Hard Determinism and Bell's Theorem

[Duxwing]

I read on Wikipedia that Hard Determinism (a.k.a, "Super-determinism" or "Determinism") allows a deterministic interpretation of Bell's Theorem, wherein quantum phenomena are proven indeterministic. I also read somewhere (likely Wikipedia) that this determinism is fiercely debated in the physical community. Have I read correctly and, if I have, which side do you favor--intuitively or for other reasons? E.g., I intuitively favor the determinists because acausal events make no sense to me.

-Duxwing

[K^2]

First of all, Quantum Mechanics, at its core, is fully deterministic. Indeterminism arises when you start doing experiments. This involves not just core QM, but also interpretations[/ulr]. Some interpretations are not deterministic. Copenhagen Interpretation was probably the earliest and best known. It is not deterministic, because collapse isn't deterministic. But collapse doesn't happen in every interpretation, and in fact, there are deterministic interpretations of quantum mechanics. The most complete and well-studied deterministic interpretation is Many Worlds Interpretation. There is no collapse in that one. Everything is fully determined by Quantum Mechanics and boundary conditions.

It's a good idea to understand several interpretations. It helps develop a much better intuition about the subject. That said, MWI is my favorite specifically because it is fully deterministic. As well as it's very good at explaining EPR, entanglement in general, and many oddities in quantum information. Quantum Teleportation, for example, is much easier to understand in MWI, despite the fact that all of the math works in Copenhagen just as well. That, by the way, brings up a very important point. Interpretations are identical in mathematical sense. They all make the same predictions. It's only the "how" that's different. So you can't say that interpretation a) is right, while interpretation is wrong. You either accept that QM is correct, and any interpretation is as good as any, since no experiment can distinguish them, or that QM is wrong, and so are all of the interpretations.

Which, of course, brings us to a philosophical question of determinism. If there are deterministic interpretations of Quantum Mechanics, but all of them say that future is indeterminate from perspective of observer, do we consider our world deterministic or not? Personally, I think that's a very beautiful solution of determinism vs freedom of will. Universe is deterministic. Your future isn't. You get to eat your pie and keep it.

[GoSlash27]

Personally, I think Schroedinger's cat is dead.

Best,

-Slashy

[Duxwing]

First of all, Quantum Mechanics, at its core, is fully deterministic.

Hooray! For years I had thought that the scientific community had discovered a deep truth beyond my ken and that I would have to force this seemingly-incomprehensible idea down my throat--ironically--for science.

Indeterminism arises when you start doing experiments. This involves not just core QM, but also interpretations[/ulr]. Some interpretations are not deterministic. Copenhagen Interpretation was probably the earliest and best known. It is not deterministic, because collapse isn't deterministic. But collapse doesn't happen in every interpretation, and in fact, there are deterministic interpretations of quantum mechanics. The most complete and well-studied deterministic interpretation is Many Worlds Interpretation. There is no collapse in that one. Everything is fully determined by Quantum Mechanics and boundary conditions.

Interesting, and hooray!

It's a good idea to understand several interpretations. It helps develop a much better intuition about the subject. That said, MWI is my favorite specifically because it is fully deterministic. As well as it's very good at explaining EPR, entanglement in general, and many oddities in quantum information. Quantum Teleportation, for example, is much easier to understand in MWI, despite the fact that all of the math works in Copenhagen just as well. That, by the way, brings up a very important point. Interpretations are identical in mathematical sense. They all make the same predictions. It's only the "how" that's different. So you can't say that interpretation a) is right, while interpretation is wrong. You either accept that QM is correct, and any interpretation is as good as any, since no experiment can distinguish them, or that QM is wrong, and so are all of the interpretations.

Oh, so I get to believe whichever one I want? This sounds too good to be true...

-Duxwing

[K^2]

Oh, so I get to believe whichever one I want?

From perspective of science, they're all equally right. Belief doesn't really enter into it. From perspective of philosophy, sure. If you want to believe that one of these is the real way the universe works, with the others just happening to agree with it on math, that's your call.

[Duxwing]

From perspective of science, they're all equally right. Belief doesn't really enter into it. From perspective of philosophy, sure. If you want to believe that one of these is the real way the universe works, with the others just happening to agree with it on math, that's your call.

How can they be equally-right if they disagree?

-Duxwing

[K^2]

How can they be equally-right if they disagree?

Because a scientific theory is only as right as its predictions. If two theories give you identical predictions, they are both equally right, even if they completely disagree.

