Susskind and Hawking on hard determinism

[TrickyDicky]

Wow, seriously? That's...um...surprising. Because there is no possible way around determinism. It is fundamentally impossible to get out of it.

A simple proof of determinism just comes from noting that the universe must be self-consistent. That is, it cannot possibly contradict itself. And if the universe is self-consistent, then it must be describable through a set of entities combined with a set of rules governing the interactions between those entities. If we write down such a set of rules, and it turns out that it appears to change dependent upon the situation, then we can simply write down a new set of rules that takes that change in situation into account. If there is an element of randomness in the universe, then it can always be described via some probability distribution.

This does not guarantee that we know what these rules are, or even that we can know them. But I'm pretty sure it's a rock-solid proof for such rules existing, provided you accept that reality cannot contradict itself.

These kind of conclusions were overcome and solved many years ago, but you maybe don't know about the "way around determinism" or due to purely emotional reasons you refuse to accept it.
The most obvious way out of determinism is called undecidability, there are questions that are undecidable and whether derterminism is true or not is one of those, you can suspect that the universe is determinist but you can't scientifically prove it, because that is in principle outside what you can know and express in rigorous, "hard" way.

You can feel assured by asserting that reality can't contradict itself, and maybe is reasonable to suppose that, but to prove it it has to be expressed with language and when you try to do that you realize that contradiction indeed arises, reality perhaps doesn't contradict itself but axiomatic proofs of that supposition certainly do, as Godel showed long ago.
So you can't scientifically assert that determinism is true, you just may infer that probably reality is that way, and others might have a different feeling, but it is undecidable on rigorous terms who's right.

 

[Chalnoth]

First of all, there is no reason why the universe must be self-consistent. There are workable systems of mathematical logic that allow for inconsistent statements, and I'm open to the possibility that the universe could be modeled by one of those systems.

Uh, what? A self-contradictory mathematical system is a fundamental impossibility, because a mathematical system is defined as being self-consistent. While there are systems of mathematical logic that have elements that map onto inconsistent statements (e.g. some three-valued logics), the mathematical logic itself is necessarily self-consistent.

It remains that any non-malformed and sufficiently-specific statement about the nature of reality is either true or false. It cannot be both. Actual contradictions are impossible. The paraconsistent logics you mention are merely consistent ways to deal with apparent contradictions, such as due to poor language or software errors.

Goedel has mathematically proved otherwise. If you have a self-consistent series of rules, there are well-posed questions that you cannot prove within the set of those rules.

Irrelevant. Our inability to prove every possible statement as being either true or false doesn't mean that these statements aren't one or the other.

You really need to read up on Kurt Goedel. because he mathematically *PROVED* that any system of logic that is more complex than arithmetic is either incomplete or inconsistent. Also you do need to read up on non-standard logic

Yes, but self-consistency is one of the things we require of mathematics, from which Goedel's incompleteness theorem indicates that either we've made a mistake, or mathematics is incomplete.

And as I've said, randomness doesn't change determinism in any way that matters. Though I would still argue that we have detected no deviations from determinism to date, I admit the possibility of randomness being an element of fundamental law. But the possibility of randomness doesn't functionally change any of the consequences of determinism.

 

[Chalnoth]

These kind of conclusions were overcome and solved many years ago, but you maybe don't know about the "way around determinism" or due to purely emotional reasons you refuse to accept it.
The most obvious way out of determinism is called undecidability, there are questions that are undecidable and whether derterminism is true or not is one of those, you can suspect that the universe is determinist but you can't scientifically prove it, because that is in principle outside what you can know and express in rigorous, "hard" way.

You can feel assured by asserting that reality can't contradict itself, and maybe is reasonable to suppose that, but to prove it it has to be expressed with language and when you try to do that you realize that contradiction indeed arises, reality perhaps doesn't contradict itself but axiomatic proofs of that supposition certainly do, as Godel showed long ago.
So you can't scientifically assert that determinism is true, you just may infer that probably reality is that way, and others might have a different feeling, but it is undecidable on rigorous terms who's right.

