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Suppose we have a Branching Timeline paradigm, in which time travel into the past creates a new timeline. Is it fair to assume that any probabalistic events which might occur might be very different to what happened in the past in your original timeline?

So for example, let's say you take yesterday's lottery numbers and travel back in time to 2 days ago. You buy a ticket and fill out your numbers. You do nothing else to interfere in the world at all (and there isn't some hidden suprise where you find out later than in fact you did). Is it fair to assume that due to the complexity and near-random nature of an event like a lottery draw, the results will be different this time around not because of some cause (even a miniscule one, i.e. a butterfly effect) but simply due to the fact that a complex, near random event is happening (as opposed to "has happened" — where the results are locked in).

Many thanks to JDługosz, and everyone else who commented on/edited this question in the sandbox. You helped turn what was a pretty convoluted way of asking this question (and I was aware of this - hence why I went to the sandbox to start with!) into a much more concise and useful question. The above paragraphs are a copy of the final edit, and are as readable as they are due to JDługosz's efforts.

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    $\begingroup$ You seem to be suggesting that two lottery draw machines, absolutely identical down to every subatomic particle, would produce different results, which I think many people would disagree with as a premise. True quantum randomness isn't the same as human-scale "randomness" we experience as a result as an inability to accurately model the underlying system. "Random" is often shorthand for "can't be predicted by humans", rather than "cannot be predicted under any circumstance". $\endgroup$ – Nuclear Wang May 18 '17 at 15:56
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    $\begingroup$ @NuclearWang I'm not necessarily suggesting that the results would be different if they were controlled down to that degree - everything that we experience as a "random" event has some degree of human agency in it, or at the very least, lack of control to the degree that you're talking about. It's the very fact that we can't control these events down to the subatomic level, and the fact that they are happening again in an alternate timeline, that leads me to believe that the results might be different even without any action by the "time traveller" $\endgroup$ – danl May 18 '17 at 16:02
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    $\begingroup$ it could go both ways depending on the needs of your story. $\endgroup$ – sphennings May 18 '17 at 16:12
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    $\begingroup$ I think the way the question is phrased is correct for Worldbuilding. If it were phrased as an exercise in perturbation theory, it'd belong on Physics, but they get a bit touchy about time travel, especially time travel models which are beyond mainstream physics. $\endgroup$ – Cort Ammon May 18 '17 at 16:40
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    $\begingroup$ @JDługosz Not one I've read before. That said, frequently time travel is used as a plot device without the author thinking about what the rules are. The TV show Continuum ended on a note that made me cry deus ex machina. The show had shown that it was a branching timeline unequivocally and then at the last moment this weird guy shows up, does a thing with a thing in a time portal, and pop, everything's fine; Double Plus Good Ending Achieved. $\endgroup$ – Draco18s May 19 '17 at 14:40
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To answer this, you need to see that there exists “randomness” that is not due to the butterfly effect, and then how that phenomenon will be affected by time travel.

chaos and determinism

Just because the random process is “complex” doesn’t mean it becomes nondeterministic. The proper phenomenon here is Chaos, and this is what leads to the so-called “butterfly effect”. If your arrival caused some air molecules to bounce differently than they had in the original timeline, and this eventually made the lottery choose different numbers, that is an example of the butterfly effect and thus not what you are wondering about.

So first, you are asking whether there even exist nondeterministic effects. In pure Newtonian physics, every action can be computed from the previous history, and everything plays out like clockwork. A deterministic system will always produce the same output from a given starting condition or initial state.

nondeterminism, or genuine quantum randomness

As it turns out, quantum mechanics does indeed have genuine randomness. The observable measurement will be chosen at random with a weight based on how close the quantum state is to each possible eigenvector. To give a concrete example without getting too deep into the quantum mechanics, consider what happens when a single photon at some random polarization angle reaches a polarizing filter that passes vertical and rejects horizontal. What if the actual light has an angle that’s not exactly vertical or horizontal, but 15° off vertical? Well, this particular photon will have a 6.1% probability of being horizontal and 93.9% chance of being vertical.

There is no cause due to prior state. There is no reason, and no way to know the result ahead of time. This is genuinely random and nondeterministic, and this is not just a limit to our knowledge. It can be logically shown that the result literally comes from nowhere. Real-world experiments back this up.

So, ultimately the bouncing of the balls in a classic random lottery machine will indeed bounce in unpredictable ways, being truly nondeterministic and not just chaotic. A modern lottery machine will probably combine traditional bounding balls with a micro-controller that uses a quality random event generator to control the precise timing of the paddles and other movements. This will, if implemented as intended, put the ball draw definitely in the genuinely random category.