[rkman]

If there are deterministic interpretations of Quantum Mechanics, but all of them say that future is indeterminate from perspective of observer, do we consider our world deterministic or not? Personally, I think that's a very beautiful solution of determinism vs freedom of will. Universe is deterministic. Your future isn't. You get to eat your pie and keep it.

Can it be said the future is generally indeterminate if in practice a lot of it can be determined (e.g. chemical processes)?

To me the more attractive idea is that we can not determine aspects of the future about which we have insufficient understanding and/or data, and/or for which we have insufficient calculation capacity to make an accurate prediction.

Is the history of science not marked by discoveries/inventions that allow us to determine things that previously could not be determined?

I should add that i think in there always will be aspects of the future which in practice can not be determined due to aforementioned limitations on human capabilities.

Edited July 7, 2014 by rkman

[Red Iron Crown]

Any discussion of determinism is incomplete without mentioning Godel's theorems. No logical system can ever be fully complete. By extension, any mathematically based model of the universe must also be incomplete.

The pun in the first sentence is deliberate.

[K^2]

No logical system can ever be fully complete. By extension, any mathematically based model of the universe must also be incomplete.

That is not a sound conclusion. There are logical statements that cannot be proven true or false, certainly, but that doesn't mean that unambiguous rules for time evolution cannot be constructed. In integer algebra, given any two numbers, you can always find a sum of these two numbers. There are no exceptions. Similar, a system can have a specific future state, given some initial state. And that's all that we need for determinism.

[Red Iron Crown]

That is not a sound conclusion. There are logical statements that cannot be proven true or false, certainly, but that doesn't mean that unambiguous rules for time evolution cannot be constructed. In integer algebra, given any two numbers, you can always find a sum of these two numbers. There are no exceptions. Similar, a system can have a specific future state, given some initial state. And that's all that we need for determinism.

That could be true, I may be misinterpreting the implications of Godel's theorems.

Does that have implications for free will? If the Universe is truly deterministic, are our actions inevitable?

[Technical Ben]

...entanglement in general...

How does MWI explain entanglement?

Also, is it not that the calculations are fully deterministic, but the results never are? Just like a dice, I can say with absolute certainty it will roll between 1 and 6. But I cannot say what it will roll.

Edited July 7, 2014 by Technical Ben

[theend3r]

How does MWI explain entanglement?

Also, is it not that the calculations are fully deterministic, but the results never are? Just like a dice, I can say with absolute certainty it will roll between 1 and 6. But I cannot say what it will roll.

You can say what it will roll if you know the circumstances under which it will be rolled.

[Duxwing]

That could be true, I may be misinterpreting the implications of Godel's theorems.

Godel's theorem's apply to Peano arithmetic systems with non-trivial number theory.

Does that have implications for free will? If the Universe is truly deterministic, are our actions inevitable?

Yes. Our actions are inevitable, and for each action that inevitability is not horrifying but trivial and banal; e.g., if I want to eat some ice-cream come, then, circumstances permitting, I will inevitably eat that cone. Horror of horrors!

-Duxwing

[K^2]

How does MWI explain entanglement?

Say I have a pair of particles in (1_up, 2_down) + (1_down, 2_up) entangled state. Now observer A comes in and does the measurement of the first particle's state. Instead of collapse, according to MWI, observer becomes part of the state.

(A_up, 1_up, 2_down) + (A_down, 1_down, 2_up)

Now, observer B does measurement of particle 2.

(A_up, 1_up, B_down, 2_down) + (A_down, 1_down, B_up, 2_up)

Now, suppose observer A goes to observer B to compare the notes. What's the state here? (A_up and B_down compare notes) + (A_down and B_up compare notes).

Despite the fact that collapse never happened, observer A that experienced outcome up can only meet with observer B who experienced outcome down. And it doesn't matter who did measurements first, or if the two measurements happened at the exact same time, while the two observers were separated by great distance. When observers compare notes, they'll always find that despite each one having random result by himself, if one got up, the other got down.

That's entanglement. And it's clear why you can't use it for communication. Everything is intuitive and there are no paradoxes.

Also, is it not that the calculations are fully deterministic, but the results never are? Just like a dice, I can say with absolute certainty it will roll between 1 and 6. But I cannot say what it will roll.

Ah, that's very different. With dice, if you had perfect information about initial conditions, you could, in principle, compute the output. There is Deterministic Chaos involved, which says that if you have even a tiniest uncertainty in initial conditions, such as you don't know exactly where every molecule of air around the die is, then your predictions ten to diverge with time. Dice, specifically, undergo several mechanical catastrophes as they hit the table, which allow for small errors due to chaotic nature of the system become discrete differences in outcome.

