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Hidden Variables

68 replies on 5 pages. Most recent reply: Sep 11, 2006 2:28 AM by Miguel Montenegro

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 Dino Octavian Posts: 15 Nickname: dinoo33 Registered: Jul, 2006
Re: Hidden Variables Posted: Jul 12, 2006 4:03 PM
> > The solution is to drop determinism entirely and find
> out
> > at every moment what works and what doesn't.
>
> I partially agree with that. The problem is not that
> determinism is an illusion...it is not. It is just us that
> we are not able to calculate the outcome. For example,
> take a French billiard table with two balls only: we can
> easily predict their trajectories, when they will collide
> etc. Add another ball, and the problem becomes very
> difficult, if not impossible, to predict. But the outcome
> is deterministic nevertheless because it is defined by
> physical laws.

The 3 billiard ball problem has deterministic solutions, however the solution is unstable (varies greatly with the initial conditions). For a given set of initial condition we can predict exactly what is going to happen. But the initial conditions have to be errorless. In some conditions (think the perfect gas) the boundary conditions cannot be determined. In this particular case, the determinism fails and all we have left is a stochastic approach to the problem.

Further on, for quantum phenomena determinism is simply denied existence (it is not a stability problem over the initial conditions).

So here is a bigger question: is software development non-deterministic because its dynamics lacks the necessary stability to allow determinism? Or is software development non-deterministic because it completely invalidates determinism?

 Achilleas Margaritis Posts: 674 Nickname: achilleas Registered: Feb, 2005
Re: Hidden Variables Posted: Jul 13, 2006 2:35 AM
> Well, you can't you understand how transistors work
> without quantum mechanics.
>
> http://www.pbs.org/transistor/science/info/quantum.html
>
> "Quanta, quanta everywhere
>
> This idea that particles could only contain lumps of
> energy in certain sizes moved into other areas of physics
> as well. Over the next decade, Niels Bohr pulled it into
> his description of how an atom worked. He said that
> electrons traveling around a nucleus couldn't have
> arbitrarily small or arbitrarily large amounts of energy,
> they could only have multiples of a standard "quantum" of
> energy.
>
> Eventually scientists realized this explained why some
> materials are conductors of electricity and some aren't --
> since atoms with differing energy electron orbits conduct
> electricity differently. This understanding was crucial
> to building a transistor
, since the crystal at its
> core is made by mixing materials with varying amounts of
> conductivity."

It only helped us understood conductivity. The idea of a transistor was developed somewhat independently:

http://nobelprize.org/educational_games/physics/transistor/history/

> Unless we can measure what causes it, it can't be
> understood with science.

But someday maybe we will be able to measure it. There is nothing that says we won't.

 Achilleas Margaritis Posts: 674 Nickname: achilleas Registered: Feb, 2005
Re: Hidden Variables Posted: Jul 13, 2006 2:39 AM
> But they don't invalidate the original theory (if it was
> good) they qualify it. Newtonian physics is supercedede
> by Einsteins theories but people sill use Newton's laws
> much more often than Einstein's theories.

I never said they always invalidate the original theory. It might invalidate the original theory, or it might not. The point is that we have not discovered 'all there is', and therefore we can only say that 'for now, the world seems random, but we are not sure of that'.

> I don't want to offend you but a lot of the things you
> have written are plainly wrong and can be easily cleared
> up with a little more knowledge.

Nothing of what I have written is plainly wrong. It is only wrong for people that want to show off, for people that like to nitpick and are absolutists.

> We can't rule it in either. There's no evidence for it.
> We can't rule out the existence of tree-spirits, gnomes,
> , fairies or anal-probing aliens either.

Exactly. Your view that "the world is not deterministic and that's it because quantum mechanics say so" is absolutist, at best.

 Achilleas Margaritis Posts: 674 Nickname: achilleas Registered: Feb, 2005
Re: Hidden Variables Posted: Jul 13, 2006 2:43 AM
> A compiler is a translator. It converts a program from one
> form to another. However, your concept of 'pseudo-run' is
> an approximation, which is basically what we do with
> testing -- in particular what you describe sounds mostly
> like testing with mock objects.

Well, indeed, but nothing says that a compiler has to be only a translator. If modern needs dictate for compilers to be more than that, then it is ok (by me, at least).

Of course by 'compiler' we can mean a range of tools, can't we? :-)

The advantage of it would be that a) most of testing would be automated b) the output would not be created if those logic errors are not fixed.

 Achilleas Margaritis Posts: 674 Nickname: achilleas Registered: Feb, 2005
Re: Hidden Variables Posted: Jul 13, 2006 2:47 AM
> So here is a bigger question: is software development
> non-deterministic because its dynamics lacks the necessary
> stability to allow determinism? Or is software development
> non-deterministic because it completely invalidates
> determinism?

Software development is deterministic because there is a clear set of rules that everything is derived from and that it can be used to prove a program's agreement with specifications.

Algorithms can not be proven correct or incorrect according to the halting problem.

