<div dir="ltr"><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">On Wed, 4 Nov 2026 at 00:03, Adrian Tymes via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org">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">> It is mathematically impossible for an observer to travel along a path and return to the exact same starting value of this coordinate.<br>
<br>
That description seems to leave a large loophole: one can not return<br>
to the exact same position at the exact same time, but that is not<br>
what is often meant by "time travel" through a closed timelike curve.<br>
You instead wind up at some other spatial coordinate at the exact same<br>
time: you may be beside yourself, but you could no more occupy the<br>
same space at the same time as you formerly occupied it, than you can<br>
occupy the same space as some other object at the same time it is<br>
there.<br>________________________________________<br></blockquote><div><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default">I gave your comment to Qwen AI and asked for an explanation.</div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default">The answer was complicated, as time travel usually gets weird!</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">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 class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">This is an excellent observation, and it highlights one of the most common—and most confusing—conceptual hurdles when translating the math of General Relativity into plain English. </span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">You are entirely correct that simply returning to a "moment in time" while being in a different place is not a Closed Timelike Curve (CTC). If you just end up somewhere else at the same time, you haven't traveled to the past; you've just moved through space. Furthermore, your point about physical occupancy (you cannot occupy the same space as your past self) is a fundamental rule of matter. </span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">To understand why Zhang's "three lines of math" actually rules out true time travel (a CTC), we have to clarify the difference between a </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">moment in time</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">, a </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">spacetime event</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">, and how a </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">null coordinate</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> behaves.</span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Here is the breakdown of why the math works and what it actually means.</span></span></div><div class="gmail-qwen-markdown-space"></div><h3 class="gmail-qwen-markdown-heading" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">1. The Geometry of the "Track" vs. The "Passenger"</span></span></h3><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">First, let's address your point about occupying the same space. </span></span></div><ul class="gmail-qwen-markdown-list" dir="ltr"><li class="gmail-qwen-markdown-list-item" dir="ltr"><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">The Passenger (Matter):</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> You are correct that two physical objects (or two versions of you) cannot occupy the exact same physical space at the same time due to the Pauli exclusion principle and basic physics.</span></span></li><li class="gmail-qwen-markdown-list-item" dir="ltr"><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">The Track (Spacetime Geometry):</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> General Relativity does not care about the passengers; it only cares about the track. A Closed Timelike Curve (CTC) is a geometric feature of the "track" of the universe. It is a path through spacetime that loops back to the </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">exact same 4D Event</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">.</span></span></li></ul><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">An "Event" in relativity is a specific point in space </span></span><em class="gmail-qwen-markdown-em" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">and</span></span></em><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> a specific point in time (e.g., "Times Square at exactly 12:00 PM on Nov 4, 2026"). If a CTC exists, the geometry of the universe allows a continuous, forward-moving path (a timelike curve) that eventually loops back to that exact 4D coordinate. The theorem proves that the </span></span><em class="gmail-qwen-markdown-em" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">track itself</span></span></em><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> cannot loop back.</span></span></div><div class="gmail-qwen-markdown-space"></div><h3 class="gmail-qwen-markdown-heading" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">2. What is the "Light-Based Coordinate" (</span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">)?</span></span></h3><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">In this theorem, the physicist is using a </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">null coordinate</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">, let's call it </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">. 
