[ExI] Time Travel Reconsidered

[BillK]

On Wed, 4 Nov 2026 at 14:51, Adrian Tymes via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> On Wed, Nov 4, 2026 at 5:09 AM BillK via extropy-chat
> <extropy-chat at lists.extropy.org> wrote:
> > 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.
>
> But it does allow interaction with your past self.
>
> > That would just be regular spatial travel.
>
    Regular spatial travel specifically does not involve returning to the

> same time, regardless of spatial coordinates.
>
> > 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.
>
> Nope.  Returning to (u=100,x=11,y=10,z=10) - notice the very slightly
> different x - would suffice.
>
> > 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.
>
> You can interact without being in the exact same position.
> _______________________________________________



Qwen went away and had a big think. Significantly longer than previous
responses.
Short answer is that Qwen agreed with your criticisms but said they
describe situations that are specifically forbidden by Zhang's theorem.
Which is why the theorem claims that time travel in our universe is
impossible.
Therefore, you need to disprove the assumptions in Zhang's theorem.
BillK

Qwen3.8 Max Thinking:

Yes — that criticism is largely correct, and it exposes an imprecise way of
explaining the theorem. The right response is:

*You do not need to return to the exact same spacetime point to interact
with your past self. But Zhang’s theorem, if its assumptions hold, rules
out that weaker “visit the past nearby” scenario too.*

The theorem is not merely saying “you cannot stand in your exact old
footprints.” Its mathematical core is stronger: *a certain null coordinate
cannot be revisited at all by any future-directed timelike traveler, not
even at a slightly different spatial location.*
------------------------------
1. What the criticism gets rightA. Interaction does not require exact
coincidence
Correct. To interact with your 10-year-old self, you do not need to occupy
the exact same event. You only need to be in the same past region and be
able to exchange signals or forces. If your younger self is at
A=(u=100,x=10,y=10,z=10)
and your older self arrives at
C=(u=100,x=11,y=10,z=10),
then, depending on the causal structure, your older self may be able to
shout, throw a rock, send a light signal, or otherwise affect the younger
self shortly afterward. Exact overlap is not required.
So the earlier claim that the worldline must intersect the exact same event
was too narrow if the goal is “meet or affect your past self.”
------------------------------
B. Ordinary spatial travel does not mean “same time, different place”
Also correct. Normal spatial travel through spacetime is still travel along
a future-directed timelike worldline. You move through space, but you also
move forward in time. In a spacetime with a well-behaved global time-like
or null coordinate, your coordinate does not remain fixed while you travel
as a massive object.
So if someone says, “I traveled spatially and returned to the same time but
a different place,” that is not ordinary spatial travel. That would already
be a violation of the usual causal ordering.
------------------------------
2. What the theorem actually proves
The theorem assumes there exists a global function u whose gradient is null
everywhere:
gab∂au∂bu=0.
This u is a “light-based” coordinate. Its level surfaces are null
hypersurfaces — roughly, surfaces swept out by light fronts.
Now take a massive observer moving along a future-directed timelike curve
with tangent vector Va. The rate of change of u along that observer’s path
is
dτdu=Va∂au.
The key algebraic fact is:

A null covector cannot be orthogonal to a timelike vector.

Therefore,
Va∂au=0.
Because the future timelike cone is connected, the sign of this quantity
cannot change. So after choosing the time orientation,
dτdu>0
along every future-directed timelike curve.
That means u is strictly monotonic along any physical observer’s worldline.
------------------------------
3. This rules out “same u, different place” too
Suppose your younger self is at
A=(u=100,x=10,y=10,z=10).
Your older self later reaches
B=(u=500,x=80,y=20,z=5).
Now the older self tries to travel to a nearby past event:
C=(u=100,x=11,y=10,z=10).
This is exactly the kind of scenario you described: not the same spatial
point, but close enough to interact.
But to go from B to C, the older self’s worldline would have to satisfy
u(B)=500,
and later
u(C)=100.
That would require
Δu=−400.
But the theorem says that along any future-directed timelike path,
Δu>0.
So the path B→C is impossible in any spacetime satisfying the theorem’s
hypothesis.
The theorem does not merely say:

You cannot return to (u=100,x=10,y=10,z=10).

It says:

You cannot return to u=100 at x=10, x=11, x=90, or anywhere else.

Once you have passed from u=100 to u=500, the value u=100 is permanently
behind you. No future-directed timelike journey can bring you back to that
null slice.
------------------------------
4. What about signals?
You might say:

Fine, maybe the older self cannot physically travel there, but could they
send a signal to the past?

