What if time paradoxes are simply allowed to exist?

[Vector_Graphics]

Basically the title.

[steelpillow]

Basically the title.

I would have gone back in time and killed you before you could post this question.

Or at least, one of my parallel-time doppelganers would. Knowing me I would have killed the wrong parallel you.

[PatrickPowers]

Deleted.

[PatrickPowers]

I don't see much that could be done about it. They are excluded from physics because no such paradox has ever been observed by physicists. That might change some day. Who knows?

Carl Jung observed something of that sort late in life. He went with a friend and saw a mural. Later he contacted the mural site, who told him that that mural hadn't existed for years. Both Jung and his friend agreed on what they had seen.

[steelpillow]

But does precognition, of the kind believed in by Jung, create a time paradox?
We already have one rule for classical mass-energy and another for quantum wave states, why not a third for pure "Platonic" information? Events in quantum-state time can appear backwards in macroscopic time (e.g. the famous entanglement experiments), might events in mental-information time not do the same? If they do, then there is no paradox, as no classical law of thermodynamics is broken.

[Frisk-256]

We would have to question what we would see these paradoxes and what physical effect they would have. Like would the timelines branch or would the entire universe be put into a superposition. The grandfather paradox really boils down to where did the person who killed the grandfather come form if he is dead. A splitting timelines would say that the person killing the grandfather came form a parallel timeline where that person exists. A superposition view would just say the person came form the other state in the superposition. But what happens when the superposition collapses? Can It be collapsed? Would it immediately reform?

[PatrickPowers]

But does precognition, of the kind believed in by Jung, create a time paradox?
We already have one rule for classical mass-energy and another for quantum wave states, why not a third for pure "Platonic" information? Events in quantum-state time can appear backwards in macroscopic time (e.g. the famous entanglement experiments), might events in mental-information time not do the same? If they do, then there is no paradox, as no classical law of thermodynamics is broken.

But Jung's experience wasn't precognition. It was something from the past appearing in the present as a material reality.

I like the idea that we are in constant travel between parallel universes. This is normal. Usually the difference isn't so radical as what Jung and friend experienced.

If that is so then are we constantly trading places with others in other parallel universes? Or am I a NPC in that alternative Universe? Or what?

I dunno that I really believe this, but it's a cool idea.

[quickfur]

The problem with time paradoxes, and time travel in general, is that it's inconsistent.

A lot of the confusion comes from an incorrect understanding of Minkowskian 4D space-time. After the initial discovery that time could be treated as a 4th dimension with some space-like qualities (but not all!), in popular opinion the idea of space-time being a geometry came to be wrongly understood as implying that you could walk along the time axis as if it were a space axis, and thereby end up in the past (or future) depending on the direction you walked.

However, that actually does not make sense, because the very act of travelling is a concept that only exists within time. If there were no time, there could also be no travel. If time were to be treated as a spatial axis (which is required for time travel to work the way we imagine it to), then there wouldn't be any time axes left for the travel to happen in. Unless you postulate a second time axis (which comes with a whole bunch of other problems), along which time travel could happen. So even though we speak of 4D Minkowskian geometry, it's not the same thing as geometry in the sense of a physical space that you can freely travel in, like a piece of terrain that you can freely explore. The coefficient of the time component in Minkowskian geometry is -1 (time-like) rather than 1 (space-like), so time behaves in an essentially different way from space. You can't just walk along the time axis like you can walk along a space axis. The concept that Minkowskian 4D geometry is like some kind of 4D terrain along which an object can move is wrong. That's simply not how Minkowskian geometry works.

The way Minkowskian geometry actually works is that the entire history of an object (moving or stationary) is described as a trajectory in the space-time geometry. For example, a bouncing ball from our 3D + time perspective is not a bouncing ball in Minkowskian geometry; it is a sinusoidal 4D spherical tube that stretches across the time axis, such that its cross-sections perpendicular to the time axis describes its position in space at that given time. The bouncing ball does not "move" in this geometry in the sense we think of movement; it is a static object that describes its entire history along both space and time.

Now, you may argue that time travel is possible if we could somehow bend our space-time trajectory such that it loops backwards. For example, if we were to postulate that our bouncing ball somehow managed to travel backwards in time, then we could imagine that in Minkowskian geometry it would look like a sinusoidal spherical tube that bent backwards along the time axis such that it formed a loop, before travelling forwards again. Well first of all, such a trajectory is impossible in the standard Minkowskian metric because the -1 coefficient on the time axis would result in imaginary quantities in the resulting computation. But OK, since we're postulating time travel, let's ignore that for the time being and declare by fiat that it's possible. What then?

