[ExI] Time Travel Reconsidered

[BillK]

On Wed, 4 Nov 2026 at 00:03, Adrian Tymes via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> > It is mathematically impossible for an observer to travel along a path
> and return to the exact same starting value of this coordinate.
>
> That description seems to leave a large loophole: one can not return
> to the exact same position at the exact same time, but that is not
> what is often meant by "time travel" through a closed timelike curve.
> You instead wind up at some other spatial coordinate at the exact same
> time: you may be beside yourself, but you could no more occupy the
> same space at the same time as you formerly occupied it, than you can
> occupy the same space as some other object at the same time it is
> there.
> ________________________________________
>

I gave your comment to Qwen AI and asked for an explanation.
The answer was complicated, as time travel usually gets weird!
BillK

Qwen3.8 Max Thinking:

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.
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.
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 *moment in
time*, a *spacetime event*, and how a *null coordinate* behaves.
Here is the breakdown of why the math works and what it actually means.
1. The Geometry of the "Track" vs. The "Passenger"
First, let's address your point about occupying the same space.

   - *The Passenger (Matter):* 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.
   - *The Track (Spacetime Geometry):* 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 *exact same 4D Event*.

An "Event" in relativity is a specific point in space *and* 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 *track itself* cannot loop
back.
2. What is the "Light-Based Coordinate" (u)?
In this theorem, the physicist is using a *null coordinate*, let's call it u.
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.

   - Slice 1 is light wave u=1.
   - Slice 2 is light wave u=2.
   - Slice 3 is light wave u=3.

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 u=1, to u=2, to u=3.
*The Math (The "Strictly Increasing" Rule):* 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 *never* run parallel to
these light slices. Therefore, your journey through the u coordinate is
strictly monotonic. *Like a taxi meter, the value of u can only ever tick
upward (or downward) along your path.* It can never stop, and it can never
reverse.
3. Why This Destroys the CTC (The Contradiction)
Now, let's look at what a Closed Timelike Curve (a time machine) requires.
A CTC is a closed loop in 4D spacetime. If you get in a time machine, fly
around, and return to the exact same *Event* (the exact same place and the
exact same time) to high-five your past self, you have completed a closed
loop.
Because you have returned to the exact same starting point in spacetime, *every
single global coordinate must return to its exact starting value.* (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).
Here is the fatal contradiction that Zhang's math exposes:

   1. To complete a time loop (CTC), the light-coordinate u *must* return
   to its starting value (e.g., start at u=5, travel, and end at u=5).
   2. The math proves that for any physical observer, the
light-coordinate u *strictly
   increases* (e.g., start at u=5, travel, and end at u=8).

*You cannot complete a closed loop in spacetime if one of the required
coordinates is strictly forbidden from returning to its starting number.*
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.
Summary
The theorem does not say "you will end up in the wrong place." It says: *"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."*
By proving that this "light coordinate" must strictly increase, the
physicist mathematically severs the track before the loop can ever close.
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