Imagine spacetime not as a ticking clock, but as a loaf of bread, where each slice is a wave of light moving through the universe. </span></span></div><ul class="gmail-qwen-markdown-list" dir="ltr"><li class="gmail-qwen-markdown-list-item" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Slice 1 is light wave </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">1</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">.</span></span></li><li class="gmail-qwen-markdown-list-item" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Slice 2 is light wave </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">2</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">.</span></span></li><li class="gmail-qwen-markdown-list-item" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Slice 3 is light wave </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">3</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">.</span></span></li></ul><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Because you are a physical observer with mass, you move slower than light. Therefore, as you travel through spacetime, you must constantly pierce forward through these slices of light. You go from </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">1</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">, to </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">2</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">, to </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">3</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">. </span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">The Math (The "Strictly Increasing" Rule):</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> 
The core of the 3-line proof relies on the geometry of spacetime (the Lorentzian signature). It proves mathematically that a physical observer's path can </span></span><em class="gmail-qwen-markdown-em" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">never</span></span></em><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> run parallel to these light slices. Therefore, your journey through the </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> coordinate is strictly monotonic. </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Like a taxi meter, the value of </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> can only ever tick upward (or downward) along your path.</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> It can never stop, and it can never reverse.</span></span></div><div class="gmail-qwen-markdown-space"></div><h3 class="gmail-qwen-markdown-heading" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">3. Why This Destroys the CTC (The Contradiction)</span></span></h3><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Now, let's look at what a Closed Timelike Curve (a time machine) requires. </span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">A CTC is a closed loop in 4D spacetime. If you get in a time machine, fly around, and return to the exact same </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Event</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> (the exact same place and the exact same time) to high-five your past self, you have completed a closed loop. </span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Because you have returned to the exact same starting point in spacetime, </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">every single global coordinate must return to its exact starting value.</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> (Just like if you walk in a circle around your neighborhood and end up back on your front porch, your GPS coordinates must be exactly what they were when you left).</span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Here is the fatal contradiction that Zhang's math exposes:</span></span></div><ol class="gmail-qwen-markdown-list" start="1" dir="ltr"><li class="gmail-qwen-markdown-list-item" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">To complete a time loop (CTC), the light-coordinate </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">must</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> return to its starting value (e.g., start at </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">5</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">, travel, and end at </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">5</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">).</span></span></li><li class="gmail-qwen-markdown-list-item" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">The math proves that for any physical observer, the light-coordinate </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">strictly increases</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> (e.g., start at </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">5</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">, travel, and end at </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">8</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">).</span></span></li></ol><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">You cannot complete a closed loop in spacetime if one of the required coordinates is strictly forbidden from returning to its starting number.</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> </span></span></div><div class="gmail-qwen-markdown-space"></div><h3 class="gmail-qwen-markdown-heading" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">4. Correcting the "Beside Yourself" Misconception</span></span></h3><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">You mentioned: </span></span><em class="gmail-qwen-markdown-em" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">"You instead wind up at some other spatial coordinate at the exact same time."</span></span></em></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">This is where the translation from math to English gets tricky. The null coordinate </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> is not "time" in the traditional sense; it is a mixture of space and time (a light wave). </span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">If you travel on a path where </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> increases, but you somehow magically managed to return to your starting spatial coordinates (</span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="gmail-mord gmail-mathnormal">x</span><span class="gmail-mpunct">,</span><span class="gmail-mspace" style="margin-right:0.1667em"></span><span class="gmail-mord gmail-mathnormal" style="margin-right:0.0359em">y</span><span class="gmail-mpunct">,</span><span class="gmail-mspace" style="margin-right:0.1667em"></span><span class="gmail-mord gmail-mathnormal" style="margin-right:0.044em">z</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">), you would </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">not</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> be at the "same time." Because your </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> 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><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">future</span></span></strong><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">. </span></span></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">To arrive in the </span></span><em class="gmail-qwen-markdown-em" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">past</span></span></em><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> (to form a CTC), you would have to travel backward through the light waves (from </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">8</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node"> back down to </span></span><span class="gmail-qwen-markdown-latex" dir="ltr" style="display:inline-block;overflow-x:visible;max-width:100%"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.4306em"></span><span class="gmail-mord gmail-mathnormal">u</span><span class="gmail-mspace" style="margin-right:0.2778em"></span><span class="gmail-mrel">=</span><span class="gmail-mspace" style="margin-right:0.2778em"></span></span><span class="gmail-katex-base"><span class="gmail-katex-strut" style="height:0.6444em"></span><span class="gmail-mord">5</span></span></span></span></span><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">). 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 class="gmail-qwen-markdown-space"></div><h3 class="gmail-qwen-markdown-heading" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">Summary</span></span></h3><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">The theorem does not say "you will end up in the wrong place." 
It says: </span></span><strong class="gmail-qwen-markdown-strong" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">"To travel to the past, your path through spacetime must loop back to your exact starting event. But the geometric rules of light dictate that your path must constantly cross into 'newer' layers of light. Because you can never cross back into an 'older' layer of light, you can never return to your starting event. Therefore, the loop is broken."</span></span></strong></div><div class="gmail-qwen-markdown-space"></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">By proving that this "light coordinate" must strictly increase, the physicist mathematically severs the track before the loop can ever close.</span></span></div><div class="gmail-qwen-markdown-paragraph" dir="ltr"><span class="gmail-qwen-markdown-text"><span class="gmail-qwen-markdown-text-node">---------------------------------------</span></span></div><br></div></div></div>