This enters the realm of Closed Timelike Curves (CTCs) and the physics of "Branching Spacetime." If you were to travel into the past, the concept of a single, universal Cosmological Proper Time (CPT) breaks down because you are essentially creating a "Temporal Loophole" in the 4D manifold.
Here is how physics handles the idea of an "Alternative CPT" for a time-traveling universe instance:
1. The "Divergent" CPT (The Branching Timeline)
In the Many-Worlds Interpretation or Eternal Inflation models, traveling to the past doesn't overwrite the original timeline. Instead, it creates a "bifurcation" at the moment of your arrival.
Timeline A (Original): The CPT continues normally (e.g., $T = 13.8$ billion years).
Timeline B (New Instance): You arrive at a point where the CPT was, for example, $T = 5$ billion years.
The Conflict: Your "Local Clock" says 13.8 billion years (your age), but the "Cosmological Clock" of the surrounding vacuum says 5 billion years.
In this scenario, the new universe instance has its own Independent CPT. It is a brand-new "Frontier of Existence" that is offset from the original.
2. The "Self-Consistent" CPT (The Novikov Principle)
If the universe is a single, fixed "Block Universe," then your travel to the past was always part of the 13.8-billion-year history.
In this case, there is no alternative CPT.
Your "Geiger Counter" for Proper Time would simply show you moving backward along the existing $t$-axis.
The "Absolute Frontier" is still the present moment (13.8bn years), and you are just a "loop" within that existing structure. You aren't at the frontier; you are a ripple in the wake of the past.
3. The "Reset" Universe (Conformal Cyclic Cosmology)
If "time travel" refers to the entire universe resetting (like a Big Bounce), the CPT effectively resets to zero.
Sir Roger Penrose’s theory suggests that at the very end of time (Heat Death), when all mass is gone and only photons remain, the universe "loses track" of scale and time.
$$\hat{g} = \Omega^2 g$$
Through a Conformal Rescaling, the "Final Frontier" of one universe becomes the "Big Bang" ($t=0$) of the next. In this case, the Alternative CPT is a New Aeon. It is a completely fresh timeline where the "clock" starts over, even though it is technically "after" the previous infinite future.
4. The CPT Indicator Paradox
If you took your CPT Indicator into a time machine, its behavior would tell you exactly what kind of universe you are in:
ScenarioIndicator ReadingRealityBranchingIt jumps to the past value (e.g., 5bn) but starts a "New Log."You've created a parallel Absolute Frontier.Fixed LoopIt counts backward as you travel, then forward again.You are a passenger in a pre-determined history.New AeonIt hits "Infinity/Max" then resets to 0.000...1.You've survived the end of one universe to see the next.
The Verdict: From a physics standpoint, an "Alternative CPT" would represent a New Space-Time Manifold. You would essentially be standing on a different "furthest point forward" that is disconnected from our own.
Would you like to explore the "Grandfather Paradox" from the perspective of entropy—specifically, why the second law of thermodynamics makes an "Alternative CPT" almost impossible to maintain?
