Grandfather paradox. Bootstrap paradox. These words are universally brought up as logical arguments to the theoretical impossibility of time travel, as its existence would violate the laws of basic logic.
However, upon closer inspection, I cannot help but posit that the problem isn't in time travel. It's in one very specific model of time travel, which seems to be the only one people ever think of. Today, I'm here to introduce an alternative model, which suffers from neither paradox.
To ensure we are all on the same page, here is an abbreviated description of the grandfather and bootstrap paradoxes. For the sake of making this text readable, we shall refer to the time traveler as "Crono".
- The grandfather paradox occurs if Crono goes to the past and prevents their grandfather from meeting their grandmother. This naturally causes their mother to never be born, causing Crono themselves to never be born, causing them to never have interfered in the past, which in turn causes them to have been born, forming a cycle. The paradox arises from how this cycle ought to switch between its two states (Crono alive and Crono dead) at an infinite frequency.
- The bootstrap paradox arises when Crono finds a book about how to build a time machine on their kitchen table. They then follow its instructions, and use the resulting time machine to put the book where and when they found it in the first place. The paradox becomes apparent by considering a simple question: who wrote the book?
There exists a number of theories that solve the paradoxes of time travel by positing branching timelines or an immutable past. A goal of timewave theory is to do neither of those things. The past really is mutable, and what is mutated really is the traveler's past.
The crucial element of timewave theory is the assumption that the ripple effect travels at a finite "speed", for lack of a better word.
In conventional time travel theories, alterations to the past cause "instantaneous" effects in the present and the future (a principle known as the "ripple effect"), regardless of how far that future may be. Crono goes five years to the past to win the lottery, then returns to the present and is a billionare in a villa. Timewave theory arises from the observation that this instantaneousness is the source of the paradoxes, and, if it is removed, said paradoxes become perfectly explicable, if perhaps strange, events.
Instead, timewave theory claims that the ripple (renamed to "timewave" to avoid confusion) moves forward in time at the same rate as everything else: one second per second. Crono wins the lottery five years ago, then returns to the present and they're as poor as when they started. This is because they "skipped" the timewave carrying their victory, and are now living in the not-yet-modified part of the timeline. If they were to wait five years (therefore reaching the tenth year after the lottery) then travel back to when they first went to the past, they would arrive just behind the timewave and be a billionaire.
For the above description to be consistent, we need to replace another traditional assumption of time travel theories: that the existence of something requires an unbroken line to its origin. Crono being poor today is caused1 by them having failed to win the lottery five years ago. If they change the past then return to the present, they end up about five years ahead of the corresponding timewave. For the five year interval between it and Crono, Crono's poverty exists, but has no cause anywhen in time.
Instead, under timewave theory, entities possess ontological inertia: for all durations ε:
- if an entity doesn't exist at time t, it will also not exist at time t+ε
- if an entity does exist at time t, it will also exist at time t+ε
unless a force intervenes to change this.
Crucially, ontological inertia does not require an entity to "justify" why it exists now by having a chain of causality to its cause. Entities that exist now just exist, and will continue to do so unless acted upon. Thus, the creation of an entity being erased from time doesn't immediately erase the entity: it only does when the force carrying this change (the timewave) arrives.
One may observe that this is not a separate assumption from the existence of timewaves, but merely a different way to view it: when a chain of causality is broken, causality is remade going forwards at a rate of one second per second, the same as the rate at which it was originally made. This moving change is known as a timewave.
- The grandfather paradox is resolved: certainly, the timewave will eventually undo Crono's birth, but by ontological inertia he continues to exist. Moreover, a stable time loop is created: as the first timewave reaches Crono's departure and erases it, the lack of Crono's departure causes a lack of his arrival in the past2, which is itself a change and spawns a timewave. Infinite timewaves will be generated by this cycle, at a consistent frequency.
- The bootstrap paradox can be resolved by simply saying the book was written at some point, but that point has been erased on the timeline. In the book's history, it has been passed from Crono to younger Crono some finite number of times, before all of which it was made.
Time travel has an annoying tendency to violate conventional laws of physics. Leaving aside causality, which would just be wrong in the presence of working time machines, we also have conservation of mass/energy to worry about.
When Crono leaves for the past, mass equivalent to one Crono disappears, after all. Also, when he arrives in the past, mass equivalent to one Crono appears. Both of these events violate a conventional understanding of conservation of mass.
Note that mass disappeared into nothing at one point, and the same mass appeared from nothing at another. Thus, we can preserve conservation by simply using Crono's disappearance to "pay for" his appearance (And we can "pay for" time travel by spending extra energy on top of that, much like we do for space travel).
A necessary consequence is that conservation of energy needs a correction: the total amount of energy in a closed system, added up along the entire duration of the system's existence, is constant. Energy may occasionally disappear from a place and appear in another, but as it is still in the system, the total is unmodified. Importantly, this law is compatible with current scientific understanding: in the absence of time travel, it is identical to the existing laws of conservation of mass/energy.
So far, we've assumed Crono's lottery time travel is the only instance of time travel that ever occurred. Let us now consider the alternative. Crono may travel five years to the past and end up in a completely different reality. This is because, across their trip, Crono moved across one or more timewaves, and thus didn't land in the past as they know it. Such past has been erased from the timeline. Likewise, Crono may witness a similar effect when traveling to the future. In fact, reality as they know it may only be a picosecond "wide", as they exist between two extremely close timewaves. Without a time machine, they would never know.
Timewave theory ultimately makes an extremely simple claim: that everything moved naturally in time at the same rate of one second per second. This includes the consequences of one's actions, and such consequences are known as timewaves.
I would like to thank the game Achron, which I have neither played nor seen be played, but which I have read a description of, for introducing me to the idea of finite-speed ripple effect and to the term "timewaves", which have since evolved into this model.