[ExI] Time Travel Reconsidered

[BillK]

On Wed, 4 Nov 2026 at 01:38, Adrian Tymes via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> And that analysis missed the objection.
>
> The objection does not discuss returning to the exact same 4D coordinate.
>
>> 4. Correcting the "Beside Yourself" Misconception
>> You mentioned: *"You instead wind up at some other spatial coordinate at
>> the exact same time."*
>> This is where the translation from math to English gets tricky. The null
>> coordinate u is not "time" in the traditional sense; it is a mixture of
>> space and time (a light wave).
>> If you travel on a path where u increases, but you somehow magically
>> managed to return to your starting spatial coordinates (x,y,z), you
>> would *not* be at the "same time." Because your u 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 *future*.
>> To arrive in the *past* (to form a CTC), you would have to travel
>> backward through the light waves (from u=8 back down to u=5). 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.
>>
>
> 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).
>
>> _______________________________________________
>


Qwen tries to explain your objection.
BillK


Qwen3.8 Max Thinking:

You are absolutely right: simply returning to the same "time" (u) at a
different "place" (x,y,z) is *not* a Closed Timelike Curve (CTC), nor does
it allow you to interact with your past self. That would just be regular
spatial travel.
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.
Here is why returning to the same u at a different spatial coordinate
doesn't save time travel, and how the math shuts it down.
1. The Geometry of "Meeting Yourself" (The Worldline)
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 *worldline*.

   - When you were 10 years old, your worldline passed through Event A: (u=
   100,x=10,y=10,z=10).
   - When you are 40 years old, your worldline is currently at Event B: (u=
   500,x=80,y=20,z=5).

To "time travel" and stand "beside yourself" to shake hands with your
10-year-old self, your current worldline must physically *intersect* the
older, already-drawn part of your worldline.
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 *Event A*. You must
return to the exact same (u,x,y,z) coordinates.
You cannot meet your 10-year-old self by returning to u=100 at a completely
different spatial location (say, x=90,y=90,z=90), because *your 10-year-old
self was never at that location!* Your younger self was at (10,10,10). If
you go to a different spatial coordinate at u=100, you are just visiting an
empty spot in space at a time when your younger self was somewhere else.
2. How Zhang's Math Kills the Scenario
Now, let's apply Zhang’s "three lines of math" to this.
The theorem proves that the light-based coordinate u acts like an *odometer*
for any physical observer. Because a massive observer can never move
perpendicular to light, the value of u must strictly, continuously tick
upward (or downward) along your entire worldline. It is strictly monotonic.
This has devastating consequences for the time traveler:

   1. *You cannot return to the same (u,x,y,z):* To meet your younger self,
   your odometer would have to roll backward from u=500 down to u=100. The
   math strictly forbids this.
   2. *You cannot return to the same u at a different (x,y,z):* Because the
   odometer strictly ticks forward, once you pass u=100, the number 100 is
   permanently in your past. You can never reach u=100 again, *anywhere in
   the entire universe*.

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 u.
3. The One Exception: The "Pac-Man" Universe
You mentioned winding up at a different spatial coordinate at the exact
same time. There is actually *one specific scenario* where returning to a
different spatial coordinate *would* allow you to meet your past self, and
it perfectly aligns with the article's mention of "escape routes."
Imagine the universe is topologically shaped like the screen in the classic
arcade game *Pac-Man*. If you walk off the right side of the screen, you
instantly reappear on the left side.

   - In this universe, the spatial coordinate (x=100,y=10) is
   mathematically the *exact same physical location* as (x=0,y=10).
   - 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.

This is what physicists call a *topological identification*, 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 *could* potentially return to your past self by traveling far enough in
one direction.
*However, Zhang's theorem explicitly rules this out for the universes it
covers.* The theorem proves that if the universe's geometry allows light to
form smooth, global layers (a "null foliation"), then u must strictly
increase. This strict increase prevents the coordinate u from ever looping
back on itself, severing the track before the "Pac-Man" loop can ever close.
Summary
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" (u) again, anywhere in the
universe. Because you can never return to the u of your past, you can never
intersect your past self's worldline, making the "beside yourself" scenario
geometrically impossible.
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