I don't see how Goedel demonstrated anything of the sort. Yes, he did prove that you can't prove the consistency of a mathematical system within that mathematical system. But that's irrelevant, because self-consistency is a defining property of a mathematical system. If it isn't self-consistent, it isn't a valid mathematical system. This isn't so much a statement about proving self-consistency, but rather that when we build up a mathematical system, we construct it by demanding self-consistency. And it turns out that the requirement of self-consistency places quite a few constraints upon possible mathematical systems.

Of course, the fact that self-consistency can't be proven for many mathematical systems means that we can't ever be sure that some mathematical systems are fully self-consistent. But that's an irrelevant point.

 

[naturale]

Yes, and I wish them well. One thing that you do end up getting is that in order to rescue determinism you have to go non-local.

What I can mathematically do demonstrate that if QM is correct, then you cannot have determinism without rejecting locality, and personally a theory that rejects locality is more aesthetically non-pleasing to me than one that is non-deterministic.

There are lots of interesting deterministic field theories, but the problem is that then you have the problem of locality. A field theory which is deterministic, but in which every particle is influenced by every other particle in the universe, becomes uncomputable, and that paper you have is non-local.

Not necessarily non-local. It could be sufficient an assumption of intrinsic periodicity for non-interacting isolated systems. You can regard the assumption of periodicity as non-lacality if you want, but this non-locality is in agreement with relativistic causality.

Scientific arguments are based on either mathematical proofs or observations. If you want to believe in determinism, that's fine, but you right now have no scientific reason to compel me to believe in that (nor I you).

Guilty as charged. But people that insist that the universe must be deterministic are doing the same thing. As long as we keep to either observational evidence or mathematical proof, there's no problem. If you argue that the universe is deterministic, then I consider this a quasi-religious belief that we can agree to disagree on.

What annoys me again is the statement that no scientist worth his salt would be a non-determinist. I have some fairly sound philosophical reasons for rejecting determinism.

You can compel me (or I you) using arguments such as mathematics and logics. If you find a deterministic theory that reproduces exactly the fundamental mathematical axioms of quantum mechanics, then you conclude that quantum mechanics is deterministic. Since Galileo this is the mean difference between science and philosophy. If you state something you must prove it scientifically.

You can create interpretations of quantum mechanics that are deterministic, but there is no experimental reason that I know of for choosing those. Now its quite possible that someone will come up with some ironclad reason in ten years showing that the universe indeed must be deterministic, and it's good that people are working on this. Fine, when someone shows me that reason, I'll change my mind.

For instance read arXiv:0903.3680.

That's really weird philosophy. I claim that there is a bengal tiger outside your room about to eat you up.

I checked, there are no bengal tigers outside my door. I have falsified you claim. (What's a weird philosophy is indeterminism. You can even replay me that the wave function of the bengal tiger was really outside my room or that is has disappear by tunneling effect, so that nothing can be definitively falsified).

 

[Chalnoth]

After reading a little bit more on this, I'll have to concede the point that indeed, there are mathematicians who have seriously looked into inconsistent mathematical structures. The vast majority merely consider such inconsistencies as an indication that the structure we have is itself incomplete, and we merely need to discover how to deal with the inconsistencies (as happened with calculus, for instance).

I still reject, however, the possibility of inconsistent objects actually existing, and am completely comfortable taking as axiomatic the assumption that reality cannot contradict itself.

Edit: To add a little bit more to this, the way that such inconsistencies are dealt with in practice is to recognize that they exist, draw a little circle around the inconsistency, declare, "Here be dragons!" and don't go there. A trivial example is division by zero. If you add division to the real numbers, then the real numbers becomes an inconsistent structure, as division by zero allows one to prove any statement using the real numbers is true. One can get around this by allowing division, but disallowing division by zero. This recovers the consistency of the rest of the formalism, while also retaining the usefulness of division.

The same is true with inconsistent physical theories. We retain the consistency of the theory by not using the theory in the regime of inconsistency. But with reality, I don't think you can do this. The inconsistencies have to be excluded by hand, but the real world doesn't "exclude" anything. I just don't think there's a way to prevent any real inconsistencies from propagating and making the entire theory trivial. This was tried, for example, in General Relativity with the cosmic censorship hypothesis, but counterexamples have been found. I believe most people expect that this is an indication that GR is merely an approximation to the underlying quantum gravity behavior.

