# Retrospective Indeterminacy

• B
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## Summary:

How does indeterminism appear if we look "backwards in time"?
I've been trying to imagine how a universe governed by indeterminism appears when viewed from present to the past.

My understanding is probably off here, so hopefully someone can point me in the right direction.

I'm thinking in terms of experiments such as the double slit experiment and Bell tests - as far as I understand them (an important caveat). Some of my terminology might be a little bit imprecise but hopefully it's accurate enough to convey the question I am trying to ask.

Starting with a Bell test for example, or an example where a choice of measurement is to be made.

A key element of the indeterminism is that "the future is open", that there are a range (no matter how limited) of branches that the experimenter's decision could follow. Of course, the same must also have been true of all the decisions taken in the past. So, instead of looking "into the future" we can look "into the past" . Looking into the past how would the Universe appear? Would it have the appearance of having followed a strictly deterministic path almost like a set of dominoes leading up to the present or am I mistaken in thinking this?

Let's say that we are at a point where the experimenter is about to make a choice (let's call the decision event A). If we stop and turn our focus backwards in time, will we see what appears to be a strict line of deterministic, causal events forming a chain up to this point in time when Choice A is about to be made? If we then jump into the future after Choice A has been made and perform the same restrospective inspection that has lead to a subsequent point, let's call it B. Will the universe appear to plot a deterministic line through the previous choice A, up to the new choice B?

Or will there be an broken chain leading back into the past, as such doing away with the notion of causality?

Perhaps this clears up a few incorrect notions of indeterminacy with regards to QM

https://en.wikipedia.org/wiki/Deterministic_system
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system.[1] A deterministic model will thus always produce the same output from a given starting condition or initial state.[2]

Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly.

In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appears to be non-deterministic.

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Lynch101
Nugatory
Mentor
I've been trying to imagine how a universe governed by indeterminism appears when viewed from present to the past.
The same way a universe governed by deterministic laws would look.

You are observing the past history of a roulette wheel. Is it producing numbers through a deterministic process that we haven’t analyzed because we don’t know the initial position and velocity of every particle making up the wheel and the ball? Or is it non-deterministic? How would it look different?

Lynch101 and PeterDonis
The same way a universe governed by deterministic laws would look.

You are observing the past history of a roulette wheel. Is it producing numbers through a deterministic process that we haven’t analyzed because we don’t know the initial position and velocity of every particle making up the wheel and the ball? Or is it non-deterministic? How would it look different?
You can still observe the mechanisms of the wheel spinning even if you can't calculate it. What TS is referring to is when you do not even see the underlying mechanisms. Like spontaneous emersion in QM. He or she also asks how spacetime would look if the future is open: meaning that every sequence that follows the next is "to be determined" rather than "already determined".

weirdoguy
PeterDonis
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2020 Award
Are you suggesting that you get different measurement result from the same initial condition in Quantum Mechanics depending on if it's your fifth or 10 000th trial?
If you are measuring an ensemble of quantum systems prepared in a state that is not an eigenstate of the measurement, yes.

PeterDonis
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2020 Award
@BruteForce1 since you evidently lack basic knowledge of QM, you have been banned from further posting in this thread, since your posts are not helping the OP.

Gold Member
The same way a universe governed by deterministic laws would look.

You are observing the past history of a roulette wheel. Is it producing numbers through a deterministic process that we haven’t analyzed because we don’t know the initial position and velocity of every particle making up the wheel and the ball? Or is it non-deterministic? How would it look different?
If we analysed the past history of the roulette wheel, would we be able to follow a "path of determinism" or a a causal chain with its indeterminism prior to each round being down to our incomplete knowledge?

Is the indeterminism of QM different from this? The impression I get is that the indeterminism isn't down to our lack of knowledge i.e. down to some hidden variable(s). Is that accurate?

Or is the indeterminism down to some hidden variable(s) but those hidden variable (s) are either not local, not real, or not locally real?

