<div dir="ltr"><div dir="ltr"><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, 4 Nov 2026 at 01:38, Adrian Tymes via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org" target="_blank">extropy-chat@lists.extropy.org</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="auto"><div dir="auto"></div><div dir="auto">And that analysis missed the objection.</div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto">The objection does not discuss returning to the exact same 4D coordinate.</div><div dir="auto"></div><div class="gmail_quote" dir="auto"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)"><div></div><h3 dir="ltr"><span><span>4. Correcting the "Beside Yourself" Misconception</span></span></h3><div dir="ltr"><span><span>You mentioned: </span></span><i dir="ltr"><span><span>"You instead wind up at some other spatial coordinate at the exact same time."</span></span></i></div><div></div><div dir="ltr"><span><span>This is where the translation from math to English gets tricky. The null coordinate </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> is not "time" in the traditional sense; it is a mixture of space and time (a light wave). </span></span></div><div></div><div dir="ltr"><span><span>If you travel on a path where </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> increases, but you somehow magically managed to return to your starting spatial coordinates (</span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.625em;vertical-align:-0.1944em"></span><span>x</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.044em">z</span></span></span></span></span><span><span>), you would </span></span><b dir="ltr"><span><span>not</span></span></b><span><span> be at the "same time." Because your </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> coordinate has increased (say, from 5 to 8), you are now intersecting a completely different light wave. In the geometry of that universe, you have arrived in the </span></span><b dir="ltr"><span><span>future</span></span></b><span><span>. </span></span></div><div></div><div dir="ltr"><span><span>To arrive in the </span></span><i dir="ltr"><span><span>past</span></span></i><span><span> (to form a CTC), you would have to travel backward through the light waves (from </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>8</span></span></span></span></span><span><span> back down to </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>5</span></span></span></span></span><span><span>). But the "three lines of math" prove that the geometry of the universe physically forbids a massive object from moving backward through a light wave.</span></span></div></div></div></div></blockquote></div><div dir="auto"><br></div><div dir="auto">The form of time travel in the objection is not returning to the same (u,x,y,z).  It is returning to the same u at some other (x,y,z).</div><div class="gmail_quote" dir="auto"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
</blockquote></div></div>
_______________________________________________<br></blockquote><div><br></div><div><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default">Qwen tries to explain your objection.</div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default">BillK</div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default">Qwen3.8 Max Thinking:</div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><div dir="ltr"><span><span>You are absolutely right: simply returning to the same "time" (</span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span>) at a different "place" (</span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.625em;vertical-align:-0.1944em"></span><span>x</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.044em">z</span></span></span></span></span><span><span>) is </span></span><b dir="ltr"><span><span>not</span></span></b><span><span> a Closed Timelike Curve (CTC), nor does it allow you to interact with your past self. That would just be regular spatial travel.</span></span></div><div></div><div dir="ltr"><span><span>To understand why Zhang’s math actually destroys the "time travel" scenario (where you get to be "beside yourself"), we have to look at how physicists visualize your life through the geometry of spacetime. </span></span></div><div></div><div dir="ltr"><span><span>Here is why returning to the same </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> at a different spatial coordinate doesn't save time travel, and how the math shuts it down.</span></span></div><div></div><h3 dir="ltr"><span><span>1. The Geometry of "Meeting Yourself" (The Worldline)</span></span></h3><div dir="ltr"><span><span>In General Relativity, your entire life—past, present, and future—is represented as a single, continuous, 1-dimensional string drawn through 4-dimensional spacetime. This is called your </span></span><b dir="ltr"><span><span>worldline</span></span></b><span><span>. </span></span></div><div></div><ul dir="ltr"><li dir="ltr"><span><span>When you were 10 years old, your worldline passed through Event A: </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>(</span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>100</span><span>,</span><span style="margin-right:0.1667em"></span><span>x</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>10</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>10</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.044em">z</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:1em;vertical-align:-0.25em"></span><span>10</span><span>)</span></span></span></span></span><span><span>.</span></span></li><li dir="ltr"><span><span>When you are 40 years old, your worldline is currently at Event B: </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>(</span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>500</span><span>,</span><span style="margin-right:0.1667em"></span><span>x</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>80</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>20</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.044em">z</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:1em;vertical-align:-0.25em"></span><span>5</span><span>)</span></span></span></span></span><span><span>.</span></span></li></ul><div></div><div dir="ltr"><span><span>To "time travel" and stand "beside yourself" to shake hands with your 10-year-old self, your current worldline must physically </span></span><b dir="ltr"><span><span>intersect</span></span></b><span><span> the older, already-drawn part of your worldline. </span></span></div><div></div><div dir="ltr"><span><span>In 4D geometry, for two segments of the same line to cross, they must cross at one specific, exact point in 4D space. Therefore, to meet your 10-year-old self, your 40-year-old self must travel to </span></span><b dir="ltr"><span><span>Event A</span></span></b><span><span>. You must return to the exact same </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>(</span><span>u</span><span>,</span><span style="margin-right:0.1667em"></span><span>x</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.044em">z</span><span>)</span></span></span></span></span><span><span> coordinates. </span></span></div><div></div><div dir="ltr"><span><span>You cannot meet your 10-year-old self by returning to </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>100</span></span></span></span></span><span><span> at a completely different spatial location (say, </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>x</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>90</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>90</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.044em">z</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>90</span></span></span></span></span><span><span>), because </span></span><b dir="ltr"><span><span>your 10-year-old self was never at that location!