Well, the thing is, a cross-section of Minkowskian space-time at some particular time t represents the state of the universe at that particular juncture. Since the trajectory of our bouncing ball is bent backwards in time (before going forwards again), that means that at some time t0 in the past it already exists in that time-slice of the universe! That means that from our perspective, while the original bouncing ball was still travelling forwards in time, a second bouncing ball would have suddenly appeared out of nowhere, alongside the original ball, and continued bouncing as it continued forwards in time. Not only so, but the backwards trajectory of the bouncing ball while it was travelling backwards in time would also exist in the intervening time-slices of the universe, as a third distinct object that's bouncing backwards. This 3rd ball splits off from the 2nd ball, and eventually collides and merges with the 1st bouncing ball and both will vanish into thin air (this is the point where the original bouncing ball started moving backwards in time), while the 2nd ball continued bouncing forwards.

But here's the thing: we would already have seen the 2nd and 3rd bouncing balls in the past, before the original ball started travelling backwards in time. If, in the past, we never saw such an event, it means that no time travel happened in the future. At no point is there a paradox (aside from our handwaving away the impossibility of time travel under the Minkowskian metric). It's not possible for the future bouncing ball to collide with the old bouncing ball and destroy it, because the old bouncing ball could not have existed in the future to travel backwards in time to begin with. The destruction would have already happened in the past, so there would have been no bouncing ball in the future to travel back in time.

Similarly, if you somehow managed to travel backwards in time from the future, it would unfold as your future self suddenly appearing out of nowhere, splitting into two, one travelling forwards, and the other travelling backwards towards where in the future you will start travelling backwards in time, at which point it will merge with your present self and vanish into thin air. Your future self can't kill your past self, because it would already have happened in the past and you wouldn't be here today. The fact that your past self is still here means that you did not get killed. The timeline does not "split" or "correct itself", or worse, "explode" because of a "logical contradiction" -- that's a nonsensical idea. Minkowskian geometry does NOT work like that.

The only thing "correcting itself" or "exploding" is our wrong, contradictory conception of space-time which does not correspond with reality. Either you treat time as time -- meaning that space-time effectively doesn't exist as a geometry and therefore time travel is impossible -- or you treat time as part of the space-time geometry -- meaning that "travel" is a fallacious concept, there are only trajectories, there is no way to "travel across the geometry" because that requires time to be not a part of the geometry. Trying to mix the two concepts results in a grand edifice of nonsense and illogical fallacies that has no bearing on how the real world works. Space-time geometry isn't some thing that you can go back and retroactively modify. You can only do that if you existed outside of space-time, and your actions are mediated by a different axis of time that's completely independent of time as we know it. (In which case, you wouldn't even be a part of space-time in the first place, so you wouldn't even be a human that exists within it. And also, any "modifications" you make to space-time would not be perceptible to beings that exist inside space-time -- they still only see a single space-time and a single history.) Time travel and time paradoxes are nonsensical, and the only thing such a hodge-podge mixture is good for is entertaining the naïve on TV.

[steelpillow]

A paradox is in effect a formal statement of inconsistency.

It is a theorem of formal logic that, where any inconsistency exists, with a little ingenuity you can rigorpusly "prove" absolutely anything at all, including complete opposites. Where such opposites are "proven", this is deemed absurd and the argument becomes a genuine reductio ad absurdum proof that the assumptions which lead to the paradox are inconsistent. It is an article of faith with scientific rationalists that the laws of nature do not entail any paradoxes and reality is consistent with itself.

Take the paradox of Zeno's arrow, for example. Here, he purports to prove that an arrow can never arrive at its target. He bases his scenario on the (correct) assumption that a certain diminishing series of distances will converge on a specific point. But he then assumes (falsely) that a similarly diminishing series of time intervals may extend indefinitely and never converge. When I express it like this, the absurdity of his paradox is easy to see. Allow his time paradox and, with a little ingenuity, your arrow can end up whenever and wherever you wish - or not, as the case may be.

If any temporal paradox whatsoever is allowed, then everything in this topic, and absolutely none of it, can all be proven as true - or false - or paradoxical - or whatever you wish. The world is your oyster - or not, as the case may be.