a physical object to be represented in Hilbert space. Quantum states can be represented as vectors in Hilbert spaces, so it might relate to the {{w|uncertainty principle}} concerning how the escaped spaceship could be anywhere.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The title text is a status report from someone in the pursuing spaceship to their leader (whom they call "my {{w|Homage (feudal)|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 {{w|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. However, Hilbert space is a mathematical construct used to describe objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it would be very unusual for a physical object to be represented in Hilbert space. Quantum states can be represented as vectors in Hilbert spaces, so it might relate to the {{w|uncertainty principle}} concerning how the escaped spaceship could be anywhere.</div></td></tr>
</table>162.158.107.30https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=290867&oldid=prev172.70.130.91: Corrected title2022-07-26T14:53:43Z<p>Corrected title</p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| number    = 2646</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| number    = 2646</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| date      = July 15, 2022</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| date      = July 15, 2022</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| title    = Minkowski<del class="diffchange diffchange-inline">'s </del>Space</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| title    = Minkowski Space</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| image    = minkowski_space.png</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| image    = minkowski_space.png</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| titletext = 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.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| titletext = 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.</div></td></tr>
</table>172.70.130.91https://www.explainxkcd.com/wiki/index.php?title=2646:_Minkowski_Space&diff=290816&oldid=prevNErDysprosium at 05:13, 26 July 20222022-07-26T05:13:49Z<p></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 05:13, 26 July 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2" >Line 2:</td>
<td colspan="2" class="diff-lineno">Line 2:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| number    = 2646</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| number    = 2646</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| date      = July 15, 2022</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| date      = July 15, 2022</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| title    = Minkowski's <del class="diffchange diffchange-inline">Cum</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| title    = Minkowski's <ins class="diffchange diffchange-inline">Space</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| image    = minkowski_space.png</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| image    = minkowski_space.png</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| titletext = 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.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| titletext = 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.</div></td></tr>
</table>NErDysprosium