</span></span></b><span><span> Your younger self was at </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>(</span><span>10</span><span>,</span><span style="margin-right:0.1667em"></span><span>10</span><span>,</span><span style="margin-right:0.1667em"></span><span>10</span><span>)</span></span></span></span></span><span><span>. If you go to a different spatial coordinate at </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>100</span></span></span></span></span><span><span>, you are just visiting an empty spot in space at a time when your younger self was somewhere else.</span></span></div><div></div><h3 dir="ltr"><span><span>2. How Zhang's Math Kills the Scenario</span></span></h3><div dir="ltr"><span><span>Now, let's apply Zhang’s "three lines of math" to this. </span></span></div><div></div><div dir="ltr"><span><span>The theorem proves that the light-based coordinate </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> acts like an </span></span><b dir="ltr"><span><span>odometer</span></span></b><span><span> for any physical observer. Because a massive observer can never move perpendicular to light, the value of </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> must strictly, continuously tick upward (or downward) along your entire worldline. It is strictly monotonic.</span></span></div><div></div><div dir="ltr"><span><span>This has devastating consequences for the time traveler:</span></span></div><ol start="1" dir="ltr"><li dir="ltr"><b dir="ltr"><span><span>You cannot return to the same </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>(</span><span>u</span><span>,</span><span style="margin-right:0.1667em"></span><span>x</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.044em">z</span><span>)</span></span></span></span></span><span><span>:</span></span></b><span><span> To meet your younger self, your odometer would have to roll backward from </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>500</span></span></span></span></span><span><span> down to </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>100</span></span></span></span></span><span><span>. The math strictly forbids this. </span></span></li><li dir="ltr"><b dir="ltr"><span><span>You cannot return to the same </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> at a different </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>(</span><span>x</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.044em">z</span><span>)</span></span></span></span></span><span><span>:</span></span></b><span><span> Because the odometer strictly ticks forward, once you pass </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>100</span></span></span></span></span><span><span>, the number </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.6444em"></span><span>100</span></span></span></span></span><span><span> is permanently in your past. You can never reach </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>100</span></span></span></span></span><span><span> again, </span></span><i dir="ltr"><span><span>anywhere in the entire universe</span></span></i><span><span>.</span></span></li></ol><div></div><div dir="ltr"><span><span>Therefore, you can never intersect your own past worldline. The "track" of your life is mathematically forced to constantly march into new, higher values of </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span>. </span></span></div><div></div><h3 dir="ltr"><span><span>3. The One Exception: The "Pac-Man" Universe</span></span></h3><div dir="ltr"><span><span>You mentioned winding up at a different spatial coordinate at the exact same time. There is actually </span></span><b dir="ltr"><span><span>one specific scenario</span></span></b><span><span> where returning to a different spatial coordinate </span></span><i dir="ltr"><span><span>would</span></span></i><span><span> allow you to meet your past self, and it perfectly aligns with the article's mention of "escape routes."</span></span></div><div></div><div dir="ltr"><span><span>Imagine the universe is topologically shaped like the screen in the classic arcade game </span></span><i dir="ltr"><span><span>Pac-Man</span></span></i><span><span>. If you walk off the right side of the screen, you instantly reappear on the left side. </span></span></div><ul dir="ltr"><li dir="ltr"><span><span>In this universe, the spatial coordinate </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>(</span><span>x</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>100</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:1em;vertical-align:-0.25em"></span><span>10</span><span>)</span></span></span></span></span><span><span> is mathematically the </span></span><b dir="ltr"><span><span>exact same physical location</span></span></b><span><span> as </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>(</span><span>x</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.8389em;vertical-align:-0.1944em"></span><span>0</span><span>,</span><span style="margin-right:0.1667em"></span><span style="margin-right:0.0359em">y</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:1em;vertical-align:-0.25em"></span><span>10</span><span>)</span></span></span></span></span><span><span>. </span></span></li><li dir="ltr"><span><span>If you traveled through space and crossed the boundary, you would return to a "different" spatial coordinate, but you would actually be standing in the exact same physical spot.</span></span></li></ul><div></div><div dir="ltr"><span><span>This is what physicists call a </span></span><b dir="ltr"><span><span>topological identification</span></span></b><span><span>, and it is the exact mechanism behind "Misner space" (one of the theoretical time machines mentioned in the article). If the universe loops back on itself spatially, you </span></span><i dir="ltr"><span><span>could</span></span></i><span><span> potentially return to your past self by traveling far enough in one direction.</span></span></div><div></div><div dir="ltr"><b dir="ltr"><span><span>However, Zhang's theorem explicitly rules this out for the universes it covers.</span></span></b><span><span> The theorem proves that if the universe's geometry allows light to form smooth, global layers (a "null foliation"), then </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> must strictly increase. This strict increase prevents the coordinate </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> from ever looping back on itself, severing the track before the "Pac-Man" loop can ever close.</span></span></div><div></div><h3 dir="ltr"><span><span>Summary</span></span></h3><div dir="ltr"><span><span>Your intuition is perfectly correct: just being at the "same time" in a "different place" isn't time travel. But Zhang’s math is even more restrictive than you thought. It doesn't just prevent you from returning to your exact starting chair; it acts as a cosmic odometer that permanently locks you out of ever experiencing that "time" (</span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span>) again, anywhere in the universe. Because you can never return to the </span></span><span dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span><span></span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span>u</span></span></span></span></span><span><span> of your past, you can never intersect your past self's worldline, making the "beside yourself" scenario geometrically impossible.</span></span></div><div dir="ltr">------------------------------</div><br></div></div></div>
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