In Quantum Mechanics, you cannot have sufficient information to make predictions about the outcome of the measurement. It's fundamentally impossible. The dynamics, in contrast, is still entirely deterministic. But there is Quantum Chaos as well, which is way, way worse than classical.

[Duxwing]

Everything is intuitive and there are no paradoxes.

Except infinitely-many universes arise from nothingness at infinite rates.

In Quantum Mechanics, you cannot have sufficient information to make predictions about the outcome of the measurement. It's fundamentally impossible. The dynamics, in contrast, is still entirely deterministic. But there is Quantum Chaos as well, which is way, way worse than classical.

Tell me more of this quantum chaos.

-Duxwing

[K^2]

Except infinitely-many universes arise from nothingness at infinite rates.

That's entirely within the eyes of the beholder. You can treat the system as observer-free, and then you have just one universe. Otherwise, you have as many universes as possible observer states you want to consider. Keep in mind that layman's statement of MWI is greatly oversimplified.

Tell me more of this quantum chaos.

It's essentially the same as classical chaos, but in different state space. In QM, the complexity of the state grows exponentially with the size. In classical mechanics, 10 particle or 11 particle systems are almost equally complex to model. In Quantum Mechanics, you get a full 10-particle problem for every possible state of the 11th particle. So it doesn't take much for chaos to take over.

[Duxwing]

That's entirely within the eyes of the beholder. You can treat the system as observer-free, and then you have just one universe. Otherwise, you have as many universes as possible observer states you want to consider. Keep in mind that layman's statement of MWI is greatly oversimplified.

This layman's statement seems dualistic: what monistic mechanism causes the splitting?

It's essentially the same as classical chaos, but in different state space. In QM, the complexity of the state grows exponentially with the size. In classical mechanics, 10 particle or 11 particle systems are almost equally complex to model. In Quantum Mechanics, you get a full 10-particle problem for every possible state of the 11th particle. So it doesn't take much for chaos to take over.

Good grief. >_<

-Duxwing

[K^2]

This layman's statement seems dualistic: what monistic mechanism causes the splitting?

There is no actual splitting. Look at the example on entanglement I've outlined above. From perspective of observer A, the time-line is split between him getting spin-up outcome and spin-down outcome. But until observer B has done an experiment or gotten entangled with all of this mess by other means, his world isn't split.

World-splitting in MWI isn't something that happens to the world, so much as to the observer. The observable world is split as a result of observation. But universe as a whole just is. Nothing ever really happens in it.

[Duxwing]

There is no actual splitting. Look at the example on entanglement I've outlined above. From perspective of observer A, the time-line is split between him getting spin-up outcome and spin-down outcome. But until observer B has done an experiment or gotten entangled with all of this mess by other means, his world isn't split.

World-splitting in MWI isn't something that happens to the world, so much as to the observer. The observable world is split as a result of observation. But universe as a whole just is. Nothing ever really happens in it.

My brain hurts. >_< *punches the accelerator on neocortex* Come on, baby, just a few more clock cycles...

I understand this interpretation is that the universe is a set of closed, four-dimensional systems (worlds) through which observers pass (split) with nothingness between. What happens if this big set is observed: what physical and metaphysical laws govern these worlds, and how do observers pass between them?

-Duxwing

[K^2]

No, the universe, as a whole, is just one of these possible states. However, you can write it as a sum of other possible states. You get splitting when relevant observer has a future state in several such possibilities. The actual future state of the observer is a superposition of these. But because observer in each one functions independently, from perspective of observer, he shifted from one state to another. This can be interpreted by the observer as either the collapse of the state or splitting into alternate worlds. But the actual state of the world has not changed. It never does.

[Duxwing]

No, the universe, as a whole, is just one of these possible states. However, you can write it as a sum of other possible states. You get splitting when relevant observer has a future state in several such possibilities. The actual future state of the observer is a superposition of these. But because observer in each one functions independently, from perspective of observer, he shifted from one state to another. This can be interpreted by the observer as either the collapse of the state or splitting into alternate worlds. But the actual state of the world has not changed. It never does.

Why does the universe care if anyone is watching? Does that interpretation contradict the scientific assumption that all rational observers share a reality?

-Duxwing

[K^2]

Why does the universe care if anyone is watching?

It doesn't.

[Duxwing]

It doesn't.

Then why the splitting?

-Duxwing

[K^2]

There is no objective splitting. Results of the measurement can be interpreted as world splitting simply because observer goes into a superposition of states. So each component of that superposition observes a different world. But the actual state of the system is the total of all possibilities, and it never splits or changes.