Now will quantum randomness play out the same way in a new timeline? That’s the question.

branching timelines keep happening

Note that this behavior itself may be the source of having multiple timelines! The Many Worlds Interpretation shows how the apparent choice of a specific value (e.g. horizontal or vertical polarization in the example above) is due to a superposition of everything including your brain’s particles with each possible outcome.

So if this is happening, there is no “choice” and you will split into two new timelines, one of which sees H and one sees V. The “you” asking this will only experience one of them, and that is randomly chosen. So it is “no different than before” in the sense that the particle went both ways in the original timeline, and it goes both ways in the new timeline. But which resulting daughter timeline from this new split you ride into may very well be different.

So from your point of view, the random events will be freshly chosen in the new timeline, and will not necessarily follow the same as in the original timeline.

Experiments over the last few decades, including practical engineering efforts into building a quantum computer, have shown that decoherence is correct, and we have things like delayed choice experiments and even quantum erasers, which suggest that the separate timelines caused by every random wavefunction decay are real.

is that the answer you wanted?

But maybe there’s more to it than that. Maybe the possibilities encoded in the entanglement of all the particles in the environment somehow get pruned back and there is a single “real” timeline, and this path is persistent so the timeline will try and recover the same path when it’s replayed. This is used to great effect in many science fiction stories where the timeline has an inertia of sorts and history is difficult to change.

Consider another concept, that of the quantum handshake. This has to do with the source and future destination of an interaction that form a transaction between the two points in time. You can read about this in John G. Cramer’s Alternate View column in Analog magazine, where I first learned of it.

In some science fiction accounts, going back in time will nullify the transactions and allow them to reform in newly-chosen ways. Under this model, quantum randomness will also be different.

But what if they are not all reset? If the other end of the transaction occurs later than when the traveler departed, maybe that end will hang onto its transaction, and the side of the transaction that the traveler experiences a second time in the new timeline will be the same. This idea more readily supports an overwritten timeline though, but you can make it branching by saying that the state is copied of the entire timeline, past and future, not just the point before the time at which the traveler arrives.

recap — quantum randomnes resets

To summarize, the easy answer that works hand-in-hand with real physics as we understand it, given the branching timeline paradigm, is that quantum randomness will be reset and will play out independently in the new timeline.

To do otherwise will take some contrivances, both in describing new physics for the timelines and in preventing the “many worlds” from making it appear that they have reset. And why do we need multiple mechanisms producing timelines that work in different ways and fight each other?

Furthermore, once anything changes, such as the specific collision of two atoms in the lotto balls, then the specific quantum events that even exist will be different in the new timeline. The butterfly effect (due to your presence, or any partial tendency to play out the same) will pull the rug out and you won’t have the same quantum events to replay, from that point forward. So making things work the same way on the new timeline really would require a higher order fate to make things restore to the same large scale state, even with the low-level details (entropy) completely randomized.

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    $\begingroup$ This is a great answer - I suspected quantum physics would probably have to come into it, and sure enough all three of the answers so far have used that as a basis. I'm more of a philosophy geek myself though, and philosophers are the worst for butchering quantum physics for their own agenda, so I really needed some idea how a science based approach would look. I'll be re-reading this answer a few times, I still don't really feel like I've taken it all in! $\endgroup$ – danl May 19 '17 at 7:59
  • $\begingroup$ Hopefully the links I included will help you. $\endgroup$ – JDługosz May 19 '17 at 14:48
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You have arrived within the past lightcone of your target event, it's fair to say that if you interact with the world it will have an effect.

You go into the shop to buy your ticket. This reminds the person behind you in the queue that they wanted to buy a ticket along with the milk and bread. You're now into human, not quantum, factors. More tickets have been sold, this means that there's a higher jackpot, which takes a different amount of time to announce before the draw. The button to start the draw is pressed at a fractionally different time, the winning numbers are different.

I'd stick to betting on horses and elections. Lay off anything even resembling true random.

While this is still part of the same philosophical principle as the butterfly effect, it's considerably stronger. The butterfly flapping its wings could potentially change the world, but usually doesn't. Human actions on the other hand routinely do change the world.

