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This question will involve concepts in quantum mechanics.

So unless you believe in many worlds theory, certain outcomes out of a series of outcomes occur. But there seems to be an assumption that one of the other outcomes in that series could have occurred at any particular instant.

This assumption seems to be because of the lack of a hidden variable (usually deterministic theory) that explains why a certain outcome occurred in quantum mechanics.

For example, in the double slit experiment, each photon arrives at a particular point on the screen when measured. A radioactive atom decays at a particular time t. These are said to occur for no further sufficient cause. But even if there is no cause for that decay time or the exact point at which the photon arrives at the screen, how do we know that any of the other outcomes could have occurred?

And if we can’t know this, in what sense do we know that they were possible? Could it still be the case that there’s only one possible branch of reality even if we can’t fundamentally predict the next part of that branch?

A possible analogy I can think of is a random sequence of numbers. Suppose there is a paper and the paper contains this entire sequence. A computer then spits out each number one by one from the paper.

So for example, the sequence might be 8 5 0 3 8 6 1 7 5 0 3 1. Suppose for whatever reason we only notice two things about the sequence: a) each digit is between 0-9 and b) over time, each digit occurs about as frequently as any other digit with a 1/10 probability. Let’s now further assume there is no pattern inherent in these numbers and no way to sort of “shorten” this sequence. This implies that there is no rule and thus no “law” that connects one element to the next. This now becomes somewhat analogous to how quantum events might be playing out in the universe. We know that the next event is among a range of possible outcomes, but we can’t actually know the exact next outcome.

Now, even though we can’t predict the next number, because this computer in my example is merely displaying that sequence, what comes next is still inevitable. Thus, in a real sense, there is only one possibility despite the lack of predictive capability of the next digit.

How do we know that the universe does not function in a similar way? Why do we make the assumption that in a real sense other outcomes were possible, and can science actually show this to be the case one way or another?

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    $\begingroup$ There's 10 possibilities (0-9 digits) what comes next, not 1. $\endgroup$ Commented Apr 2 at 5:54
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    $\begingroup$ @AgniusVasiliauskas I don’t think you understood my question $\endgroup$
    – user353810
    Commented Apr 2 at 5:59
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    $\begingroup$ Sure, I don't understand what's a "real sense". Can you define it and also prove that it's actually "real" and unambiguous,- doesn't change from Philosopher to philosopher ? $\endgroup$ Commented Apr 2 at 6:09
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    $\begingroup$ @AgniusVasiliauskas No views are left behind because they are part of the wavefunction. $\endgroup$
    – Wookie
    Commented Apr 2 at 14:55
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    $\begingroup$ This question seems more suitable to Philosophy $\endgroup$
    – Barmar
    Commented Apr 2 at 15:12

4 Answers 4

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Science cannot answer these questions, nor does it try to. The questions you ask are philosophical questions, so the philosophical terminology is useful. You speak of ontology: the study of what is "real." Is there really more than one branch? That's an ontological question. Science is an epistemological branch that speaks of what we can know. Specifically it's empirical. It's studying what we can know from observations we make. It models what the universe could be given what we know.

We may find out tomorrow that the universe is actually constructed on the hard work of angels that shout across great distances to ensure non-local consistent behavior. On that day, science is going to have to do a lot of flexing to do to fit the new observations.

In addition to such philosophical answers, you might be interested in the de Broglie-Bohm interpretation of QM. It was deterministic and inherently non-local. I heard it fell out of favor and can't express the modern understanding of QM as well, particularly the standard model, but I admit that that's hearsay -- I don't know the math of it myself.