In other words, I can make a program that computes prime numbers, I can prove that it computes prime numbers, but I can not prove that it will ever terminate, i.e. that prime numbers stop at some point.

 James Watson Posts: 2024 Nickname: watson Registered: Sep, 2005
Re: Hidden Variables Posted: Jul 13, 2006 5:32 AM
> It only helped us understood conductivity. The idea of a
> transistor was developed somewhat independently:
>
> http://nobelprize.org/educational_games/physics/transistor/
> history/

I'm not sure what that link is supposed to show. You can't understand how a transistor works (and it's unlikely you will stumble upon the creation of one) without understanding quantum mechanics.

> > Unless we can measure what causes it, it can't be
> > understood with science.
>
> But someday maybe we will be able to measure it. There is
> nothing that says we won't.

I never said there was. You were the one aserint that there must be hidden variables without a single shred of evidence.

 James Watson Posts: 2024 Nickname: watson Registered: Sep, 2005
Re: Hidden Variables Posted: Jul 13, 2006 5:34 AM
> > I don't want to offend you but a lot of the things you
> > have written are plainly wrong and can be easily
> cleared
> > up with a little more knowledge.
>
> Nothing of what I have written is plainly wrong. It is
> only wrong for people that want to show off, for people
> that like to nitpick and are absolutists.

You implied that quantum entanglement requires hidden variables. That is 'plainly wrong'.

> > We can't rule it in either. There's no evidence for
> it.
> > We can't rule out the existence of tree-spirits,
> gnomes,
> > , fairies or anal-probing aliens either.
>
> Exactly. Your view that "the world is not deterministic
> and that's it because quantum mechanics say so" is
> absolutist, at best.

When did I say 'the world is not deterministic'?

 Dino Octavian Posts: 15 Nickname: dinoo33 Registered: Jul, 2006
Re: Hidden Variables Posted: Jul 13, 2006 1:20 PM
>
> Software development is deterministic because there is a
> clear set of rules that everything is derived from and
> that it can be used to prove a program's agreement with
> specifications.
>
> Algorithms can not be proven correct or incorrect
> according to the halting problem.
>

This is determinism with small print :)
- Cause and effect are related.
- The above is undecidable.

The answer is not simple at all. We have a clear set of rules for writing programs. However, each time we find an exception to our rules, we extend the set of rules with a new one - the exception itself. However, this Goedelization process of programing is not constructive, because it ends up in a paradox: "Name the largest number that can be described in 100 words or less".

Here's why: a program is a substitution for its output. One can either say: "This is the output for this input" or write a program which calculates the output. The approaches are Turing equivalent. Out of all Turing equivalent ways to express an output, the shortest way to do has some interesting properties:
1) its bits are not compressible
2) any other way to generates the same output is Turing equivalent.
3) its size in bits is a measure for complexity
Fine with that. So?

For "Name the largest number that can be described in 100 words or less" you can write the number, write a program or simply write the phrase. However, "Name the largest number plus one that can be described in 100 words or less" is also a valid statement. The two statements are because they describe the same result, however their results differ by 1.

In programming:

Number getNumber1() {
return some_way_to_calculate_that_number();
}

Number getNumber2() {
return getNumber() + 1;
}

(shortestWayToState(a) == shortestWayToState(b) &&
a == b) is always false. You state the same number twice, but the you end up with two different numbers.

This is in fact the halting problem, which can be quickly expressed as:

boolean willHalt(Program p) {
return someHaltingAnalysis(p); // of complexity H
}

From any program a we can build program b does:
if(willHalt(a)) while(true);

For all programs a of complexity H the statement is:
willHalt(a) == willHalt(b)

however b will loop forever. That's a paradox and it can be resolved only by adding "willHalt(b) is false" as a new rule. Just in time to find the next paradox c:

if(!willHalt(b)) return;

The complexity of willHalt, a, b, c is in the relationship
willHalt = a < b < c

Back to the original topic: determinism holds only as long as the complexity of the subject of study is less or equal than the complexity of the deterministic method employed in the study. Beyond that point, all of the unaccounted complexity of the subject will be observed as random behavior.

Just having rules doesn't make things deterministic. The rules have to be complex enough for determinism to work.

 Bruce Eckel Posts: 875 Nickname: beckel Registered: Jun, 2003
Re: Hidden Variables Posted: Jul 14, 2006 7:07 AM
Dino: Thanks for illuminating that.

 Achilleas Margaritis Posts: 674 Nickname: achilleas Registered: Feb, 2005
Re: Hidden Variables Posted: Jul 17, 2006 12:59 AM
> You implied that quantum entanglement requires hidden
> variables. That is 'plainly wrong'.

No, it is not wrong by any sense. Hidden dimensions are hidden variables: there is something we can not explain yet that affects the outcome of reality.