Or am I not even in the right ball park?

DarMM
Gold Member
If there are hidden variables they are either nonlocal, retrocausal, acausal or involve multiple worlds.

Lynch101
Gold Member
If there are hidden variables they are either nonlocal, retrocausal, acausal or involve multiple worlds.
Thanks DarMM.

Are there options where there are no hidden variables?

DarMM
Gold Member
Thanks DarMM.

Are there options where there are no hidden variables?
These would all be taking the formalism as is and not supposing it involves ignorance of some hidden variables beneath.

There are two classes.

Take the theory as is and read it in a non-probabilistic way, e.g. Many Worlds or the Thermal Interpretation.

Take the theory as is and read it in a probabilistic way, e.g. Copenhagen.

Lynch101
Gold Member
If there are hidden variables they are either nonlocal, retrocausal, acausal or involve multiple worlds.
Are hidden variables theories fundamentally deterministic, with the indeterminism arising from not knowing the hidden variables?

These would all be taking the formalism as is and not supposing it involves ignorance of some hidden variables beneath.

There are two classes.

Take the theory as is and read it in a non-probabilistic way, e.g. Many Worlds or the Thermal Interpretation.
I must check the Thermal Interpretation, thanks. I've only started to hear about it.

Take the theory as is and read it in a probabilistic way, e.g. Copenhagen.
Am I correct in saying that the Copenhagen interpretation is anti-realist, or that it denies realism? My [possibly inaccurate] understanding is that Copenhagen says that the wave function of a particle doesn't represent something physical.

I'm thinking in terms of [my possibly inaccurate understanding of] the double-slit experiment: does Copenhagen say that from the time/point* of emission of the praticle/wave until just before it hits the screen the particle/wave has no objective reality? I don't think it quite says that there is nothing there, but I'm not entirely clear on what it say in that regard.

After the particle hits the screen and the wave function collapses, does the entire trajectory of the particle become known (as in looking backward in time), or is the "path" of the wave/particle from the emitter to just before the detector still unknown? As per the general topic of this thread, looking backward in time does the whole process appear deterministic or is there still some missing information?

*I'm familiar with the uncertainty principle that says there is a trade-off in measuring the precise time of emission and the engergy of particle (is that in some way accurate?).

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Nugatory
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Are hidden variables theories fundamentally deterministic, with the indeterminism arising from not knowing the hidden variables?
Not necessarily. It’s possible to construct a non-deterministic hidden variable theory in which quantum mechanical behavior is caused by some underlying mechanism that is itself non-deterministic. Any such theory would still be subject to the constraints imposed by Bell’s theorem.

This possibility doesn’t get much attention because the primary motivation for considering hidden variable theories was to remove the apparent randomness. A deterministic hidden variable theory that explained quantum randomness (analogous to the way that the random behavior of tossed coin might be predicted by a deterministic analysis starting with the position of momentum of every particle as hidden variables) does that; a non-deterministic one does not.
I'm thinking in terms of [my possibly inaccurate understanding of] the double-slit experiment: does Copenhagen say that from the time/point* of emission of the praticle/wave until just before it hits the screen the particle/wave has no objective reality? I don't think it quite says that there is nothing there, but I'm not entirely clear on what it say in that regard.
After the particle hits the screen and the wave function collapses, does the entire trajectory of the particle become known (as in looking backward in time), or is the "path" of the wave/particle from the emitter to just before the detector still unknown?
It’s more in the spirit of Copenhagen to say that there’s no point in talking about these things that weren’t measured. It’s a fact that the particle was detected at the screen at a particular time and place, but pointless to say talk about things that weren’t detected.
As per the general topic of this thread, looking backward in time does the whole process appear deterministic or is there still some missing information?
There is no way of distinguishing the output of a non-deterministic process from the output of a deterministic process. Suppose I present you with a particular sequence of ones and zeros that passes all statistical tests for randomness. There’s no way of knowing by examining the sequence after the fact whether it was the output of a deterministic computer program that prints that sequence, or the output of one particular run of a quantum random number generator.