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  • $\begingroup$ I thought the empirical predictions of each interpretation of QM are equivalent. So on what basis is one more supported than the other? Either way, thanks for your answer. I guess part of the reason I wrote this question was to see if science did have a say on it, and you seem to be implying that it does not. One thing I wonder though is my analogy wouldn’t be a theory. My question is more about whether events in the universe could be inevitable even if there was no theory underlying as a matter of fact. Angels/Bohmian mechanics may be theories that make predictions; my analogy did not $\endgroup$
    – user353810
    Commented Apr 2 at 4:46
  • $\begingroup$ I thought they were equivalent too, but along the way I got told otherwise. It may be something subtle, like the mathematics of the standard model being hard to formulate in their model. And as for whether things are inevitable without a theory to make it so, that's very much a question for Philosophy.SE. I would argue the Chinese concept of "dao" would be one you may find interest in studying. It barks up that tree. $\endgroup$
    – Cort Ammon
    Commented Apr 2 at 4:49
  • $\begingroup$ I’m interested in seeing any resources for pointing out that they aren’t equivalent. Because if they weren’t equivalent, that would be pretty big news and would likely serve as a big defeater to one of those interpretations, so I’m skeptical of that. Nevertheless, I will consider looking into what you proposed. Thank you for your answer again $\endgroup$
    – user353810
    Commented Apr 2 at 4:54
  • $\begingroup$ Bohm's interpretation is the only one that doesn't divide reality up into unattainable pieces and create unsolvable but exciting mysteries. It didn't sell well through the scientific media because, boring. $\endgroup$
    – Wookie
    Commented Apr 2 at 15:03
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    $\begingroup$ @Wookie Of course, you're downplaying the issue of non-locality, which many are hesitant to accept in light of the continued success of relativity (even if these things can be shoehorned together, though I'm no expert on that point). It's not dis-favored just because it's boring: it opens its own can of worms that some consider more distasteful than the alternatives. $\endgroup$
    – jawheele
    Commented Apr 2 at 17:14
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Can the universe be unpredictable but still have only one possible history?

Yes. Deterministic system has one possible history, but need not be predictable. See deterministic chaos.

But even if there is no cause for that decay time or the exact point at which the photon arrives at the screen, how do we know that any of the other outcomes could have occurred?

We assume, we do not know. And we assume that because that is the natural thing to assume, given incomplete knowledge about the microscopic state of the system in question, and given past observations and experiments, which show the same repeated experiment can produce various different outcomes across the assumed set.

Could it still be the case that there’s only one possible branch of reality even if we can’t fundamentally predict the next part of that branch?

Yes. Our inability to predict does not imply non-existence.

Why do we make the assumption that in a real sense other outcomes were possible, [...]

Because that is the natural assumption when using probability mathematical concepts to predict. If we did not assume that, we would be paralyzed and could not use probability theory to make predictions. When we find out the real outcome, we can stop assuming that other outcomes were possible, and think instead that only that one outcome was bound to happen, but this "change of mind" does not change anything for the next predictions, so there is no point.

[...] and can science actually show this to be the case one way or another?

I don't think so.

Could it be the case that we replay the universe, have it occur the same every time, and yet still be no deterministic theory even in principle predicting one event from the previous?

Yes it could. If the universe is a manipulable object determined by random choices made by something/someone outside it, and if these choices are made the same "on the replay", then the same course of events will be replayed. There is no theory behind those choices.

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    $\begingroup$ Doesn't deterministic chaos only apply under the assumption that you can't have perfect knowledge of all initial conditions? I think this question isn't referring to "unpredictable in practice", but "conceptually unpredictable"; that is, unpredictable even with an oracle. $\endgroup$
    – Idran
    Commented Apr 2 at 18:58
  • $\begingroup$ @Idran Yes. But even with perfect knowledge, prediction may be impossible due to computational task being too complex for any imaginable computer. This is "unpredictable in practice", but it also may be "unpredictable conceptually", because there is no conceptual way around the fact computational task for predicting chaotic systems is too big. If the computer requires more RAM bytes than atoms in the universe, and more time than the age of the universe, it's quite close to "conceptually unpredictable". $\endgroup$ Commented Apr 2 at 19:31
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    $\begingroup$ Right, but I'm pretty sure the OP's question isn't asking about practicality on any scale, but on the fundamental nature of a hypothetical universe. That's why they're asking about "one possible history": they want to know if it would be possible in a deterministic universe for the literal exact same initial conditions - the one possible history - to have different results. Or alternatively, if you could somehow observe a deterministic universe from outside and literally "rewind" it to a previous instant and resume it, if it could reach a different state than it did the "first" time. $\endgroup$
    – Idran
    Commented Apr 2 at 20:35
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    $\begingroup$ I’m not sure this applies since deterministic chaos is deterministic in principle because of a theory. In my example, there isn’t a theory that could predict the next sequence. So the question is could there no deterministic theory underlying reality while it being the case that there is only one possible branch of reality? $\endgroup$
    – user353810
    Commented Apr 2 at 20:38
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    $\begingroup$ @TruthSeeker Because if you believe there is only one (or none) outcome possible, then what is the point of calculating probabilities of various outcomes? Why would you bother introducing the concept of probability distribution over outcomes, if you believe only one outcome is possible? Probabilities are not actual observed frequencies in the usual applications of the concept in physics. In case they refer to repeatable experiment, they are the expectations, estimations of the frequency that would be observed after large number of repeats. $\endgroup$ Commented Apr 2 at 21:21
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First of all, I suggest you don't bring probabilities into this. I think the problem of philosophically understanding probability is harder, and the mathematical classical axiomatization of probability gives no answer at all (but it isn't a drawback, it just wasn't designed to).