>
> > > We can't rule it in either. There's no evidence for
> > it.
> > > We can't rule out the existence of tree-spirits,
> > gnomes,
> > > , fairies or anal-probing aliens either.
> >
> > Exactly. Your view that "the world is not deterministic
> > and that's it because quantum mechanics say so" is
> > absolutist, at best.
>
> When did I say 'the world is not deterministic'?

By insisting there are no hidden variables, you admit quantum randomness has no cause and that it is random by itself.

I know there are not "hidden variables" in the way it is meant in the literature, as the Bell experiment proves (Bell's inequalities), but there is something hidden, and you can not dispute that. I may as well call those hidden things 'variables' because they affect reality and our experiments.

 Achilleas Margaritis Posts: 674 Nickname: achilleas Registered: Feb, 2005
Re: Hidden Variables Posted: Jul 17, 2006 1:04 AM
> Back to the original topic: determinism holds only as long
> as the complexity of the subject of study is less or equal
> than the complexity of the deterministic method employed
> in the study. Beyond that point, all of the unaccounted
> complexity of the subject will be observed as random
> behavior.

Thank you for showing us the halting problem, but Wikipedia has an even better example which is much simpler.

But I insist: a program can be proven statically 100% for conformance with specifications, but its output can not be proven to be the desired one.

When we say "specifications" we mean the context of accepted values.

The reason that I insist is that whatever my brain can output as a conclusion from looking at a program, so can a compiler. If I find a bug in a program, so can an automated tool.

 James Watson Posts: 2024 Nickname: watson Registered: Sep, 2005
Re: Hidden Variables Posted: Jul 17, 2006 5:56 AM
> Software development is deterministic because there is a
> clear set of rules that everything is derived from and
> that it can be used to prove a program's agreement with
> specifications.

You are not understanding the point of the discussion. Whether software is deterministic doesn't have any bearing on the issue Bruce is talking about here.

 James Watson Posts: 2024 Nickname: watson Registered: Sep, 2005
Re: Hidden Variables Posted: Jul 17, 2006 6:01 AM
> > You implied that quantum entanglement requires hidden
> > variables. That is 'plainly wrong'.
>
> No, it is not wrong by any sense. Hidden dimensions
> are hidden variables: there is something we can not
> explain yet that affects the outcome of reality.

There is no proof that extra dimensions exist. It's just an idea.

> > > > We can't rule it in either. There's no evidence
> for
> > > it.
> > > > We can't rule out the existence of tree-spirits,
> > > gnomes,
> > > > , fairies or anal-probing aliens either.
> > >
> > > Exactly. Your view that "the world is not
> deterministic
> > > and that's it because quantum mechanics say so" is
> > > absolutist, at best.
> >
> > When did I say 'the world is not deterministic'?
>
> By insisting there are no hidden variables, you admit
> quantum randomness has no cause and that it is random by
> itself.

As far as we can tell, at this point, yes this is the case. But that doesn't make the world non-deterministic. I consider a computer to be deterministic and a computer subject to quantum randomness much more than most things we experience.

> I know there are not "hidden variables" in the way it is
> meant in the literature, as the Bell experiment proves
> (Bell's inequalities), but there is something hidden, and
> you can not dispute that.

Sure I can? Why can't I? What evidence do you have of this something?

 Achilleas Margaritis Posts: 674 Nickname: achilleas Registered: Feb, 2005
Re: Hidden Variables Posted: Jul 18, 2006 1:09 AM
> You are not understanding the point of the discussion.
> Whether software is deterministic doesn't have any
> y bearing on the issue Bruce is talking about here.

You are flamebaiting, but I won't bite. Let's keep the discussion on a good level.

 Achilleas Margaritis Posts: 674 Nickname: achilleas Registered: Feb, 2005
Re: Hidden Variables Posted: Jul 18, 2006 1:19 AM
> There is no proof that extra dimensions exist. It's just
> an idea.

Something has got to be hidden, because we haven't explained everything yet.

At least you must admit to this simple truth.

> As far as we can tell, at this point, yes this is the
> case.

No. There is nothing that suggest either this or the opposite view. There is no conclusive proof.

> But that doesn't make the world non-deterministic.
> I consider a computer to be deterministic and a computer
> r subject to quantum randomness much more than most things
> we experience.

Nothing is random in a computer. All programs are 'specifications'. If these specifications are not good enough, that's another issue.

In other words, when a program crashes, it is not because of quantum randomness, but because of bad programming.

> Sure I can? Why can't I? What evidence do you have of
> this something?

And what evidence do you have that we know all there is? especially in the face of things like quantum entanglement that we have no way to explain yet?

Let me ask you the same question in another manner: what is more possible?

A. we know and have observed all there is; there is no level of detail greater than what we have currently reached. The reason we can not explain certain phenomena is because we do not know yet how to explain them with the tools we have.

B. we have not observed all there is and unexplained observations are subject to our lack of knowledge about the underlying systems.

Occam's razor says it is B the most propable answer. Again and again in human history we have observed B. Many people supported A throughout human history, but ultimately they were proven wrong.

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