 

[twofish-quant]

Uh, what? A self-contradictory mathematical system is a fundamental impossibility, because a mathematical system is defined as being self-consistent.

Says who? I've given you references to mathematicians that are working on non-standard logical systems. I don't have any more problems with non-Aristoliean logic than I have with non-Euclidean mathematics.

It remains that any non-malformed and sufficiently-specific statement about the nature of reality is either true or false. It cannot be both. Actual contradictions are impossible.

Says who?

If you believe that the universe must be self-consistent, that's up to you. I just want you to realize that it's a quasi-theological statement that I have no particular reason to accept.

Our inability to prove every possible statement as being either true or false doesn't mean that these statements aren't one or the other.

In fact, it's perfectly possible to create a formal system in which all statements are provable. Either you make that system simple (i.e. Pressberger arithmetic) or you allow for the existence of statements that are provable true or false.

Yes, but self-consistency is one of the things we require of mathematics, from which Goedel's incompleteness theorem indicates that either we've made a mistake, or mathematics is incomplete.

Who is we? It doesn't include me, and it doesn't include people that do research into paraconsistent logic. If you insist that mathematical systems that are inconsistent must be invalid, that's up to you. My point again is not that you are wrong, but that you are making quasi-theological statements that I have no reason to accept.

 

[twofish-quant]

If it isn't self-consistent, it isn't a valid mathematical system. This isn't so much a statement about proving self-consistency, but rather that when we build up a mathematical system, we construct it by demanding self-consistency.

You keep using this "we". Who exactly are you referring to?

 

[twofish-quant]

Not necessarily non-local. It could be sufficient an assumption of intrinsic periodicity for non-interacting isolated systems. You can regard the assumption of periodicity as non-lacality if you want, but this non-locality is in agreement with relativistic causality.

At that point you have a theory that is different from quantum mechanics, and we can settle this via experiment. It's quite possible that the underlying theory that describes the universe only looks like QM for the experiments we've been able to do, but is something different.

You can compel me (or I you) using arguments such as mathematics and logics. If you find a deterministic theory that reproduces exactly the fundamental mathematical axioms of quantum mechanics, then you conclude that quantum mechanics is deterministic.

The problem with QM is that if QM is correct, then you can't have local relativistic causality. You can conclude that QM is wrong, but that's something different. The trouble with non-local deterministic theories is that if you have a computer, it influences the calculation and you have computability issues.

Since Galileo this is the mean difference between science and philosophy. If you state something you must prove it scientifically.

It's impossible to prove things scientifically.

The reason science works is that there are a core set of philosophical assumptions that scientists share and you can use that set of assumptions to come up with conclusions on a lot of issues. However, once you move out of that core set of assumptions, then there is no basis for reaching any sort of conclusion.

The fact that scientists have a core set of assumptions disguises the fact that people can disagree quite sharply outside that core set.

The other problem is that how do you "define" the philosophy of science. What happens when what scientists do is actually quite different from what the textbooks say they should do?

(What's a weird philosophy is indeterminism. You can even replay me that the wave function of the bengal tiger was really outside my room or that is has disappear by tunneling effect, so that nothing can be definitively falsified).

In which case you go into probability arguments. It's *possible* that a bengal tiger was there, but it's so unlikely that it's not worth considering.

 

[Chalnoth]

Says who? I've given you references to mathematicians that are working on non-standard logical systems. I don't have any more problems with non-Aristoliean logic than I have with non-Euclidean mathematics.

I updated that post with a reply later.

But in any case the vast majority of mathematicians still seem to prefer thinking of consistent mathematical structures as the only valid ones, with mathematical structures that are inconsistent but still useful merely being useful because they are close to some as yet unknown consistent structure (as happened with calculus).

 

[schmitmg]

Suppose there are two parallel universes exactly alike down to infintesimally small particles positions and momentums. If we then performed the exact same double slit experiment in both universes and achieved different results, would this constitute the "randomness" you speak of?

N.B.-- I should note it is very hard for me to conceptualize the possibility of achieving different results, but if science indeed proves different results, I will concede that I am not as smart as those performing the experiments and will accept this as "randomness."

If this "randomness" does exist, it reasons there are divergent, possible future realities and not a singular, inevitable future reality. And from these divergent, possible future realities we must "choose" our path so to speak. Perhaps the little particles in my brain randomnly bumping about are the keepers of my future and not my conscious mind, but they are a part of me and they are in essence "choosing" my future. No?