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  • $\begingroup$ I like this answer even though it's not as detailed as some of the quantum ones, specifically because I wasn't expressly after answers dealing with quantum physics. There are also issues of free will and consciousness - for example if alternate timelines actually exist, are the agents in them conscious or are they mere philosophical zombies? Does the presence of a conscious agent in a timeline necessitate a degree of uncertainty, if said conscious agent is to have any freedom of will at all? This is a philosophical issue rather than a quantum one but just as relevant I think $\endgroup$ – danl May 19 '17 at 10:41
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I think it is fair to assume that the more time there is before a random event, the more likely it is the random event will turn out differently.

Why? Because the world is governed by Quantum Mechanics; and we supposedly have proof (with various New Scientist articles as my source) that quantum events cannot be deterministic, and that quantum events can indeed have macroscopic effect (In the Schrodinger's Cat paradox, the setup is not in dispute: We can arrange for a cat to be killed (or a bomb to explode) if an atom emits an alpha particle; which is a random quantum event that triggers a macroscopic effect).

The Quantum events in question are a function of time, so the longer the time, the more of them occur, and the more likely it is that a chaotic system (which by definition is dependent on immeasurably tiny variations in starting conditions) will be skewed to provide a different outcome.

I would say that at the point you arrive in the past, a reset occurs: That includes re-rolling the dice on every quantum event starting at that point, which means even without any butterfly effect, the air currents blowing the lottery balls around might be slightly different and produce completely different numbers. Say some atoms decayed this time around that did not decay before, emitting energy that warmed some air molecules (or parts of the lottery machine), and vice versa; and those minute variations in heat get multiplied enough over the two days to change the outcome; one ball is deflected just a hair of a degree so its trajectory bounces off the edge of the winning ball chute; so another ball make it in there instead.

If you want to win the lottery, appear in the past about 2 minutes before the cutoff for buying a ticket; just enough time to purchase it. That makes the state of the lottery machine as close as you can get to where it was to select those particular winning numbers.

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    $\begingroup$ Because I find this interesting: QM can be deterministic. In the Copenhagen interpretation, you are absolutely correct. However, other interpretations , such as the DeBroglie-Bohem Pilot Wave interpretation, are deterministic. They do, however, pay a price. Bohem's interpretation is deterministic, but unabashedly non-local. This means that while QM is deterministic under the Bohem interpretation, your presence instantly affects the entire universe in a non-local way, which could affect the lottery just as much as re-rolling the dice on every event, Copenhagen style. QM is fascinating! $\endgroup$ – Cort Ammon May 18 '17 at 16:44
  • $\begingroup$ I don’t think that mentioning that New Scientist had articles is a good way to support it. They’ve had their share of conspicuous wrong articles. You might want to link to proof such as something about Bell’s Inequalities. $\endgroup$ – JDługosz May 18 '17 at 17:36
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In quantum mechanics, the initial state (say a Uranium-238 atom) doesn't uniquely determine the final state (when the atom decays and in what direction that alpha particle goes).

We can expect that if we were able to replay a sample of Uranium being measured by a Geiger Counter, that the amount of counts detected would be almost the same, but probably not exactly the same.

There are ways of using quantum effects (like the radioactive decay of an atom) to generate actual random numbers instead of pseudo-random numbers.

So if, in the story, someone was using hardware random number generators to make choices, (which, I think would make a nice plot device) then there would be some pretty substantial changes right away.

Barring that I don't know if it is known how significant quantum chance would have on day to day macroscopic events.

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    $\begingroup$ +1, and macroscopic events due to quantum chance could be huge. We use random numbers all the time in AI. Genetic algorithms is one example. Noise generation for fuzzing is another; adding noise to images (or numerical data in general) can help force an algorithm to generalize, or develop more robust rules of recognition. RN are also used in simulations of chaotic systems or that suffer from combinatorial explosion; like financial or weather simulations. So a HW RNG might discover a drug or material or something, or invest in something, in a rerun reality that did not happen in the original. $\endgroup$ – Amadeus May 19 '17 at 10:04
  • $\begingroup$ @Amadeus but how much of the entropy used in the random number generator comes from quantum events, vs classical chaos? $\endgroup$ – JDługosz May 19 '17 at 14:50
  • $\begingroup$ @JDługosz: I don't know, I've never studied any quantum RNG. We use very good pseudo-random generators; primarily so we can reproduce a sequence during testing to understand bugs or design problems. I was just spit-balling that a non-deterministic RNG could indeed produce, say, a novel compound to be tested deterministically that proves to be the one in one septillion chance discovery that shuts down cancer tumors, or allows super-conductivity at room temperature, or makes a 99.9% efficient solar cell. A different form of winning the lottery. $\endgroup$ – Amadeus May 19 '17 at 15:34

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