Gold Member
Thanks Nugatory.
Not necessarily. It’s possible to construct a non-deterministic hidden variable theory in which quantum mechanical behavior is caused by some underlying mechanism that is itself non-deterministic. Any such theory would still be subject to the constraints imposed by Bell’s theorem.

This possibility doesn’t get much attention because the primary motivation for considering hidden variable theories was to remove the apparent randomness. A deterministic hidden variable theory that explained quantum randomness (analogous to the way that the random behavior of tossed coin might be predicted by a deterministic analysis starting with the position of momentum of every particle as hidden variables) does that; a non-deterministic one does not.
When I think of determinism I think in terms of dominoes and a long, deterministic chain of causality. In terms of the Universe, we might think of an impossibly complex system of dominoes that is so complex it affects our ability to make definite predictions because we don't know all the details about all the dominoes. In this case, the system would appear indeterminate because we cannot predict with certainty - only with probability - the outcome of an experiment. This indeterminacy however would simply be down to our lack of knowledge of a truly determinate system.

Take the example of flipping a coin, as you mention above. If imagine that every particle represents a domino and their position and momentum determines which way they fall and which domino they knock over next. This would set off a chain reaction that would be completely deterministic but which we simply couldn't predict. The outcome would appear indeterminate but would actually be completely deterministic.

I would contrast this with true inderminacy where the outcome of an experiment is truly random and not determined by the prior state of the system. In this case however, experimental results would have to manifest "out of thin air" and the notion of causality would be void. The falling of one domino could not be traced to a prior falling domino, it would have to spontaneously fall over without any cause - because the cause of it falling over would itself be a domino to be accounted for.

To try and clarify, if we imagine a row of 10 dominoes - set up side-by-side as opposed to one in front of the other, whereby only one of the dominos will fall and it doesn't knock the other 10 dominos (hopefully what I mean is clear).
Now, we cannot predict with certainty which of the 10 dominoes will fall but we can predict the probability of which one will fall. In a deterministic system the domino which falls will have been knocked by a nother domino falling into it. However, in a truly indeterminate, truly random system the domino would have to spontaneously fall without being knocked over by a prior domino.

Is that in the right ball park?

It’s more in the spirit of Copenhagen to say that there’s no point in talking about these things that weren’t measured. It’s a fact that the particle was detected at the screen at a particular time and place, but pointless to say talk about things that weren’t detected.
Is that part of the reason why EPR concluded that QM was incomplete?

It strikes me as being somewhat problematic to say that "there's no point in talking about these things that aren't measured" (I'm taking this as your characterisation of Copenhagen as opposed to your own position on QM). Would it not be more accurate to say that it's not that there's no point rather that we can't apply certain parameters to it. We can still pose certain questions about it and make certain, if limited, deductions?

There is no way of distinguishing the output of a non-deterministic process from the output of a deterministic process. Suppose I present you with a particular sequence of ones and zeros that passes all statistical tests for randomness. There’s no way of knowing by examining the sequence after the fact whether it was the output of a deterministic computer program that prints that sequence, or the output of one particular run of a quantum random number generator.
Thanks Nugatory, I understand that we can't distinguish the outcomes but if we think in terms of dominoes again. If we look at the history of a deterministic system we might see a line of dominoes from the emitter to detector but with an indeterminate system would we see the same, or would we just see the end domino knocked over?

With a determinate system would we not see that line of dominoes either, but we would simply infer them? I know the analogy of dominoes presupposes a certain structure of the system, but the line of dominoes can represent the path of a particle or wave front.

I guess the point I'm trying to clarify is in something like the double slit experiment, when the particle registers on the screen and the wave function collapses, does the path of the particle through the experimental set-up materialise as well, or is that information simply unknowable?