And I do recognize the generally accepted definition of free-will necessitates the conscious mind is the ultimate decision maker.

One final thought, which goes back to my original post: Hawking has said it appears God does throw dice, and that sometimes He throws them where they can't be seen. This suggests to me he believes QM is non-unitary, that there is randomness. I would really like to know his thoughts on this. Any more verification on this point?

 

[Chalnoth]

Suppose there are two parallel universes exactly alike down to infintesimally small particles positions and momentums. If we then performed the exact same double slit experiment in both universes and achieved different results, would this constitute the "randomness" you speak of?

This is actually inevitable whether or not randomness is fundamental, as quantum mechanics guarantees that observers will see the appearance of randomness in any case. In the MWI, what happens is you always end up with an observer who sees every possible result of the experiment. For instance, if we just measure which slit the particle goes through, MWI will have one world where you have one observer see one result, and a different world where another observer sees a different one. This continual splitting of observers looks like randomness, as each time there is decoherence, the observer only ever sees one of the possible pathways the world takes, even though all actually occur.

If this "randomness" does exist, it reasons there are divergent, possible future realities and not a singular, inevitable future reality. And from these divergent, possible future realities we must "choose" our path so to speak. Perhaps the little particles in my brain randomnly bumping about are the keepers of my future and not my conscious mind, but they are a part of me and they are in essence "choosing" my future. No?

No, we don't choose our path, though. If we take wavefunction collapse as real, then our path is chosen for us by whatever random numbers reality pulled for us. If wavefunction collapse is not real, then all paths occur, and so there is no choice.

One final thought, which goes back to my original post: Hawking has said it appears God does throw dice, and that sometimes He throws them where they can't be seen. This suggests to me he believes QM is non-unitary, that there is randomness. I would really like to know his thoughts on this. Any more verification on this point?

According to Wikipedia, Hawking is in full support of MWI.

 

[DevilsAvocado]

I like what twofish-quant is saying... and to be 'fair' to OP, maybe we should inform that Hawking is a supporter of the http://en.wikipedia.org/wiki/Many-worlds_interpretation" (MWI), and that’s why QM probability doesn’t create a conflict with hard determinism, and that there are yet no final verdict on which QM interpretation is the right one.

Maybe this picture can help to specify what’s on the menu:

Personally I find it very difficult to comprehend that all uranium found on Earth was synthesized during a supernova explosion that occurred ~5 billion years ago, and one gram of uranium-238 contains approx 2.5 x 10²¹ atoms, and each of these atoms are identical and indistinguishable, yet about 12600 times a second, one of the atoms in that gram will decay, giving off an alpha particle – and this is ALL predetermined!?

By whom??

Now, the MWI guys will say that every one of the 2.5 x 10²¹ atoms will decay simultaneously, because they all have the same probability. We who are discussing this matter at PF, happens to stay in the same world, where this is a problem for me. Otherwise, there is no problem at all. All the decays are spread out evenly over 2.5 x 10²¹ new world branches, 12600 times per second.

To me, this is almost as saying – don’t worry, Santa handles the uranium-238 decay...

On the other hand... we have the Standard argument against free will:

Either Determinism is true or Indeterminism is true. If determinism is true, we are predictable and not free. If indeterminism is true, our actions are random and our will lacks the control to be held solely morally responsible.​

And this confuses me totally... :uhh:


Edit: And if someone thinks I’m not only confused, but drunk, I must explain that I have missed page 2 & 3 (first time this ever happen to me)... I must be tired, good night...

 

[Chalnoth]

1. Whether or not we have the ability to make unconstrained choices is irrelevant when it comes to moral considerations. These are separate issues. Morality/ethics stems from a combination of our own emotional desires and practicality. Neither of these are impacted by the nitty gritty details of fundamental physics.
2. There is no "who" that determines anything. It's just that if the laws of physics are unitary, then there is a one-to-one relationship between the state of the universe at one time and the state at another time. So ultimately the cause of the decays of those uranium atoms would be whatever physics got inflation started in our early universe. In fact, unitary physics actually precludes the possibility of there being any "who" behind any of this.