No — at least not in the class of spacetimes covered by the theorem.
For future-directed causal curves, which include both timelike and null
curves, the function u is non-decreasing:
dλdu≥0.
It is strictly increasing for massive travelers, and it can remain constant
only along special null directions tangent to the null hypersurfaces.
So if the older self is at u=500, any signal they send into the future must
go to events with
u≥500.
It cannot go to an event with
u=100.
Therefore, the theorem also rules out sending messages to the past, not
merely physically traveling to the past.
------------------------------
5. “Same u, different place” is not automatically interaction
There is one additional subtlety.
If two events have the same u but different spatial coordinates, they are
on the same null hypersurface. But that does not automatically mean they
can interact instantaneously. In relativity, interaction is local and
causal. If the events are spacelike separated, no signal can pass between
them with zero elapsed u.
So if the older self arrives at
C=(u=100,x=11,y=10,z=10),
and the younger self is at
A=(u=100,x=10,y=10,z=10),
they may be spatially close, but whether they can interact immediately
depends on the metric and on whether A and C are causally related.
However, this subtlety does not rescue time travel, because the older self
cannot get from B at u=500 to C at u=100 in the first place.
Even if the older self only needs to arrive slightly after the younger
self’s event, say
C=(u=101,x=10.1,y=10,z=10),
that is still much earlier than u=500. The trip
u=500→u=101
is still forbidden.
So the issue is not “Can they interact once nearby?” The issue is “Can they
reach that earlier era at all?” The theorem says no.
------------------------------
6. Closed timelike curves versus “visiting the past”
There is a distinction between the formal definition and the informal idea
of time travel.
Formal definition
A *closed timelike curve* is a timelike curve that loops back to its
starting event. In that strict mathematical sense, yes, the curve is
closed: after one loop, all global coordinates return to their original
values.
That is why the article says something like:

No journey can return to its starting event.

That is the standard CTC language.
Informal time travel
But in the informal sense, “time travel” usually means something like:

I, an older person, can enter the era of my younger self and interact with
them.

For that, exact return to the original event is not necessary. Arriving
nearby in the past may be enough.
Your criticism correctly points that out.
But Zhang’s proof gives a stronger consequence than merely “no closed
loop.” Because u strictly increases along every future-directed timelike
curve, the theorem also forbids:

Leaving u=100, advancing to u=500, and then returning to u=100 at a
different spatial location.

So the informal “visit the past nearby” scenario is also ruled out in any
spacetime admitting such a global null coordinate.
------------------------------
7. If such a trip were possible, the theorem’s assumptions would fail
Suppose someone constructs a spacetime where an observer can go from
B=(u=500,…)
to
C=(u=100,…)
and then interact with their younger self nearby.
That would not be a counterexample to Zhang’s theorem. It would mean that
the spacetime does *not* satisfy the theorem’s hypothesis. Specifically, it
would mean that there is no globally defined single-valued function u with
everywhere-null gradient that remains well behaved along the relevant
region.
That is exactly where the “escape routes” come in:

   1. *Twist:* the null direction field twists so that no global null
   foliation exists.
   2. *Topology:* the spacetime is identified in such a way that the
   would-be null coordinate is not globally single-valued.

If you can return to the same null slice at a different spatial point after
having advanced to a later slice, then one of those loopholes must be
present.
------------------------------
8. The corrected way to state the result
The criticism shows that the explanation should not be phrased as:

You cannot return to the exact same point, therefore no time travel.

That is too weak, because interaction with the past does not require exact
point-return.
A better phrasing is:

If a spacetime admits a global null coordinate u, then u acts like a
one-way ratchet along every future-directed timelike worldline. Once you
leave a given u-slice, you can never return to that slice again — not at
the same place, not at a nearby place, not anywhere. Therefore you cannot
enter your own past era, even slightly displaced in space.

Or even shorter:

The theorem does not merely prevent you from standing in your exact old
footprints. It prevents you from crossing back through the same
light-slice, even one meter to the left.

------------------------------
Bottom line
The criticism is right that:

   - interaction with the past does not require exact spatial coincidence;
   - returning to the same “time” at a different place would not be
   ordinary spatial travel;
   - a time traveler could in principle affect their past self from nearby.

But the theorem still answers that criticism, because the proof does not
rely on exact return to the original event. It proves that the null
coordinate u strictly increases along any physical observer’s path.
Therefore, in the class of universes covered by the theorem, a traveler
cannot return to the same u-slice at a different spatial coordinate either.
So the nearby-past scenario is not a surviving form of time travel under
the theorem. It is precisely another thing the theorem forbids.
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