Paradox-free time travel is theoretically possible

> Try dealing with something of consequence, like killing your former self (as in: the person in that point of time-space which carries the mutable signifier of “yourself” which is younger than yourself) or giving yourself a kilogram of gold from the future, which I think would violate the law of preservation of energy or whatever.

It is entirely irrelevant what it is. The point is that if the system is immutable it is impossible to represent a combination of state transitions that alters an existing state, as such the set of possible space-time combinations would in that case only include those where the time travel does not introduce a paradox that depends on change.

The same way the timeline does not include any states where I fold an elephant, because it's not possible to do so.

You have not presented any paradoxes that can work with an immutable space-time other than perhaps if said space-time introduces divergent timelines at any point of mutation, in which case the paradox can also easily be resolved.

> And yet if time travel backwards is possible you simply cannot deny that one would experience (!) that time travel as steps 1–3. Temporal experience. Hah!

You can experience it that way, but your "do something" step 2 would be deterministic and could not possibly include steps that introduced a paradox.

> There’s absolutely nothing hard about the concept of time being immutable;

You're still thinking in terms of a mutable space-time. I did not talk about time being immutable, but the entirety of space-time. Your "do something" step does nothing that changes anything in an immutable space-time, because everything is fixed from the start. Nothing moves. No action is taken. Everything is unalterable.

Time, and cause and effect, in that scenario is simply an illusion of consciousness at every point of a fixed 4d (or more) canvas that never changes in any way.

> The true puzzle is time travel which introduce paradoxes, which your original comment says absolutely nothing about.

My original comment gave immutability as an example of a possible solution. Time travel with paradoxes is not possible. That is the entire point of a paradox: The problem as stated reveals a problem with the presumed model. The solution is to identify and remove flaws in the model. Removing mutability is one such solution.

I always imagined that time travel into the past would involve some statistical uncertainty. If you got close to creating a paradox, you'd simply transition back. Disappear essentially.

Make a nice story - ghosts are time travelers, appearing and disappearing without making any permanent changes.

> It is entirely irrelevant what it is. The point is that if the system is immutable it is impossible to represent a combination of state transitions that alters an existing state,

Alters? Aha! But you cannot alter that which is immutable! Seems that you still don’t get the concept.

See how silly it is to language police people on such subjets?

> would in that case [only include those] where the time travel does not introduce a paradox that depends on change.

Highlighted the problematic part with brackets. This is just hand-waving. “Only those”? Your theory would have to be able to explain concrete examples like the grandfather problem, or else it doesn’t rise to the level of being a theory that can explain the paradox.

> The same way the timeline does not include any states where I fold an elephant, because it's not possible to do so.

Irrelevant unless there is an actual elephant folding paradox that I’m missing. Impossible things can be explained; paradoxes cannot since they reveal a contradiction in the model.

> You have not presented any paradoxes that can work with an immutable space-time other than perhaps if said space-time introduces divergent timelines at any point of mutation, in which case the paradox can also easily be resolved.

This is the first time (?) you’ve mentioned divergent timelines or hinted at non-just-straight-line-time. And yes, that would probably be perfectly adequate, and is the best answer you’ve given thus far.

> You can experience it that way, but your "do something" step 2 would be deterministic and could not possibly include steps that introduced a paradox.

“Determinism” is either irrelevant or non-sufficient. “Could not possibly” is pure hand-waving as there is nothing which makes sure that you are able to do something benign (like greet your former self) but not do something like kill yourself.

> You're still thinking in terms of a mutable space-time. I did not talk about time being immutable,

Wow, I have to hand it to you. I did mention “space-time” once (although only once) and I utterly failed to be rigorous and spell out the whole package deal, namely space-time. What an utter embarrassment.

Not that it changes my point in any way.

> My original comment gave immutability as an example of a possible solution. Time travel with paradoxes is not possible.

You can’t resolve the Barber Paradox by simply saying that the Universe wouldn’t allow the barber to shave himself. That’s effectively what you’re doing here, only using vaguely hard science terms with a seasoning of “you still don’t get it”.

Shooting yourself and then later going out to lunch is simply impossible; it is not a paradox.

A paradox is when two contradictory things are true at the same time.

The grandfather problem is a paradox if time travel is possible. If it isn’t possible then it is simply an impossibility.

> And for largely the same reason: both scenarios violate causality, so the universe can't be shaped that way.

So you agree that time travel is impossible. Great... we agree. However I was discussing this with someone who apparently thinks that it is concievable... I wasn’t merely making up impossible scenarios; I was demonstrating how their theory gives rise to paradoxical scenarios.