It depends on what "unpredictable" means. If "predictable" means something like "algorithmically predictable", or "predictable up to arbitrary precision", then the answer is more or less obviously yes: for "predictable up to arbitrary precision", this is very well-known under the name of "deterministic chaos".

If "predictable" means something like "the future is a function of the present", then the answer is no: given one configuration of the universe, if the universe is predictable in this sense, then there is only one possible history (starting from this present): the one where the future is the value of the prediction function on the present.

Let me rephrase this with a toy model. Assume we are in a universe with well-defined time, that has only two instants, $0$ and $1$, and such that at each moment, the universe can be in state $a$ or $b$ (with $a\neq b$). Then a history is just a pair amongst $(a,a), (a,b),(b,a), (b,b)$, and you could say a theory is a set of such pairs.

  • The theory $\{(a,a)\}$ is predictable: if you know that the universe is in state $a$ at instant $0$, then you know it is in state $a$ at instant $1$. This theory has only one possible history.

  • The theory $\{(a,a), (a,b)\}$ is unpredictable: if you know that state is initially in state $a$, you cannot predict at all how it will be at instant $1$. This theory has two possible histories.

  • The theory $\{(a,a),(b,b)\}$ is predictable. But it has two possible histories; it's just that these histories "do not meet", since at no instant they agree.

The third theory suggests that in order to make your question more interesting, you should specify "only one possible history for each initial condition" or something like that.

Let me add that "possible" is a logical operator in modal logic; this topic could be worth exploring, and maybe the natural framework to formalize your question.

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Person A designs a random number generator and puts it a box with a digital readout that indicates a random digit every second. He challenges B to make a similar box but the box must contain a predetermined sequence that is simply read out. B decides the easiest way to do this is to design a random generator and write down the output of this generator on a very long piece of paper. B now puts this very long piece of paper in his box and designs a mechanism to readout digits from the piece of paper and display them on the readout of box B.

A and B activate their respective boxes and no one can tell the difference between A and B and they both appear to just output random digits. B has met the challenge posed by A, but suddenly the reader in box B gets to the end of the list on the piece of paper and B's system breaks down. B can get round this pre-running his random generator for longer and generating a longer list of numbers on a longer piece of paper, but this is a big flaw in the design of box B because the list of numbers will always run out in a finite amount of time. The only way to exactly simulate box A is to pre-run the B random number generator for an infinite amount of time and write down the list of generated numbers on an infinitely long piece of paper and then fit this infinite piece of paper into a small finite box. Seems a lot simpler to just have a random generator as per design A, so Occam's razor favours box A.

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  • $\begingroup$ It is not clear how this relates to the question asked. $\endgroup$ Commented Apr 3 at 10:21
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    $\begingroup$ The OP states "Suppose there is a paper and the paper contains this entire sequence. A computer then spits out each number one by one from the paper." I was pointing out that this piece of paper would have to infinitely long and the numbers on it would have to pre-generated by random generator that would take infinitely long to generate before we can kick off the pre-ordained universe, when it would be much simpler to generate the random numbers on the fly, which would not require some infinite memory device to store the pre-ordained future of the universe. $\endgroup$
    – KDP
    Commented Apr 3 at 12:37